Collection of Research Papers Davinder K. Anand University of Maryland, College Park, Maryland 20742, USA Collection of Research Papers Davinder K. Anand University of Maryland, College Park, Maryland 20742, USA Center for Energetic Concepts Development Series FOREWORD Over the past fifty-five years, I have worked on problems related to dye dilution for the analysis of cardiac output, heat pipes as a high conductivity device, satellite attitude control, solar energy usage and design of systems for building heating and cooling applications, design and control of magnetically suspended flywheels for energy storage, design of magnetic bearings, magnetic spindles for high speed machining, manufacturing systems, system simulation and virtual environments as a design tool for a group of various mechanical components, and a number of unique problems of interest to me such as STEM education and R&D funding policy of the Navy. In most cases, my inquiry was more of an engineering nature trying to solve a specific problem or understand some special issues. I never spent sufficient time in any one area to gain either deep enough knowledge or understanding to be called an expert. I always lost interest when another interesting problem came along. Needless to say, I had a front row seat in many interesting technology issues of that period of my life. With much of the journey behind me, I decided to get most of my papers and books together, at least those I could get easily, and put them in one place. I thought a gig or two of cyber space would not significantly pollute the system and allow me to put all the information in one place. Hence the creation of this Collection of Papers and Books. The period for the papers ended around 2012 when I lost my only son. In his honor, and in my grief, I started the Neilom Foundation with a vision to help young people at the intersection of health, education and technology. Although I still wrote some books and papers, most of my work was for the Foundation. A parallel activity was Engineering for Social Change, a course offered at the university to educate a generation of technical leaders who would have interest in the more social aspects of engineering. And if I want to remembered, it is for the Neilom Foundation and the young people I have touched. Davinder K. Anand April 4, 2019 College Park, MD 20742 USA ii 2020 BRIEF Davinder Kumar Anand was born on April 4, 1939 in Krishan Nagar, Lahore (undivided India) to Shanti Devi and Anant Ram Anand, who was an Accountant with the Indian Government. The family travelled to Karachi for one year and then settled down in Delhi, where Davinder received much of his early education. He attended neighborhood schools for a year and then Church High School run by the Presbyterian Church of New Delhi. After two years, he went to the Naveen Bharat High School, which later became the Delhi Public School. He left that school at the age of twelve and joined the St. Columbas High School in New Delhi run by the Irish Christian Brothers. He received the Overseas Junior School Certificate in 1953 and the Overseas School Certificate A with First Division in 1955 from The University of Cambridge. In 1956, he left New Delhi for the United States to join his family, where his father was the Accounts Officer for the India Supply Mission in Washington D.C., working for the US-India PL480 program. In Washington D.C., he went to the Catholic University of America for one semester and transferred to The George Washington University, where he received his BME, MSME, and DSc in 1959, 1961, and 1965 respectively. He was married to Asha Vohra in 1961 and had two children, Anita (1963) and Dilip (1964). Having received his doctorate, he joined The Applied Physics Laboratory of the Johns Hopkins University in 1965 as a Senior Staff member and remained there as a Consultant until 1974. In 1965, he also joined the faculty of the Mechanical Engineering Department at the University of Maryland, College Park, where he served as Assistant Professor, Associate Professor, and Professor of Mechanical Engineering. He was Professor of Systems Research from 1989-1992. He was Chairman of the Mechanical Engineering Department during the period 1991-2001 and became Professor Emeritus in 2004. In 1998, he helped establish the Center for Energetic Concepts Development and became its Director in 1999, a position he retained for the remaining active years at the University. He served as Program Director of the Mechanical Systems Program at National Science Foundation from 1980-1981. In 1978, he founded TPI Inc, a consulting company in energy, and sold it in 1991 when he became Chair of Mechanical Engineering at the University of Maryland, College Park. In 2001, he founded Iktara and Associates, LLC, of which he was President until 2012. His technical interests were primarily in control systems and simulation applied to satellites, solar energy and manufacturing systems. His research was supported by NIH, NSF, NASA, DOE, DOD, and industry. He consulted widely with industry and government. He published twenty-two books, almost two hundred scientific papers and has one patent. He is a Fellow of ASME, and Member of Sigma Tau, Pi Tau Sigma, Sigma Xi and Tau Beta Pi. He is a Distinguished Alumnus of George Washington University. He was awarded the Outstanding and Superior Awards by the National Science Foundation in 1981 and the Outstanding Accomplishment Award by the University of Maryland in 1984. He was honored by a Maryland Senate resolution for his contributions to CECD and Southern Maryland and April 4, 2009 was designated as the Davinder K. Anand day in Maryland. He is a Fellow of ASME and a registered Professional Engineer in the State of Maryland. He is a member of the Cosmos Club. iii In 2013, he founded The Neilom Foundation in memory and honor of his only son Anil Dilip, who died of cardiac arrest on November 22, 2012 at the age of 48. He spent the remainder of his life doing charitable work helping to improve the lives of young people. SOME OUTSTANDING CONTRIBUTIONS, ACTIVITIES, AND AWARDS • Simulated the attitude and stabilization of the first gravity gradient satellite and the control system of the first drag-free satellite. • Conducted theoretical and experimental work on the first heat pipe used in space for thermal control. Research led to the first low temperature heat pipe control patent awarded. Organized and chaired the first International Heat Pipe Technology Symposium at the University of Maryland. • Lectured, twice by invitation, on spacecraft thermal and attitude control to the NATO Advanced Studies Institute in England. • Developed a new simplified design procedure for designing solar cooling systems using either stochastic methods or correlation results. • Organized and chaired the first national meeting on the use of the Second Law Analysis and Exergy considerations of thermodynamic cycles and systems driven by solar radiation. • Established and directed a new research program in mechanical systems at the National Science Foundation. Received superior and outstanding performance awards from the National Science Foundation. • Received numerous Appreciation Awards from ASME in 1988 and 1989. • Received the Outstanding Accomplishment Award in the University of Maryland in 1984. • Fellow of ASME. • Registered Professional Engineer in Maryland. • Outstanding Alumnus Award from The George Washington University, 1986. • Founded TPI Inc in 1978 and Iktara and Associates in 2001. • Listed in Who's Who in Engineering. • Given invited lectures in England, Spain, Switzerland, Canada, India, Saudi Arabia, China, Japan, Taiwan, and Hong Kong. • Member, Cosmos Club. • Honored by Maryland Senate resolution, naming April 4, 2009 as Dr. Davinder K. Anand Day in Maryland. • Published 200 scientific papers and twenty-two books. • Founded the Neilom Foundation in 2013. iv TEXTBOOKS BY DAVINDER K. ANAND Introduction to Control Systems: First Edition Davinder K. Anand 1974, Pergamon Press ISBN 0-08-017104-4 Introduction to Control Systems: Second Edition Davinder K. Anand 1984, Pergamon Press ISBN 978-0080300016 Introduction to Control Systems: Third Edition Davinder K. Anand and Ronald B. Zmood 1995, Elsevier Science & Technology Books ISBN 978-0750622981 Engineering Mechanics: Statics and Dynamics First Edition Davinder K. Anand and Patrick E. Cunniff 1973, Houghton Mifflin Harcourt ISBN 978-0395142080 v Engineering Mechanics: Statics Davinder K. Anand and Patrick E. Cunniff 1973, Houghton Mifflin Company ISBN 0-325-14210-5 Engineering Mechanics: Dynamics Davinder K. Anand and Patrick E. Cunniff 1973, Houghton Mifflin Company ISBN 0-395-14209-1-X Solutions Manual for Engineering Mechanics: Dynamics Davinder K. Anand and Patrick E. Cunniff 1973, Houghton Mifflin Company ISBN 0-395-16010-3 Solutions Manual for Engineering Mechanics: Statics Davinder K. Anand and Patrick E. Cunniff 1973, Houghton Mifflin Company ISBN 0-395-16009-X vi Mechanica Para Ingenieros: Estatica Davinder K. Anand and Patrick E. Cunniff 1976, Compania Editorial Continental, S. A. Engineering Mechanics: Statics and Dynamics Second Edition Davinder K. Anand and Patrick E. Cunniff 1984, Allyn and Bacon, Inc. ISBN 9780205078103 Engineering Mechanics: Dynamics Second Edition Davinder K. Anand and Patrick E. Cunniff 1984, Allyn and Bacon, Inc. ISBN 0-205-07785-4 Engineering Mechanics: Statics Second Edition Davinder K. Anand and Patrick E. Cunniff 1984, Allyn and Bacon, Inc. ISBN 0-205-07784-6 vii RESEARCH BOOKS BY DAVINDER K. ANAND The True Cost of Waste: Current Issues in Electronic Waste Dylan A. Hazelwood, Michael G. Pecht, Maria C. Sanchez, Davinder K. Anand 2018, CALCE EPSC Press ISBN 978-0-9777295-1-7 Engineering for Social Change: Engineering Is Not Just Engineering Davinder K. Anand, Dylan A. Hazelwood, Michael G. Pecht, Mukes Kapilashrami 2016, CALCE EPSC Press ISBN 978-0-9846274-7-9 Topics in Energetics Research and Development Invited Editor: Robert E. Kaczmarek Series Editors: James M. Short, Robert A. Kavetsky, and Satyandra K. Gupta 2013, CALCE EPSC Press ISBN 978-0-9846274-6-2 viii Energetics Science and Technology in Central Europe Invited Editor: Ronald W. Armstrong Series Editors: James M. Short, Robert A. Kavetsky, and Davinder K. Anand 2012, CALCE EPSC Press ISBN 978-0-9846274-3-1 S&T Revitalization: A New Look Davinder K. Anand, Lisa M. Frehill, Dylan A. Hazelwood, Robert A. Kavetsky, Elaine Ryan 2012, CALCE EPSC Press ISBN 978-0-9846274-5-5 Rare Earth Materials: Insights and Concerns Michael G. Pecht, Robert E. Kaczmarek, Xin Song, Dylan A. Hazelwood, Robert A. Kavetsky, and Davinder K. Anand 2012, CALCE EPSC Press ISBN 978-0-9846274-4-8 Simulation-Based Innovation and Discovery Energetics Applications Edited by Davinder K. Anand, Satyandra K. Gupta, and Robert A. Kavetsky 2011, CALCE EPSC Press ISBN 978-0-9846274-2-4 ix Energetics Science and Technology in China James M. Short, Robert A. Kavetsky, Michael G. Pecht, and Davinder K. Anand 2010, CALCE EPSC Press ISBN 978-0-9846274-0-0 From Science to Seapower. A Roadmap for S&T Revitalization. Postscript 2010 Robert A. Kavetsky, Michael L. Marshall, and Davinder K. Anand 2010, CALCE EPSC Press ISBN 978-0-9846274-1-7 Training in Virtual Environments. A Safe, Cost-Effective, and Engaging Approach to Training Satyandra K. Gupta, Davinder K. Anand, John E. Brough, Maxim Schwartz, and Robert A. Kavetsky 2008, CALCE EPSC Press ISBN 978-0-9777295-2-4 x TECHNICAL PAPERS BY DAVINDER K. ANAND Sr. Page Title of Publication No. No. D.K. Anand and L. de Pian, “Automated Procedures for Indicator-Dilution 1 Curves using a Digital Computer”, Bio/Medical Instrumentation, pp. 21-24, 1 December 1964. D.K. Anand, Mortan F. Taragin, and Louis de Pian, “On the Stability and Dynamic 2 Behavior of Cascaded Thermoelectric Devices”, Proceedings of the IEEE, Vol. 53, 5 No. 10, pp. 1637-1638, October 1965. D.K. Anand, “On the Performance of a Heat Pipe”, Journal of Spacecraft and 3 6 Rockets, Vol.3, No. 5, pp. 763-765, May 1966. D.K. Anand, P. Bainim, and D. Mackison, “Perturbations and Lyapunov Stability of a Multiply Connected Gravity Gradient Satellite at Synchronous Altitude”, 4 9 Proceedings of the fifth U.S. National Congress of Applied Mechanics, June 14-17, 1966. D.K. Anand and L. de Pian, “Scattering Matrix Parameters for Thermal 5 Transducers”, Proceedings of the IEEE, Vol. 54, No. 12, pp. 1999-2000, December 11 1966. D.K. Anand and J.M. Whisnant, “Use of Malkin’s Theorem for Satellite Stability 6 in the presence of Light Pressure”, Proceedings of the IEEE, Vol. 55, No. 3, pp. 13 444-445, March 1967. M.S. Ojalvo, D.K. Anand, and R.P. Dunbar, “Combined Forced and Free Turbulent Convection in a Vertical Circular Tube with Volume Heat Sources 7 15 and Constant Wall Heat Addition”, Transactions of the ASME - Journal of Heat Transfer, Paper No. 67 - HT-23, August 1967. D.K. Anand, A.Z. Dybbs and R.E Jenkins, “Effects of Condenser Parameters on 8 Heat Pipe Optimization”, Journal of Spacecraft and Rockets, Vol. 4, No. 5, pp. 695- 22 696, 1967. D.K. Anand, “Heat Pipe Application to a Gravity-Gradient Satellite (Explorer 9 XXXVI)”, Proceedings of the Aviation and Space Conference, ASME, pp. 634-638, 24 June 17, 1968. J.M. Whisnant and D.K. Anand, “Roll Resonance for a Gravity-Gradient Satellite”, 10 31 Journal of Spacecraft and Rockets, Vol. 5, No. 6, pp. 743-744, June 1968. D.K. Anand, J.M. Whisnant, and M. Sturmanis, “Effect of the Near Earth Environment on the Attitude of a Slowly Spinning Multibody Satellite (X-Ray 11 33 Explorer)”, AIAA Guidance, Control, and Flight Dynamics Conference, AIAA paper No. 68-856, August 12-14, 1968. D.K. Anand, J.M. Whisnant, and M. Sturmanis, “Attitude Perturbations on a 12 Slowly Spinning Multibody Satellite”, Journal of Spacecraft and Rockets, Vol. 6, 41 No. 3, pp. 324-326, March 1969. J.M. Whisnant, D.K. Anand, V.L. Pisacane, and M. Sturmanis, “The Dynamic Modeling of Hysteresis and Application to Damping of Spacecraft Librations”, 13 44 AIAA Guidance, Control, and Flight Dynamics Conference, AIAA paper No. 69-833, August 18-20, 1969. D.K. Anand, J.M. Whisnant, V.L. Pisacane, and M. Sturmanis, “The Capture and 14 Stability of the Lidos Gravity-Gradient Satellite in an Eccentric Orbit”, AIAA/AAS 52 Astrodynamics Conference, AIAA paper No. 69-921, August 20-22, 1969. D.K. Anand, J.M. Whisnant, V.L. Pisacane, and M. Sturmanis, “Gravity-Gradient 15 Capture and Stability in an Eccentric Orbit”, Journal of Spacecraft and Rockets, 61 Vol. 6, No. 12, pp. 1456-1459, December 1969. J.M. Whisnant, D.K. Anand, V.L. Pisacane, and M. Sturmanis, “Dynamic Modeling 16 of Magnetic Hysteresis”, Journal of Spacecraft and Rockets, Vol. 7, No. 6, pp. 697- 65 701, June 1970. R.E. Lohfeld, D. K. Anand, and J.M Whisnant, “Gravity-Gradient Stabilization of 17 Satellites in Highly Eccentric Orbits”, AIAA/AAS Astrodynamics Conference, July 70 16-18, 1970. 18 To V.L. Pisacane, from D.K. Anand, “Vibration Isolation”, September 4, 1970. 91 D.K. Anand and S.A. Jeter, “Passive Radiation Coolers for Infrared Sensors”, 19 98 Journal of the British Interplanetary Society, Vol. 23, pp. 495-508, 1970. D. K. Anand, R.S. Yuhasz, and J.M. Whisnant, “Attitude Motion in an Eccentric 20 112 Orbit”, Journal of Spacecraft and Rockets, Vol. 8, No. 8, pp. 903-905, August 1971. D.K. Anand and J. M. Whisnant, “Attitude Stability and Performance of a Dual- 21 Spin Satellite with Nutation Damping”, The Journal of the Astronautical Sciences, 115 Vol. XIX, No., 6, pp. 462-469, May-June 1972. To K. Potocki, from D.K. Anand, “Wave Propagation from Ribbed Structures”, 22 123 September 28, 1973. D.K. Anand and J. M. Whisnant, “Attitude Performance of some Passively 23 Stabilized Satellites”, Journal of British Interplanetary Society, Vol. 26, pp. 641- 130 661, 1973. R.E. Lohfeld, D.K. Anand, and J.M. Whisnant, “Pitch Axis Stabilization in 24 Eccentric Orbits using a Variable-Speed Rotor”, Journal of Spacecraft and 151 Rockets, Vol. 11, No. 6, pp. 430-432, June 1974. R.C. Krishnan, D.K. Anand, and F.E. Zajac III, “Relationship of Speed of Walking to the Applied Moments in the Human Leg Joints”, presented at 27th Annual 25 154 Conference on Engineering in Medicine and Biology (ACEMB), October 6-10, 1974. D.B. Kramer and D.K. Anand, “Apodization in Numerical Holography”, Journal of 26 155 Acoustical Society of America, Vol. 56, No. 5, pp. 1545-1550, November 1974. J.M. Whisnant and D.K. Anand, “Invariant Surfaces for Rotor Controlled 27 Satellites in Highly Elliptical Orbits”, ZAMM (Journal of Applied Mathematics and 162 Mechanics), Vol. 54, pp. 563-565, 1974. J.T Pritchard and D.K. Anand, “Analysis of a Nonlinear Population Ecosystem”, 28 Proceedings of the 1975 IEEE Conference on Decision & Control, pp. 717-718, 165 December 10-12, 1975. F.H. Morse, R.W. Allen, D.K. Anand, and E. Bazques, “Thermal Performance 29 Predictions of a Solar Absorption Air Conditioning System”, Solar Use Now- a 168 Resource for People : ISES, pp.390-391, 1975. D.K. Anand, R.W. Allen, and E.O. Bazques, “Weather Representation using 30 Stochastic Methods”, Second Southeastern Conference on Application of Solar 169 Energy, April 19-22, 1976. R.W. Allen, D.K. Anand, and E.O. Bazques, “Dynamic Simulation of a Solar 31 Powered Absorption Cycle”, presented at Second Southeastern Conference on 179 Application of Solar Energy, April 19-22, 1976. D.K. Anand, R.W. Allen, and E.O. Bazques, “Simulation of Synthetic Weather Data for the Design of a Solar Powered Air Conditioning System”, presented at 32 190 Seventh Annual Pittsburgh Conference on Modeling and Simulation, April 26-27, 1976. D.K. Anand, R.W. Allen, and E.O. Bazques, “Performance Predictions of a Water- 33 cooled Solar Absorption System using a Stochastic Weather Model”, presented 198 at AIAA 11th Thermophysics Conference, July 14-16, 1976. R.W. Allen and D.K. Anand, “Parametric Study of a Dynamic Solar Powered 34 Absorption Cycle”, presented at Conference: Sharing the Sun 76, pp. 27-43, 212 August 1976. D.K. Anand and R.W. Allen, “Solar Powered Absorption Air-Conditioning System 35 Performance using Real and Synthetic Weather Data”, presented at Conference: 225 Sharing the Sun 76, August 1976. W.W. Auer, R.W. Allen, and D.K. Anand, “Solar industrial Process Heat 36 236 Workshop”, presented at Conference: Sharing the Sun 76, August 1976. R.W. Allen, D.K. Anand, and A.N. Egrican, “Dynamic Simulation of a Solar 37 Powered Rankine Cycle/Vapor Compression Cycle (RC/VCC)”, presented at 245 Program- Solar Cooling and Heating: a National Forum, December 13-15, 1976. D.B. Kramer and D.K. Anand, “Numerical Reconstruction of Apodized Acoustical 38 251 Holograms”, Journal of Sound and Vibration, Vol. 49, No. 3, pp. 327-344, 1976. D.K. Anand and R.W. Allen, “Short and Long Term Comparison of Solar Absorption Air-Conditioning System Performance using Real and Synthetic 39 269 Weather Data”, presented at 11th Intersociety Energy Conversion Engineering Conference (IECEC), pp. 1354-1361, 1976. D.K. Anand and R.W. Allen, “Solar Powered Absorption Cycle Simulation using 40 277 Real and Stochastic Weather Data”, ASME Publication 76-WA/Sol-6, 1976. D.K. Anand, R.W. Allen, and E.O. Bazques, “Seasonal Stochastic Simulation 41 Experiments on Solar Air Conditioning Systems”, presented at Eighth Annual 288 Pittsburgh Conference on Modeling and Simulation, April 21-22, 1977. D.K. Anand, R.W. Allen, and E.O. Bazques, “Solar Air-Conditioning Performance 42 using Stochastic Weather Models”, Journal of Energy, Vol. 1, No. 5, pp. 319-323, 298 September-October 1977. J.A. Kirk, D.K. Anand, and C. McKindra, “Matrix Representation and Prediction of 43 Three-Dimensional Cutting Forces”, Journal of Engineering for Industry, pp. 828- 303 834, November 1977. A.N. Egrican, R.W. Allen, and D.K. Anand, “Solar Powered Rankine Cycle/Vapor Compression Cycle Modeling and Performance Prediction”, Heat Transfer in 44 310 Solar Energy Systems, presented at Winter Annual Meeting of AMSE, November27-December 2, 1977. D.K. Anand, R.W. Allen, E.O. Bazques, and I.N. Deif, “Solar Air-Conditioning Performance Predictions Using Load, Storage and Stochastic Weather Models 45 326 for Different Regions”, presented at ISES 77, Programme-Sun: Mankind’s Future Source of Energy, January 16-21, 1978. D.K. Anand, R.W. Allen, W.W. Auer, and J.M. Greyerbiehl, “Applications of Solar 46 Energy to Industrial Processes”, presented at ISES 77, Programme-Sun: 334 Mankind’s Future Source of Energy, January 16-21, 1978. D.K. Anand, R.B. Abarcar, and R.W. Allen, “A Simplified Solar Cooling Design 47 Method for Closed-Loop Liquid Systems”, presented at Solar Diversification 337 (1978 Annual Meeting of American Section of ISES), August 28-31, 1978. D.K. Anand, R.B. Abarcar, S.R. Venkateswaran, and R.W. Allen, “System Performance Predictions for Solar Heating And Cooling using Stochastic 48 341 Weather Models”, presented at Solar Diversification (1978 Annual Meeting of American Section of ISES), August 28-31, 1978. D.K. Anand, I.N. Deif, and R.W. Allen, “Stochastic Predictions of Solar Cooling 49 355 System Performance”, ASME Publication 78-WA/Sol-16, 1978. D.K. Anand, I.N. Deif, and R.W. Allen, "Stochastic predictions of solar cooling 50 368 system performance", American Society of Mechanical Engineers 1, 1978. D.K. Anand, R.B. Abarcar, S.R. Venkateswaran, and R.W. Allen, “Solar Thermal Systems Long-Term Performance Predictions using Closed-Form Solutions”, 51 376 presented at 1979 International Congress (Joint Meeting of American society of ISES), May 28-June1, 1979. D.K. Anand, R.B. Abarcar, and S.R. Venkateswaran, “Dynamic Simulation of Solar Thermal Systems using Closed-Form Solutions”, presented at the 14th 52 396 Intersociety Energy Conversion Engineering Conference (IECEC), August 5-10, 1979. D.K. Anand and I. N. Deif, “Solar Cooling Performance Predictions via Stochastic 53 400 Weather Algorithms”, Energy Vol.4, No. 4, pp. 537-548, 1979. D.K. Anand, W.J. Kennish, T.M. Knasel, and A.C. Stolarz, “Validation Methodology 54 412 for Solar Heating and Cooling Systems”, Energy Vol. 4, pp. 549-560, 1979. D.K. Anand, R.B. Abarcar, and R.W. Allen, “Long-Term Solar Cooling Systems Performance via a Simplified Design Method”, presented at Second Annual 55 424 Systems Simulation and Economic Analysis Conference (SSEA), January 23-25, 1980. S.R. Venkateswaran and D.K. Anand, “Performance Studies of Combined Photovoltaic/Thermal Solar Heating and Cooling Systems”, presented at Second 56 430 Annual Systems Simulation and Economic Analysis Conference (SSEA), January 23-25, 1980. S.R. Venkateswaran and D.K. Anand, “A Design Procedure for Combined 57 436 Photovoltaic/Thermal Solar Collector – Heat Pump Systems”. D.K. Anand, “Research in Mechanical Systems”, ASME Publication, December 58 441 1980. D.K. Anand, R.W Allen, and B. Kumar, “Transient Simulation of Absorption Machines”, presented at ASME Solar Energy Division/Third Annual Systems 59 442 Simulation and Economic Analysis. Solar Heating and Cooling Operational Results Conference pp. 239-247, April 27- May 2, 1981. D.K. Anand, B. Kumar, and R.W. Allen, “Simplified Cooling Design Charts”, 60 presented at Solar Rising (1981 Annual meeting of American Section of ISES), 452 May 26-10, 1981. D.K. Anand, B. Kumar, and R.W. Allen, “Regional Simplified Cooling Design 61 Charts”, presented at Technologies for the Transition (16th IECEC), August 9-14, 458 1981. D.K. Anand and R. LeChevalier, “Solar Cooling – An Assessment”, TPI/SR 81-01 62 469 (prepared for U.S. Dept. of Energy), 1981. James A. Kirk, D.K. Anand, Harold E. Evans, G. Ernest Rodriguez, “Magnetically 63 Suspended Flywheel System Study”, presented at the Integrated Flywheel 497 Technology – 1984 Workshop, February 7-9, 1984. E. O. Bazques, and D. K. Anand, "Control aspects of photovoltaic/thermal 64 energy systems", 19th Intersociety Energy Conversion Engineering Conference, 511 Vol. 3, pp. 1656-1662, August 19-24, 1984. D.K. Anand, K.W. Lindler, S. Schweitzer, and W.J. Kennish, “Second Law Analysis 65 of Solar Powered Absorption Cooling Cycles and Systems”, Journal of Solar 521 Energy Engineering, Vol. 106, pp.291-298, August 1984. D.K. Anand, “Supercomputers and Hierarchical Control: a System Viewpoint”, 66 presented at the NSF Study on Supercomputers in Mechanical Systems Research, 529 September 12-14, 1984. Eric O. Bazques and D.K. Anand, “Photovoltaic/Thermal System Performance 67 536 Index Based on the Second Law”, AMSE Publication 84-WA/Sol-9, 1984. Eric O. Bazques and D.K. Anand, “Use of Markov Transition Matrices in Simulating Stochastic and Persistence Effects on Weather Dependent Systems”, 68 542 Proceedings of the Sixteenth Pittsburgh Modeling and Simulation Conference, April 25-26, 1985. James A. Kirk, D.K. Anand, and Asad A. Khan, “Rotor Stresses in a Magnetically 69 Suspended Flywheel System”, presented at the 20th IECEC: Energy for the 548 Twenty-First Century, August 18-23, 1985. D.K. Anand, James A. Kirk, and David A. Frommer, “Design Considerations for 70 Magnetically Suspended Flywheel Systems”, presented at the 20th IECEC: Energy 560 for the Twenty-First Century, August 18-23, 1985. D.K. Anand, J.A. Kirk, and M. Bangham, “Design and Analysis of a Magnetically 71 Suspended Flywheel System”, presented at the Winter Annual Meeting of ASME, 566 85-WA/DE-8, November 17-21, 1985. D.K. Anand and Robert LeChevalier, “Design Considerations for Photovoltaic 72 Driven Vapor Compression Cycles”, Alternative Energy Sources VII, Vol. 2, Solar 570 Energy 2, pp. 371-383. James A. Kirk, D.K. Anand, Roger Viera, and Chaitanya P. Jayaraman, “Modeling 73 and Simulation of Magnetic Bearing Forces”, presented at the 17th Annual 585 Pittsburgh Conference on Modeling and Simulation, April 24-25, 1986. D.K. Anand, J.A. Kirk, R.B. Zmood, and P.A. Studer, “System Considerations for a 74 Magnetically Suspended Flywheel”, presented at the 21st IECEC Final Program, 593 August 25-29, 1986. D.K. Anand, J.A. Kirk, and M.L. Bangham, “Simulation, Design and Construction 75 of a Flywheel Magnetic Bearing”, presented at the Design Engineering 601 Technical Conference of ASME, October 5-8, 1986. J.A. Kirk, D.K. Anand, M. Anjanappa, “Magnetic Bearing Spindle Control in 76 Machining”, NSF Manufacturing Systems Research Conference, 127-130, 608 November 18-21, 1986. J.A. Kirk, D.K. Anand, M. Anjanappa, and R. Uppal, “Implementation of a Flexible 77 Manufacturing Protocol”, presented at the 2nd IASTED International Conference – 613 Applied Control and Identification, December 10-12, 1986. D.K. Anand, J.A. Kirk, and M. Anjanappa, “Magnetic Bearing Spindles for 78 Enhancing Tool Path Accuracy”, Advanced Manufacturing Processes, 1(2), pp. 619 245-268, 1986. J.A. Kirk, M. Anjanappa, and D.K. Anand, “Validation of a Relationship between 79 643 Cutting Force and Surface Finish for Optimal Control of End Milling”. R. B. Zmood, D. K. Anand, and J. A. Kirk, "The influence of eddy currents on 80 magnetic actuator performance", Proceedings of the IEEE Vol. 75, no. 2, 259- 651 260, February 1987. J.J. Helferty, R. Fischl, P.R. Herczfeld, T.E. Brisbane, D.K. Anand, and M. Sugisaka, “On the Selection of Distributed Parameter Models for Control Studies of Solar 81 653 Energy Systems”, presented at the 2nd ASME-JSME-JSES Solar Energy Conference, March 22-27, 1987. D.K. Anand, R. Fischl, J. Helferty, and T. Brisbane, “Dynamic Performance of 82 Absorption Systems for Control Simulation”, presented at the 2nd ASME-JSME- 665 JSES Solar Energy Conference, March 22-27, 1987. Hanseok Ko, D.K. Anand, and J.A. Kirk, “Magnetic Bearing with Non-Linear 83 Permeance”, presented at the 18th Annual Pittsburgh Conference on Modeling 672 Simulation, April 23-24, 1987. J.A. Kirk and D.K. Anand, “The Magnetically Suspended Flywheel as an Energy 84 678 Storage System”. M. Anjanappa, J. A. Kirk, and D. K. Anand. "Tool path error control in thin rib 85 machining" Proceedings of the 15th North American Manufacturing Research 690 Conference, May 27-29, 1987. D.K. Anand, “On Accuracy in Modeling and Simulation for System Control”, 86 699 presented in American Control Conference, Vol. 2 of 3, June 10-12, 1987. D.K. Anand, J. A. Kirk, and Peter Iwaskiw, “Magnetically Suspended Stacks for 87 707 Inertial Energy Storage Flywheel”. J.J. Helferty, R. Fischl, P.R. Herczfeld, M. Sugisaka, J. Adnot, and D.K. Anand, “On 88 the Observability of Solar Energy Systems”, presented in American Control 713 Conference, Vol. 2 of 3, June 10-12, 1987. David P. Plant, Chaitanya P. Jayaraman, David A. Frommer, James A. Kirk, and 89 Davinder K. Anand, “Prototype Testing of Magnetic Bearings”, an AIAA 719 Publication. R.B. Zmood and D.K. Anand, “The Design of a Magnetic Bearing for High Speed 90 723 Shaft Driven Applications”, an AIAA Publication. Kenneth Wong, J.A. Kirk, and D.K. Anand, “Dynamic Response of a Magnetically 91 729 Suspended Flywheel with Mass Unbalance”, an AIAA Publication. B. Kumar, D.K. Anand, and J.A. Kirk, “An Intelligent Feature Extractor for 92 Automated Machining”, IEEE catalog No.: 87CH2480-2, presented at the 5th 735 International Conference on Systems Engineering, September 9-11, 1987. D.K. Anand and J. A. Kirk, “Design and Analysis of Magnetic Bearings”, presented 93 at the 7th World Congress on the Theory of Machines and Mechanisms, September 741 17-22, 1987. D.K. Anand, J.A. Kirk, and M. Anjanappa, “Tool Path Error Control for End 94 Milling of Microwave Guides”, presented at the 7th World Congress on the Theory 747 of Machines and Mechanisms, September 17-22, 1987. J.A. Kirk, D.K. Anand, M. Anjanappa, and S. Shyam, “Accuracy Enhancement 95 Methodologies in Thin Rib Machining”, presented in 1987 NSF Manufacturing 751 Systems Research Conference, October 6-9, 1987. M. Anjanappa, J. A. Kirk, and D.K. Anand, “An Algorithm Relationship between 96 758 the Cutting Force and Surface Texture in Machining Processes”. K.W. Lindler and D.K. Anand, “The Second Law Analysis: When is it Useful?”, 97 762 Alternative Energy Sources VIII, Vol. 2, Research and Development, pp. 847-856. M. Anjanappa, D.K. Anand, and J.A.Kirk, “Identification and Optimal Control of 98 Thin Rib Machining”, Modeling and Control of Robotic Manipulators and 772 Manufacturing Processes, DSC-Vol. 6, pp. 15-23, December 13-18, 1987. D.K. Anand and B.Kumar, “Absorption Machine Irreversibility using New 99 782 Entropy Calculations”, Solar Energy, Vol. 39, No.3, pp. 243-256, 1987. B. Kumar, D.K. Anand, and J.A. Kirk, “Integration and Testing of an Intelligent Feature Extractor within a Flexible Manufacturing Protocol”, 16th North 100 796 American Manufacturing Research Conference Proceedings, pp. 320-328, May 24- 27, 1988. J.A. Kirk, M. Anjanappa, D.K. Anand, and W.K. Rickert, Jr., “The Use of Iges in 101 Automated CNC Machining”, Proceedings of the 3rd International Conference on 807 Computer-Aided Production Engineering, pp. 243-251, June 1-3, 1988. James T. Pritchard and D.K. Anand, “Optimal Trajectories of Robotic Manipulators”, presented at ASME’s Symposium on Flexible Automation: Control 102 817 & Design in Robotics, Autonomous Vehicles and Flexible Manufacturing Systems, July 18-20, 1988. J.A. Kirk and D.K. Anand, “Overview of a Flywheel Stack Energy Storage 103 827 System”, Proceedings of the 23rd IECEC, Vol. 2, pp. 25-30, July 31- August 5, 1988. J.A. Kirk, D.K. Anand, M. Anjanappa, and W.K. Rickert, Jr., “The use of Iges in 104 Rapid and Automated Design Prototyping”, Advances in Design Automation- 835 1988, DE-Vol. 14, pp. 27-32, September 25-28, 1988. M. Anjanappa, D.K. Anand, J.A. Kirk, and S. Shyam, “Error Correction Methodologies and Control Strategies for Numerical Controlled Machining”, 105 842 Control Methods for Manufacturing Processes, DSC-Vol. 9, 41-49, November 27- December 2, 1988. J.A. Kirk and D.K. Anand, “Satellite Power using a Magnetically Suspended 106 854 Flywheel Stack”, Journal of Power Sources, Vol. 22, pp. 301-311, 1988. D.K. Anand, J. A. Kirk, M. Anjanappa, and S. Chen, “Cell Control Structure of FMP 107 for Rapid Prototyping”, Advances in Manufacturing System Engineering – 1988, 865 PED-Vol. 31, pp. 89-99, 1988. M. Jeyaseelan, D.K. Anand, and J.A. Kirk, “A CAD Approach to Magnetic Bearing 108 877 Design”. B. Kumar, D.K. Anand, and J.A. Kirk, “Knowledge Representation Scheme for an 109 883 Intelligent Feature Extractor”. D.K. Anand, J.A. Kirk, M. Anjanappa, D, Nau, and E. Magrab, “Protocol for Flexible Manufacturing Automation with Heuristics and Intelligence”, 110 891 Proceedings of Symposium on Manufacturing Systems- Design, Integration and Control, Vol. 3, pp. 209-217, 1988. D.K. Anand, M. Anjanappa, J.A. Kirk, E. Zovi, and M. Woytowitz, “Magnetic Bearing Spindle Control”, Proceedings of the 15th Conference on Production 111 901 Research and Technology - Advances in Manufacturing Systems Integration and Processes, pp. 31-35, January 9-13, 1989. K.W. Lindler and D.K. Anand, “A Computer Aided Design Approach to the Optimization of Control Strategies for Desiccant Air Conditioning”, Solar 112 907 Engineering – 1989: Proceedings of the 11th Annual ASME Solar Energy Conference, pp. 71-76, April 2-5, 1989. C.M. Lashley, D.M. Ries, R.B. Zmood, J.A. Kirk, and D.K. Anand, “Dynamics Consideration for a Magnetically Suspended Flywheel”, Proceedings of the 24th 113 914 IECEC, Vol. 3: CH2781-3/89/0000-1511, 899465, pp. 1511-1516, August 6-11, 1989. W.L. Niemeyer, P. Studer, J.A. Kirk, D.K. Anand, and R.B. Zmood, “A High Efficiency Motor/ Generator for Magnetically Suspended Flywheel Energy 114 921 Storage System”, Proceedings of the 24th IECEC: CH2781-3/89/0000-1511, 899445, pp. 1511-1516, August 6-11, 1989. M.A. Woytowitz, D.K. Anand, J.A.Kirk, and M. Anjanappa, “Tool Path Error Analysis for High Precision Milling with a Magnetic Bearing Spindle”, Advances 115 927 in Manufacturing Systems Engineering, PED-Vol.37, pp. 129-142, December 10- 15, 1989. J.A. Kirk, D.K. Anand, J.D. Watts, “Manufacturing Automation and Prototyping 116 for Printed Wiring Boards”, 6th Symposium on Information Control Problems in 942 Manufacturing Technology, September 26-29, 141-145, 1989. B.J. Kumar, D.K. Anand, J.A. Kirk, and M. Anjanappa, “Feature Extraction and Validation within a Flexible Manufacturing Protocol”, Advances in 117 948 Manufacturing Systems Engineering, PED– Vol. 37, pp. 51-62, December 10-15, 1989. M. Anjanappa, D.K. Anand, J.A. Kirk, E. Zivi, M. Woytowitz, “Retrofitting a CNC 118 Machining Center with a Magnetic Spindle for Tool Path Error Control”, IFAC 961 Symposium, 639-643, 1989. R. B. Zmood, D. K. Anand, J. A. Kirk, and E. Zivi, "The effect of structural vibrations on magnetic bearing operation", In Energy Conversion Engineering 119 966 Conference, 1989. IECEC-89., Proceedings of the 24th Intersociety, pp. 1499- 1503. IEEE, 1989. R.B. Zmood, D.K. Anand, J.A. Kirk, “Analysis, Design, and Testing of a Magnetic 120 971 Bearing for a Centrifuge”, Transactions of the ASME, 345-350, 1989. D.P. Plant, J. A. Kirk, and D. K. Anand, "Prototype of a magnetically suspended flywheel energy storage system", Energy Conversion Engineering Conference, 121 977 1989. IECEC-89., Proceedings of the 24th Intersociety, pp. 1485-1490. IEEE, 1989. J.A. Kirk, D.K. Anand, M. Anjanappa, E. Zivi, and M. Woytowitz, “Magnetic 122 Bearing Spindle Control in Machining”, Proceedings of NSF Design and 983 Manufacturing System Conference, January 8-12, 1990. R.B. Zmood, D. Pang, D.K. Anand, J.A. Kirk, “Robust Magnetic Bearings for Flywheel Energy Storage Systems”, proceedings of the Second International 123 993 Symposium on Magnetic Bearings, SEIKEN Symposium, 123-129, July 12-14, 1990. M. Anjanappa, D.K. Anand, and J.A. Kirk, “Characterization of Errors for On-line 124 Correction with a Magnetic Bearing Spindle”, Adv. Manuf. Eng, Vol. 2, pp. 179- 1005 188, October 1990. M. Anajanappa, D.K. Anand and J.A. Kirk, “Characterization of errors for on-line 125 correction with a magnetic bearing spindle”, Adv. Manuf. Eng., Vol. 2, October 1015 1990. E.L. Zivi, D.K. Anand, M. Anjanappa, J.A. Kirk, “Magnetic Bearing Spindle Control 126 for Accuracy Enhancement in Machining”, to be presented at the 1990 ASME 1025 Winter Annual Meeting, November 1990. P. Lisiewski, M. Anjanappa, D.K. Anand, J.A. Kirk, “Enhanced Robotic Control 127 Procedures for a Flexible Manufacturing Cell”, proceedings of 13th IASTED 1040 International Symposium, 188-191, November 13-15, 1990. E.L. Zivi, D.K. Anand, J.A. Kirk, M. Anjanappa, “Magnetic Bearing Spindle Control for Accuracy Enhancement in Machining”, presented at The Winter Annual 128 1045 Meeting of The American Society of Mechanical Engineers, PED-Vol. 44, 283-297, November 25-30, 1990. D.K. Anand, M. Anjanappa, “Magnetic Bearing Applications”, proceedings of the 129 17th International Conference of Mechanical Power Engineering, Vol. 4, No. 3, 1- 1061 11, December 17-20, 1990. D. K. Anand, M. Anjanappa, J.A. Kirk, M. Jeyaseelan, “CAD for Active Magnetic 130 1073 Bearings”, published in CIME, 26-30, December 1990. M. Anjanappa, M.J. Courtright, D.K. Anand, and J. A. Kirk, “Manufacturibility 131 Analysis for a Flexible Manufacturing Cell”, Transactions of the ASME - Journal 1078 of Mechanical Design, Vol. 113, pp. 372-378, December 1991. M. Anjanappa, J.J. Dickstein, D.K. Anand, and J.A. Kirk, “Automated Inspection 132 1085 Data Analyzer for Closed Loop Manufacturing”, an ASME publication. D.C. Hudson, Da-Chen Pang, J.A. Kirk, D.K. Anand, and M. Anjanappa, “Integrated 133 1095 Computer Aided Manufacturing for Prototype Machining”, an ASME publication. C.P. Jayaraman, J.A. Kirk, D.K. Anand, and M. Anjanappa, “Rotor Dynamics of 134 Flywheel Energy Storage Systems”, Journal of Solar Energy Engineering, Vol. 1103 113, pp. 11-18, February 1991. J.A. Herndon, M. Anjanappa, D.K. Anand, and J.A. Kirk, “Frame-based 135 Implementation of a Design Knowledge-capture Scheme”, Knowledge Based 1111 Systems, Vol. 4, No. 1, pp. 35-51, March 1991. M. Anjanappa, D.K. Anand, and J.A. Kirk, “Application of Stochastic Optimal 136 Control to Thin Rib Machining”, IEE Proceedings-D, Vol. 138, No. 3, pp. 228-236, 1128 May 1991. D. Pang, J.A. Kirk, D.K. Anand, R.G. Johnson, and R.B. Zmood, “Modeling and Design for PM/EM Magnetic Bearings”, NASA Conference Publication 3152 137 1137 (Part-1): International Symposium on Magnetic Suspension Technology, August 19-23, 1991. B.S. Berger, C. Belai, D.K. Anand, “Time Series Analysis with SVD Algorithms”, 138 Transactions of the ASME, Journal of Mechanical Design, Vol. 113, No. 4, 1152 December 1991. M. Anjanappa, J.A. Kirk, D.K. Anand, and D.S. Nau, “Automated Rapid Prototyping with Heuristic and Intelligence: Part I - Configuration”, 139 1162 International Journal of Computer Integrated Manufacturing, Vol. 4, No. 4, pp. 219-231, 1991. J.A. Kirk, D.K. Anand, and M. Anjanappa, “Automated Rapid Prototyping with 140 Heuristic and Intelligence: Part II - Implementation”, International Journal of 1175 Computer Integrated Manufacturing, Vol. 4, No. 4, pp. 232-240, 1991. D.K. Anand, J. A. Kirk, R.B. Zmood, D. Pang, C. Lashley, “Final Prototype of 141 1184 Magnetically Suspended Flywheel Energy Storage System”. D. Pang, J.A. Kirk, D.K. Anand, C. Huang, “Design Optimization for Magnetic 142 1190 Bearing”. J. E. Parker, G. M. Zhang, J. A. Kirk, and Davinder K. Anand, "An integrated 143 1196 Approach to Calibrate an Untended Machining System", 1991. G.M. Zhang, T.W. Hwang, D.K. Anand, and S. Jahanmir, “Tribological Interaction 144 in Machining Aluminum Oxide Ceramics”, workshop held at U. S. Naval Academy, 1212 May 11-13, 1992. D.K. Anand, M. Anjanappa, “Accuracy Enhanced Machining with a Magnetic 145 1218 Spindle”, preprints of the IFAC SICICA’92, pp. 35-39, May 20-22, 1992. R.G. Johnson, D. Pang, J.A. Kirk and D.K. Anand, “Physical Modelling of High 146 Speed Magnetic Bearing Systems”, proceedings of the Third International 1224 Symposium on Magnetic Bearings, pp. 474-482, July 29-31, 1992. D. Pang, D.M. Ries, C.M. Lashley, J.A. Kirk and D.K. Anand, “Composite Flywheel Design for a Magnetically Suspended Flywheel Energy Storage System”, 147 1234 proceedings of the Third International Symposium on Magnetic Bearings, pp.559- 567, July 29-31, 1992. Ryan G. Johnson, Da-Chen Pang, James A. Kirk, and Davinder K. Anand, “Computer-Aided Modelling and Analysis of a Magnetic Bearing System”, 148 1244 proceedings of the 27th Intersociety Energy Conversion Engineering Conference, P-259, Vol. 4, August 3-7, 1992. Roger L. Fittro and Davinder K. Anand, “Neural Network Controller Design for a Magnetic Bearing Flywheel Energy Storage System”, proceedings of the 27th 149 1254 Intersociety Energy Conversion Engineering Conference, P-259, Vol. 4, August 3- 7, 1992. D.K. Anand, J.A. Kirk, R. Zmood, E. Rodriguez, “On the Performance and Stability 150 1260 of Magnetic Bearings”, presented at Rotordynamics, 1992. G. M. Zhang, Tsu-Wei Hwang, and Davinder K. Anand, "Chemo-mechanical 151 effects on the efficiency of machining ceramics", proceedings of the 1993 NSF 1269 Design and Manufacturing Systems Conference, 421-428, January 6-8, 1993. G.M. Zhang, D.K. Anand, S. Ghosh, and W.F. Ko, “Study of the Formation of Macro- and Micro-Cracks during Machining of Ceramics”, Proceedings of the 152 1278 International Conference on Machining of Advanced Materials (NST Special Publication 847),pp. 465-478, July 20-22, 1993. B. Kumar, D.K. Anand, M. Anjanappa, and J.A. Kirk, “Feature Extraction and 153 Validation within a Flexible Manufacturing Protocol”, Knowledge-Based 1296 Systems, Vol. 6, No. 3, pp. 130-140, September 1993. D.K. Anand, M. Anjanappa and K.H. Sung, “Adaptive Control of a Flexible 154 1308 Manipulator with Varying Payload”, presented at 12th IFAC, 1993. Abhijit Dasgupta, E.B. Magrab, D.K. Anand, Karlheinz Eisinger, James G. McLeish, Myra A. Torres, Pradeep Lall, and Terrance (Terry) J. Dishongh, 155 “Perspectives to Understand Risks in the Electronic Industry”, open forum, IEEE 1312 Transactions on Components Packaging, and Manufacturing Technology – Part A. Vol. 20, No. 4, December 1997. B.S. Berger, J.A. Manzarl, D.K. Anand and C. Belai, “Auto-Regressive SVD 156 Algorithms and Cutting State Identifications”, Journal of Sound and Vibration 1318 (2001) 248 (2), pp. 351-370, April 2001. B.S. Berger, C. Belai, D.K. Anand, “Toeplitz Matrices and Cutting State 157 Identification”, 8th International Congress on Sound and Vibration, July 2-6, 1338 2001. Stephen A. Smee, Paul C. Brand, Dwight D. Barry, Collin L. Broholm, and Dave K. Anand, "An elastic, low-background vertical focusing element for a doubly 158 focusing neutron Monochromator", Nuclear Instruments and Methods in Physics 1348 Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 466, no. 3, 513-526, 2001. B. Berger, C. Belai, D. Anand, “Chatter Identification with Mutual Information”, 159 1362 Journal of Sound and Vibration 267 (2003), pp. 178-186, December 2002. Paul Casey, D.K. Anand, and Michael Pecht, “Carbon Nanotubes and an Optical Method for Life Consumption Monitoring of Electronic Assemblies”, 160 1371 Proceedings of 8th Annual Pan Pacific Microelectronics Symposium, pp. 225-234, February 18-20, 2003. Zafer Tuncali, D.K. Anand, Robert M. Kavetsky, and Chester Clark, “MEMS Applications in Ordinance and Defense Related Systems”, Proceedings of 9th 161 1384 Annual Pan Pacific Microelectronics Symposium, pp. 387-396, February 10-12, 2004. Z. Tuncali, S.K. Gupta, D.K Anand, Z. Yao, “Design and operation of a storage 162 facility in virtual environment”, proceedings of the International Conference on 1396 Manufacturing Automation, 521-528, October 26-29, 2004. Robert A. Kavetsky, Davinder K. Anand, Michael Marshall, “The Science and 163 Engineering Workforce and National Security”, Pan Pacific Microelectronics 1406 Symposium, January, 2008. Automated Procedures for Indicator-Dilution Curves using a Digital Computer, Anand, D.K., and L. de Pian, Biollvkdical lnstntmentation, December 1964. ~ O[ruU[J Computer Applications 11 fi -------!----------------------------r-"-'~~:rJ r · 1 Aulomaled Procedures for lndicalor-Dilulion Curves using a Digital Computer BY D .. K. Anand L. de Pian Introduction of dye-injection to its appearance on the curve is a measure The purpose of this study is to investigate the feasibility of the transit time of the blood through the heart. of developing an automatic procedure, using a central Theoretically then after the density increases to a peak digital computer, that would yield, very rapidly, pertinent value it must decay to the zero level ( or density of pure information of the blood flow through the heart blood) if all the dye was pumped out. However, at the The initial plan of the work was primarily concerned aorta, some of the blood and dye that has flowed past the with the analysis, use, and extension of the indicator- sample point will re-circulate back to the input of the dilution curves. heart, thus causing the curve not to decay to zero. The The indicator-dilution technique has been used in medi~ curve would show additional, but lesser, peaks and slowly cal evaluation for some time ( 1), The method involves approach the value of the pure blood density. If a time the injection of a fluid, having an optical density different measure of the cardiac output is to be obtained, this re- from that of blood, and subsequent downstream withdrawal circulation must be eliminated. From analog studies of the heart (2) it can be shown that the decay, in the ideal case of no re-circulation, must be an exponential function of time. The exponential can be fitted by least squares from data after the peak at tm. In order to avoid uncer- tainties around the peak value, the eponential fit is obtained from a time b ( a little later than t.,,) to some time ta. The value of ts was chosen to be 3 or 4 seconds alter b. I I F.:xp-cnc-nt..ial. fit ( no re- The exact value is not too critical since several values of I l { circulatior. ) - L,- t" in this vicinity yielded the same exponential curve. For 1 ' times greater than ta an extrapolated exponential curve is 1 I 1 Re-circulation used which should lie under I I ', the actual curve. The dif-I L - ::_ _ - _I_ ference between the actual and exponential plot is some --------- I measure of recirculation. I The calculation of the cardiac output involves the con- I sideration of the following discrete areas under the dye- diluation curve: (a) from t• to tm (b) from tm to tn (c) ti.. time from ts to ta. Portions (a) and (b) are common .to both actual and extrapolated curves. Portion (c) is taken with Figure 1: The indicator-dilution curve the extrapolated curve if recirculation is to be excluded, or under the actual curve if recirculation is to be included. of the blood-indicator mixture. The optical density of the Since negative recirculation is meaningless, the area under blood-indicator mixture is determined with a densitometer the actual curve must of course be larger than that under and is related to the concentration of indicator in blood. the extr:apolated exponential curve. Usually injection is done at the inlet of the heart and Prior to the actual determination of the cardiac output, output sampling at the aorta. The data from the densito- a number of other parameters, such as the onset or initial meter yields the concentration of the sampled mixture- concentration, peak concentration etc. have to be calcu- which is plotted as a function of time. Figure 1 is an ex- lated by the computer. It is therefore appropriate at this ample of an indicator plot obtained from a densitometer. time, to review the computer program and the mathe- matical assumptions. The Indicator Curve As already mentioned, the obtaining of an indicator- Computer Program dilution plot is relatively simple. The plot gives some type As already mentioned, the initial and peak values of of functional relationship between density of mixture and ,concentration are of importance. They are found by cal- time (Fig. 1). The area under the curve is proportional culating a. running time derivative and checking for a point to the cardiac output. The initial time interval from time after which the derivative continues to increase (for ex- Bio/Medical Instrumentation/December, 1964 21 Page 1 A INPUT Determine slope Compare slope Read t , t ,At,Y\.,O, using Hannning's ' B 3 I toe, apredeter­ 1" 1 four point fit �, '-i mined constant t reached when slope larger than e and 0 Determine corresponding 1 '1 continues to increase for five ' concentration additional points co Calculate the Check for minimum Check if slope average concentra­ . slope after t >----� · increases in magni­ 3 0 tion c ' tude for five � a additional points Minimum slope - -- Calculate c Using least squares ho - - � 1 , c2, determines t , c ; ' c us:tng Hamming's ----� compute the constants 4 m m 4 if all Ci<. cm formula a,b for exponential fit Compute area c3 under extrapolated exponential Compute cardiac Print: t t c. output . 0 m C , a, b, ' A ' o' _,, Go to A __ co = K I I A m c cardiac output Litres/gin Figure 2:Program Outline ample, for at least five more points). Having satisfied Having determined to, Co, Ca, tm, and Cm, the areas under this criterion, to is established and consequently its cor­ the curve must next be found .. responding concentration Co is known. The base-line for The calcuation of areas ( to, to tm and tm to tn) which concentration Ca, is found by averaging the points before Co. The time tm of occurrence of Cm, the peak concentration, are taken under the actual curve may be calculated by is determined by the computer program when it is estab­ Simpson's rule using constant time intervals. The value lished that a minimum value of the absolute magnitude of these intervals will of course directly effect the accuracy r of the derivative is achieved. The five-point check, as in, of measuement. It was found that intervals of % second the case of the determination of the onset value, is also would produce accurate results and that shorter intervals applied here to ascertain that Cm is a true maximum. did not materially improve the accuracy. 22 Bio/Medical Instrumentation/December, 1964 Page 2 Page 3 Page 4 On the Stability and Dynamic Be- havior of Cascaded Thermoelectric l Devices T1.{x I 1 t} X The dynamic response of single-stage thermoelectric devices and the static behav- n-trye p-typs ior of single-stage and thermally cascaded devices have been studied bv many research- r,_{t) X •,. ers However, little work has been done on 'I'2(x,t) the dynamic response of cascaded devices The purpose of this correspondence is to show the effect of cascading on stability and dynamic response by analyzing the small X • •- signal transfer functions Fig I Two-stage independent current device, The device, of length 2L as shown in Fig 1, has constant area and temperature inde- pendent properties at the bias point of operation The Thompson effect being of second order is neglected in small-signal analysis [l] This would, however, not be the case in static operation [2] The partition 30 between the two stages is assumed to be a perfect thermal conductor and electrical insulator with small enough dimensions so that its heat capacity is neglected. Such a 25 view has been taken by other workers [l] The small-signal energy balance equa- tion at x = L is 20 a 2ka - [¢h, x) - q',1(,, x)] ax - a[l2q - I,.],t,,(L, s) - aT,.(L)[i2(s) - i,(s)] Fig" 2. Magnitude and percentage decrease of load disturbance function where q,(s, x) is the temperature variation about bias, i(,) is the current variation about bias, Tq and Iq_ are bias temperature and disturbance function, neglecting second- current, and a is the Seebeck coefficient The order effects, is found to be subscripts refer to the stage It is clear that if I,(s) =12(1) the equation reduces to that of L tanh v'i a single-stage device 4- a(/z,, -1,q) - ---- The load Pa(s), shown in Fig. l, can be ka y'.; GuP = -------------- represented by ,C¢o(s) -Pos, where the first term is due to the thermal capacitance of the 4[ Ck s - aI 1.] + 8-vvs cL2 tanh s- load and P,s is due to a heat source. \Ve as- sume that the thermal conductance of the and is the only function that undergoes a load is negligible, as is usually the case [1] notable change, as compared to single-stage For such a system we define the following operation, for moderate positive values of transfer functions: t,,.J = l2q - I, 0 This is a comparable condition 1) Load-disturbance function: to optimization of the device. The variation of G0 p is shown in Fig. 2 The ambient dis- G = '!':'_0)_\t,L(s)-o turbance and control functions did not ex- oP Pos i~i:~=~ hibit any appreciable change It is observed that the device has in- 2) Ambient-disturbance function: creased stability due to its comparative insensitivity to variations in loading. Fur- thermore, each section is being separately optimized instead of the entire device As is 3) Control-function Stage 1: well known. this is quite desirable DK. ANAND o(,) 1"'2L-o University of Maryland Go/1 = -,-- Pus=O 1\s) College Park, Md Z1 i 2 (~)=0- MORION F. TARAGIN 4) Control-function Stage 2: George \Vashington University \Vashington D. C G _ ~i)_ I P,;.s-o Lours DE PIAN 012 - i2(s) ~~1~;)0=o George Washingtcn University Washington. D C These can be evaluated by solving the temperature distributions using energy bal- ances and temperature continuity at the REFERENCES two ends and at the interface The load- ll] P. E. Gray. '' The effect of source and sink thermal res~stance on thermoelectric- generator perfor- mance," AIEE Tran'f: (Commun-ications and Elec- tronics), vol 79, pp. 15-19, March 1960. Manuscript received Jub,r 26, 1965. The work re- r2] \V, M, Pritchard, "The coefficient of performance ported here was supported by Navy Contract .NONR of thermoelectric cooling devices," Proc, IEEE, 761(09), vol. 52, pp 442--44.3, April 1964 Reprinted from the PROCEEDL'-IGS OF THE IEEE VOL 53, NO. 10, OCTOBER, 1965 pp. 1637-1638 Copyright 1965, and reprinted by permission of the copyri[ht owner PRINIED IN IHE US A Page 5 On the Performance of a Heat Pipe RESISTANCE HEAT WICIC D. K. ANAND* The Johns Hopkins University, Applied Physics Labomtory, Silver Spring, Md. . VAPOR FLOW No.rnenclat;ure A area of wick, ft2 C specific heat, Btu/lb-°F Fig. 1 Sealed horizontal pipe for wick boiling (insulation D diameter, ft not shown). 2 g gravity, ft/sec 2 h boiling heat-transfer coefficient for wick Q/A(T. excess fluid, the radius of meniscus may be infinite .. - Tw) The transient behavior has not been studied eirtensively, K thermal conductivity, Btu/ft hr'-°F but it would seem that this phase will not present any great L length, ft difficulty.. It is clear, however, that there will be an upper limit Np pressure number to the heat flow through the pipe, because liquid depletion Pr Prandtl number = Cµ/K rate in the evaporator must exceed the recirculation rate by p p1essure, psf capillary pumping. Q heat, Btu/hr Re Reynolds number = pvD/µ Dyna.rnic Operation r radius, ft St Stanton number= h/cw = ,pPr"NpbRe" The heat pipe comprises two domains: the vapor core and T temperature, °F the fluid annulus (fluid flowing through the wick). The flow V velocity, fps conditions in these regions merit separate attention. The w massflowrate = Q/A•A,lb/sec vapor flow in the core is similar to flow with injection or suc- X axial direction of heat pipe tion through a porous wall, since a liquid and vapor are con- (/), ?r,W constants tinually changing phase at the interface. Cotter4 has ex- 8 porosity of wick = (Pr - Pwi)/ Pl plained the dynamics of vapor flow and his explanation is p density, lb/ft3 µ viscosity, lb/hr-ft used here extensively. X latent heat of vaporization, Btu/lb Several different vapor flow regimes may be obtained, (T surface tension, lb/ft based on the Reynolds number refened to in the vapor core diameter.. For Re.» I, the velocity profile is parabolic, and Subscripts flow is similar to Poiseuille flow. The pressure decreases in f wick fiber the direction of flow with a gradient larj!;er than that of l liquid Poiseuille flow in evaporation and smaller in condensation. p pore in the wick Flow properties are obtained using constant Re.; for ahnost V vapor all cases of present interest this is justified.. For Re.» 1, the w wall velocity profile is no longer parabolic, but vapor pressure still v;i wick decreases in flow direction, and the properties of flow still may be obtained as previously shown. Introduction T For Re. = const « 1, the pressure is3 HE requirement.<, of cooling in the space environment have led researchers to study various coolants and high ther- dp/d,x = (8 µw./7rpr4) (1 + ¾R e. + .. ) (1) mal condu('tivity devices.. The heat pipe described in this note (Fig .. 1) is a self-contained device that exhibits a very Since this drop is small, the fust term usually suffices for de- high effective thermal conductivity 1 It consists of a sealed termining the pressure drop. It is appropriate to remark that tube with wick material in contact with the internal heat- the temperature drop may be obtained using the Clausius- transfer surface. The operation is based on th«::. evaporation Clapeyron equation .. of a liquid in the e,aporator section and subsequent flow in The liquid flow through the annulus is quite different from the core towards a region of low pressure. In the condenser, the core. The momentum equation for incompressible steady the liquid is condensed and flows back to the evaporato~ flow is · through the wick by capillary pumping to continue the cycle. "ilp = pg + µ!1 2v - pvt:.v (2) Under steady-state conditions, the pressme in the evaporator section is slightly less than the vapor pressme of the adjacent If an average velocity v is defined over an area of wick which liquid, thereby assming continuing evaporation. In the con- includes the solid structure, then the velocity within the pore denser section. the opposite holds, assuring continuing con- is (v)/t, where e is the wick porosity.. Observing that the densation.. O" ing to this liquid-vapor interface, the radius velocity on the pore surface vanishes and is of the mder (v)/c of curvatme of meniscus in evapmator recedes and that in the within the passage, the following approximations may be condeqser increases. In the condenser, especially if there is made: Received December 10, 1965 .. µy2v _.. µ(v)/cr 2 (3) * Engineer Space Development Division; also Assistant Pro- Since v is small, Eq. (2) becomes . fessor of Engineering, University of Maryland, College Park, Md. 'VP 9:: pg+ µV 2v (4) Reprinted from JOURNAL OF SPACECRAFT AND ROCKETS Copyright, 1966, by the American Institute of Aeronautics and Astronautics, and reprinted by permission of the copyright ovnier Page 6 764 J, SPACECRAFT YOL. 3, NO.. 5 10• ------------------, Experiments have been performed to show the temperature distribution, the boiling heat-transfer eoefficients, and the vapor temperatme and pressure drop, The experimental 5 0 setup consisted of a ¼-in.-o.d. stainless steel pipe 24 to 36 in, long, with its interior wall covered by a wick material (Fig. 1) .. The wick used was a passivated, 100-mesh stainless steel screen with porosity varying from 0.65 to 0.94. Heat was ~1~ PREVIOUS DATA added at the evaporator section by resistance heating. The 2 entire pipe was insulated using polyurethane foam. The con-ut~I0 o_,_ denser section was kept in an ice bath.. Temperatures were ~ measured using a 24-point Daystrom recorder during tran- ~ 5 sient and steady-state operation. The experiment was started by placing the tube in a vertical position and boiling off water in order to evacuate the tube of air and nonccndensible gases, W'hen there remained enough water to saturate the wick and a very small excess, the tube was sealed and placed in a horizontal position. The heat 101 L---'--~-'-l-'-_._._-4-__. .___,_....._-+-._._.._._. input (700 to 6000 Btu/hr-ft2) was adjusted to a predeter- 10-• 5 10-• 5 10-• REYNOLDS NUMBER mined value and condenser temperatme controlled, The Fig. Wick boiling heat-transfer correlation. temperature of the vapor inside the heat pipe was monitored 2 using a thermocouple embedded in an axial wire. The wick boiling heat-transfer coefficient is h = Q/A (T. - and the ratio of the two expressions in Eq. (3) yields a liquid T..,), and the liquid mass flow rate is lV = Q/Ae}... Selecting Reynold number based on v. Although the last term is 0.6 as the exponent of the Prandtl number, to correspond to neglected in the expression for the pressure drop, this Rei will liquid heating literature, the dimensionless correlation is ob- be used in the performance correlation; experiment shows tained as that indeed Rei « 1. From Eqs,. (3) and (4) the pressure drop for a horizontal pipe becomes St = 0.00051 Pr0 6 Re-1 -43 NpO 2 (8) A-Pf, = wµQX/21r(r,i - r,2) perp2L (5) The foregoing correlation is compared with previous data and shown in Fig. 2. It is clear from Fig. 2 and published pool where w is a constant depending upon the capillary structure. boiling data2 that higher results are obtained at low heat The vapor pressure drop also has been comput.ed from Eq. (1), fluxes and lower numbers at higher heat fluxes. This leads considering only the first term, and is to the confirmation of the idea t.hat wick boiling is preferable t:.p. = -4µ.QX/irpr,4L (6) at low heat fluxes. Presence of the wick material decreases It is assumed that the region between the condensing and turbulence near the surface, increases the effective surface evaporator section is perfectly insulated and that Re. « 1. area, and provides active sites for bubble formatio~, so that higher film coefficients at low heat flux are obtamed com- Correlation and Experimental Results pared to pool boiling, The conelated equation (8) affords some insight into the behavior of the heat pipe under varying As an extension to the previous study, one can correlate the heat-transfer coefficients in the evaporator section and conditions. Although the results were obtained for water, experimentation is continuing to determine applicability and thereby obtain a rather good indication of the engineering per- performance of other working fluids, formance. Since the problem is essentially that of wick boil- The temperature distribution along the heat pipe is shown ing and condensing, in the evaporator an~ condenser, dimen- in Fig. 3. The distribution is for steady-state operation and sionless analysis applied to this problem yields indicates high thennal conductivity in the axial direction. St = ,pPraN pbRe• (7) The temperature difference of the vapor and the pressure dif- where the properties for evaluating the numbers are that of ferentials was very small. Theoretical values obtained by the fluid. The correlation by these relations, and its subse- using equations from Cotter have shown this. It is clear that quent comparison with pool boiling heat-transfer coefficients, show the desirability of wick boiling at low Q and Rei. 300 300 Q,BTU/HR AVERAGE VAPOR-TEMPERATURE DROP IS 14 F 598 ac :..c.. •.. . :> li;200 ~ 0 1:/200 :, .... I. ac .0. !c :,. . . G....: G: . !: :, 257 ::E li li G: I..l.l ... :c ...... Ill ~ u 100 I if . i5.. .a.c :, 100 86 ac 0 a. ~ oL---f-----t---+---+----+--~ oL------+------+------+-- 0 10 20 30 40 !50 o ~ ~ ~ /:,.T LENGTH,INCHES Fig. 4 Heat. flow vs temperature difference between Fig. 3 Te1nperature distribution on heat pipe. average condenser and evaporator temperature. Page 7 MAY 1966 ENGINEERING NOTES 765 very small temperatuie and p1essuie differences are required propeily \Yetted with a, ery little excess, The choice of work- to supply the necessary driving forces for successful operation ing fluid is dictated by temperature limitations and \.. For and that their magnitudes are 11ot too important. example, alcohol has low A but also a lower freezing point than Figure 4 is a plot of the heat pumped, in the axial direction water. The effect of other fluid properties may be deduced off cou1se, vs the diffetence between the average evaporator from Eqs. (5, 6, and 8). There is no reason to believe that the and condenser temperature This again gi\'es us some ap- pipe will operate at any prefened temperature, although better preciation of the effective thetmal conducfoity that may be efficiencies are obtained at low heat fluxes. The temperatuie obtained .. and pressure differentials that act as driving forces are ex- Although the condense1 section was held constant in our tremely small as compared to their absolute magnitudes of T experiments, later expeiimentation included its variation. andP. Theunal runaway occuired when large quantities of working fluid were trapped in the condenser, thereby tending to de- References plete the supply in the evaporator section. The exact effect 1 Grover, G. :\I, Cotter, T .. P., and Erickson, G. F, "Struc- of other variables in thermal runaway has not yet been de- tures of very high thermal conductance," J. AppL Phys. 35, 1900 termined. (1964) 2 Allingham, W .. D.. and McEntire, J. A., "Determination of Conclusion boiling coefficient for a horizontal tube in water saturated wick The foregoing results indicate the potential usefulness of material," Transactions American Society of Mechanical Engi- the heat pipe. However, a method for actively controlling neers, Ser. C, No. l (1961) .. 3 Cotter, T.. P., "Theory of heat pipes," LA-3246-MS Los the device is needed This work is being presently pursued Alamos Scientific Lab , Los Alamos, New Mexico ( 1965). at the Applied Physics Laboratory.. It is clear that the type 4 Costello, C. P and Redeker, E .. R, "Boiling heat transfer and of wick and packing can be varied, The quantity of working maximum heat flux for a surface with coolant supplied by capil- fluid is not too important, provided that the entire wick is ary wicking," Chem. Eng Progr .. Symp. 59 (1963). Page 8 HELD AT THE UNIVERSITY OF MINNESOTA MINNEAPOLIS, MINNESOTA JUNE 14-17, 1966 EDITORIAL COMMITTEE OF THE FIFTH L. E. Goodman, Chairman B. Bernstein U. S. NATIONAL CONGRESS OF J. L. Bogdanoff 8. Budiansky J. Duffy E. R. Eckert R. Eichhorn / R. J. Grosh J. M. Hedgepeth Le G. Herrmann P. G. Hodge, Jr. A. Kantrowitz J. Kempner J. Kestin H. langhaar E. H. Lee J. l. lumley S.S. Manson H. Markovitz M. H. Martin W. C. Meecham C. Mylonas N. M. Newmark R. M. Rosenberg H. Rouse G. 8. Schubauer E. Silberman W.W. Soroka P. Wegener D.S. Wood PUBLISHED ON BEHALF OF THE CONGRESS BY THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS UNITED ENGINEERING CENTER 345 EAST 47TH STREET NEW YORK, NEW YORK 10017 Page 9 _P erturbations and Lyapunov Stability of a Multiply Connected Gravity Gradient Satellite at Synchronous Altitude D. K. ANAND, P. BAINUM, D. MACKISON The Johns Hopkins University Silver Spring, Maryland The rotational equations, for a satel- yields time dependent radiation torques and lite and two gimballed damper booms connected moment of inertia corrections caused by in at the center of mass, are derived using and out of plane bending due to thermal Lagrange's general formulation. The complete unbalance. The orbital eccentricity causes motion is thus governed by five coupled a one per orbit parametric excitation about equations where the translational orbital each axis. Finally, the instantaneous per- motion of the system is assumed not coupled turbations, considered as step inputs, occur with the rotational motion. Included are the when the satellite emerges from the earth's conservative effects of both gravitational shadow. It is learned that such perturba- and gyroscopic torques. The latter results tions give rise to appreciable deflections. from the coupling between orbital angular System stability is examined using velocity and the rotational motion in pitch- Lyapunov's direct method. The'Hamiltonian roll-yaw referenced to a local vertical is seen to be a convenient tyapunov function, frame. readily tested for positive definiteness in The motion occurs in the presence of the presence of damping and perturbations. small dynamic and instantaneous perturba- Necessary and sufficient conditions for tions. The dynamic inputs are (1) interaction stability are derived yielding constraints of solar radiation on extendible booms, for involving system parameters. varying moment, of inertia parameters for gravity stabilization, and (2) periodic excitation due to eccentricity~ The first Page 10 1966 PROCEEDINGS LEITERS 1999 Reprinted /tam the PROCEEDINGS OF THE IEEE VOL 54, NO. 12, DECEMBER, 1966 pp, 1999-2000 COPYRIGHJ: @ 1966-THE lNSIITUIE OF ELECrRICAI. AND ELECTRONICS ENGINEERS, lNC. PRINIED IN IRE U .. S A Scattering Matrix Parameters for Thermal Transducers where R,, R, Ro is thermal source resistance, electrical resistance of bar, and the normalizing number ; k is thermal conductivity of the bar ; r The static and dynamic characteristics of thermal transducers have is the thermoelectric coefficient; Q, and Q, are the square root of the been studied by considering heat flux, temperature, and current as reflected and incident powers. Note that if the normalization number variables [1 ]., In problems dealing with transducers having a thermal Ro is selected to be equal to the internal impedance [ 2] of the electrical and electrical port, Onsager's [1 ] equations have been used. In each generator, the incident electrical power is equal to the reflected power case a true thermal port is not introduced-and thermal parameters at the thermal port. characterizing the device at the port are not available, Port parameters As a second example, consider two transducers in an electrical port yield power for their product and immittance for their ratio. This is not so for the thermal port parameters available in [Q,,J = [>.] [Q;,] (3) literature. It is clear that a new set of thermal parameters must de- Q··J = [1;] [Q'.'] be Q,, Q,, [Q,, Q,, rived if the concept of thermal ports is to be introduced consistently and where X and~ are 2X2 matrices whose elements may be derived as in compatibly with electrical ports. The choice of an appropriate formu- (2). If these tr.ansducers were cascaded so that Q,, = Q,, and Q,, = Q,. lism is particularly important in theoretical studies where important then an electrical-electrical device is obtained similar to that investi- properties of the network may be obscured by complicated manipula- gated by Gottling [5]. The thermal ports are thereby eliminated and tions .. Such an appropriate formulism is the scattering matrix technique, although it has been applied exclusively to electrical networks [2].. [Q'•] = [S] [Q'.'] (4) The purpose of this letter is to show how the scattering matrix tech- Q,, Q,, nique [2] may be used to completely define thermal transducer opera- where the scattering parameters Su, are functions of electrical and ther- tion at a quiescent point [3] of operation .. Assuming a transducer mal prnperties. They may of course be evaluated by the usual network operation around a quiescent point, the scattering parameter Xis shown techniques [2], [4].. to be Finally consider the device of Fig. . 2 where the source and sensor.. is X = vP, = [~]112 a thin-film semiconductor. . It is assumed that the thermal energy is dis- v,P (I) t, sipated without any time delay within the film.. Solving the energy equation with appropriate boundary conditions, one obtains: where P, and P, are reflected and incident power t,, and t. are port and source temperature variations about a quiescent value To .. The bounds _ _[ sinh a(Lo + L,) sinh crL,,J p [sinh crL, sinh crLa.] p of>. are from O to 1 .. It is of course necessary that t,,/ t, be a characteristic ti - crkA sinh crL 1 + crkA sinh crL t property of the device. Three different examples are presented herein to _ = [sinh crL, sinh crLa] p [sinh u(La + L,) sinh uL,J show applicability. . '2 . 1 + . P2. (5) crkA smh crL crkA smh crL Consider a thermal electrical port as shown in Fig. . 1. Under steady- state conditions the scattering matrix becomes [ bR, )112 Q,, J= [( bR, +k vR4+RRRo ][Q·'• J (2) Manuscript received October I3, 1966, Ihis work was suppo1ted in part by the Q,. r R - Ro/R :R. Q;, U .. S, Depanment of the Navy, undeT Contract NONR 761-09 .. Page 11 PROCEEDINGS OF THE IEEE DECEMBER 2000 sinh uLc ] 112 X = [ ~inh u(Lb + L.) . (6) It is seen that the parameter is a characteristic of the device and corn· pletely sufficient for the analysis of the transducer as a network element. t s = T s - T 0 1n general, however, the parameter may be experimentally determined t. = T - T under known terminations.. The technique can be easily extended to p p 0 include radiative as well as convective inputs. the complete generaliza- tion of this approach is undet present study. -r 1t may be concluded that the seattering matrix notation is sufficient and complete for analyzing thermal transducers, operating about a Fig. I. Thermal and electrical port quiescent point, as network elements .. Furthermore, usual techniques of cascading, stability, etc., may be employed [2]. lt must be mentioned however that although the incident and teftected electrical power can be modified to obtain immitance formulism, this ls not true of thermal Source Setlsor power. But then, no significant information is lost due to the lack of this facility. L a ¾ L C D. K. ANAND Space :Research and A1111lysis the Johns Hopkins University c, k -x -x Appl. Physics Lab. Silver Spring, Md. -"b L. OliPiAN a C School of Engrg. and Appl. Sci. The George Washington University I 1 L Washington, D. C. I Fig .. 2.. Thin-film thermal transducer,. "" RllFERENC,ES [I] L. Onsager, "Reciprocal relations in irreversible processes,'' Phys. Rev., vol.. 37, pp. 405-426, 1931.. [21 JllE Tram. cm Circuit Theory, vol. CT0 3, Jutle 1956. [3] L. dePian, Linear Active Network Theory. Englewood Cliffs, N. J.: Prentke Ball, Where t1 and t2 are the Laplace transforms of temperature signals, k 1961. is thermal conductivity, L is defined in Fig .. 2, Pi and P2 are heat inputs [4] D. K. Anand and L. dePian, "Thermal ports in Hrtear network theory," Navy Research Lab,, Washitlgton, 0. C, Rep!. 3, NRL NONR 761 (09), June 1965 .. at one and two, and u=cs/k where c is specific heat and sis the Laplace [5] James G. Gottling, "Itlvestigation of a thin film thermal transducer/ Eleeltonic operator. From (1) the scattering parameter X becomes Systems laboratory, M.I.T., Cambridge, Mass., February 1960. . Page 12 444 PROCEEDINGS OF THE IEEE MARCH Reprinted from the PROCEEDINGS OF THE IEEE VOL 55, NO 3, MARCH, 1967 pp. 444-445 COPYRIGHI @ 1967-THE INSIITUIE OF EIECTRICAI AND EIECIRONICS ENGINEERS, INC PRINTED IN THE U.S.A Use of Malkin's Theorem for Satellite Stability positive numbers, 17 1(e) and 17 2 (E), such that each solution of (!), with in the Presence of Light Pressure initial values of x0(t = t0) satisfyii;lg Abstract-Stability of satellites subjected to persistent perturbations is examined using Malkin's theorem. Expressions are presented for disturb- (2) ing torques about all three spacecraft axes due to light pressur·e. Malkin's theorem is shown to be a valuable design tool for satellite attitude control. for arbitrary R,, which also satisfy in the region tz.t0 , llxll :::;e, and The stability of satellites in the absence of perturbations has been )IR,(.x, t)II :,:; 112(e) studied by many researchers employing the methods of Routh-Hurwitz,1 lyapunov2 and others. Also, different techniques of optimization3 have satisfies been successfully applied. However, the question of the effects of persistent light torques on stability has received lesser attention. The use of Malkin's II xii < E for t > to (3) theorem4 for such disturbances on a gravity gradient satellite has been briefly studied for a specific case of pitch accelerations only 5 The purpose Theorem-If for the variational equations of disturbed motion of this letter is to present the more general case of Malkin's theorem applied to pitch, roll, and yaw perturbations due to light pressure on satellites dx _ - = F(.x, t) + R,(.x, t), Malkin states that the zero solution of the unperturbed motion is dt stable for persistent disturbances provided there exists a positive-definite function W(t, x 1, , xN) whose total time I) the system subjected to initial conditions is asymptotically stable derivative is a negative definite function, and if in some bounded region in the Lyapunov sense, and t z. 0, Ix i :,:; H, the partial derivatives aW /ox, are finite, then the undisturbed 2) certain constraints on the magnitude of the persistent disturbance motion is stable (in the Lyapunov sense) for persistent disturbances. The is imposed exact selection of 17 1(E) and 17i(e) is usually not apparent Consider a system, with a disturbance function R,( x, t), as follows The asymptotic stability for torque free systems in a gravitational field can be ascertained (numerically or otherwise) for a set of any given dx _ _ initial conditions 00 , c/>,-0, and 1/1 0 . If indeed such stability is established, 2 - = F(x, t) + R,(x, t) (1) the comparison of the iit~fleration due to R,(x, t) to gravity suggests itself dt as an appropriate critei'tpn for selecting 17 2(e) and 17 1(e), If 17 2(e)<17 1(E) then where x represents pitch (0), roll(), and yaw (1/1), and tis time. The dis- turbance R,(x, (4) t), due to the interaction of light pressure, does not in general IR,(x, t)I < lxol become equal to zero when the variational coordinates are all simultane- ously zero is the required necessary condition for the stability of (1) The zero solution, 0==1/1=0, is termed as a stable motion for As a specific example consider a spherical satellite with two sets of constantly acting disturbances if for each positive e there exist two other booms, Fig. 1, with tip masses for the required inertia unbalance (These masses may contain magnets for dampling oscillations) Owing to light pressure and asymmetrical heating these booms bend both in and out of the plane of undeflected boom and sun vectors. The magnitude of the force 6 Manuscript received December 19, 1966 This work was supported by Naval Air Systems due to the light pressure is presented The direction of force is Command, Dept of the Navy, under contract NOw-62-0604-c 1 B E Tinling and V K Merrick, .. The exploitation of inertial coupling in passive gravity-gradient stabilized satellites," presented at the 1963 Guidance and Control Cont, f = _-_(_1 _-_P_)_s _+_2_P~Is _n_nl _. paper 63-342, Mass. Inst Tech , Cambridge, Mass 2 (5) 112 2 D. K. Aoand, P Bainum, and D L Mackison, "Perturbation and Lyapunov stability [(1 + p)2 - 4pJs x nl ] of a multiple connected gravity-gradient satellite at synchronous orbit," presented (by Dr Bainum) at the 1966 5th U. S Nat'! Congress of Applied Mechanics, Minneapolis, Minn. 3 where pis reflectivity, sand n are sun and surface normal unit vectors This "K. S P Kumar and L Teng, "Stabilization of a satellite via specific optimum control," IEEE Trans on Aerospace and Electronic,, vol AES-2, pp. 446--449, July 1966. 4 1. G. Malkin, "Theory of stability and motion," AECTR-3352, pp. 302-307, 1952. ' P M Bainum, "On the motion and stability of a multiple connected gravity-gradient 6 A A Karymov, .. Determination of forces and moments due to light pressure acting satellite with passive damping," Ph D dissertation, Catholic University, Washington, D. C, on a body in motion in cosmic space," PMM, vol 26 pp. 867-1!76, May 1962 (translations 1966 from USSR J Page 13 1967 PROCEEDINGS LETTERS 445 transformation Furthermore the gravitational torque is expressed as g = [3w2(I, - Id,j) ]i + [ 4w 2(/, - I,)O + w(lj - I, + /,)!fr }i k + [ w 2(!, - I)i/1 + w(Ii - I, + Ik)li]k Local ~ g = g,i + g2j + g3k (7) Vertical \ where w is orbital velocity and I, is satellite inertia about i-axis \ The requirement of (4) simply means that \ (8) \ j From a design viewpoint this yields a bound on the boom parameters as \ ~ well as inertias. For example, a synchronous equatorial satellite having / booms of lk= 120 ft, li=60 ft, r0 =0 021 ft, p=0.88, and r,=0173 ft, must \ / have inertias of I,=0.2x 10" gm-cm2, li>0.265 x 10", lk =1 ('q>' 625 approxi- the universal velocity and temperature profiles to be approached mately. Other trends are given in Table 2. almost exactly in pure forced-convection turbulent heat transfer Representative velocity and temperature profiles are shown in problems with negligible volume heat sources. Figs. 6, 7, 8, and 9. 3 Volume heat som·ces had negligible effect on the velocity Several test problems were run to determine the limitations of profile but had considerable effect on the temperature profile, as the computer method of solution used. No solutions were ob- would be expected from the development of the equations. tained for Re* = 10•, F = 0.1 or less, and Ra = 625 or more. 4 The program was unable to solve problems involving high Only by decreasing Ra. or increasing either Re* or F would a Rayleigh numbers and volume heat sources for low values of Re*. solution result. 5 Increasing the various input parnmeters tends to flatten the 6 Transactions of the AS ME Page 20 Table 2 Summary of effeds in combined forced and free convection Effect. on~ "'""------- Nu C cp.,.. u For an in- 'P COl!llllents crease in! Ra< 625 ae. > 625 Re* Increase Increase Increase Decrease Flattens curve Flattens F > 1 curve, makes 4>-0 Pr Increase No effect Decrease Decrease Decrease Same as above Ra No effect No effect Increase Slight de- Increase Decrease crease at high Ra Re* 0 I:icrease Inc.rease Decrease Fla't.tens curve Negligibl.a F = l ?r 0 No effect Dec::-ease Decrease No effect Negligible Ra 0 No effect No effect No effect No effect No effect Re* Inc:-ease Increase Increase De.crease Flattens curve Sarr.a as F< l F> 1 Pr Increase No ef'f'ect Increase Decrease Flattens curve same as F> 1 Ra No effect No effect Decrease No effect Flattens curve Negligible slightly For a de- Slight No ef'f'ect Decr~ase L"lcrease Flattens oi.;rve In.creasea, crease -in - increase passing F th.rn ~ero e.t F = l velocity and temperature pl'Ofiles, as would be expected. bined Free and Forced Convection in a Constant-Temperature 6 The effects of volume heat source and Rayleigh number were Vertical Tube," TRANS. ASME, Vol. 80, Dec. 1958, pp. 739-745. 5 Martinelli, R. C., and Boelter, L. M. K., "The Analytical Pre- reduced considerably by the influence of tmbulent flow. diction of Superposed Free and Forced Viscous Convection in a Vertical Pipe," University of California P.ubluations in Engineering, Acknowledgments Vol. 5, No. 2, 1942, pp. 23-58. 6 Ojalvo, M. S., and Grosh, R. J., "Combined Forced and Free The authors are grateful to the National Science Foundation Turbulent Convection in a Vertical Tube," Argonne National Labora- for supporting this research under NSF grant GP-3011 at the tory Report ANL-6528, Jan. 1962. 7 Jackson, P. Y., "Relative Viscosity in Isothermal Turbulent George Washington University, and to Dillon F. Scofield for his Flow in a Vertical Tube," MS thesis, The George Washington Uni- help in the programming. versity, June 1965. 8 Dunbar, R. P., "Combined Forced and Free Turbulent Con- References vection in a Vertical Tube With Volume Heat Sources and Constant Wall Heat Addition," MS thesis, The George Washington University, 1 Ostroumov, G. A., "Free Convection Under the Conditions June 1965. of the Internal Problem," NACA TM-1407, Apr. 1958. 9 Sesonske, A., Schrock, S. L., and Buyco, E. H., "Eddy Dif- 2 Hallman, T. l\,L, "Combined Forced and Free Convection in a fusivity Ratios for Mercury li'lowing in A Tube," Chemical Engineer- Ve1·tical Tube," PhD thesis, Purdue University, May 1958. ing Symposium, Vol. 61, No. 57, 1965. 3 Gross, J. F., and Van Ness, H. C., "A Study of Laminar Flow 10 Lykoudis, P. S., "Analytical Study of Heat Transfer in Liquid Heat Transfer in Tubes," American Institute of Chemical Engineers Metals," PhD thesis, Purdue Univrsity, Jan. 1956. Journal, Vol. 3, 1957, pp. 172-175. 11 Eckert, E. R. G., and Drake, R. lVI., Heat and .Ma8s Transfer, 4 Jackson, T. W., Harrison, W. B., and Boteler, W. C., "Com- McGraw-Hill, New York, 1959. l'rinte,, latent heat of vaporization, Btu/Ibm Applied Physics Laboratory, The Johns Hophns µ coefficient"of viscosity, lbf-sec/ft2 p University, density, lbm/ft 8 Silver Spring, Md. tr smface tension, lbf/ft Nomenclature Subscripts C condense1 parnmeter, k 1rD(T. - T0 )/ln(ro/r.), Btu/ a ambient hr-ft C wick pore D heat pipe diameter, ft f, l, V fluid, liquid, and vapor, respectively w, 0 wall, inside, and wall, outside, respectively Received January 26, 1967. This work was supported by NASA IN most applications of heat pipes, the m.a..ximum heat Headquarters, and also by the Naval Air Systems Command, transport is dependent upon liquid circulation due to Department of the Navy under Contract NOw 62-0604-c .. capillary forces in the wick.1 For a specific capillary struc- [1114] ture the local pressure difference must be • Staff Engineer, Space Power Thermal and Attitude Control Systems. p.(z) - Pi(z) :::; (2u cos0)/rc (1) t Research Fellow, DepaJtment of Mechanics, Engineering. t Engineer, Space Analysis and Research. where the equality would yield maximum heat transport. Reprinted from JOURNAL OF SPACECRAFT AND ROCKETS Copv1ight, 1967·, by the American Institute of AeronautiCl:I and A'!trnnautics, and 1eprinted by permi~sion of the copyright owner Page 22 (j!J(j J. SPACECRAFT \OL. 4, XO.~ From Eq. (5), it is seen that the opeiation of the heat pipe is constiained chiefly by condenser paiameters. Extensive T°F 0 1= 30 WATTS experimental data obtained at the Applied Physics Labora- 100 02 60 WATTS tory bear this out.. Figure 1 shows the "heat pipe regime"§ temperatures as a function of the condenser parameter C The experimental data are for the follo\\ ing heat pipe: (r,, - rv) = 0.063 in, f = 0 .. 68, r,/rw = 0.815, r, = 3.25 X 10-3 in., 75 Q = 30 w, w = 15, and fluid = ethyl alcohol. The optimum heat transp01t that could be achimed is 725 w with 0.1 effective conductivity, 60° contact angle, 1.5592 X 10-3 3 6 9 12 C BTU/HR FT !bf/ft surface tension, and a radial temperatme drop of 20° F acrnss condenser surface. The condenser surface area Fig. l Effect of condenser parameters on heat-pipe- required is 5 ft2.. The variation of C may be achieved by regime ten1perature. Condenser surface temperature = flooding, introduction of noncondensible gases, or manually 54°F. Heat-pipe-regime teinperatures exhibit a max- varying surface area. The reported data were obtained by imun1 drop of 2°F over 22 in. flooding and va1ying surface area The effect of noncon- For low Reynolds number Re, substituting the appropriate densible gases is similar although mo1e dramatic. pressure drops,1, 2 Eq .. (1) becomes The foregoing comments are based on nonradiative-type condensers. In applications where the heat is radiated 4µv(l, + L)Q + wµ1(L + l,)Q _ 2cr cos0 = O (2) away from the exterior surface of the condenser, an interest- 7rPvTv4A 21r(rw2 - Tv2)pzer}A. r, ing situation may develop. W'e have given the name "tem- perature choking" to this effect, and offer the following ex- for maximum heat transport. Here rv is equal to the inne1 planation. The equilibrium temperature of the vapor radius of the heat pipe (rw) minus the thickness of the wick; (and consequently the evaporat01 section) for a given powe1 i e , it is the inner radius of the wick. Optimum values for dissipation is determined by the temperature of the outer r, and rv can be obtained from Eq. (2), all other properties surface of the condense1.. F01 1adiative condensers, the being fixed.. The value of r, that would maximize Q is de .. equilibrium equation becomes termined from oQ/or, = 0, where Q is defined by Eq .. (2) .. This value when resubstituted into Eq .. (2) yields (6) ' ~--~µvµ!J:_, + L) 2wQ2~- - cr cos0 = 0 (3) Now, since the heat is 1emoved from the oute1 surface by pzpv1r 2eA. 2crrv4(rw 2 - rv2) cos0 1adiation, there is no longer a strong boundary condition on the temperature of the outer surface as there is in the case of It is clear that the maximizing of Q now iequires the evalua- ¾, a condenser bath. Consequently, the outer temperature tion of oQ/orv = 0. This constraint yields (rv/rw) 2 = will adjust itself so that in equilibrium the heat radiated which when substituted into Eq. (3) will yield equals the heat input. If the heat flow through the con- Q = 21rrw3 A.cr cos0 [ epvp1_] 112 denser is increased, the temperature of the outer condense1 + (4) 3(L Z,) 6wµvµz surface must now increase to radiate away the extra heat; and since the temperature difference across the composite Under steady-state conditions, the heat Q transferred condenser wall determines the heat conducted through the through the condenser may be denoted by Q = hD(Tv - wall, the temperature of the vapor core must increase even T )/ln(r /rv)L = CL. Substituting L = Q/C into Eq. (4) more. Thus, the temperature response of the vapor to heat 0 0 leads to a quadratic in Q, which yields the solution flow increases should be quite different in this case from the case of a condenser bath, where bath temperatures may be [ -1 C1rrw A.cr cos0 ( -2 -Pv-Pz -e ) 112 + independently varied. From a design viewpoint, this re--Qoptimum = 3 3 3 µvµz W quires high C v:,lues in Eq .. (5) .. -1:_ c2p]112 - C }__,_ 4 (5) References e 2 1 Cotte1, T. P, "Theory of heat pipea," Los Alamos Scientific § That segment of the heat pipe over which the temperature Lab .. , LA-3246-MS (196.5) .. drop of the vapor is small, of the order of 1-2°F.. This segment 2 Anand, D. K., "On the performance of a heat pipe," J consequently exhibits a verv high thermal conductivity Spacecraft Rockets 3, 763-765 (1966). Page 23 Page 24 (;,l ,I., e =l > u, .z... ::i::: ,~_ l"'l =l ti'J > > l"'l > .,i Cl) =l 0 ~ -0 ,I., zl"'l -l""1 z -.JI ~ .,i - (;') ("'l Ro ::i:: z > Cl) ~ F l""1 z > l""1 [.I) z ~ 0 cl l"'l l""1 z""' ("') ::;; I;') -l""1 0 =l <""' "<': cl ~ C""l)' 0 zl""1 :;,:, 0 -~ "'fl 0- .,i z z l""1 ~ ~ l""1 ~~ cl ::i::: ,_ >z .QQ. . c""l --1 > F zl"l iz:'l t"'l "'1 Session 3 9:00 a.m'. Fo,m.tain Room HEAT PIPES - ! Chairman: ERWIN FRIED, Consulting Engineer, General Electric Co , Philadelphia, Pa Application fo a Gmvity Grndient Sate!ite D. K Staff Engineer, Johns Hopkins Univ., Silver Springs, The Design of a 50,000 Watt Heat Pipe Space Radiator R. C. TURNER and W E. HARBAUGH, Electronic Components and Devices, RCA, Lancaster, Pa Heat Pipes for Spacesuit Ternperntme Control A. P SHLOSINGER, TRW Systems, Redondo Beach, Calif Total Hemispherical Emissivity Measurements by the Heat Pipe Method J. E. DEVERALL, Los Alamos Scientific Lab., Univ .. of California, Los Alamos, N. Mex. A Confo:umus Heat Pipe for Spacecraft Thermal Control E C. CONWAY and M. J. KELLEY, Space Systems, General Electric Co., Philadelphia, Pa Page 25 HEAT PIPE APPLICATION TO A GRAVITY-GRADIENT SATELLITE (EXPLORER XXXVI) D. K. Anand Space Research and Analysis The Johns Hopkins University Applied Physics laboratory Silver Spring, Maryland ABSTRACT for the thermal control of transpm:ci.ers ic GEOS-B, * a low altitude gravit~-grccsiient sate2_lite. This paper discusses the use of two heat pipes, using Freon-11, for the thermal control of trans- Orbital results are presente:.c 8.::i co ,:pc.rei with ponders in a gravity-gradient satellite, GEOS-B. theoretical]y expected terr:;1erst~rc :.:.::cc;::.s Orbital results are presented and are seen to SATELLITE APPLICA7IO: agree with theoretically expected temperature drops over the heat pipe regime, The successful demonstro.ticr..G o:"' tf'.e first hec.t pipe in a zero-g enviroru~ent ir.dicste~ the pote~ticl Continuous operation over a period of two months use of heat pipes for sate 2 lite app,. . ications. indicates no apparent degradation in heat pipe per- formance. It is concluded that the first use of heat The heating of one side :iue to long exposure co pipes for satellite thermal control is a complete solar fluxes and the simultaneous coolicg 0 0: the other success. side, due to radiation to sp2.ce, cm1 oe a pro-c:;le,.-. :"or satellites that are gravity-gra-:iier;t statilize:.c &cout INTRODUCTION all three axes, Such a thermal sit'.latior. preser:ts ar; ideal source and sink for heat pipe appUcaticr. i_1, a Owing to its froperty of high thermal conductiv- zero-g environment. ity, the heat pipe has attracted considerable inter- est in recent years. It essentially consists of a This exact situation arose q_uite accici.ent8. '_ly in sealed tube with wick material in intimate contact the GEOS-A satellite. (launche;l ir. f&l2 2.965 as a with the internal pipe surface. The operation of the part of the geodesy program.) This s2.tellite was tc heat pipe is based on the evaporation of a liquid in have been stabilized in pitch a,,:: rcJ_.:_ tut :-.ot i, - 2.w. the evaporator section and subsequent flow in the Accidentally the satellite was >'-''· stacilize~ 2.s 1-,e:_1 core towards a region of low pressure. In the con- thereby exposing one of the tr2.nspor,:iers to cc,-,t~rn~cus denser, the liquid is condensed and flows back to the solar flux and raising the ter.iperc.tc.:re :c.oove to"_er::ccle evaporator through the wick by capillary pumping to limits, whereas the other siJe st&-;ei &t r&.ther : c,.· continue the cycle. Under steady state conditions temperatures.. The situ&.tion w2.s s.;;gr2.v2.teJ e·,e~ the pressure in the evaporator section is slightly further whenever the transponier th2.t l,'-'S e::;:ose:i :c, less than the vapor pressure of the adjacent liquid, solar flux was interrogated since thi_s er:tci'e: -~ sub- thereby assuring continuing evaporation. 2 Owing to stantial heat input, This difficult- i:::poso~. cor:- this liquid-vapor interface, the l'.adius of curva- straints on the time and du:rs.tion ~- tr:.:c:1spoc1er coul6- tur·e of meniscus in the evaporator recedes, and be interrogated. that in the condenser increases .. In the condenser, especially if there is excess fluid, the radius of A thermal analysis incncai;e:.c that c01:r:ecti1:;; the meniscus may be infinite. Once the heat pipe is two transponders direct::, usin,:; the -oest ccr,iuctor charged and sealed, it essentially seeks its own would be of little value, Howes,er, the use c::" 2. heat equilibrium level which travels up and down the pipe would have decreased the ter.:pers.ture e>:c,:rsions pressure-temperature curve as the heat input is of the transponders by a factor of G, 5 SLc:e G;;:OS-B varied .. 3 This is necessarily done since the working was to have been similar to GEOS-1'.., it ,.as c:eciied to fluid and its vapor are in equilibrium in a closed fly two satellite heat pipes as a iesi,:;n ir.:r:rovement volume. It is to be noted that there is an upper in GEOS-B. If for some reason the hecet pipes :iii not limit to the heat flow through the pipe and therefore operate, the thermal excursions of GEOS-B wot;ld, at the thermal conductivity because liquid depletion rate worst, be slightly better than GE OS-A, The location in the evaporation could exceed the recirculation rate of the pipes in the spacecraft is shown in Figure 1. by capillary pumping thereby causing thermal runaway, 4 Apart from the property of high conductivity, a heat pipe is essentially reversible, Le .. , there is no *GEOS-·B was conceived as part of the Nationa.:_ Geodetic preferred direction of heat flow. For this reason it Satellite Program to study geometric 2ni gravimetric becomes useful for satellite applications5 where it geodesy. It was designed and built for the National is desired that the thermal excursions of various Aeronautics and Space Administration by the Johns components be kept to a minimum. Hopkins University Applied Physics Laboratory under the scientifi.c and engineering direction of This paper discusses the use of two heat pipes Dr. G. C. Weiffenbach and Mr. R. Willison. 634 Page 26 Two heat pipes 2 inches in diameter and 36 inches of other elements near the transponders is shown in and 20 inches long operating with Freon-11 and employ- Figure 5. It is to be noted that although the ing wire cloth mesh for wicking material were selected effective thermal conductivity of the heat pipe may be for transponder temperature control. The details of several hundred times that of the best conductor, the fabrication, qualifications, charging, etc. are dis- improvement in the thermal graciient is only 0.5.. This cussed in reference 5, is due to the thermal resistance experienced at the evaporator and condenser .. Theoretically the temperatures of the transponders ·,-:ere expected to equalize very closely owing to the From these studies it was concluded that in any high thermal conductivity of the heat pipe. But al- practical satellite application the crucial considera- though the heat pipe has high internal conductivity it tion would be the temperature cirops associated with the ne·vertheless presents substantial resistance to heat heat input and heat output. That the addition of heat input at the evaporator and heat output at the con- pipes would substantially improve the thermal design densing section. It is therefore important that these of GEOS-B was also clearly evident. resistances be minimized for more effective temperature equalization of the transponders. POST-LAUNCH RESULTS INSTRUMENTATION GEOS-B was successfully launched into orbit at 1616 UT on Day 11 in 1968 from the Vandenburg Air In order to evaluate heat pipe performance it was Force Base. The spacecraft was officially designated considered sufficient to obtain heat pipe surface 1968 02 ALHIA and titled by the National Aeronautics temperatures, transponder temperatures and an indi .. , and Space Administration as Explorer XXXVI. The orbit c"tion of the heat flux. has an inclination of 74° retrograde, 580 n.m .. perigee, and 852 n.m. apogee .. The satellite was successfully The long heat pipe was instrumented to obtain captured and is gravity-gradient stabilized about all ce~peratures at four equally spaced locations along three axes. -;;h 2 S'c.lr face. The small pipe was instrumented to yield o:ce temperature at the middle. A heat flux sensor was The twelve telemetry channels are monitored over :.:;sta.2.led between the heat pipe and the range range- each pass and the data is reduced at the Applied .. te transponder. Also temperature sensors were in- Physics Laboratory. The :information obtained from the ::s.lled on all the transponders. The location of the heat flux sensor continued to be erratic for causes sensors and various components are shown in Figure 2. unknown. Also the temperature at location B, on the :"2chniques of data reduction and all pertinent cali- long heat pipe, sometimes seems to give inconsistent ·~rstion constants appear in reference 8. numbers. The temperature of the small heat pipe is consistently between that of the C-band transponder During flight, twelve telemetry channels yield and the range transponder. Since only one temperature :ontinuous information on the heat pipe system. along this surface is available, it is not discussed further. PRELAUNCH ANALYSIS In this paper the temperature distribution ob- Prelaunch design studies were carried out at the tained from the long heat pipe and the corresponding . cp:1..ied Physics Laboratory. These studies were both temperatures of the range range-rate transponder, TR , ·:' eoretical and, experimental. and the C-band transponder, Tc , are presented and discussed. me theoretical investigations were essentially s ~".lilar to the work of Cotter, 2 The experimental work The temperature distribution along the long heat ! s aimed at obtaining heat pipe regimes and conducting pipe is presented in Figure 6 for four different times .. ~&re.,"netric study. The first plot shows the distribution three days after launch. In each case the temperature difference be- The experimental heat pipe set-up consisted of a tween the heat pipe regime and the condensing section j ir1ch O.D. stainless steel pipe, 24 to 36 inches is larger than that between the regime and evaporator · .ng, ,.ith the interior wall covered with a passi·- section. This is similar to what is observed i.n the ·.tei 100-mesh stainless steel screen (see Figure 3). laboratory .. 5 Also the temperature variation over the 'c:,t ,,:as add.eel at the evaporator section by resistance heat pipe regime is about 2°F. .:ec,t:ing. The condenser section was kept in a tempera- '. :re controlled water bath with the facility of varying The variation of the temperature drop over the ·}cc condenser length. The section between the condens- heat pipe regime for a period of two months is shown ,, ~nd evaporator section was insulated using poly .. in Figure 7. Since more than one data point is ob·- :.rcthcne foam. The working fluid was ethyl alcohol. tained on any given day, the temperature drops shown :..~,1e heat pipe was operated from 54°F to 173°F. Temper- represent daily averages., : tires were measured using a 24-point Daystrom recorder :: .ning transient and steady state operation.. Complete Also no effort is made to differenti.ate between "ctsils of the experimental set-up and the determina- steady state and transient modes., The temperature tfon of optimum heat pipe parameters has already been drop over the heat pipe regime is seen to be less than presented in references 3 and 4. 4°F about ninety-six percent of time and is never greater than 5°F. This represents performance over a The satellite thermal model was analyzed with and period of two months. ithout the heat pipe operating under orbital condi- :ions, Prototype results obtained from computer simu- Finally, the temperature difference between the :tions 7 and thermal vacuum testing are presented in range range-rate transponder and the C-band trans- ::·ifure \. Under severe orbital conditions it is seen ponder is plotted for a period of two months and shown :'c.ct the maximum temperature gradient between trans- in Figure 8. The maximum temperature difference is ·:Jon::lers is reduced by a factor of 0.5 with the use of less than 30°F. During this same period the heat pipe ,~est pipes. The decrease in the temperature excursions regime temperatures varied from a low of about 33°F to 635 Page 27 a high of 70°F and is shown in Figure 9. 2. Cotter, T. P., "Theory of Heat Pipes," Los Alamos Scientific Laboratory, IA-3246-Jv'JS. SUMMARY 3. Anand, D. K. , "On the Perfonnance of a Heat Pipe," The agreement between orbital and experL~ental ~- Spacecraft and Rockets, AIAA, May 1966. temperature drops over the heat pipe regime substanti- ates their successful performance in GEOS-B. 4. Anand, D. K., Dybbs, A., and Jenkins, R. E., "Effects of Condenser Parameters on Heat Pipe Orbital data obtained over a period of about two Optimization," ~- of _§pacecrafts and Rockets, AIAA, months indicates no degradation of heat pipe perfor- May 1967. mance. Over this time period the heat pipe operated from a low 33°F to a high of 70°F with the temperature 5. Anand, D, K,, and Hester, R. B., "Heat Pipe drop over the heat pipe regime being always under 5°F Application for Spacecraft Thermal Control," and ninety--six percent of the time under 4°F. The Technical Memo 952, The Applied Physics Laboratory, temperature difference between transponders and the August 1967. heat pipe regime indicates the importance of minimiz- ing the resistance at the evaporator and condenser in 6. Deverall, J.E., Salmi, E, W., and Knapp, R. J., future applications. "Heat Pipe Performance in a Zero-g Gravity Field," ~. Spacecraft and Rockets_, AIAA, November 1967. ACKNOWLEDGMENT 7, Willis, S., "Thermal Analysis of the GEOS-B Sat- This work was supported by the National Aeronau- ellite," May 1967, The Applied Physics Laboratory, tics and Space Administration. The prototype heat pipe Internal Memo. was built and analyzed by R. Harkness and S. Willis at the Applied Physics Laboratory. The help of J.M. 8. Peterson, M. R., "Command System Functions, Whisnant in data reduction and L. D. Eckard for Telemetry System Functions, and Calibrations for Figures 4 and 5 is appreciated. GEOS-B Satellite," Technical Memo 970, The Applied Physics Laboratory, December 1967, REFERENCES l. Grover, G. M. et al, "Structures of Very High Thermal Conductance," ~. Applied ~sics, 35, 1900 (1964) .. GRAVITY GRADIENT STABILIZATION END MASS HEAT PIPE NO. l SOLAR CELL ARRAY C-BAND VAN ATTA TRANSPONDER ARRAY C-BAND ANTENNA DUAL ...,;:~~-, --OSCILLATOR SOLAR ATTITUDE DETECTOR --. HEAT PIPE NO. 2 MEMORY BOOKS OPTICAL BEACON LASER FLASH ASSY (4) DETECTOR LASER REFLECTOR BROAD Bil ND PANELS SPIRAL ANTENNA RANGE AND RANGE RANGE AND RANGE RATE ANTENNA RATE TRANSPONDER Fig. 1 GEOS-B SPACE CRAFT 636 Page 28 HEAT PIPE HEAT FLUX SENSOR RANGE AND RANGE RATE TRANSPONDER SECTION A-A -X- +X C-BAND TRANSPONDERS -Y RANGE TRANS POND ER Fig. 2 HEAT PIPE TEMPERATURE MEASUREMENT LOCATIONS -----------------, If\N O HEAT-PIPE 99° F // --\ \-,- ---r ~u.-. 80 w \ 3 9° F 0:: => I- < 60 0:: w IN CONSTANT a.. ~ RESISTANCE TEMPERATURE BATH w I- 40 HEAT ,--- I --~-~--W-l~T.HHEA~--- I \ VIICK ~-~-Ll~]] -X - Y +X LOCATION ON THE X-Y PLANE Fig .. 4 EFFECT OF HEAT PIPE ON TRANSPONDER TEMPERATURE VAPOR FLOW II FLUID FLOW BY LC A_P_I_LL_A RY PUMPING -------------- ------~ u.. ~ w _,,,-""' '-.NO HEAT-PIPE Fig .. 3 HEAT PIPE USED FOR PRE-LAUNCH STUDIES 0:: ;: 60 ' ~, WITH HEAT-PIPE < ~ 30° F 0:: w 7 45°F -'/ 1/ ~ l _l 40 ' w I- -- L-----+---~--~-----~--~ -X _y +X +Y LOCATION ON THE X--Y PLANE Fig. 5 EFFECT OF HEAT PIPE ON ELECTRONIC PACKAGES (PACKAGES LOCATED IN A PLANE 12" ABOVE THE X-Y PLANE) 637 Page 29 70 70 LL '?__, w w "::)' :":)' ~ 60 ~ 60 w"' Tc w"' a.. a.. ::l: ::l: w w I- I- • TR B C D E B C D E HEAT PIPE LOCATIONS HEAT PIPE LOCATIONS Fig. 6(0) DAY 14, TIME 014507 Fig. 6(c) DAY 47, TIME 234630 60 50 Tc4 Tc LL LL ~ '?__, - '?__, I w r- w ,~ "::)' "::') I- ~ 50 <( 40 w"' • TR "w' a.. a.. • TR ::l: ::l: w w I- I- B C D E B C D E HEAT PIPE LOCATIONS HEAT PIPE LOCATIONS Fig. 6 (b) DAY 22, TIME 23093 Fig. 6 (d) DAY 68, TIME 141340 /5TEMPERATURE DROP OVER HEAT PIPE REGIME (°F) C .... .... .· ·. ..... ... • .. . .. . ·. . . ,.. .. . .. .. . . . .. 0 --~~-------~-----·~~-------~ W ~ 60 TIME (days) Fig .. 7 THE VARIATION OF THE TEMPERATURE DROP OVER HEAT PIPE REGIME • • 20 •• • • • •• LL • 0 • • •• • ~ 10 •• •• • 0 • • a - •• • • • ..• •• • • -• ' .. "' • • •• • • I- 0 L -• • 0 20 40 60 TIME (days) Fig. 8 ORBITAL VARIATION OF THE TEMPERATURE DIFFERENCE BETWEEN R/RR TRANSPONDER AND C-BAND TRANSPONDER LL 70 '?__, • • .. w • • • .. "::)' _. . •• • ••• ..• • •••• -· • - • .. ... ~ • ..• • 50 "w' • • a.. ::l: • •• • w I- 30 -- 0 20 40 60 TIME (days) Fig. 9 ORBITAL VARIATION OF HEAT-PIPE REGIME TEMPERATURE 638, Page 30 Roll Resonance for a Gravity- Gradient Satellite J, l\iL WHISNANT* AND D. K. ANANDt The Johns Hopkins University, Applied Physics Laboratory, Silver Spring, ]Jfd. Introduction PRE- and postlaunch studies of the geodetic satellite (GEOS-A), launched in November 1965, indicated that large roll angles could occur when the orbit was partially shadowed .. 1 An examination of the solar radiation pressure forcing function, for roll, showed that it had a component with twice-orbital frequency. Since the natural frequency of roll for this gravity-gradient satellite is also twice orbital, Received February 28, 1968; revision received April 1, 1968. This work was supported by the Geophysics and Astronomy Programs Directorate of NASA Headquarters,. The authors wish to thank R. E. Jenkins of the Applied Physics Laboratory for a helpful discussion of Eq. (5). * Mathematician, Space Research and Analysis. t Senior Engineer, Space Research and Analysis. Member AIAA. Reprinted from JOURNAL OF SPACECRAFT AND ROCKETS, Vol. 5, No. 6, June 1968, pp. 743-744 Copyright, 1968, by the American Institute of Aeronautics and Astronautics, and reprinted by permission of the copyright owner Page 31 74! J. SPACECRAFT VOL. 5, NO .. 6 ' ~. u f:\ 7 3 4"1 ,: 0, 68 0 100 200 TIME (orhit-s) f-i;-j 2TT e Fig. 3 Tin1e variation of the resonance effect: u 1.2; i = 106° (74° retrograde). Fig. 1 Solar torque for roll dul"ing one nodal period. the occurrence of resonance is clear. Furthermore, the be solved analytically, However, Patterson 3 µresented a amplitude of the roll librations was shown to be a function formula for the time that a satellite in a circular orbit spends of Q, the angle between the projection of the earth-sun line in the sun. This expression, which neglects penumbra onto the equatorial plane and the line of nodes. The purpose effects, is used to obtain of this note is to derive an expression for the value of Q which maximizes the twice orbital component of the roll forcing (6) function. where F = (1 - l/a2) 1! 2 and a is the semimajor axis in units of earth radii. Analysis Substitution of (6) into (5) yields The solar forcing function ,p in roll for a satellite whose geometry is sirnilar to that of a dumbbell is given by Ref 1 as ,p(2fJ) = _'°'._o [ COS1) -2.F- (sin21) - F2) 1i2 J (7) 2 1r sm 17 ,p = <( .,, to astronomers. 1 Since the position of stars is z !i 0: 0 -½--+---1r'll------+1--+----++----'r.--.--,1Q IX well established, it is natural that the location .,, I- of X-ray sources be made relative to the fixed I- 1- :::, :::, position of stars. Furthermore, the scanning of 0 0 the entire sphere necessitates the use of a spin- 10 <( ning satellite. The attitude of this satellite :w::, -5 '----"""--_.___ ____ .__-""-"..__ __. .__ _____ _. must be precisely known in order to interpolate g 0 400 800 .1200 between any two-star sightings should an X-ray 0 source be detected. I- TIME (seconds) The satellite to be used for this mission is Fig. l GRAVITATIONAL, SOLAR, AND MAGNETIC TORQUES a spin stabilized satellite with a spin rate of 0.5°/second (1/12 rpm). In order to provide the required angular momentum parallel to the satel- forces act on the solar paddles causing large lite's spin axis, a rotor of the type used in torques. For the condition of free molecular Nimbus II is employed, Also to avoid coning of flow, the aerodynamic forces have the same func- the spin axis an eddy-current nutation damper, tional form in terms of angle of incidence as whose plane of motion is perpendicular to the spin solar radiation pressure forces, The force on axis, is used. The satellite has four symmetri- each flat spacecraft surface may be calculated by cally located solar paddles and is in a low alti- tude (500 km) nominally circular orbit. F - 2 pv AP [sin y T - (cosy+ .54) NJ (1) where The purpose of this paper is to study the effect of the near earth environment on the A - the non-shaded projected area p dynamics of the X-ray Explorer satellite. Atti- y - angle of incidence tude errors due to external perturbations are ob- v - magnitude of relative air velocity tained, Also the pointing error of the precession p _ atmospheric density axis referred to a fixed star is established, N, T; surface normal and tangential vectors 1 Page 34 TABLE 1. Physical Parameters Main Body Rotor I = \i 22.5 .011 slug ft2 yy I zz = I xx = I 23.40 .0055 slug ft2 Mass 310 4 lbs Spin Rates 0.00875 136.5 rads/sec Area of' Each Solar Paddle 524 . 2 1!.]- Centroid of' Area from Center of' Mass 37.5 in Paddle Normal VectorS Coplanar (o .5 -.866) ( .866 .5 o) (o ,5 -.866) (.866 .5 o) Non-Coplanar (o -.5 .866) (.866 .5 o) (0 .5 +.866) (+.866 -,5 o) Orbit a = 1.087, E: = o, i = 0 TABLE 2. Density Variations f'or Years Near Solar Maximum (1969-1970) Disturbed Quiet Conditions Conditions Units Altitude 560 500 500 560 Km Solar Index 250 250 225 225 F10 , Index 300 300 230 230 7 Ap Index (Magnetic) 150 150 10 10 Night Density (Min) 2 X 10-15 4 X 10-15 2 X 10-15 1.0 10-15 1; gm/cc Day Density (Max) 3,5 10 -15 X 7 X 10-15 4 X 10-15 2 X 10-15 gm/cc Equation (1) assumes that the surfaces are homo- respective moment arm of each surface are obtained geneous and isotropic; that interactions.of air as functions of the orientation of the spacecraft molecules with one element of surface area are with respect to the air velocity vector. Two solar independent of interactions at other surfaces; paddle configurations were considered. One, having and that the relative velocity of the air flow is paddles on opposite sides of the spacecraft lying constant over the satellite's surface. Likewise, in the same plane, is referred to as the coplanar the magnitude of' the aerodynamic forces on the configuration. The second, having opposite paddles main spacecraft body (cylindrical) is given by rotated out of plane, is the non-coplanar paddle 2 configuration. The normal vectors of all paddles F pv A [l + .14 n sin p] p (2) in the body fixed coordinate system are given in Table 1. where p is the angle between the cylinder's The determination of density is based on a longitudinal axis and the relative velocity vector. model of the upper atmospheric structure due to The aerodynamic forces may be computed once the Jacchia. 2 The model, above 120 km, assumes diffu- projected areas and the atmospheric density are sion equilibrium and yields densities at any geo- determined. graphic location and height using the local exo- spheric temperature.3 This temperature is modified The projected area of a solar paddle or satel- by: lite main body surface is not only a function of 1) the contribution of the avera.ge 10.7 centi- the velocity vector and surface normal but depends meter solar flux strongly on structural shadowing. The determina- 2) daily variation of' the above tion of the shadowing with a complicated structure 3) semi-annual variations of solar flux does not lend itself to an analytical model. There- (these variations have been observed to fore a shadow study of a scale model of the satel- produce maximum densities in April and lite was conducted, The non-shaded area and its October with minimum at January and July) 2 68-856 Page 35 800~-------~ -+-------- .".' ~ oh.C.~-J.~~:::::::t::::::'.'.'...(__:'::!_I-~::.(...~~_:~ 3 ; -800~----~ 0 400 800 1200 1600 TIME (seconds) Fig. 5 NON-COPLANAR PADDLES, SPIN AXIS Fig. 2 AERODYNAMIC TORQUES IN PLANE OF ORBIT Ca3 0.4 Xe---~---::;r----.,.......---,.----X1 Sa3 "' Ye--.e:::..--:::--___:~o::-___:;__..,._-J,h---...:.... ....., ....y1 "" 0 Cl (SPIN AXIS) Ze----'----...:;;.._ __; ;i,...::__-,-_ " _i._ ___ Z1 3 ; -0.4 [Xe, Ye, Zel INERTIAL CO-ORDINATE SYSTEM -0.8 "' [X1, Y1, ZiJ BODY FIXED CO-ORDINATE SYSTEM " 0.4 " 01 3" 0 Fig. 3 CO-ORDINATE TRANSFORMATION N ti AND REFERENCE FRAMES u ~ ""ti n.2 _g ."".' M 'ti 01 .. V 3 Fig. 6 COPLANAR PADDLES, SPIN AXIS ; (\ ') 30° TO ORBIT PLANE 0.2 .".' " i..r- --~ o 3 - / ti'-0.2 "' ~ 0.00880 .----.--~-~----~-~-~-~ l:::f 1 ~IOHJ I Hid Fig. 4 COPLANAR PADDLES, SPIN AXIS IN PLANE OF ORBIT - 0. 00885 r+---,--,---,----,,1---drr--+--.------r--,-----, :" 4) the diurnal bulge is believed to lag ]". 0.00875 the sun by two migrate in lati- tude with the ) 5) the geomagnetic activity. With these considerations, the density variations for period (near solar maximum) are shown Fig. 7 NON-COPLANAR PADDLES, SPIN AXIS in Table 2.,,, densities along with the results 30° TO ORBIT PLANE 3 Page 36 0.4 .. r-..... 0 .... "' .0., -0.2 "-· -'7" ... .... 3 ;;- '\. -0.4 ' -....... ~ -0.6 "' L::1 ft± I 1 ti I u 0 00875 ..i . It ~" 0.00855 i----1r--+--+--+---1-__::,,,i,..,.....,..-1----l !::::Rliu+iE i ..M , 0_0035 .___.....,__ _O _l._ Q_H_O_U_R_--1. __L __ _j__ _J__ _j Fig. lO COPLANAR PADDLES, SPIN AXIS Fig. 8 COPLANAR PADDLES, SPIN AXIS NORMAL TO ORBIT PLANE 60° TO ORBIT PLANE 0 ."...' -0.4 .0., 3 -8 ii -0.12 0.4 "..' ~ "' 0 3" ~ 0.00875 ,...,,....<->,._......--=-r---,---,---~--~-~--- N " -0.4 .___ ___ :__:_'-..__..L__ _.L_ _j ___ _[__ _L __ _J 0.00885 rU--+-.--~--~-.h-~-~------ ~.. , 0.0086J u : Fig. 11 NON-COPLANAR PADDLES, SPIN AXIS ::;, 0 .0087 5 f-4-+--ll-fil-4+-lhl---~'-+fl--1f----¼--1!---I-JI--J-I--.J.4....-Al.,__.i,o._..w.,_J_..L...J NORMAL TO ORBIT PLANE i M . " 0. 00865 ~¥-~--_J_---l-----'"'-----'fi----''----1.---L----''---'..ll..-LIJ jectory. The attitude is specified in terms of three Euler angles, shown in Figure 3, which relate the orientation of a reference frame fixed in the Fig. 9 NON-COPLANAR PADDLES SPIN AXIS spacecraft to a reference frame whose orientation 60° TO ORBIT PLANE can be specified in inertial space as an arbitrary function of time. External forces and perturbations of the shadow studies are used to compute the aero- arising from gravitational, atmospheric, magnetic, dynamic torques which are shown in Figure 2. Com- and solar environments are included. The internal parison with Figure 1 shows that for this orbit the geomagnetic field model used in the simulation is perturbations due to aerodynamic forces are domi- one due to Cain, et al,5 and is described in terms nant. of spherical harmonics. It is essentially a field due to a dipole located at the center of the earth III. Dynamics whose axis is tilted from the earth's rotation axis. Radiation pressure forces are modeled for both the The nonlinear differential equations governing main spacecraft body and solar paddles. Aerodynamic the large-angle motion of the spacecraft must in forces are computed as described previously using general be integrated numerically. The dynamical experimental data to determine projected areas. In theory for the trajectory and attitude motion of a the determination of v, the relative air velocity spacecraft in the vici~ity of a gravitating mass was vector, the atmosphere is considered to be rotating developed by Pisacane, et al. In this develop- rigidly with the earth. ment, the spacecraft is considered to have a com- The effect* of the gravitational and atmos- pletely general configuration with mass an explicit pheric environments on the steady-state attitude of function of time and the generalized coordinates and a satellite of mass M spinning at O = 1/12 rpm velocities. The orbital motion is specified in terms is shown in Figures 4-11. All the physical para- of a perturbation from an arbitrary reference tra- *obtained for disturbed atmospheric conditions 4 68.-856 Page 37 TABIB 3. Attitude Interpolation Errors Angle Between Blade Spin Axis and i,s(min. Configuration Orbital Plane £,o:3(rad/sec) t,T(sec) of arc) t,o:(min) Non-Coplanar 0 1.48 X 10-5 20 0.127 3.0 TT 3.33 10-5 b X 20 0.286 4.o TI 5.0 X 10-5 3 20 o.429 5.3 TI 2 5.75 -6 X 10 20 0.0476 2.0 Coplanar 0 4.44 X 10- 6 20 0.038 1.32 TI 5.55 X 10-6 b -20 0.048 1.34 TI 3 2.5 X 10- 5 20 0.214 1.34 TI 8 2 0 91 X 10 -6 20 0.076 1.71 meters are the same (see Table 1) in each case. The only difference being the orientation of the k = 10- 5 I spin axis, which makes angles of o0 , 30°, 60° and 1- 900 to the orbital plane for the four runs under 10-7 ,-----·-+----- 400 , I .....L.-----+-------<•oo g I \ 1 1 ' ,-~ I ~ velocity vector must be accurately determined. The pro- :: I , 1 i ' \ i I g jected area of a satellite surface is not only a function of v, the· ::, I : - ! 1 o \ i I .. ~ rv,n.,r......i.__ _,:L/i air velocity vector, and its surface normal, but also depends ~.... A. \i "'' ~lo w i on structural shadowing. With a complicated structure, shadowing cannot be determined by an analytical model. J l\jl I : Therefore a shadow study of a scale model of the satellite was conducted. The nonshaded area and its respective moment arm of each surface are obtained as functions of the orientation of the spacecraft with respect to v. Two solar paddle con- figurations were considered. One, having paddles on opposite 0 400 800 1200 1&00 TIME (nconds) sides of the spacecraft lying in the same plane, is referred to as the coplanar configuration The second, having opposite Fig. I Disturbing torques. paddles rotated out of plane, is the noncoplanar paddle con- figuration. The normal vectors of all paddles in the body- allel to the satellite's spin axis, a rotor of the type used in fixed coordinate system are given in Table-1. Nimbus II is employed. To avoid coning of the spin axis, The determination of density is based on a model of the an eddy-cunent nutation damper, whose plane of motion is upper atmospheric structure due to Jacchia.3 The model, perpendicular to the spin axis, is used. The satellite has four above 120 km, assumes diffusion equilibrium and yields den- symmetrically located solar paddles and is in a low-altitude sities at any geographic location and height using the local (500 km), nominally circular orbit. exospheric temperature. 2•4 With these considerations, the The torques due to combined gravitational, magnetic, and density variations for period 1969-1970 (near solar maximum) solar effects are shown in Fig. la. The magnetic effect is due are shown in Table 2, These densities along with the results to the interaction of a residual magnetic dipole with the of the shadow studies are used to compute the aerodynamic Presented as Paper 68-856 at the AIAA Guidance, Control, x. 1 x, and Flight Dynamics Conference, Pasadena, Calif., August s., I 12--14, 1968; submitted August 23, 1968; revision received Jan- v. Y1 (SPIN AXIS} uary 31 1968. This work was supported by NASA. z. l z, * Senior Staff, Space Research and Analysis Branch; also Associate Professor of Mechanical Engineering, University of IXe, Ye, Zel INERTIAL CO.ORDIHATE SYSTEM Maryland. Member AIAA. t rx,. Y,, z,1 BODY FIXED CO-ORDINATE SYSTEM-Associate Mathematician, Space Research and Analysis Branch. Fig. 2· Coordinate transfortnation and reference frames. Reprinted from JOURNAL OF SPACECRAFT AND ROCKETS, Vol. 6, No. 3, March 1969, pp. 324-326 Copyright, 1969, by the American Institute of Aeronautics and Astronautics, and reprinted by permission of the copyright owner Page 41 J\IARCH 1969 ENGINEERING NOTES 325 ~ = 60° 0.2 -·········· g, 0.2 ___ ,,,,,.,. - 3 N 0 <""( Vw'l :i::.., _0_6 L.......• .....1._..1....._L,__0.:.:·:::.:20:...:Hc:..O:...:U:..:.R:........L._-1._..J b-need be considered. Thus the mcxlel netic hysteresis is extremely difficult, if not utilizes the triangular shaped area which is illus- impossible, thereby necessitating the use of numer- trated in Fig. l(b) and known as the Preisach plane. ical methods. Any reasonable representation re- If the hysteretic material is demagnitized by an quires a model that includes the ability to pre- ac decreasing field, the volume elements go to serve the history of the effect of variations in positive magnetization for a< -b and to nega- the magnetic field. 9 The theoretical model des- 10 11 tive magnetization for a> -b. This is also cribed here is attributed to F. Preisach ' and shown in Fig. l(b). is based on the domain theory of w.agnetization. It is assumed that the hysteretic material is divi- Starting from the demagnetized condition, if ded into infinitesimal volume elements, each char- H increases from H = O to H = H , then all acterized by a shifted rectangular hysteresis loop negatively magnetized elemental rec¥angular loops for which O :s: a :s: Hn will flip to positive mag- B netization. The change in the magnetization of the material is thus related to the number of do- mains whose values of a and b lie in area A1, of Fig. 2. If instead, H decreases from H = 0 b 0 b a ,, H Fig. la ELEMENTAL RECTANGULAR HYSTERESIS LOOP b Hdecreasing ' b Hincreosing - Fig. lb THEORETICAL ARRAY (PREISACH PLANE) Fig. 2 NORMAL MAGNETIZATION 2 6 9 ... 83 3 Page 46 to H = -Hn then all positively magnetized loops b for which -Hn s b s O will flip to negative mag- netization. This time the change in magnetization is related to the number of domains whose values of a and b lie in area A'2. .of Fig. 2. Thus for a change in H, there is a relationship be- tween the corresponding change in magnetization, B , and an area in the Preisach plane. A suitable definition of this relationship will yield a theo- retical model of magnetic hysteresis. It is noted that the axes a and b are the axes of increas- ing and decreasing H respectively. Suppose that for each a and b in the tri- angular array there is a weighting fu_"lction, qi(a,b), which is related to the statistical weig_ht, or frequency, of rectangular loops characterized by a and b The expression for the area dif- ferential in the Preisach plane will then be given b by dA qi(a,b) da db (l) The following, taken from Reference 9, defines the relationship between changes in B and the weight- ed areas in the Preisach plane for the theoretical model lL"lder consideration here. If the ambient field component along the axis of a hysteresis rod is increased monotonically from zero to +Hn , then decreased monotonically to -Hn, and then in- creased to +Hn again, the hysteresis loop illus- trated in Fig. 3 is obtained. Points land 3 are on the normal magnetization curve and have normal B Fig. 4 RESIDUAL MAGNETIZATION H B( 0 ,Hn ) = Jo n J- oa dA (4) and H B - r = B(O,-Hn) = -s_; J~b dA (5) n Similarly, the expression for any B between B(Hn) and B(-Hn) is B(H,Hn ) =kH + ln Ja qi db da 0 o -a H H - J/ sbn qi dadb (6) Fig. 3 SAMPLE HYSTERESIS LOOP For the general case where H is increased from zero to HJ , decreased to H2 , and then increased to H3 , ·tne corresponding magnetic induction B(H ) magnetizations B~ and Bn. The En are obtain- is obtained from 3 ed from the weighted areas illustrated in Fig. 2 and calculated from B(H3) = kJi3 + Si dA - S2 dA + S3 dA (7) H a B( +H ) kH+JnJ dA (2) The sign of each integral in Eq. (7) was determined n o n O -a by the area boundary line b = -a as illustrated in and Fig. 5. Thus the history of the effect of varia- (3) tions in the applied magnetic field is being pre- served. where dA = qi(a,b) dadb and k is the permeability 0 From symmetry considerations, the weighting of the hysteretic material in the vicinity of the function qi is defined as origin. Note that the sign of the area for nega- N • • tive normal rnangetization was set negative in Eq. qi(a,b) = L k .. (a-b)i (a+b)J (8) (3). Points 2 and 4 which correspond to H = 0 i,j=o iJ are on the residual magnetization curve and have residual magnetizations :s; and Br The Br where N is a function of the desired accuracy and are obtained from the weighted areas illustrated the kij 's are determined from experimental hys- in Fig. 4 and calculatea. from 3 Page 47 b N B(H ,H) = + B = k H + 6 k .. (ex ..H i+j+2 ) n n n on i,j=o lJ lJ n (lO) N B(H ,H ) = B+ = 6 k .. (/3 ..H i+j+2) (11) r n r i,j=o lJ 1J n For negative values of B, B~ and Br are defined similarly. Thus the polynomials P .. listed in lJ the Appendix have reduced to the form ex . •H i+j+2 lJ n and f3 .•H i +j+2 • The coefficients 1J n aij and f3ij for polynomials through sixth order in H are n listed in Table l. The discrepancies between Tableland the results of Reference 9 are due to + + + + + + + + + typographical errors in the latter. + + + + + + + + + + + + + + + + + + + + + + + + b= -a Table l 2 Fig. 5 THEORETICAL MODEL AND NET AREAS USED Coefficients of Hi+j+ in the n FOR B(H3}= k0, H3 + S1 dA -J2 dA + f3 dA Determination of B+ and B+ n r ex teresis loops. Since the complexity of the computa- ij tions is proportional to N, for the model dis- 0 l 2 3 4 cussed here i and j are restricted to the range 0 l l6/l5 0 ~ i+j ~ 4. An extension of Preisach's work which 2/3 2/3 4/5 is also concerned with the selection of ~ is l 2/3 l/3 4/l5 4/l5 given in Reference l2. Substitution of Eq. (8) into 2 2/3 4/l5 8/45 Eq. (6) yields N 3 4/5 4/15 B(H,H ) = k R + 6 kiJ" PiJ" (H,Hn) n o i,j=o 4 l6/l5 where the P .. (H,H) are pol:ynomials of order 1J n f3ij i+j+2 The pol:ynomials through P20 are listed 0 l 2 3 4 in the Appendix. The coefficients k and the 0 l/2 l/6 l/l2 l/20 l/30 0 k .. 1 s are obtained from a least-squares fit of lJ l l/2 l/6 l/l2 l/20 Eq. (9) to the experimental magnetization data. 2 7/l2 ll/60 4/45 This data is obtained by generating hysteresis loops, 3 3/4 l3/6o before the rods are plac-ed in the spacecraft, for as many values of Hn as desired. The determina- 4 3l/30 tion of k and the k .. 's for two specific cases 0 1J is given next. The details of the procedure for performing the weighted area calculations on a digi- Eqs. (10) and (ll) are then used to define the tal computer are given in Reference 9. function to be minimized It is noted that for ~=constant (N=O), the 2 F = 6 (B -B ) + (B -B )2 (l2) model described here reduces to that of Rayleigh. 13 all normal n ne r re For small values of H, he represented the sides and residual of hysteresis loops by quadratic ~urves. The same data result is obtained by substituting P from the Appendix into Eq. (9) and letting N goo • where the subscript e denotes experimental data. The minimization of -F-, in the least squares sense, yields the desired k .. 's • Consider the experi- Specific Example and Results 1J mental hysteresis data shown in Figs. 6-7. The Experience has shown that for the type of rods normal and residual magnetization data is used to used in some of the APL satellites, use of the nor- define F and subsequently determine the k .. 's lJ mal and residual magnetization data only is suffi- as listed on each figure. Determination of the cient to accurately determine the kij's. The kij's along with Eq. (9) is used to produce the rods are approximately .l inch in diameter and con- theoretical hysteresis loops also shown in the fig- sist of AEM 4750, a nickel iron alloy. The rods ures. studied varied in length from 30 to 54 inches. For this case, the positive normal and residual values In the general case, the restriction of using of B have the following form only the normal and residual experimental magneti- 4 69-833 Page 48 • zation data is removed and many data points along each hysteresis loop may be used to determine the kij's , The minimization of F was achieved after ko = 1142.25 changing Eq. (9) to orthogonal polynomial form. koo= 20,215.51 Several computer experiments indicated that N 4 (sixth order polynomials) was the optimum choice. A sample result is shown in Fig. 8. - EXPERIMENTAL LOOP eeee e THEORETICAL MODEL -.;;.- ~ 01---+---l--........ ,l'!-tilll=--+---+-------l ~ ell EXPERIMEMTAL LOOP -sool.,_..il!!!!!:~~~t::::!:::J_ _ __j ___J .,_ _ _J • THEORETICAL MODEL -0.6 -0.4 -0.2 0 0.2 0.4 0.6 H (oersteds) • -0.1 0 0.1 0.2 0.3 Fig. 8 COMPARISON BETWEEN THEORETICAL AND H (oersteds) EXPERIMENTAL LOOPS FROM AM ARTIFICIAL HYSTERESIS DEVICE, M = 4 Fig. 6 COMPARISOM BETWEEN THEORETICAL AND EXPERIMENT AL LOOPS, 30 IMCH ROD, N = 0 Evaluation of the Model k = 2134:24. The agreement between the theoretical model 0 and experimental loops is good for the type of' hys- koo = -2476.29 tere sj.s rods currently being used in some of the ko1 = -0.1233 APL satellites. For those it is sufficient o = to use only the normal and re:siclua,l magnetization k 1 283,533.83 data, as described above, in determining the k .. 's. ko2 = -65,371.74 1000 -+---------------l J..J Figs. 6-7 illustrate the comparison between experi- k11 = 0.7795 mental and theoretical hysteresis loops for a 30- k20 = -578,556.78 inch rod for different size major loops and differ- ent values of N. A comparison between unsymme- trical minor loops for a different rod is shown in Fig, 9. The major limitation on the model is that the accuracy decreases for cases where the rods be- come saturated. However, it is usually desirable (and possible) to choose rods which do not become saturated anywhere in orbit. The model may also be used to simulate loops generated by artificial hys- teresis devices. 14 A comparison between theoretical and experimental loops for such a device using all the available magnetization data and N 4, is shown in Fig. 8. Agreement with those types of hysteresis loops, usually more rectangular in shape, is not as good as that shown in Fig. 8 when only the normal and residual experimental magnetization data is used. -- EXPERIMENTAL LOOP The hysteresis model described here has been e THEORETICAL MODEL programmed in subroutine form and is currently being used in the "Digital Attitude Simulation (DAS)" com- puter program, 9 DAS is a large angle nonlinear sim- -200,~~-=-7;c----;c'-;----a+ --+.:o-.- --7:---"""'"'To.3 ulation of the attitude motion of' a spacecraft. _ _ -0.1 1 0.2 0 3 Hysteresis loops ~PnP1cAtoPn by DAS during a simula- H (oersteds) tion of a near earth nautical miles) satellite Fig. 7 COMPARISON BETWEEN THEORETICAL AND are shown in Fig. 10. Having determined B, the EXPERIMENTAL LOOPS, 30 INCH ROD, N=2 simulated torque L due to the interaction of a 5 Page 49 2400.-------,------.------.----~ where v is the rod volume. In orbit, the compo- nent of H along the axis of a rod frequently re- verses itself resulting in minor loops such as the one in Fig. 10. Unfortunately in-orbit experimental data corresponding to the theoretical results shown in Fig. 10 is not recorded. The only relevant in- orbit experimental data available consists of a time history of the spacecraft's attitude motion. .. Hence attitude results from DAS using the theoreti-"' cal hysteresis model may be compared with the exper- :, " imental attitude data. Previously, DAS results ~ have shown general agreement with attitude data from near-earth satellites with other forms of energy dissipation. 15 16 ' A comparison between sim- ulation results and flight data for a near-earth satellite with magnetic hysteresis damping is shown in Fig. 11. The agreement between the two results tends to support the validity of using this hys- teresis model. (a) -800 e e • • e FLIGHT DATA --- SIMULATION RESULTS 2400 30 • -.;.- .~ ". ' 3 0 1600 :u:c: .".' I- .::,, ii: ~ -30 al 800 (b) ~0.1 0 0.1 0.2 0.3 [\'kftfEfl H (oersteds) ~ ~ ~ G a M e • a Fig. 9 COMPARISON BETWEEN THEORETICAL AND TIME, UT ksec EXPERIMENT AL MINOR LOOPS, N = l Fig. 11 COMPARISON OF SIMULATION AND FLIGHT RESULTS FOR A NEAR EARTH SATELLITE WITH MAGNETIC 2500,---~----~-~--~-~----- HYSTERESIS DAMPING DAY 141, 1966 Cosu,ise, attitude simulation runs for near- earth satellites, including the effects of external perturbations, cost less than five dollars per or- bit using the 7094 computer. The runs took fifty percent longer than the same simulations would have taken without hysteresis. The satellites consid- ered have rods along each of two orthogonal axes. For satellites with rods along three axes or one axis, the simulation cost would change proportion- ately. Hence, while using this hysteresis model is expensive, the cost is not prohibitive. Results of an investigation into cost-accuracy tradeoffs indicate that the cost of simulating hysteresis can probably be halved for only a slight loss in accura- cy. -1000<-----'----1---'--_,L_ _, ..__ _ _._ _ __. _ ____, -0. 15 -0.10 -0.05 0 0.05 0. 10 0.15 0.20 0.25 Closure H (oersteds) The magnetic hysteresis model discussed in Fig. 10 RESULTS FROM A SIMULATION OF A NEAR-EARTH this paper is reasonably accurate, feasible cost- SATELLITE, 46 INCH ROD wise, and does not require hybrid computiri_g equip- ment. The model not only simulates the hysteresis hysteresis rod with the ambient magnetic field is phenomenon in permeaale rods, but it may also be computed by used to simulate loops generated by artificial hys-teresis devices. An extension of this work was the - L = 4Vn (B x H) (13) consideration of shapes other than tria..~gular for 6 6 9- 83 3 Page 50 the theoretical model of Fig. l(b). The techniques 11. Preisach, F., "Uber \].ie Magnetische Nachwir- described here might also be extended to the devel- kung," Zeitschrift fur Physik, Vol. 94, 1935, opment of a model for structural hysteresis. pp. 277-302. l2. Biorci, G. and Pescetti, D., "Analytical Theory of the Behavior of Ferromagnetic Materials," Acknowledgment Nuovo Cimento, Vol. 7, No. 6, March 1958, pp. 829-842. This work was supported by the U. S. Depart- 13. Bozorth, R. M., Ferromagnetism, Van Nostrand, ment of the Navy under Navy Contract NOw 62-0604-c. Princeton, 1951, pp. 489-494. The authors would like to give special thanks to 14. Alper, J. R. and O'Neill, J. P., 11A New Passive P. P. Pardoe who was involved in much of the ini- Hysteresis Damping Technique for Stabilizing tial analvtical work. Thanks also go to R. J. Gravity-Oriented. Satellites," AIM Guidance McConahy for assistance in the computations invol- and Control Conference, Seattle, August 1966. ving the orthogonal polynomials and to T. Wyatt 15. Pisacane, V. L., Pardoe, P. P., and Hook, B. J., for the attitude data and his interest in the prob- "Stabilization System Analysis and Performance lem. The experwental hysteresis loops used were of the GEOS-A Gravity-Gradient Satellite (Ex- furnished by J. A. Ford, F. F. Mobley, W. Nobles, plorer XXIX), 11 Journal of S;acecraft and Rockets, and B. E. Tossman. Vol. 4, No. 12, December 19 7, pp. 1623="1630; also TG-901, lf.1arch 1967, Applied Thysics Lab., References Johns Hopkins Univ. 16. Whisnant, J. M., Waszkiewicz, P. R., and 1. Fischell, R. E., "Magnetic and Gravity Attitude Pisacane, V. L., "Attitude Performance of the Stabilization of Earth Satellites," CM-996, May GE OS-II Gravity-Gradient Spacecraft," presented 1961, Applied Physics Lab., Johns Hopkins Univ. at the Gravity-Gradient Attitude Control Sym- 2. Anand, D. K., Whisnant, J. M., Pisacane, V. L., posiu.m, El Segundo, December 1968; also TG-1054, and Sturmanis, M., "The Capture and Stability January 1969, Applied Physics Lab., Johns Hop- of the L]])OS Gravity-Gradient Satellite in an kins Univ. Eccentric Orbit," AIM/AAS Astrodynamics Con- ference, Princeton, August 1969; also TG-1028, August 1968, Applied Physics Lab., Johns Hop- kins Univ. 3. Fischell, R. E., "Magnetic Damping of the A.rigu- Appendix lar Motions of Earth Satellites," ARS Journal, Vol. 31, No. 9, September 1961, pp--:-i2lO-l2l7. Evaluation of the polynomials, Pij(H,Hn) 4. Pisacane, V. L. , Guier, W. H. , and Pardoe, P. P. , "Dynamical Equations for the Position and Atti- For O ~ i+j ~ 2, substituting Eq. (8) into Eq. tude of a Spacecraft with Time Dependent Mass (6) and performing the indicated integrations yields and lf1ass Pr~perties," TG-919, June 1967, Applied the following polynomials. Physics Lab., Johns Hopkins Univ. 5. F'rick, R. H. and Garber, T. B., "General Equa- H2 1i:2 tions of Motion of a Satellite in a Gravita- Poo(H,Hn) = / + HJI - 2 tional Gradient Field, 11 R1"1-2527, December 1959, The Rand Corporation, Santa Monica, Calif. 6. Vanderslice, J. L., "Dynamic Analysis of Gravity- H3 H2:rr H~ H3 Gradient Satellite with Passive Damping," TG- n P (H,Hn) =b + ___g_ +-n-2 -2 502, June 1963, Applied Physics Lab., Johns 01 2 Hopkins Univ. 7. Chen, Y., "The Damped. Angular Motion of a Mag- H4 H3H H2ir2 H H3 netically Oriented Satellite, 11 Journal of the = _£ + -1'!._ +_n_ +_n_ P02(H,Hn) .it l2 2 3 l2 Franklin Institute, Vol. 280, No. 4, October 3 1965, pp. 291-306. 2 8. Gluck, R. and Wong, A., "Inline Hybrid Computer H3 H2ir H Hn n n . H3 for Simulation of Passively Stabilized Satell- PlO(H,Hn) =2 + 2 - -2- +b ites,"AIM Guidance, Control and Flig..li.t Dyna- mics Conference, Pasadena, August 1968. H4 3 3 9. Pardoe, P. P., 11A Description of the Digital H H H Hn + -1'!._ n H4 Attitude Simulation," 'rG-964, February 1968, P11(H,Hn) = b - -3-3 +b Applied Physics Lab., Johns Hopkins Univ. 10. Becker, R. and Doring, W., Ferromagnetismus, H2ir2 H H3 Edwards Brothers, Inc., Ann Arbor, 1943, pp. n +-n- 218-228. -2- 3 7 Page 51 AIAA Paper ~' No. 69-921 AMHIU~rJ/O NAU-f/CAl SOCIETY THE CAPTURE AND STABILITY OF THE LIDOS GRAVITY-GRADIENT SATELLITE IN AN ECCENTRIC ORBIT by D. K.-ANAND, J.M. WHISNANT, V. L. PISACANE and M. STURMAN IS The Johns Hopkins University Silver Spring, Maryland 1111111s 1s1rod1namics conlerence PRINCETON, NEW JERSEY /AUGUST 20-22, 1969 First publication rights reserved by American Institute of Aeronautics and Astron'i'utics., 1290 Avenue of the Americas, New York, N. Y. 10019. Abstracts may be published without permission if credit is given to author and to AIAA. (Price: AIAA Member $1.00,. Nonmember $1.50) Page 52 THE CAfTURE AND STABILITY OF THE LIDOS GRAVITY-GRADIENT SATELLITE IN AN ECCENTRIC ORBIT D. K. Anand, Senior Staff'+ J • M• Whisnant ' Associate Mathema++ti cian V. L. Pisacane, Senior Staff' M. Sturmanis, Associate Mathematician The Johns Hopkins University Applied Physics Laboratory Silver Spring, Maryland Abstract General This paper reports on the investigation of the Sate.l.lite oscillations in the plane of an elli- capture and gravity-gradient stabilization of a ptic orbit are describedJ. ' 2 by the fo.llowing differ- satellite in an orbit with an eccentricity of 0.2. ential equation The satellite is called LIDOS, and its mission is to 2 obtain geodetic information. (l+e cos v) ~ - 2e sin v ~ dv2 dv The orbit eccentricity gives rise principally + a sin~ cos~= 2e sin v to pitch librations. The amplitude of these libra- tions is about 0.26 radian which represents the where e is the eccentricity, a= 3(Ix-Iz)/Iy], ~ minimum solution to the equation of planar libra- is the pitch libration angle measured from the local tions. vertical, and v is the true anoma,ly. This equa- For an optimum selection of mass distribution tion has been investigated by researchers using numerical integration and phase space representation. and adverse orbital conditions, all the perturba- It is seenJ. ' 2 that the stab.le region is symmetrical tions combine to cause ~ roll amplitudes of 0.27 radian and close to two revolutions in yaw per or- about the local vertical at v = 0 and TT for all bit, in addition to the above mentioned pitch libra- e and a R; .3 The region of stability becomes skewed as v varies from O to TT to 2TT and also tions. shrinks as e is increased. This continues until Owing to the large eccentricity, the region of the eccentricity reaches 0.355 when g~avity-gradient stabilization is no longer possible for any config- stability, and con.sequently capture, is sma.1.1. Furthermore, the obtaining of uration. .1 rpo by conventional methods of inertia changes does not insure success- Consider a satel.lite having a R; 3 and in an ful gravity-gradient stabilization with such an orbit with 0.2 eccentricity. The resulting pitch eccentric orbit. Therefore, an e.lectromagnet is employed to maneuver the satellite into the stable oscillations have an amplitude of 0.26 radian (ini- region before capture. This is shown by phase plane tial condition of ~ = O, cp = 0.74 at v = 0). An approximation of this result can be obtained by representation. solving the Mathieu equation.3 ' 4 ' 6 (See Appendix) Introduction Note that ~ is in degrees and ~ is non-dimen- siona.lized by v(~). Gravity-gradient stabilization of arti.ficial satellites in near-circular orbits has been well For the satel:li'te under consideration, however, demonstrated in the past. In this paper the capture it is not sufficient to consider on.ly eccentricty and stabilization of a satellite in a highly eccen- effects, which primari.ly affect pitch librations. tric orbit is considered. The satellite under con- Perturbations due to thermal bending, so.lar radia- sideration is LIDOS, whose purpose is to yield tion pressure, and magnetic torques must be included. geodetic information. The inclusion of radiation pressure is princi- The sate l.lite has an unsymmetrical inertia pally felt in roll and yaw. The solar radiation ellipsoid, four solar paddles arranged in a windmill pressure forcing function in roll has a component fashion, a self-erecting boom with end mass, and with twice orbital frequency, and since :the natural permeable rods for hysteretic damping. Additionally, frequency is also the same, resonant conditions tend there is a dipole magnet for performing inversion to be set with a particular combination of orbit 6 maneuvers in case the satellite is initially cap- elements and solar aspect. This coupled with the tured in the undesired mode. eccentricity effect gives rise to large ro.11 motion, and although the pitch motion is within stable bounds, It is intended that this sate.llite be gravity- tumbling in roll can occur. gradient stabilized in an orbit having an eccentri- city of 0.2 and a semi-major axis of 1.45 earth Dynamics radii. The dynamical theory for the attitude motion + Also: Associate Professor, Department of Mechanical Engineering, University of Maryland, College Park, Maryland ++Supervisor, Theory Project, Space Research and Analysis, The J'ohns Hopkins University App.lied Physics Laboratory 69-921 l Page 53 of a spacecraft has-been developed using the Lagran- netic hysteresis damping, scheduling limitations gian and in a form suitable for computer simula- dictated use of the latter. Inversion maneuvers tion. 7 External forces that arise from the gravi- were simulated using a dipole magnet pointed in a tational, magnetic, and so.lar environments are direction opposite to the boom. Satisfactory re- included in the simulation. The solar effect con- sults were obtained using a magnet of strength sists of both thermal distortion of the stabilizing 44, 000 pole - ems. booms and a radiation pressure torque on the deform- ed spacecraft. The gravitational torque not on.1~ Stability and Capture provides the basic stabi.lizing mechanism but also introduces attitude perturbations through the It is important to know the stability region eccentricity of the orbit. The magnetic torques are before attempting to capture the satel.lite. For simulated using a geomagnetic fie.ld model written satellites in orbits of .low eccentricity (< 0.1) the in terms of spherical harmonics. An analytical point cp = O , ~ = -1 is always within the stable model for hysteretic damping has been developed and region of the phase p.lane. Therefore, if the moment is included in the simulation. 8 of inertia is adequate.ly increased anywhere in the orbit, provided cp is within stable limits, then Attitude Simulation cp "' -1 and the satellite becomes captured in the gravity-gradient mode. This maneuver has been done The coordinate transformation and system used many times and is we.11 understood. to define pitch, roll, and yaw angles are shown in Figure .1. The results of the simulation are pre- However, when e > 0.1 the above.procedure sented as plots of these three angles and the tota.l does not always insure capture since cp = -l is out off-vertical angle as a function of time for various of the stable region for certain values of the true combinations· of physical parameters. Tab.le 1 pre- anomaly •1 ' 2 Specifically, when e = 0.2, the point sents the physical properties common to all runs. cp = -1 is not inside the stable region anywhere in Unless otherwise noted, it has been assumed that at the orbit e:xcept for a small time around apogee. perigee, the point where integration begins, cp = 0 This --is shown in the stroboscopic study of Figure 6. and cp = 0. Additiona.lly, the region of stabi.lity is studied using a perturbational scheme and is reported else- The effect of eccentricity alone is felt where.19 It suffices to note, however, that the principally in pitch motion and shown in Figure 2. region of stability obtained is larger than that The peak amplitude is about 24° in pitch with no reported before. oscillations in roll and yaw. Due to the existence of perturbations l the Different orbits were studied to obtain the exact determination of the region around cp = -1 most adverse set of conditions that wou.ld yield an is difficult. Therefore, in order to effect sat- upper bound on attitude motion. 9 It was found that ellite capture anywhere in the orbit, the satellite. the orbit giving resonant conditions in roll was must be maneuvered into the stable region. such an orbit and the rest of this study is based on it. A parametric steady-state study was con- The necessary maneuvering is achieved by using ducted9 which determined that the combination of an electromagnet. The satellite is magnetical.ly 60 ft. boom length and 5 lb. end mass was optimum. stabilized and the boom is erected while the electro- The result of this simulation is shown in Figure 3. magnet is still on. The magnetic torque opposes the gravitational torque and drives the sate.llite into The yaw motion occurs since the solar padd.les the stable region, at which time the electromagnet are arranged in a windmill fashion. The energy is turned off and capture is effected. associated with yaw motion, if transferred, is capable of causing a 6° ro.11 motion. From an atti- The stability regions for 290° s; v s; 310°, tude stability viewpoint such performance is accep- 310° s; v s; 330°, and 300° s; v s; 320° are shown in table. The benefit to be derived from the yaw Figures 7a, 7b, and 7c. These charts are obtained motion is the smoothing of thermal fluctuations of for the stable initial condition cp = .18°, cp = 0 the satellite. at perigee. The equations of attitude motion are now integrated beginning at v = 262° and with dif- It is noted that the existence of perturbations ferent initial conditions. It is assumed here that causes no substantial change in pitch although ro.11 the sate.llite is magnetically stabi.lized, the boom oscil.lations increase to about 1.0° and the satel.1ite for appropriate inertia is erected, and the electro- rotates in yaw at the rate of one or two revolutions magnet is on. The resulting trajectories (cp and cp per orbit. with time as parameter) are superimposed on the sta- bility charts. Trajectories obtained with initial Transient response to an initial condition of conditions of -10°, + .10°, 0°, and zero rates in 10° pitch is shown in Figure 4(a) when two hystere- each case are shown in Figures 7a, 7b, and 7c. tic damping rods 57" long are used. Also for the same init ia:l conditions but employing four 57" rods, It is seen that the attitude motion is driven the transient response is shown in Figure 4(b). As inside the stable region and stays inside for about expected, four rods are more effective in damping. eight minutes. If the electromagnet and a.1.1 pertur- Increasing further the number of rods showed no bing effects are turned off during this time inter- improvement in performance. val, the satellite is captured. It is stressed that the exact location of the stabi.lity regions For purposes of investigating an entirely and attitude trajectories are dependent upon v and different damping scheme, a General Electric mag- the initial conditions applied at v = v • In any netically anchored damper (damping constant of practical situation this must be a real time opera- 8 x 104 dyne-cm-sec/rad.) is employed. The transient tion. behavior is shown in Figure 5. Although the results are somewhat superior than those obtained by mag- 2 Page 54 Acknowledgments 9. Anand, D. K., Whisnant, J.M., and Sturmanis, M., "The Capture and Stability of a Gravity-Gradient This work was done under Navy Contract NOw-62- Satellite in an Eccentric Orbit, 11 The Johns 06o4-c. Hopkins University App.lied Fhysics Laboratory Report TG-1028, August 1968. References 10, Anand, D. K., and Yuhasz, R., "Study of Planar l. Zlatoustov, U. A., Okhotsimsky, D. E., Sarychev, Oscil.lations in an Eccentric Orbit Via a Mod- V. A., and Torzhevsky, A. P., "Investigation of ified Perturbational Approach, 11 The Johns Hop- Satellite Oscillations in the Plane of an Elli- kins University Applied Physics Laboratory, ptic Orbit," 11th International Applied Mech- Technical Memorandum (in preparation). anics Conference, Munich, 1964. Appendix 2. Brereton, R. c., and Modi, V. J., "On the Sta- bility of Planar Librations of a Dumbbell Sat- Satellite librations in the p.lane of an elli- ellite in an Elliptic Orbit, 11 Journal of the ptic orbit are governed by the following equa- Royal Aeronautical Society, December 1'§E;C.-- tions1 ' 2 7 ' 2 .3. Graham, D. and McRuer, D., Analysis of Nonlinear -d (cp+v) + cxw 2 (l+e cosv) 3 sin

- -5 ,w.J ..-J< Cl u :z:- 10 -< ~ ,_JWI -< > I- IL 0 IL 1 I- 0 • TIME (hours) DAY 80 Fig. 2 RIGID BODY WITH NO DAMPING - 100 FEET; 2.8 POUNDS 25 :c u I- ii: -25 20 ,.J 10 ,.J 0 o: •IX -10' -20 180 90 ~ -< >-' 0 90 -180 20 ,w.J.-. I- IL OIL I I- 0 TIME (hours) DAY 80 Fig. 3 STEADY STATE-60 FEET; 5 POUNDS 69-921 5 Page 57 30 ----------------~--------,,---------,------.,.----, 0 15 !:: , 0 D- -15 -30 15 ...I , 5i 01-,::,<~++flH-1+-t-+-+H-+'r+r++t++-tt++l+l-++l++ffi-+-tt-lr-Hi"\-+H+-f-tt-'H-ti+ttt++tl-\-ttif-'c-f''7'S""?vS:7'7' u< % j:: 15 <~ ....1W 0 j!:.', !..!.L.-=...JL....:..J..!.-.J.:...!..l.....:.!:J...,!--11..!--Z.:....!....l...--!Jl--..,J;_--1.lL...!---.l.___;'1,....;:,..,i...J-;,.U,._. ......... !...,!,1_ _._---1..,__.z___.___._, <> 0 3 6 I 9 1 12 15 18 21 • 24 27, 30 33 36 39 42 45 48: 51 54 57 60 63 66 69 72 ... 11- 0 II-, ... 0, TIME (hours) DAY 80 (b) FOUR 57-INCH HYSTERESIS RODS Fig. 4 TRANSIENT RESPONSE FOR 60 FOOT BOOM AND 5 POUND END MASS 6 Page 58 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 TIME (hours) DAY 80 ·· fig. 5 TRANSi ENT 60 FEET; 5 POUNDS; GE DAMPER (k = 8 x 104 DYNE- CM-SEC/RAD) 1.0 Fig. 6 STROBOSCOPIC STUDY AT 11 =n FOR AN ECCENTRICITY OF 0.2 69-921 7 Page 59 8 '\ \ \ \ \ \ \ \ 0.4 '4 0,4 \ \ \ I \ I J I -20 0 I 20 0 20 0. ~ 0 ATTITUDE TRAJECTORY ~ (time in minutes) ~ ATTITUDE TRAJECTORY '\,., -v= 310° ~ (time in minutes) "- -- v= 330° ~ - v = 290° :::---... ---- V: 310° --..._;:--- (a) -10° INITIAL CONDITION (b) +10° INITIAL CONDITION ATTITUDE TRAJECTORY (time in minutes) 20 (c) 0° INITIAL CONDITION Fig. 7 ATTITUDE TRAJECTORIES, OF DIFFERENT INITIAL CONDITIONS AT v = 262°; SUPERIMPOSED OM THE STABILITY REGION FOR ECCENTRICITY OF 0,2 8 Page 60 Gravity-Gradient Capture and Stability in an Eccentric Orbit D. K ANAND,* J. 1\1. WHISNANT,'! V. L. PISACANE,T AND M. STURMANISf The Johns Hopkins University, Silver Spring, Md. Introduction GRAVITY-GRADIENT stabilization of artificial satellites in near-circular orbits has been well demonstrated in the past.. In this Note the capture and stabilization of a satellite in a highly eccentric orbit is considered. The satellite under consideration is Lidos, whose purpose is to yield geodetic information. It has an unsymmetrical inertia ellipsoid, four solar paddles arranged in a windmill fashion, a self-erecting boom with end mass, permeable rods for hysteretic damping and a dipole magnet for performing inversion maneuvers in case the satellite is initially captured in the undesired mode. x. coq ca3 x, -sa1 sa3 v. -··, Acaz ·, Y1 z. ca2 ca\ Z1 PITCH sin- 1 (RaltJ= ~ ROLL = tan- 1 -(Ra)23/(Ra)33 = 6 YAW = tan- I -(Rah z/(Rah l = '!' TOTAL. ANGLE cos- 1 (Ra)33 = T Fig. 1 Coordinate transformation and angle representa~ · tion. Presented as Paper 69-921 at the AIAA/A AS Astrodynarnics Conference, Princeton, N.J., August 20-22, 1969; submitted August 12, 1969; revision received September 10, 1969 This work was done under Navy Contract NOw-62-0604-c * Senior Staff, Space Research and Analysis Branch, Applied Physics Laboratory; also Associate Professor of Mechanical Engineering, University of Maryland. Member AIAA. t Associate Mathematician, Space Research and Analysis Branch, Applied Physics Laboratory. :j: Supervisor, Theory Project, Space Research and Analysis Branch, Applied Physics Laboratory Member AIAA. Reprinted from JOURNAL OF SPACECRAFT AND ROCKETS, VoL 6, No 12, December 1969, pp .. 1456-1459 Copyright, 1969, by the American Institute of Aeronautics and Astronautics, and reprinted by permission of the copyright owner Page 61 DECEMBER 1969 ENGINEERING NOTES 1457 It is to be gravity-gradient sta,bilized in an orbit having an eccentricity of 0.2 and a semimajor axis of 1.45 earth radii. Satellite oscillations in the plane of an elliptic orbit are described1 •2 by the following differential equation: d2( + <{J • d<{J • 2e , 1 e cosv ) --d- -2 - 2e smv -d + a Slll<{J cos,p = suw .v V i,.,_ 1S~M1 t1M#11r ,41 4ttM·v ¼4·I{ AW0·~ 44 v· . 1 ., ., , ~ -180 y C I ·~ where e is the eccentricity, a = 3[(!,, - I,)/I.,],

0.1, the foregoing procedure does not reflectivity = 0.8 always insure capture, since q, = -1 is out of the stable Booms: m = 0 0154 lb/ft region for certain values of the true anomaly. 1 •2 Specifically, Radius of curvature due to thermal bending = 1500 ft when e = 0.2, the point q, = -1 is not inside the stable region Surface reflectivity = 0. 88 anywhere in the orbit except for a small time around apogee. Diameter = 1 .. 27 cm This is shown in the stroboscopic study of Fig. 4. Addition- End mass: M = 5.0 lb, area = 268 cm2 ' ally, the study of the regions of stabili~y with different Solar paddles: area = 4280 cm2, surface reflectivity = 0.25 = = parameters and including perturbing forces is reported else-Magnetic rods: volume 17.56 cm3, diameter 0.275 cm; where. 9 material, AEM 4750 It suffices to note, however, that the region of stability obtained is larger than that reported before. Page 62 1458 J. SPACECRAFT VOL. 6, NO. 12 1.0 ii> • 3~FE. "0" 1\ d' .l)t) n~ i'iJI_ oliV D A ~v ,~ ;, __, .'.) ., ,'. ...- .- ,.,-_·c.··. ..,f•. -'-<......._,..,.j _30 \J " v v ,. V 'V V ~ \IV ~ J .. '., v ·· · v ., •. · 1 Fig. 4 Stroboscopic study at JI = 1r for an eooentrieity of 0.2. T ~~favJ}~dv~~1vJ\~~~o/Wvvy1~rlffrflJ must be maneuvered into the stable region. The maneuver- b) FOUR SJ.INCH HYSTERESIS RODS ing is achieved by using an electromagnet. The satellite is magnetically stabilized, and the boom is erected while the , 4o0 ~, l..\nn.o.".:: rou,, ·~if, , oe -·--A~'~ Ao/\ :·,:..:...._:2~. . :., electromagnet is still on. The magnetic torque opposes the hoA[\ I\:" • ' ;.· '; i.,;. • 'i '. ,·\·. 1~ Vt; .\< \I H \: ·• ' -.·'. · ·~, ·,• .. "1.: \.; \,Vi -40 ~ , ·' \ ~ II \. . \ gravitational torque and drives the satellite into the stable r : region, at which time the electromagnet is turned off and ; capture is effected. c0 •c ~.?i:.., 0.c,)tv°GV,'•J\A.}v\AV.\. l~~:""--..~ ~4!t'~~~~::'7~ The stability regions for 290° :s; P :s; 310°, 310° :s; P :s; 330°, and 300° :s; 11 :s; 320° are shown in Fig. 5 for the stable 180~ .../1 ('-..-~----: 11 :~~---·- - ---j initial conditions,

CJ : -180 UL, : of attitude motion are now integrated beginning at JI = 262° . and with different initial conditions. It is assumed here ~~ T 2o0 JI~.~I IJfiP,~i l\A\i~lf ':}ff t M\l\,M. J.n ~ AA~& ;;;i r. i\f: ., :i' " ~Jc ,1 ! that the satellite is magnetically stabilized, the boom for \lj.l'ir,4NVJ''fl\:/111~,·!h•1 1•Ci~1½',•' with time as parameter) TIME (hours} are superimposed on the stability charts. Trajectories ob- c) GE DAMPER (k = 8 x 104 DYNE-CM-SEC'RAD) tained with initial conditions of ~ 10°, +1 0°, 0°, and zero Fig. 3 Transient responses for 60-ft boolll and 5-lb end rates in eaeh case are shown in Figs. 5a, 5b, and 5c, inass, 80 days. respectively. It is seen that the attitude motion is driven inside the stable region and stays inside for ,...,g min. If the electro- Because of the existence of perturbations, the exact deter~ magnet and all perturbing effects are turned off during this ruination of the region around q; = -1 is difficult. Therefore, time interval, the satellite is captured. The exact locations to effect satellit€ capture anywhere in the orbit, the satellite of the stability regions and attitude trajectories depend LO ci, l.O ' I -40 -20 -10 0 0 10 ATTITUDE TRAJECTORY (time in minutes) -·v= 290° -·= 310° ,-- V: JOQO --v= 310° -- • = 330° --v = 320° a) -10° INITIAL CONDITION b) +10° INITIAL CONDITION c) 0° IHITIAL CONDITIOH Fig. S Attitude trajectories, of different initial conditions at JI = 262°, superimposed on the stability region for eccentricity of0.2. Page 63 DECEMBER 1969 ENGINEERING NOTES 1459 upon ,., and the initial conditions applied at ,., = 110. In RM-2527, Dec. 1959, The Rand Corp. any practical situation, this must be a real-time operation .. 5 Baker, R.. M. L., "Librations on a Slightly Eccentric Orbit," ARS Journal, Vol. 30, No. 1, Jan .. 1960, pp. 124-126 .. 6 Whisnant, J. M .. and Anand, D .. K .. , "Roll Resonance for a References Gravity-Gradient Satellite," Journal of Spacecraft and Rockets, 1 Zlatoustov, U A et al.., "Investigation of Satellite Oscilla- Vol. 5, No. 6, June 1968, pp .. 743-744 .. tions in the Plane of an Elliptic Orbit," Proceedings of the 11th 7 Whisnant, J .. M .. et al., "The Dynamic Modeling of Hysteresis International Congress of Applied Mechanics, Springer-Verlag, and Application to Damping of Spacecraft Librations," AIAA Berlin, 1966, pp .. 436--439. Paper 69-833, Princeton, N .. J., 1969. 2 Brereton, R. C .. and Modi, V.. J., "On the Stability of Planar 8 Anand, D. K., Whisnant, J. M., and Sturmanis, M .. , "The Librations of a Dumbbell Satellite in an Elliptic Orbit," Journal Capture and Stability of a Gravity-Gradient Satellite in an of the Royal Aeronautical Society, Vol. 70, No .. 672, Dec. 1966, Eccentric Orbit," Rept .. TG-1028, Aug. 1968, Applied Physics pp .. 1098-1102. Lab., The Johns Hopkins Univ., Silver Sp,ing, Md .. 3 Graham, D .. and McRuer, D., Analysis of Nonlinear Control 9 Anand, D .. K., Yuhasz, R. S., and Whisnant, J M .. , "Fur- Systems, Wiley, New York, 1961, p. 70. ther Comments on Attitude Motion in an Eccentric Orbit," • Frick, R. H .. and Garber, T .. B , "General Equations of a TM, Applied Physics Lab, The Johns Hopkins Univ., Silver Motion of a Satellite in a Gravitational Gradient Field," Rept. Spring, Md., in preparation. Page 64 Reprintedft'Orn JOURNAL OF SPACECRAFT AND ROCKETS, Vol. 7, No. 6,June 1970, pp. 697-701 Copyright, 1970, by the American Institute of Aeronautics and Astronautics, and reprinted by permission of the copyright owner Dynamic Mod-eling of 1\lagnetic Hysteresis J.M. WHISNANT,* D. K. ANAND,'f V. L. PISACANE,t AND lVL STURMANIS* The Joh1rn Hopkins Unive1·sity, Applied Physics Laborato1'y, Silver Spri1ig, Md. Magnetic hysteresis rods have been used successfully for da1nping the attitude lllotions of passively stabilized near-Earth satellites. This paper describes the illlplementation of a inodel of inagnetic hysteresis that is suitable for digital computer simulations of such motions. The mod.el is based on the domain theory of magnetization whicb assumes that associated with each dolllain is a shifted rectangular hystezesis loop. Coefficients used by the inodel are deter- 1nined by least-squares fitting data from experimental hysteresis loops, For a type of hys- teresis rod commonly in use, it is shown th.at a sin1plified version of the 1uodel may be used. Results from the theoretical model are compared with expedlllentall) generated loops and show good agreelllent. Nomenclature lly:stciesis rod damping i;ystems are low in cost and com- pletely passive in that they require no sensing devices or elec- a,b == axe;; of incieasiug and del~eru,-ing H in the themetical tronics, use no power, and contain no moving parts. Pas;,ive hyste1 ei;i;; model B ==" magnetic flux density a damping rod damping offerH the significant advantages of high reliability in B,. =_ B(H n), the normal flux densit,y in a rnd and a long lifetime .. B, B(H,) = B(O), the residual flux density in a wd The equations for the attitude motio11s of Earth-orbiting dA = weighted differential area in the Preisach plane Hatellites, including perturbing forceH due to the ;.1,ace en- F =- function minimized in determining ko and the k;;'::; vironment, are well covered in the literature. 4 Consequently H ambient magnetic field component along the longitud- they will not be presented here. Since in general the..'!C equa- = inal axis of a damping rod tions must be integrated numerically by means of a digital Hn normal magnetizing force along t,he axis of a l()d = computer, a model of the damping system is requited. An-H, = O, the iesidual magnetizing force along the axis of a wd alytical models of magnetic hysteresis exist for special cases ko,k,; c•oefficients determined by leaswiquares fitt.ing ex- perimental data to the theoretical model such as a sinusoidally varying magnetic field where only sym- N - parametel' that, determines the mder of the polynomials metric major loops are prnduced.. However, in satellite applications the magnetic field variatiomi produce both P;i P;; - polynomials in te1 ms of H and H,. used in the theoretical maj01 and minor loops, mrn.;t of which are not symmetric = model The modeling of hysteresis damping for satellite applications a,;,/3,; coefficients of H,. when only the normal and rei;idual by digital t-echniques has received considerable attentiou.r.-s experimental magnetization data are used = Accurate models usually are aecompanied by a high cost in ,p weighting function in the theoretical model computing time. Although one technique overcomes most of the problems associated with modeling hysteresis, it requiies Introduction au inline hybrid computer.8 Here, the impleme11tation of a model of magnetic hysteresis that is suitable for digital Rimu- THE method of utilizing in a passive sense the Earth's lation of satellite attitude motions is presented. In orde1 gravitational mid magnetic fields to establish a desired to determine the effectivene&'l of the model, the theoretical spacecraft mientation has been highly succes.~ul. In wme results are compared with experimental data. cases1•2 the damping system consisted of permeable rods of predetennined magnetic characteristic::;, As the rods ex- Modeling of Magnetic Hysteresis perience a varying magnetic field, magnetization and de- magnetization of the rods results in hysteretic losses.3 The An accm ate analytical iepresentation of magnetic hy~teresiH hyste1esis phenomenon is particularly well suited for satellite is extremely difficult, if not impos.~ible, thereby necessitating applications since the energy loss per cycle depends on the the use of numerical methods.. Any reasonable representation amplitude of oscillations rather than the rate. For gravity- 1equires a model that includes the ability to preserve the his- gradient and geomagnetically stabilized satellites, the libra- tory of the effect of variations in the magnetic field .. 9 The tional frequencies are compaiable in magnitude to the orbital theoretical model described here is attiibuted to F frequency. Permeable rods also have been used successfully l'reisach16, 11 and is based Oil the domain theory of magnetiza- in removing initial satellite spin before gravity or magnetic tion. It j,,., assumed that the hyst.eretic mat.erial consist." of capture. 1 The spin rate of a satellite with hysteretic damping infinitesimal volume elements, each characterized by a shifted decr=es linearly with time until it reaches zero.. Thus rnctangulai h.yisteresh:. loop with coercive force (a - b)/2 iapid decay of low spin rates may be achieved. aud shift (a + b)/2 where a and b are as shown in Fig. . 1 The volume elements, or domains, can be separated into two Received August, 13, 1969; rnvisiou received February 16, classes11 : 1) domains foI which a a11d b both have the same 1970. This work was done under Navy Conhact, NOw 62-- algebraic sign. The:,c domains have a known direction oi 0604-c. The authors would like t.o thank P P Pardoe who also magnetization when If = O; 2) domains for which a a11d b was involved in the initial analytical work. have different signs. The direction of magnetization fo1 * Associate Mathematician, Space Research and Analysis the..' b need be considere.d.. Thus the model utilizes the Brauch. ?.Iembei AIAA. tri~ngula1-shaped area which is illustrated in J<,ig 2 and Page 65 698 WHISNANT, ANAND, PISA.CANE, AND STUH,\IANIS J. SPACECRAFT IB I Oi ii I I Fig. l Elemental rectangular hysteresis loop. Fig. 3 Non:nal n1agnethation. known as the Prei-;ach plane. If the hysteretic material is demagnitized by an a.c .. decreasing field, the volume elements where dA = ,p(a,b) dadb and k 0 is the permeability of the hy,;- go to positive magnetization fm a< -band to negative mag- teretic material in the Yicinity of the origin. Note that the netization for a> -b This is also shown in Fig. 2 sign of the area for negative normal magnetization was set Starting from the demagnetized condition, if Ji increases negative in Eq. (3). Points 2 and 4, which correspond to from H = O to H = H n then all negatively magnetized ele- H = 0, ai e on the 1e,idual magnetization curve and have mental rectangular loops for which O S a S H n will flip 1esidual magnetization,; B, + and B, - The B, are obtained to positive magnetization. The change in the magnetization from the weighted areas illw,tiated in Fig. 5 and caleulated of the material is thus rnlated to the number of domains who,;e from values of a and b lie in area A, of Fig. 3. If, imtead, JI de- creases ftom H = 0 to H = - il n then all po,;itively mag- B,+ B(O,lln) fH"fo dA (4) netized loops for which - H,. :S b S O will flip to negative Jo -a magnetization,. This time the change in magnetization i,; related to the number of domains whose value,; ot a and b and lie in area A 2 of Fig .. 3. Thus for a change in H, there i-, a o f-b relationship between the corresponding change in magnetiza- B, - = B(0,-11,.) = - J ~ dA ( <;\ '-'J -H,, 0 tion B and an area in the J)rei,;ach plane. A suitable defi- nition of this relationship will yield a theoretical model ot Similarly, the exprn.,sion IOJ any B bNween B(Hn) and magnetic hysteiesis. It is noted that the axes a and b are B(-Hn)is the axes of increasing and decre,1,sing II, respectively. Suppose that for each a and bin the triangular array the1e BUI lln) = kolf + ( H"f" ,pdbda - f Hn f H, ,;:dadb (6) is a weighting function ,p(a,b) that is related to the statistical ' Jo -a H J1; weight, or frequency, of rectangular loops characterized by a For the gene1al case ,,heie JI is inc1ea-sed ftom zero to If,, aDd b. The expression for the area differential in the Preisach decreased to Iii, and then increased to !13, the cone,-ponling plane will then be given by magnetic induction B(//3) i;-: obtained from dA = ,p(a,b)dadb (1) The following, taken irom Ref 9, defines the 1elation,;hip between changes in B and the weighted areas in the Preisach The sign of ea,ch inte.e;ul in Eq. (7) \\a, detenniued by the plane for the theoretical model under consideiation he1e. area boundary line b = -a as illu;-:tiated in Fig 6. Thus If the ambient field component along the axis of a hysteresi;,; the histon ot the effect of variations in the applied magnetic rod is increased monotonicallY from zero to +H.,,, then de- field is being preserve::!. creased monotonically to - Jin, and then increased to + H n From symmetry con:sideration;-:, the weighting t1uwti0:1

ielcb + + + + + + + + + + + + + + + + X b = -Q B(H,Hn) = kolf + L k,,P,j(l-f,Ifn) (9) ' i+i=O Fig. 6 Theoretical 1nodel and net areas used for B(H.) where the P;i(H,H,,) a1e polynomiab of order i + j + 2. koH3 + f 1dA - f 2dA + f3dA. The polynomials through P 20 are listed in the Appendix. The coefficients ko and the k,/s are obtained from a least- square;- fit of Eq. (9) to the experimental magnetization data cients a,, and (3,j for polynomials through sixth order in This data is obtained by generating hysteresis loops, befme If,. are listed in Table 1. The diHcrepancies between Table 1 the rods are placed in the spacecraft, for as many values of and the results of Ref. 9 are due to typographical errors in the Hn as desired. The determination of k0 and the k,/s for latter. two specifie cases is given next The details of one procedme Equations (10) and (11) determine the function to be mini- for performing the weighted area eakulations on a digital mized computer are given in Ref. 9. It i'° uoted that for cp = constant (S = 0), the model F L (Bn - Bn,) 2 + (B, - Bu) 2 (12) described here reduces to that of Rayleigh .. 13 For small all normal and values of H, he represented the sides of hysteresis loops by residual data quadratic cmves The same result i~ obtaine.d by sub- where the subscript e denotes experimental data. The stituting P00 from the Appendix into Eq .. (9) and lettingN = 0. minimization of F, in the least squares sense, yields the de- sired k;/s Consider the experimental hysteresis loops shown Specific Example and Results in Figs. 7 and 8. The normal and residual magnetization data are used to determine the k;/s as listed on each figure Expe1ience has shown that for the t\ pe of rods used in the Determination of the kiJ's along with Eq. (8) is used to pro- APL satellites, use oi the normal the re,;idual magnetization duce the theoretical hysteresis loops also shown in the figures data on!\ is sufficient to accuratel1 dPte1 mine the k;/s. The In the general case, the restriction of using only the normal rod~ a1 e approximately O. 1 in. in diamete1 and consist of AEM and residual experimental magnetization data is removed and 47 50, a nickel-iron alioy The rods studied varied in length many data points along each hysteresis loop may be used to from 30 to 54 in, Fm this case, the po-;itive normal and re~- dete~mine the k;/s The minimization of F was achieved iduaJ values of B have the following form after changing Eq. (9) to orthogonal polynomial form. J,,._;· Several computer experiments indicated that N = 4 (sixth- B(H,,.Il,.) = B,,+ = kolln + L k;,(a;;Hni+H2) (10) 01der polynomials) wa.s the optimum choice. A sample i+i=O re:sult is shown in Fig 9. A B(Jlr,lin) = B,+ = L k,/{3,,Jlni+i+ 2) (l l) Evaluation of the Model i+i=Cl }'or negative values of B, Bn - and B. - are defined similarly. The agreement bet\\ een the theoretical model and experi- Thu,; the polynomial;.; Pd listed ill the Appendix have ie- mental loops is good for the type of hystere,i;a rods cmrently duced to the form a,Ji n,-.-;+2 and /3;Jf,,i+;+2 The coeffi- Table l Coefficients of Hni+1+ 2 in the determination of B" + and B,+ •• = 1\42 25 j koo= 20,215 51 l ct';.7 .i = I 0 2 3 4 ,oo.l i = 0 ., ,., 2; ;3 4 ; /u" 16/1.'i ~/U 11:~ 4 1]0 4/15 213 4 ilii 8 4,-; Fig. 7 Cmnpari-.,,, 4/5 4/1-i son bet ween the- 4 16 'l~ oretical and. ex- jol---+------1---.,E--h.t'"--l----+-- ., peri1nental ioops, 30-ino r-od, 1V = Oo .i = 0 3 4 0 1 '2 l l(i 1/20 1/30 r i 1/2 l 'f, l 1/20 EXPE,RIME-NTAL LOOP 7 /12 11 '6(1 4 -t THEO-RETICAL MODEL .-, 3 14 13 {j{} I I I 4 31 /:10 -C 1 Page 67 700 WHISNANT, ANAND, PISACANE, AND STUIL\'IANIR J. SPACECHAFT 2500•r---.---.-----,--~--~-~---~ ko = 2134 24 koc = -2476. 29 ko1=-01233 lc10'"'283,533 83 ko2 = -65,37i 74 1000 '11 = 0 7795 +---J.f--+---.i---l k10 = -578,556 78 -lOOOt-------1---+----A'------+--~I e----l 0 0, 05 0. 10 0, 15 0. 20 0 .. 25 : l H (oersteds) I- EXPERIMENi AL LOOP Fig. 11 Uesults from a sin~ulation of a near-Earth sateliite, I • THEORETICAL MODEL 46-in. rod. I -0.3 -0 t O l 02 03 H (oersteds} unsymmetrical minor loops for a different I od i,; :,;hown in Fig. 8 Cmnparison between them·etical and experimental Fig. 10. The maj01 limitation on the model is that the ac- loops, 30-in. rod, N = 2. curacy decreases for cases where the rods become saturated. However, it is usually desiiable (and pos5ible) to choose rods that do not become sat.mated anywhere in orbit. The model being used in ;;ome of the APL ;;atellite:s For those rods, it is also may be used to simulate i~JOps generated by artificial sufficient to use only the normal and residual magnetization hysteresis devices. 14 A comparison between theoretical and data, as described previou,;ly, in deteimining the k,/'f>. Fig'f>. experimental loops for such a device, using all the available magnetization data and N = 4, is shown in Fig. 9. Agree- ment with those types of hystere3is loops, usually more rec- --- EXPERIMEHTAL LOOP tangular in shape, is not as good as that shown in Fig. 9 •••••THEORETICAL MODEL when only the normal and residual experimental magnetiza- tion data are used. The hysteresis model described here has been p1ogrammed in subroutine form and is currently being used in the "Digital Attitude Simulation (DAS)" computer program .9 DAS is a large-angle nonlinear simulation of the attitude motion of a i Ot----t--+-f----+---+---1--f-------l ... spacecraft.. Hysteresis loops generated by DAS during a simulation of a near-Earth (580 naut miles) satellite are shown in Fig .. 11. B having been determined, the simulated torque due to the interaction of a hysteresis rod with the ambient magnetic field may then be computed and is propor- tional to B X ii. In orbit, the component of ii along the H (oented•) axis of a rod frequently reverses itself, resulting in minor loops such as the one in Figure 11. Unfortunately, in-orbit Fig. 9 Comparison between theoretical and experimental experimental data corresponding to the theoretical results loops from an artificial hysteresis device, 1V = 4. shown in Fig. 11 are not recorded. The only relevant in· orbit experimental datum available consists of a time history 7 and 8 illustrate the comparison between experimental and of the spacecraft's attitude motion. Hence, attitude results theoretical hysteresis loops for a 30-·in. rod for different size from DAS using the theoretical hysteresis model may be majm loops and different values of N. A comparison between compared with the expeiimental attitude data. Previously, • • • • • FLIGHT DAT A Fig. 10 Compa1·- ison between the- oretical and ex- perimental minol' loops, i'V = 1 • - TIME, UT ksec BOO•t-'- --+-r-----c.l,~--+---- f'ig. 12 Compal"ison of simulation and flight i·esults for a ~g·~1---+----o~.1---0~2---~03 near-Eal'th satellite with magnetic hysteresis daniping, day H (oersteds} 141, 1966. Page 68 JUNE 1970 DYNAMIC :.\10DELING OF MAGNETIC HYSTERESIS 701 DAS 1e,mlts ha, e shown general agieement with attitude References data from nea1-earth satellites with other forms of energy dissipation. 15 A comparison between simulation results and 1 Fischel!, R E, "Magnetic and Gravity Attitude Stabiliza- flight data for a near-Earth satellite with magnetic hysteresis tion of Earth Satellites," CM-996, May 1961, Applied Physics Lab, Johns Hopkins Univ .. , Silver Spring, Md. damping is shown in Fig. 12. The agreement between the 2 Anand, D. K et al., "Gravity-Gradient Capture and two results suppo1 ts the rnlidity of using this hyste1eisis Stability in an Eccentric Or bit,'' J ownal of Spacecraft and Rockets, model. VoL 6, No. 12, Dec 1969, pp. 1456-1459 Costwise, attitude simulation runs fo1 near-Earth satellites, 3 Fischell, R .. E , "Magnetic Damping of the Angular Motions including the effects of external perturbations, cost less than of Earth Satellites," ARS Journal, Vol. 31, No. 9, Sept .. 1961, pp. $± per orbit The runs took 50% longer than the same simu- 1210-1217 lations would have taken without hysteresis. The satellites 4 Frick, R H and Ga1ber, T. B., "General Equations of considered have rods along each of two orthogonal axes .. Motion of a Satellite in a Gravitational Gradient Field," RM- For satellites with rods along three axes or one axis, the simu- 2527, Dec .. 1959, The Rand Cmp., Santa Monica, Calif. 5 lation cost would change proportionately. Hence, while Magnetic Hysteresis Damping of Satellite Attitude Motions, Doc .. 64SD5242, Vols .. 1 and 2, Nov. 1964, General Electric Co. use of this hysteresis model is expensive, the cost is not pro- 6 Vanderslice, J. L., "Dynamic Analysis of Gravity-Gradient hibitive. Results of an investigation into cost-accuracy Satellite with Passive Damping," TG-502, June 1963, Applied tradeoffo indicate that the cost of simulating hysteresis can Physics Lab, Johns Hopkins Univ., Silver Spring, Md. probably be halved for only a slight loss in accuracy. 7 Chen, Y., "The Damped Angular Motion of a Magnetically Oriented Satellite," Journal of the Franklin Institute, Vol. 280, No. 4, Oct .. 1965, pp .. 291-306 .. Appendix: Evaluation of the 8 Gluck, Rand Wong, A., "Inline Hybrid Computer for Simu- polynomials, PtiH,Hn) lation of Passively Stabilized Satellites," Journal of Spacecraft and Rockets, Vol. 6, No. 7, July 1969, pp .. 812-818. 9 :s; + :s; Pardoe, P P , "A Description of the Digital Attitude Simu-For O i j 2, substituting Eq .. (8) into Eq. (6) and lation," TG-964, Feb. 1968, Applied Physics Lab., Johns Hopkins per/01 ming the indicated integrations yields the following Univ., Silver Spring, Md. polynomials .. 10 Becker, R. and Doring, W., Ferromagnetismus, Edwards Brothers, Ann Arbor, Mich. 1943, pp .. 218-228. Poo(H,Hn) (Hn2/2) + HnH - (JJ2/2) 11 Preisach, F., "Uber die J\1agnetische Nachwirkung," Zeit- schriftfur Physik, VoL 94, 193.5, pp .. 277-302. Pm(H,Hn) (Hn3/6) + (Hn2H/2) + (HnH 2/2) - (H 3/2) 12 Biorci, G. and Pescetti, D.., "Analytical Theory of the Be- havior of Ferromagnetic Materials," Nuovo Cimento, Vol. 7, No. 6, March 19.58, pp. 829-842 p (H H) = lln4 + Hn 3H + Hn 2H 2 + HnH3 - 7H 4 13 Bozarth, R. M., Ferromagnetism, Van Nostrand, Princeton, 02 ' n 12 3 2 3 12 1951, pp. 489-494 14 Alper, J .. R and O'Neill, J, P., "A New Passive Hysteresis Pio(H,Hn) (Hn3/2) + (Hn2H/2) (HnH 2/2) + (H 3/6) Damping Technique for Stabilizing Gravity-Oriented Satellites," Journal of Spacecraft and Rockets, VoL 4, No. 12, Dec .. 1967, pp. (H 4n/6) + (Hn 3H/3) (HnH 3/3) + (H 4/6) 1617-1622. 16 Whisnant, J .. M .. , Waszkiewicz, P. R, and Pisacane, V. L., H 2H 2 H H 3 H4 "Attitude Performance of the GEOS-II Gravity-Gradient _n_ +-"- Spacecraft," Journal of Spacecra.ft and Rockets, VoL 6, No .. 12, 2 3 12 Dec. 1969, pp .. 1379-1384 .. Page 69 GRAVITY GRADIENT STABILIZATION OF SATELLITES IN HIGHLY ECCENTRIC ORBITS by ROBERT E. LOHFE LD Computer Sciences Corporation Falls Church, i7irginia ana DAVINDER K. ANAND University of Maryland College Park, Maryland and J. MILLER WHISNANT The Applied Physics Laboratory Silver Spring, Maryland AAS/ AIAA Astrodynamics Conference Vail, Colorado/July 16-18, 1973 Page 70 GRAVITY GRADIENT STABILIZATION OF SATELLITES IN HIGHLY ECCENTRIC ORBITS R. E. Lohfeld Member of Technical Staff Computer Sciences Corporation 6565 Arlington Boulevard Falls Church, Virginia 22046 D. K. Anand Associate Professor Department of Mechanical Engineering University of Maryland College Park, Maryland 20742 J. M. Whisnant* Mathematician The Johns Hopkins University Applied Physics Laboratory 8621 Georgia Avenue Silver Spring, Maryland 20910 *This Author's work was supported by U. S. Navy Contract N00017-62-C-0604 Page 71 ABSTRACT A gravity gradient satellite in an elliptic orbit experiences planar librational motion as a result of the orbital motion influencing the attitude behavior of the satellite. The amplitude of these oscillations increases as the eccentricity of the orbit approaches O. 355. For this limiting value of eccentricity no stable motion exists. However, if the dynamical equations of motion of the satellite are modified by a variable speed control wheel, gravity gradient stabilization can be used effectively in elliptic orbits with eccentricities approaching unity. This modification to the dynamical equations, the wheel control law and the resulting stable regions are described in detail in this paper. i Page 72 I. Introduction A satellite in a non-circular orbit stabilized by the gravitational gradient across its mass distribution undergoes planar librational motion due to the influence of the orbital motion on the attitude motion. As the eccentricity of the orbit becomes large, the amplitude of the libration increases. When the orbit eccentricity exceeds 0. 355, no stable motion 5 can be found. l- This limits the use of passive gravity gradient stabili- zation to satellites whose orbit eccentricities are substantially less than 0.355. The purpose of this paper is to establish a method whereby semi-passive gravity gradient stabilization can be used effectively in orbits with eccentri- cities significantly larger than O. 355. The method used consists of modify- ing the dynamical motion of the satellite by adding a small variable speed wheel rotating· about the satellite's pitch axis. The control of the \Vheel speed is independent of the attitude motion of the satellite thus preserving the open loop stabilization system and eliminating the need for attitude sensors. The speed of the wheel is dependent only on the location of the satellite in the orbit and is therefore a function only of the time since perigee 6 passage. This technique was first considered for use in the GEOS-C satellite. However, due to a decrease in the expected orbital eccentricity, it has not been implemented for that mission. 1 Page 73 Previously, others have proposed the use of time dependent satellite 7 8 inertias for controlling satellite attitude motions. ' However, the use of a variable speed wheel is simpler, less expensive, and more reliable in practical applications. In this paper the phase plane stability regions for the satellite with- out the control wheel are discussed. The specific control law for the variable speed wheel is derived and new stability regions are obtained. It is shown that with the control wheel, gravity gradient stability can be obtained for eccentricities approaching· 1. 0. 2 Page 74 II. Analysis 4 Satellite oscillations in the plane of an elliptic orbit are described by (1 + e cosi,) (ct2ct>/dv2) - 2 e sinv (dct>/dv) +(1/2)0 sin 2¢== 2e sinf./ (1) where e is the orbital eccentricity, o == 3 [(rx - Iz) /ry], ct> is the pitch libration angle measured from the local vertical, v is the true anomaly and I , I I X y, Z are the principal moments of inertia. This equation has been investigated by researchers using both numerical integration and phase space representations. Consider a satellite with a variable speed wheel rotating about the pitch axis. The moment of inertia of the wheel is defined as I about the spin axis s and the instantaneous speed of the wheel is n. The equation of motion for such a satellite in a gravitational field can be developed using the usual Lagrangrian formulation. The equation for the pitch motion can be shown to be . . I .2. . 2J\ - " . . .. , . . (1 + e COSV) \ ct

, ~! and v for any given eccentricity. Since a closed form solution to Equation (2) has not been obtained, the stability portraits must be determined numerically. The stability portraits can be presented stroboscopically in a two dimensional phase plane which examines the trajectories at a selected 10 value of true anomaly. For example, the numerically obtained values of 4 Page 76 - 2 e sin v £52 + .!. 8 sin 2cp = 0 (5) '} di dv 2 For the case where the eccentricity is zero, the control law vanishes as expected. Thus the stable region of a gravity gradient satellite in a circular orbit either with or without a controlled wheel is identical. In . Reference 6 a similar control law was derived. However, there !1 is a function of M, the mean anomaly, instead of v and the control does not completely compensate for the inhomogeneous term in Equation (2). 6 Page 78 In order to investigate the effects of the variable speed wheel on the stability of the satellite, Equation (5) was programmed on an IBM 370 computer and numerically integrated. The integration was performed for a sequence of initial conditions and was carried out over 65 orbit periods provided that at no time the pitch angle exceeded 90 degrees. If the practical stability limit was exceeded, the integration was terminated and the next set of initial conditions was selected. The maximum stable trajectory then corresponds to finding the maximum initial rate or angle which will produce bounded motion when integrated over a large number of orbit periods. These stable trajectories were evaluated by a stroboscopic method at v = 0, 90, 180 and 270 degrees for 8 = 3 and eccentricities between 0. 2 and O. 8. The trajectories when plotted stroboscopically on a phase plane produce closed curves which are elliptical in shape. The major axis of the ellipse lies along the~ axis for v = 0 and 180 degrees, perigee and apogee respectively. For v = 9 0 degrees, the major axis of the stability ellipse is rotated clockwise on the phase plane and for v = 270 degrees (-90 degrees) the major axis is rotated counterclockwise through the same angle. The plots for v = 0, 90 and 180 degrees are shown in Figure 2 for an eccentricity of 0. 2. 7 Page 79 Figures 2 through 5 show the maximum stability regions for eccentri- cities of O. 2 through 0. 8. The stability regions shown are limited to v = 0, 90 and 180 degrees since the stability region for v = 270 degrees, can be construct- ed geometrically from the stability region for v = 90 degrees. Figures 6 and 7 show the m. aximum velocity dd

0 \ J dV \ I - .. 2 \ I / -4 '- -.6 - .. 8 -l.O -1..2 --1..4 -1..6 -l.8 -2.0 -1.6 -1.4 -1.2 -to - .. 8 - .. 6 -4 -.2 0 .2 .4 .6 8 10 1..2 1 .4 1 .0 (RADIANS) Figure 1. Maximum Stable Phase Plane Without Wheel, e 0, 2, 0 = 3, 0 V:::: 0 12 Page 84 2.0 TRUE ANOMALY 1.8 - - 1. 6 V ~ ~v ~~: ,_. 1.4 --- I'\ 0800 I,"' .... I/ / ~ K(v I/ 1. 2 II' M / J i,,,111"'" --... / ~ i\ 1.0 I '/~ ' 1 ) "' ,\ . 8 ' I /J I ' \ \ \ • 6 I ' ~'! \ \ l .4 I I ~ \ • 2 I ~o I 'I dv \ J j -.2 ,, ) -.4 \ \ I ~ -.6 \ l \ /J' ) \ ) -.8 \ \ \ ', I I \' "~ /1 '" ) -1.0 ~ \ ' V I,,._ ~ V r\.~ ~ l/ -1.2 \ ~ ..,,, V 17 -1. 4 .......... ~ -1. V 6 '" "' ....._ --V -1. 8 -2.0 -1.6-1.4 -1.2 -1.0 -.8 -.6 -.4 -.2 0 .2 .4 .6 .8 1.0 1.2 1.4 1.6 cp (Radians) Figure 2. ::\Iaximum Stable Phase Plane for e -= O. 2, B " 3 (With Wheel) 13 Page 85 2.2 TRUE ANOMALY 2.0 ~ V """"' ~ 1.8 //)~8:0° 1.6 V '\ I /Yy ~; 1. 4 I ' I/ I' 1.2 I .,,.- < / I I'( 1.0 \ I /~ / / \ • 8 I I 1 , I i,.,-- .......... ' ~ . 6 '- \ I .4 t V I/ ' ~ \ 1 . 2 \ '/ , dq> 0 J j dv . I -.2 I ' : -.4 \ /2 \ ) -.6 \ ~ / 'l \ " !llo,,... _.,,,,,- ~ , \ J I -. 8 1 r \ \ ~/ j -1.0 \ __,,,, / -1. 2 I ' I \ I -1. 4 ' \ -1.6 V / -1.8 -2.0 "' ~~ _., V ""-- -2.2 -1.6 -1.4 -1.2 -1.0 -.8 -.6 -.4 -.2 0 .2 .4 .6 .8 1.0 1.2 1.4 1.6 , (l.) Q.) "\ ~ ..b..t. ) . 5 ~ ()) Stable Region llt \ s .4 ::I ..s.. • 3 \ ~ ~ \ . 2 . 1 Y..' . 2 • 3 .4 . 5 .6 . 7 . 8 Eccentricity Figure 6. Maximum Perigee Velocity Versus Eccentricity, 6 = 3 17 Page 89 3.0 • 2. 8 I Unstable Region I 2.6 2.4 I V 0 II 2.2 / '"9- ~ Q) / ..0 2.0 ~ ~ _/~ ~~ ~ 1.8 ,,.-""" .b.... Q 0 1. 6 cu > Q) 1.4 Q) bO 0 Stable Region i 1. 2 s :s:::i ...... 1.0 ~ ~ . 8 . 6 .4 . 2 I . 2 • 3 .4 .5 . 6 . 7 .8 Eccentricity Figure 7. Maximum Apogee Velocity Versus Eccentricity, o= 3 18 Page 90 THE JOHNS HOPKINS UNIVERSITY APPLIED PHYSICS LABORATORY SlA-68-70 SILVER SPRING. MARYLAND September 4, 1970 To: V, L, Pisacane From: Do Ko Anand Subject: Vibration Isolation Introduction The vibration of machinery on board a submarine yields a distinct radiation pattern, The frequency spectrum of this pattern contains infor- mation pertaining to the frequency of the rotating machinery and its 1-6 25 component parts, ' The detection of the radiation pattern therefore can lead to the classification of a submarine, In an effort to decrease the intensity of the radiation it is necessary that the machinery be silenced as much as possible. Assuming that the machinery i.s dynamically well balanced, it can be silenced further by isolating the machinery from the main part of the submarine, The vibration isolation of machinery on board a vessel can be ach:ieved by passive or active methods, The passive techniques include the use of various materials, such as foam rubber, and laminate structures, with superior damping characteristics as well as conventional shock absorbers, The :investigation of such passive isolation methods is reported in literature :in considerable detaiL 7-i5 , 25 Investigations pertaining to active vibration isolation is reported in Ref O 15-24, I 1hese papers investigate the vibration isolation of a structure undergoing single degree of freedom motion, Ruz.i cka and others 1·9 -21 analyze a system consisting of a rigid mass mounted on a hydraulically supported platform, The motion of the mass is used as a feedback signal Page 91 THE JOHNS HOPKINS UNIVERSITY APPLIED PHYSICS LABORATORY SlA-68-70 SILVER SPRING, MARYLAND Page 2 and processed to obtain acceleration, velocity, and displacement signalso These signals control a servo-valve that regulates liquid flow into the chambers of the hydraulic systemo The overall effect is to cancel the resultant motion of the mass. When such a model is developed, the motion s) of the mass is represented operationally by the transfer function, x(s) N(s) y(s; D(s} where s) is the Laplace transform of x(t) , y(s) is the motion of the isolator, N(s) and D(s) are polynomials in s • Depending upon the nature of the feedback and the assumption employed to model the servo-valve, the order of the denominator polynomial D(s) can vary from two to 2N where N is the number of discrete frequencies where certain isolation properties are requiredo The stability of active dampers is considered on the gain-phase or Nichols charts in Ref o 220 Finally the above problem is analyzed for random inputs in ReL 23 and 240 ReL 25 is a bibliography of about 200 documents dealing with the general problem of vibration isolation. This bibliography is available from the author of this memoo The active vibration isolation using tbe counterforce method, as suggested by Dro Gar:cison, is not reported in the literature. Proposed Analysis In order to understand the problems associated with the vibration isolation of heavy machinery, it is suggested that we investigate the following problemo Consider the body B characterized by a certain mass distribution, Page 92 THE JOHNS HOPKINS UNIVERSITY APPLIED PHYSICS LABORATORY SlA-68-70 SILVER SPRING. MARYLAND Page 3 an inertia matrix, and having six degrees of freedomo The body is mounted through springs and dampers on a platform which in turn is isolated from the ship structureo The platform is flexible, ioeo, X = the purpose of an active vibration system to null the vibration of the masso The motion of the mass may be studied by first deriving the equations of motion of the mass and platformo These equations will be nonlinearo The driving force applied to the platform shall be proportional to the dis- placement, velocity, and acceleration of the masso This force may be applied by conventional .shakers or hydraulic systemo The following investigative approach is then usedo 1) Equations are linearized and the system analyzed under the assumption of continuous feedbacko This is the simplest form of the problem and should yield some quick answerso 2) Analysis similar to 1) but with discrete datao 3) The effect of introducing nonlinearities into the systemo Depending upon the complexity of the above analysis, it may be necessary to represent the system by several small discrete parts that are interconnectedo Th:is of course allows us to use the lumped parameter approach which :is well knowno In any such analysis it is important to consider two pointso 'Ihe first has to do with forcing functions o The system under consideration should be analyzed not only with deterministic inputs but random inputs as wello Secondly, it is possible that the vibrations induced in the platform, to null the mass vibration, may be of such level that it has a detrimental Page 93 THE JOHNS HOPKINS UNIVERSITY APPLIED PHYSICS LABORATORY SlA-68-70 SILVER SPRING. MARYLAND Page 4 16 overall effect o Under such conditions it may become necessary to optimize a function that includes not only the mass motion but the platform motion as welL Do K, Anand DKA/ijh Distribution: DKAnand WIBbert JGarrison JKearns RJ-McC onahy SlA File Archives (2) Page 94 THE JOHNS HOPKINS UNIVERSITY SlA-68-70 APPLIED PHYSICS LABORATORY SILVER SPRING. MARYLAND Page 5 Mass Control System Platform J_ Ship Structure Schematic of a Mass to be Isolated by Active Means Page 95 THE JOHNS HOPKINS UNIVERSITY SlA-68-70 APPLIED PHYSICS LABORATORY SILVER SPRING. MARYLAND Page 6 References L Ccimmings, W, , , Thompson, P, 0,, ii Self-noise of a deep submersible in a bio-acoustic investigation off Catalina Island, California/1 J, Acou.st. Soc. of Am,, 44, 1742 (1968), 2, J\IT,angalis, V,, 11 Acoustic radiation from a wobbling piston,'' J, Ac oust, Soc, of Am,, 40, 349, { 1966), 3. Halley, P.., nPreliminary study of resonance effects in submarine low frequency noise spectra, 11 Report No, 260, NEL Report 1500, 4, Wenz, , M,, ''Relation of equipment operating characteristics to the ooderwater radiated sound output of the USS Grouper," No, 202, NEL Report 1500. 5, Gales, R, S., and Thompson, P, 0,, 11Detectability of sounds of submarine auxiliary machinery, 11 No, 266 l\'EL Report No, 1500, 6, Beitscher, H, R,, Gales, R, S., 'jDetectability of sounds of submarine auxiliary machinery, 11 AD 86889L, 7, Huduinac, A, A., "Passive electromechanical vibration suppression,'' fill 123046. 8, J"ames, R, R,, 11 Reduction of ship 7 s noise by viscoelastic damping 9 " J, Aeons, Soc, of Am., 37, 1207 (1965), 9. Soliman, J, L, and Hallam, M, G,, nVibration isolation between non- rigid machine and non-rigid foundations," J, Sound and Vibration., §, yrp. 329-351, (1968), 10, C¾ee-Clough, D., and Waller, R, A,, 1'An improved self-damped pneumatic isolator,"~, Sound and. Vibration, §, pp, 364-376, (1968), lL Snowdon, J", • , 11 Rubberlike rcaterials, their internal damping and role in v:ibration isolation/' .~, Sound and Vibration, ~' pp, 175-193, (1965), 12, Ru.bin, S,, "Design :procedure for vibration isolation on non-rigid supporting structures/ SAE Transactions) 68) pp, 318-327, (1960), 13, Lazan, B, J,, ::Material and structural damping for vibration control, 11 SAE Transaction, 68, pp, 537-547, (1960), 14, Rodgers, P, W,, Parametric :phenomena as appli.ed to vibration isolators and mechanical amplifiers, 11 J, Sound and Vibration., 2, pp, 489-498, ( 1967), Page 96 THE JOHNS HOPKINS UNIVERSITY SlA-68-70 APPLIED PHYSICS LABORATORY SILVER SPRING. MARYLAND Page 7 l5o Wolkoviteh, Jo, HTechniques for optimizing the response of mechanical systems to shock and vibrat :ion, 11 SAE Transactions, 1968, paper 680748 0 160 Bie,s, Do Ao, nFeasibility study of a hybrid vibration isolation system," SAE 'I1ransact:ions, 1968, paper 68075L 17, Scharton, To Do, and Yang, To M", "Statistical energy analysis of vibration transmission into an instrument package, 11 SAE 'I1ransactions, 76, (1967) paper 670876" - 18" Coleman, G, Mo, 11 Impedance and power transmission detection on mech- anically vibrated structures, n AD 133154" 19" Ru.zicka, ,Jo E,, :ive vibration and shock isolation, ii SAE 'I1ransactions, 1968 paper 680747, 200 Several papers by Ruzicka, Schubert, Pepi, and Calcaterra of Barry Controls, Watertrn,rn, Massachusetts o 2L Rockwe 11, T" H, , and Lanther, J, M,, 11Theoret ical and experimental re3ults on active v:ibration dampers/ J" Acoust. Soco of Amo, 36, No, 8} PPo 1507-1515, (1964)0 22" 'I1. Po, 11 The dynamic characterization of elastomers for vibration control applications,rn 8AE Transactions, .TI., 380-386, (1965)o 23" Trikha, Ao Ko.i and Karnopp, Do C", '1A new criterion for optimizing linear vibration isolator systems subject to random input, 11 J" of Engr, for Ind,, Nov" 1969, Karnop, Co} and Trikha, A, Ko' 11 Comparat:ive study of optimization techniques for shock and vibration isolation)'" J·, of Engr. for Ind., :\Tov o 1969, Bibliography tf Secret ) of 200 documents on vibration isolation and related subjects. Page 97 Journal Of The British Interplanetary Society, Vol. 23, pp. 495-508, 1970. Passive Radiation Coolers for Infrared Sensors* D. K. ANANDt and S. A. JETER+ The Johns Hopkins University, Silver Spring, Md., USA and The University of Maryland, College Park, Md., USA The effective use of quantum IR-detectors requires that they be exposed to cryogenic temperatures. This paper studies the feasibility of using passive means to cool these detectors to the necessary temperatures when they are placed on an earth satellite in an equatorial synchronous orbit. The pertinent equations are derived considering the temperature of the cooler focus to be a function of ( 1) radiation from the sun, (2) radiation from solar paddles, (3) radiation from the reflector body, (4) conduction from the spacecraft, and (5) Joulean heating of the detector itself. These equations are solved numerically for the case of a conical reflector. The study shows that the effective operation of passive coolers depends on the radiator being an efficient specular reflector. The chief constraint on the temperature of the detector is the sun angle, an angle of less than 10° being required to yield a temperature less than 215°R for the best combination of surface properties. As the sun angle can approach 30° for a satellite placed in an equatorial orbit, active cooling methods may be necessary. Nomenclature area of cone illuminated by the sun defined in equation (9) area of surface L as seen by the other surface under consideration the determinant defined by equation (23) the cofactor of D obtained by eliminating the L th row and Mth column the solar constant evaluated at the spacecraft the fraction of energy leaving surface m directly incident upon surface L as defined for a specific case in equation ( 5) the shape factor for surface M being exposed to solar radiation fraction of energy from surface K incident on surface L after undergoing m specular reflections irradiation on surface 1 * This work was supported by the Department of the Navy, USA. t Senior Staff, The Johns Hopkins University, Applied Physics Laboratory, Silver Spring, Maryland, USA and Associate Professor of Mechanical Engineering, University of Maryland, College Park, Maryland, USA. t Graduate Student in Mechanical Engineering, University of Maryland, College Park, Maryland, USA. 495 Page 98 D. K. Anand and S. A. Jeter number of nodes on the reflector number of solar paddles coordinate of the surface normal of cone opening coordinate of point labeled 1 radius of conical radiator radius of the detector's tip surface L temperature at the center of the detector's tip temperature of surface L narrow dimension of solar paddle K wide dimension of solar paddle K cosine C1,C2,C3 coordinate system for the blades as shown in Fig. 2 dK (aK + bK)/2 eK the half length of solar paddle K as defined in Fig. 2 f Ai/(A 1 +A2) h depth of conical radiator i,j,k unit vectors representing the spacecraft coordinate system n p - //tan (v) nL local normal to surface L qL(cond.) the heat conducted into node L, it is applied as a parameter qo (Joul.) the heat into the detector from its internal Joulean heating qK* the heat into the Kth solar paddle due to solar radiation qL * the heat into the L th node due to solar radiation qK, space the net heat radiated from solar paddle K into deep space qLK (paddle) the net heat into node L on the reflector from solar paddle K qLm the net heat into node L from node m r the radius of a circle on the end of the detector vector from point O to point 1 sine x,y,z direction cosines of the sun in the spacecraft coordinate system ffp+ the function defined by equations (19), (20), (21), (22) where p and + may take on the values 1,2, ... N and ls, 2s, ... Ns the distance point O appears above the ij plane the absorptivity of the staged surface absorptivity of surface L assumed to be independent of the angle of incidence angle in the staged cooler shown in Fig. 4 the angle of the conical surfaces of the staged reflector the solar angle temperature drop from the center to the outer edge of the exposed end of the detector emissivity of surface L the angle between the normal to solar paddle K and the solar vector 496 Page 99 Passive Radiation Coolers for Infrared Sensors 8 coordinate angle for solar paddle, also angle in staged cooler shown in Fig. 4 I) angle between the satellite wall and the j axis PK distance from the origin of the ijk coordinate system to nearest point on solar paddle K PL reflectivity of surface L, taken to be diffuse unless a subscript, s, is present the Stefan-Boltzmann constant the angle between the local normal to surface 1 and the vector joining points O and 1 0 =0.0 (d2

volved in this study. \/ * Senior Staff, Space Research and Analysis Branch; also -200 0 2 3 4 5 Associate Professor of Mechanical Engineering, University of Maryland. TIME (orbital revolutions} t Associate Physicist, Space Research and Analysis Branch .. Fig. 1 Comparison of analytical and nwnerical solutions i Mathematician, Space Research and Analysis Branch .. of Eq. (I). Page 112 904 J. SPACECRAFT VOL. 8, NO. S 1,0 ~...---1 -, t-11· -.----..;-::::-;;:..... ......3 /s • 13 .... / 14 ,.!,J(

w· 3,.. .J C, z 0 < a: -3 \ w Q. -6 :I - < -9 I I I I 0 0 6 12 18 24 96 102 1~ 114 120 TIME (minuteSI FIG. 3. Transient behavior with K = 1000 dyne-cm, Kd = 500 dyne-cm-sec and no aerodynamic torques 8 Page 118 466 Anand and Whisnant 210° 200° 110° 100° H(t) "V (t) + SPIN AXIS H + ANGULAR MOMENTUM 140° (a) 230° 240° 110° 200° 100° 270° 90° 0.070 2ao0 70° 320° 330° 340° 0 300 FIG. 4. Precessional and nutational motion of spin axis Page 119 Stability and Performance of a Dual-Spin Satellite 467 The practical nutational stability of the satellite during the transient oscillations can also be established by viewing the spin axis relative to the angular momentum vector Fig. 4 shows the nutational or cone angle ¢ as a function of the precessional angle y (see Appendix for equations relating ¢ and y to the Euler angles ai ). As expected, the cone angle ¢ decreases exponentially exhibiting stable oscillations. The steady-state performance was also ascertained by integrating the equations of motion as reported in Ref. [1 J except that here the nutational damping is included. Two sets of spring Ks and damping Kd coefficients were investigated and for each set two values of 71, the angle between the spin axis and orbital plane, were also considered. It is seen in Table 1 that in each case the attitude interpolation errors as well as the pointing error, as defined in Ref. [1], are worse. The maximum attitude interpolation error, Lis, in a 20 sec. time period degraded from 0.21 'to .52 'whereas the pointing error, t'!,,0 in the same time period went from -0.84' to -1.26 'for the weaker spring and damper. Since this particular satellite is to be used for the charting of x-ray emitting sources in the celestial sphere, the effect of the nutational damper on the accuracy of the charting computations is significant. References [l] ANAND, D.K., WHISNANT, J .. M., and STURMANIS, M., "Attitude Perturbations on a Slowly Spinning Multibody Satellite," Journal of Spacecraft and Rockets, Vol. 6, No. 3, March 196Y, pp. 324-326. [2) ANAND, D.K, PARDOE, P.P., and WHISNANT, J.M., "Nutation Damping for a Slowly Spinning Satellite Stabilized with the Use of a Rotor," Johns Hopkins University Applied Physics Laboratory Report TG-997, March 1968. [3} PISACANE, V..L., GUIER, W.H., and PARDOE, P.P., "Dynamical Equations for the Position and Attitude of a Spacecraft with Time Dependent Mass and Mass Properties," Johns Hopkins University Applied Physics Laboratory Report TG-919, June 1967. [4] PARDOE, P.P., "A Description of the Digital Attitude Simulation," Johns Hopkins University Applied Physics Laboratory Report TG-964, Feb. 1968. Appendix Here we develop the necessary equations to obtain the nutational and precessional angles. Consider two coordinate systems, O fixed in the spacecraft body and O1 fixed in 8 inertial space. The transformation between the two systems is (A-1) where Ra is defined in Fig. 1. If we let the body spin-symmetry axis V be the body Y axis we obtain Page 120 468 Anand and Whisnant A A VoB YoB = [n (A-2} and [sina1 cosaj A V0/t> cosa1 cosa2 (A-3) sina2 which gives the spin axis in the inertial system. ¢, the nutational angle, is defined to be the angle between the body symmetry axis, V(t), and the angular momentum vector ii (t) as shown in Fig. 4(a). Hence¢ is given by A A cos¢= V (t),H (t). 08 08 (A-4) To compute the angular momentum vector we first need the body rates wx = a2 COSa3 - al C0Sa2 sina3 WY = a3 + H(t)] (A-8) siny [V{O) - [V(O) .ff(t)]H(t)]. [V(t) - cos¢H(t)l where here iI (A-9) and v (A-10) Page 122 THE JOHNS HOPKINS UNIVERSITY APPLIED PHYSICS LABORATORY SlA-404-73 SILVER SPRING. MARYLAND DM-1491 September 28, 1973 To: K. Potocki From: D. K. Anand Subject: Wave Propagation from Ribbed Structures A submerged and ribbed structure when excited at a point radiates acoustic energy. At certain frequencies, however, a mechanism exists whereby flexural waves are generated that travel to adjacent supports and set them into vibration. These vibrating supports then become sources of sound radi- ation. The propagation of these flexural waves occur freely only in certain frequency bands. Outside these bands, a wave, once started, will decay as it spreads. This phenomena of freely propagating and decaying flexural waves occurs in alternate bands that can be defined by a characteristic propagation constant. The frequency at which the flexural waves begin to excite adjacent supports is often referred to as the coincident frequency. We would like to apply the above notion and try to obtain the fre- quency bands in which free propagation occurs from the vibrating hull of a submarine. In analyzing this problem we note that, when viewing the acoustic field generated by a vibrating structure in the far field, one need not be concerned with the exact shape of the generating structure. It is shown in Reference [1] that the radiated field of a spherical shell asymptotically approaches the radiated field of a point excited plate. For our purposes, therefore, we may examine the vibration of a plate with appropriate constraints. Page 123 THE JOHNS HOPKINS UNIVERSITY APPLIED PHYSICS LABORATORY SILVER SPRING. MARYLAND SlA-404-73 DM-1491 Page 2 The submarine structure can be considered as a plate-like structure having parallel, regularly-spaced stiffeners. This can be initially approximated by a beam on equispaced supports, as discussed in Reference [2]. Consider an infinite beam on equispaced supports as shown in Figure l(a). At the supports are shown rotational springs having a constant of k /2. A free body diagram is shown in Figure l(b). The beam r deflection V(x) is governed by the usual wave equation having a solution given by V(x) = A cos AX+ B sin AX+ C cosh AX+ D sinh AX ( 1) where A4 2 = w ApjEI • Here A is the cross-sectional area, p is mass density. E is Young I s modulus, I is the second moment of area, and w is the frequency of excitation. Under the assumption that the rotation 0(x) is small, it can be approximated by cV(x)/cx. The boundary condi- tions for the pinned beam are 1. V(x) = 0 at X = o, i, k i, 2. c2v(tl r - 2EI c~~tl = 0 at X = 0 ( 2) cx2 k i, 3. c2v(x) r + 2EI c~~x) M = --- at X :::: ;, I 2lx2 EI .) Satisfying these boundary conditions, the constants are found to be Page 124 THE JOHNS HOPKINS UNIVERSITY APPLIED PHYSICS LABORATORY SILVER SPRING, MARYLAND SlA-404-73 DM-1491 Page 3 k J, A r ' l = -c = -2E-I (sin At - sinh At) l '! ;l k J; 2A sinh A/, - _!_.. B = 2EI (cos At - cosh At) (3) k .e D = -2A sin At r + 2EI (cos At - cosh At) J Defining the receptance ~ np as the rotational response at x = p for a moment input at x = n (see reference 3), we obtain Su - ~Vo(xx U]x =.e -- -A(sin "id,+ sinh 11..t) + B cos At + D cosh Ai, J/il/i - [ The propagation constantµ is then defined as cosh µ = - (4) where sinh At F10 = cos At - cosh Al The propagation constantµ is seen to be a function of frequency and, in general, is complex. The three possible forms ofµ are Page 125 THE JOHNS HOPKINS UNIVERSITY APPLIED PHYSICS LABORATORY SILVER SPRING. MARYLAND SlA-404-73 DM-1491 Page 4 f < -1 µ = cosh -1 f l -1 -1 < f < 1 µ = i cos f ( (5) f > 1 µ = iTI + ln[f =F f;~i] I .J If f < -1, the propagation constant is real and the wave decays exponentially. Also since there is no imaginary part, the wave in adjacent bays is in phase and is non-propagating. If f > 1, the wave is still non-propagating although waves in adjacent bays are out of phase by TI. Finally, for the case where -1 < f < 1, the propagation constant is imaginary. This means that there is a phase difference between the motion in adjacent bays. The wave is propa- gating although there is no decay from bay to bay. As an example, we consider the case of a submarine hull whose properties are close to E = 28 X 106 lb/in2, p = 0.285 lb/in3, I= 32 in4, A= 24 in2, and J = 30n. These values yield f = 0.46 for the case of an excitation of 1600 Hz. This indicates that at this frequency it is possible for wave energy to be transferred along the beam thereby causing the vibrating struc- ture to emit acoustic energy from more than one point. A complete analysis requires thatµ be plotted as a function of exci- tation frequency. The results should yield frequency bands in which free propagation is possible. These bands can then be compared to the results obtained on the lofargrams. Also for cases where we have non-propagating and decaying waves we can compare with experimental data that is obtained by recording spatial decay of vibration when a point on a submarine is excited by a shaker. D. K. Anand DKA/mjo Page 126 THE JOHNS HOPKINS UNIVERSITY APPUED PHYSICS LABORATORY SILVER $P~ING, MARYLAND SlA-404-73 Page 5 References 1. Junger, M.C. and Feib, D. MIT Press, 2. Mead, D.J., Free wave propagation in infinite beams, .:;;..:.._;;..;~=-==-.;..:;;:.;;..::;.;;;==., (2), 3, Bishop, R.E,D and Johnson, D,C., Cambridge University Press, 1966. Page 127 THE JOHNS HOPKINS UNIVERSITY APPLIED PHYSICS LABORATORY SILVER SPRING. MARYLAND SlA-404-73 C 11' l A 1 Page 128 THE JOHNS HOPKINS UNIVERSITY APPLIED PHYSICS LABORATORY SILVER SPRING, MARYLAND S]_A-404-73 Page 7 ~: H.D. Black A.C, Cotts G.W. Miner R.C, Morton K.A. Potocki J.A. Razmus A. Samec G.L. Smith C,D. West W.P. Willis R.F. Woodall D.K. Anand Archives (2) SDO Central File SlA File Page 129 Journal of the British Interplanetary Society, Vol. 26, pp. 641-661, 1973. ATTITUDE PERFORMANCE OF SOME PASSIVELY STABILIZED SA TEL LITES* D. K. ANANDt Department of Mechanical Engineering, University of Maryland, College Park, Maryland 20742, U.S.A. J.M. WHISNANT Space Research and Analysis Branch, The Johns Hopkins University, Applied Physics Laboratory, Silver Spring, Maryland 20910, U.S.A. In applications where a high degree of pointing precision is not necessary, the passive and semi-passive stabilization of satellites yields satisfactory results. Some fundamentals of such stabilization are reviewed using the OSCAR, GEOS, DOD- GE, X-RAY and LIDOS satellites (designed, built and launched by The Applied Physics Laboratory of The Johns Hopkins University) as examples. 1. INTRODUCTION IN THE LAST one and one-half decades a variety of scientific satellites have been launched and captured successfully. Once captured, the techniques used to stabilize their attitude motions generally fall into two categories: active or pass- ive. Active methods usually employ on-board sensors, jets, wheels, torquing de- vices, etc. This form of stabilization is expensive and is employed in applications where precision is important. Passive, and sometimes semi-passive methods, on the other hand, are used in situations where a high degree of pointing precision is not necessary. The methods are reliable, inexpensive, long lived, and useful for a wide variety of commercial and scientific applications where limited accuracy suffices. The various methods of passive and semi-passive stabilization are classified with the aid of the chart shown in Fig. l. There are three methods that are popu- PASSIVE & SEMI.J"ASSIVE STAB1LtATJON ,., RA VlTY-GfiAOt EN1 MAGNET1C SPIN .-----~---, I WHF NO WHEEL DUAL HYSTERESIS HYSTERESIS ._,,'\,I-:"-; BAt;. HYSTERF.SIS NUTATlON $! kF ..:S :,>'fiiNG Fig. L Methods of passive and semi-passive stabilization. * This work was done under U.S. Navy Contract NOOOl 7-62-C-0604. t Also Senior Staff, Space Research and Analysis Branch, The Johns Hopkins University Applied Physics Laboratory, Silver Spring, Maryland 20910, U.S.A. 641 Page 130 D. K. Anand larly used, viz, magnetic, spin, and gravity-gradient stabilization. Once initially stabilized in one of these modes, the satellite continues to oscillate or librate. These librations exist due to persistent perturbations such as gravity torques, mag- netic torques, radiation pressure, aerodynamic torques, micro-meteorites, as well as perturbations caused by the damping devices. If these librations are permitted to grow they can destabilize the satellite. It is therefore desirable that any stabili- zation technique include means of damping the unwanted motions. We see from Fig. 1 that damping may be achieved by using hysteresis, time-lag, ball-in-ball, spring, and nutation dampers. The particular one used is dependent upon the type of stabilization and the particular need of the mission. In magnetic stabilization, a magnet is placed in the satellite. As the satellite goes around the Earth, the magnet, which is rigidly connected to the satellite, tends to align itself with the local direction of the Earth's magnetic field hence achieving magnetic stabilization. It is interesting to note that if a magnetically oriented satellited is placed in a polar orbit it rotates at an average rate of two revolutions per orbit about the Earth. Satellite 1-B (International name 1960 Gamma 2) launched in 1960 was the first APL built satellite to successfully utilize magnetic techniques as a means of attitude orientation and stabilization. Since then, several other satellites have used this method but the method was finally abandoned owing to the rather poor orientation achievable. Although magnetic stabilization lost favour, the use of an electromagnet for inverting and manoeuvr- ing became common on satellites that were stabilized by other means. Spin stabilization exploits the gyroscopic property that we have learned in dynamics. The use of spin stabilization allows the pointing of a satellite, in inertial space, to be fixed. It also allows the scanning of a scene with a period that is an integral of the spin rate of the satellite. Basically, spin stabilization involves the obtaining of a momentum, via spinning, whose magnitude is large in comparison to the perturbative effects. Instead of spinning the satellite, it is often desirable to obtain the necessary momentum by introducing a spinning wheel but not spin- ning the main spacecraft body. In still other applications, the main body is spin- ning to provide a part of the momentum and the wheel provides the balance. These cases are often referred to as dual spin stabilization. The first APL satellite, launched successfully in 1965, that was spin stabilized was DME-A (International name l 965-98B). The precessional and nutational motions were damped using a pendulum type of passive damper. The gravity-gradient stabilization of a satellite renders one face of a satellite permanently oriented toward the Earth. In such systems, the satellite rotates at the rate of one revolution per orbit as compared to two for magnetic stabilization and zero for spin stabilization. The first experiment in gravity-gradient stabiliza- tion was conducted on the TRAAC satellite (International name 1961-Alpha Eta 1) launched in 1961. However, the experiment could not be fully performed owing to the malfunction of the drive motor that was to erect the boom necess- ary for the proper inertia ratio needed. Then after several experimental satellites, 5A-3 (International name l 963-38B) became the first satellite to be captured and stabilized in this mode. This method was then used for the first time in a fully operational satellite, SBN-2 (International name l 963-49B ). The early satellites that were gravity-gradient stabilized employed either magnetic hysteresis or mech- anical hysteresis, via a lossy spring, for the damping of excessive librations. Satel- lite SC-1 (International name 1964-26A) became the first APL satellite to show that small magnetic rods could be successfully used for the damping of satellite motions. Such damping coupled with the gravity-gradient mode is now routinely used in the operational navigation satellites. Some of the more interesting examples of satellites that these authors have been concerned with are the OSCAR, GEOS, DODGE, X-RAY and LIDOS satel- lites. These and all other satellites discussed in this paper were designed and built by The Applied Physics Laboratory of The Johns Hopkins University. Before we get into the details of the satellites, it is perhaps appropriate to say a few words about the co-ordinate system, dynamics and other analytical work done that is 642 Page 131 Attitude Performance of Some Passively Stabilized Satellites necessary in the pre-launch design studies. The reference frames used to derive the equations of motion are shown in Fig. 2. We have an inertial reference frame, local reference frame and body reference •,, ',, Fig. 2. Reference frames used to derive equations of motion. INERTIAL REFERENCE FRAME ASCENSION OF ' -..., I' ASCENDlNG NODE '--._ i'-y INCLINATION ' '// ' ' frame. The location of the center of mass relative to the inertial origin determines the orbit. The orientation of the body reference frame relative to the local frame determines the satellite attitude. The differential equations governing the large angle librational motions of a spacecraft are nonlinear and coupled and must in general be integrated numeri- cally. With this in mind, the dynamical theory for the trajectory and attitude motion of a spacecraft in the vicinity of a gravitating mass was developed in a form which is suitable for solution by digital computer [ 1, 2]. In that develop- ment the spacecraft is considered to have a general configuration with mass as an explicit function of time and the mass distribution as a function of time and of the generalized co-ordinates and velocities. The attitude is specified in terms of various Euler angle sets. A digital computer programme entitled 'Digital Attitude Simulation (DAS)' which is based on the above analytical development had been developed and is applicable to a wide class of satellite configurations (3]. DAS includes the effects of gravity-gradient torques, variable speed rotors, residual magnetic dipoles, solar radiation pressure, thermal distortion of the stabilizing booms, and both passive and semi-passive dampers. The geomagnetic field model is described in terms of spherical harmonics with a maximum order of seven. The DAS thermal bending model for the stabilizing booms includes both bending in the plane of the unde- formed boom and the Sun and bending normal to the boom-sun plane. Solar radiation pressure forces on the deformed booms, end masses and spacecraft main body are combined so as to produce the total radiation torque about the instanta- neous center of mass of the spacecraft. This simulation has been used for studies of all the satellites reported here. The details of the analytical work and computer programmes are well documented in various Applied Physics Laboratory reports. 2. THE OSCAR-14 SATELLITE OSCAR-14 is one of the navigational satellites and is shown in Fig. 3. It was de- signed and built by APL for the U.S. Navy and was launched in September 1967 in a polar, circular orbit with an altitude of 600 miles. It was powered by solar cell generators and nickel-cadmium batteries. The characteristics of the satellite and orbit appear in Table 1. The satellite was stabilized in the gravity-gradient mode using a 100 ft. self-erecting boom, manufactured by the DeHavilland Com- pany with a 2.8 lb. end mass. There is no preferred orientation about the yaw axis. 643 Page 132 D. K. Anand Fig. 3. OSCAR 14. TABLE 1. Physical parameters of OSCAR-I 4. Orbit Semimajor axis, a 1.169 Ro Eccentricity, e 0.004 Inclination, i 89.3° Spacecraft Boom length 100 ft. End mass weight 2.8 lbs. Area 269 cm2 Damping was achieved by magnetic hysteresis losses in permeable rods. As the rods experience a varying magnetic field, magnetization and demagnetization of the rods results in hysteretic losses. The hysteresis phenomenon is particularly well-suited for satellite applications since the energy loss per cycle depends on the amplitude of oscillations rather than the rate. For gravity-gradient and geo- magnetically stabilized satellites, the librational frequencies are comparable in magnitude to the orbital frequency. Hysteresis rod damping systems are low in cost and completely passive in that they require no sensing devices or electronics, use no power, and contain no mov- ing parts. In order to perform pre-launch design analyses via the computer, a model of hysteresis damping for satellite applications was developed [ 4] . The model is valid for both hysteresis rods and artificial hysteresis generating devices. The agree- 644 Page 133 Attitude Performance of Some Passively Stabilized Satellites ment between theoretical and experimental loops is shown in Fig. 4. As a further test, actual flight data from an OSCAR satellite was compared with theoretical attitude results from the DAS computer programme. The pitch and roll angles -- EXPERIMENTAL LOOP • THEORETICAL MODEL i Of----l--f-----1--+---+-I--+--~ ., H (oerded:s} Fig. 4a. Comparison between theoretical and experimental loops from an artificial hysteresis device, N = 4. J'~ml-.....\---t+'=i=":=--+--J,"--+--1--1 1---V---'----r---l'<--i--t---:--~l O 0.05 O. lO 0.15 0.20 0.25 H (oeofe1:h} Fig. 4b. Results from a simulation of a near-earth satellite, 46 inch rod. were theoretically predicted to stay bounded by ±30° and ±10° respectively. Agreement in pitch and roll motion with flight data is shown in Fig. 5. • FLIGHT DATA --- StMULAT,UNRESULTS ! ! 0 :,r 0_ 0: -30 TIME. UTksec Fig. 5. Comparison of simulation and flight results for a near ~arth satellite with magnetic hysteresis damping day 141, 1966. 645 Page 134 D. K. Anand We conclude by noting that such a stabilization method yields satisfactory results for the navigation satellites and is now in routine use. 3. THE GEOS SATELLITE The repeated success of passive gravity-gradient stabilization (GGS) systems at low altitudes has fostered interest in their use for communication and meteorolo- gical satellites at higher altitudes. At synchronous altitudes the restoring toque (which is inversely proportional to the cube of the distance of the spacecraft from the center of the Earth) is two orders of magnitude smaller than at low alti- tudes. For this reason, verification of the performance of GGS systems at low altitudes, with the intent to improve the modeling of the control system perform- ance, is important to successful GGS of high-altitude spacecraft. The GEOS-II (Geodetic Earth Orbiting Satellite-II) achieves geocentric stabilization by use of such a GGS system [5]. Although earlier work on GEOS-I showed general agree- ment between flight performance with digital simulation results, a failure in part of the attitude detection system somewhat limited that analysis [ 6] . However, flight information from GEOS-II substantiated the validity of using a digital simu- lation in performing design analyses. GEOS-II, shown in Fig. 6, was designed and built for NASA as part of the National Geodetic Satellite programme to study geometric and gravimetric geo- desy. The most severe requirement on the stabilization system was imposed by the optical beacon geodetic system, which was designed on the assumption that the deviation from the local vertical could be kept within 5° GEOS-II has a single motorized extendible boom; at its end is a magnetically anchored eddy-current damper. An important consideration in the selection of the magnetically anchored eddy-current damper was that it had been successfully END MASS WITH EDDY-CURRENT TO EARTH Fig. 6. GEOS·II spacecraft. 646 Page 135 Attitude Performance of Some Passively Stabilized Satellites demonstrated by the performance of GEOS-I. The damper is a magnet assembly which is free to lock on to the magnetic field of the Earth. Rotation of the mag- net assembly relative to a conducting spherical shell induces eddy currents in the conductor which impedes the librational motions of the spacecraft. This system provides bistable equilibrium about any axis normal to the local vertical. As de- sired for thermal uniformity, there is no preferred orientation about the longitud- inal axis. Proper stabilization can be attained if the extension of the boom is ini- tiated when the boom axis is pointing upwards and within 5 5° of the local verti- cal. To insure right-side-up capture before boom extension, an electromagnet whose axis is parallel to the boom axis was added to GEOS-II. Thus, while near the north pole and in view of the command station at the Applied Physics Labor- atory, the boom axis would be nearly aligned with the local vertical. The attitude is determined if two independent vectors are specified simultane- ously in both the satellite and local vertical reference systems [ 7]. For GEOS-II, onboard measurements determine the orientation of the satellite-sun line and magnetic field vector in the satellite reference system. These vector components, six scalar quantities in all, provide redundant information for the evaluation of the three independent Euler angles of the transformation matrix. To measure the geomagnetic field components, a three-axis set of second-harmonic flux-gate mag- netometers is employed. The satellite Sun line vector components are measured by a system of analog solar cells composed of 11 detectors with approximate co- sine response and two linear detectors with design cutoff at particular solar angles. We note that this scheme is used for most APL satellites. When the satellite is in the Earth's shadow, or when the angle between the Sun and magnetic field vec- tors becomes small, the attitude detection system no longer works. However, those two events are easily identified, and data taken during such periods is de- leted. The flight performance of GEOS-I and pre-launch analyses of GEOS-II indi- cated that the system would meet the two stabilization requirements; operational status within 15 days after launch and a maximum steady-state libration ampli- tude of 5°. GEOS-II was launched on 11 January 1968 and titled Explorer XXXVI. The satellite characteristics are shown in Table 2. The flight performance of GEOS-II on different days is shown in Fig. 7. A table showing some quantitative flight data appears in Table 3. We note that the angle off vertical was 5° or less 96% of the time and less than 7° all the time. TABLE 2. Physical parameters of GE OS-JI. Orbit Semimajor axis, a 1.208 R0 Eccentricity, e 0.032 Inclination, i 105.8° Spacecraft Launch configuration 28.1-ft. configuration I xx=I yy, slug-ft2 20.9 I xx=I yy=341. 5 I 22, slug-ft 25.6 I 22= 25.6 Weight, lbs 466.0 Damping co-efficient c = 70,000 dyne-cm-sec Radius of main body equivalent cylinder = 63.5 cm Height of main body equivalent cylinder =78.7cm Maximum thermal bending tip deflection = 8.01 cm Residual magnetic dipole components in spacecraft co-ordinate system =470, 0, 171 pole-cm The interesting phenomena of roll resonance was observed for this particular satellite. It was seen that the solar pressure tends to induce large roll angles caused 647 Page 136 D. K.Anand ,D~AY 38 ·EDAY 39, t. .. ..-•4 .. ' ... - _L ...... I 1:; ·E:LIT ~-5 EE t=E Hff EE EE 49891 5049l 50893 5U93 TtME {UT Se-conds} Fig. 7a. Flight performance of GEOS-II, three weeks after capture. ~~fj~~~ , ~53 i2 70§ HIO .:! "90 a a §J ;; 0 §] § § 215 295 535 555 620 640 TfME (UT minutu) Fig. 7b. Flight performance of GEOS-II, day 137, 1968. TABLE 3. Quantitative Flight Performance of GE OS-IL Number of Frequency Cumulative overt data points* % frequency,% 00 - 10 7 1.6 L6 10 - 20 62 14.3 15.9 20 - 30 130 30.0 45.9 30 - 40 140 32.3 78.2 40 - 50 78 18.0 96.2 50 - 60 14 3.2 99.4 60 - 70 3 0.7 100.0 * Data points recorded at one-minute intervals on days 135-138, 254 and 255, 1-968. by resonance condition [ 6 J . This was later studied and confirmed analytically [8]. It was seen that certain combinations of orbital parameters tend to cause roll resonance. As an aside we briefly discuss the thermal problem of this satellite. Since there was no yaw control, a bias in the yaw orientation tended to heat one side of the 648 Page 137 Attitude Performance os Some Passively Stabilized Satellites satellite more than the other side. This caused the electronics on one side to get hot and thereby impede satellite interrogation. In the next GEOS satellite this was remedied by installing two heat pipes connecting the hot and cold sides of the satellite. Flight data showed satisfactory results [9]. GEOS-C, currently being designed and built is discussed in Reference 10. 4. THE DODGE SATELLITE The DODGE (Department of Defense Gravity Experiment) satellite shown in Fig. 8 was designed and built for the Department of Defense to meet two object- ives. First, to demonstrate gravity-gradient stabilization near synchronous altit- udes and secondly to determine the adequacy of theoretical analyses by correla- tion between simulation results and experimental data [ 11]. On 1 July 1967 DODGE was launched into a near synchronous orbit and achieved gravity-gradient stabilization on 15 July. Fig. 8. The DODGE satellite. DODGE is equipped with ten extendible booms with end masses so that its configuration can be varied in orbit to obtain either two axis or three axis stabili- zation. The 'plus', the 'times', the 'dumbbell', and the 'dumbbell with rotor' con- figurations are illustrated in Fig. 9. These are the configurations most frequently discussed for gravity-gradient stabilization near synchronous altitudes. A constant speed rotor and a magnetic dipole were included to augment yaw stabilization. Four damping systems are available to dissipate librational energy; an enhanced magnetic hysteresis damper, an eddy current gimballed-boom damper, a magnetic hysteresis gimballed-boom damper and time-lag magnetic damper. The availability of multiple control systems provides a high degree of reliability and the opportu- nity to perform many experiments. To provide for a thorough evaluation of each configuration and damper, the mass properties of the spacecraft can be changed by individually varying the length of each boom. A detailed list of the character- istics of the spacecraft is given in Table 4. 649 Page 138 D. K. Anand l LOCAL VERTICAL PLUS BOOMS }LUS BOOM \ LOCAL VERTICAL ORBIT PLANE r I Mll'ii++l...,,,_~4"-44""~~"-""-"'-"i -15 180 ,t, oi--~~~~tft'--'-f''cftcc-:i\-J\--t1t-t-/1"'!'th"4?'"1-+"'7<1'-+H-+t-ffi -180 JO 15 Q '-=-'--'-Cl'-~--CL~.~~~~~'---".-'...UWL-LLOL...<..--L;._,__-'-"/ b) FOUR 57-INCH HYSTERESIS RODS 0 t~ t :,_:: c;J j' \', V• -10 L :o ~e 2, 30 36 42 48 54 vo 66 12 TIME {hours) Fig. 15. Transient responses for 60-ft. boom and 5 lb. end mass (LIDOS satellite). sec/rad) similar to that used for the GEOS satellites. Although the results with the GE damper are somewhat superior than those obtained by magnetic hysteresis damping, scheduling limitations dictated use of the latter. Inversion manoeuvres were simulated using a dipole magnet pointed in a direction opposite to the boom. Satisfactory results were obtained using a magnet of strength 44,000 pole-cm. It was important to determine the region of stability before attempting to capture the satellite. For orbits with eo. l, the foregoing procedure does not always insure capture, since \01=_ 1 is out of the stable region for certain values of the true anomaly. Speci- fically, when e = 0.2, the point \01= _1 is not inside the stable region anywhere in the orbit except for a small time around apogee [ 16, 17] . This is shown in the stroboscopic study of Fig. 16. Additionally, the study of the regions of stability with different parameters and including perturbing forces is reported elsewhere. It suffices to note, however, that the region of stability obtained is larger than that reported before. 658 Page 147 Attitude Performance of Some Passively Stabilized Satellites .p!d"9'e«5f H++-+----<,------1+-'--t~. 20 '\",,\ ~ I ,f"f e"· ·:,) /' w " l .i.- '.0 (bi STABLE REGIONS ATV= n/2 FOR e= 0.2, w 2 =3. -1.0 (al STABLE REGlONS AT t.'"' 0 FOR e"' 0.2. w 2 = 3. F° lf+·T·n\\" ,. \ I__ \. '., : // /, ./ . , ':·~-~' -L-,; :'!1Y// ~ ll H! ,di :-:-:-ABLE REGIONSA7 ,,.. ,.::y ,.,,, :.:... _.2,,.3_ Fig. 16. Results of stroboscopic study for LIDOS. Because of the existence of perturbations, the exact determination of the region around t.p k cl is difficult. Therefore, to effect satellite capture anywhere in the orbit, the satellite must be manoeuvred into the stable region. The manoev- ring is achieved by using an electromagnet. The satellite is magnetically stabilized, and the boom is erected while the electromagnetic is still on. The magnetic torque opposes the gravitational torque and drives the satellite into the stable region, at which time the electromagnetic is turned off and capture is effected. The stability regions for 290°¾ 1J,;;;; 310° ¾ 1J,;;;; 330°, and 300°,;;;; v,;;;; 320° are shown in Fig. 1 7 for the stable initial conditions t.p = 18°, t.p '=O at peri8ee. The equations of attitude motion are now integrated beginning at v = 262 and with different initial conditions. It is assumed here that the satellite is magnetically stabilized, the boom for appropriate inertia is erected, and the electromagnet is on. The resulting trajectories (ip and t.p 'with time as parameter) are superimposed on the stability charts. Trajectories obtained with initial conditions of-10°, +10°, 0°, and zero rates in each case are shown in Figs. 17a, 17b, and 17c, respectively. It is seen that the attitude motion is driven inside the stable region and stays 659 Page 148 D. K.Anand IG I I I 1/ ;( -v = 300° -- V :::c )10° --,,,::: 320° \ai -10° INITIAL CONDITION (bl -t10° INITIAL CONDITION le! o 0 INITIAi.. CONOITlON Fig. 17. Attitude trajectories, of different conditions at v =262°, superimposed on the stability region for oocent.ri.city of 0.2. inside for 8 min. If the electromagnet and all perturbing effects are turned off during this time interval, the satellite is captured. The exact locations of the stability regions and attitude trajectories depend upon v and the initial conditions applied at v = v0 • In any practical situation, this must be a real time operation. The LIDOS satellite was launched in August 1968. Unfortunately, the satellite did not obtain the necessary orbit. Instead it was deposited into the ocean. Although much was learned analytically, no experimental information was obtained. 7. COMMENTS A review of some of the satellites launched by APL shows that passive and semi- passive methods of satellite stabilization have been successful. These methods are generally Lnexpensive and quite satisfactory for many applications including scientific missions; photography, and a host of commercial applications. There are of course several refinements in passive and semi-passive stabilization that enhance the benefits of such methods. For example, the addition of a wheel whose rotation rate can be modulated to take an offending term out of the eccent- ric orbit equation is under consideration [ l 0, 18] . The use of large rigid structures L11 the form of a dumbbell have still not been tried. Then the use of several rotors for fine attitude control needs to be tried. Here, we have given the highlights of the scientific achievements of the satellites. Needless to say, much of the analytical work necessary to support such analysis has been deliberately suppressed. The details of this important adjunct can be found in the references cited. REFERENCES 1. V. L. Pisacane, W. H. Guier, P. P. Pardoe, 'Dynamical Equations for the Position and Attitude of a Spacecraft with the Time Dependent Mass and Mass Properties', JHU/APL Report TG-919, June 1967. 2. D. K. Anand, J.M. V'/hisnant, 'Generalized Equations for the Position and Attitude of a Multiply Connected Spacecraft 1. The Dynamic Equations', JHU/APL Report No. TG- 1163-1, Aprii 1971. 3. P. P. Pardoe, 'A Description of the Digital Attitude Simulation', JHU/APL Report TG- 964, February 1968. 4. J.M. Whisnant, D. K. Anand, V. L. Pisacane, M. Stunnanis, 'Dynamic Modelling of Mag" netic Hysteresis', Journal of Spacecraft and Rockets, 7, 697-701 (1970). 660 Page 149 Attitude Performance of Some Passively Stabilized Satellites. 5. J.M. Whisnant, P.R. Waskiewicz, V. L. Pisacane, 'Attitude Performance of the GEOS-11 Gravity-Gradient Spacecraft', Journal ofS pacecraft and Rockets, 6, 1379- 1384 (1969'). 6. V. L. Pisacane, P. P. Pardoe, B. J. Hook, 'Stabilization System Analysis and Perform- ance of the GEOS-A Gravity-Gradient Satellite (Explorer XXIX), Journal of Space- craft and Rockets, 4, 1623-1630 (1967). 7. H. D. Black, M. W. Jennings, M. Sturmanis, 'Attitude Determination Utilizing Redund- ant Sensors', Proceedings of the Fourth International Aerospace Instrumentation Symposium, Cranfield, England, March 1966. 8. J.M. Whisnant, D. K. Anand, 'Roll Resonance for a Gravity-Gradient Satellite', Journal of Spacecraft and Rockets, 5, 743-744 (1968). 9. D. K: Anand, 'Heat Pipe Application for Gravity-Gradient Satellite (Explorer XXXVI), Proceedings of the ASME Aviation and Space Conference, Los Angeles, June 1968. 10. V. L Pisacane, J. M. Whisnant, 'Attitude Stabilization of the GEOS-C Spacecraft', to appear in the Aeronautical Journal, Royal Aeronautical Society, 1973; also JHU/ APL Report TG-1139, October 1970. 11. V. L. Pisacane, P. P. Pardoe, J. M: Whisnant, 'Simulation of the Attitude Stabilization of the DODGE Spacecraft with Time-Lag Magnetic Damping', Proceedings of the XVIII th Congress of the International Astronautical Federation (Belgrade, Yugoslavia, September 1967), Pergamon Press, Oxford, pp. 437-445, 1968. 12. J. M. Whisnant, V. L. Pisacane, 'Comparison of Theoretical and Experimental Attitude Data for the DODGE Spacecraft', Proceedings of the XX th Congress of the Interna- tional Astronautical Federation (Mar de! Plata, Argentina, October 1969), Polish Scientific Publishers, Warsaw, pp. 759-778, 1972. 13. D. K. Anand, J. M: Whisnant, M. Sturmanis, 'Attitude Perturbations on a Slowly Spin- ning Multibody Satellites', Journal of Spacecraft and Rockets, 6, 324-326 (1969). 14. D. K. Anand, P. P. Pardoe, J. M: Whisnant, 'Nutational Damping of a Slowly Spinning Satellite Stabilized by Use of a Rotor', JHU/APL Report TG-997, April 1968. 15. D. K. Anand, J. MWhisnant, 'Attitude Stability and Performance of a Dual-Spin Satellite with Nutation Damping', The Journal of the Astronautical Sciences, Vol.XIX, 6, pp. 462-469, May-June 1972. 16. D. K. Anand, J. M: Whisnant, V. L. Pisacane, M. Sturmanis, 'Gravity-Gradient Capture and Stability in an Eccentric Orbit', Journal of Spacecraft and Rockets, 6,.1456-1459 (1969). 17. D. K. Anand, R.S. Yuhasz, J.M. Whisnant, 'Attitude Motion in an Eccentric Orbit', Journal of Spacecraft and Rockets, 8, 903-905 (1971). 18. R. E. Lohfcld, D. K. Anand, J. M: Whisnant, 'Gravity-Gradient Stabilization of Satellites in Highly Eccentric Orbits', Presented at AAS/AIAA Astrodynamics Con- ference, July 16-18 1973, Vail, Colorado. (Presented at the Symposium of the British Interplanetary Society on 'Earth Observation Satellites' held at University College London, 10-12 April 1973) 661 Page 150 Reprinted from JOURNAL OF SPACECRAFT AND ROCKETS, VoL 11, No. 6, June 1974, pp. 430-432 Copyright, 1974, by the American Institute of Aeronautics and Astronautics, and reprinted by permission of the copyright owner Pitch Axis Stabilization in Eccentric Analysis Orbits Using a Variable-Speed Rotor Satellite oscillations in the plane of an elliptic orbit are described by4 2 R. E. LOHFELD* (1 +e cos v)(d cj,/dv 2 )- 2e sin v(d/dv)+(l/2)o sin 2¢ = 2e sin v Computer Sciences Corporation, Falls Church, Va. (1) where e is the orbit eccentricity, o = 3[(/x-I.)/Iy], cj, is the pitch AND libration angle measured from the local vertical, v is the true D. K. ANANDt anomaly, and Ix, ly, Iz are the principal momeots of inertia. University of Maryland, College Park, Md. Consider a satellite with a variable-speed wheel rotating about the pitch axis. The moment of inertia of the rotor is defined AND as I., about the spin axis, and the instantaneous speed of the J. M. WHISNANit wheel is Q .. The equations of motion for such a satellite in a Applied Physics Laboratory, Silver Spring, Md. gravitational field can be developed using the usual Lagrangian formulation. The equation for the pitch motion is (1 +ecos v)(d2cj,/dv2)-2e sin v(dcj,/dv)+(l/2)o sin 2¢+ Introduction I,il/Iva>2(l+ecosv)3 =2esinv (2) A SATELLITE in a noncircular orbit stabilized by the gravitational gradient across its mass distribution under- where ro is like the mean motion and is defined as 2 goes planar librational motion due to the influence of the orbital v/(1 + e cos v) and C) refers to differentiation with respect to motion on the attitude motion. As the eccentricity of the orbit time. Equation (2) will be investigated here becomes large, the amplitude of the libration increases. When the orbit eccentricity exceeds 0..355, no stable motion can exist 1 - 4 This limits the use of passive gravity gradient stabiliza- Stability Regions tion to satellites whose orbit eccentricities are substantially less The criterion chosen for stable motion is that a satellite in an than 0.355 elliptic orbit exhibits a motion whose maximum librational The purpose of this Note is to establish a method whereby amplitude is limited to less than ±90.0°. This amplitude limita- semipassive gravity gradient stabilization can ba used effectively tion results from the more general requirement that one axis of a in orbits with eccentricities significantly larger than 0.355 .. The satellite is defined as Earth pointing and is used for such things method used consists of modifying the dynamical motion of the as communication antennas and Earth observation experiments satellite by adding a small variable-speed wheel rotating about The stability discussed herein is restricted to the pitch motion the satellite's pitch axis.. The control of the wheel speed is since the roll and yaw librations are only weakly coupled to the independent of the attitude motion of the satellite, thus pre- pitch motion and are normally stable. This is particularly true serving the open-loop stabilization system and eliminating the when a variable-speed wheel is used. . Since the wheel speed can need for attitude sensors. The speed of the wheel is dependent be controlled such that there is always a momentum bias; ie, only on the location of the satellite in the orbit and is therefore the wheel speed would never be zero, the roll yaw plane would a function only of the time since perigee passage. This technique be gyro stabilized provided that the pitch motion were stable. This was first considered for use in the GEOS-C satellite. 5 How- is the familiar gyrocompass stabilization concept ever, because of a decrease in the expected orbital eccentricity, The pitch axis regions of stability can be represented in a it has not been implemented for that mission three-dimensional space in terms of cj,, dldv, and v for any given Previously, others have proposed t_he use of time-dependent eccentricity. Since a closed-form solution to Eq (2) has not been satellite inertias for controlling satellite attitude motions. 6 How- obtained, the stable regions must be determined numerically. 3 ever, the use of a variable-speed wheel or rotor is simpler, less The stable regions can be presented stroboscopically in two expensive, and more reliable in practical applications dimensions(, dcj,/dv) by examining the trajectories at selected values of true anomaly. 7 For example, numerically obtained Presented at the AAS/AIAA Astrodynamics Conference, Vail, values of cj, and dcj,/dv can be plotted only at each perigee Colo, July 16-18, 1973; submitted August 17, 1973; revision received crossing, apogee crossing, or at any other true anomaly v of February 1, 1974 lhe work ot .J M. Whisnant was supported by 'interest. If these two-dimensional figures were to be obtained for US Navy Contract N00017-62-C-0604 Index category: Spacecraft Attitude Dynamics and Control all values of v, then they could be joined together to form a * Member of Technical Staff, Aerospace Systems Operation tube-shaped three-dimensional surface (see Fig. 3 of Ref 1) or t Professor of Mechanical Engineering stability portrait. The portrait need only be constructed for :j: Mathematician, Space Research and Analyses Branch values of true anomaly from O to 2n radians since, after 2n Page 151 Reprinted from JOURNAL OF SPACECRAFT AND ROCKETS, Vol 11, No. 6, June 1974, pp. 430-432 Copyright, 1974, by the American Institute of Aeronautics and Astronautics, and reprinted by permission of the copyright owner Pitch Axis Stabilization in Eccentric Analysis Orbits Using a Variable-Speed Rotor Satellite oscillations in the plane of an elliptic orbit are described by4 2 R. E. LOHFELD* (1 +ecos v)(d ¢/dv 2)-2e sin v(d = 2e sin v Computer Sciences Corporation, Falls Church, Va. (1) AND where e is the orbit eccentricity, b = 3[(Jx- lz)/1 vJ, is the pitch libration angle measured from the local vertical, v is the true D. K.. ANANDf anomaly, and Ix, ly, lz are the principal moments of inertia University of Maryland, College Park, Md. Consider a satellite with a variable-speed wheel rotating about the pitch axis .. The moment of inertia of the rotor is defined AND as J, about the spin axis, and the instantaneous speed of the J. M. WHISNANI:i wheel is Q The equations of motion for such a satellite in a Applied Physics Laboratory, Silver Spring, Md. gravitational field can be developed using the usual Lagrangian formulation. The equation for the pitch motion is Introduction (1 +e cos v)(d2+ l,il/ly w2 (1 + e cos v)3 = 2e sin v (2) A SATELLITE in a noncircular orbit stabilized by the gravitational gradient across its mass distribution under- where w is like the mean motion and is defined as 2 goes planar librational motion due to the influence of the orbital v/(1 + e cos v) and n refers to differentiation with respect to motion on the attitude motion. As the eccentricity of the orbit time. Equation (2) will be investigated here. becomes large, the amplitude of the libration increases. When the orbit eccentricity exceeds 0..355, no stable motion can exist. 1 - 4 This limits the use of passive gravity gradient stabiliza- Stability Regions tion to satellites whose orbit eccentricities are substantially less The criterion chosen for stable motion is that a satellite in an than 0.355 elliptic orbit exhibits a motion whose maximum librational The purpose of this Note is to establish a method whereby amplitude is limited to less than ±90.0° This amplitude limita- semipassive gravity gradient stabilization can be used effectively tion results from the more general requirement that one axis of a in orbits with eccentricities significantly larger than 0 .. 355. The satellite is defined as Earth pointing and is used for such things method used consists of modifying the dynamical motion of the as communication antennas and Earth observation experiments satellite by adding a small variable-speed wheel rotating about The stability discussed herein is restricted to the pitch motion the satellite's pitch axis. The control of the wheel speed is since the roll and yaw librations are only weakly coupled to the independent of the attitude motion of the satellite, thus pre- pitch motion and are normally stable. This is particularly true serving the open-loop stabilization system ,and eliminating the when a variable-speed wheel is used. Since the wheel speed can need for attitude sensors. The speed of the wheel is dependent be controlled such that there is always a momentum bias; Le, only on the location of the satellite in the orbit and is therefore the wheel speed would never be zero, the roll yaw plane would a function only of the time since perigee passage. This technique be gyrostabilized provided that the pitch motion were stable. . This was first considered for use in the GEOS-C satellite. 5 How- is the familiar gyrocompass stabilization concept ever, because of a decrease in the expected orbital eccentricity, The pitch axis regions of stability can be represented in a it has not been implemented for that mission three-dimensional space in terms of¢. d :,0 Pc ::c N..-, --- ' I i~~TION_SHI~ OF _:i~;En OF :l~_.!NG TO THE APP_!::!~_MOMENTS IN HU!-lAN LEG_J~INTS ~ I ! I "J' .,,.r ~. I ; R. C. Krishnan*, D. K. Anand·t and F. E. Zajac III~* 1 ! i J 1U ~ ;~t I,; ·u-.l lo< r,=m~ -c-n:,, t-., 0 1,,;,.., ,- -~'"!' "ld,:·c:i.-, o'.7ilic.Jicl"I ,c_! o.,:h~r ·; ore · .:c:- ,nc, OL"n~ • ,-.::'- '.,-c!-.- I ~J ~---l • ~ ~t ~ :!t .: .- !-;.;r!. w;~· ,tE.-~i1F .·ici ,dud? s.: ~ c.• f'--i 0.: t-· -'!l j -------------------------- It is necessarv to characterize normal human •••FREE SPEED FREE F,!1ST gait in ordet1 to understand'1athdl\:ig1'Cal gait and -FAST SPEED SPEED SPEED to.-devel-Oil-=thot.u: 3 :devices; --Tl.-is-%vak>pment.--. ANKLE•-.. ._ will requj.re j<.-.owledge ,of -moments, in the. . Joints of HIP the legs. The determination of these moments is a · problem in Inverse Dynamic,s 2 '. The solution to the problem was obtained by'rittm~'t-ical integration of ,the equations ofomoticin.c iResults,~ndicate that small incre!\?7,Jn SfF!' .. si,~t 1r1:: '4~tec:11ined mostly ;by hip flexors and large increases by ankle extensors. It was assumed that the propelling moments· are supplied by hip flexors and ankle extensors; , that the knee joint 'controls' the motion and that Fig. 1 (ref. 4) ' increases in step-size for fast •. speeds res~lt technique. : from larger ankle extension and hip flexion (see ! fig. i). It was also assumed that for a given Initiai conditions for ~ ••Y ~d B were~ 'desired speed of walking that lies in between from Murray (1967). The rates $ Y and Swere." learned free and fast speeds, the trajectories and 'obtained by graphical differentiation. The entire moments·generated by this analysis require minimal ,simulation was designed to allow for the genera- expenditure of energy. Preliminary computations 'tion of a complete set of trajectories and joint bear this out. moments (see fig. 2) using only the desired ;velocity as t9e input. { The meehanical !.'Odel: ! --.- -Th_~ t-hiSh;- $h;:;;n~,. foot a.!?tl toe ~,.~ madeled :Results ar...d CcUClusions: 1 as rigid sticks held together by pin joints, thus .,.-ht: re~.J.Li..~ reported. he:re at:t! for a ci.ass of yielding a two dimensional model, with the hip minimal energy learned motions in the sagittai joint tracing a velocity dependent sinusoidal ,plane only. The mechanics of step size increase pathw·ay. The equations of motion were derived of a leg in the sagittal plan in the push-off and using the Lagrangian Method. They are of the form swing phases was analyzed. lt was found that !small increases in step size are determined mostly ! /by hip flexors and large increases by ankle ! 'extensors. The results lead to the conclusion 1 + (l)i 'that provided adequate care is used to formulate -~D2 -yE2 SF 2 constraints that are consistent from the stand- ,point of anatomy, energetics and dynamics, ~D3 +yE3 + SF3 physiologically meaningful interpretations can be where the Ci's, Di's, Ei's, and F 's are iobtained in spite of the considerable scatt~r 1 fassociated with previous investigations 1 ' 2 • 3 • functions of the mass properties of the links, REFERENCES their relative angular displacements and their il. Beckett, R. and Chang, K. (1968) An evaluation relative angular rates, and include the walking of the kinematics of gait by minimum energy. velocity, the vertical excursion of the hip J. Biomechanics 1, 147--159. joint and its rates. A is the Lagrangian Mul- ·2. Chao, E.Y. and Rim, K. (1973) Application of tiplier that has been introduced to account for optimization principles in determining the the constraint that the hip, knee and ankle applied moments in human leg joints during gait. angles (¢, y and B respectively) are not J. Biomechanics 6, 497-510. independent but are related by an algebraic 3. Kralj, A. (1971) Muscle coordination studies in equation. man and their relation to functional electrical Solution Procedure: stimulation of muscle, Orthotic Systems Using Equations (1) were solved for ¢' y and 8 Functional Electrical Stimulation and Myoelec- to give equations of the form tric Control. Final Report. Project No. 19 - P-58391-F-OL Ljubljana, Yugoslavia. 1 $ - F1(¢.~.y,y,B,S,A, HIP, Ki.'IBE, A.'lKLE) 4. Murray, M.P. (1~67) Gait as a total pattern of movement, Am. J. Phy. Med. 46, 290-333. y F2 (¢,f,y,y,8,8,A, HIP, KNEE, AilKLE) } (2) 5. Vukobratovic, M., Hristic, D., Ciric, V. and Zecevic, M. (1973) Energy Demand Distribution $ F3(¢,$,y,y,B,S,A, HIP, KNEE, ANKLE) within Anthropomorphic Systems. Trans. AS~E, AckJ.c,IJyn·,~ Sys .. g~&.and-~t:irol; Bec,o; ?,'.4402.,,,;.13 •. Using the 'heel-off ankle extension angle' *lleuartment of Biomedical Engineering, 720 N. Rutland Ave., Johns Hopkins Hospital, Baltimore, and the 'heel-strike hip flexion angle' as bound-; M!le,~and 21203, U.S.A. ary constraints (see f:i.g. 1), the joint moments , ·tProfessor, Department of Mechanical Engineering, were computed as functions of time by numerically U, of Md. ,College Pk,, ~d: .Also Sr. Staff JHU/APL. integrating equations (2) using the Runge-Kutta **Assoc. Prof:"DeIJ.t.~of_ BE~-, !j_:' _of}id_. ,Col.Pi<, Md. De n::;1 t., :,-~ vr.:< ! ·;'> :,,. r___-·, ,,,, .:..,_, _ __ j 27th ACEMB MARR!OTI HOTEL PHILADELPHIA, PENNSYLVANIA OCT. 6-10, 1974 . r::---i ~-~ Page 155 Apodization in numerical holography D. B. . Kramer Operations Research, lnco,porated, Silve,- Spring, Maryland D. K. Anand University of Ma,y/a11d, College Park, Ma1yland (Received 13 July 1974) Apodization, a process in which the energy in a diffraction pattern is redistributed among the main lobes and the side lobes, has proved its usefulness in optical imaging systems and in linear sonar arrays, It can also make the numerical reconstruction of hologrnms more adaptable to varying requirements To demonstrate, the hologram of a rectangular slot is first reconstructed numerically in the conventional manner, It is then reconstructed after apodizing the diffraction pattern contained in the hologram, One type of apodization led to a reconstructed image that accentuated the discontinuity at the edge of the slot, Another type gave an image with a concentration of energy at the center of the object, thus minimizing interference from nearby objects It is expected that the method can be extended to other objects by expr-essing them as summations of rectangular slots Subject Classification: 60,30; 3S,6S, INTRODUCTION large main lobe with monotonically decreasing minor Apodization is a process that was first used to improve lobes {side lobes) on either side. The purpose of this the resolving power of optical imaging systems. Asap- paper is to describe and evaluate a method of apodiza- plied to the diffraction pattern of a point source, the tion in whicll all side lobes are lleld at a specified lev- term originally signified a redistribution of the light flux el. Consider fiI'st the diffraction pattern for a rectangu- in such a way as to reduce the energy in the side lobes. lar slot. However, the term can also be used in a broader sense, I. DIFFRACTION PATTERN FOR A RECTANGULAR as will be done here, to include either a reduction or an enlargement of the side lobes. SLOT It will be seen that either type of redistribution can be advantageous in certain A slot of width b is shown illuminated from the left circumstances. For example, if an imaging system is in Fig. 1. Point P 1 is a point in the plane of the slot, to be used to view one central object witti a minimum of poil't,F0 is a point in the plane of observation and the vec- interference from nearby objects, a diffraction pattern tor n is normal to the plane of the slot. The Huygens- with reduced side lobes is tielpful. Since the reduction Fresnel diffraction formula can be used to relate the in side lobes is always accompanied by an enlargement fielct\Strength U(P0) at P 0 to that at P 1 , where (see Ref. 3) of the central portion of the pattern, such an arrange- ment would not be helpful if the imaging system is to be used to view two adjacent objects. In this case the U(P0) = JS h(P0, P 1)U(P1)ds (1) large main lobe would impair the system's ability to s recognize two distinct objects, For this application, a small main lobe would be preferable1 even at the ex- pense of larger side lobes. >rn of ,rn illuminatt-d :slot. 1545 J, Acoust. Soc, Am., Vot 56, No. 5, November 1974 Copyright© 1974 by the Acoustical Society of America 1545 Page 156 1:,4b Kr;,mcr ,mcl An,1nd: Apodi,ation in numerical holography 1546 :.tnd th,, \n•i,•.hlinfi fundion li(/'0 • /\) isgivenhy U(P 1 ) ' Ji(l'o·, J\) l'OS(i1, ru1) l'Xp(i/.•ro1)·'_i.\101, (2) and I, 2., A, \\ lien' .\ is the wavclenglh. The stuface ot intt•g1 ation sis the apertul'e or the slot. U the slot is illuminated unilo1 mly, U(l\} can \Je descli\Jcd by a r·ec- I .O t;rngu!a1 lundion as in Fig. 2. I1 the distance z between the' ::;lnt and the ob::;e1valion plane is much larger than citlH'I' the slot dimension or the maximum dimension oi intp1 est in the obsc1vation plane, the expression for -b/2 b/2 the weighting function can be simplified to Ji(l>0 , I\)= exp(jl?r01) 1j>,.z • (3) FIG. 2. Field strength at the slot. If the distance r 01 , given by r 01 :ozll+(x0 -x1)2/z2 ]112, is replaced by the first two terms of its binomial expansion The amplitude of the composite wave at the plane of the so that r 01 "' z[ 1 + (x0 - x1) 2/2z2], the expression for the hologram is the sum of the above reference wave and the weighting function becomes object wave. The intensity pattern due to this composite wave is recorded on film and a transparency is made. The transmission function of the film is proportional to When z is large enough for Eq. 4 to be accurate, as as- the intensity patterns; therefore, sumed here, then the diffraction can be called Fresnel diffraction. Assume also that t=Ki (5) =KUU*, (10) When this condition is met, the diffraction is called Fraun- where k:, film constant, U is the amplitude of the com- hofer diffraction and the weighting function can be written posite wave given by U = U, .• t + U(P0), and U* is its complex as conjugate. h(P0,P1)=Cexp(-jkx0x/z), (6) where C=exp(jkz)exp{jkxg/2z)/jAZ. If Eq. 6 is substi- Ill. RECONSTRUCTION tuted into Eq. 1, r: The intensity described by Eq. 10 contains the follow-U(P0)=C U(P1)exp(-jkxo-,;/z)dx1 • (7) ing terms: (1) a real image, KU*(P0 )Uref> (2) a virtual image, KU(P0)U:.r, and (3) two noise terms. The real Infinite limits can be used here since it is assumed that image will be deflected by an angle B from the recording U(P1 ) is zero outside the slot aperture S. This ex- axis. The virtual image will be deflected by an angle B pression is simply the Fourier transform of U(P1) in on the other side of the axis. The real and virtual which the frequency f is defined by f = x0/>.z. Since U(P1) images will therefore be separated from each other. By is the field strength of the uniform slot, defined as in proper choice of the parameters involved in the record- Fig. 2, Eq. 7 becomes ing setup, these images can also be kept separate from f. b/ 2 the two noise terms. U(P0):oC exp(-jkx0xi/z)dx1 :oCbsinA/A, (8) -b/ 2 The hologram can be reconstructed by means of an ar- rangement such as that in Fig. 4. If the illumination is where A= kx0b/2z. Equation 8 describes the object wave from a plane wave having the same amplitude as U,et, but that will be added to the reference wave to form the at the same angle on the other side of the recording hologram, as will be seen in the next section. Note also that if U(P0) from Eq. 8 is plotted as a function of x the axis, a real image will be formed on the recording axis 0 , resulting pattern have a large central lobe with and a virtual image will be formed at an angle equal to twice will the deflection angle of the illuminating beam. This is minor lobes monotonically decreasing on either side of it. The apodization process will be applied to this pat- shown in Ref. 1, where it is also shown that the expres- sion for the real image is tern and the reconstruction process will then be carried out with this apodized pattern. The results of this recon- KUTU:~(P0):oKU,U:C*b sinA/A, (11) struction will then be compared with the results when no where A is as defined in Eq. 8 and apodization is applied. Before this is done, however, let us continue with the description of the recording process. C*=exp(jkz)exp(-jkx~/2z)/j>..z. II. RECORDING In order to determine the diffraction pattern resulting Figure 3 shows a simple setup for recording the image from the illumination of the hologram, the Huygens- of the slot defined by Eq. 8. A light source is shown Fresnel diffraction formula must be applied. Referring providing the offset reference wave and also illumina- fo Fig. 4, Eq. 11 describes the field strength at some tion for the slot. If the amplitude of the reference wave point P 0 on the x0 axis. The Huygens-Fresnel formula is Ur, then the equation for the reference wave is can be used to calculate the field strength at P in terms u. .. r = U, exp(jkx0 sinB) . (9) of the field strength at P 0• The procedure is similar to Page 157 1547 Kramer and Anand: Apodization in numerical holography 1547 ----:~cL-cc;ra'.':" Ref. 4. The result was the reconstructed image shown so·.:rce slotf ' in Fig. 5(b). Note from Fig. 5(b) that the width of the slot is 1 cm, as it should be, but the exact location of the edge of the slot is somewhat uncertain. This can be seen by comparing Fig, 5(b) with Fig. 5(c), the ideal re- constructed image. The uncertainty in location of the edge can be reduced by using more data points in taking the Fourier transform, but this also increases computer storage and calculation time. It will be seen in the next section that apodization can produce some desirable re - \I/ave sults without using more data points, pns::: V. APODIZATION IN NUMERICAL RECONSTRUCTION It has already been noted that apodization has been FIG. 3. Recording of the hologram. successfully applied to optical imaging systems and to linear sonar arrays. In both these applications the en- that used in Eqs. 1 through 8 to relate the field strength ergy in an interference pattern is redistributed among at P 1 of Fig. 1 to the field strength at P0• the main lobe and the side lobes. In this section it will be shown how this process has been successfully applied U(P)= fJxu,[?,'ut(P0)h(P, P 0)ds, (12) during numerical reconstruction of a hologram. S1 In the preceding section it was shown how the image where the surface of integration 5 1 is the aperture of the was reconstructed numerically by taking the Fourier hologram. Assuming again that the distance z is large transform of the function plotted in Fig. 5(a). This compared to the dimensions in the hologram or observa- procedure will now be repeated except that the function tion planes and applying the Fresnel and Fraunhofer con- will be apodized before taking the trans.form. The ditions, the weighting function becomes apodization will be of the type described in Ref. 2, in which the properties of Tchebyscheff polynomials are h(P, P 0 ) = C1 exp(- jkxx0/ z) , (13) used to obtain a pattern in which all side lobes are at where C1=exp(jkz)exp(jkx2/2z)/j>tz. The expression some specified level. The main lobe is then as narrow for the real image is obtained by substituting Eqs. 11 as possible for the particular side-lobe level. The and 13 into 12 to get method, described in detail in Ref. 2, will only qe out- lined here. U(P)=cf_: sinA/Aexp(-jkxxo/z)dx0 , (14) Consider the following function: where G"' KU,Utb[ exp(jkz )/j>tz ]2. The approximation sign for G indicates that the Fraunhofer approximation ~/2 was applied. Infinite limits have been used with the E= L{exp[(2m -l)ju]+exp[-(2m -l)ju]}. (16) integral of Eq. 14 since it is assumed that U(P0) is zero m=l outside the aperture of the hologram. Equation 14 is thus in the form of the Fourier transform of sinA/A . After multiplying the above expression by exp( j2u), sub- tracting Eq. 16 from it, and solving for E, the result is IV. NUMERICAL RECONSTRUCTION E = sinuiv1 I sinu . (17) The previous discussion describes a conventional op- tical reconstruction of the image, but it is also possible Equation 16 can also be expressed as a series of cosine to do part of the process numerically. For example, terms. Eq. 8 describes the object image U(P0 ) stored on the hologram. This image can be stored in digital form in a computer, and the integral in Eq. 14 can then be evaluated \ v1rtual 1r1ag~ by means of the fast Fourier transform.. Figure 5(a) is a plot of U(P0)/Cb, which, according to Eq. 8, is also equal to sinA/A . To illustrate the numerical reconstruc • tion, values have been assigned to the parameters. A= kx0b/2z (15) where b(= 1 cm) is the slot width, >t(= 0 .. 5 x 10"4 cm) is the wavelength of light, and z(= 200 cm) is the distance from image to observation plane. Figure 5(a) is a plot of U(P0)/ Cb in which x0 varies from - O. 1 cm to 0 .. 1 cm. The in.formation in Fig. 5(a) was S\.lpplied to a computer having the fast Fourier transform rnutine described in FIG. 4. Rcconstructin~ the holoµ;1am .. J. . Acoust. Soc Am .. , Vol. 56, No. . 5, November 1974 Page 158 1548 K,.,me, .md Anand: Apodizdtion in numerical holography 1548 the same onler, er1ual1· ""' lficients of like terms, and determine a set u[ 11m1t11iilr,1m !fm's. These llm's, whu, used with Eq. 22, will J'iV1: :, !unction having a main 1,,t.,, and all side lobes ol Ua, s;1ru1 height. The height of the side lobes can be spec Hi,•strncted Image amined. From Eq. 15, A= 1rbx0/"llz • JI\ norma~1zed ampl.itude ---+---, l ~ Using the values for b, A, and z shown after Eq. 15, A= 10011x0 • A reasonable choice for a maximum value of x0 is o. 5, I since this would allow for a main beam and four side I lobes. The value of M must now be chosen so that -1.,0 -.5 l ,!) x. crn JI.I~ 2001rx0(max)= 101r. (c} ideal Ir::age The Hm coefficients can be computed for values of 11.1 as FIG. 5. large as this but it presents a computational problem because it is hard to maintain sufficient accuracy when M gets much higher than 30. However, for our pur- M/2 'E poses it is not necessary to compute the H,,. coefficients. E = 2 cos[(2m ·- l)u] • (18) The apodized function can be calculated with sufficient m=l accuracy from a knowledge of the null points and posi- Therefore, from Eqs. 17 and 18, tions of the side lobes. Formulas for determining these JI/ 2 L quantities are· given on page 338 of Ref. 2, Al-! apodized sinuM/s inu = 2 cos[ (2m - 1 )u] • (19) patterns given in this paper were computed by this ap- m=l proximate procedure. Note that when the apodized func- The function to be apodized, sin A/A , can be reduced to tion is generated in this way, there is no need to keep the form of the left side of Eq. 19 by properly choosing the value of M to 30 or less. By taking larger values of M. NI, the approximation in Eq. 20a can be made more ac - sin A/A = sinM(A/M )/ M(A/ M) . (20) curate than five percent. H the absolute value of A/kl is O. 5 or less, The results of the apodization are given in Figs. 6 and 7, with the parameters having the values shown after A/M"' sin(A/,W) (20a) Eq. 15. The parameter M was taken to be 628, thus to within five percent. Equation 20 can then be written making the approximation given by Eq. 20a a very good one. Figures 6(a) through 6(c) show the results of the sin A/A = sin.lH(A/,W)/IW sin(A/lvJ) • (21) apodization applied to the function of Fig. 5(a) for side- Except for the constant factor 1/M, sinA/A is now in lobe levels of 8 dB, 16 dB, and 24 dB. Figure 7 shows the form of the left side of Eq. 19. Therefore, the results of numerically reconstructing the functions M/2 of Fig. 6. Figure 7(a) is the reconstructed image for sinA/A=L Hmcos[(2m -l)A/M], (22} Fig. 6(a}. Note that the narrow main beam and high side m=1 lobes of Fig. 6(a) have led to a reconstructed image with where all H,,.'s are constant and equal to 2/M. The func- sharp peaks to mark the edges of the slot. Note also tion to be apodized has thus been expressed as a series that these peaks were obtained at the expense of a re- of cosine terms with a constant coefficient 2/M. Now duction in signal over the central part of the image. set this equation equal to a Tchebyscheff polynomial of Figure 7(b), the reconstruction corresponding to Fig. Page 159 1549 Kramer and Anand: Apodization in numerical holography 1549 6(b), has much smaller peaks to mark the edge of the slot, but the centra.l part of the image is higher than in Fig. 7(a). Figure 7(c), corresponding to Fig. 6(c), has small peaks to mark the edge of the slot, but the most noticeable property is the concentration of the signal at the center of the image. Figures 6 and 7 thus demon- strate that the apodization described here can accentuate discontinuities in the image, as in Fig. 7(a), or concen- trate the image at the center, as in Fig. 7(c). VI. ANALOGY WITH SONAR ARRAY It is shown by Eq. 21 that the image of the slot is stored on the hologram in the following form. or:· ali~c:· t1.-:·plltucie sinM(A/M)/M sin(A/M)= sinM(1rx0b/ ,"vl"t..z)/ Msin(1rx0 b/M"t..z). (23) By substituting u =A/Al into the left side of Eq. 23, we X • C ~ can reduce it to the form of Eq. 19 and thus show that (!1) .'.>id,:; Lobes Dm ·n l;:; CiJ the slot image can be expressed as a series of cosine terms. In Ref. 2 it is shown that an array of lv1 uni- formly weighted sonar elements gives a series of cosine terms of the same form as Eq. 19, in which -td~- lt = (d1r/11.) sine ' (24) ~ .~ - 75 - so -~25 0 2:=. 5-"J 73 X C ': where dis the spacing between elements, "ti. is the wave- (c) i'>iLle tooes De,·:, 2..; -:l i: length, and e is the angle as measured from the normal FIG. 7. Apodization applied in image yeconstruction. to the array. This shows that the beam pattern for a linear sonar array has the form to which the apodization described here can be applied. 'ieam patterns of sonar arrays to improve performance This apodization has been successfully applied to the under particular circumstances. For example, a pat- tern with a narrow main beam is used when it is neces- ,.;ary to determine the angular position of a target with normalized amplitude maximum accuracy. A beam with low side lobes is used 1 .n when it is necessary to view an object with a minimum of interference from objects at different angular loca- \ tions. - 04 V!I. RESULTS AND CONCLUSIONS (a) Side !.obes Down 8 dB The apodization process described here has improved the capability of the numerical reconstruction to adapt to varying requirements. The rectangular slot used as an image ,vas reconstructed so as to accentuate the dis- continuity at the edge of the slot and thus locate the edge 1S9 with maximum accuracy. It ,,as also 1econstruded ::;o as to concentrate the image at lhc cenlcr and thn,:; mini- mize interference from nearby objects. It is exp,'cl<'d that the method will be applicable to other· obied:;, '"·'' ,.or::uli.::cd a J,litude just to rectangular slots, because all objeds cm h,, <'\.- l .'l pressed as a summation ol n dan;•ular slols. It was shown that the apodi,alion pron•ss dcscdlJed here is a11alogous to the "lll';nn 1011nin/' pnh r·,"iu 1 C'S used with linear sonar a nays.. Th is ii:: in1p1ntant because the large an1ount ol work drnw in tlw a1·ea nt l'l'a1n l,nm- ;,-~ (,! I ing can now be considen'd t,n· 11:-:,, Jn 1m11wric.tl ...,,, on .. (::' 3ldC! lot'>•'" !to\.~!l ·'1 iH strudion of holograms. Hdc rt'IK<' :, des, 1 ilw,- ,-om,, oi I JG. 6. Apodizcd diffmclion patterns. the studies in this a1·ea .. J. Acoust. Soc. Am., Vol. 56, No. 5. November 1974 Page 160 1550 Kramer and Anand: Apodization in numerical holography 1550 ·J !\)\\,:r~ l:tndt\ .u,d {i, \\ade 'Cun1pute1· H(~con.:-=:t1·uc- Xe\\ Ym:, 1968). t:,,n l 1,,m Ph,1,-('-\h11' ,tnd ,\mnlitudp-()nl\ Ho\0~1.am~. 11\. l\l. RrC'n11e1 ,. Three FORTRAN Prog;·ams That Pn/orm Acou.,t!cal Jfr,l1>~;,.,t1I \ .\. l. :\h•tht.'1'('11 and l. l.a11nntL' f//,• Coolc.1-T11/:e1 I rn11 s(on11 !.. :!, Ch:1p .. 13, pp. lBL,-~02. I cxi11,!ton. 1\hssachusetts, 28 July 1967) ~(. l l)olph P-;,Jl·,, dPlf-~" ·tm s, pp., ~l~l3-~)-l ~ t ..h n1t.• lil Hi> .. i111.{ \C rl<'ctronics-llelense Research Labo1atories. San·. l 3, J \\ . Goodman /,,/ n>ductim, t,, 1"011 > ,, ,. Of>(ic~ \!\lcG1a 11 -!!ill, B,11l1a m Cctlifornia (hn 1969/. Page 161 J }[ WHISNANT / D.. K ANAND: Invariant Surfaces for Rotor Controlled Satellites in Highly Elliptical Orbits 563 ZAl\BI iH, 563 --565 (19i4) J. :M:. °V\THISNANT*) / D. K. ANAND Invariant Surfaces for Rotor Controlled Satellites in Highly Elliptical Orbits Fur elliptische Umlaufbahnen mit Exzentrizitiiten nahe eins ist es moglich, mit Hilfe eines kontinuierlich verstell- baren Steuerrads Schwerkraft-Stabilisierung anzuwenden.. Das Radsteuergesetz sowie die sich daraus ergebenden stabilen Gebiete sind in einer fruheren Arbeit beschrieben norden, und zuar fur den Fall eines Rads, dessen Ge- schuindigkeit phasenmiij3ig mit der u;irklichen Anomalie genau iibereinstimmt .. In der vorliegenden Arbeit werden die sich fur verschiedene Werte der Phasenverschiebung ergebenden invarianten Fliichen untersucht. Gravity gradient stabilization can be used effectively in elliptic orbits with eccentricities approaching unity by the use of a variable speed control wheel. The wheel control law and the resulting stable regions have been described in a previous paper for the case where the wheel speed is exactly in phase with the true anomaly .. Here, the invariant suijaces resulting for different values of the phase shift are invest{gated . .l])rn 3JIJUIIITIIqec1rnx op6IIT C 3KcnerupnnnTeTaMII 6JIII3KIIMH ep:IIHIIne B03MOlRHO IIpIIMeHIITb rpaBII·· 1annmmoe cTa6IIJIII3IIpoBamre c IIOMOII.(bIO HerrpepbIBHO rrepecTaBmrnMoro pymr. B onnotl: II3 rrpep:brp:y- l.I.(IIX pa6oT 6bIJIII orrncaHbI 3aI-WH yrrpaBJieHHJI PYJI0M II CB.f!3aHHbie c 3TIIM ycTotl:qIIBbie o6JiaCTII B 'IaCTI-IOCTII )]:JIH 1arwro CJiy'IaH, ecJIII CKOpOCTb PYJIH no qia3e TO'IHO COBIIap:aeT C IlCfIIHHOit aHOMamretl:. B rrpep:Jiarael\rnit pa601e paccMarpIIBa!OTCH IIHBapMaHfHbie IIOBepXHOCTII, B03HIIKaIOrnIIe )]:JIH pa3HbIX BeJIII'IIIH C)]:BIIra ~ = !.<~d - ~) (8) Dover Publications, Inc., New York, 1.956. where Fis a constant matrix whose el.e·;nents are to 4. Lotka, A. J., Elements __ of: Physical __ Bfologz., The be dete.rinined. It is also assumed there exjsts a Willi.ams and Wilkens Press, 1925. mc>.tri:r.: 1i' such that the fertility rate vector is given by 5. Volterra, V., "Fluctuations in the Abundance (9) of a Species Considered Mathematically," ~. Vol. 118, 1962. The matrix Bis a function of ecological param- eters. The-problem remains to select the elements 6. Gause, G.F. and Witt, A.A., "Behavior of Mixed of I to achieve the desired stable population ~d Populations and the I'.:0blem of Natural Selec-- with the best possible transient behavior using tion," Am. ~~_t;uralig, Vol. 69, 1935, p. 596. acceptable amounts of control, This goal can be 7. Odum, E.P., Fundamentals of Ecology, W.B. approached by analyzing the closed loop behavior Saunders Co., Phila. , ·19 71, p. 214. of the ecosystem. One way to handle the constraint on u 0) 8. Koga, S. and Humphrey, A., "Study of the Dy-(u > and still stabilize the ecosystems or improve - namic Behavior of the Chemostat System," Bio- their transient response is through the use of an techno!£g_y_ _ E.nd Bio~!IB.!:.•, Vol. 9, 1967. -- optimal control approach. The closed loop equa- 9. Young, T.B., Bruley, D.F. and Bungay, H.R.III, tions are linearized, and the control law derived "A Dynamic Behavior of the Chemostat System," for the linearized equations subject to the con- Biotechnology and Bioen.&E_., Vol. 12, 1970, straint on u is applied to the nonlinear equations. p.747. Using this approach 15 , the control law for the stable system (Case 1) was found and the closed 10. D'Anas, G., Kototovic, P.V., and Gottli.ev, D., loop eigenvalues are "A Nonlinear Regulator Problem for a Model of a Bio. Waste Treatment." IEEE Trans. on Auto- Al= -7.07, A2 = -2.06, A3 = -0.262 matic Control., Vol. AC-·16, No. 4, Aug. 1971. The magnitude of these eigenvalues is greater 11. Vincent, T.L., Cliff, E.M. and Goh, Bean-San, than the three pn. i'iously obtained values, and this "Optimal Direct Control Programs for a Prey- implies that the system will stabilize more Predator Sys.," J. Automatic Controls Conf. • , rapidly than it did before with an improved 1973. transient response. The control law for the unstable system 12. Thau, F.E., "On the Feedback Control of Non- (Case 2) was also found for which the closed loop linear Population Dynamics," .IEEE Trans. on Systems, Man, and Cybernetics,July 1972,p.430, eigenvalues are Al= A2,3 • 13, Parri.sh, J.D. and Saila, S.B., "Interspecific -0.785 , -7.08 ± jl.38 Competition, Predation, and Species Divers:l.ty'' Note that as Case 2 now has stable eigenvalues, it J, of Theor. Bio •. , Vol. 27, 1970, p. 207, remains to be seen what effect the bound on the control vari.able u will have on the nonlinear eco- 14, Strobeck, C,, "N Species Competition," Eco1£lri:. system's transient response. Vol. 54, No. 3, 1973, p. 650, The response of the system with the effect of 15. Bryson, A.E. and Ho, Y., AE.Elied Optimal £2.!l= the control law present for both the bounded and trol, Ginn and Company, Massachusetts, 1969, unbounded control,. variables was studied so that P• 108, the effect of bounding the control variable could be observed. It was concluded that even with the use of bonded control the unstable ecosystem represented by Case 2 can be stabilized. 718 Page 167 Page 168 44/1 THERMAL PERFORMANCE PREDICTIONS OF A SOLAR ABSORPTION AIR CONDITIONING SYSTEM F.H. Morse; R.W. Allen~+ D.K. Anand* and E. Bazques** Department of Mechanical Engineering University of Maryland College Park, Maryland 20742 The daily and seasonal thermal performance of a solar absorption air conditioning system, subject to certain modeling constraints, has been studied. The system modeled consists of a solar collector, a tracking mechanism, and an absorption cooling machine, each represented by mathematical formulations. The daily therma·1 performance is defined as the ratio of the daily thermal energy of the chilled water produced to the daily total solar radiation incident on the collector. The sea- sonal therma 1 performance is taken to be the ratio of the chi 11 ed water produced to the daily solar radiation summed over the cooling season. Three classes of collectors were .studied, representing different levels of performance or different collector efficiency levels for the same relatively high, mean absorber-ambient temperature ~ifference. The high performance collector utilized evacuated spaces and a selective- surface absorber. The moderate performance collector, typical of a good commercially available collector, combined two cover glasses and a selec- tive surface, while the lower performance collector used a single glass cover over a non-selective surface. A linearized model was used to pre- dict the collector performance, rather than the computationally more involved Hottel, Whillier, Bliss (HWB) model. In general, the difference between the mean fluid temperature predicted by the HWB model and .that predicted by the linearized model was minimal. The collector was either stationary or it was allowed to track the sun. A tracking error relationship was used to model the tracking mechanism. Two absorption machine models were used. The most basic model con- sidered a constant COP with a linear dependence of capacity on the max- imum generator cycle temperature. The more detailed model employed a COP and capacity which were functions of the maximum generator cycle temperature for a fixed effectiveness of the solution heat exchanger. While the maximum generator cycle temperature is governed by the col- lector performance, the evaporator and the condenser/absorber temper- atures may be treated as independent variables. The condenser and absor- ber temperatures were selected to be representative of both air cooling and water cooling. The pump between the collectors and the absorption unit was started when the empty collector reached a fixed temperature equa·1 to the cut-off generator temperature of the absorption unit. The analyses were conducted for a range of clear-day insolation values and ambient air temperatures. 390 Page 169 Results are obtained for various combinations of collector, tracking and absorption machine parameters. Coefficient of Performance of the overall system is obtained for a typical day as well as a typical cool- ing season for a variety of systems. +F.H. Morse, Assoc. Prof. of Mechanical Engineering, was technical coor- dinator of the NSF/NASA Solar Energy Panel, solar energy program manager at NSF, and is a member of the Board of Directors of the ISES. ++or. Allen, Prof. of Mechanical Engineering, was responsible for the 1973 NSF Solar Heating and Cooling for Buildings Workshop and the 1973 NSF Solar Thermal Conversion Workshop. *Dr. Anand, Prof. of Mechanical Engineering, has consulted on commercial heating/air-conditioning projects and conducted system and modeling stu- dies for numerous engineering situations. **Mr. Bazques is a Ph.D. student in the Mechanical Engineering Dept. Page 170 F. W LIPPS and A. F HILDEBRANDT University of Houston Houston, TX -Central Receiver Systems for Irrigation Pumping and Cattle Feed Mill Applications J .. H.. STRICKLAND Texas Tech University Lubbock, TX -The Utilization of Solar Energy for Livestock Feedmill Operations SESSION VI Le Grand Salon West 2:00 p .. m. CO-CHAIRMEN: C .. J .. SWET Division of Conservation Research and Technology J. W. LEECH Division of Solar Energy ERDA Washington, DC 20545 G. A. LANE and H. E.. ROSSOW The Dow Chemical Company Midland, Ml -Encapsulation of Heat-of-Fusion Storage Materials L. G .. MARIANOWSKI, H. C. MARU and E.. H.. CAMARA Institute of Gas Technology Chicago, IL -Latent Heat Thermal Energy Storage at High Temperatures M.. T. HOWERTON and H.. PAPAZIAN Martin Marietta Corporation Denver, CO -Reversible Energy Storage Using Ammoniated Salts B .. SHELPUK and P F. JOY, JR Radio Corporation of America Camden, NJ -The Technical and Economic Feasibility of Thermal Energy Storage in Solar Heating Systems J .. C .. WARMAN, F. J .. MOLZ and T. E. JONES Auburn University Auburn, AL -Step Beyond Theory-Aquifer Storage of Energy CLOSING OF CONFERENCE Concluding Remarks 4:30 p.m. Page 171 Wednesday, April 21, 1976 (Con't) EA CARTER The University of Alabama in Huntsville, AL D. V.. SCULLY Total Environmental Action, Inc. -Basic Relationships to Determine Wind Harrisville, NH Power and Solar Radiation Available from the Atmosphere -Climate Based Solar House Design-Hot and Humid Charleston, SC G .. N .. KUMAR, J. H MOREHOUSE and R I. VACHON H. B .. SHERMAN, JR E Auburn University C. Maguire, Inc Providence, RI Auburn, AL and -Solar Powered Industrial Building J. R. DUNN RECEPTION-Dutch Treat Cash Bar Texas Tech University Le Grand Salon Foyer and West B 6:00 p.m Lubbock, TX BANQUET -Engineering Prediction of Solar System Long Le Grand Salon East and West A 7:00 p .. m.. Term Average Performance Speaker- A. F. CLARK R. S .. HARTENBERG Lawrence Livermore Laboratory Professor Emeritus of Mechanical Livermore, CA Engineering, Northwestern University, -Industrial Process Heat From Shallow Solar Evanston, IL; Visiting Professor of Ponds Mechanical Engineering, Louisiana State University SESSION V Le Grand Salon West B 8:30 a .. m. Thursday, April 22, 1976 CO-CHAIRMEN: SESSION IV H .. J. BRAUD, JR .. Le Grand Salon West A 8:30 a.m. Professor of Agricultural Engineering CO-CHAIRMEN: P H .. TEMPLET T P BERNAT Assistant Professor in Center for Assistant Professor of Wetland Resources Physics & Astronomy LOUISIANA STATE UNIVERSITY J. A BOWDEN Baton Rouge, LA 70803 Assistant Professor of Biochemistry H M.. CURRAN and M.. MILLER Louisiana State University Hittman Associates, Inc Baton Rouge, LA 70803 Columbia, MD J. W. RAMSEY and J T. BORZONI -Comparative Evaluation of Solar Heating Honeywell, Inc. Alternatives Minneapolis, MN R. W. ALLEN, D .. K. ANAND and EA ASTIZ -Effects of Selective Coatings on Flat Place University of Maryland Solar Collector Performance College Park MD T TANI, S .. SAWATA, T TANAKA, K Dynamic Simulation of a Solar Powered SAKUTA and T HORIGOME Absorption Cycle Electrotechnical Laboratory J. L RUSSELL and G. H .. EGGERS Tanashi, Tokyo, Japan General Atomic -A Terrestrial Solar Thermal Electric Power San Diego, CA System-Development of a Model Plant -Superdome Solar System Supply D .. K. ANAND, R. W ALLEN and E. 0. J .. T ETHERIDGE, J. R .. HOLMES and J. S. BAZOUES GOODLING University of Maryland Auburn University College Park, MD Auburn, AL -Weather Representation Using Stochastic -Analysis and Performance of a Solar Heated Methods Swimming Pool Page 172 WEATHER REPRESENTATION USING STOCHASTIC METHODS* D.K. Anand, Professor R.W. Allen, Professor E.O. Bazques, Research Assistant Department of Mechanical Engineering University of Maryland College Park, Maryland 20742 ABSTRACT The weather statistics are represented using a 5 x 5 joint probabi- lity density matrix and five constants derived from real data. From these, the hourly weather data either on a daily basis or a monthly basis can be obtained. System performance of a solar powered cooling system using real as well as synthetic data is compared. It is concluded that synthetic data allows inexpensive simulations and yields satisfactory results. INTRODUCTION For the proper calculation of solar energy contributions to the cooling load of a building and the design of air conditioning equipment, it is necessary to have a good knowledge of temperature and insolation levels and other climatological data applicable to a specific region. Such data have been recorded hourly in many locations and are available as tapes from different weather stations. The accumulated weather data have been used either on a very short time basis or on an average basis for estimating cooling loads. The first method is expensive and cumbersome and the second is often not representative. This is particularly true for computer simulations that predict performance of solar heating and cooling requirements on a long- term basis. For this reason, many formulas for estimating weather data have been presented in the literature (1,2,3,4). Notably, the linear regression models, first suggested by Jordan and Liu and subsequently refined by others, have been widely reported as alternative methods for solar applications for quick and inexpensive estimates. The dee;ree day method for calculating building thermal loads to input into solar sim- ulations are less expensive and give satisfactory average performance values but cannot be used to examine unusual conditions. It is evident that although the present methods are easy to apply, they are often *This work is supported by ERDA contract No. E(40-1)4976. Thanks are due to L. Perini and I. Deif for assistance in data reduction and com- putation. Page 173 neither consistent nor adequately take into account the probabalistic distribution of weather history. In many cases, one succeeds in sup- pressing spurious readings by approximation methods to get smooth data. Interestingly enough, the suppression of such spurious readings is often the kind of structure that one wants to retain and can only be done so on a probabalistic basis. In a recent paper (5), however, methods based on probabal:istic considerations have been suggested although details are unavailable. It is the purpose of this paper to study weather data with the view of obtaining compact information that can be used for the design of solar air-conditioning systems. Since air cooled so1ar absorption air-condi- tioning system simulations (that are particularly useful to the humid environment) require a knowledge of inso1ation and ambient dry-bulb temp- eratures at any given location and time, we limit our discussion to dry- bulb temperature and insolation. Basically, we use a statistical approach combined withstate representation and modify the data for ambient dry-bulb temperature and total insolation into a more compact, usable, inexpensive form. Recognizing that local micro-climatic conditions are important, the packaging of a large body of data into a compact format is desirable. This data can then be easily utilized for solar system design and for system performance predictions. ANALYSIS The weather statistics are represented using a 5 x 5 joint probabi- lity density matrix and fiveconstants. From these, the hourly weather data either on a daily basis or a monthly basis can be obtained. The approach used is to define a state vector X such that X = A F X = (1) where Tis the ambient dry-bulb temperature and I is the total insolation and f (t)J A = al2 J and F = f: ( ( 2) [a22 . t) where the a .. 's are constants and f 1 , f2 are time dependent functions. Defining_! i~ the estimate of the daily averages, the errors squared are expressed as: L [ (r r) -r] T T [ [ E(e e) (3) Data t t 2 Page 174 Minimizing the error, E(eTe), with respect to each parameter, Pi, leads to A-a IL, F)t - aPi \ t - J = 0 ( 4) which will then determine the constants in f 1 (t) and f 2(t). The func- tions in Fare chosen such that the insolation varies as a function of time taking the extinction coefficient into account, whereas the temper- ature is constructed by three sinusoidal terms given by T = Tav (a1 sin wt+ a 2 sin 2wt + a3 ) ( 5) I= Iav (a4 + a 5 cos eH) exp (-K/cos eH) where tis time, eH is the angle between sun vector and local normal, K is the extinct.ion coefficient, ai are constants determined by sol- ving equations ( 4) and w = 0. 2618. The scheme yields equations that can be used for reconstructing the hourly dry-bulb temperature and in- solation values for any month of the season. The amount of the diffuse radiation is assumed to be a constant fraction of the normal insolation. Although this is not quite correct, the effect in overall computations is minimal. The scatter diagrams for insolation and ambient dry-bulb temperature can be generalized using a joint probability density function. This can then be represented in matrix form as discussed by Davis in reference (5). This matrix yields a probability Pij for the occurance of some value Ti and Ij. The values for Ti and Ij are selected to represent average values± ncr where n determines the size of the probability density matrix and a is deviation. The values T. and I. are in turn used in conjunction with the fiveconstants derived ~arl:ierJto reconstruct hourly data for temperature and insolation. The cooling capacity Cij required is computed hourly using reconstructed data based on every set of (Ti, Ii) in the joint probability matrix. The total cooling capacity is o tained by computing r Cijpij. RESULTS AND CONCLUSIONS The above analysis was conducted for the month of July using data for 1954-1958. It was assumed that a12 = a21 = 0 so that cross- correlation was assumed not to exist. The joint probability density matrix for T and I is shown in Figure 1. The data was used in conjunc- 3 Page 175 tion with equations (4) and (5), and it was determined that al = 0.071, a2 = 0.0035, a3 = 0.972, a4 = 0.093, and a5 = 2.06. This in- formation is used to draw the temperature and insolation profiles shown in Figure 2. Superimposed on the plot are actual data that have been normalized. This information, in conjunction with Figure 1, is used to compute the system COP (for the system described in Ref. 6) and is shown in Figure 3. We noted that the trends confirm the fact that COP increases with T and I owing to better collector efficiency and higher heat inputs. System performance using different data is shown in Figure 4 for compar- ison purposes. We note the considerable savings in data for stochastic prediction which are very inexpensive to simulate. It is concluded that the resulting scheme gives a designer a compact and inexpensive tool for simulating weather for solar air-conditioning applications. Although only July data is being used, continuing studies are evaluating a much larger data base. REFERENCES (1) Liu, B. and R. Jordan, "The Interrelationship and Characteristic Distribution of Direct, Diffuse, and Total Solar Radiation", Solar Energy, (4), 3, July 1960. (2) Threlkeld, J.L. and R.C. Jordan, "Direct Solar Radiation Available on Clear Days 11 , ASHRAE Trans. , Vol. 64, p. 45, 1958. (3) American Society of Heating, Refrigerating, and Air-Conditioning Engineers, "Procedures for Determining Heating and Cooling Loads for Computerized Energy Calculations--Algorithms for Building Heat Transfer Subroutines", 1971. (4) Sadler, G.W., "Direct and Diffuse Insolation Using Approximation Methods Applied to Horizontal Surface Insolation", Solar Energy, (17), 1, April 1975. (5) "Extended Abstracts--1975 International Solar Energy Society Congress and Exposition", July 28-August 1, 1975, Los Angeles. (6) Morse, F.H., R.W. Allen, D.K. Anand and E.0. Bazques, "Thermal Performance Predictions of a Solar Absorption Air Conditioning System", presented at the International Solar Energy Society Coneress, July 28-August 1, 1975, Los Angeles. 4 Page 176 INSOLATION~ 38.35 135 .. 0 231.7 328.3 TEMPERATURE t 101.05 0 0 0 0 90.9 I0 .014 I 10.0601 !o.031j 0 80.7 10.1841 jo.457 j 10.1111 0.002 10.6 I 0.018 j 10.0421 0 0 60.4 0.001 0.005 0.001 0 0,- = 10.2 Ur= 96.0 FIGURE I - Joint Probability Matrix for lnsolation (BTU/hr-sq.ft.) and Temperature (°F) for July. .,. )(. x x I Data I.I o T Data 2.0 I IAv 0.96"--'----'----'-...L---'------J.-......__..__,-L_...___,___..i,;;;=-- 0. 0 8 10 12 14 16 18 TIME ( HOURS) FIGURE 2- Synthetic Temperature and lnsolation Profiles obtained for July using five years of data, compared to Real data. 5 Page 177 INSOLA TION >= 38.35 135.0 231.7 TEMPERATURE f 90.9 0.31 0.48 0.52 80.7 0.27 0.47 0.51 70.6 0.24 0.45 FIGURE 3 - Variation of daily COP for different joint probabilities. System Total T,I pairs COP lnsolation x I0 6 of data used Fixed Temperature, Hourly 0.5 746 15 (218)* Clear Day lnsolation 1957 Hourly Temperature 0.47 4.50 434 lnsolation Data Stochastic Predictions 0.43 4.15 8 * Maximum possible FIGURE 4- Comparison of system performance and data requirments. 6 Page 178 DYNAMIC SIMULATION OF A SOLAR POWERED ABSORPTION CYCLE* R.W. Allen, Professor D.K. Anand, Professor E.A. Astiz, Research Assistant Department of Mechanical Engineering University of Maryland College Park, Maryland 20742 ABSTRACT As a step in the development of an overall mathematical solar ab- sorption air conditioning model, a simulation model of the lithium oromide·-water absorption machine has been developed which includes the major heat transfer effects and which accepts as inputs UA's and the temperature and capacity rate at the water connections to the machine. A design study is presented which defines a parametric map of the Region of Permissible Designs for the simulation model in solar applications. NOMENCLATURE A heat transfer area T temperature C capacity rate U overall heat transfer coefficient e effectiveness X concentration h enthalpy Subscripts M modelling factor G generator TJl mass flow rate 1 solution heat exchanger p pressure (others defined by Figure 1) INTRODUCTION Heat-driven absorption cooling machine performance in solar cooling systems was most recently reviewed by industry engineers at the February l·-5, 1976 ASHRAE Semi-·annual Meeting Symposium, "Absorption Machine Des1gn to Meet Solar Cooling of Building Oojectives. 11 The papers presented (1-5) reviewed and extended the available information on the thermodynam- ic calculations of COP's, discussed the limitations imposed by the solar application, and presented alternative cycle and fluid approaches. rrhe absorption machine most freq_uently used in current solar energy projects is the lithium bromi.de-water machine. 'I'his machine is depicted in a simplified form, together with its P-"l'-x diagram, in Figure 1. It is genera.lly acknowledged that the advantage of deve.loping a simulstion model of the absorption machine is that it would allow the effect of absorption machine design changes to be studied in conjunction with a solar Page 179 cooling system simulation such as that presented in Ref. 6 The present paper discusses an absorption machine simulation model containing the heat transfer log-mean-temperature-difference and other improvements such as a computational scheme which accepts external water temperatures and flow rates as inputs and calculates the internal thermo- dynamic cycle that fits the external water inputs. ABSORPTION MACHINE SIMULATION The simplified lithium bromide-water absorption machine model, Fig. 1, consists of four devices, each of which provides a heat exchange par- tition between the internal cycle fluid and external water streams, and one device to provide a heat exchanger partition between concentrated and weak absorbent streams. For this study, steady-state operation is assumed. The basic governing equations are typified, with a few excep- tions, by the case of the generator for which, . q - C (T -- T ) G G Cl CO and The equation of state for the pure refrigerant and the solution relate the m's and h's to pressures and temperatures. We may define, for heat transfer only, an effective capacitance rate for the solution = The heat exchanger effectiveness equation completes the set of governing equations for the generator. Equations for the four remaining heat transfer components complete the simulation which is found to contain 17 independent quantities to be identified by the design engineer. Cooling capacity is retained by reducing the heat transfer UA factors and capacity rate C-factor to a "per ton of cooling" basis. 2 Page 180 DESIGN STUDY SIMULATION To demonstrate a design procedure, we choose a simple case with M 's of unity with the remaining 13 q_uantities chosen as indicated in Figure 2. As design values of the UA per ton in each of the four major components is reduced uniformly, the thermodynamic cycle 1233'466'1, Figure 1, contracts and vanishes at a mean UA per ton of somewhat less than o.07°F-l. The region to the right of o.070F-1 may be called the Region of Permissible Designs under the given conditions. In Figure 3, the effect of design selections of UA, C, and cooling water temperature on machine performance with 210°F H.W. is shown. It is seen that raising the cooling water temperature from 8o°F to l00°F (e.g. non-evaporative cooling) shifts the cycle vanishing point to the right on the UA scale. Lowering the design mean C per ton by a factor of 2 also shifts the cycle vanishing point to the right, but to a lesser extent. The results of Figures 2 and 3 show the usefulness of the simulation model as a design tool and shows its ability to predict internal cycle fluid temperatures when external water temperatures and flow rates are the imposed design conditions. In Figure 4 the vanishing cycle condition is plotted as a line on coordinates of cooling water temperature (Tel or TA1 ) versus mean UA per ton, with H. W. inlet temperature TGl as a parameter. rrhe Region of Per- missible Designs appears on the right--hand side of the Line of Vanishing Cycles. If the hot water inlet temperature TGJ is lowered. from 210°F to 195°F, the Region of Permissible Designs is sh1.fted farther to the right, i.e. to higher values of the mean UA per ton. In the solar cooling application, the restriction of hot water temperatures to the vicinity of 200°F forces the de-rating of conventional machines originally de- signed for 230°F hot water. Conventionally rated machines are estimated to lie in the mean UA range from O. 5op-l to O. 1 °F···1 as indicated in Figure 4. De-rating to 50% is seen to shift the design point to more acceptable cooling water temperatures in the Region of Permissible Designs in Figure 4. De-rating is accomplished in practice by changing solution concentrations. DESIGN STUDY VS. OPERATION STUDY In a design study simulation, a given value of UA per ton is selected for each compoment of the machine. By comparison, in an operating study, the design is frozen in that the design area, A,- of each component re-- mains constant. However, the cooling tonnage will vary with operating conditions as will the heat transfer U-factor. Consideration must be given to modelling the way in which the U of each component varies away 3 Page 181 from its design value as the external conditions change. The present discussion was limited to the design study. Future work will be directed toward simulating operation of an absorption machine in a solar cooling system. CONCLUSIONS A lithium bromide-water absorption machine simulation model has been developed which accepts as design study inputs UA' s, external water capa·-· city rates and temperatures. The model enables the designer to establish a parametric map of the Region of Permissible Designs for solar appli- cations. REFERENCES Note: References 1-5 were presented at the ASHRAE Semi-Annual Meeting, Dallas, '.I.'exas, February 1-5, 1976. 1. Porter, J.M., "The Use of Commercially Available Absorption Units on Solar Powered Cooling Systems". 2. Whitlow, E.P., "Relationship Between Heat Source Temperature, Heat Sink Temperature and Coefficient of Performance for Solar-Powered Absorption Air Conditioners". 3. Anderson, P. P. , "Solar Operated Absorption Water Chillers-·-A Compar·- i son of Aq_ueous Bromide and Aq_ua Ammonia Cycles". 4. Phillips, B.A., "Absorption Cycles for Air Cooled Solar Air Condi- tio:ping". 5, Macriss, R.A., "Selecting Refrigerant--Absorbent Fluid Systems for Solar Energy Utilization". 6. Morse, F.H., R.W. Allen, D.K. Anand, and E.O. Bazq_ues, "Thermal Performance Predictions of a Solar Absorption Air Conditioning System", presented at the International Solar Energy Society Congress, Los Angeles, July 28-August 1, 1915. 4 Page 182 :TGI - !:!~-~·TOR-~1/ I ~ AGE / I .. r, __ J.__ --- : : GO COLLECTO~ ' Teo I l I 4 I I L __ L =~ c:::.JJ p 7 7,8 } 4 ~ 9,10 1,2 12 .___.__,~_ __ J T TEO 2 TAI TE Tc =TA C- CONDENSOR G- GENERATOR P-T-X DIAGRAM E- EVAPORATOR A-ABSORBER FIGURE I - SOLAR ABSORPTION WATER CHILLER 200~~ isoV 0-,4 I co~ r, ,-----~ I I 100 ~!Q_ (OF) 05 160 Tc1=~00F 80 (OF) 0 '='-'=-=-'---'---.___. 0 .. 07 TJA' 1.0 (°F- 1) 60 UA : MEAN UA PER TON Te,1: 195°F 40 · TAI= IQQOF ~ UAL PER TON= 0.025°F"1 20 001 ·uA 01 (°F"'l 0 001 UA 01 (°F-1l C PER TON= 0.25 °F" 1 FIGURE 2 - EFFECT OF COMPONENT UA SELECTION ON CYCLE PERFORMANCE. 5 Page 183 T (OF) 190 170 CONDITIONS TEI =45°F 150 UAL PER TON 0.025°F·' t- r- -:-I.9_ MEAN C PER ,--Tc TON TIOO ~c 0.25°F= (OF) ~Tct =1 00° F 80 ~ / Tc.1 =80oF 0.12°F =.-=. 0.05 0.1 0.15 0.2 0.25 0.3 MEAN UA PER TON (°F) FIGURE 3- EFFECTS OF UA AND C SELECTION ON PERFORMANCE. IOOr ~~G~?~ u1- I\IU Tei 90 - DESIGNS REGION OF (OF) PERMISSIBLE DESIGNS 80,____.._ 100.------------------,--,,,...---------i .,.c, REGION J,.1.-1- LINE OF VANISHING " 9 OF NO , , J-1....L- CYCLES (TG1=195°F) (°F) 0 DESIGNS ~ REGION OF SO .t!!:.J-.1--~- PERMISSIBLE DESIGNS 0.05 0.1 015 0.2 0.25 0.3 CONVENT1o"NAri l.t' 150% DE-RATEDl._jt MEAN UA PER TON (°F-1) MACHINE __ L. MACHINE-=J ~45°F, Tc1=TAI• MEAN C PER TON= 025°F-1, UAL PER TON=0025°y=J FIGURE 4 - REGION OF PERMISSIBLE DESIGNS h Page 184 ABS COP=070 Too= 195°F Toe= 75°F CLEAR DAY INSOLATION .35 .30'----.30'----,40'---~l50----~-o---~~O--Tc_UT_·OFF FIGURE 9- SYSTEM COP AS A FUNCTIOO OF CUT-OFF TEMPERATURE. 220 Tc-o C°F) 200 180 120 IOO 80 6 8 10 12 14 16 18 TIME FIGURE IO- HOURLY COLLECTOR OUTLET TEMPERATURE FOR VARIOUS CUT-OFF TEMPERATURES. 39 2559 3 Page 185 -03: 20 :r: WASHINGTON, D.C. °t-280 LL JULY I, 1957 :3240 I- m -z2 00 0 -ti 160 5 120 U) ~ 80 40 - 0 !-'-L&J a:: =, 80 ti 0: ~ 78 ~ L&J 76 I- m 74 .~.., 72 ~ 0 70'--....J6L-----'-8--....J,1.:..o_ _. .1.12--~1~4--~,s:----1~a- T1ME (HRS) FIGURE II- REAL WEATHER FOR JULY, 1957 40 2559 S Page 186 220 COLLECTOR OUT 200 COLLECTOR IN 180 --~ 0 w 160 s ti ffi 140 Q. ~ ILi 1- 120 100 80 6 8 to 12 14 16 18 TIME (HRS) FIGURE 12- HOURLY COLLECTOR-OUTLET, MEAN PLATE, COLLECTOR-INLET AND CUT-OFF TEMPERATURES. 41 Page 187 .8 [CYCLE. .6 Q. 0 SYSTEM c.> t4 .2 6 8 IO 12 18 TIME (HRS) FIGURE 13- CYCLE AND SYSTEM COP. 6 5 ~ 4 ,c. f.... .. ::, eI- 3 t :I.cLI 2 18 TIME (HRS) FIGURE 14· HOURLY USEFUL ENERGY ANO COOLING CAPACITY DELIVERED. 42 2559 3 Page 188 I•> (11) r Data The 6 x 6 symmetric matrix .§. is defined by These error terms are computed for the entire data base that consists of one given month for several ko520 ko510 k1°1100 k1 510 k2511 k2°1011 years. The number of years chosen is generally a function of the available capacity on a computer. ko5oo k1°0100 k1 5oo k2501 k2c,1 The functions in f_(t) are selected such that f =L k3°0200 ~l:6100 k4Do1o1 k4Dm11 t k35oo k4501 kl11 sij = sji kfo2 k5C12 where tis time, e is the angle between sun vector and local normal, K is the extinction coefficient, ( 12) ai are constants determined by solving equation (Y) and w = 0.2618. The functions in f~t) are 2 Page 200 where water produced to the daily solar radiation summed over the cooling season. S \L . n t -mk/cos e The system modeled in this study was assumed nm= sin w 0 t to have quasi-steady response characteristics, L responding immediately to hourly changes in the Cnm = cos" e e-mk/cos e (13) day insolation. It was assumed that all of the t thermal transient responses equilibrated within L the hourly time interval. The simulation of the D. . = sin; wt sinj(wt+:J,)cosiee-mk/cose air-conditioning system requires the specification 1J 1m t of the generator/condenser/evaporator/absorber conditions as well as the solar collector charac- teristics. All mathematical details of the system and as weli)as its components appear in a previous paper( which dealt with a parametric study. However, since the absorption cycle was air-cooled, the cut-off temperature and coefficient of perfor- mance were assumed to be fixed. Since the present study assumes a variable wet-bulb temperature for kl = allal2 + a2la22 + a3la32 a water-cooled absorption cycle, the cut-off and cycle COP are described by k2 allal3 + a2la23 + a3la33 (14) k3 = a,22 + a222 + a322 (15) k4 = al2al3 + a22a23 + a32a33 COP(t) = 1.11 - 0.004 Tw(t) ( 16) k5 = al32 + a232 + a332 The particular system parameters used for the In summing the above terms, the data and t refer present study are listed in Table 1. The standard to the same time span. units are SI with the numbers in parentheses referring to the English system. The system Once the ai parameters have been determined in coefficient of performance is determined by these Eqs. (5-7), then the scheme yields equations that parameters as well as the forcing function repre- can be used for reconstructing the hourly dry-·bulb sented by the real or synthetic weather data. temperature, wet-bulb temperature, and insolation values for any month of the season, provided an Simulation Results average temperature and insolation is specified. The constants a. in Eqs. 5-7 were obtained The scatter diagrams for insolation, wet-bulb, using five years of data for July and aij = 1 for and dry-bulb temperature can be generalized using i = j and O for i ! j. For this case, it was a joint probability density function. This can determined that a1 = 0.078, a2 = 0.997, a3_= 9.019, then be r.(5~resented in matrix form as discussed a4 = 1.012, a5 = 0.013 and~= 2.312. This in-by Davis /, This matrix yields a probability formation is used to draw the temperature and in- Pijk for the occurance of some value Tdi• T~j and solation profiles shown in Fig. 2. Superimposed Ik· The values for Tdi• Twj• and Ik are selected on the plot are a randomly chosen set of actual to represent average values above and below no data, that have been normalized, for purposes of where n determines the size of the probability comparison. density matrix and o is the standard deviation. These values of wet-bulb temperature, dry-bulb The joint probability density for wet-bulb temperature, and insolation are in turn used in temperature, dry-bulb temperature, and insolation conjunction with the six constants derived earlier was obtained and is pictorially illustrated in to reconstruct hourly data for temperature and in- Fig. 3. The wet-bulb is divided into four inter- solation. The cooling capacity Cijk required is vals, viz. ±o, o to 20, 2o and higher, and finally computed using reconstructed data cased on every -o and lower. Similarly, the dry-bulb temperature· set of Tdi• Tw·· Ik in the joint probability and insolation are each divided into four regions, matrix. The dtal cooling capacity is obtained thus yielding a 4 x 4 x 4 joint probability matrix by computing ECijkpi "k' Similarly, we obtain an with a possibility of 64 entries. As an example, estimate of the totai solar energy incident on the Fig. 3 shows that the joint probability of Td ± collector during a given time period, as well as ord• \,; ± oTw and I ± or is 0.27. The significant the coefficient of performance (COP). probabilities are shown in Table 2. We note that only 19 are of significance with the remaining 45 System Simulated. being zero. This information, in conjunction with the results of Fig. 2, is used to compute the The system under consideration, Figure 1, system COP for a water-cooled absorption air- consists of a solar collector and an absorption conditioning system discussed earlier. The COP cooling machine. The daily thermal performance was computed for the significant probabilities and of this system is defined as the ratio of the is shown in the last column of Table 2. This daily thermal energy of the chilled water pro- information should be read in conjunction with the duced to the daily total solar radiation incident actual probability, i.e. the COP of 0.45 has a on the collector. The seasonal thermal perfor- probability of 0.27, which is the probability of mance is taken to be the ratio of the chilled having the temperatures and insolation to within 3 Page 201 ±cr of their average values as shown by the ijk = Nomenclature 222 entry. We note that the trends confirm the fact that COP increases with temperature and inso- A Correlation matrix between ambient dry- lation owing to better collector efficiency and bulb temperature and insolation higher heat inputs. Constants in the A matrix that allow study Monthly system performance is shown using of the effects of-ambient dry-bulb temper- various data in Table 3, The entries without the ature and insolation on each other; wet-bulb temper.atufe are results obtained from an i = 1 to 3, j = 1 to 3 earlier study (7,BJ. It shows a comparison of stochastic predictions to actual data for air- COP Coefficient of performance cooled absorption systems. The inclusion of wet- bulb in stochastic predictions yields a COP of Cooling capacity required for a given set 0.42 as compared to 0.44 for real data. The top of wet-bulb, dry-bulb temperatures, and entry in Table 3 of using a fixed average temper- insolation, watts (Btu/hr) ature{6) gives the largest error. The total insolation incident on the collector is shown in Cnm Coefficients defined by Eq. 13 the second column and again fairly good agreement is evident between stochastic and actual data. Coefficients defined by Eq. 13 Perhaps the most important entry is the last col- Dijlm umn. The use of synthetic data requires 8 points dn Coefficients defined by Eq.11 for COP computations for air-cooled systems and 19 points for water-cooled absorptionair-condition- Coefficients defined by Eq. 11 ing systems compared to 434 for real weather data. dnml This indicates the great savings that are incurred E Error term which is minimized in least especially when designing storage systems for square fit solar applications. F(t) State vector representing temperatures Variation of COP, total incident insolation, and total insolation profile and daily useful energy for different ai_;'s is shown in Table 4. Although case 2 appears to be Assumed ambient dry-bulb temperature the worst case and case l appears to be the best profile case as compared to real data, any definitive conclusionsat this point are not made. It is worth Assumed ambient wet-bulb temperature noting, however, that although the COP estimate profile can be acceptable, the total incident insolation should also be predicted accurately for the proper Assumed total insolation profile estimation of useful energy delivered. Hourly total (direct and diffuse) insola- The previous predictions have been limited to tion, watts/m2 (Btu/hr sq. ft.) July, 1957. Shown in Table 5 is a comparison of COP and total insolation for the stochastic pre- Average hourly insolation dictions with the years 1954 to 1958 which comprise the original data base. Fairly good agreement is Actual hourly insolation normalized by the seen in each case. daily average insolation -Co-n·cl-us-io-n K Extinction coefficient for insolation passing through atmosphere, dimensionless System COP, total insolation, and useful energy delivered using the joint probability Coefficients defined by Eq. 14 density approach seem to be in good agreement with real data. Although the present experiment has Entry in joint probability density matrix been limited to one month, its extension to in-· which specifies the probability of ob- elude a full season is straightforward. Since the taining any combination of temperatures present scheme reduces the data necessary for sim- and insolation simultaneously, i = l to 4, ulations in a local region, considerable savings j = l to 4 and k = l to 4 in system simulation, both in complexity and time, result. Any local region can be characterized Q Daily total insolation, KJ (Btu) by six constants and, in this case, nineteen data sets. Such compact information is even amenable R 6 x l matrix defined by Eq. 10 to hand calculators for design purposes. It is therefore concluded that the present scheme of Coefficients defined by Eq. 13 taking a large body of local data and compacting it while retaining its probabalistic structure Time gives the designer a compact and inexpensive tool for sizing solar systems. Tc_ (t) Temperature at which the absorption cycle 0 begins operation Hourly ambient dry-bulb temperature, 0c (OF) 4 Page 202 T (t) Hourly wet-bulb temperature, 0c (°F) (7) Anand, D.K., R.W. Allen, and E.O. Bazques, w "Weather Representation Using Stochastic Tdav Average hourly ambient dry-bulb tempera- Methods," Proceedings of the Second South-ture eastern Conference on Applications of Solar Energy, Baton Rouge, La., April, 1976. Average hourly wet-bulb temperature (8) Anand, D.K., R.W. Allen and E.O. Bazques, Actual hourly ambient dry-bulb temperature "Simulation of Synthetic Weather Data for normalized by the average dry-bulb temper- the Design of a Solar Powered Air Conditioning ature System," Proceedings of the Seventh Annual Pittsburgh Conference on Modeling and Simula- Actual hourly ambient wet-bulb temperature tion, Pittsburgh, April, 1976. normalized by the average wet-bulb tem- perature !(t) State vector representing dry-bulb and wet-bulb temperatures and insolation as functions of time X Actual hourly values of the state vector 6 x 1 matrix defined by Eq. 10 Parameters solved for in least square fit, i = l to 6 6 x 6 matrix defined by Eq. 12 w Cycle frequency, in this study 2rr/24 radians/hr A Time shift for wet-bulb temperature e Time dependent angle between the sun vector and local normal, deg. Refer~ (l) Liu, B. and R. Jordan, "The Interrelationship and Characteristic Distribution of Direct, Diffuse, and Total Solar Radiation." Solar Energy, (4), 3, July, 1960. -- (2) Threlkeld, J.L. and Jordan, R.C., "Direct Solar Radiation Available on Clear Days." ASHRAE I.rans_. Vol. 64, 1958, p. 45. (3) American Society of Heating, Refrigerating, and Air-Conditioning Engineers, "Procedures for Determining Heating and Cooling Loads for Computerized Energy Calculations--Algorithms for Building Heat Transfer Subroutines," 1971. (4) Sadler, G.W., "Direct and Diffuse Insolation Using Approximation Methods Applied to Hori- zontal Surface Insolation," Solar fr1E.9.Y.• ( 17) , l , April 197 5. (5) "Extended Abstracts--1975 International Solar Energy Society Congress and Exposition." Held July 28-August l, 1975, Los Angeles, California. (6) Morse, F.H., R.W. Allen, D.K. Anand, and E.O. Bazques, "Thermal Performance Predictions of a Solar Absorption Air Conditioning System," presented at the International Solar Energy Society Congress, Los Angeles, July 28- August l, 1975. 5 Page 203 CONDENSER ABSORBER --- AIR OR WATER ---- COOLING EVAPORATOR + + + + Q (COP) FIGURE I- SOLAR POWERED ABSORPTION AIR-CONDITIONING SYSTEM SCHEMATIC. Page 204 STOCHASTIC 1954 1955 1956 1957 1958 COEFFICIENT OF 0.42 0.44 0.43 0.43 0.44 0.42 I PERFORMANCE TOTAL 4.81 5.06 4.40 INSOLATION 4.50 4.54 4.84 X I05 (4.56) (4.80) (4.27) (4.30) (4.59) (4.17) TABLE 5- COMPARISON OF COP ANO TOTAL INSOLATION FOR DATA BASE VERSUS STOCHASTIC. Page 205 CASE I 2 3 4 REAL DATA COP 042 0.40 0.41 0.42 0.44 DAILY TOTAL INSOLATION 4.8 4 .. 4 4.6 4.6 4 .. 84 X 105 KJ (4.6) (4.2) (4.4) (4.4) (4.59) (BTU) DAILY USE- FUL ENERGY 2.02 176 1.89 1.93 2.13 (Q)(COP) (1.92) (1.67) (1.79) (1.83) (2.02) KJ (BTU) CASE 1, CASE 2• 0 ·o 0.1 OJ 0 0 OJ 0.1 0 0 0.1 0.1 CASE3= CASE 4, OJ 005 09 0.1 OJ 0.1 0.05 OJ 09 0.1 0.05 005 0.1 0.1 0.9 TABLE 4- SIMULATION EXPERIMENTS. Page 206 TOTAL SYSTEM INSOLATION DATA 5 POINTS COP X 10 KJ (BTU) USED FIXED TEMPERATURE HOURLY CLEAR DAY 0.5 7.87 15 {218)* INSOLATION (7.46) -- :::; a: 4 . 75 434 :::, Td, I 047 0 (4.50) X t! ~ ct ,n 0 Td,Tw,I 0.44 4.84 434 ~ (4.59) -(.) zU) 0.43- 4.38 8 I- 0 Td, I 045 (4.15) U) - ct ... gX ... a <.> 4.81 ~ 1ci ,Tw,I 0.42 19 U) a.. {456) * MAXIMUM POSSIBLE TABLE 3 - COMPARISON OF SYSTEM PERFORMANCE AND DATA REQUIREMENTS Page 207 i j k C O P P ( 1 ~ 1 i , T w j , I k ) 1 1 1 0 . 0 1 0 9 0 . 2 6 1 1 2 0 . 0 5 5 2 0 . 2 5 1 2 1 0 . 0 2 8 ! 0 . 4 5 1 2 2 0 . 0 2 6 2 0 . 4 3 0 . 0 2 5 7 2 1 1 0 . 2 9 2 1 2 0 . 0 7 6 2 0 . 2 8 2 1 3 0 . 0 4 6 7 0 . 2 7 2 2 1 0 . 1 0 5 7 0 . 4 7 2 2 2 0 . 2 7 0 0 0 . 4 5 0 . 0 8 7 1 0 . 4 3 2 2 3 2 3 1 0 . . 0 2 6 7 0 . 5 1 2 3 2 0 . 0 6 0 9 0 . 4 9 2 3 3 0 . 0 2 3 8 0 . 4 7 3 2 1 0 . 0 1 0 0 0 . 4 8 3 2 2 0 . 0 4 8 1 0 . 4 6 3 2 3 0 . 0 2 5 7 0 . 4 5 3 3 1 0 . 0 1 0 0 0 . 5 2 3 3 2 0 . 0 3 0 9 0 . 5 0 3 3 3 0 . 0 2 0 9 0 . 4 8 T A B L E 2 - S I G N I F I C A N T P R O B A B I L I T I E S A N D C O P F O R J U L Y . P a g e 2 0 6 P a g e 2 0 8 COLLECTOR*: UA 0567 (OJO) b 0.0027 (0.0015) A 27.87 (300) f3 36° PLATE cl.. 0.9 i, Q88 c( 0.04 DESIGN POINT TEMPERATURE: GENERATOR/CONDENSER 906/37.8 (195/100) EVAPORATOR/ABSORBER 72/37:8 (45/100) Q 10,550 (36,000) m 1134 (2500) CYCLE COP · * EVACUATED a SELECTIVE SURFACE TABLE I- PARAMETERS FOR SYSTEM LOCATED AT 36°N. Page 209 34.3 (938) ----------, P333 =0.021 I I 27.3 ----1P2 22=0.27 I (81.2) I I I II 21.0 25.t • ____1_ _- -i_ _< _,6...,;9.9..;;..;)_ __. ....;(?7_7_. I _ ) _ ~ Tw I / / I// // /r / / I / I / / ___________JI / // I / I / vt = 305.6 (97.0) (1350> 1 // Grd = 4 .. 68 (8.42) ____________________ y/ Grw = 2.64 C476l FIGURE 3- JOINT PROBABILITY MATRIX OF INSOLATION,DRY·BULB TEMPERATURE AND WET· BULB TEMPERATURE. Page 210 D ·D- I 1AV 1.0 D IQ .95 1.00 6 8 10 12 14 16 18 TIME (HOURS) FIGURE 2- NORMALIZED SYNTHETIC TEMPERATURE AND INSOLATION PROFILES OBTAINED FOR JULY USING FIVE YEARS OF DATA COMPARED TO A RANDOMLY CHOSEN SET OF REAL DATA. Page 211 Wed amB ROOM VI: MR 9, lO and 11 17. I Simulation studies Chairmen: R.DIKKERS, E.P.COCKSHUTT --~··· 1 W.C.MELTON, Jnso lation and temperature Aerospace Corporation statistics and their influenc~ on the design of solar heating systems and the electric utility interface Sharing 2 P.J.HUGHES, Simulation study of several W .A.BECKMAN, solar heating systt?IDS with theSun76 LA.DUFFIE; off-peak auxiliary University of Wisconsin Solar Technology in the Seventies A Joint Conference 3 D.K.ANAND, R. W.ALLEN Solar powered absorption aircond· University of Maryland itioning system performance using of the real and synthetic weather data American Section of the International Solar Energy THUpmA Society andthe ROOM Ill: THEATRE Solar Energy Society of Canada Inc. 3 .. 3 Cooling methods Chairmen: R. . R.VERNON, R.K.SWARTMAN August 15-20 in the 1 R. W .ALLEN, D. K. Parametric study of a dyn- ANAND; amic solar powered absorption Winnipeg Convention Centre University of Maryland cycle Winnipeg, Manitoba Canada FRlamB ROOM VI: MR 9, iO and 11 8.1 Agricultural and Industrial Chairmen: I.SHEARER, R.G.ANDERSON 6 W.W.AUER, Solar industrial process heat R.W.ALLEN, works_liop PROGRAM D.K.ANAND, University of Maryland @!Ill~ • 11'-l Page 212 PARAMETRIC STUDY OF A DYNAMIC SOLAR POWERED ABSORPTION CYCLE R.W. Allen D.K. Anand Professor Professor Department of Mechanical Engineering University of Maryland College Park, Maryland 20742 ABSTRACT The performance of a solar powered absorption cycle is simulated taking into consideration the internal heat trans- fer characteristics and the floating of the generator/ condenser/evaporator/absorber temperatures. A parametric analysis for capacity and cut-off temperatures fs conducted. The daily and seasonal system coefficient of perfonnance and capacity delivered at the evaporator is obtained with the use of real weather data. INTRODUCTION Solar energy to operate conventional absorption cycles for air- conditioning has become the subject of renewed interest and has been reported by several investigators. Basically, the solar collector provides energy to a thennodynamic cycle in which the working fluid for the system consists of a solution of a refrigerant and an absorbent. The cycle COP is determined by the generator temperature and the condenser/evaporator/absorber conditions and is defined as a ratio of the heat transfer rate at the evaporator to that at the generator. In a recent paper (1), the thermal perfonnance of a solar powered absorption cooling system was presented and the system COP predicted, In the paper. two lithium bromide-water absorption machine simulation models were used. A basic model was defined as a machine with a con- stant COP and with a linear dependence of cooling capacity on the maximum solution temperature in the generator. A more detailed model for COP and capacity as functions of the maximum general cycle tempera- ture included a prescribed fixed effectiveness of the solution heat ..exchanger: In both models the heat transfer temperature differences were neglected. Thus the maximum solution temperature was set equal to the variable collector outlet temperature. The evaporator/condenser/ absorber temperatures were treated as fixed quantities. In a companion paper (2), this ideal lithium bromide-water absorption machine was 27 Page 213 analyzed to determine heat transfer effects. The results were presented 1n tenns of the dependence of the heat transfer rates, internal cycle temperatures, and internal refrigerant and solution flow rates upon imposed fixed external water temperatures, but without considering heat exchanger effectiveness typical of real machines. Heat-driven absorption cooling machine performance in solar cooling systems was most recently reviewed by industry engineers at the February 1-5, 1976 ASHRAE Semi-Annual Meeting Symposium, 11Absorption Machine Design to Meet Solar Cooling of Building Objectives." The papers pre- sented (3-7) reviewed and extended the available information on the thennodynamic calculations of COP's, discussed the limitations imposed by the solar application, and presented alternative cycle and fluid approaches. This work did not, however, take into account heat transfer characteristics typical of actual machines. It is the purpose of the present paper to simulate a solar powered absorption air-conditioning system and obtain the daily and seasonal system performance considering o the internal heat transfer characteristics as well as flow rates of the solution, refrigerant, and secondary fluid o the floating of the internal generator/condenser/evaporator/ absorber temperatures, and o the use of real weather data. SYSTEM DESCRIPTION The system configuration defined for this study was limited to a basic arrangement consisting of a flat plate solar collector and an absorption cycle as shown in the upper portion of Figure 1. Such a sys- tem would instantly convert the incident solar radiation into a cooling effect if thermal time lags in components were negligible. The cooling ·~ produced by the instantaneous conversion process may be regarded as being stored for use "on demand. 11 The overall thermal performance factor of the solar absorption cooling system with instantaneous conversion is called the system coefficient of performance and is defined as the ratio of the cooling effect to the solar radiation incident on the collector. The system coefficient of perfonnance may be computed as an instantaneous value, a daily value, or a seasonal value. The daily and seasonal calculations involve sullllling the cooling effect and solar radiation over the day or season, respectively. The daily and seasonal thermal perfor- mance was evaluated for solar absorption cooling system models employing a high performance collector. 28 Page 214 ABSORPTION CYCLE DESCRIPTION The absorption machine used most frequently in current solar energy projects is the lithium bromide-water machine. The machine is depicted in a simplified form, together with its P-T-x diagram, in Figure l. It is generally acknowledged that the advantage of developing a simula- tion model of the absorption machine is that it would allow the effect of absorption machine design changes to be studied in conjunction with a solar cooling system simulation such as that represented in Ref. 1. The present discussion concerns an absorption machine simulation model containing the heat transfer log-mean-temperature-difference and other improvements such as a computational scheme which accepts external water temperatures and flow rates as inputs and calculates the internal thermodynamic cycle that fits the external water inputs (8,9). The simplified lithium bromide-water absorption machine model, Fig. 1, consists of four devices, each of which provides a heat exchange partition between the internal cycle fluid and external water streams, and one device to provide a heat exchanger partition between ~oncentrated and weak absorbent streams. For this study, steady-state operation is assumed. The basic governing equations of the absorption machine model with heat transfer and pressure drop effects are of the following general fonn: 1. Equations of State Solution: ' f s ( P, t, x, h) = 0 Refrigerant: fr(P,t,h) = 0 External fluids: fe(P,t,h) = 0 (e.g., water) 2. Equations for each machine component Mass: m. = 0 f 1n Chemical Component: (mx)in = 0 Energy: Heat exchangers: q + (mh)in = O Pumps: -w + (mh)in = 0 Equations of Heat Transfer: q = UA {LMTD) 29 Page 215 or £ = f£(UA,Cmin'Cmax> where C is the capacity rate of a fluid stream and (mh)in C = ----,----- tin - tout and Cmin = Cexternal fluid or Ccycle fluid and Cmax = Ccycle fluid or Cexternal fluid 3. Condition Equations for Cycle Fluid hP between components specified ht or heat loss specified between components In this study, only counterflow heat exchangers were considered for simulation of the cycle. The primary fluid is taken to be the working fluid in the cycle (either refrigerant or solution). The external fluid' used for cooling purposes (condenser, absorber) or heating of the solution (generator) or refrigerant {evaporator), will be referred to as the secondary fluid. HEAT TRANSFER EFFECTS To demonstrate a design simulation, we chose a simple case with quantities chosen as indicated in figure 2, As design values of the UA per ton in each of the four major components is reduced uniformly, the thermodynamic cycle 1233 1 466 1 1, figure 1, contracts and vanishes at a mean UA per ton of somewhat less than 0.07°F~ 1 may be called the Region of Permissible Designs under the given conditions. Once the lower boundary for the cycle was detennined, a set of values was chosen as a reference design point. Namely, COP= 0.81, a value of 0.158°F- 1 for all four capacity rates. The effectiveness of the solution heat exchanger was kept constant at 0.70. The cycle behavior was also studied for effects resulting from varying UA, within a region which included the reference design, for each individual component. The results are shown in Figures 3 and 4. 30 Page 216 Three computer runs were obtained for each component. The result- ing COP was normalized with respect to the reference design COP and plotted versus UA/TON. The conditions for each run are shown within the boxes in each figure. First, with the design value for C, the UA for each individual component in question was varied while the UA for the rest of the components was kept constant and equal to each other. This curve corresponds to a value for C of 0.25°F- 1• New values for C (0.556°F- 1 and 0.083°F- 1 ) were arbitrarily chosen and the procedure was repeated. Figure 3 shows the effect of varying UA/TON for the condenser. The cycle COP decreases whenever UA/TON for any of these components decreases. In the condenser, a decrease in UA/TON means a higher refrig- erant temperature and a consequent reduction in the heat {qE) absorbed by the refrigerant in the evaporator. Also, a higher condenser tempera- ture implies a higher generator pressure with a consequent reduction in refrigerant being evaporated. This reduces the amount of heat, qG, being transfered into the generator; this latter effect coupled with a lower qE translates into a decrease in cycle COP. Figure 4 depicts the relative weight of each component variation on cycle COP for C = 0.257°F- 1 • The total effect was obtained by chang- ing all four UA's simultaneously as it was explained at the beginning of the chapter. It must be noted that the total effect 1s equivalent to the compounded effect of each component. That is, for any value of UA/TON the COP/COPRo for the generator multiplied times the respective values for the condenser, evaporator and absorber yields the COP/COPRD for the total effect at the UA/TON. PARAMETRIC ANALYSIS The effect of varying cycle COP on system COP is shown in Figure 5 and is seen to be linear over the range considered. For this case, the outlet temperature of the collector as a function of time is shown in Figure 6. We observe that this temperature increases slightly with cycle COP. The system COP is shown as a function of the rated water temperature input to the generator in Figure 7. This is seen to be a very weak function. For the same case, the collector outlet temperature, shown in Figure 8, increases with increasing rated water temperature input to the generator. The system COP is seen to be a weak function of cut-off temperature as shown 1n Figure 9. Again, the collector outlet temperature, Figure 10, is seen to increase with increasing cut-off temperatures. Summarizing the effects shown in Figures 5 to 10 with clear-day insolation,we can state that the system COP is affected most by cycle 31 Page 217 COP and to a lesser degree by variations in cut-off temperature and rating point. This is true owing to the typical flatness of the efficiency curve of the high perfonnance collector. Real weather data shown in Figure 11 are next used to obtain the perfonnance characteristics of a system. In this simulation, the cut-off temperatures and cycle COP float as functions of wet bulb temperature (10). The collector outlet, mean plate, collector inlet, and cut-off temperatures as functions of time are shown in Figure 12. The resulting cycle and system COP's for this case are shown in Figure 13. Finally, the useful energy and cooling capacity deliveredare shown in Figure 14. Owing to the low thermal loss of a high perfonnance collec- tor, the system cooling capacity is largely governed by the insulation. Figure 15 shows the daily weather and system perfonnance for one month. It is again seen that the system perfonnance is primarily governed by the insolation values. CONCLUSION The effect of including internal heat transfer characteristics in an absorption cycle simulation is to reduce the cycle COP in comparison to the thermodynamic case. The system COP floats with ambient tempera- ture and insolation variations, with insolation as the predominant parameter owing to the low thennal loss of the high perfonnance collector. ACKNOWLEDGEMENTS This work is supported by ERDA contract No. E(40-1)4976. The assistance of I. Deif, J. Hallameyer, E. Astiz, and E. Bazques is acknowledged. REFERENCES 1. Morse, F.H., R.W. Allen, D.K. Anand, and E.O. Bazques, "Thermal Perfonnance Predictions of a Solar Absorption Air-Conditioning System," paper presented at the International SolariEnergy Society Congress, Los Angeles, July 28-August 1, 1975. · 2. Allen, R.W., F.H. Morse, A.N. Egrican, "A Thermodynamic and Heat Transfer Analysis of Solar Absorption Air Conditioning Cycles, 11 paper presented at the International Solar Energy Society Congress, Los Angeles, July 28-August 1, 1975. Note: References 3-7 were presented at the ASHRAE Semi-Annual Meeting Dallas, Texas, February 1-5, 1976. 32 Page 218 3. Porter, J.M., 11 The Use of Commercially Available Absorption Units on Solar Powered Cooling Systems. 11 4. Whitlow, E.P., "The Relationship Between Heat Source Temperature, Heat Sink Temperature and Coefficient of Perfonnance for Solar- Powered Absorption Air-Conditioners." 5. Anderson, P.P., "Solar Operated Absorption Water Chillers--A Comparison of Aqueous Bromide and Aqua Amnonia Cycles." 6. Phillips, B.A., "Absorption Cycles for Air Cooled Solar Air Conditioning." 7. Macriss, R.A., "Selecting Refrigerant-Absorbent Fluid Systems for Solar Energy Utilization. 11 8. Allen, R.W., D.K. Anand, and E.A. Astiz, "Dynamic Simulation of a Solar Powered Absorption Cycle," Presented at the Second South- eastern Conference on Applications of Solar Energy, Baton Rouge, April 1976. 9. Allen, R.W., and D.K. Anand, "Performance Studies of Solar Absorp- tion Air Conditioning Systems," First Annual Report, ERDA Contract E(40-1)4976, August 1976. 10. Anand, D.K., R.W. Allen, E.O. Bazques, 11 Perfonnance Predictions of a Water-Cooled Solar Absorption Air-Conditioning System Using a Stochastic Weather Model," Proceedings of AIAA Thermophysics Conference, San Diego, 1976, 33 Page 219 - 7 8 4 , &..,,,,!.--.!!:--....---' T TEO 2 TAI TE c= A C-CONDENSOR G·GENERATOR P-T-X DIAGRAM E- EVAPORATOR A-ABSORBER FIGURE I - SOLAR ABSORPTION WATER CHILLER 1.0-----. COP 0.5 o .01 'UA .. cor:·11 UA: MEAN UA PER TON. Tc1 •I00°F 'foi•195°F TEI: 45°F TAI• I00°F UAL PER TON•0.025°F"' UA o., 1°F'"'1 0.01 ui o., c°F·'i c PER TON. 0.2s °F"' FIGURE 2 - EFFECT OF COMPONENT UA SELECTION ON CYCLE PERFORMANCE. 34 Page 220 DESIGN WATER INLET -o- REFERENCE DESIGN TEMPERATURE COPRo =081 GEN/COND 1 ABS/EVAP UAc /TON= 0.158 (°F-1) 1.05 C/TON =O 257 (°F-1} 195/80, 80/55°F €L: 0.70 C/TON 0 a: CL 0 C•0.556°F·I u 0:: · _ ~.:..Q.25°F-I 1.00 0 -- -v--u ,,,,..,.,.,----- / / ---·C-•0·.0-83°F·I I -·- I /·". --· I / I/ 0.95 I I 0.1 0.2 UAc /TON (°F-1) i lMTo·• FIGURE 3- EFFECT OF CONDENSER UA ON COP. 35 Page 221 DESIGN WATER INLET -o- REFERENCE DESIGN TEMPERATURE COPRo=081 GEN/COND 1 ABS/EVAP UAITON =0 158 (°F"1) 1.05 195/80, 80/55 °F C/TON=O 257 (°F-1) €=0.70 0 a: a. 0 0 '0 .. LOO 0 / .,,,. -~-- -~ -----0 / ./ I /./ I./ II / -- GENERATOR I I --- CONDENSER I --- ABSORBER I i -o--o- EVAPORATOR 0.95 +-+-+- TOTAL EFFECT 0.1 0.2 UA/TON ! LMTo·t FIGURE 4 - RELATIONSHIP BETWEEN INDIVIDUAL EFFECT OF .. UAG ,UAc,UAE,UA AND COMBINED EFFECT OF UA AND COP. 36 Page 222 TGR •195°F Tc-o•l42°F Toe •75°F CLEAR DAY INSOLATION !40 ues 2: ~ .35 ~ • (I) .30 .60 .65 .70 .75 .80 CYCLE COP FIGURE 5 - EFFECT OF CYCLE COP. ABS. COP 1 .78 i80 l60 ~ 140 I ~ j 120 TGR •195°F Tc-o•l42°F Tee •75°F 100 CLEAR DAY INSOLATION 80 6 8 10 12 14 16 FIGURE 6 - COLLECTOR OUTLET TEMPERATURE AS A FUNCTION OF TIME. 37 Page 223 ABS .. COP •0.70 0.. 0 Tc-o • 142°F (.) Toe• 75°F :E I.LI CLEAR DAY INSOLATION t- (/) t .3...._ __17. ._0 __ _.18_0 __1 .._90 __2._ 0_0 __ _,21/GR FIGURE 7-SYSTEM COP AS A FUNCTION OF GENERATOR RATING 220 TGR C°F) 200 ISO ~ 160 I ~ 140 ~ ~ t- 120 ABS. COP • 0.70 Tc-o •142°F Toe •75°F 100 CLEAR DAY INSOLATION 80 6 8 10 12 14 16 18 TIME FIGURE 8· Ho.R.Y COLLECTOR OUTLET TEMPERATURE. 38 Page 224 SOLAR POWERED ABSORPTION AIR-CONDITIONING SYSTEM PERFORMANCE USING REAL AND SYNTHETIC WEATHER DATA D.K. Anand R.W. Allen Professor Professor Department of Mechanical Engineering University of Maryland College Park, Maryland 20742 ABSTRACT The performance of a solar powered absorption air- conditioning system using real and synthetic weather data is obtained. Both air-cooled and water-cooled systems are considered. The synthetic data is derived using weather history and represented by a joint probability density matrix and at most six constants. The coefficient of performance using real data and synthetic data is com- pared. Long term predictions based on synthetic data are quite good. It is concluded that the use of synthetic data allows very inexpensive simulation and yields satis- factory results for design purposes. INTRODUCTION The performance as well as design of solar powered coolings· systems, along with the solar energy contributions to the cooling load of a building, requires a good knowledge of temperature and insolation as well as other climatological data for specific regions. This data must be collected for long periods of time so as to be sufficiently repre- sentative. Such data has been recorded at short time intervals at many weather stations and is generally available on tape. In the past, the accumulated weather data has been used either on a very short time duration basis or on an average basis for estimating cooling loads. The first method is expensive and cumbersome and the second is often not representative. This is particularly true for computer simulations that predict performance of solar heating and cooling requirements on a long- term basis. For this reason, many formulas for estimating weather data have been presented in the literature (1,2,3,4). Notably, the linear regression models, first suggested by Jordan and Liu and subsequently refined by others, have been widely reported as alternative methods for solar applications for quick and inexpensive estimates. The degree day Page 225 method for calculating building thermal loads to input into solar simu- . lations are less expensive anq give satisfactory average performance values but cannot be used to examine unusual conditions. It is evident that although the present methods· are easy to apply, they are often neither consistent nor adequately take into account the probabilistic distribution of weather history. In many,cases, one succeeds in suppressing spurious readings by approximation methods to get smooth data. Interestingly epough, the suppression of such spurious readings is often the kind o.f structure one wants to retain and can only be done so on a probabilistic basis. Itta receht paper (5), however, methods based on probabilisticcorisideratigns have been suggested although details are unavailable. · The performance of ai r;..coo 1e d> solar powerecl, ai r-conditi oni ng sys- tems was reported in earlier papers (7,8). Since air-cooled absorption systems require dry-bulb temperature and solar insolatiori, the analysis was restricted to the stochastic representation·of\thelse tw()weather parameters. For systems that are water-cooled (9) r the coeffieient· of performance of the absorption cycle is dependent upon the,wet-bulb tem- perature, thus necessitating the stochastic predict ion of an additiona 1 weather parameter. This paper is a compendium of the work done on the long-tehn,per- formance predictions of air-cooled as well as water-cooled solar absorp- tion air-conditioning systems with an extension that includes personal predictions. Specifically, the calculations are based on a stochaitic model which is constructed using historical information. Basically, we. use a statistical approach combined with state representation and modify the data for ambient dry-bulb temperature, wet-bulb temperature, and total insolation into a more compact, useable, inexpensive form. Recognizing that local micro-climatic conditions are important, the packaging of a large body of data into a compact format is desirable. This data can then easily be utilized for solar system design and for system performance predictions. SYSTEM DESCRIPTION The system under consideration, Figure 1, consists of a solar col- lector and an absorption cooling machine. The daily thermal performance of this. system is defined as the ratio of the daily thermal energy of the chilled water produced to the daily total solar radiation incident on the collector. The seasonal thermal performance is taken to be the ratio of the chilled water produced to the daily solar radiation summed . over the cooling season. The system modeled in this study was assumed to have quasi-steady response characteristics, responding immediately to hourly changes, in the day insolation. It was assumed that all of the thermal transient responses equilibrated within the hourly time interval. The simulation Page 226 of the air-conditioning system requires the specification of the generator/condenser/evaporator/absorber conditions as well as,the solar collector characteristics. All mathematical details of the ·system as well as its components appear in a previous paper {Ref. 6) which dealt with a parametric study. For purposes of floating the absorption cycle. the cut-off and cycle COP are described by Tc_0 (t) = 2.35 T(t) - 73 ( l ) COP{t) = 1.11 - 0.004 T(t) (2) where T(t) is the temperature at the condenser and absorber. The par- ticular system parameters used for> the present study are listed in Table 1. The standard units are SI,,withthe numbers in parentheses referring to the English system.· The system coefficient of performance is determined by these parameters as well as the forcing function rep- resented by the real or synthetic weather data. WEATHER DATA The weather· data: for any given m6nth' and for 'severa 1 years is co 1- lected and used. in two,ways., Firstt.the houy-ly temperatures and inso;.. latfon readings are sorted so that the probability of obtaining any combination of temperatures and lnsolation is computed·· based on·all. the hourly readings for the data. base for .the· chosen month. · Secondly; this same. data base is used to obtain constants in assumed temperature and insolatfcm profiles as functions of time, via least square fitting. Although the profile has the same general form for all days, it does float dependingupon the average value for the particular day. For purposes of estimatingthe coefficient of performance, it is assumed that the daily temperature and insolation averages occur with the probabilities previously derived for the entire data base. The weather statistics therefore are represented using a joint probability density matrix and at most six constants. From these, the hourly weather data, either on a daily basis or on a monthly basis, can be obtained. For systems that are air-cooled, the weather data is limited to dry-bulb temperature and insolation whereas for water-cooled absorption systems it is necessary to include wet-bulb temperature. For water-cooled systems, the approach used is to define a state vector !(t) such that Page 227 Tit) !_(t) = I(t) (3) Tw(t) where Td(t) is the hourly dry bulb temperature, Tw{t) is the hourly wet- bulb temperature, and I(t) is the hourly solar insolation and !_(t) = A f.(t) (4) where all al2 al3 F1(t) A = a21 a22 a23 and .E.( t) = F2(t) (5) a3l a32 a33 F3(t) - ~ere a;. 's are constants that allow us to stud/ thEL effect of insola- t1on andJtemperatures on each other. If the actuathdurly values of the state vector is !, then, an estimate of the errors· s,~uared is L [~r -x{ [~r -xJ. E(.\i ( 6) Data · These error terms are computed for the entire data base that consists of one given month for several years. The numb~r of years chosen is generally a function of the available capacity on a computer. The functions in f{t) are selected such that F1(t) = Td(t) = Tdav{a1 sin wt+ a2) (7) F2(t) = I(t) = Iav(a3 + a4 cos e)exp(-K/cos e) (8) F3(t) = Tw(t) = Twav(a5 sin (wt+~)+ a6) (9) where tis time, e is the angle between sun vector and local normal, K is the extinction coefficient, a; are constants determined by solving equation (10) and w = 0.2618. The functions in f.(t) are chosen such Page 228 that the insolation varies as a function of time taking the extinction coefficient K into account, whereas the temperatures are constructed by two sinusoidal terms. Minimizing the error, E(eTe), with respect to each parameter, a;, leads to T [ [(L x)-x] -A-aa -a. (~ £) = 0 (10) Data t 1 This yields as many equations as there are unknowns, in this case six. Once the ai parameters have been determined in Eqs. (7-9), then the scheme yields equations that can be used for reconstructing the hourly dry-bulb temperature, wet-bulb temperature, and insolation values for any month of the season, provided an average temperature and inso1- ation is specified. The scatter diagrams for insolation, wet-bulb, and dry-bulb tem- perature can be generalized using a joint probability density function. This can then be represented in matrix fornra.s discussed by Davis (5). This matrix yields a probability Pijk for the occurrence of some value Tdi, Twj and Ik. The values for Tdi, TwjJ and lkare selected to represent values above and below na where n determines the size of the probability density matrix and o: is the standard deviation. These . values of wet-bulb temperature; dry".'bulb temperature, and insolation are in turn used in conjunction with the six constants derived,earlier to reconstruct hourly data for temperature:and insolation. The cooling capacity Cijk required is computed using reconstruc:teddata based on every set of Tdi, Twj, Ik in the joint probability matrix. The total cooling capacity is obtained by computing ECijkPijk· Similarly, we obtain an estimate of the total solar energy 1nc1aent on the collector during a given time period, as well as the coefficient of performance {COP). . If the system is air-cooled, the weather data, as mentioned earlier the state vector ~{t) becomes [Tit)] X{t) = ·. (11) - I(t) and !(t) = A F(t) where Page 229 ( 12) -, LB and F1(t) and F2(t) are still given by eqs. "@;6. The procedure pre- viously outlinea is again used to obtain the_ a; parameters. The scatter diagrams for insolation and ambient dry-bulb tempera- ture can be generalized using a joint probability density function. This matrix yields a probability Pij for the occurrence of some value Ti and Ij. The values of T; and Ij are selected to represent average values above and below no where n aetermines the size of the probability density matrix and cr is the standard deviation. The values T; and Ij are in turn used in conjunctio~with the five·constants derived earlier to reconstruct hourly data for temperature and insolation. The cooling capacity C;j required is computed using reconstructed da:ta based on every set of (T; , I j). __ AIR-COOLED SYSTEM SIMULATION The system performance for an air-cooled system such as that shown in Figure l, using real and synthetic data was obtained for the month of July using five years of data. The synthetic data was generated by the previously outlined method for various values of a;j. It was found (Ref. 7) that a12 = a21 ~ 0.01, a11 = a22 = 1 gave the best results. For this case, ,twas determined that a1 = 0.071, a2 = 0.972, a3= 0.093, and a4 = 2.06. This information is used to draw the temperature and insolation-profiles shown in Figure 2. Super-imposed on the plot are a randomly chosen set of actual data that have been normalized, for pur- poses of comparison. The joint probability density for temperature and insolation was obtained for a coarse as well as fine grid as shown in Tables 2 and 3. This information, in conjunction with the results of Figure 2, is used to compute the system COP for the absorption air-conditioning system described earlier. The COP was computed for all the (T,I) pairs in Table 3, but only for a selected set of pairs for the coarse grid from Table 2. A typical variation of the COP is shown in Table 4 correspond- ing to the coarse grid. This information should be read in conjunction with Table 2, i.e. the COP of 0.47 has a probability of. 0.457, which is the probability of having_T = Tav·.:!:. a and I.= Iqv .!_ a and.so on. We note that the trends confirm the fact that COP increases with tempera- ture and insolation owing to better collector efficiency and higher heat inputs. Long term (monthly) system performance using various data is shown in Table 5. Depending upon the method of estimation, the COP based on synthetic data.varies from 0.43 to 0.45 as compared to 0.46 for real data. No advantage is gained by using a fine grid which is there- fore not recommended. It is interesting to note that had the COP been Page 230 based on a normal joint probability distribution, an estimate of 0.41 is obtained. The top entry in Table 5 of using a fixed average temper- ature gives the largest error. ·.. The total insolation iritident:on the co 1l ector is shown in the second column and again> fairly good agreement is evident between stochastic and actual data~< Perhaps the rnost impor- tant entry is the last column~ The use of a coarse·gri'd for' synthetic data requires 8 points for.COP computatiqns,.compared434>forreal weather data. This indicatesthit,great saxingsthat.are incurred · especially when designing>storage;systemstfot>solar,applications ·•• . The long term (n1cmthly) 'toP'.base'd .bl rea~/iUld syrrthefic ·data is compared .to .the.,short term\(daJly) .. ··variati onin Figure• .. 3, >Clearly. the COP based on either-.set of data;is not.a goodestimate'Of short term variations.\ Ftnally~·.·.the;:long··terrnCOPfor stochastic dataandfive·. years of,real data are compared in Table 6 showing. very good agreement. ·, . '. . .. : .. The ~ystem performance for real and stochastic wea1:h~r for an entire season is shown in Table 7. Comparisons are made for the case where cut-off temperatures are fixed and also allowed to··float as a function of condensing temperature. We note that the comparisons are fairly good. WATER-COOLED SIMULATION The constants a 1 were obtained using five years of data for July a~d aij = 1 for i = J and O for i -; j. For this case, it was deter- mined that a1 = 0.078,a2 = 0.997, a3 = 0.019, a4 = 1.012, a5 = 0.013, and a6 = 2.312. This information is used to draw the temperature and insolation profiles shown in Figure 4. Superimposed on the plot are a randomly chosen set of actual data, that have been·normalized, for purposes of comparison. The joint probability density for wet-bulb temperature, dry-bulb temperature, and insolation was obtained and is pictorially illustrated in Fig. 5. The wet-bulb is divided into four intervals, viz.+ o, o to 2o, 2o and higher, and finally -o and lower. Similarly, the dry-bulb temperature and insolation are each divided into four regions, thus yielding a 4 x 4 joint probability matrix with a possibility of 64 entries. As an example, Fig. 5 shows that the joint probability of Td ±. oTd, Tw + oTw and I±. oI is 0.27. The significant probabiliti~s are shown in Table 2~ We note that only 19 areof significance with the remaining 45 being zero. This information, in conjunction with the results of Fig. 4, is used to compute the system COP for a water-tooled absorption air-conditioning system discussed earlier. The COP was computed for the significant probabilities and is shown in the last column of Table 8. This information should be read in conjunction with the actual probability, i.e. the COP of 0.45 has a probability of 0.27, which is the probability of having the temperatures andinsolation to within+ a of their average values as shown by the ijk = 222 entry. We note that the trends confirm the f.act that COP increases with Page 231 temperature and insolation owing to better collector efficiency and higher heat inputs. Monthly system performance is shown using various data in Table 9. The entries without the wet-bulb temperature are results obtained from an earlier study (7,8). It shows a comparison of stochastic predict- ions to actual data for air-cooled absorption systems. The inclusion. of wet-bulb in stochastic predictions yields a COP of 0.42 as compared to 0.44 for real data. The top entry in Table 3 of using a fixed average temperature (6) gives the largest error. The total insolation incident on the collector is shown in the second column and again fairly good agreement is evident between stochastic and actual data. Perhaps the most important entry is the last column. The use of syn- thetic data requires 8 points for COP computations for air-cooled systems and 19 points for water~cooled absorption air-conditioning systems compared to 434 for real weather data. This indicates the great savings that are incurred especially when designing storage sys- tems for solar applications. The previous predictions have been limited to July, 1957. Shown in Table 10 is a comparison of COP and total insolation for the sto- chastic predictions with the years 1954 to 1958 which comprise the original data base. Fairly good agreement is seen in each case. Finally the stochastic predictions are compared to the real data simulations for an entire season (1957) shown in Table 11. The cut- off temperature of the absorption cycle is floated as a function of the wet-bulb temperature. It is seen that the comparisons are very satis- factory. CONCLUSION System COP, total insolation, and useful energy delivered using the joint probability density approach seem to be in good agreement with real data when compared on daily, monthly and season basis. Since the present scheme reduces the data necessary for simulations in a local region, considerable savings in system simulation, both in complexity and time, result. Any local region can be characterized by six constants and, in this case, nineteen data sets. Such compact information is even amenable to hand calculators for design purposes. It is therefore concluded that the present scheme of taking a large body of local data and compacting it while retaining its probabilistic structure gives the designer a compact and inexpensive tool for sizing solar systems. Page 232 NOMENCLATURE A Correlation matrix between ambient dry-bulb temperature and insolation A Col.lector area, m2 (sq. ft.) a .. Constants in the A matrix lJ b Temperature coefficient for UA, 1/0c {l/°F) COP Coefficient of performance> Cooling capacity required for a ~iV~h sef ofwet>bulb • dry- bulb temperatures,. and' insolation, ~,atts (BTU/hr) c. . Cooling· capacity required fori a givkn set of\:iry-bulb tempera- lJ tures andinsolation, watts··(BTU/hr)· . . · · E Error term which is minimized in least square fit F(t) State vector representing temperatures and total insolation profi1 e F1 (t) Assumed ambient dry-bulb temperature profile F2(t} Assumed total .insolation profile F3(t) Assumed ambient wet-bulb temperature profile I(t) Hourly total (direct and diffuse) insolation, watts/m2 (BTU/hr sq.ft.) Average hourly insolat1on ,. I Actual hourly insolation normalized by the daily average insolation K Extinction coefficient for insolation passing through atmosphere dimensionless m Water flow rate, Kg/hr (lb/hr) p.,k Entry in joint probability density matrix which specifies the 1J probability of obtaining any combination of temperatures and insolation simultaneously, i = l to 4, j = 1 to.4, and k = 1 to 4 Q Daily total insolation," KJ (BTU) t Time Page 233 Tc_0 (t) · Temperature at which the absorption cycle begins operation Td(t) Hourly ambient dry-bulb temperature, 0c (0 F) Tw(t) Hourly wet-bulb temperature, 0 c {°F) Average hourly ambient dry-bulb temperature Average hourly wet-bulb temperature Actual hourly ambient dry-bulb temperature normalized by the average dry-bulb temperature Actual hourly ambient wet-bulb temperature normalized by the average wet-bulb temperature Collector loss coefficient, watts/0c m2 (BTU/hr °F ft2} State vector representing dry-bulb and wet-bu1b temperatures and insolation as functions of time X" Actual hourly values of the state vector a Absorptivity a. Parameters solved for in least square fit, i = 1 to 6 1 e Collector tilt angle; deg. w Cyc 1e frequency, in this study 21r/24 radians/hr A Time shift for wet-bulb temperature· e Time dependent angle between the sun vector and local normal, deg. Transmittance ACKNOWLEDGEMENT This work is supported by a continuing ERDA grant under contract No. E(40-1 )4976. The assistance of E. 0. Bazques in computer simulation work is greatly appreciated. Page 234 REFERENCES (1) Liu, 8. and R. Jordan, 11 The Interrelationship and Characteristic Distribution of Direct, Diffuse, and Total Solar Radiation." Solar Energy, (4), 3, July, 1960. (2) Threlkeld, J.L. and Jordan, R.C., 11 Direct Solar Radiation Available on Clear Days. 11 ASHRAE Trans. Vol. 64, 1958, p. 45. (3) American Society of Heating, Refrigerating, and Air-Conditioning Engineers, 11 Procedures for Determining Heating and Cooling loads for Computerized Energy Calculations--Algorithms for Building Heat Transfer S~btoutines, 11 1971. (4) Sadler, G.W., "Direct and 'Diffuse Insolation Using Approximation Methods Applied to Horizontal Surface Insolation, 11 Solar Energy, (17), l, April, 1975·. . (5) "Extended Abstracts--1975 International Solar Energy Society Congress and Exposition. 11 Held July 28-August 1, 1975, Los Angeles, California. (6) Morse, F.H., R.W. Allen, D.K. Anand, and Lb. Bazques, 11 Thermal Performance Predictions of a Solar Absorption Air-Conditioning System, 11 presented at the International Solar Erier'Ql'; Soci etl Congress, Los Angeles, July 28-August 1," 1975~ ··· (7) Anand, D. K., R.W •.A llen, and E.O. Bazques, 0~eather "Representation Using Stochastic Methods, 11 Proceedings of the ~ \ I \ z a:: 680 o w I \ I \ (200) ~ 0.. _J :wit I \ I \ 0 I CJ) I- I \ I \ ~ 15.6 510 (60) I \ I \ (150) I \ I \ I V 2 4 6 8 10 12 HOURS FIGURE 4-WEATHER DATA FOR TYPICAL DAY (JULY 4,1957) FOR WASHINGTON D.C. 8 Page 284 ~ 0 )I( ~ J: -- '::: :, I-I .C...D... . 0.65 "' \.. I 68 CJ) ' (20) ~ a.. ' I 0 I ~ () ~ w '\ I )- 0.60 51 I- _J '\ (.) \./ (15) () )- ~ (.) <;{ I (.) I (.!) I o.55 34 z (10) :J 0 0 (.) I 2 4 6 8 10 12 HOURS FIGURE 5 - FLOATING OF ABSORPTION CYCLE FOR WEATHER DATA SHOWN IN FIGURE 4. a.. 0 (.) ~ w I-- CJ) >- 0.3 (f) 10 20 30 DAYS >- 2.11 I- (2) (.)lO ~o <;{ (.) -)I( (.!) ~ 1.055 Z CD (I) _J- O-:, o:::.::: (.) 10 20 30 DAYS FIGURE 6- PERFORMANCE VARIATION FOR MONTH OF JULY. 9 Page 285 COLLECTOR*; u 0.567 (0.10) b 0.0027 (0.0015} A 27.87 (300} /3 36° PLATE o<'. 0.9 r 0.88 ,:,( 0.04 OESIGN POINT TEMPERATURE: GENERATOR/CONDENSER 90.6/37.8 (195/100) EVAPORATOR/ABSORBER 7.2/37.8 (45/100} Q 10,550 (3600) m 1134 C2 500) CYCLE COP * DOUBLE GLAZED,SELECTIVE SURFACE. TABLE I- PARAMETERS FOR SYSTEM LOCATED AT 36°N. (UNITS GIVEN IN NOMENCLATURE) INSOLATION (1)- 121.0 425.8 730.8 10'35.5 WATTS/M2 (38.35) (135.0) (231.7) (328.3) (BTU/HR FT2) TEMPERrTUR: (T_) 38.:56 C 0 0 0 0 (101.06) (°F) 32.72 Io b141 10.oso I I0 .031 I 0 (90.9) 27.06 jo.1s~I 10.4s11 @ill] 0.002 (80.7) 21.44 [ODIS! 100421 0 0 (70.6) 1!:!.78 0.001 0.005 0.001 0 (60.4) o-T =5 .7 (10.2) uy = 304.7 (96.6) TAE:ILE 2 - JOINT PROBABILITY MATRIX OF INSOLATION AND TEMPERATURE FOR JULY. 10 Page 286 INSOLATION (I)- 120.96 425.79 730.78 WATTSIM2 (38.35) (135.0) (231.7) (BTU/HR FT2) TEMPERATURE (T) ! 32.72 °C 0.31 0.48 0.52 (90.9) (°F) 27.06 0.27 0.47 0.51 (80.7) 21.44 0.24 0.45 (70.6) TABLE 3 - VARIATION OF DAILY COP FOR DIFFER- ENT JOINT PROBABILITIES FOR JULY. TOTAL COOLING SYSTEM CAPACITY T, I PAIRS USED COP x 105 KJ (BTU) 1.80 HOURLY DATA 0.36 (1.71) 434 1.66 STOCHASTIC .34 (1.57) 8 TABLE 4 - COMPARISON OF SYSTEM PERFORMANCE. 11 Page 287 • 1-c 1011s-11,,s Rm 1021> • EIGHTH ANNUAL PITTSBURGH CONFERENCE Within REDUCTION OF HIOH ORDER SYSTEMS, Session ON the Organizer ind Cheirman: N.K. SINHA, McMaster Univeroity MODELING AND SIMULATION Wet Alli "Analytieal Methods or Reducing Linear 441' Systemo•, Y. Shameah, Unlveralty or APRIL 21-22, 1977 Pitt! Pennsylvania Pho "Routh Approximation in State Space•, H1urioe r. Hutton, Tho Singer Company Benedum Engineering Hall Ho tel University of Pittsburgh 340 •on tht Controllability or Singularly Place Pitt! ferturbed Nonlinear Syate11a•, P. D Pho Sannutl, Rutgora Unlveralty 00 "Singular Perturbationa and More Than 220 Papers On: Aggregation•, J. Hiekin and N. K. Sinha, HoMaater Uni veralty • SOCIO-ECONOMIC • REGIONAL PLANNING SYSTEMS • BIOMEDICAL SYSTEMS • ENVIRONMENTAL • ECOSYSTEMS AlthOL t 1-D 10:15-11 :-5 R11 ,21 t of 1he Pittsb) ve , no SIMULATION • URBAN MODELING rooms MODELINO APPLICATIONS, Seaalon Chairman: ons as • SIMULATION IN • ENERGY RESOURCES soon AMR KHADR, The Univeroity or Pitteburgh serva- EDUCATION • TRANSPORTATION tions. • optimal reedbaok Control In a Crane • ECONOMIC MODELING • AND MANY OTHER Syatu•, S, P. Chaudhuri, The Charlea • MODELING AND SESSIONS Stark Draper Laboratory ESTIMATION "Hierarchy or Simulation Model• ror a Turbofan Oaa Engine•, W, !, Lon1enbak1r and R, J, Luka, Unhoralty or Notre 01111 No to 1ilable Sponsored by at the "Model or Ola,, rorehearth Dravdovn•, Robert R, McConnell, C1rn11l1-M1llon Unlveralty and ft, !u11ne Ooodaon, Purdue Department of Electrical Engineering Unlveralty School of Engineering •A Dyna•io Modal ot a Recuperated University of Pittsburgh lnduatrial rurneoe•, Nealey M, Rohrer, Pittsburgh, Pennsylvania Univeralty or Pltteburgh Regis! •seaeonal Stochaatlo Simulation !xperl- Ion is In Cooperation With availa unta on Solar Air Condltfonlng /h" is mailec Syateme•, ! . O Bnque,, D. K. Anand and ation R. W. Allon, Univeraity or Maryland The Pittsburgh Sections and lume PROO of the tes at the Cc Institute of Electrical and Electronic Engineers and The Instrument Society of America and The Systems, Man and Cybernetics Society The Society for Computer Simulation The International Association for Mathematics and Computers in Simulation (formerly AICA) Additional Events on Thursday Conference Committee April 21, 1977 Michael A. Shanblatt Martin Savol C. P. Fong Leone Monticone Chin Shiek Jang G. Lee Chang-Eun Kim Khe-Tai Ma Suk H. Lee Aly Abulleil COMPLIMENTARY COCKTAIL PARTY -5:00-6:oo p.m. See Registration Desk for Location Conference Co-Chairmen William G. Vogt Marlin H. Mickle See Registration Desk for Additional Listings Page 288 SEASONAL STOCHASTIC SIMULATION EXPERIMENTS ON SOLAR AIR CONDITIONING SYSTEMS D.K. Anand R.W. Allen E.O. Bazques Professor Professor Research Assistant Department of Mechanical Engineering University of Maryland College Park, Maryland 20742 ABSTRACT Real weather data and stochastic weather models are s~ntation of these two. weather paramters. For used in simulating the perfonnance of solar powered systems· that are water-cooled (9), the coefficient air•cooled and water-cooled air conditioning sys• of performance of the absorption cycle is dependent tems for an entire cooling season. The simulations uJ)On the wet-bulb temperature, thus necessitating included various parametric models for the absorp- the stochastic prediction of an·additional weather tion machine and variation of collector area and parameter. mass flow rates. It is concluded that the stochas- tic data yield satisfactory results for various This paper is a compendium of the work done on the system configurations while permitting very in- long-term perfonnance predictions of air-cooled expensive simulations. as well as water-cooled solar J)OWered absorption air-conditioning systems. Specifically, the INTRODUCTION calculations are based on a stochastic model of the weather parameters, dry-bulb temperature, wet-bulb The performance as well as design of solar powered temperature, and insolation which is constructed cooling systems, along with the solar energy con- using historical information. Basically, a statis- tributions to the cooling load of a building, re- tical approach is used combined with state represen- quires a good knowledge of temperature and insola- tation and this weather data is modified into a tion as well as other climatological data for more compact, useable, inexp~nsive form. specific regions. This data must be collected for long periods of time so as to be sufficiently rep- The weather data for any given month and for several resentative. Such data has been recorded, usually years is collected and used in two ways. First, on an hourly basis, at many weather stations and is the hourly temperatures and insolation readings readily available. In the past, the accumulated are sorted so that the probability of obtaining weather data has been used either on a very short any combination of temperatures and insolation is time duration basis or on an average basis for computed, based on all the hourly readings for the estimating cooling loads. The first method is data base for the chosen month. Secondly, this expensive and the second is often not representa- same data base is used to obtain constants in tive. This is particularly true for computer sim- assumed temperature and insolation profiles as ulations that predict performance of solar heating functions of time, via least square fitting. and cooling requirements on a seasonal basis. For Although the profile has the same general form for this reason, many forlll.llas for estimating weather a11 days, it does float, depending upon the average data have been presented in the literature (l, 2, value for the particular day. For purposes of 3, 4). Although the present methods are easy to estimating the coefficient of performance, it is apply, they are often neither consistent nor do assumed that the daily temperature and insolation they adequately take into account the probabalistic averages occur with the probabilities previously distribution of weather history. One often succeeds derived for the entire data base. The weather in supressing spurious readings by approximation statistics therefore are represented using a joint methods to get smooth data. Such spurious readings probability density matrix and at most six con- result in the kind of structure one wants to re- stants. From these, the hourly weather data. tain and this can only be done on a probabalistic either on a daily basis or on a monthly basis. can basis. In a recent paper (5), however, methods be obtained. based on probabablistic considerations have been suggested although details are unavailable. A simple schematic of the general steps involved in stochastic versus actual hourly data system simula- The performance of air-cooled solar powered air- tion is shown in Figure l. conditioning systems was reported in earlier papers (7, 8). Since air-cooled absorption systems require For systems that are air-cooled, the weather data dry-bulb temperature and solar insolation, the is limited to dry-bulb temperature and insolation, analysis was restricted to the stochastic repre- requiring, as will be seen, specification of five Page 289 constants in the two assumed profiles. However, for water-cooled absorption systems it is necessary to also include wet-bulb temperature, requiring calculation of six constants in the three assumed profiles. AIR COOLED SYSTEM I [~ ! - i ]T ! .:. ( L [) I= 0 Data 1 t (7) If the system is air-cooled, the weather data required, as mentioned earlier, is dry-bulb temper- ature and insolation as functions of time. As stated in Ref. (8), the approach used is to define This yields as many equations as there are unknowns, a state vector _!(t) such that in this case five. Tit)] Once the ai parameters have been determined in Eq. [ (5-6), then the scheme yields equations that can !(t) = ( l ) be used for reconstructing the hourly dry-bulb I ( t) temperature and insolation values for any month of the season, provided an average temperature and insolation is specified. where Td(t) is the hourly ambient dry-bulb tempera- ture, l\t) is the hourly total insolation and The scatter diagrams for insolation and ambient dry-bulb temperature can be generalized using a !(t) = t .E(t) (2) joint probability density function. This can then be represented in matrix form as discussed by Davis in Ref.{5). This matrix yields a probability Pij for the occurance of some value Ti and J .• The where values for T; and I· are selected to reptesent l average values abov~ and below ncr where n determines (3) the size of the probability density matrix and a ! . [ ::: :::] '"' I(tl • [:: ::: is the standard deviation. The values Ti and I· are in turn used in conjunction with the five c5n- stants derived earlier to reconstruct hourly data for temperature and insolation. The cooling capa- city Cij required is computed using reconstructed Here ai .'s are constants that allow us to study the data based on every set of {T·, I·) in the joint effect ~f insolation and dry-bulb temperature on probability matrix. The totai colling capacity each other. If the actual hourly values of the is obtained by using rcjjpij· Similarly, we obtain state vector are X, then an estimate of the errors an estimate of the total solar energy incident on squared is - the collector during a given time period, as well as the coefficient of performance {COP). I [I !] The general form of the 5 x 5 joint probability X - !]T[I ! - = E(eTe) (4) density matrix used in the air-cooled system study Data t t is shown in Figure (2). It is noted that the dry-bulb temperature and insolation divisions in this matrix are equal to 1.0 a. WATER-COOLED SYSTEM These error terms are computed for the entire data base that consists of one given month for several The analytical development for treatment of weather years. parameters necessary for water-cooled system sim- ulations is similar to that for the air-cooled case. Choosing the weather profiles However, in addition to dry-bulb temperature and insolation, wet-bulb temperature must now also be ( 5) specified. Thus, for water-cooled systems, the approach used is to define a state vector X(t) such that - F2(t) " (a4 + a5 cos e)exp (-K/cos e) (6) and minimizing the error, E(eTe), with respect to ,!(t) " (8) each parameter, a; • 1e ads to I ( t) Page 290 where Td(t) is the hourly dry-bulb temperature, Tw(t) is the hourly wet-bulb temperature, and I(t) is the hourly solar insolation and !(t) = A f(t) (9) ( 16) where all [ ··. . \_ A = a . 21 (10) The 6 xi6. symmetic matrix ! is defined by '' 831 Here aij's are constants that again allow study of the eftect of insolation and dry and wet-bulb temperatures on each other. If the actual hourly values of the state vector is X, then an estimate kOS20 ko510 k1°1100 k1S10 k2S11 k2D1o11 of the errors squared is given-again in state fonn by equation (4). These error terms are computed ko5oo t1°0100 • k1 5oo t~,n 1tzC11 for the entire data base that consists of one given month for several years. The functions in F(t) "3°0200 k3Do1oo t4Dti1~1 "4°om (17) are selected such that - k}oo k4So1 "l11 F ( t) = Tit) = Td a v ( ex1 s i n wt + a ) ( 11 ) 8ij .. 8ji 1 2 "sC02 k5C12 k5Czz F2(t) = Tw(t) = Twav (a3 sin(wt +A)+ a4) (12) F3(t) = I(t) = !av (ex5+a6cos8)exp(-K/cos8) ( 13) where sin" wt 8-mk/cos e where ai are constants detennined by solving 5nm = I equation (14) and A represents a wet-bulb tempera- t ture phase shift. (18) Minimizing the error, E(eTe), with respect to each cnm cosn 8 e-mk/cos e = parameter, a;, leads to the state equation (7). I t This yields as many equations as there are unknowns, in this case six. Computing the partials and solv- ing for the parameters ai leads to Dijlm = L siniwt sinj(wtH)cos1e e-mk/cose -1 t .!! = ~ .!! (14) where and a, d110 a2 dOlO ex = Cl3 R = d021 ( 15) Cl4 d020 (19) Cl5 do k2 = 111 813 + 821 123 + 831 833 a6 dl 2 2 2 k3 = 812 + 822 + a32 Page 291 thermal performance is taken to be the ratio of the chilled water produced to the daily solar rad- iation sul!lned over the cooling season. k4 = al2al3 + a22a23 + a32a33 ( 19) The system modeled in this study was assumed to have quasi-steady response characteristics, res- k5 = al32 + a232 + a332 ponding il!lnediately to hourly changes in the day insolation. It was assumed that all of the thermal transient responses equilibrated within the hourly In sulllning the above tenns, the data and t refer time interval. The simulation of the air-condi- to the same time span. tioning system requires the specification of the generator/condenser/evaporator/absorber conditions Once the a1 parameters have been determined in as well as the solar collector characteristics. Equations lll-13), then the scheme yields equations All mathematical details of the system as well as that can be used for reconstructing the hourly dry- its components appear in a previous paper (Ref. 6) bulb temperature, wet-bulb temperature, and insola- which dealt with a parametric study. For purposes tion values for any month of the season, provided of floating the absorption cycle, the cut-off an average temperature and insolation is specified. temperature and cycle COP are given by four options; three for the air-cooled case and one for the water- The scatter diagrams for insolation, wet-bulb, and cooled case: dry-bulb temperature can again be generalized using a joint probability density function. This can AIR COOLED: then be represented in matrix form. This matrix Enql 1sh Units SI Units yields a probability Pijk for the occurance of some value Tdi' Twj• ano Ik selected to repre- Option 1 COP(t) • l.025 • 0.005 Td(t) COP(t) • 0.865 • 0.009 Td(t) sent values aoove and below no where n detennines Tc_0 (t)• 2.35 Td(t) • 73.0 Tc.0 (t) • 2.35 Td(t) • 16.6 the size of the probability density matrix and cr Option 2 COP(t) • 0.85 COP(t) • 0.85 is the standard deviation. These values of wet- bulb temperature, dry-bulb temperature, and insola- T,.0(t)• 170.0 r,.0 (tl • 76.67 tion are in turn used in conjunction with the six Option 3 COP(t) • 1.05 • 0.004 Td(t) COP(t) • 0.922 • 0.0072 Td(t) constants derived earlier to reconstruct hourly data r,.0(t)• 2.35 Td(t) • 34.0 r,.0(t) • 4.23 Td(t) • 41.2 for temperature and insolation. The cooling capa- city Cijk required is computed using reconstructed WATER COOLED: data based on every set of Tdi• T ·, Ik in the joint probability matrix. T~e to!~, cooling capa- Option 4 COP(t) • 1.11 • 0.004 Tw(t) COP(t) • 0.982 • 0.0072 T,,(t) city is obtained by computing rcijkpijk· Similarly, Tc_0(t)• 2.35 Tw(t) • 13.0 Tc.0(t) • 2.35 Tw(t) • 16.6 we obtain an estimate of the total solar energy incident on the collector during a given time where the T(t) is the temperature at the condenser period, as well as the coefficient of perfonnance and absorber. Option 3 represents a system with a of the system. heat exchanger with a low efficiency while Option 1 is closer to a thermodynamic simulation. The par- The general form of the 4 x 4 x 4 joint probability ticular system parameters used for the present density matrix used in the water-cooled system study are listed in Table (1). The system coeffi- study is shown in Figure ( 3). It is noted that the cient of perfonnance is detennined by these para- dry-bulb temperature, wet-bulb temperature, and meters as well as the forcing function represented insolation divisions in this matrix are equal to by the real or synthetic weather data. 1.0 cr. Figure (4) demonstrates two typical entries in a 4 x 4 x 4 matrix for May. SYSTEM SIMULATION RESULTS In addition to the 1.0 a division 4 x 4 x 4 matrix, In the execution of system simulations for air- two 3 x 3 x 3 joint probability matrices are cooled and water-cooled systems, several effects studied. One also uses 1.0 a divisions but can be studied simultaneously. Among those of "compacts" the information available in the fourth interest are: the use of the different COP, Tc-Q (k) entries in the 4 x 4 x 4 matrix into the third options on system performance, the use of differing (k) entries in the 3 x 3 x 3 matrix, thus decreas- numbers of years of weather information as data ing the loss of infonnation which occurs when a bases, the use of differing joint probability fourth entry probability is eliminated. A "coarse" density matrices in the stochastic calculations, 3 x 3 x 3 matrix is also applied in the simulations the effect of using different aij values in the of water-cooled systems which uses 1.5 o divisions correlation matrix A, and finally, what effect, if and also compacts the fourth entries. any, the use of dif1erent Tw phase shifts has on the simulations. The accuracy of these system SYSTEM DESCRIPTION simulations is then determined by comparison to si1111lations using real hourly weather data through- The system under consideration consists of a solar out the cooling season. An over-view of the many collector and an absorption cooling machine. The simulation possibilities is given in Figure (5), daily thermal performance of this system is defined as the ratio of.the daily thermal energy of the It should be noted that for air-cooled systems, use chilled water produced to the daily total solar of a fine grid (0.5 o division) and nonnally dis- radiation incident on the co 11 ector. The seasona 1 tributed 5 x 5 joint probability matrix was studied in a previous paper (Ref. 7) and not recommeded and Page 292 hence is not studied here. Also, the use of the storage systems for solar applications. correlation matrices 2. The trends confinn the fact that COP increases with temperature and insolation, owing to 0.8 0.0] better collector efficiency and high heat A = [ inputs. 0.2 0.8 3. For both air-cooled and water-cooled systems, the increase of the data base from 5 to 7 years for air-cooled systems and significantly improved the accuracy of the stochastic predictions. Hence a large histor- ical weather data base for a region is desirable 0.9 0.1 when using the stochastic method. 0.1] ~ = [ 0.1 0.9 0.1 4. Stochastic estimation of total insolation is 0.1 0.1 0.9 usually more accurate than estimation of system COP due to the anomaly of cut-off temperature in absorption systems at low insolation levels. for water cooled systems is due to accurate simula- 5. The best stochastic simulation results during tion results obtained using them in previous the cooling season occur with June, July, stochastic simulation experiments (Ref. 7, 8, 9). August, and September. Early (May) or late (October) in the cooling season, the results Typical stochastic simulation results are shown for tend to be less reliable. a seven year basis for uncoupled~ matrices and compared to the actual weather data runs in Table 6. The use of an~ correlation matrix which gives (2). Stochastic prediction on a monthly and a slight correlation of temperatures to insola- seasonal basis is seen to be quite good. tion in both air and water-cooled systems tends to give better simulation results when Table (3) indicates the great savings that are compared to an~ matrix which uncouples these incurred with stochastic simulations if the prob- parameters. ability matrices and temperature-insolation profile constants are available for a region. The use of 7. The simulations using actual 1975 data for the synthetic data requires only 9 points for COP Washington, D.C. area given results which are computations for air-cooled systems and 19 points comparable to those obtained for the years for water-ccoled systems compared to 434 for real 1954-1960. The total insolation is slightly weather data, and the stochastic predictions are lower than that of the base years, possibly accurate enough for system sizing. owing to the increase in air pollution in the 15 year interval. The parametric effects on system performance of varying the area of the flat plate collector, A, 8. In water-cooled simulations, the use of the and the mass flow rate of fluid through the col- 4 x 4 x 4 matrix gives much better results than lector, m, is studied also. Two approaches are the use of the coarse 3 x 3 x 3 matrix and used: 1) set A equal to a constant of 300 ft2 and hence is recommended over the latter. Also, vary mass flow rate from 2000 to 3500 lb/hr in the wet-bulb temperature phase shift has little 250 lb/hr increments, 2) set me qual to a constant overall effect on system performance predictions of 2500 lb/hr and vary area from 200 to 400 ft. or the resulting accuracy of these predictions, In all the present cases, rated evaporator tonnage, although use of the -3 hour Tw shift.gave qer• is constant at 3 tons (36,000 Btu/hr). Also slightly better results. constant are generator COP, rated generator temper- ature Tqr• and cut-off temperature Tc-o· System 9. For cases of varying collector area and mass performance, namely total insolation, total cool- flow rates, the stochastic formulation models ing effect, and system COP is then investigated the real data simulations very well even with through computer simulation runs for both stochas- a disparate data base and simplifications in tic and non-stochastic (actual) weather data for the heat transfer equations. the month of July, 1957 for the Washington, O,C, area. Trends in variation of system perfonnance CONCLUSIONS due to these varying areas and mass flow rates are then noted and the stochastic and non-stochas- System COP, total insolation, and useful energy de- tic results compared, some of which are shown in livered using the joint probability density approach Figures (6,7, 8}. are seen to be in good agreement with real data when compared on a daily, monthly, and seasonal basis. OBSERVATIONS Since the present scheme reduces the data necessary for simulations in a local region, considerable 1. The use of synthetic data required 9 points for savings in system simulation, both in complexity and COP computations for air-cooled systems and 19 time, result. Any local region can be characterized points for water-cooled absorption air-condi- by five or six constants and from nine to nineteen tioning systems compared to 434 for real wea- data sets. Such compact information is even amen- ther data. This indicates the great savings able to hand calculators for design purposes. It that are incurred, especially when designing Page 293 is therefore concluded that the present scheme of (6) Morse, F.H., Allen, R.W., Anand, D.K. and taking a large body of data and compacting it Bazques, E. 0., "Thermal Performance Predictions while retaining its probabalistic structure gives of a Solar Absorption Air-Conditioning System," the designer a compact and inexpensive tool for presented at the International Solar Energy sizing solar systems. Society Congress, Los Angeles, July 28-August 1, 1975. REFERENCES (7) Anand, D.K., Allen, R.W., and Bazques, E.O., (1) Liu, B. and Jordan, R., "The Interrelation- "Short and Long Term Comparison of Solar Ab- ship and Characteristic Distribution of sorption Air Conditioning System Performance Direct, Diffuse, and Total Solar Radiation," Using Real and Synthetic Weather Data," Proc. Solar Energy, (4), 3, July 1960. Eleventh IECEC, Lake Tahoe, September 19~ (2) Threlkeld, J. L. and Jordan, R.C., "Direct (8) Anand, D.K., Allen, R.W., and Bazques, E.O., Solar Radiation Available on Clear Days," "Simulation of Synthetic Weather Data for ASHRAE Trans., Vol. 64, 1958, p. 45. the Design of a Solar Powered Air Conditioning System," Proc. of the Seventh Annual Pitts- (3) American Society of Heating, Refrigerating, burgh Conference on Modeling and Simulation, and Air-Conditioning Engineers, "Procedures Pittsburgh, April 1976. for Determining Heating and Cooling Loads for Computerized Energy Calculations - Algor- (9) Anand, D.K., Allen, R.W., and Bazques, E.O., ithms for Building Heat Transfer Subroutines," "Solar Powered Absorption Air Conditioning 1971. System Performance Using Real and Synthetic Weather Data," Proceedings of the Interna- (4) Sadler, G.W., "Direct and Diffuse Insolation tional Solar Energy Society Conference, Using Approximation Methods Applied to Hori- Winnipeg, Canada, August 1976. zontal Surface Insolation, 11 Solar Energy, (17), l, April 1975. ACKNOWLEDGMENT (5) "Extended Abstracts - 1975 International Solar The work covered by this report was supported by U.S. Energy Society Congress and Exposition," Energy Research and Development Administration Contract Los Angeles, July 28-August 1, 1975. No. E(40-1)4976. SYSTEM TOTAL INSOLATIOU SIMULATION and SYSTEM COP T + 2o ~ ~...,. .. ...,o~ :-, ,§- >'fd + 2o ~ ~ I " I HOUR~1 DATA 'fd + 2o I I I 'fd :t " ,C--- ---- P(Td; •Ij ---- .,__~ I I I ALGORITHM; SYSTEM _,. TOTAL INSOLATION ld - 2o a) least square SIMULATION and I specification of SYSTEM COP I temperature(s) I and insolation I cld - 2o profiles b) joint probability density 111trices ' FIGURE 1 - COMPARISON BETWEEN NON-STOCHASTIC FIGURE 2 - GENERAL FORM OF 5 x 5 JOINT PROB- (ACTUAL DATA) AND STOCHASTIC STEPS ABILITY DENSITY MATRIX USED IN TO ABSORPTION SYSTEM SIMULATION AIR-COOLED STOCHASTIC SYSTEM SIMULATIONS Page 294 28.28 (82.91 2129 (7033) Tw // // I I // // I I / / I I / / ~ +2cr I I/ / (13431.190.7> 6 __________ _.I, )I" / / >~+2Ci I / 1 / Oi • 335.78(106.47) (292.3.8.14) 4 _____________. .,,, ON 14 16 18 HOUR FIGURE 8 - VARIATION IN Tc1N AND TcouT FOR JULY 7, 1957 WEATHER DATA FOR CONSTANT AREA AND VARIABLE FLOW RATES . I ,I ,I Page 296 l 'I AIR-COOLED AIR-COOLED AIR-COOLEO WATER-wuLEO COP, Te•o OPTION 1 COP, Te•o OPTION 2 COP, \:-o OPTION 3 COP, Te-o OPTION 4~1 O OJ [1 oJ JUS~ING ~ • 0 1 : ~. [~ ~] USING [1 USING T SHIFT • •3 HRS A • 0 1 0 5x5 A• OJ SxS w - 0 0 1 MONTH JPOM - 0 1 JPOM USING 4x4x4 JPOM ACTUAt STOCHA~Tff " arTU., < IC ACTUAL STOCHASTIC ACTUAL STOCHASTIC TOTAL .;YST. TOTAL YST. TOIAL ,,~,. TOTAL )YST. TOTAL ~YST. TOTAL i:,YST 1u1AL SYST. iTOTAL SYS1. I X COP I x COP I X COP I x COP I X COP I X COP l x COP I X COP 105 I(. 105 K. }~!,~· ?~!.~ 105 I(,: IRTUI i/RTU\ liim11 Jg;11~' 105 KJ IIITlll rn~,f' 4.52 4.67 4.52 4.6~, 4.52 4.67 4.52 4.63 ""y (4.28 0.391 (4.43: p.369 (4.28) 1).414 (4.43 b.37! (4.28) o.m (4.43 P.37, (4.28) 0.502 (4.39) 0.485 4.71 4.60 4.71 4.60 4.71 4.60 4.71 4.70 JUNE (4.46 p.366 (4.36; p.349 (4.46) b.427 (4.36 kl.40! (4.46) 0.393 (4.36 kl.38 (4.46) 0.486 (4.54) 0.475 4.46 4.63 4.46 4.63 4.46 4.63 4.46 4.61 JULY (4.23 p.352 (4.39] p.342 (4.23) k>.439 (4.39 k>.42! (4.23) 0.385 (4.39 b.37 .4.23) 0.478 (4.37) 0.464 4.25 4.18 4.25 4.18 4.25 4.18 4.25 4.07 AUGUST (4.03) P.360 (3.96) 0.346 k4.03} 0,431 (3.96 0.421 (4.03) 0.387 (3.96 0,37! (4.03) 0.481 (3.86) 0,467 3.82 3.77 1,3.82 3.77 3.82 3.77 3.82 3.70 SEPTEMBER (3.62) P.384 '3.57) J.376 ~3.62) b.426 (3.57 b.413 (3.62) 0.406 (3.57 (3.62) 0.501 (3.51) 0.475 2.91 3.37 ~2.91 3.37 2.91 3.37 2.91 3.24 OCTOBER (2.76) ).416 3.19) ~.404 ~2.76) ll.369 (3.19 b.370 (2.76) 0.412 (3.19 b.42l (2.76) 0.524 (3.07) 0.510 VERAGE OVER 4.11 4.20 4.11 4.20 4.11 4.20 4. 11 4.18 COOLING (3. 90 • 378 3. 98 0. 364 (3. 90) 0.418 (3. 98 SEASON (3.90) 0.39 (3.98 .38 (3.90) 0.495 (3.96) 0.479 TABLE 2 - COMPARISON OF STOCHASTIC TO NON-STOCHASTIC (ACTUAL DATA) SYSTEM RUNS - SEVEN YEAR BASIS TOTAL INSO'iTION SYSTEM DATA X 10 KJ COP POINTS (BTU) USED FIXED TEMPERATURE HOURLY CLEAR DAY 7.87 0.50 15 (218)* INSOLATION (7.46) Td, I .~i!. i AIR-COOLED 4.43 COP, (4.20) 0.350 434 _, Tc -o OPTION 1 i"1" ",,_' Td' Tw• 1 ~... WATER-COOLED 4.43 .... COP, (4.20) 0.475 434 .:.:.., \-o OPTION 4 Td' I I AIR-COOLED § COP, Tc·r OPTION 1 4,63 0,342 c:, -A • 01 o (4.39) 9 1J , f 7 YEAR BASIS I Td, Tw• I WrA,T1ER -COOLED COP, o,no, 4 4.61 A• 01 0 (4.37) 0.464 19 ij 1 00~ * MAXIMUM POSSIBLE - 0 0 1 , 7. YEAR BASIS TABLE 3 - COMPARISON OF SYSTEM PERFORMANCE AND DATA REQUIREMENTS Page 297 Reprinted from JOURNAL OF ENER_GY, Vol. 1, No. 5,_September-_October 1977,_P{! 319-323 . Copyright, 1977, by the American Institute of Aeronautics and Astronautics, and reprmted by perm1ss1on of the copyright owner Solar Air-Conditioning Performance Using Stochastic Weather Models D.K. Anand,* R.W. Allen,* and E.0. Bazquest University of Maryland, College Park, Md. The performance of a solar-powered water-cooled absorption air-conditioning system is obtained using real and synthetic data. The synthetic data are derived using five years of weather history and represented by a joint probability density matrix and six constants. The system performance is defined as the useful capacity of the absorption air conditioner divided by the total radiation incident on the collector. This performance is obtained as a function of dry-bulb temperature, wet-bulb temperature, and solar insolation. The coefficient of per- formance using real data and synthetic data is compared and the predictions based on synthetic data are quite good. It is concluded that synthetic data allow very inexpensive simulation and yield satisfactory results for design purposes. Nomenclature = average hourly wet-bulb temperature A = correlation matrix between ambient dry-bulb = actual hourly ambient dry-bulb temperature temperature and insolation normalized by the average dry-bulb temperature = constants in the A matrix that allow study of the =actual hourly ambient wet-bulb temperature effects of ambient dry-bulb temperature and in- normalized by the average wet-bulb temperature solation on each other; i = 1 to 3,j = 1 to 3. X(t) = state vector representing dry-bulb and wet-bulb = coefficient of performance temperatures and insolation as functions of time = cooling capacity required for a given set of wet- x = actual hourly values of the state vector bulb, dry-bulb temperatures, and insolation, watts 0/ = 6 x 1 matrix defined by Eq. (A 10) (Btu/hr) = parameters solved for in least-square fit; i = 1 to 6 cnm = coefficients defined by Eq. (A 13) =6 x 6 matrix defined by Eq. (A12) Du,m = coefficients defined by Eq. (Al3) w = cycle frequency, in this study 21r /24 rad/hr dn =coefficients defined by Eq. (Al 1) 'A =time shift for wet-bulb temperature 0 = time dependent angle between the sun vector and dnml =coefficients defined by Eq. (Al 1) E = error term which is minimized in least-square fit local normal, deg F(t) = state vector representing temperatures and total insolation profile Introduction F1U) = assumed ambient dry-bulb temperature profile = assumed ambient wet-bulb temperature profile I N designing solar-powered air-conditioning systems, F2 (t) F1 (t) = assumed total insolation profile especially as far as storage capacity is concerned, it is = hourly total (direct and diffuse) insolation, necessary to have a good knowledge of temperature, in-/(t) watts/m 2 (Btu/hr-ft 2 solation levels, and other climatological data for that region. ) = average hourly insolation Such data have been recorded hourly in many locations and are available in the form of tapes for different regions. = actual hourly insolation normalized by the daily The accumulated weather data have been used either on a average insolation very-short-time duration basis or on an average basis for K =extinction coefficient for insolation passing estimating cooling loads. The first method is expensive and through atmosphere, dimensionless cumbersome and the second is often not representativ·e. This =coefficients defined by Eq. (A14) is particularly true for computer simulations that predict =entry in joint probability density matrix which performance of solar heating and cooling requirements on a specifies the probability of obtaining any com- long-term basis. For this reason, many formulas for con- bination of temperatures and insolation structing weather data have been presented in the literature. 1-4 simultaneously; i = 1 to 4,) =Ito 4, and k = 1 to 4 Notably, the linear regression models, first suggested by Q =daily total insolation, kj (Btu) Jordan and Liu and subsequently refined by others, have been R = 6 x 1 matrix defined by Eq. (A 10) snm widely reported as alternative methods for solar applications = coefficients defined by Eq. (A I 3) for quick and inexpensive estimates. The degree-day method t =time for calculating building thermal loads to input into solar TC-0 (t) = temperature at which the absorption cycle begins simulations are less expensive and give satisfactory average operation performance values but cannot be used to examine unusual =hourly ambient dry-bulb temperature, °C (°F) conditions. It is evident that although the present methods are =hourly wet-bulb temperature, °C (°F) easy to apply, often they are neither consistent nor do they = average hourly ambient dry-bulb temperature adequately take into account the probabilistic distribution of weather history. In many cases, one succeeds in suppressing Presented as Paper 76-448 at the AIAA 11th Thermophysics spurious readings by approximation methods to get smooth Conference, San Diego, Calif., July 14-16, 1976; submitted May 5, 1977; revision received July 22, 1977. qata. Interestingly enough, such spurious readings result in Index categories: Solar Thermal Power; Thermal Modeling and the kind of structure one wants to retain, and this can only be Analysis. done on a probabilistic basis. In a recent paper, 5 however, *Professor, Mechanical Engineering, Solar Energy Projects. methods based on probabilistic considerations have been tResearch Asst., Mechanical Engineering, Solar Energy Projects. suggested, although details are unavailable. Page 298 320 ANAND, ALLEN, AND BAZQUES J. ENERGY The performance of air-cooled solar-powered air- above and below na, where n determines the size of the conditioning systems was reported in earlier papers. 7•8 Since probability density matrix and a is the standard deviation. air-cooled absorption systems require dry-bulb temperature These values of wet-bulb temperature, dry-bulb temperature, and solar insolation, the analysis was restricted to the and insolation are in turn used in conjunction with the six stochastic representation of these two weather parameters. constants derived earlier to reconstruct hourly data for For systems that are water-cooled, the coefficient of per- temperature and insolation. The cooling capacity Cu, formance of the absorption cycle is dependent upon the wet- required is computed using reconstructed data based on every bulb temperature, thus necessitating the stochastic prediction set of T"" T,,1 , I, in the joint probability matrix. The total of an additional weather parameter. cooling capacity is obtained by computing EC;1,P;1,. This paper is concerned with the long-term performance Similarly, we obtain an estimate of the total solar energy predictions of water-cooled solar absorption air-conditioning incident on the collector during a given time period, as well as storage systems. Specifically, the calculations are based on a the coefficient of performance (COP). stochastic model which is constructed using historical in- formation on weather from the Washington, D.C. area. System Simulation Basically, we use a statistical approach combined with state The system under consideration (Fig. I) consists of a solar representation and modify the data for ambient dry-bulb collector and an absorption cooling machine. The daily temperature, wet-bulb temperature, and total insolation into thermal performance of this system is defined as the ratio of a more compact, usable, inexpensive form. Recognizing that the useful daily capacity of the air-conditioner divided by the local microclimatic conditions are important, the packaging daily total solar radiation incident on the collector. The of a large body of data into a compact format is desirable. seasonal thermal performance is taken to be the ratio of the These data can then easily be utilized for solar system chilled water produced to the daily solar radiation summed design and for system design and performance predictions. over the cooling season. Weather Data Daily useful capacity of air conditioner The weather data for any given month and for several years [COP] ua.iy (la) Total incident radiation on collector are collected and used in two ways. First, the hourly dry-bulb and wet-bulb temperature and insolation readings are sorted so that the probability of obtaining any combination of E Daily useful capacity of air conditioner temperatures and insolation is computed based on all the cop sea\on r l seasonal = hourly readings for the data base for the chosen month. Secondly, this same data base is used to obtain constants in E Total incident radiation on collector assumed temperature and insolation profiles as functions of season (lb) time, via least-square fitting. Although the profile has the same general form for all days, it does float depending upon The system modeled in this study was assumed to have the average value for the particular day. For purposes of quasisteady response characteristics, responding immediately estimating the coefficient of performance, it is assumed that to hourly changes in the day insolation. It was assumed that the daily temperature and insolation averages occur with the all of the thermal transient responses equilibrated within the probabilities previously derived for the entire data base. The hourly time interval. The simulation of the air-conditioning weather statistics therefore are represented using a joint system requires the specification of the generator/con- probability density matrix and six constants. From these, the denser/evaporator/absorber conditions as well as the solar hourly weather data, either on a daily basis or a monthly collector characteristics. All mathematical details of the basis, can be obtained (see Appendix). system as well as its components appear in a previous paper 6 The scatter diagrams for insolation, wet-bulb, and dry-bulb which dealt with a parametric study. However, since the temperature can be generalized using a joint probability absorption cycle was air-cooled, the cutoff temperature and density function. This can then be represented in matrix form, coefficient of performance were assumed to be fixed. Since as discussed by Davis. 5 This matrix yields a probability P 11 , the present study assumed a variable wet-bulb temperature for for the occurrence of some value Tr1;, T.,'i, and h. The values a water-cooled absorption cycle, the cutoff and cycle COP are for Td;, Twj, and l, are selected to represent average values described by T,_0 (t) =2.35T.,. (/) -16.6 (2) COP(t) =0.982-0.0072Tw(tl (3) The particular system parameters used for the present study are listed in Table I. The standard units are SI with the numbers in parentheses referring to the English system. The system coefficient of performance is determined by these parameters as well as the forcing function represented by the real or synthetic weather data. Simulation Results The constants a; in Eqs. (A5) through (A 7) were obtained using five years of data for July and au= I for i = j and O for i"i"c-). For this case, it was determined that a 1 =0.078, CX2 =0.997, CX3 =0.019, CX4 = 1.012, CX5 =0.013, and a6 =2.312. This information is used to draw the temperature and in- solation profiles shown in Fig. 2. Superimposed on the plot, for purposes of comparison, are a randomly chosen set of L____ + + + + actual data that has been normalized. Q (COP) The joint probability density for wet-bulb temperature, Fig. 1 Solar-powered absorption air-conditioning system schematic. dry-bulb temperature, and insolation was obtained and is Page 299 SEPT.-OCT. 1977 SOLAR AIR-CONDITIONING PERFORMANCE 321 Table I Parameters for system located at 36° :'I Table 2 Significant probabilities and COP for Jub· COLLECTOR a 0567 (010) i j k P(Tdi ,Twj ,Ik) COP 0.0027 (00015) 2787 (300) 36° Ill 0.0109 0.26 PLATE 0.9 112 0,0552 0.25 0.88 121 0.0281 0.45 "' 0.04 122 0.0262 0.43 DESIGN POlNT TEMPERATURE 211 0.0257 0,29 GENERATOR/CONDENSER 906/378 ( 195/100) 212 0.0762 028 EVAPORATOR/ABSORBER 72/378 (45/100) 213 0.0467 0,27 Q 10,550 (36,000) 221 0.1057 0.47 m 1134 (2500) 222 0.2700 0.45 CYCLE COP 223 0.0871 0.43 a Evacuated and selective surface. 231 00267 0.51 232 0.0609 0.49 233 0,0238 0.47 321 0.0100 048 322 0.0481 0.46 323 0.0257 0.45 331 0.0100 0.52 332 0,0309 0.50 333 0.0209 0.48 Table3 Comparison of system performance and data requirements TOTAL SYSTEM DATA INSOLATION POINTS COP x I05 KJ (BTU) USED FIXED TEMPERATURE 8 10 12 14 16 18 15 (218)a HOURLY CLEAR DAY 0.5 7.87 TIME (HOURS) INSOLATION (746) flg. 2 Normalized synthetic temperature and insolation profiles ~ obtained for July using five years of data compared to a randomly 0:: 475 434 :, Td, I 047 0 (4.50) chosen set of real data. :,: I"-" ....,. 0" ' ~ Td,,;.,r 0.44 4.84 434 (459) u ., 0.43- - z 4.38 Td, I 8 ~Q 0.45 (415) :",:' Iu- g~ 4.81 19 I- 0:: ld,Tw,I 0.42 VJ 0.. (4.56) a Maximum possible. has a probability of 0.27, which is the probability of having the temperatures and insolation to within ± a of their average "i ' 3056 19701 values as shown by the ijk = 222 entry. We note that the trends Grd = 468 (842) confirm the fact that COP increases with temperature and 8870 Gr...,= 2 64 (476) insolation owing to better collector efficiency and hign heat 12816) inputs. Monthly system performance is shown using various data in fig. 3 .Joint probability matrix of insulation, dry-bulb temperature, Table 3. The entries without the wet-bulb temperature are and wet-bulb temperature. results obtained from an earlier study. 7•8 It shows a com- parison of stochastic predictions to actual data for air-cooled absorption systems. The inclusion of wet-bulb in stochastic pictorially illustrated in Fig. 3. The wet-bulb is divided into predictions yields a COP of 0.42 as compared to 0.44 for real four intervals, viz. ±a, a to 2a, 2a and higher, and finally, data. The top entry in Table 3 of using a fixed average - a and lower. Similarly, the dry-bulb temperature and in- temperature 6 gives the largest error. The total insolation solation are each divided into four regions, thus yielding a incident on the collector is shown in the second column and, 4 x 4 x 4 joint probability matrix with a possibility of 64 again, fairly good agreement is evident between stochastic and entries. As an example, Fig. 3 shows that the joint probability actual data. Perhaps the most important entry is the last of Td ± aTd, Tw ± aTw and J± a1 is 0.27. The significant column. The use of synthetic data requires 8 points for COP probabilities are shown in Table 2. We note that only 19 are of computations for air-cooled systems and 19 points for water- significance, the remaining 45 being zero. This information, cooled absorption air-conditioning systems, compared to 434 in conjunction with the results of Fig. 2, is used to compute for real weather data. This indicates the great savings that are the system COP for a water-cooled absorption air- incurred especially when designing storage systems for solar conditioning system discussed earlier. The COP was com- applications. puted for the significant probabilities and is shown in the last Variation of COP, total insolation, and daily useful energy column of Table 2. This information should be read in for different au's is shown in Table 4. Although case 2 ap- conjunction with the actual probability, i.e. the COP of 0.45 pears to be the worst case and case I appears to be the best Page 300 322 ANAND,ALLEN,ANDBAZQUES J.ENERGY Table 4 Simulation experiments where Td (() is the hourly dry-bulb temperature, T.,, ( t) is the hourly wet-bulb temperature, and /(t) is the hourly solar CASE 4 REAL I 2 3 DATA insolation, and COP 0.42 040 0.41 0.42 0.44 DAILY TOTAL X(t) =A F(t) (A2) INSOLATION 4.8 4.4 46 4.6 4.84 x 10 5 KJ (46) (42) (4.4) (44) (4.59) \BTU) where DAILY USE· FUL ENERGY 2.02 1.76 1.89 1.93 2.13 \Q}{COP) (1.92) (\.67) (\79) (202) au a12 a13 Fi (t) (\.83) KJ (BTU) A= a21 a22 a2.1 F(t) = F2 (t) (A3) CASE 1, a.11 a.12 a33 F.1(t) 0 0 o.1'j 0 :).I Here a/s are constants that allow us to study the effect of insolation and temperatures on each other. If the actual 0 I hourly values of the state vector is X, then an estimate of the CASE 3, CASE 4, errors squared is Oil 01 ::1 r:~ :~ ::1 E [( E x)-xr [ E X-x] =E(eTe) (A4) [ Data f t 005 005 I 01 01 09 These error terms are computed for the entire data base that consists of one given month for several years. The number of years chosen is generally a function of the available capacity Table 5 Comparison of COP and total insolation for data on a computer. base vs stochastic The functions of F(t) are selected such that STOCHASTIC 1954 1955 \956 1957 1958 COEFFICIENT OF 0.42 044 043 043 044 0 42 PERFORMANCE - TOTAL F2 (t) = Tw (t) = Twav(-.) Data (Al) X(t)= dn= E (a13Td+a23Tw+a33{)e-K!co,ecos0 (Al 1) Data Page 301 SEPT.-OCT. 1977 SOLAR AIR-CONDITIONING PERFORMANCE 323 The 6 x 6 symmetric matrix fl is defined by In summing the above terms, the data and t refer to the same time span. \koS20 koS,o k,D1100 k,St0 k2S11 k2Dt011 Once the cx, parameters have been determined in Eqs. (A5) I : through (A 7), the scheme then yields equations that can be koSoo k,Do,oo k,Soo k2So, k2C11 used for reconstructing the hourly dry-bulb temperature, wet- fl=EI bulb temperature, and insolation values for any month of the k3Do200 k1Dotoo k4Do101 k4Du111 season, provided an average temperature and insolation is I I specified. I k1Soo k4So, k4C 11 Acknowledgment I !3u =f11, ksC02 ksC12 This work is supported by a continuing ERDA grant under L ksC22 contract no. E(40-1)4976. (Al2) References 1 Liu, B. and Jordan, R., "The Interrelationship and Characteristic where Distribution of Direct, Diffuse, and Total Solar Radiation," Solar Energy, Vol. 4, July I960, pp. 1-19. Sn m-- £' .\.J' sin 11 wte-mK/cosl1 2 Threlkeld, J.L. and Jordan, R.C., "Direct Solar Radiation Available on Clear Days," ASHR AE Trans., Vol. 64, I 958, p. 45. 3 American Society of Heating, Refrigerating, and Air- C - '\' cos"ee-mK!co,O Conditioning Engineers, "Procedures for Determining Heating and 11111- '-' Cooling Loads for Computerized Energy Calculations-Algorithms for Building Heat Transfer Subroutines," 1971. 4 Sadler, G.W., "Direct and Diffuse lnsolation Using Ap- (Al3) proximation Methods Applied to Horizontal Surface Insolation," Solar Energy, Vol. 17, April 1975, pp. 39-46. 5 "Extended Abstracts-I 975 International Solar Energy Society and Congress and Exposition," Los Angeles, Calif., July 28-Aug. I, 1975. 6 Morse, F.H., Allen, R.W., Anand, D.K., and Bazques, E.O., ko=a11 2+a21 2+a31 2 "Thermal Performance Predictions of a Solar Absorption Air- Conditioning System," presented at the International Solar Energy Society Congress, Los Angeles, Calif., July 28-Aug. I, 1975. 7 Anand, D.K., Allen, R.W., Bazques, E.O., "Weather Representation Using Stochastic Methods," Proceedings of the Second Southeastern Conference on Appiications of Solar Energy, Baton Rouge, La., April 1976, pp. 375-380. k3 =a122 +a222 +a322 8 Anand, D.K., Allen, R.W., and Bazques, E.O., "Simulation of k =a a +a a +a a Synthetic Weather Data for the Design of a Solar Powered Air-4 12 13 22 23 21 33 Conditioning System," Proceedings of the Seventh Annual Piusburgh Conference on Modeling and Simulation, Pittsburgh, Pa., April 1976, (Al4) pp.1121-1I27. Page 302 J. A. Kirk Asst. Professor. Matrix Representation and Assoc. Mem. ASME D.K.Anand Prediction of Three-Dimensional Professor. Cutting Forces C. McKindra Research Asst. Matrix geometry techniques are applied to predicting three-dimensional cutting forces. In the present model a specific cutting plane is located and two-dimensional metal cut- Department of Mechanical Engineering, ting theory is applied. Force predictions in this plane are then matrix transformed to University of Maryland, three orthogonal forces acting on the cutting tool. Experimental results show the matrix College Park, Md. model accurately predicts three-dimensional cutting forces in turning of long slender workpieces. Experimental results are also compared to other analytical models described in the literature. Introduction The metal cutting process is one of the oldest and most funda- mental methods of reshaping metal into functional items. \Vork in the mechanics of the metal cutting process can be traced back as far as 1873 with the research of the French scientist Tresca. Since that time, much of the work has been of an empirical nature and has been V concerned with reducing the machining costs or producing compo- nents with better accuracy and surface finish. To improve understanding of three-dimensional turning, it is useful to have a mathematical model which predicts three-dimensional cutting forces for this process. One method of predicting three-di- mensional cutting forces is to apply two-dimensional metal cutting theory on a plane (which must be identified) where the cutting process appears to be two-dimensional. The forces which act on the workpiece in the radial, tangential, and axial directions can then be obtained by WORK PIECE a coordinate transformation. The purpose of this paper is to apply the concepts developed for two-dimensional metal cutting to a matrix Fig. 1 Schematic representation of two-dimensional orthogonal cutting model which predicts three-dimensional metal cutting forces. Pre- dictions of the matrix model (i.e., cutting forces) are compared to another model and to experimental data obtained in a turning oper- ation. Orthogonal Cutting The mechanics of the metal cutting process involve the removal of material in the form of chips. In orthogonal metal cutting, the cutting edge of the tool is perpendicular to the cutting velocity ( V). This condition is illustrated schematically in Fig. 1. Past work by Merchant [1-3]1; Shaw, Cook, and Sqiith [4); Shaw, Cook, and Finnie [5); and Shaw [6); among others, have suggested that 1 Numbers in brackets designate References at end of paper. Contributed by tbe Production Engineering Division for publication in the ,JOURNAL OF ENGINEERING FOR INDUSTRY. Manuscript received at ASME H119dquarters, November 4, 1976. Fig. 2 Force vector diagram for two-dimensional cutting 828 / NOVEMBER 1977 Transactions of the ASME Page 303 the two-dimensional process shown in Fig. 1 has a force diagram as Table 1 Machining parameters from reference data shown in Fig. 2. If it is assumed that F= µN (1) where µ, the friction coefficient between the chip and tool, is given by: µ = tan- 1 /3 (2) then the following equations may be obtained. Fp =[(µsin «e + cos «e]N (3) Fq = [(µ cos °'e - sin ae]N (4) Equations (3) and (4) may be converted to the following form (see Cook, reference [7]), (/) LtJ F _ TsBeSe COS (/3 - ae) (5a) a Lt:J P - sin e[cos (e + /3 - a,)] fil 40 0 ~ Fq = --Ts-BeS-e -sin- (/3- --°'-e) - (5b) ,g" sin e[cos (e + /3 - ae)] LtJ 30 where Be is the effective width of cut, Se the effective depth of cut, ..J and Ts is the shear strength of the work material. ! To predict values for Fp and Fq, the following parameters must be a: 20 e ). STABL R ~o -10 0 10 20 30 40 50 60 The remaining parameters are fixed by the machine settings (Be, Se) .8-"'t.,DEGREES or tool workpiece geometry (ae). Fig. 3 Plot of effective shear angle versus f3 - a. (Results taken from various The shear stress and friction coefficient for the particular materials Investigators as Indicated.). considered for this paper were obtained from the literature and are shown in Table 1. These values were obtained from the references indicated and, in most cases, they represent properties which were obtained under actual machining conditions. In some cases (such as stress, and shear angle, shown in Table 1, applies in the absence of 303 free cutting stainless steel) identical materials were not available other experimental data. If other data is available, then it may be used in the literature and an approximate value was obtained (from the to refine the initial choices ofµ, T.s and e to obtain a better correlation reference indicated) by choosing a material whose behavior was with the experimental results. In fact, if cutting forces are measured thought to be similar to the material listed in Table 1. As will be ex- experimentally, the constants of Table 1 may be refined in a sys- plained later, the values in Table 1 were only used as initial starting tematic manner, such that the following equations hold: values when correlating the theoretical force predictions with ex- perimental results. Fp = K1BeSe (6a) The shear angle, e, may be obtained from work by Hili [16], Stabler Fq = K2BeSe (6b) [17], Lee and Shaffer [18], Kronenberg [19], and Krystoff [20], among others. These investigators have derived formulas which allow the where K I and K 2 are constants for a given tool, workpiece, and cutting shear angle to be obtained if the friction angle, /3, and effective rake geometry. In reality, three-dimensional cutting forces will be exper- angle, "e, are known. The results of these investigators leads to a range imentally measured for this paper, and the actual refinement ofµ, Ts, of q.,, values for a known /3 - °'e value as shown in Fig. 3. The shear and e carried out on the formulas which predict the theoretical angle for materials evaluated in this paper are shown in Table 1. three-dimensional forces. This procedure is discussed in detail in the It should be recognized that the data for friction coefficient, shear Discussion. -----Nomenclature·----------------------------------------- A0 = shear plane cutting area, m2 N = rake face normal force, N a, = tool side rake angle, deg B = machine set depth of cut in turning op- N* = normalizing magnitude for vector ep' n, * = modified side rake angle, deg eration, m and eq', (-) {3 = friction angle between F and N (/3 = Be = effective width of cut, m p' - q' = orthogonal coordinate system Ce = tan-1 µ), (-) tool end cutting edge angle, deg where cutting is 2-D, (-) Cs = tool side cutting edge angle, deg '1 = location angle for chip flow direction, R 1, R 2 = coordinate transformation matrices, F = rake face friction force, N deg (-) Fp = power force in 2-D cutting, N 'le = chip flow angle in the rake face plane, S = machine set feed rate in turning opera- Fp' = power force in p' - q' plane, N deg tions, m/rev Fq = normal force in 2-D cutting, N >,.=normalizing scalar,(-) Fq' = normal force in p' - q' plane, N lY = location angle for chip flow direction, µ = friction coefficient along tool rake face, Fx = power force at cutting tool, N deg (-) Fy = feed force at cutting tool, N ab = tool back rake angle, deg Ts = shear yield stress of workpiece material, F, = radial force at cutting tool, N e = effective shear angle of cut, deg Journal of Engineering for Industry NOVEMBER 1977 / 829 Page 304 X1 ;2 -sin a l AQ = -[-sin as*] [ cos a cos_ '7 AD - COS a 8 * -cos a sm '7 0 A---- -sin ab l -sin i l AF= [ o AC = [ -sin Cs cos i. -COS CTb -cos c., cos l where ab is the back rake angle, a is the angle formed by the inter- section oflines AQ and BQ, and a 5 * is a modified side rake angle. The angle <>s* is related to the true side rake angle (a,) by the following equation. t an as * -_ --:---c:-o-s:- -i~ c..o:..s:. :C...s.: ..'c.'o...s:: .C:::,. .:s2i_n= :<'.>.s'. ..-.::'.s!.i.n..' .C'..'.,. '.s.'i..n..' .i.. .__ cos i sin Cs sin C, + cos i cos Cs cos C, cos <>s The location of the p' - q' plane can be identified as the plane containing the friction force and the force normal to the tool face. The direction of these forces are given by the two unit vectors ep• and eq•, defined in the x, y, z system as where N* = cos2 <>s * + sin2 <>s * cos2 <>b Fig. 4 Schematic of a three-dimensional cutting tool To predict the location of the p' - q' plane, two assumptions must be made about the chip flow direction. As Cook [7], Shaw [4--6], and Stabler [14] have shown, a reasonable assumption is 'le = i, where i is the inclination angle of the tool (a geometric property of the tool), Modeling Three-Dimensional Cutting and 'le is the angle of the chip flow direction (AQ), in the rake plane (ACD), from a reference line (AD') which is perpendicular to AC in From the results of the previous section (o rthogonal cutting) it is the rake plane (ACD). Also, it must be assumed that the chip flow possible to predict cutting forces from the material and cutting pa- direction and friction force direction coincide, which is also a rea- rameters of the machining process. sonable assumption based on Shaw [4]. By knowing '1e it is possible In modeling three-dimensional cutting, it is convenient to define to predict first '1 and then a, and then to determine ep• and eq'· a plane (p' - q') which contains both the cutting velocity and chip velocity vectors. In this plane, the methods for predicting two-di- Since AQ is on the plane ADC, then X(AD X AF) = AQ x AC: where A is a normalizing scalar. This leads to three scalar equations: mensional cutting forces are applied. It is proposed to analyze the single point turning operation by first 1 X(cos <>s* cos ab) = cos a cos i (cos 11 cos (3 + sin '1 sin (3) predicting the location of the p' - q' plane and then referring the 2 A(sin as* cos ab) = cos a cos ~ cos i - cos c, sin r; sin i forces acting in this plane to a set of x, y and z axes located-On the 3 ;\(-cos <>s* sin <>b) = -sin a cos (3 cos i - cos a cos '1 sin i machine tool structure. In the present situation, x, y, and z are di- If these equations are solved simultaneously, then the following re- rections in which the forces are experimentally measured. lationship is obtained. A schematic of the cutting edge of an idealized tool is shown in Fig. tan a = tan a cos '7 + tan ab sin 11 (8) 4. To reference the position of this tool to the actual turning operation, z is equivalent to the radial direction (depth of cut), y is equivalent In order to obtain a, '1 must be specified. If we define AD' in the plane to the negative feed direction (chip thickness) and xis equivalent to ADC (perpendicular to AC), then '1e is the angle between AD' and the the tangential direction (power force direction). The chip/tool contact directio~ of the chip flow in the plane ADC. Since sin 'le = IAQ X ACI, face is designated by plane AEC. The other angles which are shown we obtam will be defined in the context of the discussion which follows. cos '1e = !(cos a cos '1e cos (11 - (3))2 To simplify the mathematical analyses, the cutting tool is modeled without a side relief angle, nose radius or end relief angle. Although + (sin a cos (3 cos i - cos a sin '1 sin i)2 these angles will be present on a "real cutting tool," their effect is + (sin a sin (3 cos i - cos a cos '7 sin i)2!112 (9) believed to be secondary compared to those of the angles which are Since '1e is assumed equal to i, then the above equation, together included in the analysis. Since the present modeling is to be used for with equation (8), can be solved simultaneously to yield '7 and a. predicting steady state forces and then regenerative force (in later Fig. 5 shows a cross section of the total perpendicular to the p' - work), it /s interesting to note that Arnold (21) has shown that the q' plane. The angle a, in this figure is the effective rake angle. This amplitude of chatter vibration increases as the flank wear of the tool is the three-dimensional equivalent of the rake angle in orthogonal increases. This observation provides confidence in that the tool model cutting. An expression for the effective rake angle is given by Cook shown in Fig. 4 provides the most reasonable geometry to predict the [7] as onset of regenerative chatter. Referring to Fig. 4, AQ is defined as the direction of chip flow, and sin ae = sin '1c sin i + cos '1c cos i cos <>n (10) '7 as the angle AQ makes with AD (the front edge of the tool). The direction of AQ, AD, AF, and AC become: where an is the normal rake angle. 830 / NOVEMBER 1977 Transactions of the ASME Page 305 p Table 2 Calculated machining parameters p 1020H.R. 6061-T6 )0) Stainless 1 Parameter Steel Alut:1inum n - Brass Stee! I Chip flow angle Equations 14.8° 18.6° 14.8° I (0) 8, 9 Chip flow angle Equation,. 14.2° (0) 8, 9 Effective rake Equation 14.1° 27.2° 27 .2° 14.1° angle (ae) 10 Rake face chip Equations t..Oo 9.8° 9.8° 4.0° flow angle(nc) 10 & 11 I -----~--~------------------------- = TsB,S, Fig. 5 Cross section of cutting tool on plane p' - q' (On this plane, cutting Fx F power=--------- Is two-dimensional.). sin e cos (c/>e + /3 - ae) + [sin (a - ae) cos (/3 - e cos(, + /3 - e + /3 - :nd Cut ting Edge (C~) 1.0· JO.O" Si!le Cutting I:d1::e (C,) u.r 12.a• Se= S cos (C,) (15) Nose Radius (c111} lnclin•tion •ngle (i) 4.)" 10.3" where Band Sare the depth of cut and feed rate, respectively, in the turning operation. Modifi<>tl Side take 18.1° sngh (u• 5 ) Performing the matrix algebra of equation (13) results in: Journal of Engineering for Industry NOVEMBER 1977 / 831 Page 306 Table 4 Test condHlons I I Fpower I feed raf<'(S,.l, wn/rev I •,ndth of cu~ (B.,l, .4 - 3.0 .S - .4 -1.4 .4 - 1.0 EXPERIMENTAL e FORCE DATA I cuttin,; sp,:,ed, J] (NJ 1020 (HR) STEEL cm/sec S8 =.25mm/rev I cutting speed, " llO 110 66 ~ =.72 I .. ft/mm 1360 e-Fpower I 1:1-Ffeed I 1200 ~-Fradiol -MA=rRIX corresponds identically to the model which was analyzed previously I --A8c8 inFig.4. I Test specimens were 2.54 cm (1 in.) in diameter and 61 cm (24 in.) 104 I / long. One end of the specimen was mounted in a self-centering three I 0 / jaw chuck and the other end was supported by a live center. Test 800 I / conditions are shown in Table 4, and a typical test consisted of cen- I / tering the tip of the cutting tool on the center line of the workpiece 8 / and selecting cutting speed, depth of cut, and feed rate, and initiating 720 I 13 cutting from the liver center end of the test specimen. Cutting forces I / fteed were monitored over the entire length of the cut, and it was observed " / that they were approximately constant. In cases where workpiece 560 I / [3 chatter occurred there was notable oscillation in the cutting forces. I / 0 These tests were not included in the steady-state analysis, however, / 40 I they did point out the limitations of metal removal rate that exist in 0 / practical machining operations (i.e., tool chatter). / 24 Discussion Shown in Figs. 6-11 are plots of the experimentally measured cutting forces for various depths of cut (for conditions shown in Tables 80 2 and 3). Also shown on these plots are the best predictions of the matrix model (equations (19)-(21)) and the Armarego and Brown [22) .025 075 .125 .175 .225 275 .3251b~)H model. Fig. 7 Experimental cutting data for 1020 steel-feed rate 0.25 mm/rev I / Fpower I EXPERIMENTAL EXPERIMENTAL I FORCE DATA (NJ FORCE DATA I .. 6061-T6 ALUMINUM (NJ 1020 (HR) STEEL Se =.Imm/rev 680 Se= .I mm/rev I >J = 1.07 JJ ~ .71 0 -Fpower 680 e -fpower o-Ffeed 13 -Ffeed .,.-Fradi91 --MATHIX 600 A-Frodial - -A 8c B --M-AATaRsI X Q 520 440 //Ffeed 360 / / 280 / 280 / • / El 0 200 200 El ----o - Ffeed 120 120 ,.._,,.-A--•- ~ --·---C' 40 r rradial 40L...J~=,::l~~~~~~====::=__;,F.~radial _.,,,- 025 075 .125 .175 225 275 .325 WIDTH 025 075 .125 .175 .225 .275 (c~ Fig. 8 Experimental cutting data for 6061-TS aluminum-feed rate 0.1 Fig. 6 Experimental cutting data for 1020 atee1....:.1eed rate 0.1 mm/rev mm/rev 832 / NOVEMBER 1977 Transactions of the ASME Page 307 EXPERIMENTAL I FORCE DATA (N) I 6061-T6 ALUMINUM I Se= .25 mm/rev I I Fpower Fpower 680 JJ = 92 I EXPERIMENTAL I e-Fpower I DATA FOR I a-Ffeed ,l (N) 303F STAINLESS I 600 t>-Fradial I STEEL --MATRIX I Se= .I mm/rev I --A 8 B 9' 680 )J = .77 I 5'20 0/ o-Fpower I "/ 600 0 -Ffeed I o I 8 440 I t--Fradial I --MATRIX I GI I I 520 --AS B I e 360 I, I I) /; 440 I 280 0 0 tJ I 0 I 360 Fteed 20 / ~ .,,,- Ffeed I " / / ~- 280 I 12 D D .A/ ::; .,-: i .,..-c:::: 200 I 1:1 " 40 O' ~ - ----- Fradial I -- ~-6 &. !I IL 0 25 .075 .125 .175 .225 275 .375 Vf1RJH 120 Fig. 9 Experimental cutting data for 6061-TS aluminum-feed rate 0.25 mm/rev 025 .(J75 .125 .175 .225 .275 .325 WIDT)H (cm Fig. 11 Experimental cutting data for 303 stainless steel-feed rate 0. 1 mm/rev EXPERIMENTAL FORCE DATA Cutting force predictions of both the matrix and Armarego and (N) FREE CUTTING BRASS Se= .I mm;rev Brown models were obtained for the same conditions which were used = .74 to generate the experimental data. The data shown in Table 1 was )J 680 Fpower originally used. The initial theoretical force predictions of both models 0 - were in good agreement with each other (using the data from Table a - Ffeed 1), but neither were in good agreement with the experimental data . 60 .. - Fradiol MATRIX This was expected since the values of Ts, µ, and reduces the turbine If the design UA/qE and/or the qesign C/qE are enthalpy drop per poun~ of R'.'."114. > At the sa.ine time, increased, heat transfer temperature differences de- the turbine flow·rate} computed by Eq). 3, drops. crease, and the diagonal line of vanishing designs, The resulting reducedworkrateoutpuienters the left Figure 7, will be shifted to the .left toward the hand side of Eq'. 9, redttcirig•the work rate input to the line of vanishing designs for infinite UA and C. compressor ••. This ·in turn reduc~~ the refrigerant This enlargement of the temperature zone of design is (R-22) handling capacitY," of the compressor (left- shown by two triangular insets in Figure 9. The hand side of Eq •..~ ) I"~~11ltfog in: a reduced compressor plot of Figure 9 shows only the effect of increasing speed. The reduced compressor speedresults in a the design UA. Other free parameters are held con- reduced turbine blade velocity (VB) via Eq. 5. The stant as indicated. As UA (i.e. UA/qE ) is in- creased above the level for which there is no Rankine ~:;_!:~:\:tth!t!f~~!f ~h~;B~!PJ~/t)1!:/a 1~ :::r cycle, the OCCOP rises rapidly and levels off as it OCCOP. The corresponding Case I trends in Figure 11 becomes asymptotic to the maximum OCCOP value for show the OCCDP decreasing with decreasing hot water infinite UA (i.e. t:,.T = O, in Figure 9). The choice inlet temperature. Near the design point in Figure of the appropriate design value for UA must be de'"'. J.l, the cuz-ve is relatively flat, but as the hot water termined by weighing increased capital cost against inlet temperature is lowered below 180 deg F, the OCCOP savings resulting from higher performance. A point drops off rapidly and operation ceases at a cut-off such as "Y" on the "knee" of the curve symbolizes temperature of J.27 deg F. The Case I capacity trend, this choice. Figure 12, is nearly a straight line through points Up to this point, heat transfer conductances, .(o, 127 deg F) and (1.0~ 200 deg F). UA's, and capacity rates, C's, in all four heat Cases II and III, Figure 12, are somewhat simi- transfer components of Figure 1 have been given lar to Case I in that cooling capacity is more or less identical values. When only one UA (i.e. boiler, linearly dependent upon the inlet cooling water and condenser, or evaporator) is varied while other UA's inlet chilled water temperatures, respectively. The arid C'sare held constant, the results are as shown capacity trends of Cases II and II in the neighborhood in Figure 10. In each case there is a minimum UA of the design point "D" are steeper than for Case I. at·whicb:the cycle·vanishes because all available Also, in Figure 11, the OCCOP trends of Cases II and t:i.T is consumed by heat transfer processes. The tem- III in the neighborhood of the design point "D" are perat~e•conditions of Figure 10 are the same as those steeper than for Case I. This is mainly due to the given iri: Figu.re 9• In Figure 10 it will be noted iact that the design point.thermodynamic cycle condi- , consistent with Figure 8, the slopes of OCCOP tion is for a much smaller temperature difference petween the condenser and evaporator inlet water Page 316 l temperatures (85 deg F - 55 deg F) compared to the actuate the cooling process. It was shown that the difference between the boiler and condenser inlet vanishing design condition established a diagonal water temperatures (200 deg F - 85 deg F). That is, line of vanishing designs on a plot of inlet cooling the former VCC overall thermodynamic cycle tempera- water versus inlet hot water temperature. This line, ture difference is more sensitive to a unit (1 deg F) together with a horizontal line at the wet bulb tem- change than is the latter RC overall thermodynamic perature and a vertical line at the maximum allowable cycle temperature difference. collector/storage temperature was shown to form a Figures 8 and 11 provide an interesting compar- triangular temperature zone of design. ison in that Figure 8 OCCOP curves are the loci of The operation of a selected design in the off- design points whereas the Figure 11 OCCOP curves are design mode was also simulated and sample trends of loci of off-design points. Neglecting the minor off-design OCCOP and off-design cooling capacity were change in the UA/qE and C/qE values (0.277 deg F-1 generated. The inlet water temperature conditions to 0.222 deg F-1), it is seen that corresponding were established at which the cooling subsystem curves have roughly similar trends. For example, capacity was zero. This cut-off condition was shown design curve "B" in Figure 8 corresponds to the off- to occur at a substantial difference in temperature design curve of Case I, Figure 11, in that inlet- between the inlet hot water and the inlet cooling hot water temperature is the variable and in that the water. The cut-off conditions were also shown to trends are roughly similar. Other pairs that may be define a diagonal line, called the cut-off line, on compared are C and II or E and III. A comparison also a plot of inlet cooling water temperature versus in- may be made between the vanishing point X of the de- let hot water temperature. A triangle forming the sign simulation, Figure 8, and the cut-off point X' temperature zone of off-design operation was shown of the off-design simulation, Figure 11. Points Y to be larger than the triangle enclosing the design and Y' may be compared also. For an exact comparison zone. of X and X' or Y and Y', the two simulations must be carried out for the same prescribed UA/g_E and C/g_E' ACKNOWLEDGEMENT such as the fixed value 0.222 deg F-1 . In Figure 13, we show a temperature zone of The work reported in this paper was supported design for the UA/qE and C/qE value of 0.222 deg F-1 . by ERDA Contract No. E(40-1)4976, The line of vanishing designs for this zone may be compared with the line of vanishing designs in REFERENCES Figure 7, and it will be seen that the position is such that the temperature zone of design is smaller 1, Eisenstadt, M.,Flanigan, F.M., and Farber in Figure 13, A second diagonal line is shown in E.A., "Tests Prove Feasibility of Solar Air Condi- Figure 13 to represent the cut-off condition for tioning," Heating, Piping, and Air Conditioning, off-design cycles having the design point "D". This Vol. 32, No. 11, 1960. diagonal line, which is defined in terms of X' and 2. Chung, R., Duffie, J.A., and L8f, G.O.G., Y', lies to the left of the line of vanishing designs "A Study of a Solar Air Conditioner," Mech. Engr., and defines a second triangular region which may be Vol. 85, 1963, called the temperature zone of off-design operation. 3, Kennedy, D.M., "A,G,A. Air Conditioning This latter zone is defined relative to design point Research - Past Prospects, Present Perspectives," "D". The reason the cut-off line lies to the left Second Conference on Natural Gas Research and Tech- of the line of vanishing designs is that as this line nology, Institute of Gas Technology, Chicago, 1972, is approached from inside the triangle, off-design 4. Allen, R.W., editor, Proceedings of the operation continues at reduced cooling capacity until Solar Heating and Cooling for Buildings Workshop, the cooling capacity reaches zero at the cut-off March 21-23, 1973, Part I - Technical Sessions, condition. 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Biancardi, F.R., "Needed Research on Solar Rankine Systems," Workshop on Solar Cooling for Buildings, 1974, pp. 193-199, 26. Jordan, R.C. and Priester, G.B., Refriger- ation and Air Conditioning, Prentice-Hall, New York, 1948. 27. McAdams, W.H., E::::~--=£!:!:!~2.:~!:.£f:!., McGraw- Hill, 1954. 28. ABHRAE Handbook and Directory, 1975, Eguipment, American Society of Heating, Refrigerating and Air Conditioning Engineers, Inc., New York, 1975. 29. Egrican, A.N., "Modeling of Rankine Cycle/ Vapor Compression Cycle Cooling Systems for Solar Energy Applications," Ph.D. thesis, University of Maryland, 1977, , Page 318 >- 0 z w u [;: LL ,::- (.) - ,::- 0.. w ,::- HW >- (!) f-ll'. ..-::, . 0.. u qC V C 7 ~ ll. EXPANDER (/) ~8 (.) 0 ll'. > ll'. zo:: 0) (.) \ 0 w .w... ffiwwu 0 0 0 0 cw w I- ........ ::;; cw -~ WT <( r:iJ: - ll'. w ll. ~ (.) 0 CHW z ll'. (!) ::l~o > w 2 0) 0 0 U) <(::, <( <( <( <( <( w o::o ::, ::, ::, ::, :::, 0 wz >O Oo w _J t;ll! 0) _J .J ::> ~ w -+ qB I!,/ . --+WT ffiw~._ .ln ._u ._u ._w f-!;i::;; 5' ; 1':i 3'~ 7~Wc ll'. 0:: w w 0:: .... (/) a:: (/) 0 0 ~IA f 73 z z z w l!s ~ !;i (/) w (/) z wll'. z z 0:: w 0 0 0 fl. .J (.) (.) a'. z 0:: ENTHALPY, h in 0.. 0.. ::;; 6 0 g ll'. ::;; §; ~ ::> FIGURE L 0 w F A RANKINE 0) ll'. CYCLE; VAPOR (.) (.) fl. COMPRESSION CYCLE (RCIVCC) SOLAR COOLING SYSTEM WITH SOLAR COLLECTOR AND CHILLED WATER CONNECTIONS. Page 319 Page 320 W O R l < I N G F L U I D C Y C L E T E M P E R A T U R E S B O I L E R C O N D E N s r n E V A P O I \ A T O R \ o R C I N L E T W A T E R T E M P E R A T U R E S H O T W A T E R ( H W ) T s , R A N K I N E C Y C L E ( C W ) i c l R C C O O L I N G W A T E R \ m e V A P O R C O M P I \ E S S I O N 1 ( C W ) C Y G L E C O O L I N G c 1 v c W A T E R C H I L L E D W A T E R ( C H W ) F I G U R E 3 . T E M P E R A T U R E P R O F I L E I N R A N K I N E C Y C L E C O N D E N S E R H E A T E X C H A N G E R . F I G U R E 2 . T E M P E R A T U R E N O M E N C L A T U R E ( A L S O S E E F l G U R E 1 . ) u t= (J) ii w 9 t; i:c .u~ ,. uz uw G: .. uw.. 8 >"'I.. zw ai 0:: ::> st: -/ .... 0 w (J) ...J ::> a. ;§ N 0 .i. u a: ~ 0 d:I ..:, Ci Ci ~ +' w 0:: ~ ::> u".. D SPEED FIGURE 5. AN ASSUMED LINEAR RELATIONSHIP BETWEEN REFRIGERANT FLOW RATE AND COMPRESSOR SPEED FOR A TYPICAL RECIPROCATING COMPRESSOR . Page 321 Page 322 1 3 0 L I N E O F V A N I S H I N G D E S I G N S F O R I N F I N I T E U A A N D C p L I N E O F V A N I S H I N G D E S I G N S O R F O R U A / 9 E ~ 0 . 2 7 7 ° F - f T ' - - ' G / 9 E = 0 2 7 7 ° F - I § ? t - 2 9 I I ( . ) " " I o a 7 W E T B U L B T E M P E R A T U R E 6 0 ® 5 0 I 0 0 ) 0 - 1 1 2 ~ 0 1 ~ 1 4 i n o - ~ t 6 0 ~ - - , ~ a o : : - - - - ; ; 2 ~ 0 : : : : - - 0 ~ 2 2 ~ 0 , - - - . , a . 2 4 - . . J 0 F I G U R E 6 . A R E P R E S E N T A T I O N O F H E A T T R A N S F E R T E R M I N A L T E M P D I F F E R E N C E S O N T H E T H E R M O D Y N A M I C P - H D I A G R A M . F I G U R E 7 . T E M P E R A T U R E Z O N E O F D E S I G N . Page 323 C i T = O ' " " " " ' » ' » ' » [ l G E I . O - 2 0 0 2 0 0 0 8 B 8 5 - 8 5 T B = 2 0 0 " F 1 5 5 5 5 - T c r n c = T c 1 v c = 8 5 ° F ' E r 0 8 T E = 5 S ° F 1 E X P A N O E R - G O I V P R E S S O R ' 1 t 7 c = 0 5 0 6 I H E A T T R A N S F E R I 1 I U A l 9 1 : . = Q 2 7 7 ° r : ' I 0 6 \ I N L E T W A T E R F L O W Q _ 1 I o _ C I 9 E = Q 2 7 7 ° F I 0 I ( . ) 0 I o O A I u 0 I I I N S E T - 2 U o . 4 I I 0 I I I 0 2 ® ; ~ I I I 0 2 I N S E T - I y X X 0 2 4 0 - , 1 2 0 1 6 0 2 0 0 8 1 1 8 5 1 0 5 1 6 5 - - - G I R c " C I V C o ~ - , ; 0 ~ 1 - ~ o . ; , 2 - - : o t 3 , - - ; o ! - - ; 4 - - - , o ' - = s = - - _ j o _ 6 _ _o . . 1 . 7 _ J 5 5 7 5 3 5 - · - · T E I U A / q / ° F ) F I G U R E 8 . D E S I G N S T U D Y : E F F E C T O F D E S I G N I N L E T W A T E R F I G U R E 9 . D E S I G N S T U D Y : E F F E C T O F O V E R A L L C O N D U C T - T E M P E R A T U R E S ( T , T C I R C , T C I V C , T E l ) O N T H E 8 1 A N C E P E R U N I T C O O L I N G C A P A C I T Y ( U , i \ / q E ) O N C O E F F I C I E N T O F P E R F O R M A N C E ( O C C O P ) O F A T H E C O E F F I C I E N T O F P E R F O R M A N C E ( O C C O P ) O F T Y P I C A L R C / V C C S Y S T E M . T Y P I C A L R C / V C C S Y S T E M S . Page 324 - 1 D E S I G N P O I N T P A R A M E T E R S O T H E I ' . U A / q _ = 0 2 7 7 ° F - ~ . , , . , . . . . . . - - - - . - - - , , - - - ; ' t . . \ I N L E T T E M P E f \ A T U R E S : C l e f 0 2 7 7 ° F 0 8 C . 8 2 0 0 / 8 5 , 8 5 / 5 5 ° F C O O L I N G 8 5 - 8 5 E X P A N D E R · G O M P P , E S S O R : _ _ _ _ _ . . C H I L L E D 5 5 5 5 - ' ? i ' ? c : 0 , 5 - - - - - = - = - - - - - - \ ~ - \ H E A T T R A N S F E R : I \ U A / q £ = 0 . 2 2 2 ° F · ' \ I \ I N L E T W A T E R F L O W : 1 G / c \ = 0 . 2 2 2 ° F · 0 . . . \ 0 i \ G A S E I 0 \ 0 0 4 I \ o · \ i \ \ \ C A S E J I \ \ \ \ 0 2 \ ' \ 0 2 \ \ \ \ I : \ I \ Q ) L J l ~ - - . . . 1 - - - L - - - ' - ' - " 7 . : : - - _ . . . •_- - : , : ; - - " ' 0 . 1 o . 3 I o . s 0 . 1 2 4 0 - T 3 1 o ' ) ( ) 2 2 0 1 8 0 U A 9 E ( ° F ) - 8 & G f l C 1 1 2 5 - - - • c 1 r 1 c = c 1 v c - - - · e v e 8 5 1 0 5 6 5 1 - · - · E - · - E I 5 5 7 5 3 5 F I G U R E 1 0 . D E S I G N S T U D Y : E F F E C T O F C H A N G E S I N I N D I V I D U A L F I G U R E 1 1 . O F F - D E S I G N O P E R A T I O N : E F F E C T O F O F F - D E S I G N C O M P O N E N T H E A T T R A N S F E R O V E R A L L C O N D U C T - 1 I N L E T W A T E R T E M P E R A T U R E S ( 1 0 1 , T c 1 R c = 1 : 1 v c , E 1 ) A N C E S O N T H E C O E F F I C I E N T O F P E R F O R M A N C E O N T H E C O E F F I C I E N T O F P E R F O R M A N C E ( O C C O P ) ( O C C O P I O F T Y P I C A L R C / V C C S Y S T E M S . O F A T Y P I C A L R C / V C C S Y S T E M . Page 325 D E S K ; N P O I N T P A R A M E T E R S I N L E T T E M P E R A T U R E S : 2 0 0 / 8 5 8 5 / 5 5 ° F 1 4 0 / r ; C A S E I E X P A N D E R - C O M P R E S S O R I ' l f ' l . = 0 . 5 : 3 \ ' I H E A T r R A N S F E R I \ U A / 9 E = 0 . 2 2 2 ° F - I I l t - l L E i W A T E R F L O W - - 1 G I \ = 0 2 2 2 ° F 1 . 0 0 . 1 1 0 0 \ ' \ > - , , . . . . . . . . _ 1 - \ C A S E I I L L 1 0 0 \ 0 ~ \ Q . : ' - ' \ < ( 0 \ 2 ' . . V \ \ t - 2 < ) I I I \ ~ Q S u I c : : \ I G e \ § \ I I \ W E T B U L B T E M P E R A T U R E 7 \ \ 6 \ : f ~ 0 ' : - : : 0 : - - - - - - - ' - - = i ' - - 1 - - - - - ' - - - - ' - - - ' - - - - ' - - - - ' - ~ . . J X ' 1 4 0 1 8 0 2 2 0 - T m 5 0 1 . . - - . . . . . l : : a = : : ! l ' - - . . . . L . - - A - l ' * - - - ' - - ~ - - . . L . , - . . . . . . J . , . . , . . . j 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 2 4 0 6 5 a s 1 0 5 - - - ' a R C = T a v c 3 5 5 5 7 5 - · - · T E ! ( ° F ) T a r F I G U R E 1 2 O F F - D E S I G N O P E R A T I O N : E F F E C T O F O F F - D E S I G N I N L E T W A T E R T E M P E R A T U R E S ( T s , , T c 1 R C = 1 i : 1 v c • T E I ) T E M P E R A T U R E Z O N E O F D E S I G N A N D T E M P E R A T U R E F I G U R E 1 3 O N C O O L I N G C A P A C I T Y O F A T Y P I C A L R C / V C C Z O N E O F O P E R A T I O N . S Y S T E M INTERNATIONAL 68 SOLAR ENERGY 51-4 ~gricl;11tural_ and l_ndustrial Applica-tions _including Dist illation : Refri- geration and Industrial Applications CONGRESS Chairmen: E.D. HOWE, M.V. KRISHNAMURTHY PROGRAMM 0216 M ~HDI N. BAHADORI, ALI KOSAR!, Pahlavi Univ., Shiraz, Iran Performance of the Natural Ice Makers. VIGYAN BHAWAN 0042 M AHESH CHANDRA, Indian Inst. of Tech NEW DELHI- IND IA New Delhi, India; R.K. MEHROTRA, J.S. s'AINI, JANUARY 16-21 , 1978 C.P. GUPTA, Univ. of Roorkee, India Design and Fabrication of a Solar Ice Making SUN : MANKIND'S FUTU RE SOU RCE OF ENERGY Machine. 0082 N.K. GIRi, K.M . BARVE, Jyoti Ltd, Baroda, India Solar Ammonia- Water Absorption System for Cold Storage Application. 1101 RAIMUND HAUSE, Dornier System GmbH, FRG Design Criteria of Solar Absorption Cooling System for Food Products . 0325 M.C. GUPTA, P. GANDHIDASAN, Indian Inst. of Tech., Madras, India Open Cycle 3-ton Solar Air-conditioner : Concept, Design and Cycle Analysis. 0359 S.B. GHOSH, C.L. REDDY, H.V. RAO, C.P. GUPTA, Indian Inst. of Tech ., Kharagpur, India Design of a Solar Energy Operated Lithium Bromide- Water Absorption Refrigeration System for Refrigeration Storage. 0328 J .P. GUPTA, V.S. DAVE, M.V.N. RAO, Defonce Lab., Jodhpur, India Performance Study of Cold Box based on Natural Cooling. 1049 D.K. ANAND, R.W. ALLEN, Univ. of Maryland, USA; W.W. AUER, J .M. GREYERBIEHL, ERDA Washington DC,USA Applications of Solar Energy to Industrial Processes. 0081 R.K. GUPTA, A.M . DESHPANDE, K.M . BARVE, Jyoti Ltd, Baroda, India Development of 1 kW Solar Powered Reciprocating Engine for Rural Applications. CONGRESS OF THE FRI 20 JAN INTERNATIONAL SOLAR ENERGY SOCIETY Room H • SPONSORED BY THE 1100-1230 hours SOLAR ENERGY SOCIETY OF INDIA Page 326 Abstract No. 1048 SOLAR AIR-CONDITIONING SYSTEM PERFORMANCE PREDICTIONS USING LOAD, STORAGE, AND STOCHASTIC WEATHER MODELS FOR DIFFERENT REGIONS By: D. K. Anand, Professor; R. W. Allen, Professor; E. 0. Bazques, Graduate Student; I. N. Deif, Graduate Student Solar Energy Projects/ Department of Mechanical Engineering/ University of Maryland/ College Park, Maryland 20742/ U.S.A. The performance and design of solar air-conditioning systems has generally been obtained by using real climatological data collected locally. Since the data and system simulations have often required lengthy computations, various models as well as degree-day methods have been devised (1-3). Recently a probabalistic approach, which retains the weather history, has been used to predict system performance for a simple system with good results (4). In these studies, the perfonnance of air-cooled and water-cooled solar powered air-conditioning systems for the Washington, D.C. area was reported. The work was based on a system that consisted of a flat-plate collector coupled to a LiBr air-conditioner. The air-cooled absorption system required dry-bulb temperature and solar insolation; hence the analysis was restricted to the stochastic representa- tion of these two weather parameters. For the systems that were water-cooled, the coefficient of performance of the absorption cycle was dependent upon the wet-bulb temperature, thus necessitating the stochastic prediction of this additional weather parameter. The calculations were based on a stochastic model of dry-bulb temperature, wet-bulb temperature, and insolation which was Page 327 -2- constructed using historical information. Basically, a statistical approach was used combined with state representation which modified this weather data into a more compact and hence inexpensive form. The stochastic constants generated for the Washington, O.C. area with their attendant joint probability density matrices were found to greatly decrease computations in system simulations with little loss of accuracy as compared to those performed using actual hour by hour weather data. While the data used is considerably less, the stochastic predictions are sufficiently accurate for system sizing. Although earlier work was based on a fixed collector area and flow rate, later studies investigated the effect of varying collector area and flow rate (5). It was shown that the stochastic and real predictions were still in fairly good agreement. In the present paper, the above study is expanded to a total of four major cities, in diverse climatic regjons of the United States, these being Madison, Wisconsin; Fort Worth, Texas; and Fresno, California; in addition to Washington, O.C. The current study is performed using a larger system simulation that features load calculations, which depend on building structure and contents, as well as storage which uses inputted (preset, non-calculated) loss factors. One of the interesting features of the system studied is that it incorporates automatic controls that make decisions to turn pumps on and off at various system locations or to open or shut valves along the system network. These Page 328 -3- simulated pumps and valves can be seen in the system schematic. The controls also make the decision of switching to auxiliary energy to ensure that the load is satisfied at any given time. The controls run on a one hour time- step, but the various heat quantities in the system are integrated over their specific time periods. For example if at the beginning of an hour the controls sequence arrives at the decision that auxiliary energy is needed, a calculation is made as to how long the auxiliary energy will have to be supplied - it is not assumed that the auxiliary will remain on for the entire hour. On the whole, it was attempted to simulate a realistic system as much as possible while retaining simplicity. For example the collectors' performance was calculated by curve-fitting existing test results performed on these collectors. The computational steps required for systems simulations using stochastic weather data are straightforward. First, assumed temperature and insolation profiles are constructed based on weather models presented in the literature and previous experience. These profiles are equations which are time (hour of day and month of year) dependent. The unknown constants in these equa- tions are then obtained by minimizing the error through a least square comparison to actual hour by hour weather data for a particular area. Once the unknown parameters have been determined in the synthetic weather profiles, one has a method for reconstructing the hourly temperature and insolation values for any month of the year for a particular region, provided an average temperature and insolation is specified. The scatter diagrams Page 329 -4- for the temperature and insolation based on actual local weather data can be generalized using a joint probability density matrix. This can then be represented in matrix form. For a water cooled air-conditioning simulation for example, this matrix yields a probability P. 'k for the occurrence of lJ some value Td'' T ., and Ik selected to represent values above and below 1 WJ 11CJ where n determinesthe size of the probability density matrix and a is the standard deviation of the respective weather parameter. These values of wet-bulb temperature, dry-bulb temperature, and insolation are in turn used in conjunction with the weather constants derived earlier in the least square fit to reconstruct hourly data for temperature and in- solation. The cooling capacity C. 'k required is computed using recons- lJ tructed data based on every set of Td., T ., and Ik in the joint probab- 1 WJ ility matrix. The total cooling capacity is obtained by computing Ic .. kP. 'k' In a similar manner, we obtain an estimate of the total solar lJ lJ energy incident on the collector during a given time period, as well as the coefficient of performance of the system. System COP, total insolation, and useful energy delivered using the stochastic approach are seen to be in good agreement with real data when compared over the cooling season for the various cities for both air-cooled and water-cooled systems. The data necessary for simulations in a local region is reduced; hence considerable savings in system simulation result. It is seen that any local region can be characterized by four or six constants in the reconstructed weather parameter profiles and from nine to nineteen data sets in the historical joint probability density matrices. It is there- fore concluded that even for diverse climatic regions the present scheme of Page 330 -5- taking a large body of local data and compacting it while retaining its probabilistic structure gives the designer a compact and inexpensive tool for sizing solar systems. Page 331 -6- References (1) Klein, S.A., P.I. Cooper, J.L. Freeman, D.M. Beekman, W.A. Beckman, and J.A. Duffie, 11A Method of Simulation of Solar Processes and Its Appli- cation'', Solar Energy, Vol.17, pp.29-37, 1975. (2) Winn, C.B., G.R. Johnson, "Dynamic Simulation for Performance Analysis of Solar Heated and Cooled Buildings". Presented at the American Society of Mechanical Engineers Winter Annual Meeting, New York, N.Y., Nov. 1974, Paper 74-WA/Sol-8. (3) Card, W.H., E.E. Drucker, M. Ucar and J.E. La Graff, "Generalized Weather Functions for Computer Analysis of a Solar-Assisted HVAC System". Presented at the American Society of Mechanical Engineers Winter Annual Meeting, New York, N.Y., Dec. 1976. Paper 76-WA/Sol-20. (4) Anand, D.K. and R.W. Allen, "Solar Powered Absorption Cycle Simulation Using Real and Stochastic Weather Data, 11 presented at the American Society of Mechanical Engineers Winter Annual Meeting, New York City, November 1976. Paper 76-WA/Sol-6. (5) Anand, D.K., R.W. Allen, and E.O. Bazques, "Solar Powered Absorption Air-Conditioning System Performance Predictions Using Stochastic Weather Models, 11 Solar Energy Projects Report, Department of Mechanical Engineering, University of Maryland, College Park, Md., February 1977. Page 332 Page 333 S O L A R A I R - C O N D I T I O N I N G , H E A T I N G A N D D O M E S T I C H O T W A T E R S Y S T E M S C H E M A T I C . C w z w O U . . . . . ~ 0 ( 1 ) A H l z 0 ( . ) F V 9 E S A . C . t - - - - + - - - 0 o - . . . . . . , _ _ . - f . . D . W . H . W . C I T Y c . w . - , F V F V 5 . - - - - i . . - E S · A . C . - A I R C O N D I T I O N I N G U N I T - - M - - - - - + - - . . . . . _ - - - 1 H . P . - H E A T P U M P H . P . H . W - H O T W A T E R S T O R A G E C W . - C H I L L E D W A T E R S T O R A G E - M - - - - A H 3 D . W - D O M E S T I C H O T W A T E R A . H . - A U X I L I A R Y H E A T E R S E - I N P U T P O W E R F ' s - C O N T R O L F U N C T I O N S , I - O N , 0 - O F F Abstract No. 1049 APPLICATIONS OF SOLAR ENERGY TO INDUSTRIAL PROCESSES By: D. K. Anand and R. W. Allen, Professors, Department of Mechanical Engineering, University of Maryland, College Park, Maryland 20742/U.S.A. and: W.W. Auer and J.M. Greyerbiehl, Program Managers, Agricultural and Process Heat Branch, U.S. Energy Research & Development Administration, Washington, D.C. 20545/U.S.A. Since industrial process heat consumes over 15 quadrillion British thennal units per year, a contribution by solar energy means a significant savings in the overall energy consumption. Therefore, in order to enhance the ways in which solar energy can effectively contribute to the nation 1s energy needs, a program has been initiated and supported by the Energy Research and Development Administration (ERDA) to develop systems capable of supply- ing cost-effective solar industrial process heat, using state-of-the-art technology, especially since there exist many industrial activities in which low grade heat deriv.ed fr.om solar energy can be successfully used. In recognition of the potential benefit to be derived from industrial uses of solar energy, two Workshops on Solar Industrial Process Heat have been sponsored by the ERDA Division of Solar Energy (DSE}. The University of Maryland Department of Mechanical Engineering acted as Workshop organizer and coordinator, in consultation with the Agricultural and Process Heat Branch, DSE, ERDA. The primary purpose of the workshops was to stress user involvement and ta be a forum for ERDA-sponsored as well as other projects in the industrial Page 334 -2- sector. The workshops were generally considered successful. ERDA-DSE has either funded or is currently funding projects in: Can washing Textile drying Textile dyeing Lumber drying Laundry services Fruit drying Food drying Process heat surveys Crop dehydration Shallow Solar ponds Concrete block curing Process steam Systems for these processes consist of primary and secondary heat transfer loops with process temperatures up to 350°F. In all, there were five projects dealing with hot water applications, and seven dealing with hot air applications, and two in process steam applications. The objectives of these projects is to design and demonstrate the use of solar energy in a variety of industrial process applications using state-of-the-art technology. In a parallel effort two ~urveys of industrial process heat were conducted. The objective of the process heat surveys was to identify the various possible uses of solar energy for industrial processes, to quantify current needs, to assess the impact in terms of potential energy savings, to formulate and evaluate concepts for different systems and finally to assess relevant non-technical issues. The current status is that the survey studies have been completed, and approximately twelve projects are or have been funded for completion and demonstration. The objective of the present paper is to: 1. Present a survey of industrial heat applications where solar energy can make rapid inroads, especially at low and moderate temperatures. 2. Discuss the progress and technical achievements of the current Page 335 -3- demonstration projects. 3. Present the results of the two workshops on Industrial Process Heat held at the University of Maryland. References 1. 11 Solar Industrial Process Heat Workshop," by W.W. Auer, R. W. Allen, and D. K. Anand. Paper presented at ISES Conference, Winnipeg, Canada, August 1976. 2. Proceedings of the Solar Industrial Process Heat Workshop, edited by the Department of Mechanical Engineering, University of Maryland, August 1976, Report CONF-760655. 3. Proceedings of the Second Solar Industrial Process Heat Symposium and Review, edited by the Department of Mechanical Engineering, University of Maryland, November 1977. Page 336 A SIMPLIFIED SOLAR COOLING DESIGN METHOD FOR CLOSED-LOOP LIQUID SYSTEMS D.K. Anand, Professor R.B. Abarcar, Research Associate R.W. Allen, Professor Solar Energy Projects Department of Mechanical Engineering University of Maryland College Park, Maryland ABSTRACT At the present state-of-the-art, solar cool- develop simplified cooling design charts. ing system performance can be predicted only by using a detailed computer simulation. A simulation program, SHASP has been success- 2. SYSTEM DESCRIPTION fully used in solar cooling systems analy- sis. However, since not all designers have The basic solar cooling system is shown in access to computers that can handle detailed Fig. 1. The control strategy used in the simulation, a viable alternative is a sim- simulation runs was based on a previous plified cooling design method derived from study of solar cooling systems (6). the correlation of detailed simulation Basically, all of the useful energy collected results. One such correlation is the cool- by the flat plate collectors is sent to a ing fraction, fc-chart developed using liquid storage tank and stored as sensible SHAS~. The f -chart can be used to predict heat. Whenever there is a cooling demand, solar coolin{ contribution to 1-!ith:in 5% of the the generator of the absorption chiller actual SHASP result, and as such can be a draws off hot water from storage. If the hot very useful design tool. water temperature is such that the chiller cannot satisfy the cooling load, then auxil- iary energy is used to fully supply the 1. INTRODUCTION generator requirements. The design of solar cooling systems has not yet been developed to the same state as the 3. ANALYSIS design of solar heating systems. Although the f-chart (1), which was the result of Energy balance of the solar cooling system the correlation of detailed simulation runs yields on TRNSYS (2), is already widely accepted and used for solar heating, no similar prog- liE (1) ress has been made in solar cooling. The f,0 chart (3) approach which uses the uti- lizability curves of Liu and Jordan (4), where has been proposed, but is limited to con- stant COP cooling applications. Qu = useful collected heat A computer simulation program called SHASP QL space cooling load (5) has been developed by the Solar Energy Projects Group at the University of Mary- COP average chiller COP av land. The program uses a generalized chiller model so that different chillers auxiliary energy required can be used in the simulation. A variable load model which is dependent on ambient t,E change in capacity of the hot storage air temperature, insolation and heat genera- tank tion is used since there is a dynamic interaction between the load and the chiller Eq. (1) is applicable to any system where which becomes more important in solar cool- the load is met 100% of the time. For a ing. A wide range of system parameters and system which is undersized, the cooling load weather data are used in detailed simulation cannot be met at all times and QL in Eq. (1) runs and the results are correlated to should be replaced by the total cooling Page 337 supplied by the system. In considering the long term system perfor- f (11) C mance, 6E will be small compared to the other energy quantities and Eq. (1) reduces to: QL COP 0 (2) av Eq. (2) is applicable to a system using an The integrals in Eq. 11 cannot be evaluated absorption chiller where Qaux is input to easily since the insolation and the dry-bulh temperature are not continuous mathematical the generator of the chiller. It is also functions. Moreover, the relationship be- applicable to an RC/VCC cycle where the tween the solar thermal system, the chiller auxiliary energy is an input to the boiler and the load is both complex and dynamic. As of the RC cycle. an alternative, detailed simulation runs can be made using SHASP with real weather inputs The average cooling supplied by auxiliary is and an average daily value of the solar cool- given by: ing fraction, fc for any cooling month can be ( 3) calculated. As suggested by the grouping of terms in Eq. 11, the long term average daily value can be correlated into: The portion of the load satisfied by solar 2 2 will then be: f a + b Y + ex + dY + ex (12) C ~L - QC (4) where: I aux X F'U A (T f - Td)6t/(Q /COP ) (13) QC = QL 1- COP (Q ) (5) R 1 c re 1 av sol av aux y FR'taI A /(Q /COP ) (14) The solar cooling fraction is then: c c 1 av t Since there is a limit to the maximum QC generator temperature of an absorption chill- f sol QL - COP av (Qaux) (6) er (because of recrystallization), a c=~= QL reference temperature, T f=96.l C (205 F) is re used. In Eqs. (12), (13), and (14), the long-term average daily values can be used. Hence, f (7) C IC average total daily insola- T tion Eq. 2, therefore, gives the cooling fraction in terms of Qu as: QL average total daily load COP average daily COP av fc = l - (Q /COP ) (8) 1 av Td average daily dry-bulb temperature The instantaneous useful heat collected by an area AC is given by: A collector area C F;rn, F;u1 collector parameters 6t 24 hrs. (9) Page 338 4. RESULTS following procedure can be followed: Detailed simulation runs were made using X 22 whenever calculated X > 22 SHASP and real weather data for Washington, D. C., Charleston, S. C. and Madison, WI for and Y 8 whenever calculated Y > 8 the months of May to October. The range of otherwise: use calculated X and Y values. parameters used in the runs for which the correlation would be valid are: 5. SAMPLE EXAMPLE Collector: The following example illustrates how the simplified cooling design chart, together with information available from other sources (Ref. 7 & 8.) can be used to predict solar 2 0 3.123 ::_ (F{i_UL) ::_ 5.452 W/m - C cooling performance. 2 Consider a solar cooling system where: 51.1 < A < 92.9 m C 2 A 51.1 m C -10° < (0 - S) ::_ + 10° F~rn 0.68 2 0 m r:.s FiUL 3.123 W/m - C A= 48.8 2 c m -hr M 4377Kg c!L = A 85 .66~}) C m Hot storage: TDump 96.1° C 2 48.8 < (M/A) < 87.9 Kg/m For a house in Washington, D. C. for which - C the average daily July load is 248.93 MJ, the solar cooling fraction is computed as 96.1 < T < 100° C - Dump follows: Absorption chiller: From Ref. 7' for Washington, D. C. 2 76.7 C ::_ TG min::_ 85 C H 22.12 MJ /m -day 0.55 with the generator operating from storage at ~ temperatures 25° C Td TG min::_ TG < 96.1 C For KT 0.55 and (latitude-tilt) 0, A polynomial regression c_orrelation with two independent variables of the form of R 0.875 Eq. 12 was made on the results of the de- tailed SHASP runs. The coefficients were MJ and I 0.875 X 22.12 19.36 estimated using the least squares method and CT m - day the constant cooling fraction curves were plotted as shown in Fig. 2. A statistical From Ref. 8, there are 15 hours for which the analysis of the error between the simplified design predictions and the detailed simula- ambient air is above 23.9° C (75° F), the tion runs indicate a mean error of -0.0035 room set temperature. For this 15 hour peri- with a standard deviation of 0.0407 for the od, the chiller must provide an average values of X and Y covered in Fig. 2. Over cooling of the range of values 248.93 = _ MJ 0 < X < 22 16 595 15 hr 0 < Y < 8 Assuming that an available 3 ton absorption chiller is used, the manufacturer's data the mean error is 0.00 with a standard shows that the chiller operating at an aver- deviation of 0.0618. A comparison of the age hot water inlet tempetature of 83.1 C simplified design predictions with the (181.5 F) with an available cooling water detailed simulation runs is shown in Fig. 3. temperature of 32.2 C (90 F) will provide 16.595 MJ/hr of cooling with a generator To predict the solar cooling fraction out- input of 27.261 MJ/hr. The average chiller side the range of X and Y as indicated, the Page 339 COP is then Vol. 22, pp. 269-282, 1979. COP 16.595/27.261 0.609 4. Liu, B.Y .H., and R.C. Jordan, "The Inter-av relationship and Characteristic Distribution of Direct, Diffuse, and Total Solar Radia- tion", Solar Energy, Vol. 4, No. 3, pp. 1-19, (F~UL)Ac(Tref - Td)6t 1960. X (QL/COP ) 5. "SHASP, Solar Heating and Air-Condition-av ing Simulation Programs", Solar Energy Projects, Mechanical Engineering Department, (3.123)(51.1)(96.1 - 25)(24) 2.398 University of Maryland, College Park, Mary- (248.93/0.609)(277.8) land, December 1978. 6. "Control Strategy Studies of Solar Heat- y (0.68)(51.1)(19.355) ing and Cooling Systems", Solar Energy QL/COPav 248.93/0.609 Projects, Mechanical Engineering Department, University of Maryland, College Park, Mary- 1.645 land, November 1978. From Fig. 2, fc = 0.7566 for the above val- 7. Beckman, W.A., S.A. Klein, and J.A. ues of X and Y. Duffie, Solar Heating Design by the f- The detailed simulation (SHASP) gives a Chart Method, John Wiley and Sons, 1977. value f = 0.7637 making the value predicted from th~ simplified design method off by 1%. 8. "Solar Heating and Cooling of Buildings", (Phase 0), Vol. I to III, TRW Report pre- 6. CONCLUSIO:; pared for NSF/RANN, May 31, 1974. The example problem discussed in the previ- ous section illustrates the ease with which the simplified cooling design method can Ou be used. The amount of look-up data and E~ 0z ~ effort in calculation is very much less than z0 l. l that required by other design methods and AH3 MYI I IHC2 SW3 the result is accurate enough for solar cooling systems performance predictions. Comparison of the prediction with the de- tailed simulation results shows an accuracy of 10% in the range of reasonable expected values of load, insolation, and dry-bulb , HW temperature. .~~~-'-!-,~ V7 Future work on the simplified solar cooling -,,...--~~-~-----;.,--;i--11-----~ Fv design method would include expanding the AC -A!R CONOlTIONING U"i,T correlation to more cities with diverse HW-HOT WATER STORAGE CW -Cl·Ul.LED WAT[A STORMGE OW-00J.£STIC HOT WATER climatic conditions to make the design AH-AUXILIAR'r HEAHf.lS [ - INPUT POWE A chart region independent. f 's-CONTAOl Fut.Cl IONS, 1- 01\', 0- OFF fig. l Scher-.atic D1agra~ of the Sola• Cool in~ Syste~ 7. ACKNOWLEDGEMENT This work is supported by the U. S. Depart- ment of Energy R & D Branch, Office of ,o Conservation and Solar Applications con- tract #EY 76-S-05-4976. 8. REFERENCES 2 0 1. "FCHART, An Interactive Program for Designing Solar Heating Systems", University of Wisconsin, June 1978. 1.0 2. "TRNSYS, A Transient Simulation Pro- gran", Solar Energy Laboratory, University of Wisconsin, Madison, February 1978. fc ~ 0.32.85B9 -10 15769\X + I05~3BJr + lO 005135lX 2 -(0DJrmanesh, Ra, Hou,manes.~ and Ov.1,ld B. Elmer Ranch" · Architecte O.U.H., France - Texas A' & MU niversity Benjamin T. Rngers, New Mexico "Performance of a Low-CJpacity Retrofit Trombe - Michel Wall". "Solar Wall" "Results from PassiW1 -Solar Test ROOfft Investigations in , Cold Alvin 0. Converse Mo Hourmanesh, Ray Hourmanesh and Donald B. Elmer Climate · Thayer School of Enaineerin&, Dartmouth Teus A&M University Robert t Jones, Jr. "Passive Solar Remodeling in NOl!llern Climates" "An Experimen'41 S~Jdy of Stora,e Elevation in a Them,osyphon Hot ukeheJd University, Ontario Donald Schramm Water System" "Measvred and Modeled PassiWI Performance in Mon/Im" Dept of Engineerin& & Applied Science University of Wisconsin - J. W. Baughn and llaren Crowther Larry Palmrter, Bil! Caswell and Bob Corbett Extension · University of California/Davis NCAT "Cost Effectiveness of a Passive Solar He.linf Retrofit" "HeoophaseN Solar Hot Water System" Butte, Montana Timothy I. Michels ,- Fred ll Manasse and John A. O'Leary "EViluation of Passive Solar Hutini'' 1.Dnde, Parker, Michels, Consultan15; SI. Louis The Aeta Corporation, New Hampshire J. 0. Balcomb and W. 0. Wray ''Effect of Moisture Conter.t on the ·Thermal Properties of Sun-Dried Los Allmos Scientific Laboratory Adobe" Benjamin T. Roeers. New Mexico "Molded Glass Fiber ReinlOfced Cement Buadin1 Pant/ Applications in Loi, Cost Solar Heated and Eflfff1·Cons,min1 Structure~ " Tamil 0. Bauch and Morton Schiff EGGE Reseat?, New- Yark -... ,:,:.• '" .... ,. ';U. . - ~-.. ~ "' _.., .... ·~ .- ·- IG Solar bdiation I IH Solar Radiation II lntemational Prov,;ms Chai'lllfSOI: Eldon Boes 11 Cllairperso11: William Shropshire . Cltli111moir. Bill Duff "On the Nature and Oistribution of Solar Radiation" "Mullispectra/ Measurement of Direct and Dittus. Sollr Radiation at "What's With 1111.ernatianll Slur Cooperation?" Arthur 0. Watt Groe ,,.,, Prv;tt:t" C. N. Vittillle and f. Biggs "Estimating lnsolition Levels on Tilled Surt1'es from HllfizonW. Fred Dubin Sandia laborllories M~" Dubin-Bloome As1oc, New YOfk - "Generation of a Typig/ ~IY ear" Chattes D. BeKh and Thomas f. Tiedemann t Boes ."The Stitus ol lM /EA and CCIIS Multi-literal l'rofra1111 in Solar . ' L J. HaU, R. R. Prairie, H. E. Anderson and C. Sandia laboralllrils . Florida Solar Enern Center , He.lint and Ccalint" "The Regional Variation in SoGt Radiation Araillbility" SheiLa Blum "Estimmon of llontllly AW!f.qe Diff= Radi:ition" Klein Duffie Ray Bahm · University ol Maryland $. A. Ind J. A. Solar Eneru The Univfflily of New Mexico Laboratory "Solir RMlillion llonilorin1 in the Slate ol Ore,an" University of WtSCOnsin-Madison ... • H. D. Kaehn, M. S. Baker and D. K. Mc Daniels .,._,. Univfflity ol Or "Vllidalionof~erModelsUs.dloiPredictin,R~tionLe.els'' ion:n 1. ur.U and C. Byron Winn S::1:1 Enriron111e11III fncjneerill& Co. ( Page 343 SYSTEM PERFORMANCE PREDICTIONS FOR SOLAR HEATING AND COOLING USING STOCHASTIC WEATIIER MODELS D. K. Anand, Professor R. B. Abarcar, Research Associate S. R. Venkateswaran, Research Assistant R. W. Allen, Professor Solar Energy Projects Department of Mechanical Engineering University of Maryland College Park, Maryland 20742 ABSTRACT A solar powered heating and cooling system performance of air-cooled solar powered air-cond- with storage as well as automatic controls and itioning systems for the Washington, D.C. area time dependent load is simulated using both real was reported. The work was based on a flat-plate and stochastic weather as input. The stochastic collector coupled to a LiBr air-conditioner. The weather is generated using a probabilistic model calculations were based on a stochastic model of of insolation and dry-bulb temperature which was dry-bulb temperature and insolation which was constructed from five years of real weather constructed using historical information. history for several regions. The stochastic Basically, a statistical approach was used comb- constants, with their attendant joint probability ined with state representation which modified this matrices represents data which are considerably weather data into a more compact and hence inex- less than hour by hour insolation and temper- pensive form. The stochastic constants generated ature data needed for long-term system perfor- for the Washington, D.C. area with their attendant mance predictions. joint probability density matrices werefo:1nd to _ greatly decrease computations in system simulations with little loss of accuracy as compared to those The system performance is predicted for performed using actual hour by hour weather data. the real and stochastic cases. The system While the data used is considerably less, the performance indices show that system simulation stochastic predictions are sufficiently accurate using stochastic weather gives results which for system sizing. are comparable to real weather simulation while at the sarr,e :ime us:ng considerably less data. In this paper, a solar powered heating and Stochastic predictions are also sufficiently cooling system is simulated using both real and accurate for use in system sizing. stochastic weather data as input. The stochastic weather is generated using a data base of five years of real weather history for several regions. Probabalistic considerations and minimization of the covariance between actual weather data and assumed temperature and insolation profiles formed the basis of the stochastic weather models. The system performance, measured through use of several performance indices, is predicted for the Simulations of solar heating and cooling real and stochastic cases. systems are generally performed using hour by hour weatJ-.er data or averaged weather parameters as input. Hour by hour insolation and temperature SYSTEM DESCRIPTION data driving the system is the most realistic vet most expensive and cumbersome method of sim- A schematic of the system is given in Figure ~lation. Although SOLMET weather tapes now 1. A computer program to simulate this system make input of weather data into solar simulation was written. This simulation features load cal- computer programs much easier, this drawback is culations, storage as well as various automatic not alleviatec. As an alternate approach several controls to turn pumps on and off or to operate em~irical methods have been devised but with valves along the system network in accordance mixed results (1-3). The present scheme of sys- with specified control strategies. Details of terr performance prediction uses a probabalistic the simulated system are given in Table 1 and 2. approach which retains the weather history. This The various constants for subsystems are discussed probabalistic approach has been used previously under the cooling and heating simulation sections. with ~ood results (4). In these studies, the Page 344 STOCHASTIC WEATHER DATA Time dependent ambient dry-bulb temperature, °C (°F) The computation2J steps required for systems simulations using stochastic weather data are TROOM Set room temperature, °C (°F) straightfon.:3rJ. First, assumed temperature and insolat1on rrofiles are constructed based on weather K Fraction of incident insolation codels presenteci in the literature and previous absorbed by the structure, dimen- experience. ThesP profiles are equations which sionless are time (:iou1 of dav and month of year) dependent. The unknc11,T constants in these equations are then P..yOT Total surface area exposed to obtained by minimizing the error through a least insolation, m2 (ft 2) square compariso;i to actual hour by hour weather data for a p,,rticula1 area. Once the unknown para- I(t-1) Time dependent lnsolation on a meters have been determined in the synthetic weather horizontal surface per unit area, profiles, one hAs 8 methou for reconstructing the K.J/m 2hr (BTu/ft 2hr) huurly temperature and insolation values for any month of the yeAr for a particular region, provided Sensible heat generation from an average teG~erature and insolation is specified. occupants, appliances etc., Tn£ scatter diagrdms for the temperature and in- K.J/hr (BTu/hr) ~olatlon hRsej on actual local weather data can be generalizeo using a joint probability density catrix. This can then be represented in matrix The system simulated is based on the assump- fom. This matrix together with the profile are tion that energy from the collector is used at the used tc sit:t.;late weather. Mathematical details of generator as soon as the temperature of thE ~ater this are given in reference 6. leaving the collector matches that needed to sat- isfy the load. COOLii,·~ SYSTE'l ANALYSIS For this control strategy, the following parameters are obtained using the stochastic The chiller performance is given by approach and using real weather: 2 aE + EE TG + ~E TG (1) I = Incident Solar Radiation Useful Solar Energy Collected (2) Load where Cooling Supplied .· C..\P (TG) Evaporator capacity, K.J /hr (BTu/hr) Auxiliary Energy used QGr::CTGJ Generator heat input K.J/hr (BTu/hr) Percent of Load Supplied by Solar Energy TG Ho~ water inlet temperature to the generator °C (°F) Average chiller coefficient of performance Evaporator coefficient from curve fit of performance data Ratio of solar cooling delivered without auxiliary to total insol- Generator coefficient from curve ation on collector fit of performance data Same as COP but includes parasitic and the load is computed by 2 energy use + n Average collector efficiency This information is obtained for Charleston, S.C. !{,\TOT I(t-J) + QCONST (3) and Washington, D.C. for the summer months using 1954-1957 weather data. A sample of typical res- ults are shown in Tables 3, 4, and 5. where Table 3 shows system simulation predictions QLOAD(t) = Time dependent total load, KJ/hr for Charleston, S.C. for June 1957 for two cases, (BTu/hr) viz. with auxiliary energy use and without auxi- liary energy use and with no service hot water. Tota} co~ductance of walls, floors We note that the% solar, n and the various COP and ceiling, KJ/°C hr (BTu/°F hr) values computed using stochastic weather agree to within less than 10~ to those computed using real weather. The same is true of the total Page 345 incident insolation, useful energy collected and CONCLUSION load. However, the stochastic system is unable to predict the actual amount of auxiliary energv For the two cities studied, the total used. Similar conclusions can b~ made from Table insolation, useful energy and load computations ~ for the month of August for Charleston, S.C. for the heating and cooling season using stoch- astic weather are teen to be in fairly good Tahle 5 shows a comparison of stochastic pre- agreement with real weather predictions. However, dictions with real weather for Washington, D.C. the auxiliary energy calculations do not agree for June 1957. Again for the case where no aux1- to within acceptable limits. For many design liary energv is used, we note that all the indices problems this is not particular drawback. Con- calculated using stochastic weather agree well sidering the small amount of data for stochastic with that obtained using real weather. However, weather predictions, this scheme is deernPd the comparisons are not as good for the case when attractive as a simplified approach to system auxiliary energy is used. Although these compar- design and analysis. isons can he improved for some cases by shifting the joint probability matrix, no clear direction is obtained. We therefore conclude that on a ACKNOWLEDGEMENT tentative Lasis the stochastic predictions compare well with real weather prediction for cases where This work is supported by the Department of it is not necessary to obtain auxiliary energy Energy, Division of Conservation and Solar predictions. It may be possible hovever, to Applications, Contract# EY 76-S-05-4976 A003. correlate the auxiliary energy predicted using Contributors to this paper include: E. 0. Bazques real and stochastic weather and remove this res- and I. N. Deif. tric :ion in the future. This problem is under furt.1er study. REFERENCES HEATING SYSTEM ANALYSIS 1. Klein, S.A., Cooper, P.I., Freeman, J.L., Beekman, D.M., Beckman, W.A., and Duffie, J.A., The system parameters for the heating analysis "A Method of Simulation of Solar Processes are given in Table 2. In addition the folloving and Its Application", Solar Energy, Vol. 17, assumptions apply: pp. 29-37, 1975. 1. No service hot water is included. 2. Winn, C.B., Johnson, G.R., "Dynamic Simul-2. No collector-tank heat exchanger is used. 3. The auxiliary energy is in parallel supplying ation for Performance Analysis of Solar that part of load which cannot be met from Heated and Cooled Buildings", Presented at storage or directly from collector. the American Society of Mechanical Engineers 4. The load is directly supplied from the coll- Winter Annual Meeting, New York, New York, ector when the collector outlet temperature Nov. 1974, Paper 74-WA/Sol-8. is rufficient to meet the entire load. Card, W.H., Drucker, E.E., Ucar, M, and 5. The spac~ load is modelled by degree hour 3. approach La Graff, J.E., "Generalized Weather Func- tions for Computer Analysis of a Solar- Assisted HVAC System", Presented at the American Society of Mechanical Engineers Winter Annual Meeting, New York, New York, The room temperature is set at 70°F and T b Dec. 1976, Paper 76-WA/Sol-20. is obLained either using the stochastic am io"7u]a•ion or real weather. The hot storage 4. Anand, D.K., Allen, R.W., and Bazques, E.O., io;;s coefi ici enc is set at 2_· 26 B/hrF. "Short and Long Term Comparison of Solar Absorption Air Conditioning System Performance Results of the simulation for four months Using Real and Synthetic Weather Data", in 1957 for Washington, D.C. are shown in Table 6. Proceedings of the Eleventh IECEC, Lake The top entry in each row is for a 3 x 3 joint Tahoe, September 1976. probability matrix whereas the second and third entry refer to a 3 x 4 and a 4 x 4 matrix. We s. Anand, D.K., and Allen, R.W., "Solar Powered note that as the matrix grid is enlarged, the Absorption Cycle Simulation Using Real and co~?arisons improve. The total incident insolation Stochastic Weather Data", ASME Winter Annual co~pares to within 15% for December and to within Meeting, Paper 76-WA/Sol-6, New York, December 2% for the other months. In general all the 1976. various energy quantities agree to within 10/2 with the poorest agreement in the auxiliary energy 6. Anand, D.K., Allen, R.W., and Bazques, E.O., calculation. The values of% solar and n are seen "Solar Powered Absorption Air-Conditioning to compare within 5%. Although these are very System Performance Predictions Using Stoch- preliminary, the results appear to be very en- astic Weather Models", Solar Energv Projects couraging. Report, Department of Mechanical Engineering, University of Maryland, College Park, MD, February 1977. Page 346 7. Anand, D.K., Allen. R.W., and Bazques, E.O., "Solar Air-Conditioning Performance Using Stoch2stic \.leather Models", Journal of Energv, Vol. 1, ~o. 5, September-October 1977, pp. 319-323. Page 347 a w z w O u i = c t _ O e n z 0 u S W 1 - + + - - - - A H 3 S W 3 S W 5 £ 5 A C . C C 1 S U P P L Y o . w . H W . C I T Y c . w . f o _ , _ • t V 6 V 7 - , F V F V 5 M V 2 C C J A C . - A I R C O N D I T I O N I N G U N I T H P . - H E A T P U M P H . P . H W - H O T W A T E R S T O R A G E o - C W - C H I L L E D W A T E R S T O R A G E O W - D O M E S T I C H O T W A T E R V 1 2 t C > O A . H . - A U X I U A R Y H E A T E R S E - I N P U T P O W E R t E 7 F ' 5 - C O N T R O l . F U N C T I O N S , I - O N , 0 - O F F I I f i g u r e 1 . S O L ~ , . . t ' ~ . : ~ ~ ~ O I T I O N I N G H E A T : I N : G - : _ _ : A : N ~ o _ . o ~ O ~ M = - F ~ ~ : _ : _ T : _ : l r . _ : _ _ P a g e 3 4 8 COLLECTOR (DOUBLE-GLAZE, SELECTIVE SURFACE) 0.68 (0.68) 3. 123 w (0.55 Btu ) m2_oc hrft2F Area 51. 1 2 m (550 ft 2) s (tilt) 36° - Washington, D. C. 33° - Charleston, S.C. Latitude 36° North,Washington, D. C. 33° North,Charleston, S.C. DESIGN POINT TEMPERATURES: Generator/Condenser 90.6/32.2 cc ( 195/90 F) Evaporator/Absorber 7.2/32.2 cc ( 45/90 F) QE 8001 W (27,300 ~;u) m (to the generator) 2494 ~ hr (5500 ~~) CHILLED (WATER-COOLED): QE = -1 .45 x 10 5 + 3037.6 TG 2 14.85 TG w 5 (-6.96 x 10 + 6759.0 TG - 2 15.64 TG ) (BTU/hr) 2 QG = -9.73 X 10 4 + 1757.7 TG - 5.97 TG w 5 2 (-4.45 X 10 + 3734.3 TG - 6.29 TG) (BTU/hr) TG, oc (s I) TG, °F (English) HOT WATER STORAGE (FULLY MIXED): 4376 Kg (9,650 lb.) CHILLED WATER STORAGE: 2268 Kg (5,000 lb.) Table 5-1 - PARAf~ETERS FOR COOLING SYSTEM SIMULATION 29 Page 349 COLLECTOR (DOUBLE-GLAZE, SELECTIVE SURFACE) Kl 0.68 (0.68) 11.24 KJ (0.55 Btu K2 ) hrm 2C hrft 2F 2 Area 51.1 2m (550 ft ) S(tilt) 36° - Washington, D.C. Latitude 36° North - Washington, D.C. HOT WATER STORAGE (FULLY MIXED) 4376 Kg (9650 lb) SPACE HEATING LOAD: KJ Building UA 3798 hrC (2000 Btu ) hrF KJ Load Heat Exchanger (EC . ) min 6836 brC (3600 Btu ) hrF TABLE 2 - PARAMETERS FOR HEATING SYSTEM SIMULATION Page 350 Page 351 C H I L L E R T U R N E D O N L O A D M E T 1 0 0 % ( A U X I L I A R Y P R O V I D E S O N L Y W H E N T G > T m i n B A L A N C E O F E N E R G Y ( L O A D N O T M E T 1 0 0 % ) R E Q U I R E D ) S T O C H . R E A L R E A L S T O C H . - 2 - 1 2 0 , 3 1 6 1 9 , 9 4 1 1 9 , 9 4 1 2 0 , 3 1 6 H , K J - m - D A Y ( 1 7 5 6 ) ( 1 7 8 9 ) ( 1 7 5 6 ) ( 1 7 8 9 ) 2 - 1 ( B t u - f t - D A Y ) 3 3 4 , 0 1 5 E Q , K J - D A Y - l 3 2 4 , 5 8 5 3 3 0 , 6 3 4 3 3 0 , 7 1 5 u - 1 ( 3 1 3 , 3 9 8 ) ( 3 1 6 , 6 0 2 ) ( 3 0 7 , 6 6 4 ) ( 3 1 3 , 4 7 4 ) ( B t u - D A Y ) K J - D A Y - l 2 1 7 , 5 1 8 2 1 8 , 3 7 9 2 1 7 , 5 1 8 2 1 8 , 3 8 6 E L ( 2 0 6 , 1 7 8 ) ( 2 0 6 , 9 9 5 ) ( 2 0 6 , 1 7 8 ) ( 2 0 7 , 0 0 1 ) - 1 ( B t u - D A Y ) K J - D A Y - l 2 1 7 , 5 1 8 2 1 8 , 3 7 9 1 8 7 , 7 2 0 1 8 5 , 2 6 7 E Q S ( 2 0 6 , 1 7 8 ) ( 2 0 6 , 9 9 5 ) ( 1 7 7 , 9 3 4 ) ( 1 7 5 , 6 0 9 ) - 1 ( B t u - D A Y ) 7 7 . 6 6 8 . 8 5 8 2 . 4 8 4 . 8 % S O L A R . 5 6 9 6 . 5 7 6 9 . 5 3 9 8 . 5 5 5 8 C O P 1 . 1 7 8 4 . 1 8 2 3 . 1 4 4 8 . 1 5 7 6 C O P 2 . 1 8 1 2 C O P . 1 7 7 1 . 1 4 3 8 . 1 5 6 6 3 3 1 . 8 5 3 0 . 9 3 1 . 8 5 n % 3 1 . 9 9 - 1 7 6 , 5 4 2 5 0 , 8 9 2 0 0 E Q A U X K . J - D A Y - 1 ( 7 2 , 5 5 2 ) ( 4 8 , 2 3 9 ) ( B t u - D A Y ) T a b l e 3 . C o m p a r i s o n o f S t o c h a s t i c t o R e a l W e a t h e r S y s t e m S i m u l a t i o n P r e d i c t i o n s f o r J u n e , C h a r l e s t o n , S . C . Page 352 L O A D M E T 1 0 0 % C H I L L E R T U R N E D O N ( A U X I L I A R Y P R O V I D E S O N L Y W l l E N T G > T m i n B A L A N C E O F E N E R G Y R E Q U I R E D ) ( L O A D N O T M E T 1 0 0 % ) S T O C H . R E A L S T O C H . R E A L - 2 - 1 2 0 , 3 6 1 1 9 , 7 9 3 1 9 , 7 9 3 2 0 , 3 6 1 H , K J - m - D A Y ( 1 7 9 3 ) ( 1 7 4 3 ) ( 1 7 4 3 ) ( 1 7 9 3 ) - 2 - 1 ( B t u - F T - D A Y ) K J - D A Y - l 4 2 3 , 5 8 5 3 3 0 , 7 1 5 3 3 8 , 7 4 7 3 3 6 , 7 2 9 E Q ' u ( 3 1 3 , 4 7 4 ) ( 3 0 7 , 6 6 4 ) ( 3 2 1 , 0 8 8 ) ( 3 1 9 , 1 7 5 ) - 1 ( B t u - D A Y ) K J - D A Y - l 2 6 3 , 1 2 9 2 4 6 , 8 7 8 2 6 3 , 1 2 9 2 4 6 , 8 7 8 E L ( 2 4 9 , 4 1 2 ) ( 2 3 4 , 0 0 8 ) ( 2 4 9 , 4 1 2 ) ( 2 3 4 , 0 0 8 ) - 1 ( B t u - D A Y ) K J - D A Y - l 2 6 3 , 1 2 9 2 4 6 , 8 7 8 1 9 3 , 9 2 5 1 8 7 , 0 9 0 E Q S ( 2 4 9 , 4 1 2 ) ( 1 8 3 , 8 1 5 ) ( 2 3 4 , 0 0 8 ) ( 1 7 7 , 3 3 7 ) ( B t u - D A Y - l ) 6 9 . 3 6 1 . 7 2 7 5 . 8 7 9 . 6 % S O L A R . 5 4 2 7 . 5 4 4 6 . 5 5 6 9 . 5 5 4 1 C O P l . 1 4 8 4 . 1 5 4 0 . 1 8 8 6 . 1 7 8 3 C O P 2 . 1 5 2 9 . 1 8 7 9 . 1 4 7 2 . 1 7 9 8 C O P 3 3 1 . 8 7 3 1 . 8 0 3 2 . 2 6 3 2 . 0 4 n % - 1 1 2 4 , 3 5 5 0 9 9 , 7 0 3 0 Q A U X K J - D A Y ( 1 1 7 , 8 7 2 ) ( 9 4 , 5 0 5 ) - 1 ( B t u - D A Y ) T a b l e 4 . C o m p a r i s o n o f S t o c h a s t i c t o R e a l W e a t h e r S y s t e m S i m u l a t i o n P r e d i c t i o n s f o r A u g u s t , C h a r l e s t o n , S . C . Page 353 C H I L L E R T U R N E D O N L O A D M E T 1 0 0 % > T ( A U X I L I A R Y P R O V I D E S B A L A N C E O N L Y W H E N T G m i n O F E N E R G Y R E Q U I R E D ) ( L O A D N O T M E T 1 0 0 % ) S T O C H . R E A L S T O C H . R E A L 2 H , K J m - - D A Y - l 1 7 , 1 1 3 1 7 , 4 0 9 1 7 , 1 1 3 1 7 , 4 0 9 ( 1 5 0 7 ) ( 1 5 3 3 ) ( 1 5 0 7 ) ( 1 5 3 3 ) 2 - 1 ( B t u - f t - D A Y ) E Q , K J - D A Y - l 2 4 3 , 8 5 4 2 2 1 , 4 1 7 2 1 9 , 8 4 9 2 4 2 , 6 8 6 u - 1 ( 2 0 9 , 8 7 4 ) ( 2 3 1 , 1 4 2 ) ( 2 0 8 , 3 8 8 ) ( 2 3 0 , 0 3 4 ) ( B t u - D A Y ) K J - D A Y - l 1 4 1 , 4 3 4 1 5 4 , 1 7 1 1 4 1 , 4 3 4 1 5 4 , 1 7 1 E L ( 1 3 4 , 0 6 1 ) ( 1 4 6 , 1 3 4 ) ( 1 3 4 , 0 6 1 ) ( 1 4 6 , 1 3 4 ) - 1 ( B t u - D A Y ) K J - D A Y - l 1 2 4 , 0 3 4 1 4 2 , 8 7 7 1 4 1 , 4 3 4 1 5 4 , 1 7 1 E Q S ( 1 1 7 , 5 6 8 ) ( 1 3 5 , 4 2 9 ) ( 1 3 4 , 0 6 1 ) ( 1 4 6 , 1 3 4 ) - 1 ( B t u - D A Y ) 8 7 . 7 % S O L A R 8 8 . 6 7 6 . 4 0 8 6 . 8 C O P . 5 7 6 0 . 5 4 9 0 . 5 5 8 0 . 5 5 7 7 1 C O P . 1 4 1 9 . 1 4 0 4 . 1 1 8 4 . 1 3 5 4 2 C O P . 1 4 1 3 . 1 4 3 8 . 1 1 7 8 . 1 3 4 7 3 2 5 . 3 3 2 3 . 1 2 n % 2 4 . 1 2 3 . 0 1 - 1 0 0 4 0 , 6 8 1 2 4 , 6 1 2 E Q A U X K . J - D A Y - 1 ( 3 8 , 5 6 0 ) ( 2 3 , 3 2 9 ) ( B t u - D A Y ) T a b l e 5 . C o m p a r i s o n o f S t o c h a s t i c t o R e a l W e a t h e r S y s t e m S i m u l a t i o n P r e d i c t i o n s f o r J u n e , W a s h i n g t o n , D . C . Page 354 I D E C E M B E R J A N U A R Y F E B R U A R Y M A R C H ~ - - R E A L S T O C H . R E A L S T O C H R E A L R E A L S T O C H . S T O C H , 1 1 7 0 8 ( 1 0 2 1 ) 1 2 3 3 9 ( 1 0 7 6 ) 1 1 3 5 3 ( 9 9 0 ) 2 1 4 7 9 3 ( 1 2 9 0 ) K J / m - D A Y n 1 1 9 2 6 1 4 3 1 1 1 4 7 5 9 1 6 4 1 0 1 3 1 1 9 ( 1 1 4 4 ) 1 3 4 7 4 ( 1 1 7 5 ) 2 1 3 3 3 7 ( 1 1 6 3 ) 1 6 5 2 5 ( 1 4 4 1 ) ( 1 0 4 0 ) ( 1 2 4 8 ) ( 1 2 8 7 ) ( 1 4 3 1 ) ( B t u / f t - D A Y ) 1 3 8 6 4 ( 1 2 0 9 ) 1 4 3 8 0 ( 1 2 5 4 ) 1 4 4 8 3 ( 1 2 6 3 ) 1 7 0 6 3 ( 1 4 8 8 ) 3 2 5 2 4 2 ( 3 0 8 2 8 6 ) 2 9 6 9 5 7 ( 2 8 1 4 7 6 ) 3 6 8 4 0 5 ( 3 4 9 1 9 9 ) 3 0 9 4 9 4 ( 2 9 3 3 5 9 ) K J / D A Y 1 : Q 3 8 5 6 4 8 4 2 1 7 4 1 3 0 6 8 2 0 3 7 3 6 3 6 u 3 4 2 7 8 2 ( 3 2 4 9 1 2 ) 3 4 4 4 6 2 ( 3 2 6 5 0 4 ) 4 3 9 3 6 0 ( 3 3 1 1 4 7 ) 3 9 5 7 0 8 ( 3 7 5 0 7 9 ) ( 3 6 5 5 4 3 ) ( 3 9 9 7 5 5 ) ( 2 9 0 8 2 5 ) ( 3 5 4 1 5 7 ) ( B t u / D A Y ) 3 6 9 4 2 9 ( 3 5 0 1 7 0 ) 3 7 0 2 6 8 ( 3 5 0 9 6 5 ) 4 0 9 5 5 1 ( 3 8 8 2 0 0 ) 3 6 0 6 3 0 ( 3 4 1 8 2 9 ) 6 8 5 9 3 0 ( 6 5 0 1 7 1 ) 7 5 0 5 2 5 ( 7 1 1 3 9 8 ) 6 0 1 3 6 4 ( 5 7 0 0 1 3 ) 6 4 2 3 3 0 ( 6 0 8 8 4 4 ) K J / D A Y r t 8 7 2 3 9 9 1 0 0 6 6 2 3 9 2 3 0 4 9 6 9 2 7 8 4 8 1 2 3 0 7 ( 7 6 9 9 5 9 ) 8 5 2 3 0 7 ( 8 0 7 8 7 4 ) 7 5 3 9 3 8 ( 7 1 4 6 3 3 ) 6 6 5 2 7 0 ( 6 3 0 5 8 8 ) ( 8 2 6 9 1 8 ) ( 9 5 4 1 4 5 ) ( 8 7 4 9 2 8 ) ( 6 5 6 6 6 7 ) ( B t u / D A Y ) 8 7 7 8 5 2 ( 8 3 2 0 8 7 ) 9 5 0 4 8 0 ( 9 0 0 9 2 9 ) 8 2 2 7 5 5 ( 7 7 9 8 6 3 ) 6 9 5 5 5 0 ( 6 5 9 2 8 9 ) 3 7 9 1 6 0 ( 3 5 9 3 9 3 ) 4 2 7 0 0 0 ( 4 0 4 7 3 9 ) 3 0 9 5 3 5 ( 2 9 3 3 9 8 ) 2 9 3 9 0 0 ( 2 7 8 5 7 9 ) K J / D A Y 1 : Q A U X 5 6 6 6 0 0 6 3 4 6 4 7 5 3 8 9 0 7 2 7 5 5 2 5 4 7 0 9 1 3 ( 4 4 6 3 6 3 ) 5 0 6 6 8 4 ( 4 8 0 2 6 9 ) 4 1 9 3 1 1 ( 3 9 7 4 5 1 ) 2 9 5 7 3 0 ( 2 8 0 3 1 3 ) ( 5 3 7 0 6 2 ) ( 6 0 1 5 6 1 ) ( 5 1 0 8 1 2 ) ( 2 6 1 1 6 1 ) ( B t u / D A Y ) 5 2 0 1 7 2 ( 4 9 3 0 5 4 ) 5 8 5 0 9 1 ( 5 5 4 5 8 9 ) 4 6 3 1 8 8 ( 4 3 9 0 4 1 ) 3 1 2 3 0 1 ( 2 9 6 0 2 0 ) 4 4 . 7 4 3 . 1 4 8 . 5 5 4 . 2 3 5 . 0 3 6 , 9 4 1 . . 6 _ 4 2 . 0 4 0 . 6 % S O L 4 4 . 4 6 0 . 2 5 5 . 5 4 0 . 7 3 8 . 4 4 3 . 7 5 5 . 1 5 2 . 2 5 2 . 1 3 9 . 4 4 9 . 2 5 0 . 8 5 1 . 9 5 1 . 2 5 1 . 6 5 0 . 8 5 1 . 6 4 7 . 3 5 0 . 8 n 5 1 . 4 5 0 . 8 5 0 . 5 4 7 . 4 T a b l e 6 C o m p a r i s o n o f S t o c h a s t i c t o R e a l W e a t h e r S y s t e m S i m u l a t i o n P r e d i c t i o n s f o r D e c e m b e r , J a n u a r y , F e b r u a r y t M a r c h , W a s h i n g t o n , D . C . ( H e a t i n g C a s e ) . The Society shall not be responsible for statements or opinions advanced in papers or in discussion at meetings of the Society or of its Divisions or Sections, or printed in its publlcations. Discussion is printed only if the paper is published in an ASME journal or Proceedings. Released for general publication upon presentation. Full credit should be given to ASME, the Technical Division, and the author(s). $3.00 PER COPY $1.50 TO ASME MEMBERS Stochastic Predictions of Solar Cooling System Performance;:: D.K.ANAND Professor, Mem. ASME I.N.DEIF Research Assistant R. W.ALLEN Professor, Mem ASME Solar Energy Projects, Department of Mechanical Engineering, University of Maryland, College Park, Md. The use of computerized system simulations for sizing and performance predictions of various solar systems requires some form of weather input to act as system stimulus When actual weather data is used, simulations run on an hourly basis are expensive and require considerable data handling. For many design procedures, however, hourly informaJion is not needed, and simpler methods are desirable. One such method employs a probabilistic approach This method involves the use of an algorithm that generates a probabilistic matrix, and an analytical formulation which is used to generate synthetic weather data. The approach has been found to be satisfactory This work uses the stochastic (probabilistic) method to produce representative weather for five geographic regions in the U .S for the summer months Parallel runs are conducted with real and stochastic weather A comparison of the results clearly shows that the probabilistic approach can satisfactorily substitute for real weather for the purpose of system simulation, at reduced cost and data handling Contributed by the Solar Ener·gy Division of The American Society of Mechanical Engineers for presentation at the Winter Annual Meeting, San Francisco, Calif., December 10-15, 1978. Manuscript received at ASME Headquarters August 22, 1978. Copies will be available until September 1, 1979. THEAIIERICAN$0CIETY OF·Nl~CHANitAL·ENGINEERS, UNITED ENGINEERING CENTER, 345 EAST 47th STREET, NEW YORK, N.Y. 10017 Page 355 Stochastic Predictions of Solar Cooling System Performance D. K.ANAND I.N.DEIF R. W.ALLEN ABSTRACT and temperature readings is sorted out, and the proba- bility of obtaining any combination of the two or more The use of computerized system simulations for parameters (within certain ranges) is computed. Then, sizing and performance predictions of various solar the same data base is run through a least squares fit- systems requires some form of weather input to act as ting program, to obtain constants in assumed temperature system stimulus, When actual weather data is used, and insolation profiles as functions of time. The com- simulations run on an hourly basis are expensive and binations of temperalure and insolation probability require considerable data handling. For many design tables are combined with the constants obtained from procedures, however, hourly information is not needed, the least squares fitting to construct temperature and and simpler methods are desirable. insolation profiles on a daily basis. The general One such method employs a probabilistic approach. shapes of the profiles are similar, but their magnitudes This method involves the use of an algorithm that differ according to the averages used to obtain them. generates a probabilistic matrix, and an analytical Since each set of temperature insolation pairs has an formulation which is used to generate synthetic associated probability, it is assumed that the weather weather data. The approach has been found to be sat- profiles occur with those same probabilities. The isfactory, weather statistics are thus represented using a joint This work uses the stochastic (probabilistic) probability density matrix and four constants (two for method to produce representative weather for five insolation and two for dry-bulb temperature in this geographic regions in the U.S. for the summer months, study). Parallel runs are conducted with real and stochastic In order to examine the generality of the technique weather. A comparison of the results clearly shows geographically, it was applied to five different loca- that the probabilistic approach can satisfactorily tions in the United States, and these were: 1) Wash- substitute for real weather for the purpose of system ington D,C,, 2) Charleston, South Carolina, 3) Madison, simulation, at reduced cost and data handling. Wisconsin, 4) Fresno, California, 5) Forth Worth, Texas, and these cities were chosen for climate and geograph.:. INTRODUCTION ical diversity. The present study expands on previous efforts. The use of computers for the analysis of solar The simulation program previously used modelled a very systems consists of the construction of one or more simple system consisting of flat plate collectors cou- simulation programs that model the various components pled to an absorption machine which was allowed to pro- of these systems, and predict their performance. vide as much cooling as it could, using the hot water These programs are dependent on some form of weather from the collectors. The new system simulation, on the input to drive the simulations; generally real weather other hand, models a more realistic system. This system data obtained on magnetic computer tape from various includes collectors, hot side storage, auxiliary heat sources, such as the National Weather Bureau, or NOAA. supply, pumps and valves, and features automatic con- As an alternative to the use of real weather data, trols, weather dependent loads and a control strategy. statistical methods have been developed that can arti- The results obtained using stochastic (probal5i- fically produce weather parameters to drive system listic) and real weather were compared. The comparative simulations. A probabilistic method was recently deve- study included total insolation, daily total collected loped that takes a large base of weather data, and energy, daily total Cooling load, fraction of the load while essentially retaining the weather's history, satisfied by solar means without auxiliary energy compacts the information to a form much more convenient (percent solar), and average cycle COP. The results for use in computer simulation. The above method showed that the stochastic approach compared favorably essentially provides a reconstruction of the data on with the real weather method, and that it can be used which it is based, in the form of a single day's to drive system simulations at much reduced cost and weather information, so a one day simulation driven data handling. by this reconstructed weather can give results similar to those obtained via the use of the original data. SYSTEM MODELL TNG The procedure used in this consists of two parts. First, the data base consisting of hourly insolation A typical solar powered cooling system is illus- trated in Figure 1. The simulation of such a system requires the modelling of various sub-systems as well * This work is supported by th.e Department of Energy, as input data dependent on weather. Specifically, for Division of Conservation and Solar Application, the system to be simulated in this study, the fol- Contract# EY 76-S-05-4976 A003. lowing sub-systems need to be modelled: 1) Collectors, 1 Page 356 2) Absorption Cooling (Chiller), 3) Hot Storage Tank, WEATHER ALGORITHM 4) Control Strategy, 5) Load, 6) Weather. The details of the models for the above sub-systems are presented The weather sub-system model is constructed via in reference 3. a two part process. The first part is a purely statis- The control strategy for the simulation system is tical procedure in which a data base of weather is the result of logical decisions, made at various sorted out, and averages and standard deviations are parts of the system, that can be lumped together under calculated. The second part involves the development the heading of "control component" and is based on of an analytical model by employing a least squares the premise that solar energy should be used as soon error technique on the data base of weather .. The pro- as it is collected. cedure yields a set of curve fit constants that shape The demand pump is turned on automatically by a the model, and conform it to the original data supplied. differential thermostat when the collector exit tem- The model thus becomes representative of the real perature (static) is greater than the temperature of weather data used to construct it. the hot storage tank by 6ToN of 8.3 C (15 F). As The first of the two part procedure - the the storage tank experiences a rise in temperature, statistical manipulation of the data - is concerned the temperature differential decreases, until at last with sorting out the pairs of insolation - ambient it drops below ~TO F of 1.7 C (3 F) at which time the temperatures that occur in the weather data, and placing demand pump is swilched off automatically. It is them within prescribed ranges. Thus, for a particular desirable to avoid on-off cycling of the demand pump, value of insolation and a particular value of dry-bulb and to have one start-up in the morning and one shut- temperature, the appropriate range in which the insola- down in the evening. Constant mass flow rates, on- tion value falls is found, and the appropriate range in off pump controls and open-close valve controls are which the dry-bulb temperature value falls is also used in order to reduce the complexity of the control found. The combination of the two ranges has thus strategy, and avoid some of the difficulties that can occurred for the particular set of data viewed, and the be encountered in the operation of the system. number of all such occurrences is retained. This num- When the room temperature rises above TE.OOM ber is an indicator of the probability of the above OF 23.8 C (75 F), the demand pump is automaticaTly combination, and is very important in weighting the turned on, and the control strategy goes as follows: model to be later constructed. After all the data has If the storage tank temperature is less than 76.6 C been screened, and all range combinations have occurred, (170 F) when the demand pump is turned on, the aux- average values for these ranges are calculated, and iliary by-pass valves close and the energy required these, along with the aforementioned probabilities at the generator of the absorption cooler is supplied are essential to the successful modelling of the weath- entirely from the auxiliary heater, If the temper- er data. It is important to note that the above ranges ature of the supply water is between 76.6 C (170 F) into which the weather data is placed, are flexible, and 87.7 C (190 F) auxiliary heat is added to boost and their widths are determined by how fine or how the capacity up to where it can meet the load require- coarse a model is desired. The statistical procedure ment. When the demand pump is on and the collector just mentioned is carried out by a computer program exit temperature is above 87. 7 C (190 F) or 11.l C which is described in reference 3. A typical prob- (20 F) or more above the storage tank temperature, ability entry is shown in Figure 2. the by-pass valves will automatically open, allowing The second of the two programs is the least squares hot water from the collectors to go directly to the fitting program, which proceeds to curve fit the hourly generator of the absorption chiller. data with the following equations: Since the cooling supply must satisfy the load, and since the supply capacity of the chiller is a function of the water temperature going to the gener- For insolation: I(t) (o: + o: cos8) exp -c 4 a tor, it is sometimes necessary to raise the temper- 3 cos0 IAVE a tu re of the generator supply water through the use of an auxiliary heater in order for the chiller to Td ( t) For temperature: deliver the required capacity. If the temperature TAVE of the water supply to the generator is above 76.6 C (170 F), but not high enough to deliver the required cooling, just enough auxiliary heat is added to where I is insolation, 0 is sun angle, c is the ex·- "boost" the temperature up to a level where the chil··· tinction c0efficient, Td is dry-bulb temperature, ler can provide the cooling required and meet the w is daily frequency, and tis time. The least load. If, on the other hand, the supply temperature squares prodecure yields o: , o: , o: , and a 4 . to the generator is below 76 .. 6 C (170 F), the tank 1 2 3Having thus obtained the curve fit constants, the by·-pass valves are opened automatic ally, and the en- model is constructed by substituting the a's into the tire generator load is carried by the auxiliary heater. previous equation and inserting the appropriate values In either case, the chiller will not be able to meet of TAVE and IAVE' The TAVE and IAVE values actually a demand higher than its maximum capacity. occur in pairs, since they are the averages calculated The hourly sensible cooling load based upon the for the combination of ranges according to the pro- outside ambient temperature and the insolation of any cedure mentioned above. given hour is calculated. The load calculation is Each pair has an associated probability of occurrence- in the form as previously mentioned, and it is this probability which "weights" the results of the simulation con- A(TA-TROOM) + B(Insolation) + C ducted using the pair. Therefore, if there are nine pairs of TAVE and IAVE' each pair is used in these where A is a factor based on the size of the area equations, and the simulation is run accordingly. The whose load is being calculated, on the insulation results are then multiplied by the probability of the and on the various amounts of infiltration, while B pair of averages, and combining the nine sets of results is dependent on the surface area facing the sun, and obtained via the nine pairs finally yields the overall C is a constant load. TROOM is the desired temper- simulation results. As examples, the .JPDM and a's ature, and IA is the ambient dry-bulb temperature. for Fort Worth, Texas, and Charleston, South Carolina, 2 Page 357 are shown in Figures 3 and 4. 3) Average Cycle COP: The average cycle COP is an indicator of the performance of the absorp- SYSTEM SIMULATION tion machine, which is wholly dependent on the supply temperature to the generator. A few The system described previously and the weather degrees Fahrenheit difference in that supply algorithm were programmed on a UNIVAC 1108. The de- temperature can cause the COP to change tails of this program are given in reference 3. noticeably, and thus the average COP gives a The runs are performed by constructing the closer, more detailed indication of system weather profiles for each significant probability, temperature, and can thus show the response running the simulation program, and then weighting of the system itself to the weather input the results according to the probability associated provided. Since the system is only quasi- with the particular weather profile used. In the linear, it is obvious that a percentage error end, there would be as many sets of weighted results in the daily total insolation does not pro- as there were significant probabilities, and by sim- duce the same percentage error in the average ply adding the results together, a final picture, cycle COP, and as was found from the results, with a probability of 1.0 emergeL actually produces a larger percentage error. When the simulation runs were performed, it was 4) System COP: The system COP, as the name im- found that using each stochastic probability case plies, is an indicator of the performance of for a one day run was inadequate because of the non- the overall system, and along with the average linearity inherent in the sys tern, It was found that cycle COP, gives an idea of how the system while in the real weather simulation the overall reacts to the weather input, change in the energy of the hot storage tank was very small, the change in the stochastic runs was quite It was felt that the above parameters could give large. The solution used for this problem was to a good indication of system performance, and could run each stochastic probability case for a number of serve as an effective basis for comparison and eval- consecutive days, thus allowing the hot storage tank uation of the stochastic approach to weather representa- to stabilize, and then considering the final day as tion. the representative one. The number of days used for the stochastic simulation was chosen to be four. SIMULATION RESULTS Generally speaking, the results obtained via the System Output stochastic method of weather generation compared quite In order to obtain a good picture of how well the well with the results obtained by using real weather. stochastic weather technique modelled the real weather, It would be advantageous, however, to look at the it was necessary to look at the following: weather-related results separately from those results that are dependent on the weather-system interaction. 1) Daily total insolation: The total insolation is an important indicator and is the first thing that must be checked for agreement. Weather Dependent Parameters 2) Daily Total load: This factor is strongly Under this heading we find the following: dependent on ambient dry-bulb temperature, l) Daily Insolation. and to a much lesser extent, on insolation, 2) Daily Total Cooling Load, Good agreement between real weather and sto- 3) Daily Total Collected Energy (Useful). chastic weather loads is a good indicator that the temperature parameter simulation is The daily collected energy is to some extent good. dependent on the system behavior, but since it is a much stronger function of insolation and ambient The above results, as indicative as they may be temperature, it will be considered as weather-related of how well the weather parameters are simulated, only. were not enough to tell how successful the stochastic weather was in driving a program simulation of a sys- tem with nonlinearities inherently present due to the Daily Insolation use of a hot storage tank and a floating (temperature The daily insolation calculated by both methods dependent) COP absorption machine, To gauge the compares very well as seen in Figures 5-9 .. The sto- success of the stochastic technique, there were other chastic insolation results are generally less than 5% results to be evaluated, viz. off from the real insolation obtained from the weather data tapes. The largest error is 13%, and occurs in 1) Collector Efficiency: This is the useful the month of October. In fact, the resu1ts are worst heat collected by the flat plate collectors for October because the weather data is most incomplete over the course of the day divided by the in- for that month, and the simulation tends to be bad due solation incident. While it is strongly de- to the bad data base used .. October is a fringe month pendent on insolation and ambient dry-bulb with relatively much less importance than the other temperature, it is, to a lesser extent, de- five months involved, since the cooling loads during pendent on collector fluid inlet temperature, the month tend to be small, and the use of cooling and thus on the behavior of the system, machines during the month is limited, 2) Per cent Solar: This is the ratio of energy supplied by the collectors or by hot storage without any auxiliary energy being used, to Daily Load the total energy supplied to meet the load. The daily cooling load is a very strong function This is also dependent on insolation, but of ambient dry-bulb temperature, and is thus a good due to the automatic controls in the system, indicator of how well the stochastic temperature pro- is quite sensitive to system temperatures file follows the real data. The load curves in Figure and valve controls. 5-9 show that they match very well, the largest error 3 Page 358 being 13%, but with normal error in the neighborhood largest error occurs for Madison which has the lowest of 5%. It is noted that the stochastic loads are loads of all the five cities. less than the real loads in all cases. This is due to the fact that the real data seems to have greater Per Cent Solar. The percentage of the total energy extremes (higher maximum temperature, lower minimum supplied to the generator that comes from either the temperature) than the stochastic data. Thus, at the collectors or from the hot storage tank - without part of the day when the maximum loads are found, boosting, is what is called the "Per Cent Solar". It the real weather produces higher loads, while at the indicates that fraction of time when the load can be minima, no loads are produced. Therefore, it is to met strictly by solar means. Due to the automatic be expected that the real weather loads will always control feature of the system, boosting occurs unless be slightly higher than the stochastic loads, since the supply temperature to the generator is equal to the simulation is "weighted" on the side of the real or higher than the temperature required to meet the data; as far as load calculation is concerned. In demand. When there is boosting of the supply temper- fact, the regions with the largest fluctuations in ature to the generator, the amount of energy supplied hourly temperature; Fresno, California and Madison, by solar means is not considered in the per cent solar Wisconsin show the largest discrepancies, while the calculation, Therefore, it is important that internal other three regions with less fluctuation show a system temperatures be similar if the per cent solar closer correlation between the real and the stochas- is expected to be similar, Higher values of this param- tic loads, eter would be expected for lower loads and/or higher values of insolation, Viewing the per cent solar curves in the aforementioned figures, the trends are Daily Total Useful Heat seen very clearly. The graphs for the city of Fresno The amount of energy collected over the course show that the percentage for stochastic is larger than of the day is strongly dependent on insolation, but for real weather, and referring back to the load curve is also a function of dry-bulb temperature, and the for Fresno (Figure 7), it is found that the stochastic water inlet temperature to the collector. The re- load is less than the real load for all months, How- sults for both real and stochastic runs match well, ever, the curves show that the percentage supplied by except for when low loads occur, as shown in Figures solar means is, in most cases, quite similar for the 5-9. Indeed, since the month of October always pre- real and the stochastic weather simulations. This in- sents low loads, the largest discrepancies of useful dicates that insofar as meeting the load either di-" heat occur for that month. For example, the average rectly from the collectors, or from hot storage, the summer season error in useful heat for the city of stochastic and real weather system simulations agree Fresno is found to be 9.3%. However, if the error well, Even better agreement could be achieved if the for October (which has a low cooling load) is not definition of per cent solar was modified to include included, the average error for the other five months all cooling supplied by solar means, even if that sup- is only 5.8%. For Washington, D.C., the error in- ply were boosted. cluding October is 10.4%, but excluding October is At this point, it can be seen that the stochastic only 3.0%. The same occurs for all cities studied; approach is useful not only for simulating insolation except for Madison, Wisconsin, which has low loads and predicting load and useful energy, but can also for all six months of the cooling season. Overall give an accurate picture of collector performance, average error for the five cities studied when Octo- and a rougher, but reliable estimate of the per cent ber is included is 13.2%, but if that month is ex- solar or the percentage of the load satisfied ex- cluded, the error is only 7.6%. clusively by solar means. Parameters Dependent on Weather-System Interaction Average Cycle COP. The coefficient of performance of The coupling of the weather "driver" to a system an absorption cycle is mainly dependent on the supply that includes a variable COP absorption machine and temperature to the generator. It is thus a measure a hot storage tank, meant that a study of the sto- of the internal temperature of the system, and shows, chastic weather generation technique would be incom- on average, how the system responds to the weather in- plete if it only covered the weather-related param- put. When the supply temperatures differ in the real eters but did not extend to the area of system per- and stochastic cases, so do the cycle COP's. Indeed, formance as affected by the weather "driver", Thus, the effect of varying the supply temperature is im- the following system outputs are studied: portant because of the nature of the relation between it and the COP of the absorption machine. That re- 1) Collector Efficiency lation is not linear, Another source of nonlinearity 2) Per Cent Solar in the system is the hot side storage tank. Even 3) Average Cycle COP though the tank is modelled by linear equations, when 4) System COP it is combined with the absorption chiller it exhibits nonlinear behavior. If the system were linear, it Collector Efficiency. The efficiency of the col- would be expected that the error in the average cycle lectors is affected by the inlet temperature and the COP closely paralled the errors in the insolation ambient dry-bulb temperature. Thus, through the in- and dry-bulb temperature profiles. However, due to teraction of the two, the collector efficiency is the nonlinearities present in the system because of determined. Where inlet temperatures and dry-bulb the introduction of the hot storage tank and the vari- temperatures are similar, collector efficiency will able-COP absorption chiller, the average cycle COP's also be similar as shown in Figures 10 to 14. The for the real weather and the stochastic weather cases match is not as good for months where there are low do not always match well. The largest errors occur loads. These affect inlet temperatures to the col- in the fringe months, notably October, when the loads lectors, causing error in collector efficiency cal- are low, and the insolations are also low. Since the culations. Excluding the month of October, the average COP is a function of the system temperature, average error in the efficiency, for the five remain- it can be seen that the system's nonlinerities have ing months and for all five cities is 6%, while in- quite an effect on the system, strongly influencing cluding October it is 11%. On a city basis, the temperature. 4 Page 359 System COP. As was just noted, the cycle COP shows REFERENCES signs that nonlinearities affect the weather-system interaction. Since the nonlinearities are in the hot 1 Anand, D.K., Allen, R.W., and Bazques, E.O., storage tank and the absorption machine, it is under- "Solar Air-Conditioning Performance Using Stochastic standable that measuring their performance - as with Weather Models", Journal of Energy, Vol. 1, No. 5, the average cycle COP - will produce the largest Sept - Oct, 1977, pp. 319-323. errors. As the area of concern grows to encompass 2 Anand, D.K., Allen, R.W., Bazques, E.O., more than the above two components, and as more "Solar Powered Air-Conditioning System Performance linear components are added, however, the behavior Predictions Using Stochastic Weather Models", tends more towards linearity, and the error decreases. Feb 1977, Solar Energy Projects, Department of Thus, when viewing the overall system, a measurement Mechanical Engineering, University of Maryland, of its coefficient of performance should show a College Park, Maryland. closer match between real and stochastic values as 3 Deif, I. N., "Solar Powered Cooling Performance shown in Figures 15 to 19. The average error in the Using a Stochastic Method", Aug 1978, Master of system COP values for all cities studied is only Science Thesis, Department of Mechanical Engineering, 12%, but if the month of October is again excluded University of Maryland, College Park, Maryland. for having low loads and thus making the results inaccurate, the error becomes only 8%. Thus, system performance can be reliably predicted, while per- formance of an absorption cycle or a hot storage tank cannot be very accurately predicted or repro- duced via the stochastic technique of weather gener- ation. This indicates that the technique has the limitation that it cannot accurately reproduce the internal temperatures of a system when there are sources of nonlinearity in that system. CONCLUSIONS The use of a probabilistic approach for gener- ating artifical weather profiles is seen to be a viable alternative in the running of computerized systems simulations. Caution must be exercised, however, in order to make certain that the results obtained are truly representative of system perfor- mance under real weather stimuli. To accurately gauge the probabilistic weather method in its capac- ity as driver or stimulus for a system simulation, it is not enough to study the insolation and temper- ature profiles. It is important to look at other indicators of system performance. From the present study, the following was found: 1) The probabilistic or "stochastic" approach for generating weather profiles that are representative of a given weather history proved to be quite successful. 2) The artificially generated weather, when used to drive a system simulation, showed similar results to those obtained from the same system simulation when driven by real weather data. 3) For all the geographical locations studied, the method generated insolation and temper- ature profiles that accurately reproduced loads and callee tor performance. 4) System performance, as a whole, can be pre- dicted by the use of the stochastic weather method. 5) The results are not dependable for low loads, and when such low loads are calculated, almost all the associated results are suspect. 6) Overall, this method produces good results, and can prove a useful tool for system sizing and/or simulation, at much reduced cost and data handling. 5 Page 360 CONDI Tl ONED SPACE AC = Air Conditioning Unit HW = Hot Water Storage AH = Auxiliary Heater F's ,.. Control Functions H.W. FV5 Figure 1 - System Schematic T + Zci .yd • lo + I I 'I'd • 2o I I I yd • • <--- --- P(T01 ,lj ---- -+ I 'rd • 2o I I I .rd • 2. I 'f Figure 2 - Typical entry in a 5 x 5 Joint Probability Density Matrix 6 Page 361 CITY: Charleston, f"aaH: Hay DAY: 141 K: 196 S C (!TY: Fort Worth, rtx,.rn,; June DAY: 172 K: . 20s T exas I AVE Trf,VE f'RoBP.B!LlTY I AVE Trf,VE f'ROBABILITY 104 3 66 3 01342 150 6 79 2 05333 144 3 66 3 08724 180, l 79. 2 11334 173 5 66 3 09396 208 1 79.2 04000 104 3 72 5 09396 150 6 85 1 04000 144 3 72 5 1409l 180.1 85 1 23333 173. 5 72 5 13423 208 l 85 1 . 07333 104 3 77 6 . 10738 150 6 90, 4 00667 144 3 77. 6 .10738 180, 1 90, 4 12667 173. 5 77 6 . 16778 208 1 90. 4 21333 21 4 66 3 02013 114 7 79 2 05334 59 8 72 5 10067 75 8 79 2 04667 a, 0465927 al 11656297 a, 36269224 a, . 09763727 a, 2.148367 02 99624184 a, 1. 69142452 a, . 96970605 FIGURE 3 - J P. D .. M, CASES AND ASSOCIAIED PROBABILIIIES FIGURE 4 - J P.D M. CASES MID ASSOCIAIED PROBABilIIIES LEASI SQUARES FII CONSIANIS LEASI SQUARES FII CONSIANIS 0 0 1118 66 (Btu- DAY.1) (Btu-ff' DAY-1) 2000 350,000 1800 1600 300,000 1400 250,000 rl I >- - "p " ::, f- 200,000 0:, rl 7 >- p" "' 150,000 ---, "" LI, LI, 0 rl 50,000 stochastic insolation real insolation stochastic useful heat real useful heat stochastic load real load 0 M J J A s 0 Figure 8 - Comparison of real and stochastic outputs for Madison, Wisconsin [:) 0 • • .,, ( Btu-DAY-1) (Blu·ft:l!DAY- 1 2200 ' 400,000 2000 1800 350,000 1400 \ 300,000 ~ 7 >- ' \ -<"( LI, Q LI, 0 .--i 150,000 100,000 A stochastic insolation b 6 real insolation 8 stochastic useful heat D real useful heat e stochastic load O real load 0 M J J A s 0 Figure 9 - Comparison of red and stochastic output for Fort Worth, Iexas 9 Page 364 100 100 r-._ -- ,,,,.,,. ,, / / / / / / / 80 / / 80 -----,,,,, i %/S/ /// ,,,, ,, / / /. ..,: ' .__ __ _..., 60 60 ' -- 40 40 20 20 0 0 M J J A s 0 M J J A s 0 Figure 10 - Comparison of real and stochastic per cent solar and collector efficiency for Washington, D.C. Figure 11 - Comparison of real and stochastic per cent solar and collector efficiency for Charleston, S.c. %$ 100 --------------~-----------·-==--=--- 100 80 80 60 60 40 40 20 20 0 L--......----..---.----,-----, 0 L-----..----.----,-----, M J J A S 0 M J J A Figure 12 - Comparison of real and stochastic per cent solar and collector efficiency for Fresno, California. Figure 13 - Comparison of real and stochastic per cent solar and collector efficiency for Madison, Wisconsin. 10 Page 365 4 .. 100 80 ...--------:c:,-- ...... -6 ---- l ~,,~ .2 COP Av ',, ..... , 60 ' ' ' ' ' ' ' ' ' 40 ' ' ' .5 .. I 20 o----~--~---.,....---.----- s .4 +----,------,----,------,-----r 0 M J J A 0 M J J A s 0 Figure 14 - Comparison of real and stochastic per cent solar and Figure 15 - Comparison of real and stochastic cycle COP and collector efficiency for Fort Worth, Texas. system COP for Washington, D.C. ,/2/ COP Av _ _.._ ____ & II C:l -- _,.,-.,,,,, ~-----....---- .5 .. 2 .5 .2 ~COPs ~- .4 .I .4 .. I .3 +---,----,----,----r-------t-0 .3 M J J A s 0 M J J A s 0 Figure 16 - Comparison of real and stochastic cycle COP and system COP for Charleston, S. C. Figure 17 - Comparison of real and stochastic cycle COP and system COP for Fresno, California. 11 Page 366 Q& __ - COP Av,,. .,,..,,.,, ,,.>----- •C:J /A.6 ----..,. .... ____ • C:l ____ ...._,_ / ............ .................. _____ _..,,,,, ' .11-(COPs .. 5 ' ,,2 .5 .2 "' \ \ .I .4 .I 4 0 .. 3 -t----,-----,------.-----.----+- 0 . :3 s M J J A s 0 M J J A 0 Figure 19 - Comparison of real and stochastic cycle COP and Figure 18 - Comparison of real and stochastic cycle COP and system COP for Fort Worth, Texas. system COP for Madison, Wisconsin j,2 Page 367 0. K. Anand Professor, Stochastic Predictions of Solar Mem.ASME I. N. Oeif Cooling Systen1 Perfor1nance 1 Research Ass1sta11t. The use of computerized .system simulations for sizing and performance predictions of various solar systems rt'quires so,ne form of weather input to act as a system E. 0. Bazques stimulus. 11,.hcn actual wear her data are 11sed, simulations run on an hourly basis are Hesearcl1 As'.;is1,1,·,t. expensive and require considerah!e dala handling. For many design procedures, Mein. ASME '-' howcva, huuriy inji)rrnation i., no/ nct'ded, and simpler methods arc desirable. One such method i'f/l{Jloys a prohuhi!istic approach. This mf(hod involves the use of an R. W. A!len algorilhm that genemtcs a pmha/,ili.l'lic matrix, and r.m analytical formulation which is used to genera re .',rn1hetic weather data. The approach has been found to Prolessor. be satisfactory. This work uses the .11oclwslic (probabilistic) m,:thod to produce Mern t,SM[ representath•f' weather fnr ,J,;'"1.'(' geogra11!iic regions in the U.S. for the summer months. Parallel runs are comiucted with real and stochastic wea1her. A com- Solar Enerny Pro1ects. parison oft he r<'sul1s c/rnrly .1/11> w.1 rh ar I he probabilistic approach can satisfacwrily Departc1ent ul Mechanical l::ng1ne~r111g substi/Ule j,Jr real weather for 1hc purpose (({system si111u/ation, at reduced cost and Un 1vers1ty ol Maryland rfala handling. co:1ege Park. MD 20,.i; lnirnduciion The use of computers for the analysi, of solar sy,tem, temperature and insolation probability tables are combined consists of the constrnction of one or more simulation with the rnnstant~ obtained from the least squares fitting to programs that model the various cc,mponents of these systems nrn,t rue! tempt:rat ure and insolation profiles on a daily basis. and predict their performance. Thc,e programs are dependent The general shapes of the profiles are similar, but their lll1 ,ome form of weather i11put to drive the simulations, mag11itud,:s differ according to the average:; used to obtain generally real weather data obtained on magnetic computer them. Since each set of temperatme insolation pairs has an tape from various sources, such as the National Weather a,sociatt:d probability, it is assumed t.hat the weather profiles Bureau, or NOAA. occur with those ,ame probabilities. The weather statistics are !\, an alternative to the use of real v:eather data, statistical thus represented using a joint probability density matrix llll'tlwd, h,nc bern lkvelopcd that can artificially produce (J PD1'v1) and four constants (two for insolation and two for \\ cat her parameters to drive sy:;1ern simulations. A prob- dry-bulb temperature in this study), abilistic method was recently developed that take5 a large base In order to examine the generality of the technique of weather data, and while essentiall:,, retaining the weather's geographically, it was applied to five different locations in the his1ory, compacts the information to a form much more United States, namely: (I) Vl/ashington D. C., (2) Charleston, ninvenient for u,e in computer simula1ion. The above method S. C., (]) Madison, Wisc., (4) Fresno, Calif., and (5) Forth e,senl ially provides a reconstnH.:tio11 of the data on which it is Worth, Tex. These cities were chosen for climate and ba,cd, in the form of a single day's weather information, so a geographical diversity. one dav simulation driven by this reconstructtd weather can The present study expands on previous efforts. Th~ give re;ults similar to those obtained via the use of the original simulation program previously used modelled a very simple data. The procedure used in this consists of two parts. First, system rnnsisting of flat plate co!Iectors coupled to an ab- the data base consistmg of hourly insolation and temperature sorption machine which was allowed to provide as much 1 eadings is ~orted out. and the probability of obtaining any cooling a., it could, using the hot water supplied from the combi~arion of the two paramders (within ,ertain ranges) is collector,,. f he new simulation models a more realistic system (ornputcd. Then, the ,arnc data base is run through a least which ,n,:ludcs colkctors, hot side storage, auxiliary heat squares fitting program to obtain constants in assumed supply, pumps and valves, and features automatic controls 1cmpcrntur•: and insolation profiles as functions of time. The and wea(licr dependent loads. The rc:,ult, ohtained using stochastic (probabilistic) weather and real ,vc;nhcr were compared. The comparative study 1 I hi-. i~ .. upp,irt,·d the Department l:ncrgy, Con- indodcd iota! insolation, daily total collected energy, daily \\OJ~ by t.if D!v1\ion l)!° s,i.:rvaoon und ~i)laI Aprli,::ition..,, l nnn;h·t Nn. EY ?fi-S-05-497() AOd·i H.JN1.;_ re.:eivt'J ai AS~H: t-kndqoanns Ck· JI, !979 comp:m:d iavor:ibly with the real weather method, and that it 11;ht·1 Page 368 down in !he evening. In practice, however, more cycling than 1his u,ually ocrnrs. Con,1ant mass now rates, on-off pump control, a11d open-close valve controls are used in order to reduce !he complexity of the control strategy, and lo avoid some nf the difficuhie:; that ;can be encountered in the ,iperation of tlw sy.,tcnL \\!hen the room temperature rises above TROOM, set at 23.8"C (75°F), the demand pump is automatically turned on, and !he control '1ratcgy goes as follows: If the storage tank temperature is icss than 76.6'C (170°F) when the demand pumr i~ turned on, the auxiliary by-pass valves close and the energy 1equirui at the generator of the absorption cooler is supplied entlldy from the auxiliary heater. If the tempcrarnre of the ~upply waler is between 76.6°C (170°F) and 87.7°C (190° F} mniliary hear is added to boost the capacity up to Fig. 1 Systematic schamatic where it can meet the load requirement. When the demand can be used to drive system simulations at much reduced cost pump is on and the collector exit temperature is above 87.7°C and data handling. (I 90° F) or ! l. I ° C (2.0° F) or more above the storage tank tempcralure, the by-pass valves will automatically open, S) stem Modelling allowing hnt waler from the collectors to go directly to the gencrat~r of the absorption chiller. A typical solar powered cooling system is illustrated in fig. Since the cooling supply must satisfy the load, and since the l. The simulation of such a system requires the modelling of supply capacity of the chiller is a function of the water various rnb-svstems as well as input data dependent on temperature going to the generator, it is sometimes necessary weather. Specifically, for the syst<.:m to be simulated in this lo raise the temperature of the gcnertor supply water through ~tudy, the following sub-systems need to be modelled: (I) the use ,,fan auxiliary heater in order for the chiller to deliver ,'(ilkcwrs, (2) absorption cooling (chiller), (3) hot storage the requi-red Capacity. If the temperature of the water supply tank, (4) control strategy, (5) load, (6) weather. The details of to the gen-eiator is above 76.6 °C (I 70°F), but not high enough t ht· models for the above sub-systems are presented in [3]. to deliver tfie required cooling, just enough auxiliary heat is Tlh· control strategy for the simulated system is the result of added lo "lwost" the temperature up to a level where the lngical decisions, made a! variou;: parts of the system, that can chiller Gm provide the cooling required and meet the load. Jf, be lumped together under the heading of "control com- on the other hand, the supply temperature to the generator is p<.rnent" and is based on the premi:;c that solar energy should beiow 76.6 °C (l 70°F), the tank by-pass valves are opened he H,ed as soon as it is colleC!ed. au1omaticatly, and the enlirc generator load is carried by the The demand pump i, turned on auromaticaUy by a dif- auxiliary heater. In either case, the chiller will not be able to frrcrn 1al 1he1 mostat when the culkctor exit temperature meet a dcmand higher than its maximum capacity. t~t:1tic) i~ greater than the temperature of the hot storage tank The hourly \cnsihle cooling load based upon the outsid,, b) ::.T0 " of 8.3°C (l:5°F). As th,, sl\lrage tank l"Xperiens:cs a ambiem 1emprra1urc and the imola1i0n of any given hour is ri,e in temperature, the temperature C:ifferrntial decreases, CI 111 value of dry-bulb temperature, the appropriate range in which ,ii(lf,t,7 the insolation value falls is found, and the appropriate range .!.'It-" 1,1 whi,h the dry-bulb temperature value falls is also found. .'Jl!J 1 he combination of the two ranges has thus occurred for the parti,·ular set of data viewed, and the number or :.ll such c)c,·u1rencc., is retained. Tl1io number is an imli(ator of the , ,11.i,t,' probabiiliy of the abuve combination, and is important in 11<:ighting the model to be later constructed.After all the data have been screened, and all range cnmbinations have oc- curred, average values for these ranges are calculated. These ranges along with the aforementioned probabilities are _,,,,·,,1· c,scn! ial to tht' successful modelling of the weather data. lt is important to note that the above ranges into which the <),,,.·,),, l'Cathi:r data are placed, are flexible, and their widths arc determined by how fine or how coarse a model is desired. The ·-~-------~--------·----·-... ,1atistical procedure just mentioned i, carried out by a Fig. 4 Joint probabi!lty density matrix lnsolallon and temperoturn p11irs and assoclntod probabllltlos; loa11t oquare Ill constants for June computer progr,1m which is described in [3]. A typical in Fort Worth, Tex. probability entry is shown in Fig. 2. weather tapes, w is a constant, 0 is calculated for the given The second of the lWo programs is the least squares fitting location and time, and c is input as a constant for the 21st day program, which proceeds to curve fit th,'. hourly data with the of the approp1iate month is given by ASHRAE. The least following equations: squares prou:dure yields ci 1, a 2 , a 3 , and a 4 • The synthetic / (I) -c weather profiles given above were chosen after study of many For ir,solation: (o:_i +,t.1 cosO(I) )exp -- '·\Vl- cos//(!) real weather profiles plotted from weather tapes from several regions. Temperature followed a sinusoidal pattern with a 1;,1n phase shift such thol the lowest temperatures would occur at For temperature: approximcittly 3 a.m .. The basid insolation profile was T,,\VI'. suggested in tile /JSHRAE Handbook of Fundamentals ( 1972). Pints ol rl'al weather compared favorably with the \\ ht:1<'. / is imulation, II is the ,un angle, c is the t'X(innion ,ynth,'tic wcath,:r generated by the above profiles and coefficient, T,1 is dry-hulh temperature, c.J is daily frequency, cakulaied con.,ta11ts. The mathematical formulation of the and 1 1s time. The i11solation and rcmperatml' arc inr,ut frorn weather algorithm is given in the Appendix. Page 370 On;;e thr curve fit constants are obtaincJ, the model is the rt:al weather data need never be useJ again. Thus, if the .. 01htructcd by sub'>iituling the a's into the previous equations stochastic technique was universally accepted, only one aild inserting the appropriate val mis of T1,. v1, and I/\ Vt. The researcher would have to initially pro,:ess the weather - after r,, 1 and l,.,v 1, values actually occur in pairs, since they are that the weather "data" for a city could be distributed in 1 he averages calculated for the combination or ranges ac· compact form in the appropriate JPDM and weather profile ,,,rding to the procedure mentioned above. constants. Fa,.·il pair has an associated probability of occurrence, as previously mentioned, and it is this probability which weighs Sy.~lem 011lp11I. l n order to obtain an accurate picture of 1h e results of the simulation conducted using thl'. pair. !low well the •;tmha,tic weather technique modelled the real lhnei'ore, if there an:: I I pairs of T,._q. and 1,wl', each pair is weather, it wa, necessary to look at the following: ;1,t:d in these equations, and the simulation is run accordingly. i i1c n·sult, are theu multiplied by the probability of the pair I Daily Total lnsola!ion: The total insolation is an im- ,.ii averages. Combining the eleven sets of results obtained via portant indicatnr and is the first quantity that must be t ilf deven pair, finally yields the overall stochastic simulation checked for agreement. 1r :-,ult\. As examples, the JPDM and tx's for Charleston, S. 2 Daily Total Loatl: This factor is strongly dependent on ( ., and Fort Worth, Tex., are shown in Figs. 3 and 4, ambient dry-bulb trmrcrature, and to a much lesser extent, on rt:,,pectively. A 5 x 5 joint probability dcn,ity matrix as insolation. Close agreement between real weather and ,hown in Fig. 2 was used for all five cities which would imply ,tochastic weath•:! loads indicates that the temperature i\1cnty-five probability entries in the JPDM. However, as parameter simulation is accurate. .shown in Figs. 3 and 4, there were typically only eleven The above comparisons, though indicative of how well the ,.ignificant probabilities which had to be used in the stochastic weather parameters are simulated, were not enough to tell -i111ulations. The other 14 entries in the JPDM were between how successful the stochastic weather was in driving a :ero and one half of one percent and could be discarded with \ ny little error as their sum seldom reached even two percent. program simulation ol a system with nonlinearities inherently present due to the use of a hot storage tank and a floating (temperature dependent) COP absorption machine. To gauge the success of the, stochastic technique, there were other System Simulation results to be evallTatc(f, viz. The ,ystem described previously and the weather algorithm 11erc programmed on a UNIVAC I 108. The details of this l Collector Efficiency: This is the useful heat collected by I he flat plate eolb:tors over the course of the day divided by program are available in [3). the insolation incident. While it is strongly dependent on The runs are performed by constructing the weather insolation and ambient dry-bulb temperature, it is, to a lesser p1 orilt", for ead1 oignificant probability, running the exte11t, dependent nn l'olle,;tor fluid inlet temperature, and , 11nuLll inn prngrnrn, and then weighting the results accorJing thus on the bchc1vior of the system. ill the probability associated with the particular weather 2 Percent Solar· This is the rntio of energy supplied by the ;'n,lile used. In the end, there would be as many set, of collectors or by hot storngi.: without any auxiliary energy being ,,cighted resulto as there were: significant probabilities, and by used, tot.he total energy supplied to meet the load. This is also ,11llpi1 adding the results together, a final picture, with a ckpcndcn1 on insolation, but due to the automatic controls in pi obability of 1.0 emerges. \\'hen the sirnulati,in nrns were performed, it was found the system, is quite ,cnsitivc to system temperatures and valve ilia\ using each stochastic probability case for a one day run controls. ,1 as inadl'quate bc,:ausc of the 11011lirh?arity i11hcrcnt in the 3 Average C>dc COP: The avcrge cycle COP is an in- ·.\ ,te1n. lt was tound 1hat while in the real wnther simulation dicator or the pcrfmrn<1r1cc of the absorption machine, which , h~ u·:,:rall change in the energy of the hot storage tank was is wholly dependent on the supply temperature to the 1 L'IY small, the change in tlic stochastiL' mil, was quite large. generator. A kw degrees difference in that supply tem- !he solution used this problem was to run each stochastic perature ..:an cau,:l: the COP to change noticeably, and thus fo1 :1,t1bability case fur a number of consi:cutive tbys, ,hus the avnage COP gives a closer. more detailed indication of .. ,.iiuwing the hut storage tank to stabili1e, and then con· syston temperature, and can thus show the response of the ,,,kring the final day as a representative orw. The number of sy;,tem itself to thl' weather input provided. Since the system is d,,v, med for the swcha,tic simulation wai, chosen to be four only quasilinear, it is obvious that a percentage error in the for all rl'gions, ,rabilization occurred :ifler four days or daily total insolation doe\ not produce the same percentage ·,!Jc,:e. error in the a verge cycle COP, and as was found from the IL'\\. results, actuaily produces a larger percentage error. Having to use four days in thi, manner in th•: s1ochastic 4 System COP: The system COP, as the name implies, is an ·,111rnlatium unfortunately increased the computer time. indicator of the performance of the overall syr;tcm, and along I lu\\e\cr, u,ing synthetic weather prorilc,, even for four with the average cycle COP, give~ an idea of how the systt~m , 1ays, requires much less computer time and daw reacts to the weather input. manipulation than the use of hour by hour real weather data, c-.pccial!y if several years of real data were used for 3 given It was felt that the at,ovc parameters could give a good ,'llll1ih and location. If only one design is to be cvaiuated, indication of system performance, and could serve as an : 11cre 1s 11d reduction in rffort through 11sc of the stochastic effective ba,is for comparison and evaluation of the ,ccirniqu,, 111 fact it would actually be increased. The real stochastic approach to weather rcpre~cntation. :1,l\ a:Jtagc is tn repeated runs with th,: same weather and di! lcrent dc,igns, In ,Hlditiun, the stocha~tic technique uses Simulation Results ,c\ era! years of data as a base (in this ,tudy five) anJ thus "i vc:, better long term performance predictions than a Cencrally spc,1king, the rc,ults obtained via the stochastic dnrnla1iun performed with a year of real weather data which method of wcm her generation compared quite well with the ,,ui,l be: atypical for the region. It should be noted that to results obtained by using real weather. It would be ad- t"1:llerate the ,tocha,tic base, weather tapes arc still required. vantageous, however, to look at the weather-related results l h iwcver, once the J PDM and least square constrants are separately from those resulrs that are dependent on the .-,ailabk fo1 a city rm the desired 111011th, of ihc ~imula1.ion, weather-system inkractinn. Page 371 60 · ! 40 ·1 \ 20 l:- +1 C · ···-- - ,--------:--r---------,-----, M A s 0 Fig. 7 CompMison ol real and slochastc perceni solar and colleclor alliclancy of Washington, D.C. M A s 0 month of October. probably due to the fact ·that October had Fig. 5 Comparison o! real and stochas!ic outputs for Washington, the largest weather e:~tremes of any month. October is a fringe D.C. month with relatively much less imponance 1han the other five months invol;,·ed, .•,ince the cooling loads during the month tend to IJc. \mall; and the use of cooling machines during the month is limited. Daily Load. Tht: daily cooling load is a very strong function of ambient dry-bulb tcmperatme, and i~ thus a good indicator of how well the ~tochastic temperature profile follows the real data. The load cu1 vcs in Fig,. 5 and 6 show that they match very well, the largcq error being 13 percent, but with usual error close to 5 percent. It is noted that the stochastic loads are less than the real loads in all cases. This is due to the fact that the real data seems to have greater extremes (higher maximum temperature, lower minimum temperature) than the stochastic data. l hus, at the pan of the day when the maximum loads arc found, the real weather produces higher loads, while a1 rhc minima, no loads arc produced. Therefore, it is to be expected that the real weather loads will always be ,iightly higher than the stochastic loads since the simulation is weighted on the ,ide of the real data, as far as load cah.:ulation i, concerned. In faci, the regions with the largest fluctuations in hourly tcmperatur<:, namely, Fresno, Calif. and Madison, Wi,c., show (h:H the largest discrepancies, while the other t hrce regions wif h k:-,, fluctuation show a closer correlation between the ru1l and stochastic loads. Fig. 6 Comparison ol real and stochastic oulpuis for Madison, Wisc. Dail)· Tot2I Useful Heat. The amount of energy collected over the cmmc or the day is strongly dependent on insolation, \'1t•a!bcr Depr1Hlent Parnmeter,. Under this heading the but is also a function of Jry-bulb temperature, and the water to!l,,wing ar" included: inlet temperature ,o the collector. The results for both real and stochastic runs match well, except for when low loads Daily !nsolation. occur, as shown ,11 hg:;. 5 and 6. Indeed, since the month of , Daily Total Cooling Load. October alway,. rnc,cnls !ow loads, the largest discrepancies 3 Daily Total Collected Energy (Useful). of useful heat occur for that month. For example, the average The daily collected energy is to some l'Xt{'lll dcpcndcm on summer ,c;,.,011 error i11 uscl"ul heat for the city of Fresno is t Ile system behavior, but since it is a 111uvh stronger function found to he 9 ..1 percent. However, if the error for October, ,11111\olation and ambient temperature, it will be considered which ha, a low cooling load, is not included, the average as \'.Cather·rdated only. error for the other five months is only 5.8 percent. For Dail~ !nsolaHon. The daily in:,.o!ation calcula!et.l by both Washing\on, D. C., the error including October is 10.4 n1e1hot.ls compares very well as seen in Fig,. 5 and 6. The percent; bul excluding October it is only 3.0 percent. The ~,tocha,tic insolation results generally differ by less than 5 same occurs !or 311 <.:itics studied except for Madison, Wisc,, pcH-cnt from the real insolation obtained from the weather which has low loads for all six months of the cooling season. data rnpcs. The largest error i~ 13 percent, and occurs in the Overall averagL· error for the five cities studied when October Page 372 f,'[ll! -··-N lilO sr,i~11\~ ll - -· -- RE Al '."TCOv\STIC - - - 100 80 .6 2 60 40 \ M J J A s 0 \ Fig. 8 Comparison of real and stoch!lstic percent solar and collector 4 l---- ········,··--- -·-·--· ·-·--r------r-----,--····- 0 etfidency for Madison, Wisc. M J A s 0 i, i11dudcd is 13.2 pen:ent; but if that 111unth is excluded, the Fig. 9 Comparison of real and stochastic cycle COP and system COP error i, only 7 .6 percent. for Washington, D.C. · Parameten; Dependent on Wea!hcr-S)·stem Interaction. , COP Av The coupling of the weather "driver" to a system that in- 6 £ t-- ./ · (V ,.._cit__---- s:luck~ a variable COP absorption machine and a hot storage 1 --. .. _--·-. ..,.,-···- \ .._ ___ _ ' .~ ' tank, meant that a study of the stocha,tic weather generation /' .,--· \, ll'd111ique 1, ,:uld be incomplete if it only rnvcred the wcathei- / \\ 1d alL'd p:1ra111eters and did not CXtcnd 10 the arl'a of .';ystern peri'orrnance as affected by the weather input stimulus. Thus. 1h ,: fol!uwing system outputs are studied: 5 I / 2 Colkctor Efficiency I _/ COP \\ 2 Percent Sular ,/ .A>,. /1/ 3 Average Cycle COP II /A····, \ 4 Sy,ti:m COP Coikctor EHidenc). The efficiency of the col!eciors is 4 al'kcted by the inkt temperature and the ambient dry-bulb 1crnr1erature. Thus, through the interas:tion of the two, the ..:olkctor efficiency is determined. Where inlet temperatures and dry-bulb ti:mperatures are similar, collec\Or efficiency will also he similar as shown in Figs. 7 and 8. The match is not ,1s good for months where there are low loads. These affect inlet temperatures to the collectors, causing error in collector 3 --------1---------1--~1------...,-- 0 efficiency calculations. Excluding the month of October, the M J J A s 0 a veragc error in the efficiency, for the five remaining months Fig. 10 Comparison of mat and stochastic cycle COP and system COP and all five cities is 6 percent, while including October it is I! for Madison, Wisc. pcrc<.:nt. On a city ba~is, the largest error occurs for l'v1adison which has the lowest loads of all the five cities. However, the curves show that the percentage supplied by solar means is, in most cases, quite similar for the real and the Pt·n·enl Solar. Tlie percentage of the total energy supplied stochastic .weather simulations. This indicates that insofar as 10 the generator that comes from either the collectors or from meeting the lo,1d either directly from the collectors, or from the hot swrage tank - without boosting - is called the hot storage, 1h 1: stochastic and real weather system perce:11t solar. ! t indicates that fraction of time when the load simulal ions agree well. Even better agreement could be can be met strictly by solar means. Due to the automatic achieved if the definition of percent solar was modified to ,on1rol feature of the system, boosting occurs unless the incl11de all co,,ling .,upplied by solar means, even if that .supply temperatun: to the generator is equal to N higher than supply were bo11i,tcd. !he 1cmperature required to meet the demand. When there is At this poi111, ii can be seen that the stochastic approach is ho,lsting of tlw supply temperature to thr: generator, the useful not only llir simulating insobtion and predicting load .rnrnunt of energy supplied by solar means is not considered in and usel'ul ene1 gy, hut can also give an accurate picture of 1lie percent solar calculation. Therefore, it is important that collector performance, and a rougher, but reliable estimate of 111rcrn,tl system temperatures be similar if the percent solar i,; the percent sol:ir ,>r the percentage of the load satisfied ex- l':,;,ected to be similar. Higher values of this parameter would clu\ively by rn!ar mean:,. ,;,: C.\Jh:ct,·d for lower loads and/ or highi:r values of in- ,oht ion. Viewing the percent solar curves in the aforl'rnen- A ier:.ige Cy cir COP. The coefficient of performance of an :" n1ed figures, the trends arc seen very clearly. Generally, the ab\orption cycle is mainly dependent on the supply tem- i'\'! cent solar fo, .,tochastic is larger than for real weather and perature to the gcnc1ator. It is thus a measure of the internal : lie stochastic· load is less than the real load for all monl hs. rcmpcratu1T of !he :;yqcm, and ,hows, on average, how the Page 373 sy~lcm responds to the wt:alhcr input. When the supply From the· prcc;l'11t study, the following was found: temperatures differ in the real and stochastic cas,~s, so do the cycle COP's. Indeed, the effect of varying the supply tem- l The probabilistic or sto(bastic approach for generating perature is important because of the nature of the relation weather profiles that are representative of a given weather between it and the COP of the absorption machine. That history proved to be quite succe~sfu!., relation is not linear. Another source of nonlinearity in the 2 The artificially generated weather, when used to drive a sy:,tcm is the hot side storage tank. Even though the tank is system simula1ion, showed similar results to those obtained modelled by linear equations, when it is combined with the from the system ,imulation driven by real weather data. abaorption chiller it exhibits nonlinear behavior. If the system 3 For :di the g(·ographical locations studied, the method were linear, it would be expected that the error in the average generated insolation and temperature profiles that accurately cycle COP would closely parallel the errors in the insolation reproduced l•)ad, and collector performance. and dry-bulb temperature profiles. However, due to the 4 System performance, as a whole, can be predicted by me noniincarities present in the svstcm because of the in- of the stochastic weather method. troduction of the hot storage t;nk and the variable COP 5 The results are not dependable for low cooling loads, and ab,orption chiller, the average cycle COP's for the real when such low loads arc calculated, almost all of the weather and the stochastic weather cases do not always match associated results arc suspect. well. The largest errors occur in the fringe months, notably 6 Overall, this method produces good results, and can (ktober, when the loads are low, and the insolations are abo prove a useful tnol for system sizing and/or simulation, at low. Since the average COP is a function of the system much redu<:cd cm! and data handling. 'This is especially true temperature, it can be seen that the system's nonlinearities for investigating di ffcrent system designs using the same have quite an effect on the system, strongly influencing weather data or if the weather data are pre-processed using temperature. the stochastic technique at a central source. System COP. As we just noted, the cycle COP shows signs 1llat nonliiwarities affect the weather-svstem interaction. Since the nonlinenrities arc in the hot ,ll;ragc tank and the absorption machine, it is understandable that measuring their pcrformance - a:, with the average cycle COP -- will produce APPENDIX the largest errors. As the area of concern grows to encompass Mathemal!rnl Formulation ot' lhc Weather Algorithm more than the above two cornpcrnc1Hs. and as more linear components art! added, however, the behavior tends more The analytical representation of the insolation and ambient towards linearity, and the error decreases. Hllls, when dry-bulb tempcrnlure parameters, discussed in the section on \ 1ewing the overall system, a measurement of its coefficient of the weather algorithm, requires that lhe error between the real pcrt,irrnancc should show a clo,c, match between real and weather ,·:lluc :ind lhc ,ynthctic weather value at a given hour \t ochastic values as shown in Figs. 9 and l 0. The average be minimized. · en or in the system COi' i alucs for all citil'S studied is only 12 The rcnerai In 1 m or I he error equation is as follows: percent, bu! if the month of October i:, again excluded- fo1 having low loads and thus making the resul!s inacn11atc, the sin,.-/ 1 n 2 -- 7}2 + [[ (oiJ error becomes only 8 percent. Thus, ,y,tem perfonnancc can be reliably predicted, while perform,111cc nf an absorption l rmancl' under real weather stimuli. To accuratl:!y gauge the ' -c probabilistic weather method in its l'cipacity as driver or cmU(I) )cosl/(r) exw -----,----. cosO(t) '.,trn1ulus for a system simulation, it is not enough to study the in~olation and temperature profiles. lt is irnponant to look.at = }:!co,8(/)e:>.D --~~_c__ (A7) utlic1 indicators of system perforlll,llh'l'. , · cmli(I) Page 374 These four equations in four unknowns can be represented by sin 2 wt sinwl 0 0 f,inw/ sinv:/ 0 0 (t, t -c -c -c () 0 cxp2 co~() ( t) exp2 -··----·- /exp cosll(f) cosO (I\ co,O (() -(' -- C - -- C 0 0 c.:osO (I) exp2 ·------·-- cos2 0 (I) exp2 /cosO(t)exp ----- cosO(I) cos/)(£) cosli (I) Lich entry in the coefficient matrix and solution vector is 111ii.krsiood to be summed over the entire data base for a given Refrrem:es I, ,,·at i,)11 and month. The solar elevation angles, 0, which are ! 1n1<· of dav and site dependent are calculated during thi~ I Anand, I)_ K., .-\1\rn, R. W., nnd lla1quc;, E, 0., "Solar Air- proccs, and the appropriate extinction coefficient for the Conditioning Performance U,ing Stochastic Weather Mode!,," Journal of E11agy, Vol. l, No, 5. Sep!. - Oc1., 1977, pp, 319-.123. rnont Ii under s1 udy is entered. A standard matrix inversion 2 Anand, D. K., i\l!cn, R. W,, lla1ques, E. 0., "Solar Powered Air- c·rnnputer program is then used to solve for u 1 through cx4 • Conditioning Sy,rem l'crformance Predictions Using Stochastic Weather 011<.·e the weather data is so processed, these four constants Model,," Solar Energy Projects, Department of Mechanical Engineering, 1, ii h 1he appropriate insolation and dry-hulb temperature l lnivc, ,,ity of Ida, y!a11d, Colkge Pnrk, MD, Feb_ 1977, 1 !kif, I. N., "Sol,11 l'owcrcd Cooling Performance Using a Stochas1ic a-. er age ,·,dues can then be used to reconstruct synthetic ~le1hod," Ma'1er of Science Thesis. Department of Mechanical Engineering, 1.,,:ather profiles for use in system simulations. University of Mar) land, College l';,rk, MD, Aug, 1978, Page 375 il"VI r Jubilee l 1979 International Congress Joint Meeting with the American Section of the International Solar Energy Society May 28- June 1 Georgia World Congress Center Atlanta, Georgia PRELIMINARY.® PROGRAM Page 376 SOLAR THERMAL SYSTEMS LONG-TERM PERFORMANCE PREDICTIONS USING CLOSED-FORM SOLUTIONS D. K. Anand, Professor R. B. Abarcar, Research Associate S. R. Venkateswaran, Research Assistant R, W. Allen, Professor Solar Energy Projects Department of Mechanical Engineering University of Maryland College Park, Maryland 20742 Page 377 1. ABSTRACT In this paper? a closed-loop feedback control system representation of a solar thermal system is derived for each of the various modes of operation, Analysis of the transfer functions resulted in identifying the various system parameters which must be optimized in order to obtain the maximum system response to a con- tinuous input weather function. Using a stochastic weather model, which has been validated through the detailed simulation program SHASP, as input, the ther- mal response of the system is obtained in a closed-form. A methodology for using the closed-form solution to represent the response, and the joint proba- bility density matrix to represent the probabilistic nature of the weather to obtain the long-term system perfonnance is presented. The results are com- pared to the predictions of both the detailed simulation and the simplified design method. 2. INTRODUCTION The analysis of solar thermal systems has generally been conducted through the use of a detailed system simulation programs such as TRNSYS or SHASP with real climatological data as input. Identifying and optimizing important system parameters usually require many hours of detailed simulation runs and thorough analysis of the outputs. The optimized parameters are then used in system design and long-term system performance predictions. The use of a stochastic weather model in place of real weather data as a detailed system simulation driving function has been demonstrated in long-term system performance predictions. In this approach, the stochastic weather is generated using a probabilistic model of insolation and dry-bulb temperature which was derived from five years of real weather history for several regions. The stochastic constants, with their attendant joint probability matrices, represent data which are considerably less than real hour insolation and 1 Page 378 temperature data needed for long-term system performance predictions. This paper presents an analys;is whereby a solar thermal system is reduced to a feedback control system representation which can be analyzed with regards to thermal responses to insolation and dry-bulb temperature input functions. The important system parameters which have direct influence on the system response are identified from the transfer function and can be analyzed for purposes of optimizing the system response. The closed-form solution of the system re- sponse to continuous weather functions are obtained and the probabilistic nature of the weather in system performance predictions is taken into account. Th2 closed-form solutions together with the stochastic weather represen- tation, presents a simulation model of a solar thermal system which is both compact in size and easy to execute, making long-term systems performance pre- dictions inexpensive to obtain. 3. SYSTEM DESCRIPTION The system configuration and control strategy adopted here is based on a previously conducted control strategy study of solar cooling systems (Ref. 4). Basically, all of the useful collected energy is sent to hot storage. Whenever there is a cooling demand the absorption chiller generator draws off hot water from storage. If the temperature of the hot water from storage is such that the chiller cannot satisfy the load, then auxiliary energy is used to fully supply the generator requirements. The mathematical models are developed for the major solar cooling system components, i.e. solar collector, thermal stor- age tank and absorption chiller. A cooling load model which is weather related is also developed in order that there will be a dynamic interaction between the solar thermal system and the conditioned space. The basic solar cooling system is shown in Fig. 1. 2 Page 379 4. SYSTEM COMPONENT MODELS The different system components are modeled as ~ollows: A, Flat plate collector - the instantaneous performance of the collector is given by: Tf. - T n = K - K l a (1) 1 2 I C q = n I A (2) U C C qu "'T +mC- (3) fi p B. Hot Water Storage - the hot water storage used is a well insulated, fully mixed tank whose temperature is given by the differential equation, (4) Here F2 and F are either O or 1 depending upon demand and collector operation. 3 C. Absorption Chiller - the instantaneous energy requirements and cooling capacity of the evaporator are given by: qG = aG + SGTG (5) qE = aE + SETG (6) qG TL = T -.- - (7) m1cp 3 Page 380 The stochastic weather representation of insolation and dry bulb temper- ature are functions that are Laplace transformable. The Laplace transforms of Eqs. (1) to (7) are taken and the transfer functions of the basic operation- al modes of the solar thermal system are obtained. 5. SYSTEM CONTROL TRANSFER FUNCTIONS The three basic modes of operation of the solar thermal system and their corresponding overall transfer functions are now considered: Mode 1: Solar Energy Collection and Storage ----1 Tfe T ( t) a T T ..I 1-------- T ( s) In this mode, the solar energy is collected and stored. The input or stimuli to the system consists of solar radiation and heat transfer with the ambient. The output is the temperature of the fluid leaving the tank. Sub- stituting Eq. (1) into (2) and using (3) yields A = Tfi (s) +~ (8) me p 4 Page 381 where (9) Assuming that there are no losses, so that Tfi(t) = T(t), and noting that in the collection mode F = 1 and F = 0 for no demand, Eq. (4) together with 2 3 Eq. (8) yields (10) The transfer function that describes the collection process is then given by: T(s) (11) F (s) 1 Mode 2: Solar Energy Collection and Storage, Plus Load Supply From Storage I ( t) T T fe -----~ '1'8 ( t) T ( t) In this mode, the load is an added stimuli to the system. In Eq. (4), F = 1 and F = 1 since the system is both collecting and storing solar energy 2 3 as well as supplying the demand. Assuming that there are no losses as the hot water goes to the load, TG(t) = T(t) and substituting Eq. (5) into (7), the temperature TL is obtained, SG = T(s) - . °'GC (]cs) - -.- T(s) (12) ml p mlcp 5 Page 382 Equations (8) and (12) substituted into (4) yields - mC 1-1 ~a c + -;S.a - T(s) J (13) 1 p s m m c ' 1 p 1 p Simplifying Eq. (13), the transfer function that describes mode 2 is given by (14) s + rK1:c (~) + m(3~ (:1)] p 1 p . where: (15) Mode 3: Load Supply From Storage T T ( t) 1------,-- T ( s) The system operates in this mode whenever there is no solar energy to be collected (F = O) but the load demands hot water from storage (F 2 3 = 1). Substituting Eq. (12) into (4) yields the transfer function in the form T (s) = G ( ) - (~) 8 (16) F/s) 3 s +(~l Hfu:u 6 Page 383 where: (¼) (17) The closed-form solution for the tank temperature is obtained as: -1 T = T(t) = L T(s) (18) For modes 2 and 3, the cooling supplied and heat input are given by: (19) (20) The total cooling supplied by solar over any period of time can be ob- tained by integration of Eq. F, thus (21) Over the same period of time, the solar thermal system provided input to the generator by an amount given by (22) The integrals given by Eqs. 21 and 22 are evaluated only for the times that the system is operating either in mode 2 or 3. At any other time that cooling is provided by auxiliary alone, the cooling supplied is equal to the load and the auxiliary provides all the generator requirements. We note that this cooling is supplied to the load as determined by a control strategy. The actual cooling required, although computed for obtaining solar fraction fC does not interact directly with the cooling supplied by the machine. The cooling load is considered weather dependent and given by (23) 7 Page 384 The total cooling load £:or the day ;is then 24 Q :=1 q dt (24) L O L The solar cooling fraction is calculated as (25) and the average chiller COP is COP (26) av 6, SIMULATION AND RESULTS A computer program which uses the closed form responses of the three basic modes to stochastic weather inputs to model the solar absorption cooling system performance, was developed for use in the UNIVAC 1100/40 system at the Univer- sity of Maryland. Depending on the available insolation, the storage temperature and the cooling load, the program decides in which of the three possible modes the system will operate and for how long. The closed form res- ponse corresponding to that operating mode is used to monitor the storage tank temperature, available evaporator capacity and the auxiliary heat requirements. This enables the simulation to closely track the actual dynamic state of the system and come up with accurate estimates of the system performance. The closed form program was used to estimate the monthly average per- formance of the system shown in Fig. 1, during the cooling season (May - September) for the cities of Washington, D. C.; Charleston, S. C. and Madison, WI. Hourly stochastic insolation and ambient temperature inputs were used to drive the simulations. In order to establish the validity of the model, a comparison was made with the detailed system simulation program, SHASP. This was run with the same absorption chiller characterized by a linear curve fit 8 Page 385 performance equation and the same SOLMET real weather base from which the stochastic weather profiles for the closed form program runs were generated. The results compared include the monthly average daily total insolation, cool- ing load, solar cooling supplied, monthly percent solar, average chiller and system COP's. In this study, the solar system COP is defined as the ratio of the evaporator cooling supplied to the insolation available on the collector. A comparison of the stochastic closed form simulations and SHASP results are shown in Figures 2 to 7 for the three locations studied. In general, the monthly averages plotted are found to agree within 10%. The largest deviations occu.:!:" during the fringe months of the cooling season, which has a relatively marginal effect on the seasonal performance. The comparisons for Madison, WI. are found to be relatively poor because the entire cooling season there is characterized by smaller loads. 7, CONCLUSIONS The closed form response simulation technique can be expected to generate more accurate dynamic performance estimates for solar thermal systems since it uses the exact solution to the governing differential equation of the storage tank temperature. Detailed simulation programs have generally used quasi- steady energy rates and finite difference equations, and hence, will generate results whose accuracy depend on the approximate solution of the equation. The closed form solution used takes into account both steady state and tran- sient responses and is therefore more sensitive to weather inputs. The simplifying assumptions introduced in the closed-form simulation has reduced the size of the whole simulation program by about 75% and the com- puter execution time by about 67%. Also the simplicity of the equations in the closed form simulation made them readily adaptable for use in a program- mable calculator and can therefore perform simulations at a very low cost. 9 Page 386 Use of the stochastic weather significantly reduces the amount of input data to be processed as well as the computing time required to carry out long term performance simulations. The stochastic-closed form approach therefore constitutes a comparatively quick and inexpensive method for obtaining long- term performance predictions for use in design and system evaluation. 8. ACKNOWLEDGEMENT This work is supported by the Department of Energy, R & D Branch, Division of Conservation and Solar Applications, Contract #EY76-S-05-4976. 9. NOMENCLATURE A == collector area C C ca fluid specific heat p F2' F3 = collector pump and demand pump controls I = insolation incident on the collector C Kl' K2 = collector parameters as determined by tests or as given by the manufacturer M = total mass of storage m = flow rate to the collector ml = flow rate to the load qE = evaporator capacity qG = generator input qu = useful energy collected T = instantaneous tank temperature T = ambient air temperature a Tfi = fluid inlet temperature Tfe = fluid exit temperature TG = generator water inlet temperature TL = temperature of the water coming from the load aE, SE = evaporator parameters Page 387 10 aG, BG= generator para.meters n = collector efficiency 10. REFERENCES L Anand, D,K., Allen, R.W. and Bazques, E.O., "Solar Air-Conditioning Performance Using Stochastic Weather Models", Journal of Energy, Vol. 1, No, 5, September-October 1977, pp, 319~323. 2. Anand, D,K., Abarcar, R.B., Venkateswaran, S.R. and Allen, R.W., "System Performance Predictions for Solar Heating and Cooling Using Stochastic Weather Models", Proceedings of the 1978 Annual Meeting of the American Section of the International Solar Energy Society, Inc., Denver, Colorado, August 1978. 3. Anand, D.K. and Deif, I.N., "Solar Cooling Performance Predictions via Stochastic Weather Algorithms", to be published in the International Journal of Energy, 1979. 4. "Control Strategy Studies of Solar Heating and Cooling Systems", Solar Energy Projects, Mechanical Engineering Department, University of Maryland, College Park, Maryland, November 1978. 5. "SHASP - Solar Heating and Air-Conditioning Simulation Programs", Solar Energy Projects, Mechanical Engineering Department, University of Maryland, College Park, Maryland, 1978. 6. "TRNSYS, A Transient Simulation Program", Solar Energy Laboratory, University of Wisconsin, Madison, February 1978. 11 Page 388 CONDITIONED SPACE AC= Air Conditioning Unit ES HW = Hot Water Storage AH• Auxiliary Heater F's• Control Functions HW. • FV5 Figure 1 - System Schematic Page 389 ------ CLOSED FORM - -----0- SHASP 0.. 0 0.7 0 a:: tu ...J ...J :i: 0 0.6 ~ 0.2 -~ 0 ~ tu ~ U) >- U) 0.1 100 90 a:: ~ ...J 0 ui 80 ~ z tu 0 a:: tu a. 70 MAY JUNE JULY AUG. SEPT. MONTH OF THE COOLING SEASON FIGURE 2. COMPARISON OF THE STOCHASTIC CLOSED FORM AND REAL SHASP SIMULATIONS (WASHINGTON,DC) Page 390 2000 >, 0 N"._0 :.:.:: ::, '°1750 z 0 ~ 0- - --0- - -0-- - .J --0- - --0 i1500 z .J ~ 0 t- 300 0"" ..0.. . ::.:, .,,m 200 I 0 X 0 gcs: 100 (!) z_, 0 0 0 0 CLOSED FORM - --0- SHASP :,., 300 0 '." : .:, m '1 200 0 X (!) z 5100 0 0 Ir c_s,: 0 Cl> 0 MAY JUNE JULY AUG. SEPT. MONTH OF THE COOLING SEASON FIGURE 3. COMPARISON OF THE STOCHASTIC CLOSED FORM AND REAL SHASP SIMULATIONS (WASHINGTON,DC) Page 391 CLOSED FORM - --0-- SHASP Q. 0 o0.7 ' a: II.I ...J ...J ::c o0.6 Q. o0.2 c., :E .I,I_.I Vi (>/)- 0.1 100 \ / 90 / a: < ...J 0 v.,_, 80 z / II.I 0 a: II.I '~ a. 70 MAY JUNE JULY AUG. SEPT. MONTH OF THE COOL I NG SEASON FIGURE 4. COMPARISON OF THE STOCHASTIC CLOSED FORM AND REAL SHASP SIMULATIONS (CHARLESTON,SC) Page 392 2000 >. C "ti (I-I..·. . '.:. :.., m 1750 z 0--_ --0- 0 .... - --0-- - C( ...J 0 ti) z 1500 ...J .C..(. .0.. . 300 >, D 0 p '.:. .:., / .,,m 200 ~ I Q X 0 C( 0 100 ...J (!) z :::; CLOS ED FORM 0 0 C.> 0 --0-SHASP 300 >, 0 0 ': :, .,m, 'o 200 ·-- --e---~ ' X ~ (!) z ...J 0 100 0 C.> £r C( ...J 0 ti) 0 MAY JUNE JULY AUG. SEPT. MONTH OF THE COOLING SEASON FIGURE 5. COMPARISON OF THE STOCHASTIC CLOSED FORM .l\ND REAL SHASP SIMULATIONS (CHARLESTON,SC) Page 393 ------ CLOSEO FORM - --0-- SHASP Q. ~ 0.7 a:: LLJ .J .J :i: 0 0.6 ~0.2 0 :IE UJ t- (/) ~0.1 100 90 a:: ci .J 0 U) .,_ 80 z LLJ 0 a:: LLJ CL 70 MAY JUNE JULY AUG. SEPT. MONTH OF THE COOLING SEASON FIGURE 6. COMPARISON OF THE STOCHASTIC CLOSED FORM AND REAL SHASP SIMULATIONS (MADISON,WI) Page 394 2000 >, ' N.. ti O •... '~ 1750 :::--,o-----0 z .2.. C( ..J 0 1000 (/) z ..J .C..( .0. . 300 >, ti .C. ': :, ..m, 200 I 0 X ~ C C( ' 0 100 / ..J (!) ~ z d/ :J 0 0 0 0 CLOSED FORM --0-- SHASP >, 300 C '.0 : .:, m l"l I 0 200 X ---0- - (!) z /r- ~ :J 0 100 / ' 0 0 ~ ~ 0:: C( ..J 0 (/) 0 MAY JUNE JULY AUG. SEPT. MONTH Of THE COOLING SEASON FIGURE 7. COMPARISON OF THE STOCHASTIC CLOSED FORM AND REAL SHASP SIMULATIONS (MADISON,WI). Page 395 Tuesday Morning August 7 - 9:00 A.M. Solar Thermal Systems Session I Commonwealth Room Organizer: H . Yeh, University of Pennsylvania 799011 Advanced Solar Thermal Technology: Potential and Progress, L.P. Leibowitz, Jet Propulsion Laboratory. 799012 Solar Thermal Systems Long-Tenn Performance Pre- dictions Using Closed-Form Solutions, D.K. Anand, R.B . Abarcar and S.R. Venkatewaran, University of Maryland. 799013 A Distributed Micro Computer-Based Control System for a Large Scale Solar Tota] Energy System, J.O. Farrell and R.S . Reska, General Electric Company. 799014 The Control System for Fort Hood Solar Total Energy System, D.L. Black and F.C. Luffey, Westinghouse Electric Corporation. 799015 The Role of External Energy Supply in the Design Optimization of Solar Energy Districts, R. Decher. University of Washington. 799016 Perspectives on Developing Country Solar Energy Applications. R. Ramakumar and J.C. Beavers, Okla- homa State University. Compressed Air Energy Storage Technology Fairfax Room Organizers: J.H. Swisher and G.C. Chang, U .S. Department of Energy Chairman: G.F. Pezdirtz, U.S. Department of Energy 799089 Coal-Fired Fluid Bed Compressed Air Energy Storage Power Plants: A Preliminary Technical Assessment, R.D. Lessard, A.J. Giramonti and R.L. Sadala , United Technologies Research Center. 799090 Incremental Cost Analysis for Advanced Compressed Air Energy Storage Concepts, C.A. Knutsen, Knutsen Research Services; M.A. McKinnon and S.C. Schulte, Battelle Pacific Northwest Laboratory. 799091 On the Formulation of Stability and Design Criteria for Compressed Air Energy Storage in Hard Rock Caverns, A.F. Fossum and P.F. Gnirk, RE/SPEC, Inc. 18 Page 396 DYNAMIC SIMULATION OF SOLAR THERMAL SYSTEMS USING CLOSED-FORM SOLUTIONS* D. K. Anand, Professor R. B. Abarcar, Research Associate S. R. Venkateswaran, Research Assistant Solar Energy Projects Department of Mechanical Engineering University of Maryland College Park, Maryland 20742 Abstract In this paper, the closed-loop feedback control system representation of a solar thermal system is presented. The basic operational modes identified for the system are: (a) solar energy collection and storage, (b) solar energy collection and storage with load supply from storage, (c) load supply directly from storage. The governing transfer functions for each of the different modes are obtained from the governing differential/alqebraic equations. The important system parameters which have direct influence on the system response can be identified from the transfer functions and can be optimized for maximum solar energy usage from available insolation and dry-bulb temperature inputs. Real solar thermal systems operate on a combination of the three basic modes and a single closed form system response is not obtainable even with continuous weather function inputs. As an alternative, hourly step inputs for insolation and dry-bulb temperature are assumed and the closed form responses of the three basic modes to these inputs are obtained. The total system response would then be a combination of the three responses depending on the control strategy dictated by the load, weather and system interactions. * This work is supported by the Department of Energy contract #EY-76-S-05- 4976 Page 397 A computer program using the closed-form solutions to model the system response to step weather inputs is written and validated using a detailed simulation program SHASP.(l). Real weather data for the cities of Washington, D.C. ,':harleston, South Carolina and Madison, Wisconsin are used in both simu- lation programs. The calculated system performance indices compare to within 5% of each other for all the indices. In comparison to other detailed simulation programs, the closed form model is more compact in program size, faster to run and more sensitive to weather perturbations since both transient and steady state responses are considered. The stochastic technique of compactingmany years of real temperature and insolation data for a location into a small number of constants while retaining the probabili;tic structure of the real weather data has been successful in previous detailed simulation studies (2 to 5). The stochastic constants, with their attendant point probably density matrices represent data which are considerably less than hour by hour insolation and temperature data needed for long term system performance predictions. The stochastic weather data was also used as input in the closed form simulation and the results compared with the real weather results. The calculated performance indices agree to within 10% and at the same time, the compact weather representation reduced the simulation using time further. References 1. "SHASP, Solar Heating and Air-Conditioning Simulation Programs", Solar Energy Projects, Mechanical Engineering Department University of Maryland, College Park, Maryland, November'l978. 2. Anand, D. K., R. W. Allen, and E. 0. Bazques, "Solar Air- Conditioning Performance Using Stochastic Weather Models", Journal of Energy, Vol. 1, No. 5, September-October 1977, pp. 319-323. Page 398 3. Anand, D. K., R. B. Abarcar, S. R. Venkateswaran, and R. W. Allen, 11 System Performance Predictions for Solar Heating and Cooling Using Stochastic Weather Models 11 , proceedings of the 1978 Annual Meeting of the American Section of the International Solar Energy Society, Inc. Denver, Colorado, August 1978. 4. Anand, D. K., I. N. Deif, and R. W. Allen, 11 Stochastic Predictions of Solar Cooling System Performance", ASME Winter Annual Meeting, San Francisco, California, December 1978. 5. Anand, D. K., and I. N. Deif, "Solar Cooling Performance Predictions Via Stochastic Weather Algorithms 11 , to be published in the Inter- national Journal of Energy, 1979. Page 399 Fnenn V nL ...t. pp. SJ 7 - 5,~g Pl'fV~;ninn PH>-" i !d .. l i;"1() SOLAR COOLING PERFORI\rtANCE PREDICTIONS VIA STOCHASTIC WEATHER ALGORITHMS D. K. ANAND and I. N. Orn Solar Energy Projects, Department of Mechanical l'nginecring, University of Marybnd, College Park, MD ::'1)742. i i_S_r\ (/11 nTi.,ed/,wm I .July 1978) Abstrnct--System simulations for sizing and performance predictions of various solar systems require some form or weather input tc, act ,ls a system stimulus. \Vhcn aetual weather data is used, hourly simulations are expensive and require considerable data handling. For many design procedures, however, hourly information is not needed, and simpier methods are desirable. One such method employs a probabilistic approach. This method involves !he use of an algorithm that generates a probabilistic matrix, and an analytical formulation which is used to generate synthetic weather data. The approach has been found to be satisfactory. This work uses the stochastic (probabiistic) method to produce representative weather for five geographic regions in the U.S. for the summer months. Parallel runs are conducted with real and stochastic weather. A comparison of the results clearly shows that the probabilistic approach can satis- factorily substitute for real weather for long-term system performance. I. INTRODUCTION The simulation of solar heating or cooling systems can either be conducted over a short lime interval for detailed analysis, or over longer time intervals for estimating average performance. In order to obtain a good estimate of system performance, whether detailed or average, it is necessary to have a good knowledge of temperature, isolation levels and other climatological data for that region, Such data have been recorded hourly in many locations and are available in the form of tapes for different regions. These tapes are available from various sources such as the National Weather Bureau, or NOAA. As an alternative to the use of real weather data, statistical methods have been devel- oped that can artificially produce weather parameters to drive system simulations. 1 5 -- A probabilistic method was recently developed that takes a large base of weather data, and while essentially retaining the weather's history, compacts the information to a form much more convenient for use in computer simulation. The above method essen- tially provides a reconstruction of the data on which it is based, in the form of a single day's weather information, so a 1-day simulation driven by this reconstructed ,veather can give results similar to those obtained via the use of the original data. The procedure used consists of two parts. First, the data base consisting of hourly isolation and temperature readings is sorted and the probability of obtaining any com- bination of two or more parameters (within given ranges) is computed. Then, the same data base is run through a least squares fitting program, to obtain constants in assumed temperature and insolation profiles as functions of time. The combinations of tempera- ture and insolation probability tables are combined with the constants obtained from the least squares fitting to construct temperature and insolation profiles on a daily basis. The general shapes of the profiles are similar, but their magnitudes differ according to the averages used to obtain them. Since each set of temperature insolation pairs has an associated probability, it is assumed that the weather profiles occur with those same probabilities. For simuiations of air-cooled systems, the weather statistics are thus represented by a joint probability density matrix and four constants (two for insolation and two for dry-bulb temperature in this study). For water-cooled systems, the coefficient of performance of the absorption cycle is dependent upon the wet-bulb temperature, thus necessitating the stochastic prediction of an additional weather parameter. The 5]7 EGY Vol_ ,t Ne,. 4---E Page 400 53?\ D. K. ANAND and L N. DEIF joint probability density matrix therefore becomes three dimensional and six constants are necessary. Fortunately, even with a three-dimensional probability matrix. the number of useable entries is not large since many are zero or very small. This approach has been well documented in Ref. 5. This paper attempts to do three things: (l) Review some of the previous work. (2) Extend the application to several new geographical areas usmg a solar cooling system that has storage and load. (3) Discuss and present ways to correct some problem areas. In earlier work, 1 5 the simulation program modelled a very simple system of flat piate collectors coupled to an absorption machine which was allowed to provide as much cooling as it could. This system had no storage or control strategy. The stochas- tic approach was used for air-cooled and water-cooled air-conditioning systems using Washington, D.C. weather. The coefficients of performance estimated for these cases agreed very favorably with those obtained via detailed simulations. The present simula- tion analyzes a more relaistic system. It includes collectors, hot side storage, auxiliary heat supply, pumps and valves, automatic controls, weather dependent loads and a control strategy. The stochastic approach is also applied to five different locations in the United States: (1) Washington, D.C., (2) Charleston, SC, (3) Madison, WI. (4) Fresno, CA, (5) Fort Worth, TX. These cities were chosen for climatic and geographical diversity. Stochastic and real weather results were compared on the basis of total insolation, daily total collected energy, daily total cooling load, fraction of the load satisfied by solar means without auxiliary energy (percent solar), and average cycle COP. The results showed that the stochastic approach compared favorably with the real weather method, and that it can be used to drive system simulations at much reduced cost and data handling. 2. SYSTEM MODELLING A typical solar powered cooling system is illustrated in Fig. 1. The simulation of such a system required the modelling of various sub-systems as well as input weather data. Specifically, in this study the following sub-systems need to be modelled: (I\ collectors, (2) absorption cooling (chiller), (3) hot storage tank, (4) control strategy, (5) load, (6) weather. The details of the models for the above sub-systems arc presented in Ref. 3. The control strategy for the simulation system is the result of logical decisions made at various parts of the system on the premise that solar energy should be used as soon as it is collected. The demand pump is automatically turned on by a di!li:~renlial thermostat when the collector exit temperature (static) is greater than the temperature of the hot storage tank by t...T0 N of 15°F. As the storage tank experiences a rise in temperature, the temperature differential decreases, until at last it drops belov, l".ToFF of 3°F at which time the demand pump is switched off automatically. It is desirable to avoid on-off cycling of the demand pump, and to have one start-up in the morning and one shutdown in the evening. Constant mass flow rates, on-off pump controls and open-close valve controls arc used in order to reduce the complexity of the control strategy and avoid some of the difficulties that can be encountered in the operation of the system. When the room temperature rises above 75°F, the demand pump is automatically turned on, and the control strategy goes as follows: If the stroage tank temperature is less than 170"F when the demand pump is turned on, the auxiliary by-pass valves dose and the energy required at the generator of the absorption cooler is supplied entirely from the auxiliary heater. If the temperature of the supply water is between 170":F and 190 F, auxiliary heat is added to boost the capacity to meet the load require- ment. When the demand pump is on, the collector exit temperature is either higher Page 401 Solar cooling performance prcdictit>ns / CONDITIONED / SPACE \\ 11 AC "' Air Condit ioninR Unit HU "" Hot Water Storage AH - .Au-;dlinry Healer F's ... Control functions H.W . 1. ., -,FV FVS Fig. I. System schematic. than l 9ff"F or at least 20'T above the storage tank temperature, by-pass valves automati- cally open to allow the flow of hot water from the collectors to the absorption chiller generator. Since the cooling supply must satisfy the load, and since the supply capacity of the chiller ,s a function of the water temperature going to the generator, it is sometimes necessary to raise the temperature of the generator supply water through the use of an auxiliary heater in order for the chiller to deliver the required capacity. ff the tempera- ture of the water supply to the generator is above 170°F, but not high enough to deliver the required cooling, just enough auxiliary heat is added to boost the temperature until the chiller can provide the required cooling. If, on the other hand, the supply temperature to the generator is below 170'F, the tank by-pass valves are opened automa- tically, and the entire generator load is carried by the auxiliary heater. In either case, the chiller will not be able to meet a demand higher than its maximum capacity. The hourly sensible cooling load based upon the outside ambient temperature and the insolation of any given hour is calculated using form: LOAD = A(T,1 -- TRooM) + B(lnso!ation) + C (1) where A is a factor based on the size of the area whose load is being calculated, insula- tion and infiltration. B is dependent on the surface area facing the sun and C is a constant load. TRooM is the desired temperature, and T~ is the ambient dry-bulb temperature. 3. WEATHER ALGORITHM The weather sub-system model is constructed via a two-part process. The first is a purely statistical procedure in which a data base of weather is sorted, and averages and standard deviations are calculated. The second part involves the deveiopment of an analytical model by employing a least squares error technique on the data base of weather. The procedure yields a set of curve fit constants that shape the model, and conform it to the original data supplied. The model thus becomes representative of the real weather data used to construct it. The first part of the procedure-the statistical manipulation of the data-is concerned with sorting simultaneous pairs of insolation, ambient temperatures in the weather data, and placing them within prescribed ranges. Thus, for a particular value of insolation and a particular va1ue of dry-bulb temperature, the appropriate range in which the insolation value fo.lls is found, and the appropriate range in which the dry-bulb tempera- Page 402 540 D. K. ANAND and I. N. DE!F t---· ' < T - 2o I T • 2c I f t o T + 2c j ,T • 2c I I ' i :."id + 2tr I ~ c-·---- rd --'t±-1; 2v ~ti + I I I I rd = cr <- -+- -- I P{T '--~ ~-:1 0 i ,J j I - fd - 2o : ·- ~d • 2° J_ _____ t I Fig. :'a. (;cnc:r;d f,,rm nf 5 x 5 joint probability dcnsily matrix used in air-cooled stochaslic syslem simulations. ,~~ r------ -: 'm"''" 27.l ! "u:2•0.27 ! {012)1·----1 I I I I I 210 25! -~--+ (699) (771) Tw ' I ,, , / Il i ,, / / / ,.( / / II ,, ,, I / / ,, I / (:r::-:;-;-/------------------------J-/- - l ,,/ / " vj • :305.5 (970) Ci,, , 4.68 !S42) _j,,' Viv g 2.64 (41'6) l Fig. 2b. Joint probability matrix of insolation, dry-bulb temperature and wet bulb temperature. ture value falls is also found. The combination of the two ranges has thus occurred for the particular set of data viewed, and the number of all such occurrences is retained. The number is an indicator of the probability of the above combination, and is very important in weighting the final model (Ref. 5). After all the data has been screened, and all range combinations have occurred, average values fur these ranges are calculated. It is important to note that the above weather ranges are flexible. Their widths are determined by how fine or how coarse a model is desired. The statistical procedure just mentioned is carried out by a computer program described in Ref. L The mathemati- cal development is available in Refs 2 and 3. A typical probability entry is shown in Fig. 2. The second of the two procedures is the least squares fitting program. which proceeds to curve fit the hourly data with the following equations: l(t)/lAvE = (cx 3 + cx 4 cos8)exp(-c/cos 0) (2) Tir)/1:._v, = (o: 1 sin wt+ C< 2 ) (3) 'J~,.(t)/T,,,,vt = (C< 5 sin wt+ et:6 ) (4) where I is insolation, 0 is sun angle, c is the extinction coefficient, Ta is dry-bulb tempera- ture, Tw is wet-bulb temperature, w is daily frequency, and f is time. The least squan:s procedure yields a 1. tx. 2 , o:.i, c,: 4 , rx 5 , and a. 6 . The mathematical procedures and details are given in Ref. 5. Page 403 Solar cooling performance predictions 541 1.2 3.0 • I DATA u o T DATA 20 096.__.,___a!--'--1.._o__.__1,.,.,2__...,__1,_4__.__.___,__::i,,.....,o 0 TIME ( HOURS) Fig. 3a. Synthetic temperature and insolation profiles obtained for July usmg 5 yr of data. compared to a randomly chosen set of real data. -o- ..::.- 0 ·O· 1.1 I T.., I ! Td&v I 1w,,.,I D r;. 1 r I I I. o a "' .o 0 ... .95 LlOO D1/ ? ~ 6 8 IQ Fig. 3b. Normalized synthetic temperature and isolation profiles obtained for July usmg 5 yr of data compared to a randomly chosen set of real data. Having thus obtained the curve fit constants, the model is constructed by substituting the :x's into the previous equations and inserting the appropriate values of TAVE and /Av,. if the system is air-cooled. If the system is water-cooled. the wet bulb temperature must also be used. For simplicity we only consider air-cooled systems. The TAVE and /An values actually occur in pairs, since they are the averages calculated for the com- bination of ranges according to the procedure mentioned above. For purposes of simpli- city, we will only discuss two variables, /(t) and 'T;i(t). Each pair has an associated probability of occurrences as previously mentioned, and it is this probability which "weights" the results of the simulation conducted using each pair. Therefore, if there arc nine pair:; of J~_v 1 and JAVE, each pair is used m these equations, and the simulation is nm accordingly. The results are then multiplied by the probability of the pair of averages, and combining the nine sets of results obtained via the nine pairs finally yields the overall simulation results. As examples, the joint probability density matrix (JPDrv1) and x's for Charleston, SC are shown in Fig. 4. This is derived from 5 years' data. 4. SYSTEM SII'vl ULA TION The system described previously and the weather algorithm were programmed on a UNIV AC l 108. The details of this program are given in Ref. 1. The runs are performed by first constructing the weather profiles given in eqns 2 anJ 3. Using these profiles, the simulation program is run for each ternperature-insola- tion pair. The results are then weighted in accordance with the probability associated with the particular insolation-temperature pair used. In the end, there would be as many sets of weighted results as there were significant probabilities, and by simply adding the results together, a final picture, with a probability of 1.0 emerges. Page 404 S42 D. K. A"1AND and L N. DElF (!n· CharJ-e:ston, ~·n-c M.ay DAY: 121+20 .. Jl.,l K: .196 r--s- .c... ~ iAVf. PR~~ 104. J 66.) .0114,1 11.4. J 06. 3 173. 5 66. _) I 104,} 72. S .09}% 14I1,) 72. 5 .14094 12. S . l }l.2) 104. "¼ 77 .6 .1073£1 144. 3 77.6 .10738 173.5 77 .6 . H,77B 21. 4 66.3 .02:01 j 72. 5 .10067 n 3 I. 0'6i'l'7 0 i . 116S&297 I o, I2 .14B)b) ___ .__°"2_ _,_• 99624184_ ___ _J Fig. 4. J.P.D.M. cases and associated probabilities least squares fit constanls. When the simulation runs were performed, it was found that using each stochastic case for a 1-day run was inadequate because while in the real weather simulation the overall change in the energy of the hot storage tank was very sma!L the change in the stochastic runs was quite large. The solution to this problem was to run each stochastic case for a number of consecutive days, thus allowing the hot storage tank to stabilize, and then considering the final day as the representative one. The number of days used for the stochastic simulation was chosen to be 4. 4.1 System output In order to obtain a good picture of how well the stochastic weather technique modelled the real weather, it was necessary to look at the following: (l) Daily total insolation. (2) Daily total load: (this factor is strongly dependent on ambient dry--bulb tempera- ture, and to a much lesser extent, on insolation). (3) Collector efficiency. (4) Per cent solar: (this is the ratio of energy supplied by the collectors or by hot storage without any auxiliary energy being used, to the total energy supplied to meet the load. This is also dependent on insolation, but due to the automatic controls in the system, is quite sensitive to system temperatures and valve controls). (5) Average cycle COP: (the average cycle COP is an indicator of the performance of the absorption machine, which is wholly dependent on the supply temperature to the generator). (6) System COP. It was felt that the above parameters could give a good indication of system perform- ance, and could serve as an effective basis for comparison and evaluation of the stochas- tic approach to weather representation. Page 405 Solar cooling performance predictions 54} 4.2 Simulation results Generally speaking. the results obtained via the stochastic method of weather gcncr- ati,rn compared quite well with the results obtained by using real weather. It would be advantageous, however, to look at the weather-related results separately from those results that are dependent on the weather-system interaction. 4.3 l·-Veather dqiendent parami!lers Under this heading we find: (l) Daily insolation, (2) daily total cooling load, (3) daily total collected energy (useful). The daily collected energy is to some extent depen- dent on the system behavior, but since it is a much stronger function of insolation and ambient temperature, it will be considered as weather-related only. Detailed outputs are shown in Refs 3 and 4 with only a few reproduced here for illustrative purposes. Although results were obtained for all five cities, a few representative results are included from each city. 4.4 Dailv insolation The daily inso!ation calculated by both methods compares very well as shown in 5. The stochastic insolation results are generally less than 5'>0 off the real insolation obtained from the weather data tapes. The largest error is l 3° 0 , and occurs in the month of October. In fact the results are worst for October because the weather data is most incomplete for that month, and the simulation tends to be bad due to the bad data base used. October is a fringe month with relatively much less importance than the other 5 months since the use of cooling machines during the month is limited due to small cooling loads. 4. 5 Daily load The daily cooling load is a very strong function of ambient dry-bulb temperature, and is thus a good indicator of how well the stochastic temperature profile follows the real data. The load curves in Fig. 5 show that they match very well; the largest error being l but with normal error in the neighborhood of 5''.~. It is noted that the stochastic loads are less than the real loads in all cases. This is due to the fact that the real data seems to have greater extremes {higher maximum temperature, lower minimum temperature) than the stochastic data. Thus, at the part of the day when the maximurn loads are found, the real weather produces higher loads, whiie at the minimum, no loads are produced. Therefore, it is to be expected that the real weather loads will always be slightly higher than the stochastic loads, since the simulation is ··weighted" on the side of the real data, as far as load calculation is concerned. In fact the regions with the largest fluctuations in hourly temperature; Fresno, California ,md Madison, Wisconsin, show the largest discrepancies, while the other three regions with less fluctuation show a closer correlation between the real and the stochastic loads. 4.6 Daily total use/iii heat The amount of energy collected over the course of the day is strongly dependent on insolation, but is also a function of dry-bulb temperature and the water inlet tempera- ture to the co!leclor. The results for both real and stochastic runs match we!L except for when low loads occur, as shown in Fig. 5. Indeed, since the month of October .1lways presents lmv loads, the largest discrepancies of useful heat occur for that month. or example, the average summer season error in useful heat for the city of Fresno is found to be 9.3°/0 • However, if the error for October (which has a low cooling load) is not included, the average error for the other 5 months is only 5.8~,~- For Washington, D.C, the error including October is 10.4~'~, but excluding October is only 3.0%. The same occurs for all cities studied; except for Madison, Wisonsin, which has low loads f,)r all 6 months of the cooling season. Overall average error for the five cities studied \.\hen October is included is 13.2~,~' but if that month is excluded, the error is only 7 Page 406 544 D. K. A;;,;;o and L X Dur CC tA a .. \ Blu-DAY- 1/ { l!H1,,1- ff1DAY-i 2000 1800 !600 !400 \ \ \ \ \ !00,000 \ \ ' 50,000 A st,;,,ba,ntc lr,,.ol.ati0.~ 0 r~_,,1 ir.iol.ot:ion 8 ~tochas.i;: u.t!i-~i'-1 h,.H 9 gto;:t,.,sac lo;i~ 0 ;,:;;l load 0 ~ M J J A s 0 Fig. 5a. Comparison of real and stoch:l'JOl,Hion II Hs>cf',utic ~e-!ul hut 0 nJ1l u.u,ful hut ill: Hoch,ur.tc 1011d 0-t-Qnt-&l -lo:;i-::I .---~-----~-- M A s 0 Fig. 5b. Comparison of real and stochastic output for Fort Worth, Tex2.s. 4.7 Parameters dependent on weather-system imeraction The coupling of the weather "driver" to a system that includes a variable COP absorp- tion machine and a hot storage tank, meant that a study of the stochastic weather generation technique would be incomplete if it only covered the weather-related par- ameters but did not extend to the area of system performance as affected by the weather "driver". Thus, the following system outputs are studied: ( l) collector efficiency, (2) per cent solar, (3) average cycle COP and (4) system COP. Collector Efjiciencv. The efficiency of the collectors is affected by the inlet temperature and the ambient dry-bulb temperature. As seen in Fig. 6, collectors subjected to similar inlet and ambient dry-bulb temperatures will ha vc similar efficiency. The match is not as good for months with low loads. These affect inlet temperatures to the collectors, Page 407 Solar cooling performance prcdictwns 545 100 ,,.. __ /' /' -- / / 80 / / ,, / / / 60 40 20 0 M J J A s 0 Fig. 6a. Comparison of real and stochastic per ccm solar and collector efficiency for Washington. D.C 100 / / ,.,,/ ,, / 80 -----, "/.,S ,/ / ' ' / ' / ' ' -- _..,, / / ' 60 "-- 40 20 0 +------.-----r------,.-----.-----. M J J A s 0 Fig. 6b. Comparison of real and stochastic per cent solar and collector c11iciency for Charleston, S.C. causing error in collector efficiency calculations. In all five cities. the average error in efficiency for May through September is 6~~- Including October increases the average error to 11 ",~. The largest error for a single city occurs for Madison which has the lowest loads of all five cities. Per cent solar. The percentage of the total generator input energy supplied by either the collectors or the hot storage tank (without boosting) is defined as "Per cent solar". It indicates that fraction of time when the load can be met strictly by solar means. Due to the automatic control feature of the system, boosting occurs unless the supply temperature to the generator is equal to or higher than the temperature required to meet the demand. When there is boosting of the supply temperature to the generator, the amount of energy supplied by solar means is not considered in the per cent solar Page 408 546 0. K. ANA'.sD and l. N. Drn· .... ___ __._ ___/7 180 _ / COP II., ~~---.- --- Ir 2 '\ .4 ' \ lr I .3 +------~---~- 0 M J J A s 0 Fig. 7a. Comparison llf real an\llk. MD 20705. L: :;Srn:nn: ,\pplicati,H1s. lnc. S40ll Dri\c Md.c,11. VA 11 102. (/11 1, I J<, ,i /rlf//1 i J11/r ll);~) Ah,!rnct ·1 Ile 1alirL:t11111 lll s,1Iar hcat11tt! ,rnd v10\111g computer 1, ,1 ii! 111 the r:arly ,tares of dc\clupn11:nt S,Hnc worh has hec11 do11e 111 the area hut more ts required hdr,rc u k\d oi' u1nli,k11cc can he ;i,,ouatcd \\ 1th tlw the ,,I th..: A I ahdattnn rcp\lrl which c'<1mi·,l ·, ,,I .\ lncb, w1th rc,pc:ct 11, 1mm,Hkkd fhttamctcrs or ph,;nomcna. Lewi 2 addrcs:,c'S tli,· intrnducnl in ,irnpl,ticd analy,is procedure, due tll unmo,kkd amckr \,triation 1,\11ic k1cl 3 deals 111th as,,c·,,mcnl of ,ariation 111 result, due lo the 1,111,11ir,111 of modl'kd p;i1;1111clcr,. l.c1cl 4 p1,,1i,lcs a 1cri!1cc1lic>n ,,I the <1f kvcl conq,,m,on ,111d1cs wllh licld p,·r lllrm.111c·c d«w Th,· 1c ,ult 1s ;1 cunlidcncc with which the :,impltlicd an;,i:, ,I', p1,1,~1am can be ·r o illustrate the Monte C1rlo techn1q,,es suggested in levels twp and three, ,t case study \\,i,. prcp,uc·d. Th,· results lnllll the caw sJudv are helpful tn apprcci,11.111g the method proposed ;i11d <.",p,:,:kd rc,.,ilt:, l1u111 th,,t method T!rc' "i\,,Luiun pwccdurc dcscnhcd 111 this d,1cumcnt 11111 result 111 the cstahlisl!!rn:nl .,,f kvch "f c,,nll,kncc with which u c;in predict pnln1111,1111.:c Tlw metl111d11h1gi \\ill ;tis\\ :1ssis1 111 the cslahltshmenl nl ;i me,rn,n~lul ;ind ,nl,,i s\ analytic,d nwdcb may he cumpari:d m an 11alytical model rnc1y be Cl1mparcd tu :.1 ri:al system. In case of the latter. it is that validatiun is tr:sting the between the behavior of the niodd and that ul the real system 2 ,rnd drnwin,' cnne!us1011s as to the usefulness uf the model. In !he former cornparisun, the validation is no! as easy in that it 1s nut known a priori \VhiL'IJ of the two models arc closer to the real Validation in this case mw,t s1mpl1 be a compar,1ti,·e study without any confidence level on either model. A model of a real system is a mathematical or statistical nf a systt'm, subsystem \)f component. A simulation mimics the bchavinr of a system a m()dd !P stimuli, !'he purpose of valida- tion i:, then tn either insure that tw() models of the same system when usc>d in a simula- tion give comparable ri:sulls ur tu insure that a mudd used in a simulation represents the real s\ stem in an acceptable man net. The rornwr is oftl'.n referred to as softw:.1rc software validation, whereas the latter is referred to hardware/software val1datio11 Snmc typical paths ol such validation arc illustrakd in l 1 We note that the particular validation path must be specified bcforl' any methodology is used, Although !ll()st modcb arc ha~ed on physical laws and material properties, modelers u:,ually rccPgnili: the need for experimental dat:1 to support the model's predictions, The purpo~c \ll' 1hc data is to e~tahli\h confidence m the mmk:I\ formulation so the mndd can ht used to predict performance at where data docs 1101 exist This alluw~ the analyst to i:\'aluate the pcrformanu: of the ,ystcm for many parametric com- binations. Such cvaluatiun could be L"Xlrerncly time consuming and expensive if done entirely cxperimentalh The 1wtural (1utgrnwth of the ;nailability nf an analytical model Page 412 ''ti( l :u•.i'lM' -, ~l -==\iM:;';l :; I: i' \ ["{::I J,; ]1;•r Pk.OC,H :U\f r I -~,c -,'it\ ~ / / J s_·,tl1dat1ot1 ,,,,'' '-t ~-·-1 !; "'"' r-1----1 ' Fiµ "" Paths for cornpuncnt n1ut.h.·i or ..;;,tern nH)dd ,~diJaiion. PR(Ot(f(('NS I L .. _r IV l fY ANii..l ONf ronn c+tEcK, ,1.vtRAf;t rrHfOHMJ\NCE I J';:-iC l-C/Mi1 f\Rl':,(JW, [ rnn 1,rn_~- r'--:-:-:-·~1,_-~_~-_1 _J ' ------------ TO MOD£L I Ui Mi t !M! 1 (H( () if•! h' lt-l'Hll ii} i;; l'AH.l;,MfHH) Page 413 .'·' I the ability tu m pc1ramc!cr opt1m1/ation. It i\ \Cry d1!1icult Ill accu idcn! optimal raramclcr cnmhinations alh: lwwn(:r. th,.: a\:u\c1hili1y ,ir a \alidatcd rn,1,kl ,dlov,~ paramch:r optimi1:l11011 \iu:cd with cunli ... km:c at rnrnim,il c,1st. In a situation where d1iciency. 1ime. and c,,'it arc important. ,uch the s()lar of tPd:1y. mod<:ls become of paramount importance. The current problems a•,snciatcJ with solar heating :rnd c,H1 iing S)skm mudds fall irn,, t,,n ha-,ic calt.:gories Fir~!. a grc:t! nurnhci uf models :ire hc111g and disscmina!cd without cxpi.:r1mc111al fnundal!n. some problems haH: occurrcJ with the sys;tem operation itscif. Data tapt:~ han· bc~·n plagued with gap~ due to inslrumcntallon drted in thc rcf.:rcnccs. It b interesting t,l note that among these studies no common mctlwdoh)gy is used. As a part ,)f several on-going software software \alidation studies, FCHART and SOLCOST have been c,lmpared for the heating and service hot water mo,k 1\gain. no cnuling comparisons have been a1tcmp1cd. The validation of passive solar sy:;tem prPgrams has no! dcH:lopnl to any kvi:I sincc the passive solar system simulat,on capability has to be formulated into a general purpw,c program. Develop- ment of such a prngram is currently undcnvay. Similarly. v;ilidati,m of building !oad programs needs attcnt1on although a \alidatiun plan docs exist for DOE! Programs such ,h DOEL MITRA, BLAST NBSLD, and Pthns all have the capability lo calculate building h,ads. Howcvt:r. the programs vary in lcchni4ue and level of sophis- ticatiun and therefore d,, not predict idcnticd performance given 1dcntical building t.:haractu,\lics. At !his time no one program f\ir bu!ldiug load" h;i;, emerged as the standard. hut the public offering of DOE I on the Cybcrrn:t sys!crn may focus attention of that program. All of thc:,c program,, still r,:qmrc a ):'.rc11 dca! ol' validation hdorc ,hs:y may he tl'.>l'.d with cnnfakncc in solar hc:,ting ,md u,,)!ing design studies. In reolgrnllllll of tht: current slatu, and the need f,,r a ,;didai1Pn program. the DOE has ini!1akd a ta,U spcci!ically lo addrc"s the ,:didatinu of mudels ,)r solar heating Page 414 and cooling of buildings ·rhb task include, the (I) Determine the cu1Tciit validation s!:_•, tt,s ,,, 1· ti,-,~, \ :irlt)US compnncnL ! 11 ~I system models. Iden! !'uturc effor·ts. (2) Develop a wdl-ddin,:d v;didalion m<:thodology. This .:!fort should include llll nary validation sllhh·s \V1th real data to determine weaknesses of the tcdrniuue (?) l_)escribe sources of data (controlled and uncontrolled) which can be u;cd m ihc valldat1on program. These sources should include government ac·•demic ·, 1,-1 indu, : ,! facilities: The DOE I ll':.l!ing and Cooling DernonsTralion Pr,,~rar~. EPR i" l~~: 110 /~cl' · "" mternational sources should also be considered. · (4) Eslahlish working relationships with those data sources which will be validation studies. F:-,tahlish reporting formats for validation subcontracto, _{5) Perform validation studies as daia becomes available. Establi~h communication: \Vlth code developers This wor~ is hc.i'.1g reported . SAi as it is ,:omp!ctcd under contr;;ei. In tl1i:,; p:qwr. we will discuss I ask 2 und give an example by citing a case sl . The p;irer ,'i\ some broad conclusion, and a biblingraphy of some useful papers - , ' i' k I l l'/ 1 \ I D \ \ L ! U ·1 ! 0 '\ l L i H (l D n I I J ( ; 1 'f he de\ i id \._ 11 nq.ur~:r prugrarn··- and caJcu Hun~il procedure~ L_)r t 11<)!) of \ct L",, confidence limits for the rrediction of the above listed quantities. If components arc being tested, the rcs,:archcr should determine which quantities arc of primary importance tu the analysis of th: cumponcnt performance. This decision should be based on which variables of tlnt u,mponcn! v,,·ill have the most impact on other components and the system performance. 6 Li'Vl·l ~ \',\LIUAIION Level 1 rnlidatiun ts similar tP level one in that the validation procedure is directed Page 417 toward the identification of maccuracies uf the predictions du.: to tl1c assumptions inher- ent in the program formulation. The diff~rencc is that Inc! lwti addn::-,scs the v:didation of simpii!kd analysis tools such as FCH/\ R'L SOL COST, etc. rath..:r than the dt:taikd analysis programs described ahovc. Since we assume that a more detailed prngram than the simpli!icd lcchni4ucs exist:-., Wl'. can ,·ary many ul the simpldicd unmodekd parameters in the detailed program and evaluate the potential error which is introduced into the simplified model. In addition to this confidence hand one needs lO add the ,..:onlidcnce band of the detaikd mock] estahlished in level one. This conildc11ec band now represents the total unccrt;,inty in the simplified model mnput due to 1111111r>dcinl raramcters. It is still assumed !hat the parameters which arc used in the ~irnpiiiied analysis accurately represent that system. The data required for this phase of \aliJation 'Nill he estimatcs ,,f the variability of the unmodcled parameters. Performance data is 1101 required since the studies arc ~oftware/softwarc comparisons. The methodology used for cstahlishing the variability in performance given random distributions of parameter values will be thoroughly de- scribed in the following section. The comparisons can be made on the key variables presented in level one. H additional variables arc found important for a particular appli- cation then they should be added to !he analysis. The final statement should be a description of the 95''., confidence limit Jue to unmoddcd errors for each generic system. 7. LEVi'I ' VALIDATION This portion of the validation methodology Jcals with Lkt.ermina!1on of the inaccura- cies of simplified pruccdurcs with respect to the Jcsigni.:r. Fur \,didation at this level, one must determine the potential error:,, b<:twcen predicted design performance vn of the results obtained in level 3. Data for a wide variety of field mstalled systems will he obtained and compared to predicted values. The comparisons should fall within the tolcrunces cstabli,bcJ in level .3 approxi- Page 418 556 mately 95" 0 of the time. If the results do not agree in this way. then an should be sought and level three analysis reevaluated. For example, it may that significant jrnnt probabilities exist among parameters 'Nhich were ignored I the ivfontc Carlo an,dy sis. i.e. if one system parameter is bad, some other parameter :~ also bad. Special techniques are not required for this level since the study will be forward comparisuns of predicted and measured performance data. The data for this level of v<1!idation should be monthly or annual data from many source,. The quality need not he as high as in !eve! one but some credibility in the measuremc,·: must exist. Such programs as the DOE Heating and Cooling Demonstration EPRI. utilities and others should be appropriate. 'i C1\ SL STU DY In the development of the \alidation methodology, It was necessary lo formulate a method for obtaining confidence limits of performance estimates given probabiti,.,, distributions of certain parameters. This method, commonly referred tc~ as a Mc· Carlo analysis, is required for level 2 and level 3 validation. The second level of tion identifies the u 11cc.-rLlinty of simplified analysis predictions due to the variabi!i 1;, in unnwdelcd par:1mc!LTS ( un nh)dclcd in the simpi ificd Th is is hy varying the paramdt.:r:~ in a detailed mode! lo establish the unmodclcd v:mahiln, Level 3 \alidallun idcntdit:s the u1Kcrtainly in simplilicetoc '100, o.,,.,,,~ •0.0 I I lO t ;\Zli'l'Ot.h Anqle -,)-(:(_j.1-ti!J IJ.0 \ ] ,, I ---r 11 <;tor.age (,aµ.ic•ty m::mz- 256.0 -+---·------, " l 6000 _... }0,)00 Ltbk I Paum:.:tcrs used m FC!IART Page 419 Fig. 5. Hypo1hc,i1cd numbc·r nl ohscnati,111, \,. ,C,,.,,, l 1Ai; /0 10 .&8 14,20 0.59C S,040 10, l )04. S 11.5 ~z. a 1~ .40 0,650 ),840 1?3.5 1.:.s IJ.00 J.S'10 4_080 22.) 465.5 IS S 44 5 19.00 /J.':>lO 1. J(fU \9, ~ Ji}. ':i 44, I 11.80 ('1,6\0 SD. 5 1 LOO 0,6SU I l.5 62.) 19.00 O.S10 4.)20 Hi.I J%.S l ~. 5 ·HUl 10 16.60 0.610 J,360 23.7 327.S 1),5 '.d.4 11 16.60 0. ~',{) 4.:i.ao 19,ti 2!1L) 12.'i so. t II 11.8-0 (), '.!JO 1,600 u. 1 46~.s i b. ~ 48 1 IJ l0,20 O.'.,lU 4.0HO 11.';, 3%.S 14.'., 14 lfi.60 0,610 J.360 n .1 488.S H,.S 4fl,,' IS 19.00 0.610 4, J:IJ v.. J ~65. S l2.S ,. 11 .a.o 0.510 4.320 2). 7 442. S i}.) ,t1.s Ii 11.8.0 Cl. S70 ~.J~O lt,.7 44?.S it<,,':, ')],,1 IB 11,!JO o.s:o 4. ,., 14.20 W.6JG L)b\J n. ! 281.5 10 !9.00 0,6 HJ 14.S Sl 21 16.6,) 0, bJO 1. 120 19. S l2 7, 5 \l,) bl I ZI 16.60 0,tilO J,3b0 57.6 1J 1: l,JRO Tahk 2. R,rndom values Page 420 I l 2', t II I~ rlI I z 0 '"r I l5 \l I ~1_51 10 , 1 , I l11 1 ___9 j i I I , [ , 1 . . 1 I 1 1 r~n tiLLL IJJJ __ . -4] number,., (p:1r:t111cicr \;dui:s) which \viii have the dc,.ircd distrihuti,HL ! oi this case st the parameters w:rc nJ11sidcrni independent. Joint prohabilitics n,ulJ he if known. Distrihuti,,,b were selected using engineering judgement since the ncccs·;;in infmmalion from the t<..·stmg prngram 1s 1wt yet a\ailablc. Once a rand,,m li,t or ;1:nclcr values wa~ generated, they v,cn: fed into FCI IARTt. Each rand,,m cici nr p::r- arnctcrs pr,,duccd a pcrft,rmancc value. On lnmdred such comhinalit)l1S \\ere C\alu with I Cl IART pn,ducing 100 random values of solar fracliull. The complete sd of parameters used as the design ca.-:c i~ giH.'.11 in Tabk l. system described i;.. similar to the standard prohlem being used in <,ncra! The par.1me1<:rs in Lihlc ! whid1 han· ranges listed arc the si,,, parameters \aricd tvlon!e Carlo sirnuL1tion. The othc:r parameters were held ;_·pn~Iant al design conditi, ·· Figures 5 and 6 illu"tr;l!c the distributions assumed for tv,o parameters. Simil:,r (.fo,trih:- tions \Vcrc construlled for all paramct<:rs. Although these arc fo.:titious cuncs. an ;1ttcmp! was made to appro:,,imatc the actual situation. A typical set of random \alucs for parameter me s!Hrn 11 rn Table 2 along with the result solar fraction f,lr each of paramcil'rs 1-i)'llr,: 7 is ;1 di,,tr;hu!;()n curve for the sobr rraction vaiues round T;1hk 2. Note th:1! !lie \olar fract1nn appc:11:-: tu be tending toward a Gaussian distnhu- tion as Wtluld he C.\pccted. The average suiar fraction is 51"., compared to the value of 5W'.,. This rt'sult is not surprising since several of the p:iramdcr distrihutimb were strongly skL'wcd lP\\arJ degradation. The standard deviati,,n was found tu be 5.5'' ,,. Therefore, the J 2rr limits (approximately 95'\ limits for a Gaussian distribu1icn) arc 40 .-, 62" sobr fraction. These bounds will be scnsiti\C to the design, For 0 ex:1mpk, if the sy-.,1crn :s o\·crdcsigncd, then an analysis wuuld indicate a strung skcwnc\s toward the dcgLHbli,,n s;idc. Scatlcr plots were made for each varying parameter ,,olar fraction. Fit,'urC X is an i!lus!ratic~ll of the kind of results that were obtained This figure is a plut of the solar fraction I YS R'(rct). The plot shows that the solar fraction and I R'(nl arc not strongly correlated. The lack of a strong correlation fur two of the si\ par:m1eters studied indicates tha1 these parameter \ariations arc nnl dominating the rcsuih pf the stuJy. This conclusion is also true of the remaining par- amdcrs whose ,1..-;11 lc'r pi Ph were uncnrrdakd. These results do show how the variah!i of phy~,ical pa1 ,1m,:!crs c:rn afkcl the performance of a systcin. They also demonstrah: the usdulnc~s in 11s1ng the i\1untc Carlo method lo determine these dTccts. This method can now he used to initiate a well-structured !s:s!ing and validation program. Dctaiis of this 1..·ase s!udy ;is; wdl as others arc under preparation as a contract report. Page 421 ;;, l 0 60 l 0 0 0 0 i 0 I 0 0 a) 0 i S5 }- 0 0 I 8 0 I 0 I 8 ~o 0 ~ 0 ~ 0 0 0 8 0 0 0 0 7 I 0 0 0 0 0 0 ~ 0 ~ .; iI 0 0 () ~ 0 0 0 0 <( ~ I 0 t 0 40 10 ~ i "' :'!es tqn '' .JQ l_.L.----•--~-·- · -- --- ---L-~----il> .48 • Si . ;& ,60 .tA • 6:Y An :1pprndch to nwdd validation has hl'.cn presented which will rc~uit rn levels ur confidt:n,:c associ:ttcd with tile use of detailed and simplified analysis models. The cis<: study has ckrnonslr:ilcd the practicality of this approach and illustrates lht: type of rc:,tilts which can he niwcted. Given the \alidat1un methodology dL~crihcd nbme. the DOE can dnelup a ,\ell .. foundcd and dficicnl testing program which will support the validatiun uf snlar heating and cooling ;inalvsis programs. ldd11 1H'/(',fUt'n1nif Thi~ \\n1 ~ i:-. hci11g supp,)rtcd hy the l .S. D·L'p;.utincnt uf Fnc1 ~.\. l)l\ i~.inn nl' (\in:-.cr\..1tion and Slllar A1'phca11nn. Rc,c;ir,·h ,1ml Dc,cloprncnl Branch. Systems Anahsi, Prni'ram. Cn1,:rac! IM~,:.( .!),\-,.\.'<,l REFERENCES I. W1lh;im J. Kc:nnish. ,\n appr\iad1 ln the ,aiidation ,)f computer simulatiun cndcs. Systc:ms Analysis Di,·i- :;,nn. Sandia L1bnra!nri,·,. I' 0 Bu, 'iXOO, Albuqucrqu<:, N!\·1 ~;7185, Report Nn SAND 7X-04}3 !"larch l'r'i-.), ' (jc·nrgc S. Fishman ,ind l'h1hp .l. 1'..1,1at, .\fw1\11/1·1w·111 St'it"ncc 13, N,,. 7. 525 557 I :\larch 19671. T Frcc·mctn. M. \la> b:inm and S. Chandra, A comparison of four solnr system simulation programs 111 .sohing a snlar l,c,;ting prnhkm, Dept. pf l'ncrgy, 20 Massaclrnsc!ts A1e.. N.W .. \Vashingtnn. D.C. (April lum wood frame townhouse, National Bui c:;iu of Standards Report, Washington. D.C. (April 1975). , J. !bkumh, R. McFarland and S i\1oorc. S1mu!at1>ln analysis of passi~c sol,n· h,:a!ed huilding,: comparisc,n with h:,t mom rcsulls, l.ns ;\l:,n1<.1s Sc:ic:ntt!k L1bn1a1ngltrn. D.C. 20214, Lc:llcr Report (ll/7S1. Page 422 560 D. K. AlsANll cl ul. 10. Byron(". \Vinn, Richard L t·r~tun und ( 1. R ...h ,1Hht)n. V..1iidat!,)n nf ,1 cornputc·r aided design nH)1_kl for s.olar heating and c~H. . )\1 ng or bu i!di ngs. Pron·t·dintJs o( rht' i ·1-> Suni1Fcr ( 1 ,::1ru !iT Sinw!ur ion Confcn·n 15 X • (QL/COP av) and Y • 6 whenever calculated Y > 6 (3,123)(51,1)(96.1 - 29)(24). • (366.22)(277.8) otherwise: use calculated values of X and Y ,61 • l.541 SAMPLE EXAMPLE (FiTa) A I The following example illustrates the ease with c CT (.68)(51,1)(22.11) y • -.,-(Q --./C -0-P---:),- • (3 66. 22) which the solar cooling fraction can be predicted 1 av ,61 using the method discussed in this paper together with information available from other sources • l.280 [6,7]. This example considers the performance of a residential solar cooling system in Ft. Worth, Equation (15) gives a solar cooling fraction of TX for the month of July. The system parameters .5964. The detailed simulation (SHASP) gives a are: value of 0.5897, The predicted value using the 2 2 simplified method is 1% higher than the detailed A = 51.1 m (550 ft ) simulation value, C Fita = 0.68 CONCLUSION Future work on the simplified solar cooling design method would include expanding the simulation runs M = 4377 Kg (9650 lb.) to cover all the fourteen (14) representative cities for which TRW [7] has collected data. For a residence whose average daily July load is Although the differences between the predicted 366.217 MJ (347,105 Btu) the solar cooling cooling fraction and the cooling fraction obtained fraction is computed as follows: via detailed simulation are all within the al- lowable engineering errors,there are indications From Ref. 6, for Ft. Worth (32.5° N lat.) that better correlations would result by grouping 2 cities into at least two types of cooling regions. H 25.59 Mj/m Better agreement can be expected,for example,if cities like Miami, Charleston and Washington, D. C. ~= .64 are grouped into one regional design chart and cities like Pheonix and Ft. Worth into another Td = 29.0° C design chart. On going research is presently geared towards this goal, For KT• 0.64 and (0 - S) = 0. R .. .864 ACKNOWLEDGEMENT The total incident radiation is This work is supported by the U, S. Department of Energy, Systems Development Division under IC • (.864)(25.59) = 22.11 2 MJ Contract No, DE AC03-79C S 30202, T m - day From Ref. 7, there are 21 hours for which the ambient air is above 23.9° C (75° F), the room set temperature. For this 21 hour period, the chiller must provide an average cooling of 366.217 qE = 21 17.44 MJ (16 529 Btu) hr ' hr Page 427 NOMENCLATURE REFERENCES A collector area, m 2 1, "FCHART, An Interactive Program for Designing C Solar Heating Systems", University of Wisconsin, COP av average chiller COP June 1978. LIE change in storage capacity 2. "TRNSYS, A Transient Simulation Program", fc solar cooling fraction Solar Energy Laboratory, University of Wisconsin, Madison, February 1978. FR' TO, FR'U L collector parameters 3. Klein, S,A., and W.A. Beclanan, "A General T average hourly insolation on the plane Design Method for Closed-Loop Solar Energy Sys- CT of the collector - ( Btu ) tems", Solar Energy, Vol. 22, pp. 269-282, 1979. -'-"M~J __ 2 m - day fl - day 4, "SHASP, Solar Heating and Air-Conditioning Simulation Programs"• Solar Energy Proj,ects, average daily auxiliary energy Mechanical Engineering Department, University of MJ Btu Maryland, College Park, Maryland, December 1978. day (day) average space cooling load 5. "Control Strategy Studies of Solar Heating and Cooling Systems", Solar Energy Projects, average useful collected energy Mechanical Engineering Department, University of Maryland, College Park, Maryland, November 1978. evaporator capacity~; __ Me::trnc __ -{oc 're Details of the mathematical models appear in 10,000 --- further detail in reference 8. (9,480) 0 PV/T -25 -5 35 Collector 15 (-13) (23) (59) (95) SOURCE/SINK TEMPERATURE - C (F) ' U,,,t.l,l.H, y Figure 2 - Heat Pump Operating Characteris- !1 tics for Heating and Cooling ·,. ·-c:=J ·q=1----c::=J t-1"""" I (Carrier Model 50YQ030) ~--·~ L,_ __ -e] lation, ambient dry bulb temperature and wind speed data characteristic of three US locations (Washington D.C., Madison and Phoenix) are read Figure l - Combined Photovoltaic/Thermal from TMY tapes to drive the simulations. The Collector- Series Heat Pump three locations are chosen to represent a diver- Schematic sity of weather and building load patteras. Madison is characterized by high winter heating loads while Phoenix is subject to high summertime SYSTEM SIMULATIONS air conditioning loads with Washington, D.C. some- where inbetween. The performance indices used as A cor.iputer program is developed to s:i.mulate the indicators of the system electrical and thermal year-round performance of the PV/T solar collec- performance are detailed in the next section. tor-heat pump system described in the preceeding section. A detailed listing of the program and Performance Measures input variables is given in reference 8. The indices of major interest in this work are In order to evaluate the effect of system design those based on long term integrated energy quan- parameters on the long term performance, a series tities. Besides the collector electrical and of simulations are made over the period of one thermal efficiency and the heat pump COP, these year, with the design parameters being varied in include: an orderly fashion. Other variables are main- a) Thermal Solar Fraction ( fth): The thermal tained at baseline values representing state- solar fraction is an indicator of the ther- of-the-art components found in literature. The mal subsystem performance and can be defined design parameters of interest include the collec- as: tor area, flow rate, orientation and perfor- mance constants; electrical and thermal storage fth ( QLT ,_ QAUXT -WHPH)/QLT (1) size, control temperatures and location depen- dent weather and building loads. Performance where: QLT QSW + QSH (2) measures averaged over a monthly or yearly basis ·are compared. .;L~irnl.llation_ timesteJ) _of .one- Here, the effective thermal load (QLT) that hour is used in every case. Hourly inso- the system tries to satisfy is the sum of Page 432 the service water (QSW) and space heating performance. Figure 3 presents the variation of (QSH) loads. The fraction of this thermal 2 Fe with the battery ca~aci ty for 50, 75 and 100 m load not supplied by the solar thermal sub- (538, 807 and 1075 ft ) collector area systems system either by direct or heat pump heating located in Washington, D. C. Insufficient battery appears as auxiliary space heat and service capacity results in a sharp increase in the photo- water load (QAUXT) and heat pump electrical voltaic energy dumped. As the collector size goes input (WHPH). up, this increasing imbalance between array out- put and demand causes further degradation of the b) Electrical Solar Fraction (fe): The fraction electrical performance at low battery sizes. How- of the system electrical load satisfied by ever, above 250 ampere-hours any additional capac- solar (fe) is given by: ity does not result in any significant increase of Fe. These results demonstrate the need to incor- f = (QLE - QUTIL)/GLE (3) porate electrical storage capability in the sys- e tem and to optimize its size for any particular Where QUTIL is the required utility backup application, in order to best utilize the avail- power. The effective electrical load (QLE) able photovoltaic output. that the system sees is the sum of ta.1 service water and space heating auxiliary ( QAUXT) , the heat pump electrical input in the heating (WHPH) and cooling (WHPC) modes and the diver- sified building electrical load (QDIV). 0 ,5 e QLE = QAUXT + WHPH + WHPC + QDIV ( 4) j c) Net Solar Fraction (f): The single most ~ "' informative indicator of the hybrid system 0 ~ 2 ~ performance is the fraction of the total ~ 0 4 --------------- 75 rr load (QL) met by solar. Considering the ~ total system energy load as the sum of the ~ space heating, space cooling, service water and diversified load leads to defining of i f as: 0 3 f = ( QL - QUTIL) /QL (5) ~ --------------- 50 / where: QL = QSW + QSH + QSC + QDIV (6) COP C 0, 2 500 lOOC 150" d) System COP (COP): This is an indicator of 8A7T£RY CAPACJTY (Ampere--Hours) the overall syst~m energy conversion effi- ciency and is defined as the fraction of the incident collector insolation that is avail- Figure 3 - Jl.. rn1ue.l E.lectrical Sola:r Fraction (Fe) able at point of use as either electrical or vs. Battery Capacity (Washington, D.C.) thermal energy. Figures 4 and 5 show the effect of flow rate (G) and thermal loss coefficient (U1) on the electri- COP = (QL - QUTIL)/QI (7) s cal (ne) and thermal (nth) efficiencies of the collector. As expected, low values of U1 result where QI= total solar radiation incident on the collector. in higher thermal efficiencies due to reduced heat losses from the collector. But the resulting higher absorber plate temperature causes a deteri,- Results oration of the electrical output. 'l'he simulation results are summarized in the Similar collector efficiency plots showing the conclusions. Some of the more interesting effect of the (ra) product for a 1, 2, and 3- results are presented below in greater detail. cover system and the photovoltaic cell reference Although the results shown in this paper are pri- efficiency (k1) are presented in Fig. 6 and 7. marily based on simulations for Washington, D.C., nQ increases linearly with k1 as expected while those for Madison and Phoenix lead to the same n;h suffers a drop because a smaller fraction of general conclusions and are available in reference the incident energy is available for thermal con- 8. version. However, increasing the transmittance of the covers or the absorptance of the photovoltaic In order to generate data on sizing of the stor- cells improves both ne and nth, because a larger age components, a series of simulations are made fraction of the incident solar radiation is avail- to study the sensitivity of the system perfor- able for conversion. But the resulting increase mance to changes in the electrical and thermal in the average collector temperature would tend to storage capacity. The direct effect of changing offset some of this improvement. These results battery capacity is on the electrical subsystem indicate that single-glazed low performance flat Page 433 0 4 plate collectors of inexpensive design coupled with efficient photovoltaic modules would serve ~ u the purpose of achieving efficient photovoltaic conversion while providing reasonable thermal out- < put. I 0 3 I Cover 0 .10 ~ 8 -----------===-=-=-=-=-=-= 23 Coovvee.r-ss 0 2 0 .04 0 08 0 12 0 16 PHOTOVOLTAIC CELL REFERENCE EFFICIENCY .Figure 7 - Effect of'"""TrarismI ttance-Absorptance Product and Photovoltaic Cell Reference Efficiency on Collector Thermal Efficiency 0 20 40 60 (0) (0 98) ( 1 96) (2 94) Figure 8 presents the energy savings per unit collector area achieved by installing the PV/T THER~.AL LOSS COEFFICIENT - KJ/hr-m2-C (8to/hr-·ft2-F) collector system in Washington, D.C., Madison of Phoenix. The maximum energy savings are attained Figure 4 -:_ -Effect Fluid Flowrate (G) and in Madison over most of the range of collector Thermal Loss Coefficient (UL) on areas of practical interest. Madison is charac- the Collector Electrical Efficiency terized by high thermal loads and results in max- imum utilization of the PV/T collector output. In the case of Phoenix which is subject to lower 0 5 thermal loads all year round, the system tends to be thermally oversized most of the time. This > uz results in elevated storage temperatures and lower w u collector efficiencies except at very small callee-· ~ tor areas where there is more of a balance between w 0 3 supply and demand. I ~ -a ~ C u "" 2.5 :: (0 22) 8 ~ 0 I i ·---Phoe:·x 0 20 40 eO -------· W~sri.-:;~~ ... (0) (0 98) (1 96) (2 94) --- MaC·sor THERMAL LOSS COEFFICIENT - KJ/hr-m2-c(Bto/hr··ft2-F) 2.0 (0 18) Figure 5 - Effect of Fluid Flowrate (G) and Thermal Loss Coefficient (UL) on the Collector Thermal Efficiency 1.5 (0.13) 0 10 > u 1.0 z w (0 09) u ~ ~ w ~ < u 0 05 -a u 0 5 80 120 a 0 40 (0) (430 l) (860 2) (129, J: ~ COLLECTOR AREA .. m2 ( ft2) 0 04 0 08 0 12 e 16 PHOTOVOLTAIC CELL REFERENCE EFFICIENCY Figure 8 - Comparison of Annual Energy savings Figure 6 Effect of ~ransmittance-Absorptance per Unit Collector Area for Madison, Product and Photovoltaic Cell Washington and Phoenix Reference Efficiency on Collector Electr~cal Efficiency Page 434 CONCLUSIONS REFERENCES 1) The electrical and thermal storage capacities 1. L. W. Florschuetz, "Eictension of the Hottel- as well as the collector flowrate are found to Whillier-Bliss Model to the Analysis of Cor.1- have only a small effect on the long term per- bined Photovoltaic/Thermal F.lat Plate Collec- formance of the PV/T col.lector-heat pump sys- tors", Sharing the Sun Joint Conference, tem over a wide range of values of practical Vol. 6, Winnipeg (1979). interest. However, very small values of the battery capacity, therma.l storage size and 2. D.L. Evans, et al., "Combined Photovoltaic/ collector flowrate below 250 ampere-hours, 100 kg/m2 (20.5 kg/rt 2 ) and 50 kg/hr m2 Thermal System Studies", SA..l'ID78-7031, Arizona State University, August 1978. (10.3 lb/hr rt2) respectively,tend to pena- .lize long term performance. 3. S.D. Hendrie, "Eva.luation of Combined Photo- voltaic/Thermal Collectors", 1979 ISES Inter- 2) From point of view of maximizing photovoltaic national Congress, At.lanta, May 1979 output,expensive collector thermal designs with low heat loss coefficients and employing 4. E.C. Kern, M.C. Russel, "Hybrid Photovoltaic/ multiple glazings are not justified. Therma.l Solar Energy Systems", MIT, Linco.ln Laboratory Report No. C00-4577-1, March 1978 3) A minimum storage temperature of 30°c (86°F) for direct space heating minimizes auxiliary 5. Westinghouse Corporation, "Conceptual Design energy usage. and System Ana.lysis of' Photovoltaic Systems", AL0-2744-13, May 1977. 4) Combined PV/T col.lector systems have the potential for achieving maximum energy savings 6. General E.lectric Company, "Conceptua.l Design in cold climates characterized by high ther- and System Analysis of Photovoltaic Systems", mal .loads. AL0-3686-14, March 1977. 5) The long term system performance is found to 7. Bechtel Corporation, "Energy Storage and Power drop off rapidly at small collector areas Conditioning Aspects of Photovoltaic Solar because 'starvation' of the heat pump evap- Power Systems", Volume 1, C00/2748-75/TI, orator results in poor utilization of the October 1975. series heat pump capability. Large collector areas however lead to elevated storage temp- 8. S.R. Venkateswaran, "Simulation Study of' erature and degraded collector efficiencies, Combined Photovoltaic/Thermal Solar Heating because the system tends to be thermally over- and Cooling Systems, MS Thesis, Mechanica.l sized a lot of the time. The optimum system Engineering Department, University of Mary- size can be determined by examining system land, College Park, November 1979. costs, fue.l savings and other economic fac- tors. ACKNOWLEDGEMENT This work is supported by the Department of Energy, Division of Conservation and Solar Applications and the Computer Science Center of the Univer- sity of Maryland. NOMENCLATURE f - Monthly solar fraction F - Annual solar fraction G - Collector fluid flowrate per unit area (kg/hr-m2 ) k1- Photovoltaic cell reference efficiency UL- Collector thermal loss coefficient (KJ/hr-m2- 0 c) ri - Collector efficiency ( ra. )- Collector transmittance - absorptance product Subscripts e - Electrical th - Thermal Page 435 A DESIGN PROCEDURE FOR COMBINED PHOTOVOLTAIC/THERMAL SOLAR COLLECTOR - HEAT PUMP SYSTEMS S.R. Venkateswaran, Research Assistant D.K. Anand, Professor Solar Energy Projects Department of Mechanical Engineering University of Maryl and College Park, Ma~yland 20742 ABSTRACT This paper presents a general design proce- with the thermal storage as the evaporator dure for combined photovoltaic/thermal (PV/T) heat source. Auxiliary heat is provided solar collector - series heat pump systems by induct resistance coils. The cooling applied to heating and cooling of buildings. load is met.entirely by the heat pump Analysis of the PV/T solar collector system rejecting heat to the ambient. on a long term basis indicates that the electrical and thermal performance can be The photovoltaic subsystem supplies the heat correlated to four dimensionless parameters. pump electrical input, space heating and These account for the PV/T collector perfor- service water auxiliary loads and the diver- mance characteristics, building energy loads, sified building electrical demand associated average ambient temperature, insolation and with lighting and appliances. A lead acid heat pump performance. battery module supplies electrical storage capability. The power conditioning equip- A detailed computer simulation program ment consists of a regulator that controls incorporating performance models for the the charging rates of the battery and a PV/T collector, electrical and thermal stor- DC/AC power inverter operating in parallel age, heat pump and building load is used to with the utility. 1 Details of the system carry out simulations of tiie year-round description and mathematical models appear system performance under varying weather in references l, 2. conditions and locations. The detailed simulation results are used to correlate the Simulations [l] of year-round performance monthly electrical and thermal solar frac- were carried out to gauge the sensitivity tions to the dimensionless design parameters. of the long term performance to the various Long term energy usage estimates based on system design parameters. Several design these design correlations are found to agree variables including the electrical and with simulation predictions to within three thermal storage size and the collector flow percent. These charts therefore constitute rate were found to have onlv a small effect a convenient method to design and/or evaluate on sys tern performance for a- ~Ii de ranoe of system performance at reduced cost and data values of practical interest. Optiwu~ handling. ranges were established to size these com- ponents. Other parameters includinq the collector area, performance, weather and 1. INTRODUCTION building loads were found to significantly effect performance over the practical range In an earlier paper [l], a computer simula- and should be considered in any design tion model capable of estimating the long procedure. term performance of a combined PV/T collector- heat pump system was presented. The The detailed simulation model is primarily system is designed to supply the space designed for use as a research tool, to heating and cooling, service hot water aod estimate the dynamic performance of the miscellaneous electrical loads of a 112mL solar energy system for parametric, control all-electric residential building. A studies, etc. For the use of architects schematic of the system is shown in Fig. 1. and solar engineers who are concerned with the design of small buildings of a standard The primary solar energy collection function configuration, it becomes necessary to is accomplished by a combined PV/T collector develop a simplified methodology to estimate consisting of a liquid cooled flat plate the year round performance based on easy thermal collector with silicon photovoltaic to use design charts and readily available cells affixed on its absorber surface. A data. heat pump supplies the space heating demand Page 436 The approach adopted in this work is to use where the average heating CoPh of the series the results from detailed simulations to heat pump is expressed in terms of the develop generalized performance charts that average storage temperature, Ts would essentially correlate the monthly electrical and thermal solar fractions (2) achieved by the PV/T collector system to dimensionless groups that account for the system design parameters, average weather and building loads. This approach has been r=lftT·dt (3) S t o S used in the past to develop the f-chart method [3] for direct solar heating system Neglecting storage and pioing thermal losses design and at the University of Maryland for as well as the internal energy change of design of solar absorption cooling systems the storage tank over the period of 1 month [4]. In the case of the PV/T collector in comparison to the useful heat output of system considered in this work, the inclu- the collector yields sion of a heat pump for space heating and cooling and the photovoltaic subsystem (4) introduces additional variables and consid- erations of both the electrical and thermal A relationship suggested by Florschuetz· [5] performances that complicates the development to estimate the useful thermal output of a of a design method. PV/T collector is used here on a long term basis with the average storage temperature. The design correlations developed in this Along with Eqs, 1, 2 and 4 this yields work are applicable to both the heating and cooling modes but are restricted to liquid f = A/R FcT(a-n;s> - ul/ra)] (5) based collector systems only. When combined with system costs and other economic indices th Qsw + Qsh (1-1/(ah+shTs)] for the location in question, these charts Carrying out the algebraic simplification can be used to economically size the PV/T and neglecting remainder terms gives, collector designs. (6) 2. CORRELATION OF SYSTEM PERFORMANCE The most useful measure of long term perfor- mance from the point of view of design is the fraction (f) of the total building energy load supplied by solar energy. The .elec- trical (fe) and thermal (fthl solar fractions are measures of the electrical and thermal subsystem performance. The approach adopted here is to individually estimate the monthly values of fth and fe and combine them with the corresponding thermal and electrical + ah UL(ah-1)] + a~ UL Qsw/ loads to obtain the net solar fraction, f. 2 (8) [ Qsh \d h- l) + Qsw ah] An analysis of the system energy balance equations suggests that the monthly fth and fe can be correlated to four dimensionless The total energy load (L) that the system groups inco.rporating average system, weather tries to satisfy either electrically or and load parameters. Initial attempts to thermally consists of include the direct space heating option from storage were dropped because the therma 1 performance correlations were found to be unreliable. The relative magnitude of the space heating load supolied directly and where by the heat pump are a strong function of the weather and load distribution and cannot ( 10) be adequately correlated to the average COPC = a + S Ta C C values. The fraction of this total load that cannot 2.1 Derivation of Nondimensional Design be satisfied thermally appear: as the ·--··Parameters electrical subsystem load, Le The monthly average load (Lth) that the ( 11) thermal subsystem tries to satisfy is: Lth = Qsw + Qsh (1-1/COPh) (1) Page 437 The photovoltaic energy available to satisfy Leis the useful electrical output of the (17) PV/T collector, neglecting battery and dumping losses as well as the change in battery stored energy over a month. A relation suggested by Florschuetz [5] _is used on a long term basis to estimate Que of the PV/T collector. 2.2 Development of Design Charts Que. ne _ [ f = --- = A I ~ Hour-by-hour simulations of the PV/T e Le cc T as collector-heat pump system year round performance are made using a detailed computer simulation model [2] and TMY weather data for Washington, D.C., Madison, and Phoenix. Th thermal storage size is held at 100 kg/m 2 with a battery of 250 amp-hours capacity and fixed building and heat pump characteristics [2]. The other Nondimensionalizing Eq. 12 [3] gives fe as collector and system parameters are varied over a wide range of practical values listed f = X - Y (f -f )/(T ef-fa) (13) in Table l. A least squares polynomial e e e s a r. curve fit is used to correlate the monthly fth and fe values to the dimensionless where groups Xth, Yth and Xe, Ye, respectively. The correlation is found to be good in both the cases with correlation coefficients in the range of 0.95. 2 K/3 re T(cx-nas) (1-FR)] (14) fth = 0.1666 + O.l022·Xth - 0.00934·Xth UL + 0.09072-Yth - 0.003887;Yth2 (18) f e = - 0.0134 + l.072l·X e - 0.2623·X 2 e - 0.7716·Ye + l.0926·Ye2 (19) Eqs. 18 and 19 are plotted in Figures 2 and 3 as constant fth and fe curves. The design procedure adopted is to e~timate fth for each month from Fig. 2. Ts, COPh lheating Eqs. 6 and 13 for fth and f~ cannot be months only), Lth, Land Le are calculated evaluated explicitly as Ts 1s a complicated in that order from Eqs. 6, 2, l, 9 and 11 function of the load, insolation and ambient respectively. The net solar fraction is temperature. However if hour-by-hour estimated from Eq. 17. computer simulation is used to evaluate the monthly integral of the storage temperature, 3. VALIDATION OF DESIGN CORRELATIONS the resulting ftb and fe may be correlated using the dimensionless parameters Xth• Yth and Xe, Ye respectively. In order to demonstrate the validity of the design correlations, they are applied to five 'That fraction of the total load not supplied test sy tems located in Washington, D.C. by the solar thermal or electrical subsystems (Ac=50m 2), Madison (Ac=4om2), Phoenix is supplied by auxiliary power (QAux) from (Ac=30m2), Fort Worth (30m2) a~d Miami (40m2). the utility. Writing an energy balance for Monthly values of fth• fe and fare generated the entire system with the assumptions made from detailed simulations and he design earlier, method and compared for a 112m 2single-family residence with a thermal storage size of L = Que·ne + Qut + QAUX (16) 100 kg/m2, 250 amp-hours battery capacity and a standard 3-ton heat pump. Dividing by Land rewriting in terms of Le, Lth• fth• and fe, Table 2 presents comparisons of the monthly net solar fraction, f for the five test · ---~- _ tfue· ne ( ~) Qut (!:.th.) cases. The design method and si~1ulation f - l - QAux1L - L L + L L estimates are found to be in good agreement th with maximum observed differences of around 0.05, corresponding to an error of five Page 438 percent of the total load. A study of the on these correlations agree with detailed monthly ftb and fe comparisons presented simulation predictions to within three per- in Ref. 2 indicates that the electrical cent for all locations and system sizes fractions in general correlate better (to considered . .w ithin ±Q.05) than the thermal fractions (!0.10). This can be attributed to the 2) The design fth and f charts are presence of the heat pump operating at applicable without modif,cation to both varying source temperatures and COP's that heating and cooling months as long as accurate complicates the estimation of the average estimates of the corresponding space loads thermal performance. The more reliable are available. Attempts to include the fe correlations lead to consistantly more direct heating from storage option in the accurate energy usage estimates for the design procedure have not been successful summer months, when the load is predominantly and further work is required on this problem. electrical. This can be seen from Table 2. 3) The correlations for the electrical per- The purpose behind using this design method fonnance are in general more reliable than is however not to provide an accurate those for the thermal performance. This can estimation of system performance for any be attributed to the problem of modeling the particular month but rather for the year average heat pump performance especi a 11 y average or long term. Table 3 compares the during the fringe heating months. annual percent solar and auxiliary energy usage for the five cities. Th~ design method is found to be in good general agree- 5. ACKNOWLEDGEMENT ment with the simulation results in all the cases with a maximum error of 2.7 percent in This work is supported by the Department of the annual auxiliary energy estimate. Since Energy, Division of Conservation and Solar the correlations are based on simulations Applications and the Computer Science Center for Washington, Madison and Phoenix, the of the University of Maryl and. good comparisons for Miami and Fort Worth help to demostrate their location indepen- dence. 6. NOMENCLATURE Ac - Collector Area (m2) 4. CONCLUSIONS f - Monthly solar fraction Tc - Average Collector Insolation (KJ/day·m2) 1) The long term electrical and thennal K1, K2, K3 - Photovoltaic Cell Performance performance of a PV/T collector-heat pump Constants (Ref. 2). sys tern can be corre 1a ted to four dimension- L - Monthly average load (KJ/day) 1e ss design parameters which account for the Osw - Service Water Load (KJ/day) collector and heat pump performance charac- Osh - Space Heating Load (KJ/day) teristics and average weather and building Osc - Space Cooling Load (KJ/day) loads. Annual energy usage estimates based 0DIV - Diversified Electrical Load (KJ/day) Aux __ Heat Punp ---, PV/T Collector I ~~-- ~l~ ________._ ..___-CJ-4--1-' ~--------------- I I .,,;,I Utility .Q,,;.I, Power o• I I :>:J I o..._ __ -4.___P_T. ._.. ...~ ----1.__R'"T"'eg._ ..J~----j Inv. ~--f---jHt.Pump I l I I I ~I ---J Oiv.Elecj lead Acid I Battery I L---!Auxil. j Fig. - Combined PV/T Collector - Series Heat Pump System Schematic Page 439 Qut - Collector useful thermal output (KJ/da_y) 3) S.A. Klein, et. al., "A Design Procedure Que - Collector useful electrical output for Solar Heating S_ystems," Solar Energy, 18, (KJ/day) , pp. 113-127 (1976). Tref - Reference Temperature (loo0 c) UL - Collector Thermal Loss toefficient. 2 4) D.K. Anand, R.B. Abarcar and R.W. Allen, (KJ/m ·day 0 c) _ _ "A Simplified Solar Cooling Design Method for nas - PV Cell efficiency at le and Ta Closed Loop Systems", 1979 I SES Congress, ne - Electrical power conditioning efficiency Atlanta, May 1979. 5) L.W. Florschuetz, "Extension of the 7. REFERENCES Hottel-Whill ier-Bl iss Model to the Analysis of Combined Photovoltaic/Thermal Flat Plate 1) S .R. Venkateswaran, D.K. Anand, "Perfor- Collectors", Sharing the Sun Joint Conference, mance Studies of Combined Photovoltaic/Thermal Vol. 6, Winnipeg (1976). Solar Heating and Cooling Systems", Second SSEA Conference, San Diego, January 1980. 2) S.R. Venkateswaran, "Simulation Study of Fig. 3 - Design Chart for Estimating Electrical Combined Photovoltaic/Thermal Solar Heating Solar Fraction (\) .:· and Cooling Systems", MS Thesis, Mechanical Engineering Department, University of Mary- land, College Park, November 1979. Fig. 2 - Design Chart for Estimating Thermal Solar Fraction (fth) 12. 8 . .s:: >-..,, 4. 0.4 .4 0. • 3 8. 1o . 0. Table 1. - Range of System Parameters Used to Derive Design Charts o. 0.5 1.0 1. 5 Table 2. - Comparison of Monthly Solar Fraction (f) 0.6 ~ (ta) ~ 0.9 ------W--A-S-H-I-N-G-T-O-~-, ----M-A-D-I -S-O-~-, -----P-H-O-E-~-I-X-, ----F-O-k-TW--O-R-T-H-, ----"-IA--•-!-,- -- D,C, •l AZ TX fl 5 ~ Ac ~ 120 m2 M--O-NT-H- ----S-IM--, --D-E-S-, ----S-J-~-. --D-E-S-, ----s-1-•-. --D-E-S-, ----S-l-~-. --D-E-S-, ----s-1-•-.- -D-E-S-, 0.6 ~ F' ~ 0.9 41 JAN. • ~ .:3~~fsr :t; :~~i :~H :~~§ :m :ii? :~t~ :FI -20 ~ (t - s) ~ 20 degrees !~~: :~f2 ,4~' .~~t ,SH ,5f9 ,554 .5~9 ,47?. ,4<: -PR. .663 .697 .575 .5°2 .462 .474 .512 .544 .445 .~59 "AY ,6,4 ,62C ,Sc2 ,6"4 ,341 ,373 ,415 ,4<.~ ,3\14 ,4<2 5 ~ UL ~ 50 KJ/hr • m2 •c j~~~ :zz~ :zz; :z~; :z;J :~~~ :~ii :;~t :;;r :;~r :~~% .08 ~ Kl ~ .15 ~U • -1 ig G:. :.4iH53 .464 :§Jj :l;Z :~£~ :5~~ :;2? :~i§ :4Z~ :~~~ :~~~ ,59" ,504 ,3e9 ,375 ,406 ,4n .3aa .30: .003 ~ K ~ .007 C ~ov. ,555 ,5.,3 ,3?2 ,3~9 ,51" ,534 ,5J4 ,5?6 ,421 ,1,"7 3 DEC, ,59e ,563 ,2,- ,2~7 ,542 ,53? ,460 ,442 ,S~! ,535 • 7 ~ ne ~ 1.0 -----------------------------------------------------------------Table 3. - Comparison of Annual Percent Ms = 100 Kg/m2 Solar and Auxiliary Energy Usage BC = 250 amp-hrs CITY P'RCE~T AUXILIARY 2 SOL AR ENERGY G = 50 Kg/hr - m (GJ/YEAR) SI~, DES, SIM, DES, Tmin • 3• C wlS~l~GTO~ 5 7 ,7 52,9 56,6 56,3" UAS = 23,4 KJ/hr - •c HADJSO~ 39,9 40,5 91,9 90,0 PHOr~JX 3~,2 40,9 64,5 62,7 Fi~T~O~TH 41.7 41.7 6r.4 60.4 cc= 0.75 MI~~! 4~.g 42.1 5!.6 52.5 --------------------------------- Page 440 From the Divisions Research In Mechanical Systems The National Science Foundation Act states that the NSF posals sent for consideration by the Mechanical Systems exists "to promote the progress of science; to advance the Program are an indication ot the needs ot the research national health, prosperity, and welfare; to secure the community, and are therefore used to determine the national defense; and for other purposes." One of the budget This then becomes an effective tool for mechanical Foundation's general functions Is to initiate and support engineers to compete for a larger share of the research basic scientific research and programs to strengthen the budget Finally, the offer to review proposals is important scientific research potential and programs at all levels, In that it not only helps the reviewer keep pace with the and to appraise the impact of research upon industrial state-of-the-art of a research topic but ensures that the development and the general welfare. . program has broad-based support and that NSF funds are In recognition of our country's lagging industrial produc- being used for superior and timely research proposals. tivity, the NSF established, In 1980, the Mechanical There are four types of research proposals that the Systems Program. The primary purpose of this program is Mechanical Systems Program can support These are: to fund basic research in a variety of areas that would spur 1 Research Initiation Grants (RIG) activity and strengthen the research base as it pertains to 2 Research Equipment Industrial productivity. The program supports research in 3 Unsolicited the following areas: 4 Industry/University Cooperative (IUC). 1 Machine Dynamics-kinematics and dynamics of The RIG's are designed to provide opportunities In machines, gears, linkages, etc., robotics and manipulators, engineering research to new investigators through an vibration, mechanical control systems, and machine Engineering Research Initiation Grants program. This acoustics program is directed toward full-time engineering faculty 2 Tribology-metal defonnation and removal, members who are at the professional level and have had lubrication and friction and problems associated with no substantial research support high-speed manufacturing NSF normally provides funds for research equipment 3 Design -computer-aided design, use of micro- as part of regular research grants. But separate awards are processor technology in mechanical systems, methods of also made for specialized research equlpmenfto Improve rational and optimum design, failure analysis and reliability. the quality and scope of research at proposing institutions. Support is provided in the form of grants to academic Unsolicited proposals constitute the largest percentage of Institutions and nonprofit research institutions, as well as research awards made by the program. These proposals are Industry when teamed with academic institutions. generally made to established re~arc!wrs to pursue work As in any new program, the direction and aims of the In their chosen specialties. program depend upon the support, interest, and-most The IUC proposals require that industry share costs In Important-the input of the research community. For the the research, and are generally larger in scope and dollars purposes of the research community, the needs of this than the other three forms of award program require the follOVJ!ng: Currently the program is supporting 27 projects: six • Input on the program fonnulatlon, i.e., Is the program RIG's, three equipment grants, 17 unsolicited proposals, sufficiently focused to meet the research needs as they and one IUC. In terms of dollars, the program has pertain to industrial productivity in the mechanical committed $1.37 million this year and hopes to commit engineering area? What should be emphasized or from $1 million to $4 million during fiscal year 1980. de-emphasized? In conclusion, it should be emphasized that this program • Identification of areas of research requiring priority represents an opportunity for mechanical engineers and consideration others to obtain support for their research while making a • Convening of workshops, seminars, etc., for the contribution to an important national need, i.e., increasing discussion of specific problem areas, and perhaps for the technology base, via research, for improving industrial determining the relative importance of research needs productivity Dave K. Anand, Program Director, • Proposals In mechanical systems Mechanical Systems, National Science Foundation. • Offer to review proposals. The last two items require some comment The pro- Sponsored by the ASME Design Engineering Division. MECHANICAL ENGINEERING/ DECEMBER 1980 / 79 Page 441 WEDNESDAY, APRIL 29 SESSION 10 (continued) Interaction of a Solar Space Heating System with the Thermal Behavior of a Building C. VILMER, M. L. WARREN and D. AUSLANDER, Lawrence Berkeley Laboratory, Berkeley, CA Thermal Modeling of Multi-Room Structures A . F. EMERY, C. J. KIPPENHAN and D. R. HEERWAGEN, U. of Washington , Seattle , WA SESSION 11 9:00 am -12:00 noon Capltol 1 SOLAR COMPONENT SIMULATION Co-Chairman: J . W. ANDREWS, Brookhaven National Laboratory , Upton , NY Co-Chairman: A. CLAUSING , University of Illinois, Urbana , IL A Reliable Method for Rating Solar Collectors G. 0 . G. LOF, D. JONES, and L. E. SHAW, Solaron Cor- poration , Englewood, CO Design and Control In Tradeoffs for Rockblns In Passively Solar Heated Houses with High Solar Fractions G. VERED and A. V. SEBALD, University of California , San Diego , La Jolla , CA Transient Simulation of Absorption Machines .,,,-,r: , D. K. ANAND, R. W. ALLEN and B. KUMAR, University of Maryland , College Park, MD Ground Coupled Solar Heat Pump: Analysis of Four Options J . W. ANDREWS, Brookhaven National Laboratory , Upton , NY Optimum Operating Conditions of Absorption Refrigeration Systems for Flat-Plate Collector Tem- peratures G. S. KOCHHAR and S. SATCUNATHAN , U. West Indies - St . Augustine , Trindad , WEST INDIES SESSION 12 ROUNDTABLE 12:00 noon · 2:00 pm Adelphi THE SOLAR INDUSTRY IN THE UNITED STATES: ITS. STATUS AND PROSPECTS Speaker: DR. JOHN A. CLARK Professor University of Michigan Ann Arbor, Ml 13 Page 442 Transient Simulation of Absorption Machines D.K.Anand Professor R. W.All en Professor B.Kumar Research Assistant Mechanical Engineering Department University of Maryland College Park, MD ABSTRACT Specific enthalpy of strong solution This paper presents a model for a water-cooled h Boiling heat-transfer coefficient V Lithium-Bromide/water absorption chiller and predicts h Specific enthalpy of weak solution its transient response both during the start-up phase w and during the shut-off period. The simulation model ifg Enthalpy of liquid-vapor conversion incorporates such influencing factors as the thermo- k Thermal conductivity dynamic properties of the working fluid, the kf Thermal conductivity at film temperature absorbent, the heat-transfer config~ration of differ- ent components of the chiller and related physical L Vertical length of condensate film data. The time constants of different components Mg en Lumped mass for generator solution are controlled by a set of key parameters that have Msoln Generator solution mass been identified in this study. The results show a variable but at times significant amount of time Ms ump Mass of sump solution delay before the chiller capacity gets close to its Mass of heat transfer wall in generator steady-state value. The model is intended to pro- ~w vide an insight into the mechanism of build-up to mb,\', Mass of condensate film steady-state performance. By recognizing the sig- ID Condensing water mass flow rate nificant factors contributing to transient degradation, .cond steps can be taken to reduce such degradation. The m Chilled water mass flow rate CW evaluation of the residual capacity in the shut-off m Vapor evaporation rate period will yield more realistic estimates of chiller e COP for a chiller satisfying dynamic space cooling ~w Hot water mass flow rate load. Condensate boundary layer bulk flow rate 1'.1L m Refrigerant vapor release rate NOMENCLATURE r ID Strong solution mass flow rate s A Heat exchanger surface area m Weak solution mass flow rate At Surface area for generator tubes ,w m Mass flow rate of wetting of evaporation cf Specific heat at film temperature wet tubes cP Specific heat at constant pressure for chilled pab Absorber pressure cw water q Heat exchange per unit refrigerant mass Csoln Thermal capacity of generator solution qE Heat exchange per unit refrigerant mass in Heat-transfer wall thermal capacitance evaporator CTW ql Heat flux from hot water into generator d Outside tube diameter tube wall 0 Acceleration due to gravity q2 Heat flux from generator tube wall to g solution h Specific enthalpy h. Inside heat-transfer coefficient R Outer radius of condenser tube l. T Temperature h Outside heat-transfer coefficient Tamb Ambient temperature 0 239 Page 443 Tchwi Chilled water inlet temperature each other and when connected together to form a com- plete chiller. Tconwi Cooling water inlet temperature (T ) . Initial generator solution temperature COMPONENT MODELING gen 1. Thwi Hot water inlet temperature A lithium-bromide/water absorption machine con- T Alternative notation for chilled water sisting of a generator, a condenser, an evaporator, h1 inlet temperature an absorber, a pump, and a solution heat exchanger T Evaporator saturation temperature interposed between the absorber and the generator is s shown in Figure 1. Heat exchanger components of such (T ) . Initial sump temperature sump J. a machine are usually manufactured in the shell-and- Generator solution temperature tube configuration. Large absorption machines are equipped with spray headers in the absorber and evap- T Wall temperature w orator components, whereas residential-sized units u Overall heat-transfer coefficient are usually equipped with drip headers in the absorber UA Overall conductance and evaporator components. One intermediate-sized xinit Initial concentration in sump and generator commercial machine utilizes a drip header in the generator so as to provide liquid-film boiling instead X Concentration at absorber outlet 0 of pool boiling of the solution. The present transient Concentration of the strong solution modeling effort is based on a residential machine with a pool boiling generator and drip headers in the Volume expansion coefficient for the fluid absorber and evaporator components. Film thickness Average film thickness Wall thickness water flows through the tubes of the pool Critical value of average film thickness boiling generator, Figure 2, heating the generator Instantaneous temperature-drop across film solution. Solution heating in the first phase takes Dynamic viscosity at film temperature place by natural convection modeled by the tube-to- Kinematic viscosity of fluid solution heat transfer coefficient General notation for density Fluid density Vapor density The first phase ends when the solution reaches its Surface tension General notation for time and notation for saturation temperature and is followed by a second fluid-fluid shear stress phase in which boiling takes place. The tube-to-solution boiling heat-transfer coefficient was modeled Time-constant associated with system effects to follow the logarithmic relationship between the tube wall and the vapor temperature, INTRODUCTION (2) Computer simulation of a solar-powered absorp- tion air conditioning system requires modeling of the which is valid for the degree of superheat encountered. absorption chiller and, since the space cooling load In both phases, the governing equations for heat trans- changes with time, inclusion of the transient charac- fer between the hot water and the tube wall, and teristic of the chiller is important. Modeling of between the tube wall and the solution are, respec- the dynamic performance of a water-cooled chiller, tively, based on manufacturer's data, has been empirically carried out and incorporated into the TRNSYS program (T-T) ( 3) [1]. Experimentally, a thermally activated hardware w ) ( :~) simulator, developed at the Brookhaven National Lab- atory [2, 3], has been used to determine the steady state and transient start up and "spin-down" per- (T -T ) ~ ( l_ + 6x ) ( ~ ) (4) formance characteristics of a residential-sized water w sol h 2k At 0 cooled chiller. Results, in the form of COP and where the hot water side heat transfer coefficient for capacity versus time, show an essentially exponential type of behavior. Other experiments carried out at the insides of the tubes were calculated on the basis of a typical water flow rate of 5-10 ft/sec. The co- the Arizona State University [4] system test facility have determined the transient performance of a LiBr- efficient h in Eq. 4 applies in the first phase and is replaced0 by h in the boiling phase. Thermal H2o absorption chiller, The results, reported in terms of a set of computer algorithms, express the capacitance is m½deled for the heat exchanger tube time to steady-state performance as a linear function wall on the one hand and both the well-mixed of the steady-state water supply temperatures. These solution and the generator shell on the other hand. experiments revealed that the transi.ent characteristics Thus the rates of temperature rise of the tube wall of external heat exchangers can affect the test-stand and the combined solution and shell are governed by results for a given chiller. the respective equations, The present study concerns the modeling of the transient behavior of a chiller during the start-up ( (5) and shut-down periods and the predicted transient behavior during these periods. A set of key parameters are identified that directly affect the time constants of individual chiller components when isolated from 240 Page 444 follo1:7ing function of the incoming refrigerant flow dT ~ + (~ m rate m ' Cs oln · h - h )/A (6) r dT s s w w t -BT where the mass of the solution in the generator re- (11) mains essentially constant. The absence of a x-e -ST transient equation for the hot water side of the generator is due to the fact that analysis and ex- perience have shown this transient process to be where a m .C ( T (x-1) extremely fast and well approximated by steady state cw pew hl heat transfer relations in the present context. up of the condenser, Figure 3, also may be into two phases. In the first phase, the condensate film builds on the tubes until the film has grown to a thickness at which drops form and are released. In the second phase, the inside surface of the shell is wetted and the hot well and operation of the absorber, Figure the U-tube connected to it fills. 5, occurs in three phases when the entire machine For heat-transfer analysis, the tube wall surface is considered. In the first phase, generator boil- was approximated by a vertical wall of height 2.5 ing has not started, thus the temperature of the times the tube diameter and when the transient mass absorbent solution dripping onto the absorber tubing balance on the liquid film, starts to rise as the generator solution warms up. In the second phase boiling commences in the generator, d~.Q, + and the entering absorbent solution concentration mr ~ ~ mL (7) becomes higher as its mass flow rate drops a small amount. In the third phase dripping on to the evap- was incorporated into Nusselt's steady state film orator tubes commences and evaporated water vapor condensation model, the governing equation for the passes over to the absorber. Because of the absorp- film temperature difference across the film was found tion of water vapor, the average absorber solution to be concentration drops and the average temperature in the absorber rises as heat m (8) r - (~ + (12) s where 54 C L5/4 .p 1 is released due to absorption. = J?.~ C3 L3/4 MODELING OF THE COMPLETE CHILLER 3V 1 ' The water-cooled absorption chiller transient The transient liquid drop model considered the model links the individual component models to- growing weight of the liquid film on a tube to be balanced by the vertical component of viscous drag gether, with certain si.mplifications. Results from the simulation of isolated components of a chiller, for from the wall and the force due to the surface tension example, show that the time constant of the condenser of the fluid. Stability analysis yielded the film release thickness condensate film growth and the time constant of the absorber are small compared to the other components. Therefore their models were replaced by quasi-steady b. (9) models in forming the overall chiller model. er Table 1 presents a list of independent vari- ables appearing in the model. These variables fall at which level of growth the film drains off the tube in three categories and a new film starts to form. 1. Initial conditions 2. Cycle variables 3. Machine configuration. evaporator start-up, drops of liquid Initial conditions include the initial solution tem- refrigerant fi.rst wet the top-most tube until the film peratures in the generator and sump, the ambient thickness on the top-most tube approaches the equip- temperature and the initial concentrati.on of the librium film thickness whereupon drops fall from the generator and sump solutions. The initial concen- top-most tube to the next row of tubes below, Figure 4. tration was assumed to be uniform. At the start of a Because this process continues until all the tubes chiller simulation run, the solution pump was started are wet, a variable area evaporator model was used. when heating of the generator solution was initiated. From a consideration of film growth, Cycle variables are the steady-state inlet temperature and mass flow rate of the external water (10) supplied to each of the components, the steady-state conductance or effectiveness for each of the heat- When this relation was introduced into an NTU relation- exchanger components and the pumping rate of the ship, and rearranged and integrated, the resulting weak solution. transient cooling capacity was found to be the In the analysis of the complete chiller, the variables depending upon machine configuration were 241 Page 445 the solution masses for generator and sump, the mass the chilled water are considered to come to and of condensate required in the condenser before the remain at - constant levels. The cooling capacity flash chamber overflowed and the steady-state refrig- results shown in Figure 7 are based on the selected erant film thickness on the evaporator tubes. The respective hot water cooling water and chilled water evaporator film thickness was calculated from the temperatures 210/85/60 °F (100/30/16 °c) and the relationship derived earlier for horizontal tubes and respective mass flow rates of 5500/6000/3600 lb/hr checked for the correctness of the associated heat (0.7/0.8/0.5 kg/s). ln Figure 7, the evaporator film transfer coefficient. For results presented in this thickness is used as a parameter. A similar plot, study, manufacturer's data were used as a guide in Figure 8 is obtained if the parameter is the surface estimating the variables that depend upon machine area of the evaporator. Typical values of film thick- configuration. When such data were not readily nesses of 0.01 to 0,03 inch (0.03 to 0.08 cm) and available, they were acquired from D. O. E. reports typical values of evaporator areas cf 10 to 30 ft 2 and by private communication. (1 to 3 m2) were used. The 4.5 minute delay in the production of cool- RESULTS FOR ISOLATED COMPONENTS ing capacity in Figures 7 and 8 was due to the delay in the vapor production by the generator followed by a The results obtained for the transient per- second delay as condensate built up on the condenser formance of isolated components of a 3-ton (10.55 kW) tube, in the shell, and in the hot well and U-tube, chiller are presented in this section. Start-up and The major portion of the 4.5 minute delay occurred "spin-down" performance are both included, The not a,, a result of heat transfer delay but as a result initial conditions, as well as the selected values of the accumulation of 2.5 lb (1 kg) of condensate of different parameters, are shown in Table 2, which (see ~,Q,' Table 2) at these locations. When this table includes values appliable to the model of the mass accumulation was satisfied, dripping commenced complete chiller. in the evaporator. For the generator, a typical of area to Following the start of dripping in the evapo- solution mass ratio, was found to be O. to 2.0 ft2/lb r~tor, the transient response was found to be quite (0.1 to 0.5 m2/kg) and the typical range o[ overall s~nsltive to the film thickness. The thicker the heat transfer coefficients for the natural convection 2 film, the more time it took to reach the steady-state. phase was found to be 100 to 200 Btu/ft °Fhr (570 to Por the range of film thickness covered, 1140 W/m2 OC). For these ranges, simulation results to a range of typical commercial film heat showed isolated generator transient time constant to coefficients, the time taken to reach 90% of steady- vary from 20 sec to 100 sec, approximately, Similarly state capacity ranged from 6 to 30 minutes. Figure 9 it was found that the time taken to reach steady-state shows the variation in the COP of the isolated chiller in an isolated condenser varied from 10 to 30 seconds, with time. The conditions are the same as described On the other hand, the transient response of an for Figure 7 and the nature of the COP response is isolated evaporator was found to be slower, Theim- posed isolated conditions on the evaporator were identical to the nature of the capacity response. In order to make the data points compatible for constant temperature for chilled water inlet, a con- comparison with hardware simulation results, the stant rate of liquid refrigerant flow into the chiller capacity values of The Brookhaven National evaporator, and an overall heat transfer coefficient Laboratory (BNL), [2, 3] data were normalized to a ranging from 100 to 200 Btu/ft 2hr °F (570 to 1140 W/m2c) for typical values of film thicknesses of 0.02 to 0.04 steady-state capacity of 3 tons, which is the steady- state chiller capacity for simulation results. More inches (O .OS to O .10 cm), The transient chilling importantly, the instant at which evaporator dripping effect of the evaporator, calculated by determining the instantaneous wetted tube area, was found to be commences was obtained from the BNL data by joining the data points by a smooth curve and back-extrapo- sensitive to the film-thickness as shown in Figure 6 the left hand side to zero capacity. The where the time taken to reach 90% of steady-state instant obtained from the BNL was shifted to match capacity is seen to vary from 5 to 20 minutes for the the instant at which evaporator dripping commenced range covered in the figure. in the present model. The latter instant is a Since the solution is pumped, the time taken function of the selected generator tube-surface area by the gravity flaw of strong solution to pass over to solut:ion mass ratio and quantity of liquid the tube bank is small. The performance of the required to fill up condenser hot-well and U-tube absorber is therefore analyzed in a quasi-steady which was unknown for the BNL machine, The predicted state manner using the rate of vapor absorptio~ as the trend of capacity and COP following the onset of independent variable. The quasi-steady characteristics evaporator dripping compares favorably with the BNL are. obtained for constant inlet water temperature, results as shown in Fi.gores 10 and 11. constant solution mass flow rate at inlet and a con- The BNL results showed some overshoot in capac- stant concentration of the solution at inlet. As ity and COP during start up. This overshoot, earlier would be expected, it is found that as the vapor ab- observed by Froeming et al [S], and later discussed sorption rate increases, the outlet concentration by Guertin and Wood [4] has been attributed to system goes down and tends to steady-state sump concen- effects. While a detailed comparison with data from tration, while the outlet temperature and the heat Guertin and Wood [4] was not carried out in this absorption rates rise from a low initial value to study, it should be mentione.d that when external heat their steady state values. exchanger effects were introduced into the present model by using an exponential for the returning (inlet) RESULTS FOR A COMPLETE CHILLER cooling water inlet temperature rise, overshoot was Results for transient cooling capacity of a predicted, The predicted overshoot, shown in Figure 12, is followed by a gradual decline to steady-state value. complete chiller isolated from the influence of the Figure 13 shows a plot of spin-down character- time constants of system heat exchangers and system :isti.cs for an isolated chiller. The parameter here piping is shown in Figures 7 and 8. When the chiller is assumed to be isolated in this respect, the inlet is the evaporator film thickness. In the spin-down temperatures for the hot water, cooling water and mode of operation, when the bot-water supply is 242 Page 446 turned off, the rest of the chiller components are operated normally. As expected, the results show REFERENCES that more residual cooling capacity is obtained for a thicker film (O .03 inch) than for a thin film [1] Blinn, J.C., Mitchell, J.W. and Duffie, J.A. "Modeling of Transient Performance of Residential' (O .01). A favorable comparison is also shown between Solar Absorption Air Conditioning System," Pro- the predicted and BNL [ 3, 4] expe.rimental spin-down capacity trends. ceedings of the 1973 International Solar Energy Congress, May, 1979. CONCLUSIONS [2] Auh, P. C., "Deve.lopment of Hardware Simulators On the basis of the results obtained, it was for Tests of Solar Cooling/Heating Subsystems and found that the transient response of the isolated Systems," Phase I. Residential Subsystem Hardware Simulator and Steady State Simulation, Brookhaven chiller is mainly influenced by three factors: 1. The natural convection time to heat up National Laboratory, September, 1979. the generator solution to boiling temperature. This is directly controlled by the ratio of generator [3] Auh, P.C., "Development of Hardware Simulators for Tests of Solar Cooling/Heating Subsystems and tubing surface area to solution mass ratio such that Systems," Phase II. Unsteady State Hardware for a range from 0.5 to 2.0 ft2/lb (0.1 to 0.5 m2/kg) and a hot water inlet temperature range of 200 to 210°p Simulation of Residential Absorption Chiller, Brook- (93 to 99 °c),the predicted time changes from haven National Laboratory, September, 1979. 20 sec to a few minutes. 2. The time required to fill up the hot-well [4] Guertin, ,J.A. and Wood, B.D., "Transient Effects under the condenser tubing. For a well volume on the Performance of a Residential Solar Absorption that is 3 inches on a side, this is of the order of Chiller." Proceedings of the 1980 Annual 5 minutes. Meeting of AS/ISES, Phoenix, Arizona, pg. 186. 3. The building-up of the liquid film on the wetted area of the evaporator tubes. For a film Froerruning, J., Wood, B. D, and Guertin, J., ASHRAE thickness of 0.01 to 0.03 inch (0,03 to 0.08 c:m) and a Transactions, 1979, pp. 777-786. constant temperature at chilled water inlet, the predicted time to reach 90% of steady-state capac.Hy [6] Anand, D.K., Allen, R.W. and Kumar, B.J., varies from 6 minutes to 25 minutes. "Transient Simulation of Absorption Machines," Solar The present model also gives information about Energy Projects, Mechanical Engineering, Department, the residual cooling obtained during the 'spin-down' University of Maryland, October, 1980. mode of operation. This recovery of thermal energy, stored during start up improves the value of the average COP for the system and brings it close to steady-state COP. Improvements will be more signifi- cant for smaller periods (- 15 min) of operation, which are characteristic of small residential systems meeting a dynamic load. For system-influenced chillers, it is possible for system effects to predominate. In such cases, the condenser pressure can take on the order of 5-10 minutes to balance to steady-state pressure and a hump is observed. Since it is desirable to mlnj mize the degradation of chiller performance due to transient effects during the start-up phase of chiller operation, the present model will be useful in reducing such degradation by appropriate selection of the parameters that control it. 243 Page 447 Table 1 List of Independent Variables and Parameters Component Initial Initial Steady-state External Steady-state Mass (lb) Time Pump Temper- Concen- External Water Conductance or Film Const, Rate ture tration Water Inlet Mass or Effective- Thickness Temperature Flow ness Rate (lb/hr) (Btu/hr OF) (Inch) (Sec) (lb/hr) Generator (T ) . (UA)gen Mg gen i ~w en Condenser m cond (UA)cond ~9, Evaporator rn CW (UA)evap Absorber (T corn) i mco nd (UA) abs Sump (T ) sump i Ms ump Solu- m tion w Heat- ex- changer System T Effects amb T sys (ambient tempera- ture) Tab le 2 Selected Values of Initial Conditions And Other Independent Variables (Tgen)i 70 (UA) gen 3600 Btu/°F/hr (Tsump)i 85 (UA) cond 3600 Btu/°F/hr 0.582 (UA) 3600 Btu/°F/hr xinit evap Tc r, (Thw)i 209 OF (UA) abs 3600 Btu/°F/hr OF (T chw) i 60 25 lb 2. 5 lb l-SOLUTION HEAT (Tconw) i 85 ~9, EXCMANGER 1\1w 5500 lb/hr 0film 0.010 inch m 6000 lb/hr Ms ump 40 lb cond (] m cw 3600 lb/hr Ta mb 60 F ENTHALPY 115 Btu Te: Ti Tc (ho)average TEMPERATURE .hr.°F (h) 500 Btu Fig. 1 Lithium bromide/water absorption cooling cycle v average .hr. 244 Page 448 J "'"''''"""' --1,11 Fig. 3 Condenser Fig. 2 Generator l0r1der1~ 111~/ Wd ter ou l U11lled vapor (hl~ c==::=::::::=::::;=::::;:=;::::-!.J wUtl'r 111 Liql11d retr1qe1,1111 Fig. 4 Evaporator Fig. 5 Absorber 245 Page 449 \,./\,,n,.n 1(1,w, 2)01°1,/60 ~, "\1iil'"cof11/e:rnw 11,11;,n err> on11m>1 , nn.1111111 0 0 \ 1~[11 • 1•\"F\([ !lrH 1ll,\\', •'f I r, I;; r ' ~. 11 /\I' ' r r 111111 IO Tll-'i''. fR(l'l ,TAfH llf l'R!!'PI ~l, M!.~11rrs Fig. 6 Evaporator trRnsients fer VRrying vRlues of Fig. 7 Transient chiller capacity nf an isolated overall heat-transfer coefficient chiller 1,1\.1\ / Ii l'~WI i II 'I I l lll/i<'./1 !I "1 (\O/M1&0 "1 "'111./""r,'lriw'"'!tl\.l 11/1?/li'f,J'·• 1111n1,, r,1>1" ''O.O! 1,0,0, ,\, '\','''''"Alr>I• "111"M,I ,l~I~ (\I' ff ) IO 11 ,. Tl l'T, HI HUT(~ Fig. 8 Transient chiller capacity of an isolated Fig. 9 Transient COP of an isolated chiller chiller --SlllUlA110~HE5\lll'i ( I rm;vrRTrO B~L OAT/\ Sll'M~TION nts(ll,S !\ ANl DA/A 1),\\1 lrJ',\I nn.' p1rt1 1 o.o> ;nr11 -----·-,c--- I 0,0J lf•C•f ------··-- ~ Q,0? ill[H TIM[, HINIJT[.~ rm:.11rnuns " Fig. 10 Comparison with BNL transient data Fig. 11 Comparison with BNL transient data 246 Page 450 SHUT-OFF P..ESPC~ISC: f'OR SHti'T~OFF AT 15 HINl.iTES 6 ~ EVAPORATOR fl~M"Hl!(r.fl(SS O 0.0\ !NCh FROM START-t:P SYSTfll (5(t0t10!:i) , z 0 B:-.L DATA 6 "" 0.0) rNCH .5 ,. 0,01 I~CH 10 11 14 b Trfof: F/1011 STARTA!P, M!IJUTES TIME FROM SH!.iT~·OfF' ,!'1Hll'TES Fig. 12 Effect of system transients on chiller Fig. 13 Comparison of spin-down capacity with BNL capacity data 247 Page 451 II Solar Rising The 1981 Annual Meeting and Product Exposition of the American Section of the International Solar _1_:4_0_p_.m_. _- 3_:2_o_p_.m_. _Te_c_hn_i_ca_l _se_s_sio_n_s ____ _· ,1 Energy Society, Inc. {AS/I SES) EH-7 Room 313 Active System Design Methods (2) Chair: May 26-30, 1981 R. Bennett - . The Philadelphia Civic Center D. K. Anand Simplified Cooling Design Charts Philadelphia, Pennsylvania B. Kumar R. W. Allen Page 452 SIMPLIFIED COOLING DESIGN CHARTS D. K. Anand B. Kumar R. W. Allen Solar Energy Projects Department of Mechanical Engineering University of t1aryland College Park, Md. 20742 INTRODUCTION Predictions of the performance of solar cool- results. ing systems on a long term basis have been generally obtained through the use of detail- ed simulation programs [l-7]. However, use SYSTEM DES CR I PT ION ArlD ArlAL VS IS of these programs becomes expensive for de- sign purposes; in addition, not all designers The basic solar cooling system is shown in have access to computers that can handle Fig. l. The control strategy used in the detailed simulations. An alternative simulation runs was based on a previous study approach is a simplified cooling design cor- [6] of solar cooling systems. The control relation similar to the f-chart method for strategy is such that all the useful energ.;' heating designs which was based on a direct collected by the flat plate collector is sent correlation of the results from detailed to a liquid stroage tank and stored as sensi- simulation runs. ble heat. When there is a cooling demand, the generator of the absorption chiller draws Analysis of a solar cooling system on a long- off hot water from storage, except when the term basis [8,9], has shown that the solar hot water temperature is not sufficiently cooling fraction can be correlated in terms high, in which case, auxiliary energy is used of two dimensionless parameters which incor- to fully supply the generator requirements porate the long-term average of values of the and no hot water is used. Also the storage insolation, ambient temperature, cooling load, temperature is not allowed to exceed a pre- the long-term collector parameters and the determined temperature. For this simulation chiller COP. In the present work, regional this temperature can vary from 205°F to solar cooling fraction charts have been con- 21 2 ° F. structed using the two derived dimensionless parameters . Previous analysis [P,9~ yields the expression for solar cooling fraction as Previously [8,9], the simplified cooling design chart method was validated by direct f -1F8,a Ic.Acdt -1-FRULAc(T-Tdb) .dt (l) comparison of systems performance predictions with detailed system simulation results ob- c QLtcogv QL;cogv tained via SHASP[5]. The current paper extends the previous approach in that three which, for correlation purposes, suggests geographical regions are considered although the following two dimensionless parameters only one region is reported here. Within the regions, the selection of cities, whose x = FRUL.Ac(Tref-Td)/(OL/COPav) ( 2) weather data were used in the simulation runs, was based on a climatic classification for y FRrn HT"Ac/(OL/COP avl ( 3) the cooling season representing wide varia- tions in the combinations of available Since there is a limit to the maximum genera- insolation and expected cooling loads. The tor temperature of an absorption chiller design chart correlation equations are de- (because of crystallization), a reference rived from detailed simulation results for temperature of Tref = 205°F is used in the specific region. equation (2). Long-term average daily values of weather parameters are used in equations A representative plot of a design chart cor- (2) and (3). This information is readily relation is obtained in this work, together available in Ref. 7 and 10. with the attendant results of a comparison with SHASP. These results apply to one specific region. This paper also includes a design example as well as a discussion of the Page 453 RESULTS TACLE 1 DETAILS OF REGION A RPgion Corres- Btu/ ft 2 Representative cooling cities were selected Total t'ames of from a climatic classification for the cool- Name ponding Cooling riti es ing season, published by TRW [10]. This TRWP~ f\egree ronsirlered classification establishes geographical Region f\ays regions based on combinations of available insolation and expected cooling degree-days. tas ri ngton rr Three different regions, namely regions A,B 4 1661- l 000- Charleston,SC and C were considered, although only the A and 1845 4000 region A is reported here. Table l lists 5 Nashville,TN the correspondence with TR~/ regions and the f"i ami, FL names of the cities that constitute region A. Typical meteorological year (TMY) weather data available in SOLMET tapes were procured TABLE 2 RANGE OF THE DESWJ Pl-'.RAf"ETERS for the representative cities and used as input to the detailed simulation (SHASP) Name of Lower Upper Unit runs. Hourly system performance indices parameter 1 imi t 1 imit were condensed into average monthly values for the cooling season comprising of the FRrn 0.6 0.8 - months of May through October. The solar cooling fractions were correlated from FRUL 0.4 1 .0 8tu/hrft 2 F approxima\ely one thousand simulation runs. The polynomial used to represent the solar A 200 600 ft2 coolin9 fraction is given by C 3 . . 1 205 212 f = :E(b.x 1+ y ) + xy(d1+d x+d y) (4) Tdump F C i =l 1 C 2 3 t1 = 15 .Ac 1 b The nine constants of the polynomial were 08tai ned by a least squares fit for P.egi on m = 1O .Ac 1b /Hr A. These correlations are valid over a range h of parameters shown in Table 2. The values of the coefficients for equation (4), to- gether with the average and standard 2 deviations, are presented in Table 3. A A = 300 ftC typical plot of the cooling design chart is F' 0.7 shown in Fig. 2. In this figure, curves of 2 constant solar cooling fraction fc are FRUL = 0.7 Btu/hrft F plotted in the domain of dimensionless para- meters X and Y which take values ranging Since t1/A must be 15, this provides storage from,:ero to 10 and 4 respectively. Such a so that t~c= 4500 1 b domain covers most of the typical combina- tions of insolation and dry-bulk temperature For nashville, rn, the following weather values for days with a cooling load. As information is obtained, for the month of expected, fc decreases with increasing July, from ref. 7, X (corresponding to higher losses) when Y is H = 23.13 MJ/m2 = 2037 Btu/ft2 held constant. On the other hand, if X is held constant, fc has an increasing nature kt= 0.57 with Y (corresponding to more efficient Td = 26°c = 7R.Pr, latitude= ?3.'.5° transmission-absorption of the incident insolation). ~gure 3 shows variation of For, (latitude - tilt)= 0., the geometrical the correlated results with the simulated factor becomes R = 0.87. Using this, the results. The range of variation of the de- total radiation incident on. the collector sign parameters is shown on Figures 2 and 3. becomes - - - 2 ;,AMPLE PROBLEM Ht= H x R = 2037 x O.P7 = 1772 Ctu/ft Using the average daily load and a COP of To illustrate the use of the simplified de- 0.6, the dimensionless parameters are sign method, we consider an average residence in Nashville,TN whose average cooling load 0.7.300.(205-78.8).24 Q1 is estimated to be 200,000 BTU/day. vie (200,000/0.(.) s~lect the following system parameters 1. ()1 Page 454 TABLE 3 CONSTANTS OF CORRELATION FOR REGION - A (of Table l) F' Ta FRUL i b. c. d. R 1 1 1 l~I 6 0.4- l -35 .6473 114. 888 12.2710 0.6 - 0.7 2 l. 3040 -33.023 2.4273 2.06 2.52 0.7 3 -0. 54785 5.0825 -5.4150 0.7- l -20. 6897 82.4277 -18.334 l. 0 2 4.3124 18. 7227 -0.16992 2. 00 2.5S 3 -0.18457 - 7. 8711 4. 5391 0.4- l -29.0659 104.502 11. 5781 0.7 - 0.7 2 -0.21973 -25.707 - l . 3594 1.86 2. 31 0.8 3 0 .17 58 -0.7383 2. 261 7 0.7- l -26.0659 97.0430 0.7988 l . 0 2 l . 5508 -12.2090 -2.9414 2. 01 2.50 3 0.33984 -5.9258 7. 3516 TABLE 4 cm1PARISONS OF TYPICAL VALUES OF SIMULATE[' AND CORRELATED RESULTS FOR REGION A 2 Ac= 300 ft , FRTa = o.7, FR UL= 0.7 _B_t_u~_ hrft2°F S: Simulated C: Correlated ~ i/as hi ngton Charles ton Nash vi 11 e r1i ami h DC SC Ttl FL May s 0.85 0.73 0.81 0.4'l C 0.89 0. 75 O.S3 0.50 June s 0.75 0.50 0.64 0. 34 C 0 .70 0.48 0.60 0.36 July s 0.43 0.40 0.49 0.36 C 0.45 0.41 0.50 0. 3') August s 0.62 0.53 0. 61 0.42 C 0.62 0.49 0. 59 0.43 September s 0. 79 0.70 0.80 0.45 C 0.82 0.65 0.80 0.46 October s l. 0 1. 0 l . 0 0.5R C 1. 0 1. 0 1. 0 0.58 Page 455 y FRTa.Ac.Ht = 0.7.300. 1772 1. 12 =(QL/COP av ) (200,000/0.6) Tr ef Reference temperature In Time interval (24 Hrs) for dimension- Using the correlation for region A in the 1e ss parameter appropriate range of parameters, the solar contribution is calculated to be 50.7 If 6 Average error detailed simulation SHASP is used with o Standard deviation appropriate values to give Qb= 200,000 Btu/ day and an average chiller C P of 0.6, then the solar fraction is computed to be about ACKNOl1LEDGEl1ENTS 50%. Similar results appear in Table 4. This vmrk has been conducted under con ti nui ng DOE contract DE - I\C03 - 79CS30204. The DISCUSSION AND CONCLUSIONS computer-time for this project was supported in part through the facilities of the computer For a complete comparison, many different science center of the University of Maryland. runs must be made and the errors analyzed. It is perhaps worth noting that the SHASP runs were made for a 3 ton chiller. This REFERENCES was done to match the peak demand on a hot day. In future designs it may appear l. F-Chart, An Interactive Program for prudent to select smaller sizes, and there- Designing Solar Heating Systems, fore more inexpensive systems and satisfy University of v/isconsin, June 197P. the load only 90% of the time. This re- quires that the solar fraction be investigat- 2. TRNSYS, A Transient Simulation Program, ed on a per ton basis. Solar Energy Laboratory, University of Wisconsin, t1adison, February l97f'. Indications are that the simplified design method, together with information already 3. Klein, S.A. and vi. A. Beckman, "/',, General availa~e in literature, could make the Design Method for Closed Loop Solar design considerably simpler. Further Energy Systems," ISES, Orlando, FL, studies for this region as well as the June 1977. remaining regions is under investigation. 4. Liu, B.Y.H. and R.C. Jordan, "The Inter- relationship and Characteristic Distribu- NOMENCLATURE tion of Direct, Diffuse and Total Solar Radiation," Solar Energy, Vol. 4(3), l\ Collector area pp 1-19. COPav Average COP 5. SHASP, Solar Heating and Air-Conditioning fc Solar cooling fraction Simulation Programs, Solar Energy Pro- jects, t1echanical Engineering Department, FRrn Collector parameters for design University of Maryland, College Park, FiA October 197P. H Average insolation along horizontal 6. Control Strategy Studies of Solar Heatino plane and Cooling Systems, Solar Energy Pro- Ht Average insolation on collector jects, ~echanical Engineering Department, University of t1aryland, College Park, kT Monthly average cloudiness index August 197f:. M Storage mass 7. Deckman, W.A., S.A. ~ein and J.A. Duffie, Solar Heating Design by the F-Chart qe Evaporator capacity Method, John Wiley and Sons, 1977. QL Space cooling load 8 . An and , D. K. , R. B. Ab a rear an d R. W. I\ 11 en , "A Simplified Cooling Design Method for R Geometrical factor Closed-Loop Liquid Systems," ISES, Atlanta, t1ay 1979. Td Average daily dry-bulb temperature 9. Anand, D.K., R.B. Abarcar and R.v/. l\llen, "Long Term Solar Cooling Systems Per- Tdb Dry-bulb temperature formance Predictions via a Simplified Design Method," SSEA Conference, San Tdump Temperature above which the energy Diego, CA, January 1980. from hot water is dumped Ta Transmittance-absorptance product Page 456 r,. ((OEHICIENTS IN l"8Lf 3) AC - Alfl CotiEolTIONNG U!ilT KW-HOT •n11 SfOflA,G£ CW -OIIU.£0 •nM STCJAAG£ tl'a-OC*ESTICl'IOT•TtR ~-.t.uxa..lM'f l, Jr r,;5) Page 457 TUESDAY, AUGUST 11 1981 SESSION 27 16th INTERSOCIETY ENERGY CONVERSION ENGINEERING CONFERENCE Organizer and Chairman: P F MASSIER, Jet Propulsion Laboratory, Pasadena, CA 819280 NASA/Hampton Refuse-Fired Steam Plant-A Muni- cipal/Federal Cooperative Effort FINAL PROGRAM H L. GREENE, NASA Langley Research Center, Hampton, VA, D. E MCCOY, F. Keeler Company, Williamsport, PA and H F TAYLOR, Charles R Velzy Associates, Inc , Richmond, VA 819281 Performance of a Revised Overtire Air Injection System in a Wood Refuse Fired Spreader Stoker Furnace G E. THORNBURGH and D. C JUNGE, Oregon State University, Corvallis, OR 819282 Development of a High Efficiency Warm Air Furnace Using Heat Pipe Principles W. E. THOMAS, JR , Thermacore, Inc., Lancaster, PA and H IHLENFIELD, SJC Corporation, Elyria, OH 819283 High Efficiency Compact Boiler J. R. HURLEY and A. H LEVINE. Thermo Electron Corporation, Waltham, MA 819284 Field Testing of a High-Efficiency Integrated Residential Boiler and Domestic Hot Water Appliance A. D. VASILAKIS and J GERSTMANN, Advanced Mechanical Technology, Inc., Newton, MA and D. SCHWARTZ, Innovative Technology, Inc., Esmond, RI Organizer: H. M CURRAN, Hittman Associates, Inc , Columbia, MD Chairman: W KENNISH, TPI Inc , Beltsville, MD 819711 Cooled Bed Solar Powered Desiccant Air Conditioning Z LAVAN, J. B. MONNIER and W M. WOREK, Illinois Institute of Technology, Chicago, IL 819713 Solar/Fossil Rankine Cooling H M CURRAN, Hittman Associates, Inc , Columbia, MD 819714 Cooling System Design D K. ANAND, University of Maryland, College Park, MO 819715 Future Directions of Solar Cooling Equipment J. H. MOREHOUSE, Science Applications Inc., Mclean, VA 25 Page 458 Regional Simplified Solar Cooling Design Charts D. K. Anand Professor B. Kumar Research Assistant R. W. Allen Professor Mechanical Engineering Department University of Maryland, College Park Supported by U. S. Department of Energy Systems Development Division Contract # DE-AC03-79CS30204 Page 459 REGIONAL SIMPLIFIED SOLAR COOLING DESIGN CHARTS D. K. Anand B. Kumar R. W. A11en Solar Energy Projects Department of Mechanical Engineering University of Maryl and College Park, Md. 20742 ABSTRACT An alternative to detailed computer simulation as with utilization curves of Liu and Jordan [4] was a means of obtaining solar fraction is the corre- made by Klein et al [3]. The charts were established lation of numerous simulation results that cover a by using synthetic weather data and assuming a wide range of system parameters and weather condi- uniform cooling load over a 12-hour day. Compari- tions. The design method presented in this paper sons made with results from TRNSYS runs (using uses a solar cooling fraction, f -chart, correlating real weather data and hence a non-uniform cooling detailed SHASP (Solar Heating an& Air Conditioning load) produced significantly different values of Simulation Programs) runs of solar cooling system cooling fraction at certain points. operating under varying real weather conditions obtained for three geographical regions. Several Previous work [11] has also reported on the corre- examples are included with prediction results lation approaches based on simulations with real having an error bounded by + 6%. It is seen that weather data but only for one geographical region. this approach is satisfactory as a first approxi- This paper amplifies the work presented earlier mation for many solar cooling designs. and extends it to all the geographical regions in the U.S., where annual cooling loads are signifi- cant. The correlation approach is based on de- INTRODUCTION tailed simulation runs using SHASP. The analysis of solar thermal systems has generally been conducted through the use of detailed system SYSTEM DESCRIPTION simulation programs with real climatological data as input [1-7]. Identifying and optimizing impor- The basic solar cooling system is shown in Fig. 1. tant system parameters usually requires many hours The cooling machine us,ed is a hot water fired of detailed simulation runs and thorough analysis absorption chiller where cooling capacity is of the outputs. The optimized parameters are then dependent on the hot water supply temperature. used in system design and long-term system per- The cooling load is dependent on the ambient air formance predictions. The use of these programs temperature, insolation and heat generation. The becomes expensive for design purposes and, in addi- control strategy used to simulate the system oper- tion, not all designers have access to the programs ation is based on a previous study of solar cooling or computers for detailed simulation. Also, some- systems [5]. Basicaiiy, ali of the usefui energy times it is necessary to obtain quick estimates collected by the solar collector is sent to a liq- before one embarks on detailed studies. A viable uid storage tank and stored as sensible heat. alternative would be a simplified design method Whenever there is a cooling demand, the absorption similar to the f-chart for heating which was a chiller draws off hot water from storage and direct correlation of detailed simulations. delivers enough cooling to satisfy the demand. If the temperature of the hot water in storage is such Several approaches to obtaining simplified cooling that the chiller cannot satisfy the load, then design methods have been investigated in the past. auxiliary is used to fully supply the generator These include: requirements. 1. Use of stochastic weather models [5]. SIMULATION APPROACH AND RESULTS 2. Use of closed form solutions. Previous analysis yields the expression for solar 3. Correlation of detailed simulations [8, 9]. cooling fraction as: The use of stochastic weather models as well as the f =f FR.rn IcAcdt -/ !RUL (T-Tdb) dt (1) closed form approach has been reported before. c QL/COP av QL/COP av Although these methods yield good ~pproximations in several applications, work remains to be done which,for correlation purposes, suggests the to refine these approaches. This work is continuing following two dimensionless parameters: and will be reported later. An earlier attempt to link the cooling design Page 460 X FRUL Ac (Tref -Td) bt/(QL/COPav) (2) TABLE l PETAILS OF REGIONS Region 2 Total Cities Y FRraTctAc/(QL/COPav) (3) Corres- Btu/ft Name ponding TRW[l O] (tl.J/m 2) Cooling Degree Since there is a limit to the maximum generator Days temperature of an absorption chiller (because of crystallization), a reference temperature of I Tref= 205 F is used in equation (2). Long term A 4 and 1661- l 000- Washington, DC average daily values of weather parameters are 5 1845 4000 Charles ton, SC used in equations (2) and (3). This information (18.86- Nashville, TN is readily available in ref. [7] and [10]. 20.95) Miami , FL Detailed simulations were conducted to obtain B 1 1845- 2000- Fortworth, TX correlations for two and three ton systems. Since 2399 4000 Phoenix, AZ the determination of x and y do not involve the (20.95- size of the units used in the correlation, the 27.24) re qui red size for the optimum f can be obtained by checking the two ton as well ascthe three ton C 2 1845- 2000- Albuquerque, NM correlation plots. 2399 4000 Fresno, er,. (20.95- For correlation purposes.a selection of regions 27.24) with significant cooling loads was made from the TRW [10] classification based on insolation-degree days combinations. The selected regions are shown in Fig. 2. These are designated by A, B, C and TABLE 2 RANGE OF DESIGN PARAl!ETERS corresponding TRW regions are shown in the Fig. 2 and Table l . Name of Lower Upper Unit Parameter Limit Limit Typical meteorological year (TMY) weather data available in SOLMET tapes.were procured for the representative cities within these regions and used F~ rn 0.6 O.P as input to the detailed simulation (SHASP) runs. 2 Hourly system performance indices were condensed FRUL 0.4 1.0 Btu/hrft F into average monthly values for the cooling season (2.27) (5.68) (W/m2 0 c) comprising of the months of May through October. The solar cooling fractions were correlated from Ac 200 600 ft2 approximately two thousand simulation runs. The (18.58) (55.74) (m 2 ), polynomial used to represent the solar cooling fraction is given by: Td ump 205 212 F 3 . . 1 1 fc=~ (bix +ciy + xy (d,+d2x+d3Yl (4) (96 .11) ( l 00) (oc) ) i=l M=15Ac 3000 9000 lb The nine constants ot tne polynomial were obtained ( D6l ) ( 4083 ) (kg) by a least squares fit for Regions A, B and C.. These correlations are valid over a range of para- inh =l O. Ac 2000 6000 lb/hr meters shown in Table 2 .. The values of the co- ( 907 ) ( 2722 ) (kg/hr) efficients for equation (4), together with the average and standard deviations, are presented in Tables 3 and 4.. The coefficients for a 3-ton 2 2 chiller are covered in Table 3 and those for a 2- H = 19.32 MJ/m (1948 Btu/ft ) ton chiller are presented in Table 4. Corresponding design charts are presented in Fig. 3-6. The KT = 0.53, latitude = 38.5° nature of variation of the curves with the dimen- sionless parameters is consistent with results Td= 24°c (75 .2F) observed earlier [11 J. For (latitude-tilt) = o, this yields a geometrical SAl1PLE EXAMPLES factor R = 0.967 Example (1) \=RxH = 1645 Btu/ft 2 (18.68 MJ/m2) For Region A, consider a residence in 1-'.ashington, Selecting collector design parameters as DC, where the average cooling load for the month of August is 148,000 Btu/day (156 ~J/d~y) supplied FRra = 0.6, FRUL = 0.4 Btu/hrft2F (2.27 w;m2 0 c) by a 2-ton chiller at an average COP of 0.6. The weather data obtained from ref. [7] for Washington, DC. Page 461 TABLE 3 CONSTANTS OF CORRELATION FOR A 2-TON CHILLER fc=L3 . . 1 1(b;x +c;y ) + xY (d1+d2x+df) i =l Range of Parameters for this tab 1e Only Range of Parameters for this table Only 0.6 < FR.rn < 0.7 0.6 < FR TC( < 0.7 2 0.4 2 < FR.UL < 1.0 Btu/hrft F 0.4 R & D c o n t i n u i n g w i t h e n c o u r a g i n g r e s u l t s 7 6 L B L A i r c o o l e d , h i g h e r e f f i c i e n c y a 1 1 1 1 1 0 n i a - w a t e r I a b s o r p t i o n c h i l l e r s P r o j e c t t r a n s f e r r e d a f t e r P h a s e I t o t h e D O E 7 7 E i C S o l i d p h a s e a b s o r p t i o n a i r c o n d i t i o n e r c h e m i c a l h e a t p u m p p r o g r c 1 1 1 h a v i n g a i r c o o l e d c a p a b i l i t y P r o m i s i n g a n a l y t i c a l r e s u l t s . E f f o r t o n - g o i n g 7 9 U . T e x a s H i g h e f f i c i e n c y d o u b l e e f f e c t a b s o r p t i o n s t u d i e s P r o m i s i n g p r o t o t y p e b u i l t a n d t e s t e d . S t i l l S o l a r p o w e r e d R a n k i n e h e a t p u m p f o r m u l t i f a m i l y 7 5 U T R C i n d e v e l o p m e n t a n d l i g h t c o 1 1 V T 1 e r c i a l a p p l i c a t i o n P r o m i s i n g p r o t o t y p e b u i l t . S o m e t e s t i n g C a r r i e r S o l a r p o w e r e d R a n k i n e a i r c o n d i t i o n e r f o r 7 7 p e r f o r m e d b u t t e r m i n a t e d d u e t o l a c k o f f u n d s m u l t i f a m i l y / l i g h t c o f l J l l e r c i a l a p p l i c a t i o n S u c c e s s f u l b r e a d b o a r d t u r b i n e c o n s t r u c t e d . F o s s i l a u g m e n t e d R a n k i n e c h i l l e r w i t h s u b s t a n t i a l 7 7 E T I P r o j e c t c o m p l e t e d p e r f o r m a n c e i m p r o v e m e n t s 7 7 I n p r o g r e s s U . P e n n s y l v a n i a F o s s i l a u g m e n t e d R a n k i n e c h i l l e r w i t h s u b s t a n t i a l p e r f o r m a n c e i m p r o v e m e n t s E f f o r t s u n s u c c e s s f u l b e y o n d l a b o r a t o r y s t a g e 7 6 R e s i d e n t i a l s o l a r p o w e r e d R a n k i n e h e a t p u m p G E s y s t e m s Page 487 T ~ B L E 2 . S I G N I F I C A N T P R O J E C T S I N S O L A R C O O L I N G F u n d i n g O r g a n i z a t i o n / P r o j e c t O b j e c t i v e S t a r t S t a t u s C a r r i e r S t u d y c h e m i c a l a d d i t i v e s f o r a b s o r p t i o n p a i r s 7 7 P r o j e c t s u c c e s s f u l a n d n e w a i r c o o l e d c h i l l e r t o p e r m i t a i r c o o l i n g a t u s a b l e t e m p e r a t u r e s s t i l l u n d e r d e v e l o p m e n t L A N L C o m p a r a t i v e t e s t e v a l u a t i o n o f a b s o r p t i o n 7 7 P r o j e c t s u c c e s s f u l a n d s y s t e m s s t i l l o p e r a t i o n a l a n d R a n k i n e s y s t e m s B r o o k h a v e n D e v e l o p t e s t f a c i l i t y f o r a b s o r p t i o n a i r 7 7 T e s t c o m p l e t e d N a t i o n a l L a b . c o n d i t i o n e r s a n d e v a l u a t e e q u i p m e n t A R K L A D e v e l o p s y s t e m p a c k a g e u s i n g 3 t o n a b s o r p t i o n 7 7 S y s t e m i n s t a l l e d a n d t e s t e d s i n c e 1 9 7 8 C a r r i e r P a c k a g i n g a n d o p e r a t i o n a l t e s t i n g o f 2 2 5 - t o n 7 8 S y s t e m s i n s t a l l e d i n t o o p e r a t i o n a l t e s t s i t e s a b s o r p t i o n s y s t e m s a n d e v a l u a t e d U . M a r y l a n d D e v e l o p a n a l y t i c a l m o d e l s f o r r e s e a r c h a n d 7 5 O n - g o i n g t e c h n i c a l c o n s u l t i n g H i t t m a n S t u d i e s o f a d v a n c e d c o n c e p t s a n d t e c h n i c a l 7 5 O n - g o i n g c o n s u l t i n g S c i e n c e D e v e l o p a n a l y t i c a l m o d e l s a n d c o m p a r a t i v e 7 8 O n - g o i n g A p p l i c a t i o n s c o o l i n g a n a l y s e s I n c . P l a n c o M a r k e t s t u d i e s a n d e c o n o m i c a n a l y s e s C o m p l e t e d 8 0 N e o m a t h i c s C o n s u m e r m a r k e t s t u d i e s 8 0 C o m p l e t e d L e s t e r B . K n i g h t T e c h n i c a l c o n s u l t i n g O n - g o i n g 8 0 H o n e y w e l l / L e n n o x R e s i d e n t i a l a n d c o J I J l l e r c i a l s o l a r p o w e r e d 7 6 3 a n d 2 5 t o n p r o t o t y p e s c 0 1 1 1 P l e t e d a n d R a n k i n e c h i l l e r s y s t e m s i n s t a l l e d i n t o t e s t s i t e s P r o t o t y p e c o n s t r u c t e d a n d l a b t e s t s c o m p l e t e d I G T D e v e l o p a n d t e s t d e s i c c a n t a i r c o n d i t i o n e r f o r 7 7 c o o l i n g a n d d e h u m i d i f i c a t i o n Page 488 T A B L E 2 . S I G N I F I C A N T P R O J E C T S I N S O L A R C O O L I N G F u n d i n g O r g a n i z a t i o n / P r o j e c t O b j e c t i v e S t a r t S t a t u s s o l a r p o w e r e d R a n k i n e 7 6 H i g h s p e e d b e a r i n g p r o b l e a s a n d o t h e r t e c h n i c a l A i r e s e a r c h R e s i d e n t i a l a n d c o r r m e r c i a l p r o b l e m s r e s u l t e d i n t e n n i n a t i o n o f t h e p r o g r a m h e a t p u m p s y s t e m s E x p e r i m e n t a l s y s t e m s i n s t a l l e d i n t o t e s t 7 5 C o l o r a d o S t a t e E x p e r i m e n t a l s o l a r c o o l i n g s t u d i e s f a c i l i t i e s a n d t e s t i n g c o n U n u i n g U n i v e r s i t y I n p r o g r e s s 8 0 S t a n f o r d R e s e a r c h A b s o r p t i o n f l u i d s t u d i e s I n s t i t u t e . . . . . . O ' . ) a t t r a c t i v e D i s c o n t i n u e d , c o n c e p t n o t e c o n o m i c a l l y 7 6 D e v e l o p n i t i n o l e n g i n e L B L I C o m p l e t e d a n d o p e r a t i o n i n s c h o o l s 7 3 i n N S F ( 1 p r o j e c t ) D e m o n s t r a t i o n o f c o o l i n g a n d i n o p e r a t i o n C o m p l e t e d i n 1 3 i n s t i t u t i o n a l 7 4 N S F ( 1 3 p r o j e c t s ) D e m o n s t r a t i o n o f c o o l i n g b u i l d i n g s C o m p l e t e d a n d i n o p e r a t i o n i n n i n e b u i l d i n g s 7 5 P r o g r a m O p p o r t u n i t y D e m o n s t r a t i o n o f c o o l i n g N o t i c e # 1 ( 9 p r o j e c t s ) C o m p l e t e d a n d i n o p e r a t i o n 1 5 b u i l d i n g s 7 5 D e m o n s t r a t i o n o f c o o l i n g i n P r o g r a m O p p o r t u n i t y N o t i c e # 2 ( 1 5 p r o j e c t s ) i n o p e r a t i o n C o m p l e t e d a n d 1 9 b u i l d i n g s 7 8 P r o g r a m O p p o r t u n i t y D e m o n s t r a t i o n o f c o o l i n g i n N o t i c e # 3 C o m p l e t e d a n d i n o p e r a t i o n b u i l d i n g s 7 9 P r o g r a m O p p o r t u n i t y D e m o n s t r a t i o n o f c o o l i n g i n N o t i c e # 4 i n C o m p l e t e d a n d o p e r a t i o n 1 3 b u i l d i n g s 7 6 F e d e r a l B u i l d i n g s D e m o n s t r a t i o n o f c o o l i n g i n P r o g r a m I n p r o g r e s s s y s t e m s t u d i e s 7 9 D e s i c c a n t c o m p o n e n t a n d U . W i s c o n s i n I n p r o g r e s s 7 9 D e s i c c a n t c o m p o n e n t a n d c o n c e p t s t u d i e s S E R I Page 489 T A B L E 2 . S I G N I F I C A N T P R O J E C T S I N S O L A R C O O L I N G F u n d i n g O r g a n i z a t i o n / P r o j e c t O b j e c t i v e S t a r t S t a t u s 7 7 R & D t e r m i n a t e d d u e t o u n r e s o l v e d t e c h n i c a l I I T C r o s s f l o w d e s i c c a n t a i r c o n d i t i o n e r f o r a n d p r o d u c t i o n p r o b l e m s c o o l i n g a n d d e h u m i d i f i c a t i o n A i r e s e a r c h R o t a r y d e s i c c a n t a i r c o n d i t i o n e r 7 7 C o n c e p t u a l f e a s i b i l i t y d e m o n s t r a t e d b u t n o t s u f f i c i e n t l y c o s t e f f e c t i v e t o j u s t i f y c o n t i n u a t i o n S u c c e s s f u l p r o t o t y p e s d e v e l o p e d a n d i n s t a l l e d i n Z e o p o w e r D e s i c c a n t c o o l i n g a n d r e f r i g e r a t i o n s y s t e m 7 8 , _ _ . t e s t s i t e s \ . D I B r e a d b o a r d c o m p l e t e d a n d d i s c o n t i n u e d C E M R e s i d e n t i a l d e s i c c a n t a i r c o n d i t i o n e r 7 5 S t u d y c o m p l e t e d S o l a r o n R e s i d e n t i a l d e s i c c a n t s y s t e m s t u d y 7 6 T e c h n i c a l l y u n a t t r a c t i v e . d i s c o n t i n u e d B i - P h a s e T w o p h a s e t u r b i n e s t u d i e s 7 6 T e c h n i c a l l y u n a t t r a c t i v e . d i s c o n t i n u e d S c i e n t i f i c A t l a n t a F r e e p i s t o n c o m p r e s s o r 7 6 S t u d i e s i d e n t i f i e d s e v e r a l p o t e n t i a l l y u s e f u l I G T S t u d y n e w a b s o r p t i o n m a t e r i a l s a n d b a c k g r o u n d 7 7 f l u i d s . i n f o r m a t i o n n e e d e d t o u s e t h e s e m a t e r i a l s S t u d i e s d i d n o t p r o d u c e a n y n e w m a t e r i a l s 7 7 S o . R e s e a r c h I n s t . S t u d y n e w a b s o r p t i o n m a t e r i a l s f o r l o w t e m p e r a t u r e o p e r a t i o n I n p r o g r e s s L o c k h e e d L i q u i d d e s i c c a n t d e h u m i d i f i e r d e v e l o p m e n t 8 0 I n p r o g r e s s T h e r m o E l e c t r o n E v a l u a t e R a n k i n e f l u i d s t a b i l i t y 8 0 -20- VI. ACHIEVEMENTS The solar cooling program, although far from completed, has already succeeded in achieving many of its original objectives dealing with technical feasibility. Substantial experimental effort has been initiated toward the development of components and systems in each of the five R&D paths associated with absorption, Rankine, desiccant and heat pump technologies. A total of 37 major research and development programs were initiated over this eight-year period which were directly related to the development of improved cooling components or systems. They were: 8 desiccant and associated component development projects 15 absorption technology projects 9 Rankine technology projects 5 thermodynamic cycle and innovative concept studies. Of these contractual programs, 20 were involved in the developn~nt of the chiller component and 8 in the packaging of these components into complete systems. Nine special materials studies were funded. There were numerous related projects funded for the development and testing of collector and storage components required for successful solar cooling systems; these are not included in Table 2. Solar cooling demonstrations which began in 1973 resulted in 20 commercial cooling demonstrations and 157 residential cooling demonstrations. Page 490 -21- As a direct result of these R&D and demonstration program activities, some notable achievements and promising activities are: 1. A solar cooling community has resulted consisting of universities, research institutes, small business developers, large business developers, manufacturers, test laboratories, architects, and system design engineers. 2. Significant component developments have resulted in the following areas: • Collectors - Newer generations of evacuated tube and concentrat- ing collectors have demonstrated efficiencies at least 50% greater than earlier flat plate collectors. • Storage - There is available a better understanding of the optimum storage design techniques, insulation, requirements and packaging for the installation site. • Controls - Packaged, high reliability, controllers designed specifically for solar have resulted in significant operational performance and reliability. • Chillers - The most significant improvements have occurred in this area as follows: air cooled absorption units for the small residential market and operating at temperatures 205° F and less are under development conventional absorption chillers have been redesigned to operate efficiently at temperatures as low as 1800 F for use with flat plate collectors successful development of a 3 ton evaporatively cooled absorption chiller, eliminating the need for a separate cooling tower has been accomplished Page 491 -22- the first generation of package designs of air conditioners using the Rankine cycle and absorption cycle are under laboratory testing technical feasibility and field operation have been achieved for 3 ton and 25 ton Rankine cooling systems successful laboratory and field testing of prototype 18 ton Rankine cycle heat pump for cooling and heating has been completed a new fluid has been discovered for optimum operation of air cooled operation of absorption machines and successfully tested the use of spin-up and spin-down concepts in chiller control for improved system performance has been developed a one ton liquid desiccant (zeolite) cooler has been developed and tested. This cooler has the capability of providing self contained storage and could prove to have significant system performance improvements. 3. Average daily solar powered system performance has been substantially improved from .3 to .6. 4. Indications from industry are that the economics of solar cooling have improved substantially from $25,000/ton of installed cooling to less than $10,000/ton of installed cooling. 5. Analytical tools and design methods for solar systems are now available and further improvements are underway. 6. Advanced research on new concepts has ·indicated the possibility of higher efficiencies using the double effect chiller and fossil augmented systems. Page 492 -23- Clearly the achievements in the solar cooling program have resulted not only because of direct R&D in problems relating to cooling, but also due to synergistic effects on heating. From a national viewpoint, a successful by-product of the program has been the spawning of an emerging scientific, technical and management infrastructure that would transform solar cooling into a reality. Page 493 -?4- VII. CONCLUSIONS/RECOMMENDATIONS Based upon the status of solar cooling in 1973, considerable progress has been made in several aspects of .this problem as outlined under accom- plishments. However, solar cooling systems are not available, acceptable nor cost effective except in several anomalous locations. This is the case principally due to one or more of the following technical reasons: Much of the work is still in the R&D stage There is no industrial mass production The coefficient of performance is not sufficiently high for any technology Air cooling is not widely available Sufficient reliability and maintainability data is not available since the systems have not been in use for a sufficiently long period of time. The formulation of detailed and specific recommendations require the determination of quantitative goa 1 s for performance and cost that would make solar cooling systems competitive \'iith conventional cooling systems. This task is currently being carried out. However, certain general recommendations can be made. These are Conduct the R&D on components and systems that are likely to proceed down the pathway to cost-effective solar cooling systems as determined by the performance/cost goal study. Initiate new high risk/high payoff concepts and advanced techniques. Complete low risk/high payoff concepts currently under R&D. This should primarily deal with research into techniques to raise system coefficients of performance by improving existing prototype absorption and Rankine chillers. This includes pri- marily the control strategy and improving heat transfer surfaces. Page 494 -25- Hybrid schemes using chillers for high sensible loads and desiccants for primarily latent loads. Efficient methods of cooling storage integrated with high performance chillers. From a national viewpoint, since considerable progress has been made and a scientific and technical infrastructure as well as the management system is in place, the cost in the long run of continuing an aggessive R&D program is less expensive than abandoning it altogether. It is estimated that the expenditure of one twentieth of one percent (0.05%) of the total current equivalent fuel usage for cooling would be adequate to fund an aggressive R&D program with potentially high payoff at minimal risk. Based upon the fact that sixteen billion dollars is expended upon space cooling, such an R&D program would cost eight million dollars annually. An eight million dollar annual R&D program is a small price for an industry with a $17,000,000,000 annual fuel appetite. Page 495 -26- REFERENCES (1) NSF/RANN Workshop Proceedings for Solar Cooling for Buildings, February 6-8, 1974, Los Angeles. (2) National Solar Energy Research and Development Plan, ERDA-48, October 1975. (3) National Program for Solar Heating and Cooling, Residential and Commercial Applications, ERDA 76-6, October 1976. (4) National Program Plan for Research and Development in Solar Heating and Cooling for Buildings, Agricultural and Industrial Applications, DOE/CS-0008. (5) National Plan for Energy, Research, Development, and Demonstration, 1975. (6) The Use of Solar Energy for the Cooling of Buildings, August 4-6, 1975. (7) Proceedings of the Third Workshop on The Use of Solar Energy for the Cooling of Buildings, 1978. (8) Annual DOE Active Solar Heating and Cooling Contractors Review Meeting, June 1980, CONF 800540. (9) Active Solar Heating and Cooling Systems Development Proceedings, October 1980, DOE/CS/30211. (10) Proceedings of Annual DOE Active Solar Heating and Cooling Contractors Review Meeting, March 1980, CONF 800340. Page 496 MAGNETICALLY SUSPENDED FLYWHEEL SYSTEM STUDY by Dr. James A. Kirk and Dr. D. K. Anand University of Maryland Mechanical Engineering Department College Park, MD 20742 [(301)454-5842] Mr. Harold E. Evans Advanced Technology and Research, Inc. Burtonsville, MD 20866 and Mr. G. Ernest Rodriguez Goddard Space Flight Center Greenbelt, MD Presented at the Integrated Flywheel Technology - 1984 Workshop NASA-Marshall Space Flight Center Huntsville, Alabama 35812 February 7-9, 1984 Page 497 MAGNETICALLY SUSPENDED FLYWHEEL SYSTEM STUDY J. A. Kirk and D. K. Anand University of Maryland College Park, Maryland H. E. Evans Advanced Technology and Research, Inc. Burtonsville, Maryland G. E. Rodriguez NASA Goddard Space Flight Certer Greenbelt, Maryland 307 Page 498 ABSTRACT The Goddard Space Flight Center (GSFC) and the University of Maryland (UM) Mechanical Engineering Department have a common interest in flywheels and have cooperated since the midrl970 1 s in designing and testing flywheel components. GSFC/UM is currently involved in studying application of a graphite/epoxy, magnetically suspended, pierced disk flywheel for the combined function of spacecraft attitude control and energy storage (ACES). Past achievements of the GSFC/UM magnetically suspended flywheel program include design and analysis computer codes for the flywheel rotor, a magneti- cally suspended flywheel model, and graphite/epoxy rotor rings that have been successfully prestressed via interference assembly. All hardware has success- fully demonstrated operation of the necessary subsystems which form a complete ACES design. Areas of future GSFC/UM work include additional rotor design research, system definition and control strategies, prototype developement, and design/construction of a UM/GSFC spin test facility. The results of applying design and analysis computer codes to a magneti- cally suspended interference assembled rotor show specific energy densities of 42 Wh/lb (92.4 Wh/kg) are obtained for a 1.6 kWh system. 308 Page 499 INTRODUCTION The Goddard Space Flight Center has been active in the development of high efficiency motor/generator and magnetic suspension systems since the early 1960 1 s. One outcome of this work resulted in a magnetically suspended momen- tum wheel for spacecraft application [1,2,3]*. Based upon this earl~ work at GSFC it appeared useful to consider a system which can provide for the joint functions of attitude control and energy storage. Since the mid~l970 1s GSFC and the University of Maryland have been active in a joint program on the various aspects of a magnetically suspended flywheel system. Recently GSFC/UM has addressed the problems of the joint solution of attitude control and energy storage. The program is termed ACES (~ttitude f_ontrol and fnergy Storage) and it involves hardware definition and problem identification/solution of all aspects of a magneticafly suspended flywheel system. The purpose of this paper is to provide a brief review of the GSFC/UM ACES effort, to present some of the hardware currently undergoing testing, and to identify the areas of future work. * Brackets denote references at end of paper. 309 Page 500 SYSTEMS BACKGROUND In designing a magnetically suspended flywheel system, GSFC/UM has concluded [4,5,6] that a pierced disk of uniform thickness provides a desirable rotor geometry from both a performance and manufacturing point of view. Shown in Figure 1 is a cross-sectional view of the original GSFC/UM magne- tically suspended flywheel design. The original design consists of 2 rings with the outermost ring being made of a filamentary wound composite material and the inner ring being made of continuous iron bonded to the filamentary wound ring. The stator of this design fits in the "hole" of the 2 ring rotor and it carries the magnetic suspension and motor/generator electronics. The original GSFC/UM design was configured around a homopolar permanent magnet motor/generator with variable field flux for maintaining constant voltage out- put as rotational speed varies [4]. The magnetic suspension system is an integral part of the motor/generator design and it utilizes permanent magnets to establish a steady state magnetic flux, which is then modulated via sensor feedback [4]. Shown in Figure 2 is a photograph of the current test system which GSFC/UM is using to establish rotational losses and efficiencies for the motor/generator and magnetic suspension concepts embodied in the original GSFC/UM design. Testing is currently under way on this first generation ACES design and preliminary results are encouraging and support the performance projections previously presented in the literature [4,6]. 310 Page 501 ROTOR DESIGN CONSIDERATIONS RCA [7] and J.A. Kirk, under contract to GSFC, have done additional work on the original GSFC/UM design. It was concluded that a multiring, interference assembled rotor, such as shown in Figure 3, would provide for substantial improvements over the original GSFC/UM,design. The modified GSFC/UM design, shown in Figure 3, differs from the original GSFC/UM design in the following areas: 1. The rotor is composed of a number of individual filamentary wound rings, rather than being one continuous ring. 2. The inside diameter (ID) to outside diameter (OD) rotor ratio (ID/OD) is smaller than the original GSFC/UM design. 3. The innermost ring is made of iron and is segmented into discrete pie- shaped 11 chunks 11 • Each of the above changes was made in the original GSFC/UM design in order to improve the overall performance of the system. The reasoning behind the changes has been documented by Kirk and Huntington [8,9,10,11] and a brief explanation follows: 1. The rotor is made of a number of composite material rings which are interference assembled. The reason behind this change fs to favorably prestress the rotor so higher rotational speeds and energy densities can be obtained before a limiting performance constraint is encountered. 2. The ID/OD ratio has been lowered. The reason behind this change is that the original GSFC design was of a "thin hoop" type and suffered excessive 11 gap 11 growth between the rotor and the stator as it spun. 311 Page 502 Since gap growth will degrade electrical performance, it must be controlled, and the best way to achieve this control is by decreasing the ID/OD ratio. 3. The innermost ring must be made of iron and is now segmented instead of being continuous. This change has been made because the iron ring would always reach its limiting strength long before the filamentary wound composite ring(s) reached their strength limit. To overcome this limitation a "segmented" inner ring is now proposed for use on the magnetically suspended flywheel system. The important point to note is that the inner iron ring will have all the necessary magnetic properties but will consist of a number of pie-shaped segments which are bonded to the inside diameter of the first filamentary \-/Ound ring. The iron ring thus has no stiffness in a 11 hoop 11 or tangential direction and presents an "inner loading" on the filamentary wound composite ring to which it is attached. The three changes described above have no impact on the motor/generator or magnetic suspension system. The effect that these changes have on the pro- jected system performance is dramatic and has been documented via a recent GSFC contractor report [12]. ROTOR ANALYSIS TOOLS GSFC/UM realize that the final rotor design dimensions must evolve in parallel with the magnetic suspension and motor generator designs (as they impact on the dimensions and weight of iron inner ring). Obviously then, the most useful rotor design a~d analysis tools are those which most closely model the real physical system and are convenient to apply as the iron inner ring 312 Page 503 design evolves. GSFC/UM has developed two (2) design and analysis tools for this purpose. Both tools are computer codes which perform detailed stress analysis and final dimension selection (including component tolerances) for all the components of the ring rotor. The analysis code is called FLYANS (FLYwheel ANalylis) and the sizing code is called FLYSIZE (FLYwheel SIZE. The interested reader will find a description of these codes in References 8 and 12. Shown in Figure 4 is a schematic diagram of the multiring rotor which is modeled by the FLYANS and FLYSIZE codes. Each of the rotor rings is the same axial thickness and the stresses in each ring consist of a hoop or tangential stress (cr 0 ) and a radial stress (crr)• If power is being put in or taken out of the system there is an additional shear stress (Tre) in each ring. It is assumed that the flywheel rings are in a state of plane stress, meaning that there is no variation of the cr 0 and crr stresses in the axial direction. The materials which comprise the multiring rotor are modeled as homoge- neous, linearly elastic, orthotropic materials [13], with material properties specified in the radial and tangential direction. The current GSFC/UM design is based on Celion 6000/epoxy for the filamentary wound com- posite rings [12],. It should also be pointed out that any new or hypothetical materials can easily be added to the computer code data base with minimal effort. The total stress distribution in one ring of the multiring flywheel is the superposition of the five stress distributions due to the following: 1. Rotation of the ring at constant angular velocity. 2. Interaction with adjoining rings due to rotational expansion. 313 Page 504 3. Interference assembly of the rings. 4. Residual stresses due to curing. 5. Angular acceleration of the entire assembly. The stress distribution for the entire flywheel is the summation of the above 5 stresses for each flywheel ring. Of the 5 stress distributions given above, no. 3, interference assembly, is under the direct control of the designer. The FLYANS code provides an algorithm for the selection of interference pressures in order to optimize the stored energy per unit weight of the rotor. It will be instructive at this point to consider the hypothetical example of how interference stresses interact with rotational stresses in a simple 2 ring "pierced disk" rotor. Shown in Figure 5 is the stress distribution which occurs when 2 rings of the same material are interference assembled. When the interference stress distribution is added to the rotational stress distribution the net result is as shown in Figure 6. In Figure 6 the stresses have been made nondimensional by the factor 2 2 p 1w b (units are psi) where pl= mass density for the first ring of the assembly (value is weight density in lb/in 3 divided by g = 386 in/sec2 ) w ~ rotational speed (rad/sec) b = outer radius of the flywheel (inches) The solid line shown in each of the plots in Figure 6 represents the stress 314 Page 505 distribution which occurs when the 2 rings are spun without any interference assembly present. The dotted lines show the stress distribution when the 2 rings are interference assembled and then spun. Consider the lower plot in Figure 6. If the working tangential stress of the material, cre, is constant, then the limiting value of cr /p 2 2 0 1w b is = 0.97 with no interference present, and 0.94 with interference present. For a fixed value of band cra it is clear the interference assembled flywheel has a larger w, and therefore a larger kinetic energy per unit weight over the non-interference assembled flywheel. GSFC/UM has done preliminary testing of interference assembly of composite rings and has found that a conical taper of approximately 1 degree between the inside diameter and outside diameter of adjacent rings will permit press assembly of the rings. Shown in Figure 7 are two graphite epoxy rings that were assembled and pressed together at the Hercules Alleghany Ballistics Laboratory (Cumberland, MD) in 1978. The two rings are 8 inches in OD, 7 inches in ID and are each 1/2 inch in radial thickness. The two rings have approximately 0.3% interference and the ring interface was lubricated with epoxy before pressing together. The collection of wires shown in Figure 7 is for strain gage instrumentation placed on the rings. The ring assembly shown in Figure 7 was donated to the University of Maryland and is currently undergoing further testing as part of the GSFC/UM ACES program. The results of applying the FLXANS and FLYSIZE computer codes to a 1.6 kWh GSFC/UM design [12] have shown that it is possible to design a 6 ring rotor with an iron inner ring. The rotor has an inside diameter of 8 inches and an outside diameter of 20 inches. Using Celion 6000/epoxy for all the filamentary wound composite material rings, the projected specific energy density is 41.9 Wh/lb 315 Page 506 {92.2 Wh/kg) and the inner radius displacement (i.e., air gap growth) will not exceed .040 inch (from Oto burst speed). CURRENT WORK GSFC and UM are currently engaged in a detailed study which will signifi- cantly advance understanding of the magnetically suspended flywheel for ACES. The following three major tasks are currently being worked on: 1. Rim research requirements 2. Systems research requirements 3. UM/GSFC prototype development and spin test facility. Task 1: Rim Research Requirements The purpose of this task is to conduct a detailed analytical analysis of the mechanical properties and stresses of a composite material rim. Specifically the analysis will include: • Analytical determination of the stress distribution in the rim. This will include the loading of the iron at the inner radius. The simulation of the stress distribution will be initially represented by closed form solu- tions, although standard finite element codes may be applied if the authors feel their use is warranted. • Determination of the effect of mechanical stresses on the magnetic proper- ties of the iron with specific consideration of hysteresis. • Identification of optimum materials and manufacturing/assembly methods for present and future rims with an aim towards maximizing performance. • The use of multirings that are interference assembled for prestressing. • Identification of detection mechanisms for rotor failure and system 316 Page 507 shutdown prior to destructive failure. The overall goal is to clearly define the present state of technology and future problems that must be solved r'or a viable design. -Task- 2: System Research Requirements The purpose of this task is to conduct a study in order to establish the feasibility of the complete ACES system. Three major sub-tasks have been identified. These are: o System definition * Control strategies o System testing System definition includes the characterization of the subsystems needed for the entire system. This includes specifying, at least generally, the require- ments of commutation, microprocessing, containment and interactions, and iden- tifying the problems of failure and shutdown. The identification of control strategies for the system is quite unique. Certainly the inertial coupling and control of the momentum require careful analysis. The interaction of the magnetic field and other perturbations on stability and attitude control are also important areas requiring careful characterization. The system testing component of this task is specifically concerned with testing the GSFC/UM model. This model will be modified for maximum perfor- mance by redesigning the rotor initially. The primary thrust of this exercise is to identify important parameters that must be studied for future component and system design. Task 3: UM/GSFC Prototype Development and Spin Test Facility An important adjunct to the current research tasks is to foster continued 317 Page 508 long-term involvement between the University of Maryland and GSFC. At the end of FY 84 it is envisioned that GSFC/NASA Headquarters will continue UM funding for development of the ACES system. In particular, the next phase of the work will involve development of a 500 watt hour ACES system along with design and construction of test facilities suitable for evaluating the 500 watt hour system. The proposed UM test facilities will provide for experimental moni- toring of the performance of the rim, motor/generator, and magnetic suspension systems. The 500 watt hour system will be designed for ease in the replace- ment of all components. It is expected that the 500 watt hour system will serve the purpose of both a showpiece working model and a facility to try out enhancements which can improve system performance. Not only will UM be a NASA/GSFC resource but, in addition to that, NASA contractors producing deli- verable magnetically suspended flywheel systems will find UM to be a valuable analysis, test, and evaluation facility. CONCLUSIONS The concept of using a magnetically suspended flywheel for the combined function of spacecraft attitude control and energy storage (ACES) is extremely viable. Several pieces of hardware have been built and are undergoing testing to evaluate the various subsystems used in ACES. Based upon reasonable and well founded projections, an ACES magnetically suspended flywheel system could easily store 1.6 kWh with a rotor specific energy density of 42 Wh/lb (92.2 Wh/kg). The areas of study which will be required to integrate the ACES subsystems into a complete working system have been identified and are currently under detailed study. The results of the current study will project a workable 318 Page 509 5-year plan between UM and NASA/GSFC to turn the already documented successes of the magnetically suspended flywheel system into a complete ACES. system. 319 Page 510 IECEC PRELIMINARY Page 511 SESSION 34 SOLAR ENERGY CONVERSION ENGINEERING 2:00 p.m. Tuesday, August 21 Continental Ballroom 2 Organizer: B. Braun, Bechtel Group, Inc. Chairman: H. Seielstad, Pacific Gas & Electric Company Co-Chairman: H. Yeh, University of Pennsylvania A Solar Micro-Utility System for Buildings Terry R. Galloway Mittelhauser Corporation Berkeley, CA Thermodrculation Heat Transfer in a Solar Chimney Pietro Mazzei lnstituto di Fisica Technica Napoli, Italy 0. Manca R. Mastrullo Thermally Decoupled Combined Quantum Thermal Conversion of Solar Energy to Useful Work D. H. Johnson SERI Golden, CO Control Aspects of Photovoltaic/Thermal Energy Systems Eric 0. Bazques Congress of the United States Washington, DC D. K. Anand Enhanced Solar Desalination Unit: Modified Cascade Still Abdel-Monem A. EI-Bassuoni United Arab Emirates U. Dhaharan, Saudi Arabia Development of a Solar Warehouse with a Coinstant Temperature T. Horigome New Energy Dev. Organization Tokyo, Japan N. Ikeda H. Gotoh K. Nishino Solar Drying Studies in a Low Humidity Environment 0. Mojola Univ. of IFE Nigeria Page 512 19th INTERSOCIETY ENERGY CONVERSION ENGINEERING CONFERENCE VOLUME3 "ADVANCED ENERGY SYSTEMS - THEIR ROLE IN OUR FUTURE" Participating Societies II SAN FRANCISCO HILTON HOTEL SAN FRANCISCO, CALIFORNIA AUGUST 19·24, 1984 Page 513 849136 CONTROL ASPECTS OF PHOTOVOLTAIC/THERMAL ENERGY SYSTEMS Eric O. Bazques Office of Technology Assessment U.S. Congress, Washington, D.C. 20510 Dave K. Anand Mechanical Engineering Department University of Maryland, College Park, Maryland 20742 ABSTRACT The objective of this research is thus to apply optimal control techniques to a realistic, Cogeneration of electric and thermal energy simulated, residential PV/T energy system, In through use of combined solar photovoltaic/ther- doing this, demonstrate whether the use of this mal (PV/T) collectors is a method for improving advanced control, while maintaining adequate the overall efficiency of solar electric energy comfort conditions, can substantially improve systems. The control of a PV/T system in gener- photovoltaic output and reduce auxiliary energy al and optimization of performance in particular requirements when compared to conventional through use of state space control methods, is control strategies. addressed in this study. Significant improve- ment in system performance is noted using op- SYSTEM DESCRIPTION AND MODELING timal control when compared to conventional con- trollers for deterministic weather forcing func- A practical PV/T solar heating and cooling tions. Optimal system control, analyzed first system consists of several components which in- through use of Pontryagin's Minimum Principle teract to collect and transform incident solar and then implemented by specification of a per- radiation (insolation) into useful electric and formance index and solution of matrix Riccati thermal energy for use in a residence, Figure 1 equations, is shown to be a viable and useful is a schematic for a combined PV/T solar energy strategy for these hybrid sys terns. system which utilizes a series heat pump for satisfying residence thermal loads (heating or INTRODUCTION cooling). For convenience, the upper portion of the schematic encompasses the thermal subsystem A photovoltaic/thermal (PV/T) solar collec- while the lower portion portrays the electric tor essentially combines a photovoltaic module subsystem. and a solar thermal collector in a single unit which is achieved most simply by affixing photo- To the upper left of Figure 1, the PV /T voltaic cells on the absorber surface of a flat collector is shown which collects solar inso- plate collector (1,2). This PV/T collector thus lation I (when the solar intensity is great provides electric power generated by the photo- enough) with the ambient temperature at Ta· The voltaic cells as well as low grade thermal out- collector pump pumps a heat transfer fluid (usu- put by active cooling of the photovoltaic array, ally a water-ethylene glycol solution to prevent The collectors in this study are liquid cooled. freezing) at flow rate Int through the collector in a closed circuit through a heat exchanger Cogeneration of electric and thermal energy (not shown) with given effectiveness in the through use of hybrid PV/T collectors is a thermal storage tank, The PV/T collector mean lllethod for improving the overall efficiency of plate temperature is Tc, the collector fluid Bolar electric energy systems, Solar cell elec- outlet temperature is Tf, and the thermal stor- trical performance decreases linea,ly with age tank temperature is T • Water of thermal increasing cell operating temperature, thus energy content Qshw is taten from the thermal active cooling maintains the cells closer to storage tank to satisfy service hot water loads their optimum achievable electric output. In of the residence with the water being replaced turn, satisfying on-site thermal loads through from the city mains at temperature Tmain· use of the heat generated by cooling of the Cells improves net energy usage and overall If the room enclosure at temperature T ~~stem performance. Combined collectors can (surrounded by ambient air at temperature Ta} us be more space effective, inexpensive, and requires heating, there are several methods for ct an provide improved system performance compared satisfying the thermal load. If the thermal t~i the other options. The incentive for using storage is of sufficiently high temperature, 8 type of system will increase if the PV /T then the thermal storage pump can pump heated 0 ; -llector sys tern can be controlled so as to not water at flow rate ins along path O shown in t~nalize the photovoltaic electric production Figure 1 and directly heat the room when the 1 rough excessive thermal energy production and room fan moves air at flow rate mr over the e: maximizing the effective use of the thermal heating coils. This heats the room air to Tri ergy which is produced, (room inlet temperature), As energy is extract- 1656 Page 514 ed from the circulating water, the temperature Figure 2 is schematic of a combined PV/T is reduced to Tsr ( thermal storage return tem- system which utilizes a parallel heat pump. lt perature). Another method for heating the en- follows that the only difference in operation of closure is to operate the series heat pump. The this system compared to that of the series heat thermal storage fluid follows path 1 in Figure 1 pump system described above is in the heat pump and serves as the heat source for the series mode of operation, The parallel heat pump is, heat pump evaporator. Operating the heat pump in essence, thermally separate from the solar with this elevated temperature heat source in- energy system, The disadvantage of this is that creases the COP over that which would be obtain- the COP of the parallel heat pump in winter is ed if the heat pump used the colder ambient air generally lower than that of the series heat as the heat source and hence improves overall pump and the parallel heat pump requires a de- system performance, Again the fan with air flow frost cycle. The advantages are that the paral- rate of i\, extracts heat from the heat pump lel heat pump arrangement is less complex and condenser coil and distributes it to the room less expensive than the series heat pump' system enclosure, Another heating method for this and, in addition, the parallel heat pump can be system is to operate the auxiliary heat coil better optimized for summer cooling operation with electricity, Qaux• as an electric resis- than the series can, The parallel heat pump tance heater. As this is an expensive way to PV/T system can also provide direct heating in a heat an enclosure, it is a method that is best manner similar to the series configuration, avoided. However, it can be used in conjunction with either direct heat or the series heat pump The six system configurations investigated in case either cannot completely satisfy the in this research are 1) series heat pump-direct structure thermal load. heat winter, 2) parallel heat pump-direct heat winter, 3) series heat pump-solar assisted heat If the structure requires cooling in the pump winter, 4) parallel heat pump-winter, 5) summer, the series heat pump uses the room en- series heat pump-summer cooling, and 6) parallel closure as a heat source for the evaporator and heat pump-summer cooling, "pumps" thermal energy to the condenser outdoor coil, which acts as a heat sink at temperature In simulating the PV/T system, energy bal- Ta. As auxiliary cooling is not possible as ances are performed on the collector, collector auxiliary heating was for the heating season, fluid, storage tank, and room enclosure respec- care must be exercised to properly size the heat tively. These four equations specify the four pump to satisfy the expected cooling loads. In state variables, Tc, Tf, Ts' and Tr, Several the summer, the thermal energy collected is used bilinear terms occur in these equations where a to satisfy service hot water needs. If the control variable (mass flow rate) multiplies a thermal storage becomes fully charged (approach- state variable (temperature). The electric out- ing l00°c), subsequent thermal energy collected put from the photovoltaic modules, the thermal must be dumped through a relief valve. Proper storage return temperature, and room air inlet sizing of thermal storage generally prevents temperature are also computed, Finally, the to- this type of energy waste. tal electric backup used which consists of the total electric used minus the electric output Referring to the electric subsystem in from the photovoltaic cells in the PV /T collec- Figure 1, the photovoltaic direct current output tor is calculated. from the PV/T solar collector is monitored by a maximum power tracker and is then inverted to CONVENTIONAL AND OPTIMAL CONTROL STRATEGIES alternating current in the DC/AC inverter. The current then flows to the utility interface The state variables for the system are the which is an electronic device which acts as a four temperatures mentioned previously, The gate for flow of electricity between the solar disturbances on the system are the weather in- cells, utility, and the electric loads of the puts, insolation, I, and ambient dry-bulb tem- structure, If the photovoltaic output is suffi- perature, Ta. The control variables are the cient to satisfy the electric loads which in- collector fluid mass flow rate, mf, and the mass cludes operation of pumps, fans, heat pump com- flow rate from storage, ms' The general control pressor, diversified electric (lighting, appli- problem is to control the specified plant, which ances), and, if necessary, auxiliary heat, then is being disturbed by the weather inputs, the interface directly supplies the loads from through the mass flow control variables so as to the inverter. If the photovoltaic output is in bring about desired comfort conditions, The op- excess of that required by the structure and timal control problem is more specific and is to occupants, the excess is sold to the utility at monitor the state variables and, while the plant whatever the buyback and full-avoided costs are is being disturbed by the weather inputs, opti- set at, If the photovoltaic output is less than mize the performance of the system through that required by the residence (such as at night appropriate changes in the control variables, when the photovoltaic cells are not operating), In the optimal control problem, performance is then electricity is purchased from the utility optimized through minimizing auxiliary energY at the prevailing sell back rate, usage while maintaining com£ort conditions, 1857 Page 515 Four different controllers were chosen, that the gains thus generated minimize a quadra- The first three, namely, on/off with hysteresis, tic performance index. In practice, the optimal multilevel, and proportional, are considered gain computation employs linear regulator theory "conventional" controllers since they are in with the addition of set points for both the various stages of commercialization. With these control and state variables. controllers, feedback information is derived from thermostats, and no microprocessor is A detailed feedback flow diagram for the required. The control methodology is estab- linear optimal PV/T system is shown in Figure lished a priori since controller set points and 3. This figure demonstrates how the set varia- deadbands are set at the factory (or in the bles, constraint matrices, equilibrium point field) for average or best guess conditions. variables, and derived matrices combine to pro- The fourth type of controller is the optimal vide optimal control of the system. controller which requires a microprocessor and is not yet commercially developed (3). How well SIMULATION RESULTS these four controllers perform with this PV/T system in various configurations for heating and Figure 4 demonstrates the effect of parasi- cooling seasons follows. tic pump electric energy on PV/T collector out- put (thermal plus electric) for various flow Generally, the more sophisticated the con- rates for a typical case of winter heating using trol, the better the potential performance (and proportional control. The gross collector out- flexibility) of the system but at the cost of put shown in the figure represents no parasitic greater complexity, expense, and less available losses and demonstrates that total PV/T collect- hardware (or software development in the case of or output continuously increases with increasing the microprocessor) (4). Whether the advantages coolant mass flow rate, although the rate of in- of optimal control significantly outweigh the crease becomes small above 2500 kg/hr flow rate, disadvantages for this PV /T system is one ques- In a real system however, the pump power can be tion this research addresses. represented as an exponential relationship. The cases for exponent values of 1 and 3 are shown The first formulation of optimal control in Figure 4 which demonstrate a peak for net uses Pontryagin's Minimum Principle with the collector output. Thus, there is an important objective being to minimize the total auxiliary tradeoff between maximizing thermal (and hence energy used (5,6). A cost functional based on electric) energy extraction and minimizing para- total auxiliary energy use is defined and mini- sitic losses. At very low flow rates there can mized subject to the state equations governing be a 5 percent difference between gross and net the system behavior and to control constraints, output while at very high flow rates the differ- Each system configuration has a different state ence can be as high as 15 to 25 percent. Fortu- equation and control constraint where the con- nately, it is noted in the figure that there is straint determines the approach of the verifica- a broad operating range where losses are accept- tion. A formal optimum of on/off control, dic- able which allows flexibility in operation tated by sys tern parameter values and operating between low and medium flow rates. mode, is obtained in all cases investigated. However, the structuring of an optimal control The combined PV/T collector mean plate tem- problem, for it to be solvable, often requires perature while using conventional and optimal restrictive assumptions -- as is the case in controllers is shown in Figure 5 for the winter this investigation (details on the system equa- direct heating case. The higher the temperature tions, assumptions, and application of the Mini- of the cells, the lower the electrical efficien- mum Principle are available in (7)). Thus a cy (but thermal extraction efficiency from the linear optimal control solution is derived and collector will be enhanced). In the figure, it simulated since this is a more practical optimal is noted that on/off with hysteresis causes the control which has the potential for implementa- collector to run at the highest temperatures. tion on a real PV/T system. Decreasing temperatures follow increasing con- trol sophistication. The largest difference The formulation of the linear optimal con- between highest and lowest mean plate tempera- trol problem requires: 1) a mathematical de- ture, between 6 to 8 percent, occurs at the peak scription (or model) of the process to be con- of the curve (at 1300 hours). The ef feet is trolled, 2) a statement of the physical con- less pronounced elsewhere. straints, and 3) specification of a performance Criteria. The PV/T system model is described by Total auxiliary energy requirements for the a non-linear vector differential equation. The winter direct heating system is shown in Figure equations are then linearized about an equili- 6. In the figure, a large difference in auxili- brium point with the disturbance variables held ary energy use is noted between on/off with hys- constant during the adaptation (controlled) in- teresis and the other three control modes. The terval. Optimal linear regulator theory is ap- on/off with hysteresis auxiliary energy use does Plied to the linearized equations of the system drop below the others at the hour of 1000 but to obtain the optimal feedback gains of the two this does not make up for the significantly fluid pumps. "Optimal" is used in the sense higher energy required from 0600 tb 1000. The 1658 Page 516 multilevel and proportional conventional control life of the system, strategies perform well with the optimal control using the least amount of.auxiliary energy. The next system configuration considered was that of parallel heat pump heating during The mass flow rate through the PV/T collec- the winter season, Total auxiliary energy re- tor is shown in Figure 7 detailing the early quired by the system while using the different morning hours in order to show the morning controllers is shown in Figure 9. In this case, start-up time, It is seen that optimal control the parallel heat pump uses as its heat source causes the earliest start-up of the collector, the ambient air (relatively cold winter outside allowing maximum collection of early morning in- air) and is not assisted by the solar thermal solation. Under optimal control, the collector system, Comparing Figure 9 to Figure 8 shows flow rate also reaches its maximum value of 2400 that the energy penalty can be significant and kg/hr later than the other three control modes can approach a doubling of auxiliary energy use. (at the hour of 1000). The collector mass flow However, the initial capital cost and subsequent rate approaching the evening shut-off time maintenance cost of the parallel heat pump will behaved. in a similar manner, Here the optimal be significantly lower than that of the series control shuts off the collector the latest, tak- system, As seen in Figure 9, total auxiliary ing maximum advantage of the evening insolation. energy use decreases with increasing control sophistication, Optimal control gives a 23,4 For the direct heat in winter case a signi- percent improvement in lowered auxiliary energy ficant improvement in system operation (longer requirements compared to on/off with hysteresis operating times, more total collected energy, and performs well even when compared to the and less auxiliary energy required) is noted other conventional controllers, when more sophisticated control schemes are im- plemented, particularly when using on/off with The first summer cooling season system con- hysteresis as the benchmark, Relative differ- figuration to be considered is that of parallel ences between multilevel, proportional, and op- heat pump cooling. Figure 10 shows the total timal control are, however, small, If the dif- auxiliary energy required by the system while ferences remained this small for all system con- using the various controllers, It is noted that figurations, optimal control would be too com- auxiliary energy differences here are less pro- plex and expensive to be justified, However, in nounced than was the case for winter heating the system configurations which follow, the per- although the sophisticated controllers do per- formance advantages of optimal control become form better than the on/off with hysteresis, more pronounced, The optimal control pattern is smooth but tends to be a bit higher than expected at the early The total auxiliary energy required by the morning and late evening hours. Here the advan- solar assisted series heat pump heating system tage between optimal control and proportional while using the different controllers is shown control appears slight, in Figure 8, The proportional and optimal con- trollers show significant savings in auxiliary For parallel heat pump cooling using dif- energy use over the other two controllers, The ferent controllers, the multilevel improvement difference is particularly dramatic for the over on/off with hysteresis is small and would on/ off with hys ters is benchmark case. Towards not justify the multilevel control complexitY• the end of the days solar operation (1400 to The proportional and linear optimal control 1800 hours) there is some crossover of auxiliary percent improvement in auxiliary energy savings energy use relative rankings, but these are of 10,7 and 15,4 percent respectively are signi- minor compared to the large differences which ficant and may well justify the increased con- occur during the peak hours of solar operation trol complexity. This would be particularlY (0600 to 1400 hours), true if electricity time-of-day rates come into effect since most utilities are still summer As was the case for direct heating, linear peaking, Collector operation gets longer for optimal control maximizes useful total (thermal increasingly sophisticated controllers but dif- plus electric) energy collected and produces the ferences in start-up or shut-off time are less lowest system requirements for auxiliary energy. than for winter simulations, The percent performance improvement of the more advanced controllers over the benchmark on/off The last system configuration investigated with hysteresis is seen to be significant, Of is that of series heat pump cooling, Since the particular interest is the fact that optimal series heat pump in cooling uses the same source control is clearly superior to the multilevel and sink as does the parallel heat pump in cool- and proportional conventional controllers - a ing, performance characteristics are similar, fact that was not as evident in the direct heat However, parallel heat pump performance can be case, With optimal control reducing auxiliary better optimized for summer operation than ca~ energy use by 25,6 percent over on/off with hys- the series, The total auxiliary energy require teresis, and performing well even against more by the PV/T system while using the different advanced conventional controllers, its added controllers is shown for series heat pump co ol-, to cost and complexity may be justified over the ing in Figure 11. The pattern is similar 1659 Page 517 that for parallel heat pump cooling shown previ- in auxiliary energy usage and improved ously in Figure 10, As expected, auxiliary overall system performance, energy use is slightly higher for the series heat pump case, As shown in Figure 11, the more 3, Use of the series heat pump configuration sophisticated the control, the better the per- offers definite performance advantages formance of the system, Proportional and opti- over the parallel design (due to the mal control percent improvement in decreased higher evaporator source temperature in auxiliary energy use are 12,6 and 16,5 percent the winter), respectively, Thus the series heat pump cooling system uses more energy than the parallel heat 4, Standard linear optimal control techniques pump case, but benefits slightly more from the are effective in controlling this PV/T implementation of optimal control. Again, the system in an optimal manner, potential energy savings benefits through use of optimal control are significant, Whether improvement in system performance justifies the added cost and complexity of opti- It is seen that for all system configura- mal controllers will depend upon future costs of tions, for both the heating and cooling seasons, conventional fuels, photovoltaic devices, and that increasing the control sophistication im- microprocessors, The techniques used in opti- proves system performance, This is particularly mizing PV/T system performance in this study can true for the most advanced control methodology, also be applied to other energy systems where namely, optimal control. Performance improve- tradeoffs exist between electric and thermal ment by use of optimal control is very pro- outputs such as conventional or advanced cogen- nounced relative to on/off with hysteresis in eration systems, all cases, Relative to the other two conven- tional controllers, optimal control performance REFERENCES improvement is most pronounced for solar assisted series heat pump heating, parallel heat 1) Evans, D,L,, W,A, Facinelli, and R,T, Otter- pump heating, parallel heat pump cooling, and bein, "Combined Photovoltaic /Thermal Sys tern series heat pump cooling, The least pronounced Studies," Arizona State University, Mechani- improvement is for the direct heating case. The cal Engineering Department, Tempe, Arizona, improved system performance through use of opti- SAND78-7031, August 1978, mal control runs the gamut from decreased PV /T collector operating temperatures, increased col- 2) Florschuetz, L.W., "Extension of the Hottel- lector operating time, increased total energy Whillier Model to the Analysis of Combined collected, and decreased needs for auxiliary Photovoltaic/Thermal Flat Plate Colectors," energy, Whether optimal control is justified Solar Energy, Vol, 22, pp, 361-366, 1979, thus becomes an economic rather than a perfor- mance question. 3) Dorato, P,, "A Review of the Application of Modern Control Theory to Solar Energy Sys- SUMMARY AND CONCLUSIONS tems, 11 Proceedings of the 18th IEEE Confer- ence on Decision and Control, Ft. Lauder- One method of improving the overall effi- dale, Florida, December 1979, ciency of solar electric systems is to make use of the waste heat generated to supply on-site 4) Herczfeld, P.R., et al., "Experimental Vali- thermal loads, This cogeneration process occurs dation of Dynamic Control Models, 11 Proceed- during operation of a PV/T system, Another ings of the Third Systems Simulation and method of improving energy system efficiency is Economic Analysis Conference, Reno, Nevada, to monitor the thermal state of the sys tern and American Society of Mechanical Engineers, to make optimum adjustments to controllable var- New York, New York, April 1981. iables when the sys tern is subjected to uncon- trollable inputs, such as those due to weather, 5) Winn, C.B. and D.E. Hull, "Optimal Control- This research combined these two approaches of lers of the Second Kind," Solar Energy, Vol. energy cogeneration and optimal control, and 23, No. 6, pp, 529-534, 1979. studied the effectiveness of the combination, 6) Auslander, D,M,, M. Tomizuka, and H. Lee, Several of the more important findings are "An Optimal Standard for Solar Heating Sys- listed below: tems," Transactions of the ASME, Journal of Dynamic Systems Measurement, and Control, 1. The tradeoff between increased temperature Vol. 101, pp. 138-149, June 1979. of the solar cells (lower collector mass flow rate) and the decrease in overall 7) Bazques, E.O., Control and Performance of a system efficiency does exist, and is a Photovoltaic/Thermal Energy System, doctoral significant design consideration. dissertation, Department of Mechanical Engi- neering, University of Maryland, College 2, Increasing sophistication in the control Park, December 1983. mode does lead to a significant decrease 1660 Page 518 ......---1, I ....1 ..1t 1.~ - tr.,l• -q. .. -,.,. -,, - ... .,. ......., ...c 1 . . ,. ... •.rtlh ,._.. ,, t u.u ... 1.£:olll r ltalc PltH ... f'Mlt ... D.e. c.u D,C. '• un Al, O.t,-t Ot.it,-t -·--· ,K. I.M..:. .. .,.,,.r1 ... llHU"iC \.Hill ·--·- K/M; ..... ,,. . ll•cntc Lo-'• l, , ..... , .. , ...r iff t. , ..I.t.,. , ... J,.l.f..f.t..,.-.,.. l•l..4 .t,U.1t'l.C_ 2, .. _, C..u••H J, ll'Ntnlfl. . J. DtftHUlH 11:nu, ll"ntc 1 ,:uu.,, llffcrtc Figure 1. Combined Photovoltaic/Thermal Energy Figure 2. Combined Photovoltaic/Thermal Energy System Utilizing a Series Heat Pump System Utilizing a Parallel Heat Pump R Q Equilibrium Riccati Point Equation !•.Q. + J!. --------1J!*-rlB!Kx:,-1"""-.;.;1<_ __________________. ..J 1l Figure 3. Information Flow Diagram for Optimal Photovoltaic/Thermal Solar Heating and Cooling System with Linearized Equations Optimal OOO F'V /T Colloclol' Ou14Nt MJ/ 1 100Fco~ll~oct~«;;_;T~-~pon,tun,==:...,;;(C"---------------------, 900 90 1900 eo 700 70 1900 IIO 300 30 200 20 ,oo 10 0 '::-0---1:-.:000':-:----2"'000':-:----,3000~,--..-..-...=., ----...=..... _ __&0 00.....J 0 '="ooo""""--o'"'o100~-;_""""':-:----,""200..,._ ___1 _&00..,._ __2 ,...ooo'---2-o100...J Coolont hlou Flow Role (k9/hr) 11tno ., 0oy ~ionol Control - Winter lliNcl Hoolin9, llaaollM ~tom. WintM Sirnulotion Figure 4. Effect of PV/T Collector Coolant Flow Figure S. Combined PV/T Colle~tor Mean Plate Tem- Rate on Gross and Net Collector Output perature while using Different Control 1661 Page 519 - (MJ/hr) ~ ;:.-=...l::!i!!!.I'-.------------------. 20 2000 15 1500 IQ 1000 0 ~ooo=--~~:-----=oaoo'*=--.i..,.,,:<200~---1eoo"'-:----2000...__=-2-400..J O: ::oaoo=---.....::::....::::::.. ___. J...._,OIOO,±~---.L-..l._ ___100 0_J Time of Day - of Day Ohct llecUng, 8oMIIM S)'Stem, - 5lmuiatlon Dnct IMotlng. lloMllne S)'Stem, - S1tnu1o11on Figure 6. Total Auxiliary Energy Required by the Figure 7. Detail of Mass Flow Rate through the System while using Different Controllers PV/T Collector Showing Morning Start Up Time ,=::::.L..:En4t'g)<=!!...>.(W~/hr:.:.l,.._ _______________ 25 20 15 IQ 0 '=---:-:'::-:----~,----,.,.,._ __, .._ ___ _. ___. ....J 0400 oaoo 1200 1 eoo 2000 2400 COO 0400 0800 1200 1!500 2000 2400 Time of Oc,y Time of Oc,y s.riu Hool Pump Healing, Bonlln• Syai.m, Wintor SlmuloUon Porollol Hool Pump Hootlnq, BoHlfno Syatem, Wlntor Simulation Figure 8. Total Auxiliary Energy Required by the Figure 9. Total Auxiliary Energy Required by the System while using Different Controllers System while using Different Control ~ rhJ::::•::::illory=..::En:.:=.i~(W:=L/hr:.::..!..) ________________~ 18 20 12 15 10 10 0 ;;:aoo~---,o,.:400~---,oaoo"""':-----,1.,,200,.,,.----,1_,eo_o ____20 00_._ __ _J oeoo 1200 , eoo 2000 2400 Tune of Day Time of Oc,y Parallel Hoot Pump Cooling, Bonlln• Syat.m, Summer Simulation Series lloot Pump Coolinq, 8asollne System, s..mm.r Simulation Figure 10. Total Auxiliary Energy Required by the Figure 11. Total Auxiliary Energy Required by the System while using Different Control System while using Diffe~ent Control 1662 Page 520 Reprinted from August 1984, Vol. l 06, Journal of Solar Energy Engineering D. K. Anand 1 Professor ot Mechanical Engineering, University of Maryland, College Park. Md. 207 42 Second Law Analysis of Solar K. W. Lindler Engineer. Powered Absorption Cooling TPI Inc .. Bethesda, Md. 20817 Cycles and Systems S. Schweitzer The Second Law of Thermodynamics is used to analyze solar powered absorption Office of Solar Heat cooling cycles and systems. Irreversibility is used as a figure of merit for com- Technologies. ponents and cycles. The irreversibility of individual components is determined for U.S. Department of Energy, several solar-powered absorption cycles and systems. The understanding of the Washington, D.C. causes of these irreversibilities identifies the areas of possible cycle and system improvements. W. J. Kennish Engineer, TPI Inc., Bethesda, Md. 20817 Introduction In recent years there has been growing interest in the use of useful consumption and the unrecoverable losses of exergy. fundamental thermodynamic principles for comprehensively These consumptions and losses of exergy generally point the analyzing and evaluating energy demand as well as way to improvement of a system. Exergy, then, can be technologies available to meet it. Specifically, the Second Law thought of as a "commodity of value" which can be con- of Thermodynamics has been used to better understand the sumed to effect a useful purpose or is lost due to the inherent irreversible nature of real processes and systems and thereby design or constraints imposed on a system or process. define the upper bounds of available energy. 2 This available Many researchers have been active in the Second Law energy is defined as the theoretical maximum total work that analysis of various energy conversion components and is derivable by the interaction of an energy resource with the systems (reference [1-16]). Of particular interest in this study environment. Exergy or available energy is irreversibly is the work done in the Second Law analysis of refrigeration consumed in any process where a potential to produce work is cycles. For example, in reference [6], Tripp presents a Second allowed to decrease without causing a fully equivalent rise in Law analysis of vapor compression refrigeration systems. His potential elsewhere. paper deals with the creation of entropy and the destruction of For a complete system analysis and optimization study of available energy due to deviations of actual cycles from competing systems, it is exergy analysis, not energy analysis, Carnot cycles. In reference [7], Briggs applies the Second Law which is the appropriate tool. This is because exergy or to an ammonia-water absorption cycle. He presents the available energy is the common denominator since all forms Second Law as an "accounting tool" to be used to determine of available energy are equivalent to each other as measures of where improvements might be made in the cycle. In reference depature from equilibrium. [41, Lavan et al. use the Second Law to demonstrate the way It is important to recognize, however, that exergy or in which the reversible coefficient of performance of an open- available energy analysis is intended to complement, not to cycle desiccant cooling system depends on humidity ratios as replace, energy analysis. Energy balances, when used in well as temperatures. conjunction with mass balances and other physical principles, In recognition of the essential role that a Second Law help define the desired system. The system that satisfies the analysis plays in the understanding and evaluation of energy imposed constraints (such as thermal and economic) and systems, a meeting of researchers active in thermodynamics minimizes exergy losses is the optimal system. More im- was held on May 9-10, 1983 in Washington, D.C. to discuss portantly, a Second Law analysis pin points and quantifies the the implications of the Second Law of Thermodynamics (references [17-30]) as they apply to irreversibilities in solar 1 Also, President, TPl, Inc., Bethesda, Md. 20817. systems in general and solar cooling in particular. 2 Also called essergy, exergy, useful energy, equivalent work, and others. This study is concerned with the use of the Second Law of Thermodynamics for (a) the analysis of basic irreversibilities Contributed by the Solar Energy Division for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING. Manuscript received by the Solar Energy associated with absorption cycles and the components that Division, October, 1983. comprise it and (b) analysis of two complete solar driven Journal of Solar Energy Engineering AUGUST 1984, Vol. 106 / 291 Page 521 coolimg systems using absorption cycles. Mathematical and When heat is added there will be a corresponding increase in computational details omitted here, for brevity, are discussed s 2 and/or s 0 which will result in a net increase of irrever- in detail in reference [16). sibility. An expression for the reversible work and irreversibility Thermodynamic Principles that provides a different insight into the thermodynamic process can be derived using the availability functions f (per For the Second Law to be used to analyze solar cooling unit mass/low) and (per unit mass in the control volume). systems, component-by-component as well as systems as a whole, it is necessary to develop the Second Law for the uniform-state, uniform-flow (USUF) process. Appropriate simplifications will yield the necessary equations for the steady-state, steady-flow process and for a thermodynamic cycle. To derive expressions for irreversibility, we consider a real and reversible USUF process. In the real process, heat Qn. is (4) transferred from the surroundings at temperature T0 and heat The last term is the availability or "exergy" associated with Qfl is transferred from a source at temperature T fl· In a reversible process having the same inlet, exit, initial, the heat transferred from the source maintained at a tem- and final states as the real process, two Carnot engines are perature T fl. added so that the heat transferred across a finite temperature The work done by the control volume can be separated into difference can be accomplished reversibly. useful work ( W11 ) and the work necessary to displace the surroundings. For a real system, the First Law readily yields (1) wcv = Wu +PoCV2 -¥1) (5) The irreversibility becomes where v2 6En.=m2(u2+ ~~ +gz2)-m1(u1+ ~T +gz1) l=Em;if;,-Emcfe+m1 (¢1 +- -f +gz1) For the reversible process, the First and Second Law provide -m, 0 ( ri-., + -V~ +g"', ) +Q ( 1--T - ) -W (6) " '1'- 2 ~L fl T fl 11 Note that the work required to displace the surroundings +QH(1-~) (2) P 0 (-¥2 --¥i) cancels out of equation (6). Even though this TH work is not "useful" it is not an irreversibility because the The irreversibility ([) of a process is the difference between associated availability of the system is completely regained if the reversible work that could theoretically be produced and the control volume returns to its initial volume, V1 • the work that is actually produced, thus For steady-state steady-flow applications, the previous equations can easily be written as rate equations. l= EmeTose -EmiT0 s1 +m2 T 0 s2 Referring to equation (4) it can be seen that heat Q added to a control volume from a source at temperature T has an -m1Tos1 -Qn,-Qfl( ;: ) (3) "equivalent work" (EW) value given by Conclusions drawn from equation (3) can be misleading since (7) it first appears as though heat transferred from the surrounding QCl' or heat transferred from the heat source QH where T 0 is the ambient temperature. The previous equations decrease the irreversibility of the process which is not the case. can thus be modified using this definition. ----Nomenclature = (u - u0 )+P0 (v-v0 )-T0 (s-s ) 0 COP coefficient of performance 'I efficiency E energy, E= Em (h + ~ + gz) Subscripts A absorber EW equivalent work; exergy of heat C condenser h enthalpy cu control volume I irreversibility cycle thermodynamic cycle m mass E evaporator Q heat transfer e exit s specific entropy G generator T temperature H heat source u specific internal energy HX heat exchanger V velocity i inlet ¥,u volume, specific volume L chilled water w work max maximum z elevation V" 0 ambient f availability for mass flow, f = ( h - T 0 s + +gz) rev reversible 2 u useful 1 initial 2 final 292 / Vol. 106, AUGUST 1984 Transactions of the ASME Page 522 For a thermodynamic cycle exchanging heat with more than one source (as well as with the surroundings) equation (6) reduces to . = . ( To) . . . f,ycle EQ 1 - T - Wu= EEW- W,, (8) (The dot ( ) signifies the first derivative with respect to time.) Equation (8) can be used to determine the overall irreversibility for an absorption cycle. Equations (3) and (6) can be used to determine the contribution of each component 0 to the overall irreversibility of the cycle. An equation relating °V') overall cycle irreversibility to system COP is desirable in that I it allows an immediate determination of the increase in the coefficient of performance for a given decrease in overall cycle irreversibility. For a given heat source, evaporator, and ambient tem- perature, the coefficient of performance can be shown to be COP= COP (1- Bi,yc/e ) max V (9) G where (10) and COPmax= TL ( TH T 0 ) (11) T11 T() -TL Thus for constant EWc , the COP decreases linearly with increasing irreversibility. Absorption Cycle Irreversibility For the absorption cycle, there are four main causes of irreversibility. They are: 1. Heat transfer through a finite temperature difference; 2. Mixing two fluids of different temperatures; 3. Mixing two fluids with different concentrations; 4. Unrestrained expansion during a throttling process. One or more of these causes affects the irreversibility of each of the components. The overall cycle irreversibility as obtained from equation (8) should be equal to the sum of the individual component irreversibilities as determined by equation (3) or (6). The detailed computations for an ammonia-water ab- sorption cycle and the lithium bromide-water absorption cycles are given in references [7] and [16]. The results are shown in Table 1 and the appropriate temperatures are presented in Table 2. Preliminary calculations of the single-effect lithium bromide-water absorption cycle resulted m a predicted coefficient of performance of 0.827 which is somewhat higher than that achieved in practice. The difference lies in the simplifying assumptions made for the calculations which include the following: 1. Neglecting pressure losses (assume generator and condenser pressures are equal); 2. Assuming the stroag solution leaving the generator is saturated; 3. Assuming the weak solution leaving the absorber 1s saturated; 4. Neglecting the dumpjng of excess liquid refrigerant into the solution sump; 5. Neglecting undesirable heat transfer to the evaporator; 6. Neglecting heat loss from the generator to the ambient; 7. Neglecting heat loss from the solution heat exchanger; 8. Assuming a solution heat exchanger effectiveness of 1. Journal of Solar Energy Engineering AUGUST 1984, Vol.106/293 Page 523 Table 2 Assumed temperatures for the absorption cycle calculations Single-effect Double-effect Lithium Bromide- Lithium Bromide- Ammonia-water cycle water cycle water cycle Heat source T1-1 450°F 200°F 292"F Generator Tc; 364°F 190"F 282"F Condenser Tc 172"-123"F JOO"F I00°F Evaporator Tf 38°-SO"F 45"F 45"F Chilled water T1 60°F 55"F 55°F Absorber T,1 l30°F JOO"F lOO"F Ambient T., 95°F 85°F 85°F --------------------- Table 3 Definition of the First and Second Law efficiencies Mode Control strategy (energy flow) First Law efficiency Second Law efficiency ------- ] off 0 0 2 collector-ballast increase in stored energy increase in stored exergy energy striking the collector exergy striking the collector 3 collector - ballast-cooling cooling energy + stored energy cooling exergy + stored exergy storaoe . energy striking the collector exergy striking the collector 4 collector - balla~t - cooling same as mode 3 5 storage collector- ballast same as mode 2 6 ballast -cooling cooling energy cooling exergy decrease in stored energy decrease in stored exergy 7 storage-cooling same as mode 6 8 freeze protection 0 0 9 heat dump 0 0 cooling energy cooling exergy ---------- Overall' energy striking the collector ex erg y striking 1he collector ---------------·---- 'Assumes change in stored energy from day to day is negligible. Relaxation of these assumptions for the single-effect LiBr- H 20 absorption cycle leads to a lower and more realistic COP of 0. 719 as shown in Table 1. The major differences obtained with the more realistic assumptions are an increase in EWc , a decrease in EW1c, and an increase in generator and absorber irreversibilities. It should be noted that the more realistic assumptions are not representative of off-design per- formance. An off-design study would have to include the effect that raising and lowering the generator, evaporation, and ambient temperature has on the cycle. From the previous analysis (and from equation (9)), it is clear that for the cycle COP to increase, the individual irreversibilities of the components must decrease. This can be achieved in a variety of ways. For example, an improvement in COP from 0.827 to 0.844 can be obtained by allowing the fluid leaving the evaporator to precool the fluid leaving the condenser or by subcooling the fluid with a larger condenser. These and other modifications were investigated in detail in reference [16]. It was found, for example, that the addition of Fig. 1 Schematic of the LBL solar cooling system a pregenerator and a preabsorber improved the COP from 0.844 to 0.864. Clearly, such an improvement in COP cannot economically justify the addition of two components to the basic cycle. 190°F to 200°F resulted in a decrease in COP. This result can A parameteric study was undertaken for which the heat be understood by examining the effect that the elevated transfer for the generator, condenser, evaporator, and ab- generator temperature has on the change in irreversibility for sorber was assumed to take place across a zero degree tem- each of the system components. Elevating the generator perature difference (100 percent heat exchanger ef- temperature resulted in an increase in irreversibility for the fectiveness). A solution heat exchanger effectiveness of both heat exchanger and condenser that was greater than the 7 5 and 100 percent was considered. It was determined that the decrease in irreversibility for the absorber and generator, biggest improvement in COP was obtained by improving the leading to an overall increase in irreversibility. This increase solution and evaporator heat exchangers. Improvement in the in cycle irreversibility results in a decrease in COP as dictated absorber and condenser heat exchangers resulted in a smaller by equation (9). improvement in COP. In general, it can be concluded that modifications that are It was found that for a 100 percent solution heat exchanger made to reduce the irreversibility of a single component will effectiveness, increasing the generator temperature from not necessarily lead to a reduced overall irreversibility. The 294 / Vol. 106, AUGUST 1984 Transactions of the ASME Page 524 Page 525 c . . . 0 C : . . . : I ! ! ? . 2 . ( / ) 0 0 ) . . . m : I ( 1 ) . . . T a b l e 4 E n e r g y a n d e x e r g y b a l a n c e f o r L B L c o o l i n g s y s t e m ( s i m u l a t e d d a t a ) ( 0 ' < m E n e r g y i n t E n e r g y s t o r e d E n e r g y o u t : I ( 0 a b s o r b e r E n e r g y : I p i p e s + E f f - / * M o d e H r C o l l e c t o r c o o l i n g B a l l a s t + s t o r a g e = t o t a l C o l l e c t o r + h e a t d u m p + b a l l a s t + s t o r a g e + c o n d e n s e r + m i x e r s = t o t a l b a l a n c e ( 1 ) ( 1 ) - 3 . 2 - 8 . 9 - 1 2 . 1 3 . 2 8 . 9 0 . 0 0 . 0 1 8 . 9 6 9 2 4 . 8 0 . 0 2 4 . 8 0 . 0 0 . 0 0 . 0 0 . 0 3 6 . 9 : : ! . : I 2 . 4 0 6 - 2 . 5 1 6 7 . 4 2 . 5 0 . 0 2 9 6 6 . 6 0 . 0 1 7 0 . 0 7 6 5 . 4 0 . 0 0 . 8 0 . 0 3 0 . 4 0 . 0 1 7 . 3 7 9 9 . 2 ( 0 2 . 2 5 0 - 1 8 . 8 - 2 . 1 2 . 1 0 . 0 2 5 . 2 2 2 3 7 . 3 5 8 3 . 6 2 0 . 9 1 4 0 5 . 3 0 . 0 0 . 9 1 4 0 4 . 2 2 9 . 3 2 8 4 1 . 8 0 . 0 3 - . 2 7 . 0 9 4 - 1 0 8 . 1 0 . 0 4 9 1 5 2 . 5 1 9 0 2 . 1 1 1 7 3 . 4 1 0 6 5 . 3 5 2 9 7 . 5 0 . 0 3 . 1 8 . 3 4 5 7 7 . 6 1 0 2 . 9 9 9 8 9 . 4 3 2 . 4 0 . 0 . 0 0 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 5 0 . 0 0 . 0 0 . 0 - 8 . 0 0 . 0 . 0 3 1 - 8 . 0 0 . 0 0 . 0 1 3 . 5 0 . 0 1 3 . 6 0 . 0 6 8 . 6 6 0 . 0 5 . 5 0 . 0 0 . 0 0 . 0 3 . 2 5 0 8 1 8 . 3 2 2 . 9 - 1 1 3 3 . 4 - 1 1 5 6 . 3 0 . 0 1 . 4 1 9 6 9 . 6 0 . 0 0 . 0 1 9 9 3 . 3 0 . 0 7 0 . 8 7 1 8 . 8 1 8 . 8 3 . 6 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 . 0 0 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 8 0 . 0 0 . 0 0 . 0 9 . 0 0 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 - 0 . 2 2 5 . 3 7 9 6 5 . 0 1 6 2 . 6 0 . 0 1 5 6 7 4 . J 2 6 . 7 2 4 . 0 0 0 1 2 3 9 9 . 9 3 3 0 9 . 4 9 . 0 2 6 . 4 3 5 . 5 7 5 I I . 7 0 . 0 9 . 4 E x e r g y i n t E x e r g y s t o r e d C o m p o n e n t i r r e v e r s i b i l i t y E x e r g y p i p e s + b a l a n c e E f f - I I * H r C o l l e c t o r c o o l i n g s t o r a g e = C o l l e c t o r + h e a t d u m p + b a l l a s t + s t o r a g e + c h i l l e r + m i x e r s = t o t a l M o d e B a l l a s t + t o t a l - 1 . 2 0 . 0 8 . 9 6 9 0 . 0 - 0 . 4 1 . 6 2 4 . 8 0 . 0 . 4 0 . 0 0 . 0 2 6 . 4 0 . 0 0 . 0 1 2 4 . 8 1 . 2 2 . 4 0 6 - 0 . 4 2 4 . 6 0 . 0 . 6 0 . 0 4 . 3 0 . 0 9 4 2 . 1 0 . 0 2 . 5 2 9 6 6 . 6 0 . 0 2 5 . 0 9 3 6 . 8 0 . 4 2 . 2 0 5 - 4 6 . 2 - 0 . 7 - 0 . 3 - 1 . 0 1 . 7 7 4 . 4 4 . 5 4 . 0 2 1 9 2 . 1 0 . 0 2 . 0 2 2 3 7 . 3 2 1 0 7 . 2 0 . 0 0 . 3 3 - . 2 7 . 0 9 4 - 1 5 0 . 7 - 1 8 . 3 1 9 0 . 8 1 . 7 2 4 6 . 2 1 8 . 2 7 0 . 0 8 8 2 9 . 4 3 . 5 4 9 1 5 2 . 5 1 7 2 . 5 8 4 8 5 . 6 0 . 0 7 . 7 . 0 0 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 . 0 0 . 0 0 . 0 5 0 . 0 0 . 0 0 . 0 0 . 0 - 0 . 4 - I . I . 0 3 1 0 . 0 0 . 0 0 . 0 0 . 6 0 . 0 0 . 0 . 6 0 . 0 4 0 . 4 6 0 . 0 1 . 1 0 . 0 0 . 0 - 6 4 . 8 - 1 8 5 . 5 7 3 . 2 5 0 1 8 . 8 - 3 . 2 1 8 8 . 7 1 8 . 8 0 . 0 3 . 6 7 . 5 1 0 3 . 2 0 . 0 9 . 6 1 4 2 . 6 0 . 0 3 4 . 4 0 . 0 . 0 0 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 . 0 0 . 0 8 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 . 0 0 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 . 0 0 . 0 9 0 . 0 0 . 0 0 . 0 0 . 0 ) > - 0 . 2 - 2 6 2 . 3 4 . 7 8 . 1 1 7 . 1 4 2 4 . 4 2 7 . 0 8 3 . 5 1 2 1 3 3 . 2 2 . 1 2 4 . 0 0 0 1 2 3 9 9 . 9 1 . 2 3 . 5 1 1 5 7 3 . 2 0 . 0 C G ) * T h e F i r s t a n d S e c o n d L a w e f f i c i e n c i e s a r e d e f i n e d i n T a b l e 3 . C ( / ) t A l l e n e r g y a n d e x e r g y q u a n t i t i e s a r e i n M J . - - l ( 0 0 0 + s o < 0 0 0 ) I \ ) ( 0 c . n First Law Analysis Cooling Energy Energy Striking (26. 7) Collector ( 100) Co 11 ector Pi oe Storage Chiller Loss Loss Loss Inefficiency (GO. 6) ( 1. 3) (. 3) (10.3) Second Law Analysis Cooling Exergy Exergy Stri kin a Supplied Co 11 ector (2 .12) (100) Collector Pipe Storage Mixer Chiller Irreversibility I rrevers i - Irreversi- Irreversi- I rrevers i - (93. 33) bil ity bility bility bil ity (. 22) (. 20) (. 67) (3.42) Fig. 2 First and second yaw analysis of the LBL cooling system (July 27) First La1< Analysis Cooling Energy Energy Strikinn (9. 5) Collector (100) Collector Pipe Storage Chiller Loss Loss Loss Inefficiency (79.8) (4.4) (2. 3) (6. 3) Second Law Analysis Cooling Exergy Exergy Striking Supplied Co 11 ector (. 34) (100) Co 11 ector Collector Pipe Storage Mixer & Other Chiller I rrevers i - Irreversibility Irreversi- Pipes Irre- Irreversibility bil ity (. 36) . bility versibility (1.77) (97. 05) ( .42) (. 39) Fig. 3 First and second law analysis of the San Anselmo School effect on the entire cycle must be kept in mind when con- The simulated output was used as the input data for the sidering a change in the basic cycle. Second Law analysis program (IRREVS) which calculates the irreversibility of each of the system components for each Case Study - Simulated Data timestep of the simulation. Output from IRREVS includes a table providing a complete energy and exergy balance of each The Second Law of Thermodynamics has been used to operating mode of the system - an example of which is shown analyze all of the major components of two existing solar- in Table 4. This information is then used to prepare the energy powered absorption systems. Both systems use a single-effect and exergy chart shown in Fig. 2 which clearly identifies the lithium bromide-water absorption chiller powered by First and Second Law losses. evacuated tube collectors. It is interesting to note the contrast in the First and Second The first cycle considered was the solar-driven chiller used Law efficiencies. For example, referring to Fig. 2, we see that for the Lawrence Berkeley Laboratory Heavy Ion Accelerator the First Law efficiency of the collector is 39.4 percent while building (LBL) in Berkeley, California. As no real per- the Second Law efficiency is only 6.67 percent. This is due to formance data is yet available for this site, a computer model the fact that the thermal energy collected is available at a was developed to simulate the system. A schematic of the temperature that is much lower than that of the sun. Also note system is shown in Fig. 1. that the irreversibility due to mixing does not appear as a First The system has a control strategy that has nine operating Law loss. modes which are described in Table 3. The simulated data used for the Second Law analysis of the LBL solar cooling site Case Study - Experimental Data was generated using a computer simulation program (reference [31]). The second system considered was the solar-driven chiller 296/Vol.106, AUGUST 1984 Transactions of the ASME Page 526 used for the San Anselmo School of San Jose, California. Real data was used to analyze the system. The advantage of using real data is that it emphasizes the fact that systems do not always operate as they are designed, owing to larger system irreversibilities and control system malfunctions that are not anticipated. A computer program, SANIRR, was used to provide a complete First and Second Law analysis of real data for five .... consecutive days in July 1981. ~ Table 5 shows the energy and exergy balance for the five- :u2 day period with an energy and exergy chart shown in Fig. 3. Both the First and Second Law analysis indicates that the system performance is poor with the collector being the biggest offender. An evaluation of the data indicates that the poor collector performance can be attributed to malfunc- tioning controls. When the collector exit temperature exceeds 17 5 ° F all of the collector flow should be directed through the storage. The data indicates that much of the flow is bypassing the storage resulting in a higher collector operating tem- perature and thus a lower efficiency. The data also indicates --oV'l- oo that the collector is being deactivated too early (2:30 p.m.) ("f)("f"')("f"')('l("f') :!; resulting in large afternoon and evening losses. It is in- teresting to note that although more "cooling energy" was supplied on Wednesday than Friday, more "cooling exergy" was supplied on Friday. This is due to the fact that on Friday .... the chilled water provided was at a lower temperature. The .... -0v"' -0v"' First Law does not attempt to place a higher value on colder () 0. () 0. V·- =V ·- chilled water while the Second Law does. In practice, colder 0- 0. 0. u u0 chilled water is more valuable because it requires smaller heat exchangers and has the potential for more latent cooling . .... .... .8 .8 Conclusions () () ~ ~ 0u u0 Based on the results of this study, the major conclusions are as follows: A Second Law analysis of the system appears to give more information in that the performance of individual components can be ascertained. For example, the per- formance degradation due to mixers and storage can only 00\0("1")00 ~ be determined from exergy analysis. '-nNtn~O M I ;:: For the absorption cycle, there are four main causes of irreversibility as detailed earlier yielding a COP of 0.83. However, second-order effects combine to reduce the single-effect absorption cycle COP from 0.83 to 0.72. .... This is primarily due to an increase in generator and ~ absorber irreversibilities. :2 * u Modifications made to reduce the irreversibility of a ·=>, single component will not necessarily lead to a reduced .O..J. ) V overall irreversibility since the effect on the entire cycle ,:: µ.i .... must be analyzed. 8 () V An improvement of the effectiveness of the solution heat ::g u exchanger and evaporator results in the biggest increase in the overall cycle COP. Elevating the generator temperature (for the single-effect cycle) is not worthwhile. However, the addition of a second generator for the double-effect cycle results in large decreases in irreversibility for both the generator and condenser and yields a higher cycle COP. Acknowledgment This work was supported by the Division of Solar Heat Technologies, Department of Energy, under contract DE- AC03-82SF11644. Data on the Federal Buildings Program was provided by Vitro Laboratories and ETECH, a division of Rockwell International. Journal of Solar Energy Engineering AUGUST 1984, Vol. 106 / 297 Page 527 References 18 Gaggioli, R., "Available Energy as the Commodity of Value,". presentation at the Meeting on Second Law and Irreversibility Considerations I Kestin, J., "Availability: The Concept and Associated Terminology," in Solar Cooling, May 9-10, 1983, Washington, D.C. Energy, Vol. 5. 1980, p. 697. 19 El Sayed, Y., "Minimum and Optimum Lost Work in Solar Cooling 2 Bejan, A., Kearney, D. W., and Kreith, F., "Second Law Analysis and Systems," presentation at the Meeting on Second Law and Irreversibility Synthesis of Solar Collector Systems," Journal of Solar Energy Engineering, Considerations in Solar Cooling, May 9-10, 1983, Washington, D.C. Vol. 103, Feb. 1981, pp. 23-28. 20 Anand, D. K., Lindler, K. W., and Kennish, W. J., "Second Law 3 Jeter, S. M., "Maximum Conversion Efficiency for the Utilization of Analysis of Absorption Cycles," presentation at the Meeting on Second Law Direct Solar Radiation," Solar Energy, Vol. 26, 1981, pp.231-236. and Irreversibility Considerations in Solar Cooling, May 9-JO, l 983, 4 Lavan, Z., Monnier, J.-B., and Worek, W. M., "Second Law Analysis of Washington, D.C. Desiccant Cooling Systems," submitted to ASME, JOURNAL OF SOLAR ENERGY 21 London, L., "Identifying lrreversibilities in Solar Absorption Systems," ENGINEERING, 1982. presentation at the Meeting on Second Law and Irreversibility Considerations 5 Bejan, A., "Second Law Analysis in Heat Transfer," Energy, Vol. 5, in Solar Cooling, May 9-10, 1983, Washington, D.C. 1980, pp. 721-732. 22 Wahlig, M., "Analysis and Experiments on Advanced Absorption 6 Tripp, W ., "Second Law Analysis of Compression Refrigeration Cycles," presentation at the Meeting on Second Law and Irreversibility Systems," ASHRAE Journal, Jan. 1966, p. 49. 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J., "The Second Law Efficiency of a Systems," presentation at the Meeting on Second Law and Irreversibility Heat Pump System," Energy, Vol. 5, 1980, pp. 853-863. Considerations in Solar Cooling, May9-10, 1983, Washington, D.C. II De Nevers, Noel, and Seader, J. D., "Lost Work: A Measure of Ther- 26 Edgerton, R., "Atmospheric Effects on Available Energy," presentation modynamic Efficiency," Energy, Vol. 5, 1980, pp. 757-769. at the Meeting on Second Law and Irreversibility Considerations in Solar 12 Evans, Robert B., "Thermoeconomic Isolation and Essergy Analysis," Cooling, May 9-10, 1983, Washington, D.C. Energy, Vol. 5, 1980, pp. 805-821. 27 Osterle, F., "Second Law Thermodynamics of Solar Radiation," 13 Gaggioli, R. A., and Wepfer, W. 0., "Exergy Economics," Energy, Vol. presentation at the Meeting on Second Law and Irreversibility Considerations 5, 1980, pp. 823-827. in Solar Cooling, May 9-10, 1983, Washington, D.C. 14 Newton, A. B., "Optimizing Solar Cooling Systems," ASHRAE 28 Gyftopoulos, E., "Is Entropy Limiting Our Use of Solar Energy?" Journal, Nov. 1976, pp. 26-31. presentation at the Meeting on Second Law and Irreversibility Considerations 15 Fewell, M. E., "A First and Second Law Analysis of Steam Stability in Solar Cooling, May9-l0, 1983, Washington, D.C. Flowing through Constant Diameter Pipes," Solar Engineering-1981, pp. 29 Bejan, A., "Second Law Analysis of Solar Collectors," presentation at 712-718. the Meeting on Second Law and Irreversibility Considerations in Solar Cooling, 16 Anand, D. K., Lindler, K. W., and Kennish, W. J ., "State-of-the-Art May 9-10, 1983, Washington, D.C. Assessment of the Thermodynamic Aspects of Solar Cooling," TPI Special 30 Scholten, W., "Exergy Output of Solar Collectors," presentation at the Report 83-05, Sept. l 983, Contract DE-AC03-82-SFl 1644. Meeting on Second Law and Irreversibility Considerations in Solar Cooling, 17 Kestin, J., "Overview of Second Law Analysis," presentation at the May 9-10, 1983, Washington, D.C. Meeting on Second Law and Irreversibility Considerations in Solar Cooling, 31 "TRNSYS-A Transient Simulation Program," Version ll.l, Solar May9-I0, 1983, Washington, D.C. Energy Laboratory, University of Wisconsin, Madison, Wis., Apr. 1981. 298 / Vol. 106, AUGUST 1984 Transactions of the ASME Page 528 Page 529 ~ C I I f E . . f h _ / l · . o e g e o n g 1 n e e n n g o . t e . c 0 , , , 0 , ~ ~ - O k l a h o m a S t a t e U n 1 v e r s 1 t y T h i s C e r t i f i c a t e i s a w a r d e d t o Dr . D a v e K . A n a n d ~ . ? : : . . . . -. i n r e c o g n i t i o n o f p a r t i c i p a t i o n i n t h e c : V l l o - t - ~ N S F S t u d y o n S u p e r c o m p u t e r s i n M e c h a n i c a l S y s t e m s R e s e a r c h . . r . . - . ~ S e p t . 1 2 · 1 4 , 1 9 8 4 S u p p o r t e d b y t h e = - N a t i o n a l S c i e n c e F o u n d a t i o n a n d / C o n d u c t e d a t t h e L a w r e n c e L i v e r m o r e N a t i o n a l L a b o r a t o r y L i v e r m o r e , C a l i f o r n i a ~ - ~ - ~ - . D I R E C T O R O F T H E S T U D ~ - - D E A N , C O L L E G E O F E N G I N E E R I N G , O S U T h e s o u t h - p o i n t i n g c h a r i o t , v e r y l i k e l y i n v e n t e d b y M a C h U n , t h i r d c e n f u r y SUPERCOMPUTERS AND HIERARCHICAL CONTROL: A SYSTEMS VIEWPOINT D. K. Anand, Professor J. A. Kirk, Associate Professor M. Anjanappa, Westinghouse Research Fellow M. Pecht, Assistant Professor Department of Mechanical Engineering University of Maryland College Park, Maryland 20742 Abstract research related to national security. 2 One common thread in all these applications, and those Although the computational and control needs of requiring supercomputers, is the need to efficiently the factory of the future dictate the use of super- handle very large matrices or perform many iterative computers, the use of Hierarchical control can some- computations. It is however interesting to note times suggest a different alternative. A Flexible that the current supercomputers are st il 1 not ade- Manufacturing Cell and System are used as examples quate for solving continuous problems described by to illustrate this idea. In either event, there are the Navier-Stokes equation and the Euler equations. significant research needs in computer architecture and related software specifically as these relate to This paper presents a comparative study of the concept of "concurrency" in mechanical system choosing between centralized control of a system design. using a dedicated supercomputer and Hierarchical control using a conventional computer and several Introduction microcomputers. As an example we use a Flexible Manufacturing System of the type to be used in the If a system is 1a rge enough and the number of factory of the future. Also important research real time computations are substantial, the need of areas created by the use of supercomputers in mecha- a supercomputer is generally clear. However, a nical systems are identified. detailed analysis of the system requirements can often lead to a different conclusion, especially Flexible Manufacturing System (FMS) when the concept of an Intelligent Assistant and Hierarchical Col')trol is employed. As an example, in An FMS 3 14 - would typically consist of several the case of a Flexible Manufacturing System (FMS) a (say 22) machining centers, some material handling supercomputer appears to be an ideal choice although robots (say 6) and a conveyor system to transport on further study the application of Hierarchical raw material into the system and to transfer Control with system expertness may be another alter- finished goods out of the system, for· assembling, or native, to the finished goods store. Automatic inspection stations are usually provided to make it autonomous. Although there is no firm definition of a As an alternative approach an FMS can be built by "Supercomputer" it is generally accepted as a grouping several Flexible Manufacturing Cells (FMC) machine capable of executing at least 100M Floa~ing- linked together by a public conveyor system. Each point operations per second (10 8flops) and having a FMC by itself is a complete modular system typically word length of 64 bits and a memory size measured in consisting of one machining center, one robot and a millions. For example Cyber-205, manufactured by pallet shuttle system. The approach of developing Control Data Corporation, has vector processing an FMS gradually by beginning with a single FMC has capability along with a very fpt scalar processor gained more popularity mainly due to low initial with a main memory of 32M byte • Some of the other investment costs, reliability, minimum down time as Supercomputers that are marketed are Control Data well as all the attributes acquired due to the use Corporations COC-6600, Burroughs Illiac IV, Cray of modularity. Research's Cray-1 and Cray-XMP. All the above supercomputers are of either Single-Instruction The FMS operation is controlled by a System Multiple-Data (SIMO) or of the Vector Processor Control whose requirements are as follows: (pipeline) architecture. The supercomputers are further classified as General-purpose and Special- • Input/output tasks are primarily those asso- purpose machines. An example of a Special purpose ciated with transfer of part programs, sensory data machine is the Finite-element problem solver built and control of cell components. The I/0 response at NASA-Langley Research Laboratory. must be fast enough to process potential catastrophic events which may arise in the manufac- In the United States, at present no supercom- turing environment on a real time basis. The speed puters are dedicated for use in manufacturing or the associated with normal work-in-process tasks of an commercial sector. They are, however, used for high FMS is generally not a critical factor, however, speed computational tasks in field problems, multi-tasking requires that timing be considered. aircraft and weapon designs, simulations and Page 530 • Data management pertains to the efficient and machine tools and robots are not designed to be orderly storage of sensory data, contextua: infor- supervised by a central computer. Furthermore, in mation and control data. Presently, a typical FMS order to have the capability of introducing new may require lM b¥t~ of main m~mory and 4M bytes of innovations quickly, the property of 'evolutionary auxiliary memory Just to monitor and control the current work-in-process of the cell components. design' must be built into the system. To make this Additional memory is needed to store data for long evolutionary approach successful, the design must term engineering and manufacturing functions. _This include the long-term goal of flexibility and auto- information may be divided, but must be accessible nomy and the cell must be structured as an to support all interrelated processes without human hierarchy. "The cell host computer is responsible intervention and flexible enough to accomodate the for activities like parts flow and machine coor- needs of different applications, dination. The machine controllers act as interfaces between the eel 1 host and the ma chining or handling o Computational Power refers to ~nalysis ~apabi- processes and they control the individual machines. lities necessary for such manufacturing functions Sensors provide information to the machine tools and 6 as editing part programs, scheduling work pieces to the cell host computer." using simulation, automated inspection, adaptive control for tool wear, thermal deformation, chatter We take note of several useful properties of and vibration geometrical variation using error this arrangement, viz. matrix, etc. 'In addition capability to ide~tify catastrophic failures either as general or isolated. • The idiosyncrasies of each cell are hidden In order to attain long term performance and • The cell and its parts are modular accuracy it is necesary to build-in knowledge base • Levels of hierarchy are a matter of choice enhancement capability by maintaining a large data • The cell provides statistical information to a base. higher level • There exists a trade-off between the degree of • Fault-tolerance and diagnostics refers to the autonomy and computer size monitoring and correction of a problem. Thi~ is generally handled by introducing_redundanct into the Several projects, including NBS' s Automated system as well as on-line analysis of machine per- Manufacturing Research Facility (AMRF), and the U.S. formance data. Air Force CAM and Computer-Aided Manufacturing International CAM-I have been developing alternative Supercomputer Control computer architectures for an automated factory. The general consensus is to employ a hierachical A typical information flow diagram for an FMS is structure in which the fl ow of command and control shown in Figure 1. In this approach, at the lowest is vertical, although sensory, internal contextual level, there are controllers on each device of the and sequencing data could flow in a variety of FMS whose job is to accept part programs from the directions. supercomputer and execute the program using an on-board scalar processor while acting as an inter- Figure 2 shows the information flow using face between the actual machine tool and the super- Hierarchical control and conventional machines. An computer. In addition the controllers will collect example of a conventional machine could be a VAX data from on-board sensors and activate control 11/780 and microcomputers could be INTEL MCS-51 systems, algorithms. Some or all sensor data are also sent to the supercomputer for further processing if The system shown is a distributed intelligence necessary. Some potential catastrophic events are system. There are three levels of hierarchy in this corrected immediately using on-board coding. system. At the lowest level of hierarchy, the In the upper level, the supercomputer through controller acts as an interface between the cell component and the cell host computer. The the I/0 handler will accept part programs eit~er controllers receive the part programs from the cell created externally or via an interactive terminal host and execute them. Also the sensor data from and transfer these programs to individual devices as the eel 1 component is either transferred to eel l and when required thus minimizing the memory host for collection and or processing or processes requirement of the controller. The supercomputer itself if it turns out to be a potential then collects sensor data from various devices simu- catastrophic failure. The controller can also be latneously and process them, either using ~lgorithms interactive so that minor adjustments can be done at involving predetermined constants or algorithms the component level without disturbing the system involving variable parameters where values need ~o components. Some controllers may also provide be determined on-line and in real-time. A classic program editing capability which when done will be example of on-line determination of variables to be relayed back to the cell host so that corrective used in a service algorithm is adaptive control for actions can be taken. tool wear. The supercomputer, in addition, ma~n- . tains a data base which will be enhanced to maintain In the second level of hierarchy the eel l host long term performance and accuracy. acts as an interface between the cell component controllers and the conventional computers. The Hierarchical Control cell host can also receive part programs from the conventional computer and transmit to cell component Not mentioned earlier but very important to the controllers as and when needed. Interactive ter- system control of an FMS is the fact that most minals hooked up to the cell host can be used to controllers for existing (and projected for new) create the part programs at the cell host and Page 531 relayed to both sides of the hierarchical flow. An advantage of an hierarchical control system Cell host coordinates the devices within a cell and is that if a cell host fails, only that particular relays all the information required to the conven- cell needs to be shut down and work in the remainder tional computer to enable the conventional computer of the FMS can continue, thereby increasing the to coordinate between cells. reliability. Also since by virtue of more flexibi- lity of an FMC the number of different parts that At the highest level of hierarchy the conven- can be manufactured by individual FMC's are high tional computer has the final authority to delegate (e.g., 30-5go different parts in a size of 20-500 to parts to various cells and to override any par- be feasible ). Finally, hierarchical control ticular cell from doing its routine work. The con- systems are more cost effective and more easily ventional computer maintains and enhances a medium modified, For instance, pe formance improvements in size data base for long term performance, centralized control systems 1 are expensive and do not concentrate improvements in the areas where they Discussion are needed most. In an hierarchical system where the intelligence is distributed, only the specific The choice between a supercomputer and parts of the system that require enhancement need be hierarchical control should be based on the need of modified. Even more importantly, the introduction a particular system. A chip forming FMS is chosen of innovation is a simple task with an FMC. Control as the system for the following discussion, systems based on distributed intelligence have less difficulty in responding to the external environment A general purpose supercomputer is specifically because they have less to manage. Comparison of tailored to make high ¥olume computations at a very operation time using Supercomputer and Hierarchical fast rate (at least 10 fl ops). In order to make use Control is shown in Figure 3 subject to the of its parallel processing capacity to its full following assumptions: extent, the software also has to be specific, Some of the situations where a supercomputer can increase • There are 30 devices in the FMS the performance and make it possible to use some • Each device consists of about 25 sen- methodologies which otherwise are very time con- sors counting for redundance suming, are discussed in the next paragraph. • The word length used for comparison = 32 bits Consider the adaptive control for thermal defor- • Number of decimal point accuracy used mation during a metal cutting operation, If the for comparison= 8 unsteady state heat distribution need to be modelled • Maximum number of sensors, requesting for very accurate adaptive control, and if the service at any given time, that material is nonhomogeneous then the resulting demand high volume computation in a algorithm has to be based on a numerical approach very short time = 10 1 ike the finite-element method to attain a useful • The computational i1tens i ve service value in real time, Though a single cutting opera- routines are written to take full tion could be handled using conventional computers, advantage of the supercomputers it needs a supercomputer if many cutting operations multiprocessing capability, are done simultaneously. Also with a supercomputer the result obtainable is of higher accuracy due to Mechani ca 1 Systems increased resolution capability needed for precision machining as discussed by others. Returning now to the issue of research in super- computers for application in mechanical systems, we Another exampl~ would be collision avoidance of first take note of the fact that continued advances two or more robots operating in a single common in microelectronics, artificial intelligence and space, In this case the computer has to go through architecture will provide for fast and smarter com- an iteration of strategies to find an optimum path puters. Although there are packaging problems it for all but one robot, which is a time consuming suffices to note that with the achievement of lOOM computation. This becomes imperative if the sequential instructions per second coupled with available space does not permit the assignment of access to a gigabyte memory, improvements in the unique workspaces for each robot. electronics area cannot be gigantic. However, when we note that insects exhibit more intelligence than Some of the other instances where high volume that attained by a computer, the progress in artifi- computation become essential are, Artificial cial intelligence will indeed be significant. What Intelligence, real time simulation to attain an this means is that although rnnputers will get optimum path for a new product, pattern recognition, smarter, the speed beyond 10 fl op per second may very fast response times if the number of sensors to stil 1 be the 1 imi t in the near future. be serviced in parallel becomes very large for a conventional computer and capability to handle high There must be other fundamental changes to level language at all levels, achieve necessary efficiency and power and this will occur with the redesign of computer architecture in The disadvangtages of a supercomputer control the broadest sense. For example, the sequential are a system breakdown resulting in shutting off the machine architecture that has been the mainstay of entire FMS thereby reducing reliability. Also since computers will gradually give way to the multiple the number of different products that can be pro- instruciton multiple data approach which will be duced are small in an FMS (typicaly 4-50 ~ifferent made more powerful using new symbolic languages, parts in a size of 50-2000 to be feasible ), there is a low level of flexibility co[)lpared to an FMC. As users, researchers and mechanical engineers, I believe our contributions are generally going to Page 532 be in the last area, i ,e, in computer architecture 6, Cutkosky, M,R., Fussell, P,S,, Milligan, Jr., including software algorithms, etc, Let me give you R., "Precision Flexible Machining Cells with in two examples, The first is parallel architecture, a Manufacturing System", Technical Report i ,e, how can a given algorithm be implemented on a CMU-RI-TR-83-2, Carnegie Mellon Univ., The multi-processor, This requires that we use Robotics Institute, Mar,, 83. "concurrency" in our technical thinking - something that is contrary to our natural "one thing at a 7, Fussell, P. S,, Wright, P,K., Bourne, D., "A time" reasoning, For this reason speed is linear Design of a Controller as a Component of a and programming is done "by the yard," Needless to Robotic Manufacturing System", Journal of say, but with tongue in check, the limiting time for Manufacturing Systems, Vol, 3, No, 1, 84, p. performing concurrent operations is zero - so there 1-11. is considerable margin for improvement! 8. Suri, R., Whitney, C.K., "Decision Support The second example deals with the fact that Requirements in Flexible Manufacturing", innovative ideas can be generated and explored more Journal of Manufacturing Systems, Vol. 3, No. rapidly by researchers using integrated circuit 1, 1984, p. 61-69, design and fabricaiton facilities instead of discrete devices as in the past. "Designers submit 9. Novak, A,, "The Concept of Artifical their designs, possibly via an intermediate agent Intelligence in Unmanned Production-Application called a broker, on an arms length basis,1wuch like of Adaptive Control", Proc. 2nd Int. Conf, on an author-publisher-printer interaction," The FMS, Oct. 26-28, 83, London, U,K. result is that hundreds of ideas are explored since the fabrication time is only a month or two, Thus 10, Warnecke, H.-J., "New International innovative ideas can be explored more rapidly, The Developments for Flexible Automation in FMS", generation of a whole class of design methodologies, Proc. 2nd Int. Conf, on FMS, Oct. 26-28, 83, including heuristics, becomes an important area for London, U.K. our inquiry, 11. Becker, G,, "Flexible Machining System: The Conclusion Economical production between 1983 and the year 2000", Proc. 2nd Int. Conf. on FMS, Oct, 26-28, Supercomputer control can improve-the perfor- 83, London, U,K, mance of a system by its enhanced computation a 1 power and make some methodologies plausible which 12, Solberg, J.J,, Anderson, D,C., Paul, R.P., "The were prohibitively time consuming for a real time Factory of the Future: A Framework for application with the conventional computers, Research", Proc. 11th Conf. on Production However, the use of hierarchical control may suggest Research and Technology, May 21-23, 84, p, an alternative approach in application where a 53-58. system may be structured to take advantage of this attribute, Additionally it is clear that signifi- 13. Kanal, L. N., Lambi rd, B,A., "Progress Report cant advances in computer architecture and software, on IRRIS-100- An Image Registration, for appl icaiton in mechanical systems, must be based Recognition, and Inspection System", Proc. on multiple processing and the use of symbolic 11th Conf. on Production Research and languages. Technology, May 21-23, 84, p. 263, Acknowledgement 14. Bourne, D,A,, Fox, M.S., "Autonomous Ma nu fact ur ing: Automating the Job Shop", The This work was done partially under the support Robotic Institute-1983 Annual Research Review, of the Westinghouse Corporation, Carnegie-Mellon Univ., Pittsburgh, Pa. 15. "Di st ri buted Cont ro 1 Modu 1e s Databook", Inte 1 References Corp. Literature. 1. Norrie, C., "Supercomputer for Superproblems: 16. Kahn, R. E., "A New Generation in Computing," An Architectural Introduction", Computer, Vol. IEEE Spectrum, Vol. 20, No. 1, November 1983, 17, No. 3, Mar, 84, p, 62-74. pp. 36-44. 2. "Teams and Players", IEEE Spectrum, Vol. 20, 17. Levine, R. D., "Supercomputers", Scientific No. 11, Nov. 83, p. 45-72. American, Vol. 246, No. 1, January 1982, pp. 118-135. 3. "Computers in Manutacturi ng," by the editors of American Machinist, McGraw-Hill Publications 18, "OEM Systems Handbook", Intel Corp. Literature. Company, New York, 1983. 4, Freund, E., Hoyer, H., "Hierarchical Control for Cooperating Robots in Flexible Manufacturing Systems," Proc. 2nd Int, Conf. on FMS, Oct. 26-28, 83, London, U.K. 5, Wada, R., "Advanced Flexible Manufacturing System TIPROS-90", Proc. 2nd Int. Conf, on FMS, Oct. 26-28, 83, London, U.K. Page 533 Supercomputer Auxiliary Memory 1/0 Handler Peripherals Data Base Public Bus ,-- ' r-- -J ,- -1 I I I Contr. j J Contr. ! Contr Contr. I I j I I I 'C": I L .., ._, j I I I j ~~ ~ I I - C: 0 i I j Inspection ! I I Conveyor ~~ ~ /! I I . . Stat ion I l.1: ______ ::::!J L_ ______ J l!: ____ ~ 1 ___ 1 L:: ____ :..l FHC wl FHC In Figure 1: Supercomputer Control for an FMS Auxiliary Memory Conventional Computer Peripherals Data Base Public Bus ]-- ---i i - ---i ,- --i I I Con tr. I I Con tr. I I I I I I I I i I I I I I Inspection I I Conveyor I I Stat ion I I _'C": .L, .., ...,, I I c:.., I I ·--eaC: .0a .2 c"' I i I .. I I ~ I L.::: ______ ::'.J L ______ I J I ~--- ::J l.l:: ___ J FIIC #1 FMC #n Figure 2: Hierarchical Control for an FMS Page 534 :iupercomputer He1rarcn1ca1 control control Controller Cell Host Conventional Computer Typical Machine Cyber-205 Intel 18 VAX 11/730 VAX 11/780 MCS-51 Capacity in flopsa 108b 5xl03 105 2xl06 Needed Operations in fl op 2.lxl07 ---- ---- 10 6 Operation time in sec 0.21 ---- ---- 0.5 # of sensors requesting for service simul- Needed taneously, which Average # of sensors Average # of fl op operations are not * program + requesting for * program per in fl op computational length in service sim- length in Fortran intensive plus Fortran ultaneously, Fortran statement diagnostics, which are data base enhan- computational cement etc. intensive For Supercomputer: [(1000*2000}+(10* 10000}]' (10}=2.lxl0 7 For Conventional Computer [(O* 2000}+(10* 10000}]' (10}=10 6 Operation time in sec= Needed operations (flop)/capacity (flops} Fig. 3: Comparison of operation time for Supercomputer and Hirarchical control. a: fl ops - fl oat i ng-poi nt 19 perat ions per second b: For an ideal situation Page 535 tK,AM,RiCJ.NS0¢1fyoi-~eJJA. . l~A~_ENG1Nl:ERs· · 345:J:. 47 St.,_New ¥ork,.Nlf. 19017 _-- :_; ·- --- ._-__- -- -_-_ -_-_-_· ,__-__: , _- ---- -_____ ;_ - -_- - __. _._-__ --------- - _- -__ ._ >_ _ ; _-_--_-_-_-_ Tire Soeiety soaU n~t be responslble for statsm,enis or Ol)lnions advanced in pap_ers or in dlscuss,oo lli me13Ungs ot tile $oci~y or_ of Jts Pivisions\or l>ections. ~r printed- in .Its put>lications. Discussion_ ii, i>1nted only if lhe µap_er :is pl.ibHsned in an ASME Journal. Released_-fpr {l8fle~ p~bl !catl o~ U?Ofl'Pfe~n!ation, FuU <:red it i,tiould be qiven. to ASME; thel'epllnical0ivisl~n,_;a11d 1hEl ~~ho!'{liJ:Papers a~av.allable from ASMEfor nine mon\ni1 afterll)e m~~ing, - - - - - PrJntiid 1iio$A; Photovoltaic/Thermal System Performance Index Based on the Second Law ERIC 0. BAZOUES U. . S Congress, Office of Technology Assessment Washington, D.C Associate Member ASME DAVE K. ANAND Mechanical Engineering Department University of Maryland, College Park Fellow ASME ABSTRACT this investigation the situation is particularly complex since both system outputs and loads - are dependent upon Photovoltaic/ thermal (PV /T) solar collectors are a two exogenous weather parameters, which cannot be known viable yet still experimental system for satisfying both a priori, namely, incident solar radiation and ambient electric and thermal loads. Several tradeoffs are dry-bulb temperature. involved in optimizing PV /T system performance includ- ing: (1) maximizing photovoltaic output by active cool- In this paper photovoltaic/thermal system perform- ing of the photovoltaic cells without inordinately ance optimization and its requisite control methodology sacrificing thermal output from the combined collector, is successfully implemented by application of the prin- (2) adequately cooling the cells without requiring ex- ciples of the second law of thermodynamics. This is cessive mass flowrates as this would increase pump para- accomplished by first computing the separate PV/T system sitic losses, (3) recognizing that electric output from component irreversibilities and then minimizing a the collector array is a higher form of energy in a performance index based on total system irreversibil- second law sense and may or may not be more useful to ity. A control methodology is then derived through use the structure compared to the thermal output, and ( 4) of this performance index. Use of the second law in the optimizing total system performance involves investiga- analysis of complex energy systems such as this one is tion of the interaction of all system components includ- shown to be an effective, and increasingly necessary ing thermal storage, heat pumps, and structure thermal system performance optimization technique. and electric loads. In this research, system performance optimization and control is successfully SYSTEM DESCRIPTION AND MODELING implemented by tracking the separate component irrevers- ibilities and by minimizing a performance index based on A practical photovoltaic/thermal solar heating and total system irreversibility. Use of the second law in cooling system consists of several components which the analysis of complex energy systems such as this one interact to collect and transform incident solar radia- is shown to be an effective and increasingly necessary tion (insolation) into useful electric and thermal system performance optimization technique. energy for use in a structure. Figure 1 is a schematic for a combined photovoltaic/thermal solar energy system INTRODUCTION which utilizes a series heat pump for satisfying resi- dence thermal loads (heating or cooling). For conven- Cogeneration of electric and thermal energy through ience, the upper portion of the schematic encompasses use of combined solar photovoltaic/thermal (PV/T) col- the thermal subsystem while the lower portion portrays lectors is a method for improving the overall efficiency the electric subsystem. A fairly detailed explanation of solar electric energy systems. Active coo ling main- of how the system in Figure 1 functions is given below. tains the photovoltaic cells closer to their optimum This will facilitate understanding system operating achievable electric output while use of the heat gener-- modes and subsequent system modeling. ated by cooling of the cells for satisfying onsite thermal loads improves net energy usage and overall To the upper left of Figure 1 the PV /T collector is system performance. However, with this system which shown which collects the solar insolation HT (when the produces both thermal energy and electric power, maxi- solar intensity is great enough) with the ambient mizing one output can be detrimental to the other. Thus, temperature at Ta• The collector pump pumps a heat a proper balance between subsystems must be maintained transfer fluid at flowrate mf through the collector in a when satisfying thermal and electric loads in order to closed circuit through a heat exchanger (not shown) with maintain comfort conditions in the structure, keep 'effectiveness sc in the thermal storage tank. The PV/T control energy requirements within bounds, and minimize collector mean plate temperature is Tc, the collector auxiliary energy usage and pump parasitic losses. In fluid outlet temperature is Tf, and the thermal storage Page 536 tank temperature is Ts. Water of thermal energy content the residence (such as at night when the photovoltaic Qshw is taken from the thermal storage tank to satisfy cells are not operating), then electricity is purchased service hot water loads of the residence with the water from the utility at the prevailing sellback rate. Since being replaced from the city mains at temperature Tmain" the PV /T system is interconnected with the electric utility (as allowed by PURPA and recently upheld in If the room enclosure at temperature Tr (surrounded court) there is no need for expensive electric storage by ambient air at temperature T) requires heating, batteries. If battery storage were desired (for a there are several methods for satisfying the thermal remote stand-alone system for example), this could be load. If the thermal storage is of sufficiently high modeled by using a battery voltage-current-state of temperature, then the thermal storage pump can pump charge relationship, with the battery state of charge heated water at flowrate ms along path O shown in Figure becoming a state variable of the system. This was 1 and directly heat the room when the room fan moves air pursued at the early stages of this research but was not at flowrate mr over the heating coils. This heats the continued due to the commercial unavailability of appro- room air to Tri (room inlet temperature). As energy is priate deep-discharge batteries, their high cost, and extracted from the circulating water, the temperature is the liberalization and decreased costs of small-power reduced to T r ( thermal storage return temperature). producer interconnections. Another methoJ for heating the enclosure is to operate the series heat pump. The thermal storage fluid follows Figure 2 is a schematic of a combined photovol- path 1 in Figure 1 and serves as the heat source for the taic/thermal solar energy system which utilizes a paral- series heat pump evaporator. Operating the heat pump lel heat pump. It follows that the only difference in with this elevated temperature heat source increases the operation of this system compared to that of the series coefficient of performance (COP) over that which would heat pump system described above is in the heat pump be obtained if the heat pump used the colder ambient air mode of operation. The parallel heat pump is, in as the heat source and hence improves overall system essence, thermally separate from the solar energy sys- performance. Again the fan with air flowrate of m tem. The electricity to drive its compressor is derived extracts heat from the heat pump condenser coil an~ from the photovoltaic cells but the heat source for the distributes it to the room enclosure. Another heating heat pump is the ambient air at Ta and not heated water method for this system is to operate the auxiliary heat from thermal storage. The disadvantage of this is that coil with electricity, Qaux• as an electric resistance the COP of the parallel heat pump in winter is generally heater. As this is an expensive method for space heat- lower than that of the series heat pump and the parallel ing it is a method that is best avoided. However, it heat pump requires a defrost cycle. The advantages are can be used in conjunction with either direct heat or that the parallel heat pump arrangement is a less com- the series heat pump in case either cannot completely plex and less expensive system than the series heat pump satisfy the structure thermal load. It should be noted system and, in addition, the parallel heat pump can be that the series heat pump is not a dual-source heat pump better optimized for summer cooling operation than the which can choose between the thermal storage fluid or series can. The parallel heat pump PV/T system shown in the ambient air as a heat source, whichever is warmer. Figure 2 can, however, provide direct heating in a man- ner similar to the series configuration when the thermal If the structure requires cooling in the summer, storage temperature is high enough to provide for effi·- the series heat pump uses the room enclosure as a heat cient operation of the enclosure side heat exchanger. source for the evaporator and "pumps" thermal energy to the condenser outdoor coil, which acts as a heat sink at SECOND LAW FORMULATION temperature Ta· As auxiliary cooling is not possible as auxiliary heating was for the heating season, care must The photovoltaic/thermal system considered in the be exercised to properly size the heat pump to satisfy second law analysis is as shown in Figures 1 and 2. the expected cooling loads. In the summer, the thermal Second law analysis of this system requires some general energy collected is used to satisfy service hot water assumptions: 1) Fluid through the system is water, needs. If the thermal storage becomes fully charged hence the collector is a drain down sys tern for freeze (approaching l00°c), subsequent thermal energy collected protection; 2) No vapors exist in the collector which is must be dumped through a relief valve. Proper sizing of thus not a pressurized system. Hence steam tables for thermal storage generally prevents this type of energy saturated steam are used for fluid enthalpy and entropy waste. properties; 3) Pipe energy losses due to fluid friction are accounted for through use of pump power; 4) Pipe Referring to the electric subsystem in Figure 1, heat losses are assumed negligible since the pipes are the photovoltaic direct current output from the PV /T assumed to be short and well insulated; 5) Kinetic solar collector is monitored by a maximum power tracker energy terms and potential energy terms in the irrevers- of efficiency ntr and is then inverted to alternating ibility calculations are assumed negligible; 6) Steady- current in the DC/AC inverter of efficiency ninv· The state, steady-flow (SSSF) conditions are assumed (1,2); DC is inverted since residences (except for some mobile and 7) The convention used is that heat in and work out homes) operate on AC current. The current then flows to are positive. the utility interface which is an electronic device of efficiency ninter which acts as a gate for flow of The irreversibility of a process is the difference electricity between the solar cells, utility, and the between the reversible work that could be theoretically electric loads of the structure. If the photovoltaic produced and work that is actually produced, or (~): output is sufficient to satisfy the electric loads which includes operation of pumps, fans, heat pump compressor, I (1) diversified electric (lighting, apppliances), and, if necessary, auxiliary heat, then the interface directly From Anand et.al. (_l) this yields: supplies the loads from the inverter. If the photovol- taic output is in excess of that required by the struc- I LmeTose - LmiTosi + m2Tos2 ture and occupants, the excess is sold to the utility at whatever the buyback and full-avoided costs are set at. (2) - m1T 0 s1 - Qcv - QR(~:) If the photovoltaic output is less than that required by 2 Page 537 for the irreversibility of a uniforni-s tate, uniform-flow where Pk represent different sys tern parameters of (USUF) process for given inlet, exit, initial, and final interest which appear in the component irreversibility states and given amounts of heat transferred Qcv and equations. A Pk of. obvious interest from a system QW Conclusions drawn from Eq. (2) can be misleading control standpoint is mf, the mass flowrate through the since it first appears as though heat transferred from PV /T collector although others, such as mass flowrate the surrounding Qcv or heat transferred from the heat from storage, ms, could be chosen. source QH decrease the irreversibility of the process which is not the case. This is not the case since when As an example for the direct heating case, Eq. (6) heat is added there will be a corresponding increase in is used for investigating mf optimum flowrates for given s 2 and/or se which will result in a net increase of insolation values. Thus, irreversibility (1). For steady-state, steady-flow, m1T s 1 equals m2T ~ 2 and hence Eq. (2) becomes 0 (7) 0 0 i LmeTose - LmiTosi - Qcv - QH C:) (3) Trial and error solution for mf for given insolation values produced results close to the optimums obtained Equations (2) and (3) are used extensively in the by simulation given in the following section in most analysis which follows. syst~m operating mode cases. This analytic method, how- ever, does not take into account superimposed control Several subsystem control volumes are appropriate requirements such as collector stagnation turn-on or for analysis of this PV/T system. These are the 1) flat collector/ storage temperature differential set points. plate PV /T collector array, 2) thermal storage, 3) room Analytic solution for optimal flowrate based on the enclosure, 4) series heat pump, 5) parallel heat pump, second law was also performed for ins (mass flowrate from 6) electrical subsystem, 7) fluid pumps, and 8) air fan. thermal storage), but the results are not as significant The model equations and the necessary irreversibility as those for mf (mass flowrate through the collector). equations for all of these components are derived in (1_). This process of using Eq. (6) is effective but rather lengthy, particularly for control variables of The total system irrevei;:sibility is given by the interest. At least for this PV /T system with highly summation of the individual subsystem irreversibilities non-linear equations, these variables tend to be deeply appropriate to the system operating mode, or embedded in irreversibility equations making differenti- ation difficult. Also, trial and error solutions using IPV/T Isystem (4) a computer usually are required. Simulation of the sys- system components tem, with irreversibility calculations being performed in a subroutine is the recommended route, as more infor- mation regarding system performance and individual SYSTEM OPTIMIZATION BY USING IRREVERSIBILITY component irreversibility contributions are obtained in CONSIDERATIONS this manner. The performance index, J, selected for this SYSTEM SIMULATION USING SECOND LAW ANALYSIS analysis consists of the sum of the several component irreversibili ties, namely, The photovoltaic/ thermal system is simulated for L three locations, namely Madison, Wisconsin, Washington, J = isystem (5) D.C., and Charleston, South Carolina utilizing the irre- components versibility expressions derived earlier. All sys tern operating modes for the heating and cooling seasons are This performance index is calculated for the appropriate investigated. System component irreversibilities appro- PV/T system mode, Le., direct heat, solar assist series priate to the operating mode are calculated for vai:·ying heat pump heating, parallel heat pump heating, series collector mass flowrates and insolation levels with the heat pump cooling, or parallel heat pump cooling and total system irreversibility being the sum of the ideally could be driven to zero. In a practical system, separate component irreversibilities. however, J will not be zero but it should be minimized in order to reduce irreversibility and hence reduce Photovoltaic/thermal subsystem and total irreversi- destruction of exergy. This, in turn, preserves energy bility for a variable collector mass flowrate for resources. Charleston, South Carolina, winter direct heat mode, for a fixed insolation of 500 kJ /hr is given in Fig. 3. It It should be noted that if the radiation incident is noted in the figure that the major component contri- on a collector is increased, the operating temperature butions to total system irreversibility are the PV/T of the collector increases, and the system irreversibil- collector and the room enclosure. Irreversibility ity increases. However, more available energy (or decreases slightly with increased mass flowrates for the exergy is obtained which seems to violate the fact that collector since it operates at lower temperatures as mf minimum irreversibility gives an optimum system. But, increases. In the same manner, thermal storage irre- this is not the way to look at a system. The correct versibility decreases with increased collector mass way to look at a system is to say that for a given and flowrate. The room enclosure irreversibility increases fixed incident solar radiation level, the minimum exergy with increased mf since ins from storage to the room loss does lead to an optimum system and one can define a enclosure must increase in order to satisfy room loads performance index based on irreversibility. with lower temperature storage water. Pump and fan ir- reversibility increases slightly with increased collec-· The best method for system optimization is thus to tor mass flowrate, as expected, but makes only a small set contribution to the total system irreversibility. As collector mass flowrate is increased, collector operat- 0 (6) ing temperature is decreased and photovoltaic cell effi- ciency is increased. Thus, thermal energy output of the 3 Page 538 PV /T collector is sacrificed for production of more dictated by total PV /T system irreversibility considera- electric energy leading to increased irreversibility of tions appears inversely related to location latitude. the electric interface, but again with small magnitudes The irreversibilities inherent in the operation of the compared to total system irreversibility. The total PV /T collector are the major concerns but are also the irreversibility plot shown in Figure 3 demonstrates that most difficult to remedy. In decreasing order of irre- its value is fairly flat over this range of mass flow- versibility concern are the room enclosure, thermal rate for this insolation level but a minimum appears to storage, pumps and fans, and electric interface with the exist at the 400 kg/hr rate. Figure 4 which shows the latter two being almost negligible. The system mode total irreversibility in more detail demonstrates that deserving of most attention in a second law sense is this is indeed the case, with a collector mass flowrate winter direct heat since the PV/T collector, room of 400 kg/hr yielding the minimum total system irrevers- enclosure, and thermal storage interaction is at its ibility for this mode and city. This result comes with- peak in this mode. in 13 percent of the analytic solution for this case which is 347.2 kg/hr. SUMMARY AND CONCLUSIONS Figures 5 and 6 parallel Figures 3 and 4 but for an In this research, the second law of thermodynamics increased insolation level of 1000 kJ/hr. In this case, is applied to the study of subsystem and total PV/T the optimum collector mass flowrate in a second law system irreversibility. A performance index is mini·- sense is given by 900 kg/hr. Figures 7 and 8 demon- mized based on total system irreversibility and is used strate the case for an insolation value of 2000 kJ/hr to derive a control strategy. Applying the second law with the respective optimum collector mass flowrate of thermodynamics to calculate subsystem and total PV /T being 1800 kg/hr. It is noted from Figures 3 to 8 that system irreversibilities produces a viable control total system irreversibility increases with increased methodology. This optimum second law-based control is insolation levels, as would be expected. approximated for both heating and cooling seasons for any locale by a proportional type controller. The PV/T CONTROL METHODOLOGY DERIVED USING THE SECOND LAW proper proportionality constant is obtained by calcu- lating minimum total system irreversibility at moderate The second law simulation procedure described above to high ambient insolation levels. This mass flowrate for a direct heat case is performed for all sys tern oper- point, plus the origin yields the control line. The ating modes for all cities under study. The optimum slope of this control line is inversely related to mass flowrates for given insolation levels are then location latitude. plotted as shown in Figures 9 to 12. For example, for the Charleston, South Carolina direct heat case just The second law also helps pinpoint which system described, plot ting the optimum flowrates at given components or operating modes are most likely candidates insolation values yields the top (solid) line in Figure for improvement. Efforts should be expended most on 9. Figure 9 graphs control strategy derived for mini- reducing the irreversibility of the PV/T collector and mizing PV /T system irreversibility for the direct heat room enclosure in that order. Less attention need be case for the three cities; Figure 10 does the same for paid to the irreversibility of thermal storage, pumps the solar assisted series heat pump heating case; Fig. and fans, and electric interface in that order. In 11 does the same for the parallel heat pump heating addition, irreversibilities of the system heating modes case; and finally, Figure 12 yields the control strategy are more critical than those of the system cooling based on second law considerations for the series and modes. parallel heat pump cooling cases. In Figure 12, the collector mass flowrate reaches its maximum possible Recommendations for future work could include value of 2400 kg/hr at insolation values of 2600 kJ/hr applying the second law analysis techniques put forward and 3000 kJ/hr for Charleston and Washington, D.C., in this research to other energy systems such as concen- respectively. trating PV /T industrial systems, traditional topping and bottoming cycle cogeneration systems, or electric utili- It is noted from all four figures that proportional ty fuel cell or battery electric load-leveling control is warranted. The linear fit is fairly good for technologies. the heating season modes but less sq for the cooling cases. In the cooling season, the collector mass flow- REFERENCES rate should run slightly higher for a given insolation level than is indicated by a proportional control (1) Anand, D.K., et.al., "Second Law Analysis of methodology. The slope of the control line decreases Absorption Cycles," report prepared by TPI, Inc., with increasing latitude angle (Charleston to Beltsville, Maryland, for the U.S. Department of Washington, D.C. to Madison). The Charleston and Energy, Washington, D.C., April 1983. Washington, D.C. lines cluster closer to each other than to Madison because the wea½her patterns of the former (2) Van Wylen, G.J. and R.E. Sonntag, Fundamentals of two have some similarities. Classical Thermodynamics, John Wiley and Sons, Inc., New York, New York, 1965. Second law analysis is shown to be a viable and effective analysis technique for this PV /T system. (3) Bazques, E.O., Control and Performance of a Photo-· System optimization through use of irreversibility voltaic/Thermal Energy System, doctoral disserta- considerations yields a proportional controller which is tion, Department of Mechanical Engineering, consistent with the excellent system performance noted University of Maryland, College Park, December with this type of controller in (4). This control 1983. occurred for all locales for both seasons, but works best for the heating season. The proportionality (4) Bazques, E.O. and D.K. Anand, "Control Aspects of constant is easily derived through a one point minimum Photovoltaic/Thermal Energy Systems," Proceedings total system irreversibility calculation, or preferably, of the 19th Intersociety Energy Conversion simulation, since the control must pass through the Engineering Conference (IECEC), San Francisco, origin. In a coarse sense, the control function slope California, August 1984. 4 Page 539 I,- ----(, Au,:lliaJ}y ,-----(, --To J.oo• Heat Tri Oau,. AudliaJ}I --To Rooa nat Plan Heat Tti PV /1 Col h•ct or Arny ::...------I+ • the user is now free to specify the following parameters: * 1. The outside radius of the flywheel. This 0 ej = 80ejw + 0 eji ( 4) selection then sets the maximum flywheel rotational speed (called NMAX). 2. The required stored kinetic energy. In the absence of interference Orji and creji This selection sets the flywheel are zero and there exists one va 1 ue of f3 which thickness. will cause either orj or oej to reach its 3. The speed range over which the kinetic 2.457 Page 554 energy is to be delivered. This ment {called air gap growth) should not selection determines the useable energy be exceeded. density. Shown in Figure 4 is a di a gram which sum- Kirk and Evans [11], and Khan [14] have marizes the results of maximizing the SEO for a outlined the flywheel sizing procedure and have 300 Watt hour flywheel system. The detailed developed a computer program {FLYSIZE) which will FLYSIZE output of this design has been presented interactively carry out the Flywheel sizing in Appendix C. The pertinent constraints for details. Typically the FLYANS program is first this example are: used to select a best multiring arrangement and 1. The stored energy is 300 Wh interference pressure set which will maximize 2. The speed change is 37. 5% to 75% of the SED. The pertinent outputs of FLYANS for the maximum speed. best configuration are then stored in temporary 3. An air gap growth of 0.040 inches must files and the FLYSIZE program is executed to not be exceeded. provide the design details. A typical output of 4. The ring to ring percent interference FLYSIZE for a 6 ring flywheel is shown in must not exceed 0.6%. Appendix C. . For the example shown in Appendix C the kine- 300 WH ROTOR tic energy of the flywheel 1s delivered over a 2 to 1 speed range {37.5% to 75% of the maximum RADIAL STRESSES vs flywheel speed). Since the flywheel stresses are RADIUS RA TIO proportional to the square of speed, the stresses 1.00 wi 11 be between 14% and 56% of the maxi mum ma teri a 1 strengths. A 2 to 1 speed range was 0.75 selected to permit reasonable motor/generator design and the actual upper and lower limits were 1 selected to minimize fatigue effects in the 0.5 flywheel composite materials [14]. - 300 WH FLYWHEEL STORAGE SYSTEM -Cl) Cl>-0.2 -(.I..) Cl)-0.50 optimized .!-0.1 -0 co ~1.00 lat NMAXj Figure 5 - Radial Stress Distribution for a 6 ring Rotor Two of the more interesting effects on flywheel performance are how the radial stresses MMAX - 83,000 rpm 00-10.1 in 10-4.6 in T-4.0 in have been redistributed by interference assembly MuPPER - 61,000 rpm TOTAL ROTATING WEIGHT - 17.3 lbs and how the inner radius displacement (air gap MLOWER - 31,000 rpm SED(USEABLE) -.17.3 Wh/lb growth) is minimized. Shown in Figure 5 is a plot of radial stress vs. radius ratio for both the unoptimized and optomized (i.e •• interference assembled) 300 Watt-hour design. These stress plots show the significant reduction in radial Figure 4 - Summary Schematic Diagram of 300 Watt- tensile stresses that occur when the flywheel is hour Flywhee 1 Energy Storage Sy stem operating at its maximum speed {NMAX) due to interference· assembly. Without interference the RESULTS AND DISCUSSION flywheel maximum speed is limited by radial ten- sile stresses in the composite material {at r • In sizing a magnetically suspended flywheel O. 7). With interference, the radial stresses no energy storage system the design goa 1 is to maxi - longer limit performance and the maximum speed is mize the SEO subject to the following limited by tensile hoop stresses in the outer constraints: ring { see Appendix C). 1. The flywheel stresses at maximum speed Shown in Figure 6 is a plot of the optimized should not exceed ma teri a 1 strength. radial stress in the flywheel when it is 2. The user specified percent interference operating at 75% NMAX. At this speed all radial (%Int) should not be exceeded, stresses are compressive. Past experience from 3. The user specified inner radius displace- the Department of Energy Flywheel Program has 2.458 Page 555 shown that the radi a 1 ten s11 e strength for for this model has been di scusseq ~nd a nondimen- filament wound composite materials oftentimes sional stress parameter, B = p 1w b , has been limits flywheel performance. With the use of presented for maximizing SEO. To analyze a interference assembly the radial stresses are flywheel configuration the following information kept compressive and should not limit flywheel must be specified: performance. In addition, since radial stresses 1. The nondimensional radius ratios of each stay compressive over the entire operating speed flywheel ring. This specifies the rela- range (i.e., 75% to 37.5% of NMAX) fatigue tive shape of the flywheel but not its effects should also be reduced. Also, if the size. flywheel speed increases above 75% NMAX the 2. Material properties for each flywheel radial stresses begin to go tensile in the outer ring. rings first, as shown in figure 5. If the outer 3. Constraints on inner ring displacement 1 or 2 rings were weakly bonded together an and interference. overspeed condition could selectively release an Once the above items are specified, an optimized entire outer ring and, perhaps, prevent a total value of Bis calculated. Typically through the system failure. use of interference assembly B can be increased The inner radius displacement (air gap by a factor of 2 or roore. growth) o.' the design has been minimized because An example of a 6 ring 300 Watt-hour flywheel the overa 1 flywheel inside to outside diameter energy storage system has been presented. This has been reduced to 0.45. Without the beneficial flywheel operates over a speed range from 37.5% effects of interference assembly this reduction to 75% of its maximum speed and delivers 300 of air gap growth would not have been possible. Watt-hours of energy. Interference assembly was shown to have the following benefits for this design: 1. The burst SEO was increased from 41 Wh/kg (18.6 wh/lb) to 90 Wh/kg (41.1 wh/lb). 2. The interference assembled useable SED is 300 Wh ROTOR 35 Wh/kg (17.3 wh/lb). Radial Stress vs Radius Ratio 3. The overall inside to outside diameter ratio is 0.-+5. 4. The radial stresses are compresshe over 0.25 the operating speed range. 5. At speeds above 75% of the maximum speed 0.00 the outer ring interfaces begin to go tensile and selective dropping off of the Cl) -0.25 Cl) outer rings, to avoid complete rotor w ... failure, is possible. 0: r -0.50 Cl) ,..., iii ACKNOWLEDGMENTS ..J ... -0.75 ce.b... The authors would like to thank Mr. G. Ernest C )( -1.00 Rodriguez and Mr. Philip A. Studer of < 0: '"" lat 75%NMAX I NASA/Goddard Space Flight Center for their tech- -1.25 nical assistance in carrying out the work reported here. The authors also gratefully acknowledge the financial support for the work provided by NASA grant NAG 5-396 and computer time provided by the University of Maryland Figure 6 - Radial stress distribution for a Computer Science Center. 6 ring rotor REFERENCES CONCLUSIONS 1. Rodriquez, G.E., Studer, P.A. and Baer, D.A., For spacecraft applications a magnetically "Assessment of Flywheel Energy Storage for suspended flywheel energy storage system offers Spacecraft Power Systems", NASA Technical significant advantages in both cycle life and Memorandum 85061, May 1983. specific energy density (SEO) compared to 2. Kirk, J.A., Studer, P.A. and Evans, H.E., electrochemical systems. To achieve these advan- "Mechanical Gapaci tor", NASA TND-8185, 1976. tages interference assembly (prestressing) of 3. Kirk, J.A., "Flywheel Energy Storage, Part I the flywheel will be required. - Basic Concepts". Interna ti ona 1 Journa 1 of A multiring flywheel model consisting of any Mechanical Sciences, Vol. 19, No. 4, 1977, number of constant thickness nested rings has pp. 223-231. been presented, This roodel may be applied to 4. Kirk. J.A. and Studer, P.A., "Flywheel Energy either solid rrultiring/multimaterial flywheels or Storage, Part II - Magnetically Suspended to a magnetically suspended flywheel consisting Super fl ywhee 1", Interna ti ona 1 Journa 1 of of an iron inner ring and composite material Mechanical Sciences, Vol. 19, No. 4, 1977, outer rings. The complete stress distribution pp. 233-245. 2,459 Page 556 5. Anand, D.K., Kirk, J.A. and Frormier, D.A., -N.-3 "Design Considerations for a Magnetically 2 { 1 N .-3 0 * . = -(3+v .)r - A J.r J + A J.r J } Suspended Flywheel System", Paper number rJ r-0J (9-Nj 2 ) 5 6 859069 presented at the 20th IECEC, Miami Beach, Florida, August 18-23, 1985. (A-1) 6. Genera 1 Dynamics, Conva i r Division, "Review of Advanced Composite Ma teri a 1 s", given to NASA/Goddard Space Flight Center, 1975. 7. Celanese data sheet on Celion 6000/Epoxy. * 8. Kirk, J.A. and Huntington, R.A., "Energy 00j Storage - An Interference Assembled Multiring Superflywheel", Proceedings of the 12th Inter society Energy Conversion Engineering + Conference, Aug. 28-Sept. 2, 1977, pp. 517-524. (A-2) 9. Kirk, J.A. and Huntington, R.A., "Stress Analysis and Maximization of Energy Density for a Magnetically Suspended Flywheel", ASME where: paper 77-WA/DE-24, 1977. 10. Kirk, J.A. and Huntington, R.A., "Stress Redistribution for the Multiring Flywheel", ASME paper 77-WA/DE-26, 1977. 11. Kirk, J.A. and Evans, H.E., "Inertial Energy Storage Hardware Definition Study -- Ring Rotor", NASA CR-175217, 1984. 12. Evans, H.E. and Kirk, J.A., "Inertial Energy = (a:j+3aiNj - a~Nja~j+3) Storage, Magnetically Levitated Ring Rotor". Paper number 859019 presented at the 20th (9-N .2)~ IECEC, Miami Beach, Florida, August 18-23, J 1985. 13. Huntington, R. A. "Stress Analysis and Maximization of Performance for a Multiring • a2N. 2N. "'= i J- aj J Flywheel", M.S. Thesis, University of Maryland, College Park, 1978. 14. Khan, A.A., "Maximization of Flywheel The centrifugal forces tend to expand the Performance", M.S. Thesis, University of rings of the rotor. To keep the rings in contact Maryland, College Park 1984. at all speeds, a constraint was applied which required the inner radius expansion of ring j to be equa 1 to the outer radius expansion of the ring j-1. The effect of this displacement APPENDIX A - ROTATIONAL STRESS EQUATIONS constraint is to cause a radial interface stress to be present between rings. These interface Shown in Figure 3 is a schematic of the stresses can be solved for [13,14] and their multiring flywheel. The rotor consists of n con- effect can then be included in a second rota- centric, constant thickness rings. It has an tional stress distribution which is given by overall outer radius of b, with this dimension normalized to form a nondimensional outer radius * * NJ.-1 -N .-1 of 1. The innermost ring is designated as ring C1 . -- S . { "' 1J· r - "'z J.r J } 1, with the remaining rings numbered con- rJ 1 secutively to ring n. The radial position of a point in the multiring model is given as the non- dimensional ratio of the radius {a) and b. This (A-3) forms the normalized radius ratio r. Using this scheme, the inner and outer radii of the jth ring are given by a; and aj, respectively {where i = j-1). In this manner, the geometry of the multiring may be specified completely by the N.-1 -N -1 nondimensional terms a0 through an-1• in addition * * oej = s Nj { Al{ J - l.2{ j } to the outer radius band axial thickness t. 1 The non-dimensional radial and tangential stresses which are caused by centrifugal forces N.-1 -N .-1 are given by Huntington [13] and Khan [14) as: -S*jN } l.3{ J - l.4{ J } {A-4) where: 2.460 Page 557 * N.-1 -N -1 Si = Boundary stress at the 1th interface divided j 0eji = P N} "1{J -by B 1 "2{ N -1 -NJ.- 1 l N.+l } l Ntl 2Nj -PjNj{ "3{j - "4{ (B-2) .. 1: ai J ; l N.+l "lj "2j = -fl ai aJ. • "3j "'TjJ ; The interference stress distribution is calcu- lated by taking a user specified percent inter- face between rings and then calculating the interface pressures that occur as a result of interference. The ring interface pressures are then used in the above equations to obtain the The complete rotational stress distribution is stress distribution in ring j. The details of the sum of equations (A-1) through (A-4). The the calculation method may be found in reference advantage of putting the rota ti ona 1 stress [13]. distribution into the form shown above is that the form of interference assembly stresses will be identical to equations (A-3) and (A-4). Examination of the expressions for rotational stress show that they are dependent on 5 non- dimensional variables for each ring. These are: (a) ai which specifies the ratio of the inner radius of the ring to the outer radius of the flywheel (b) Eej/Ee1, material ratio of the tangential modulus of elasticity of ring j to that of ring l (c) Nj, material parameter (Nj = iEej/Erj) (d) Pj/P1, material ratio of the density of ring j to that of ring l . (e) vrej, Poisson's ratio. Specification of each of these variables for each ring will allow the nondimensional radial and tangentia 1 stress di stri buti ons to be obtained. However, it is also necessary to pro- vide the working stresses for each ring and the weight density and tangential modulus of elasti- city of ring 1, so that a complete analysis, including energy storage capability, can be per- formed. APPENDIX B - INTERFERENCE ASSEMBLY STRESS EQUATIONS The radial and tangential interference stress distributions for ring j are given by Huntington [13] and Khan [14] as slight modifications of equations (A-3) and (A-4). They are: (B-1) 2.461 Page 558 Appendix C RUN IDENTIFICATION -----300WH OPT ROTOR OPTIMIZED CONFIGURATION RING IN. R. INSIDE OUTSIDE RING WEIGHT NO. RATIO RADIUS RADIUS WEIGHT DENSITY (--) (--) ( IN) ( IN) (LBS) ( LBS/ IN**3) l .453 2.283 2.520 4.1 .2890 2 .soo 2.520 3.029 1.9 .0550 3 .600 3.024 3.546 2.3 .0550 4 .700 3.528 4.043 2.6 .0550 5 .800 4.032 4.547 3.0 .0550 6 .900 4.536 5.040 3.3 .0550 RING ASSEMBLY RADIAL s MIN OUTER RAD FORCE ADDED TO PRESSURE MISMATCH INT TAPER DISP DUE TO REQ. PREV. RING INT ASSEMBLY (--) (KPSI) (IN) ( 10**-3) (DEG) ( IN) (KPS) 2 .001 .0000 .oo .ooo .00000 .006 3 2.817 .0050 1.67 .072 .00272 27 .014 4 9.703 .0212 6.00 .303 .01270 108.558 5 9.084 .0242 6.00 .346 .01552 116.151 6 8.483 .0272 6.00 .390 .01834 122.025 RING THICKNESS (INCHES) ----------------------- 4.000 MAX. ANGULAR SPEED (RPM) -----------------------82749 ANGULAR SPEED VARIES BETWEEN (RPM) -----------31031-62062 SEO AT BURST (WH/LB) --------------------------- 41.110 SEO USEABLE (WH/LB)----------------------------- 17.345 VED AT BURST (WH/FT**3)-------------------------3850.00 VED USEABLE (WH/FT**3) -------------------------1624.22 USEABLE STORED ENERGY (WH)---------------------- 300.00 BURST STORED ENERGY (WH) ---------------------- 711.11 TOTAL FLYWHEEL WEIGHT (LBS) ------------------- 17.296 AIR GAP GROWTH@ N(LOWER)(INCHES) ------------- .0034 AIR GAP GORWTH@ N(UPPER)(INCHES) ------------- .0137 AT BURST PERFORMANCE LIMITED BY THE STRESSES IN RING I 6 LIMITING LOCATION (INCHES)------------------- .4536+001 RADIAL STRESS (PSI)-------------------------- .1942+004 TANGENTIAL STRESS (PSI)---------------------- .2456+006 SHEAR STRESS (PSI)-------------------------- .2032+000 NORMALIZED EQUIVALENT STRESS--------------- .1000+001 RADIAL RESIDUAL STRESS (PSI)----------------- -.8483+004 TANGENTIAL RESIDUAL STRESS (PSI)------------- .8669+005 RING NUMBER --- l ----MATERIAL----- CONTINUOUS IRON RING NUMBER --- 2 --- MATERIAL---- CELION 6000/EPOXY RING NUMBER --- 3 --- MATERIAL----- CELION 6000/EPOXY RING NUMBER --- 4 ----MATERIAL---- CELION 6000/EPOXY RING NUMBER---- 5 --- MATERIAL---- CELION 6000/EPOXY RING NUMBER --- 6 --- MATERIAL---- CELION 6000/EPOXY 2.462 Page 559 ~A 11f!!! The Engineering Resource For Advancing Mobility 400 COMMONWEAL TH DRIVE WARRENDALE, PA 15096 SAE Technical Paper Series 859069 DESIGN CONSIDERATIONS POR MAGNETICALLY SUSPENDED FLYWHEEL SYSTEMS Davinder Anand, James A. Kirk, and David A. Frommer University of Maryland College Park, MD Reprinted from P-164- Proceedings of the 20th lntenociety Energy Conversion Engineering Conference · ,. 20th IECEC Miami Beach, Florida August 18-23, 1985 Page 560 859069 DESIGN CONSIDERATIONS FOR MAGNETICALLY SUSPENDED FLYWHEEL SYSTEMS Davinder Anand, James A. Kirk, and David A. Frommer University of Maryland College Park, MO ABSTRACT tested at over 2500 rpm with satisfactory perfor- mance. Particular attention has been given to This paper reports upon research activities system operation in the virtual zero power (VZP) that are being cooperatively conducted by the mode of operation in which the flywheel is Goddard Space Flight Center and The University of controlled to suspend in a position in which all Maryland. Specifically. this work includes the of the steady-state loads are carried by per- design, fabrication and testing of an experimen- manent magnets [5]. The details of the flywheel tal energy storage flywheel system {Prototype 11) and associate stabilization and power electronics and the conceptual design of a 300 Wh flywheel. have been referenced in several papers published Although the basic concepts of the earlier [4,5]. motor/generator and magnetic stabilization design The current study builds upon earlier con- are similar to our earlier ideas, several signi- cepts and is directed to achieve: ficant innovations have been included. • Design, fabrication and testing of proto- The successful design of the 300 Wh flywheel type II ystem is dependent upon • Conceptual design of a 300 Wh model • composite material flywheel Prototype II is intended for use in studying • motor/generator problems of reproducibility, improved electronics • magnetic suspension and flexibility of control 100des. The 300 Wh Current studies indicate that the critical flywheel is primarily intended to serve as an problems in these areas can be successfully intermediate technology for l~rger sizes in the addressed. vicinity of 1.6 kwh and for use in low earth orbit spacecrafts. PROTOTYPE II THE USE OF MAGNETICALLY suspended flywheels for Since the objective of building this irodel is energy storage have been proposed, conceptually to primarily study reproducability, the original designed and fabricated by severa 1 re searchers in design was used without major nodifications. the past [l-14]. One particular technique of This design_ is illustrated in Fig. l and has the radially supporting and stabilizing the rotor has following important components: been previously studied at GSFC .and the • The passive suspension is achieved University of Maryland [2-4]. This approach uses statically in the axial direction by four a motor/ genera tor embedded in the fl ywhee 1 which samaril.111 cobalt permanent magnets. is stabilized around a stator that al so houses • Active control in the radial-'.4irection is. the magnets and the electronics. Static stabili- achieved with eight coils. -· zation in all three transitional coordinates is • The bearing assembly was machined using achieved using samarium cobalt magnets and dyna- Nickel-iron and the machined parts were mic stabilization in the radial direction is hydrogen annealed. achieved via electromagnets that are driven by an An expanded view of the bearing itself is shown error signal generated by radial position sen- in Fig. 2. We note that the magnetic plate. is sors. These sensors are located orthogonal to slotted to yield four independent quadrants for each other in order to obtain decoupling between control. The slotted area was filled with epOXY motion in the x and y directions. The for mechanical strength and ease of handling. _ motor/generator is based on the brushless Since the epoxy material represented very low DC-Permanent Magnet/ironless technology using permeability it had no effect upon the magnetic '!lectronic co11111utation. The system has been circuit. 2.449 Page 561 The sensing for the active· control of the suspended flywheel is achieved with two orthogo- nally mounted Kaman sensors of the eddy current type. These sensors are used to obtain radial displacement. The signal is processed and filtered before being used to energize electro-magnetic coils that produce the flux for dynamic control. This control system is reproduced for the x and y direction. The con tro1 system i s designed to main ta i n a nomina 1 radial gap of 0.02 in between stator and flywheel. The four coils, representing one of the control directions, are energized in parallel so that the flux is additive on one side of the stator while subtracting 1so• away thereby introducing a net correction force. The flywheel used for energy storage is discussed in detail in a companion paper [5]. The inner ring, attached to the flywheel and used for completing the magnetic circuit, is constructed using nickel iron. This ring was a 1 so hydrogen annea 1e d to re 11 eve stress in the material, promote grain growth, and reduce carbon content (which generally improves the magnetic Figure 1 Magnetic Suspended Flywheel properties¥. For prototype II the suspended Prototype I and II flywheel weighed 2.0 lbs and the inner ring weighed 0.25 lb. It can be shown that a weight ratio of less than 1/10 is necessary for the stored energy density to be above 15 Wh/lb and therefore competitive with other methods of MAGNETIC SUSPENSION ASSEMBLY energy storage [l]. ROTATING P.M. Figure 2 Magnetic suspension Assembly The equivalent ma.gnetic circuit has been . Figure 3 Motor/Generator Assembly derived for simulating the static and dynamic • ~-,.,J,-{ ' ~ performance of the bearing. The permeances were . The mtor/genera.tor design, like the earlier computed using flux lines and the •pping of the version. is illustrated in Fig. 3. lt basically flux lines as well as the Schwartz-Christofell shows transformation. This circuit was used to obtain • Eighteen permanent ma.gnets uniformly the leakage coefficient. For our particular embedded in the flywheel design it was found that a leakage coefficient of • An iron return ring around 3.6 was obtained indicating excessive • lronless armature attached to the base leakage. This result will be used to roodify the plate. design for the larger sizes. 2.450 Page 562 The motor/generator uses IR sensors for deter- mining position in order to obtain electronic commutation. The power electronics yield a P. M. MOTOR DESIGN vo 1 tage which is directly proportiona 1 to the rotational speed of the rotating flywheel. It is noted that the ironless armature and the rotating return ring helps in minimizing the losses. The inner ring design, however, is very poor and conducive to large losses since it sees a rotating mgnetic field. This is particularly true for higher rotational speeds. It is anticipated that the new design will use laminates in order to minimize hysteresis and eddy current losses. For testing purposes, the motor/generator part of the system was separated from the flywheel. This allowed the power generation to be studied independently of the magnetic suspen- sion. For prototype II, no data on the power generation was obtained. The magnetic suspension of prototype II was MULTI RING initially difficult to achieve. The control system itself required careful balancing. Fine tuning of this system gave the necessary suspension. Rotation speeds, using an aluminum Figure 5 Motor Design for the 300 Wh System flywheel were achieved at 2500 rpm. It was noted that perturbation orthogonal to the spin axis as 300 WH DESIGN well as dynamic cross-coupling rendered the system to chatter and became unstable. Any new design The successful fabrication ~nd testing of must address this very important issue for high Prototype II has provided the necessary con- speed application. fidence to proceed to a larger size. More impor- Prototype II was primarily constructed to tantly it has indicated the necessity of study reproducability and the validation of the controlling additional degrees of freedom in concept. Such important issues such as bearing order to obtain stable dynamic suspension at power requirements, nntor efficiency, windage and higher rpm. This has led to the design concept other losses were not addressed. However, these illustrated in Figs. 4-6. The two magnetic considerations were included in the conceptual design of the 300 Wh fl ywhee 1 system. STATOR STACK 6 1 1 TOUCHDOWN IEARING1i I MAGNETIC BEARiNG 2 ARMATURE WINDINGS IRONLESS I FLYWHEEL 3 PERMANENT MAGNETS .. f . IEARING RING ' ' .· c 4 INNER RETURN RING Figure 6 Cross-sectional View of 300 Wh System Figure 4 Stator. Stack Arrangement for the 300 Wh System bearings themselves will follow the earlier designs. The principal difference here being the 2.451. Page 563 use of two bearings with the motor I genera tor an TABLE 3: Wheel Specifications for 300Wh integral part of the stator and restricted to the inside diameter. Since these magnetic bearings are at least 2" apart, it will be possible to Inner Diameter 4 inches sense and control the rocking instability that Outer Diameter 10 inches was a problem in earlier designs. Thickness 4 inches The system characteristics of the energy Confi gura ti on Multi ring flywheel for application in a low earth orbit 1 iron inner ring (LEO) are given in Table 1. This table indicates 5 graphite/epoxy rings that this particular design is capable of Burst Speed : 79,000 rpm delivering 300 Wh energy as the flywheel de-spins Maximum Operating Speed: 60,000 rpm from 60 lcrpm to 30 krpm with a round trip Weight 18 lbs efficiency around 801. The power budget in Table Usable Energy Density 16 wh/lb 2 indicates that of the total loss of 60 w. the Burst Energy Density 39 Wh/lb maximum rotating loss (at rated 60 krpm) is 32 W with the balance of 28 Wa llocated to armature los.ses and the suspension/power electronics. The wheel specifications are given in Table 3. It shows that the 18 lb wheel 1111st be 10• OD and consist of 5 graphite/epoxy rings that are 4" TABLE 1: System Characteristics for LEO thick. This is discussed further in a companion paper. We note however that this particular design yields usable energy density of around 20 Orbit: LEO (90 minutes) Wh/lb. Average Delivered Power 600 w Average Generator Power 660 w CONCLUSIONS Energfy Delivered 300 wh Energy Generated 330 wh The basic concept of the suspension scheme Burst Speed 75 k rpm discussed here has been validated using Prototype Upper Operating Speed : 60 k rpm 11 at 2500 rpm. The principal problem of stabi- Lower Operating Speed : 30 k rpm lity due to orthogonal perturbations has led to a Generator Voltage Const.: 3 V/k rpm new design for 300 Wh applications. · Initial con- Charge cycle : 60 minutes cepts and design studies indicate that a 300 Wh Discharge cycle : 30 min (variable) flywheel storage system can be successfully Load Profile : 1125 w for 9 minutes constructed. This activity is currently under 374 w for 21 min way. Round trip z 801 ACKNOWLEDGMENTS The many detailed discussions with Phil Studer and E. Rodriquez of GSFC have been crucial to the continuing success of this project. Some of the work reported here has been sup- ported under NASA Grant NAG 5-396. TABLE 2: Power Budget for 300Wh Flywheel REFERENCES .. l. Rodriquez, G.E •• Studer, P.A. and Baer, D.A •• Suspension Circuitry . 6 watts •Assessment of Flywheel Energy Storage for Position Control . 1 watt Spacecraft Power Systems", NASA Technical Communication Circuitry: 5 watts Memorandum 85061, May 1983. Communications Transduction 4 watts 2. Kirk, J.A., Studer, P.A. and Evans, H.E •• Rotating Losses .. •Mechanical capacitor•, NASA TND-8185, 1976. (allocated) 32 watts Anlilture Losses . 3. Kirk, J.A •• •nywheel Energy Storage, Part l (Allocated) ~. . -12 watts - Basic Concepts•, International Journal of ;. '!, • .,· ' ..... ,: . ~ Mechanical Sciences, Vol. 19, No. 4, 1977, Total Power ,C on suned .. 60 wa ttf pp. ~23-231. ~- , : -: .:~~ /:t· ·,,·. ·"'"". 4. Kirk,. J.A. and Studer, P.A.; •Flywheel Energy Storage, Part II - Magnetically suspended Superflywhee1•, International Journal of Mechanical Sciences, Vol. 19, No. 4, 1977, pp. 233-245. 2.452 Page 564 5. Studer, P.A., •Magnetic Bearings for Instruments in the Space Environment". NASA Techni ca 1 Memorandum 78048. January 1978. 6. General Dynamics. Convair Division, •Review of Advanced Composite Materials". given to NASA/Goddard Space Flight Center, 1975. 7. Celanese data sheet on Ce lion 6000/Epoxy. 8. Kirk, J.A. and Huntington, R.A., "Energy Storage - An Interference Assembled Multiring Superflywheel", Proceedings of the 12th Intersociety Energy Conversion Engineering Conference, Aug. 28-Sept. 2, 1977, pp. 517-524. 9. Kirk, J.A. and Huntington, R.A •• "Stress Analysis and Maximization of Energy Density for a Magnetically Suspended Flywheel", ASME paper 77-WA/DE-24, 1977. 10. Kirk. J.A. and Huntington, R.A •• "Stress Redistribution for the Multiring Flywheel", ASHE paper 77-WA/DE-26, 1977. 11. Kirk, J.A. and Evans, H.E., "Inertial Energy Storage Hardware Oefi ni tion Study -- Ring Rotor•, NASA CR-175217, 1984. 12. Huntington, R.A. •stress Analysis and Maximization of Performance for a Multiring Flywheel". M.S. Thesis, University of Maryland, College Park, 1978. 13. Khan, A.A., "Maximization of Flywheel Performance", M.S. Thesis, University of Maryland, College Park 1984. 14. Anand, D.K •• Kirk, J.A. and Bangham, M• • "Design and Analysis of a Magnetically Suspended Flywheel System". Presented at ASHE Winter Annual Meeting, Miami Beach, Fla. Nov. 11-21. 1985. 2.453 Page 565 THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 85-WA/DE-8 345 E. 47St., New York, N.Y.10017 The Society shall not be responsible for statements or opinions advanced in papers or in dis- cussion at meetings of the Society or of its Divisions or Sections, or printed in its publications. Discussion is. printed only if the paper is published in an ASME Journal. Papers are available from ASM E for fifteen months after the meeting. Printed in USA. Design and Analysis of a Magnetically Suspended Flywheel System D.. K.. ANAND, Professor, J. A. KIRK, Associate Professor, M. Bangham, Graduate Student Department of Mechanical Engineering University of Maryland College Park, MD 20742 Abstract Flywheel Design Considerations This paper reports upon research activities on the Shown in Figure 1 is the current geometry which is design, fabrication and testing of a magnetically preferred for the magnetically suspended flywheel. The suspended experimental energy storage flywheel system. unique characteristics of the flywheel rotor for this The successful design of the flywheel system is system are: dependent upon 1. There is no shaft to flywheel connection • composite materials required. • motor/generator 2. The geometry of the rotating element is such • magnetic suspension that no stress concentration elements are pre- Current studies indicate that the critical problems in sent. these areas can be successfully addressed for the 3. The composite wheel is pre-stressed and filament design and construction of much larger systems. wound to achieve an overall inside to outside diameter ratio of 0.4, thereby minimizing inner Introduction radius displacement. In flywheel energy storage systems one of the The use of magnetically suspended flywheels for important performance indicators is the stored kinetic energy storage have been proposed, conceptually energy per unit of flywheel weight. This indicator is designed and fabricated by several researchers in the specific energy density (SED} and for isotropic past. [1-7] materials a simple formula can be developed [4] as Rodriguez, Studer and Baer [1,2] have assessed the shown be 1 ow: benefits of flywheel energy storage for spacecraft and have concluded that the advantages over electrochemical systems are : 1. long 1 ife (20-·30 years} N/\5/\ 2. simple charge detection and control 3. high pulse power capabilities 4. high energy densities (stored energy per unit weight} 5. large momentum available for attitude GSFC + UMME = ACES contro 1 The authors further suggest that the inherent advan- tages of flywheel energy storage systems can be A-COMPOSITE achieved thru composite material, magnetic suspension, WHEEL and permanent magnet-ironless armature-brushless B-MAGNETIC motor/generator technologies. SUSPENSION Kirk, Studer and Evans [3] have proposed a magneti- C-MOTOR/ cally suspended flywheel system which utilizes the GENERATOR above technologies. Kirk and Studer [4,5] have discussed their systems in detail and have concluded that a composite material, magnetically suspended ring, which al so serves as the rotor of a motor generator system, is an ideal geometry for flywheel energy storage systems. Fig. 1 Conceptual Design of Current Prototype Presented at the Winter Annual Meeting Miami Beach, Florida-November 17-21, 1985 Page 566 Stored Kinetic Energy SED ( 1) Flywheel Weight (2) where Ks is a non-dimensional shape factor between 0 and 1, and cr/y is the specific strength of the flywhee 1 material. . The SED of a flywheel is maxi mi zed when every point in the flywheel reaches it radial and tangential working strengths simultaneously. All practical designs are a compromise between maximizing SEO a~d obtaining a flywheel which can be reasonably fabr1- cated. Since SED depends on a nondimensional shape factor whose range is limited, it is desirable to choose flywheel materials which have high specific strengths to maximize SEO. Typically the specific strength of a composite material, such as graphite epoxy (e.g., 70 wh/kg), is 5 or more times greater than high strength steels (e.g., 13 wh/kg). Thu~ the_ choi:e of composite ma teri a 1 s for fl ywhee 1 app 11 ca t1 on s ~ s mandatory whenever maxi mi zing SED is important, as 1 t is in spacecraft applications. To overcome the limited radial tensile strength of composite materials an interference assembly o~ nested rings is proposed. A complete stress analys1 s of a multiring/multimaterial flywheel is discussed [8] and it is shown that the SED of a given geometry can be Fig. 2 Stator Assembly for Magnetic Suspension increased by a factor of 2 or more through interference assembly. It is al so shown that the radial stresses 2. Note that the magnetic plate is slotted to pro- can be redistributed with interference assembly so that vide four independent quadrants for control. The the outer flywheel rings will separate at their inter- slotted area is fil 1e d with epoxy for mechanical faces if a given flywheel speed is excee_ded. Pr?per strength and ease of handling. Si nee the epoxy use of this condition will minimize containment we1ght material retains very low permeability it has no effect requirements for the system. upon the magnetic circuit. Kirk, Anand and Khan [6,8] have outlined the The equivalent magnetic circuit was derived to flywheel sizing procedure and have developed a FORTRAN simulate the static and dynamic performance of the computer program (FLYSIZE) which will interactively bearing. The permeance s were computed by mapping of carry out the Flywheel sizing details. Typical 1~ ~he the flux lines to satisfy Laplace's equation as well as FLYANS program is first used to select a best ~ult1r~ng using the Schwarz-Chri stoffe 11 tran sforma ti on. This arrangement and interference pressure set wh1 ch w111 circuit was used to obtain the leakage and fringing maximize SEO. The pertinent output of FLYANS for the coefficients. For our particular design it was found best configuration are then stored in temporary files that a leakage coefficient of around 3.6 was obtained and the FLYSIZE program is executed to provide the indicating excessive leakage. This result will be used design details. to modify the design for the larger sizes. It is noted that the computation procedure should include the Suspension/Power Design determination of saturation conditions. The sensing for the active control of the suspended The power transfer is achieved using a flywheel is achieved with two orthogonally mounted motor/generator embedded in the flywheel which is sta- Kaman sensors of the eddy current type. These sensors bilized around a stator. The stator houses the per- are used to energize the control system illustrated in manent and electro-magnets for stabilization, the Fig. 3. This control system is identical for the x and necessary transducers, and all of the electronics. y directions and is designed to maintain a nominal Static stabil i za ti on is achieved using Samarium Cobalt radial gap of 0.02 in between the stator and the magnets and dynamic stabilization is achieved via flywheel. The four coils, representing one of the electromagnets that are driven by an error signal control directions, are energized in parallel so that generated by radial position sensors. These sensors the flux is. additive on one side of the stator while are located orthogonal to each other in order to obtain subtracting 180° away thereby introducing a net decoupling between motion in the x and y directions. correction force opposing the direction of radial The motor/generator is based on the brushless motion. DC-PM/ironless armature technology using electronic The motor/ genera tor design is i 11 u stra ted in Fig. commutation. 4. It basically shows This design [7] has the fol lowing important com- • Eighteen permanent magnets uniformly ponents: embedded in the flywheel • The passive suspension is achieved by four • An iron return ring Samarium Cobalt permanent magnets • Ironless armature attached to the base plate. • Active control is achieved with eight coils each The motor/generator uses IR sensors :or determi~ing of 1000 turns of #34 copper wire. position in order to obtain electron1c commutat10n. • The bearing assembly, machined using Nickel- The power electronics yield a voltage which is direc~ly iron, is hydrogen annealed. proportional to the rotational speed of the rotating An expanded view of the bearing itself is shown in Fig. , flywheel. 2 Page 567 X v, R (sR,C +1) V, v, 2 1 R1+R 2 +sR1R2C 1 Fig. 3 Control System for Radial Gap tially difficult to achieve. This was due to the fact that the magnetic circuit was saturated. Additionally, it was determined that the control coils were not sufficiently strong to move the suspended flywheel from one extreme position to the other. The existence of weak coils and saturation meant that there was no ROTATING p M active control or that the control region was non-existent. The actual stabilization was finally achieved when the magnet surface area was decrea sect significantly to eliminate saturation. Rotation speeds, using an aluminum flywheel were achieved at 2500 rpm. It was noted that perturbation orthogonal to the spin axis as well as dynamic cross- coupling rendered the system to chatter and i nstabi- 1 ity. Any new design must address this very important issue for high speed application. 1700 •(t660rpm,1 25A} 1600 No Return Ring 1500 (t480rpm 1 15A) 1400 With Return Fig. 4 Motor/Generator Assembly Ring 1300 It is noted that although the ironless armature and • {t149rpm 1.25.A) 1100 the rotating return ring helps to minimize the losses 1000 the inner ring design is very poor and conducive to ::E a. 900 large losses. This is due to the fact that the inner a: 800 ring sees a rotating magnetic field which gives rise to 700 significant hysteresis and eddy-current losses. This 800 500 is particularly true for higher rotational speeds. It 400 is anticipated that the new design will use laminates 300 in order to minimize these losses. 200 100 Test and Simulation Results 10 t 5 ,o 30 35 40 For testing purposes, the motor/generator was Voltage se~arated from the magnetically suspended flywheel. This allowed the power generation to be studied inde- Fig. 5 Effect of Return Ring on pendently of the magnetic suspension. For this phase Motor/Generator Performance of work no data on the power generation was obtained although the motor/generator assembly was satisfac- The FLYANS program was used to design and optimize torily tested up to 1500 rpm. Al so performance of the a particular configuration shown in Figure 6. Shown in motor/generator was investigated with and without the Figure 6 is a plot of radial stress vs. radius ratios return ring as shown in Figure 5. The figure indicates for both the unoptimized and optomized (i.e., inter- that although higher rpm can be achieved for a fixed ference assembled) 300 Watt-hour design. These stress ~rmature e~citation voltage, the armateure amperage plots show the significant reduction in radial tensile increases ,n order to compensate for the increased stresses that occur when the flywheel is operating at ma~netic losses •. T~is also shows the desirability of its maximum speed ( NMAX) due to interference assembly. using a return ring ,n future designs. The magnetic suspension of the bearing was ini- 3 Page 568 Without interference the flywheel maximum speed is above 75% NMAX the radial stresses would begin to go 1 imited by radial tensile stresses in the composite tensile in the outer rings first. If the outer 1 or 2 material (at r/b"' 0,7). With interference, the radial rings were weakly bonded together an over speed con- stresses no longer limit performance and the maximum di ti on could selectively release an entire outer ring speed is 1 i mi ted by tensile hoop stresses in the outer and, perhaps, pr.event a total system failure. Most ring. certainly the containment problem of an overspeeding flywheel is greatly simplified if entire rings can be designed to drop off. The inner radius displacement (air gap growth) of the design has been minimized because the overall 300 WH ROTOR flywheel inside to outside diameter has been reduced to RADIAL STRESSES (psi) vs O. 45. Without the benefi ci a 1 effects of interference assembly this reduction of air gap growth would not RADIUS RA TIO have been possible[8]. 1 00 0 7 5 CONCLUSIONS 10 50 For spacecraft applications a magnetically r/) unoptimized suspended fl ywhee 1 energy storage system offers si gni - .O .o 2s fi cant advantages in both cycle 1 ife and specific 0 energy density (SEO) compared to electrochemical systems. To achieve these advantages an interference assembly (prestressing) of the flywheel will be r/) U>-0 25 required, (1) ~ The basic concept of the su spen si on scheme C/)-0 50 discussed here has been validated at 2500 rpm. The --optimized principal problem of stability due to orthogonal per- -~-0 75 turbations has led to a new design for a 300 Wh appli- "O «l /atNMAXI cations. Initial concepts and design studies indicate CC- 1 00 that a 300 Wh flywheel storage can be successfully constructed. This activity is currently under way. ACKNOWLEDGMENTS The authors would like to thank Mr. G. Ernest Rodriguez and Mr. Philip A. Studer of NASA/Goddard Space Flight Center for their technical assistance in Fig. 6 Radial Stress Distribution carrying out the work reported here. The authors al so for a 6 Ring Rotor gratefully acknowledge the financial support for the 300 Wh ROTOR work provided by IJASA grant NAG 5-396 and computer time provided by the University of Maryland Computer Science Radial Stress vs r/b Center. REFERENCES 0 25 rib- 1. Rodriquez, G.E., Studer, P.A. and Baer, D.A., "Assessment of Flywhee 1 Energy Storage for Spacecraft Power Systems", NASA Technical Cl) -0 25 Memorandum 85061, May 1983, Cl) w 2. Studer, P.A., "Magnetic Bearings for Instruments in a: the Space Environment", NASA Tech Memo 78048, f- January 1978. Cl) ,-.. 3. Kirk, J.A., Studer, P.A. and Evans, H.L, , J (.) ·i 10 .... o .... w w '-I C0 ~ a> ~ C w a, 5 1 0 • I I 0.09 0,10 0.11 0.12 0.13 0.14 0.15 0.16 n ( Overal I Efficiency) 0 Figure 2 FBrformance of Various Cell-Module Areas Page 579 20000 I j J u(Cost of PV in $/watt) I I ~ I i5000 ~ 1 vi u0 j -E (1) , en .w.... 0 ~ t0 -;§ -I 0 ~ 5000 0.09 0.10 0.11 0.12 013 0.14 0.15 0.16 n0 (Overall Efficiency) Figure 3 Cost-Performance for a PV Module of 40 ft~ Page 580 20000 I I j I u( Cost ~ PV In I -j I 15000 u=20 .-.-. 1 "0 ' 0 ~ E !(I) 10000 w c i co 0 ~ J 0 I I 5000 0 I I 0 09 0.10 0.11 0,12 0.13 0.14 0.15 0.16 n (Overal! Efficiency) 0 Figure 4 Cost-Performance for a PV Module of 80 ft2. Page 581 The specific area of PV/VCC for air conditioning and/or refrigeration is basi- cally conceptual with few complete experiments and no sustained long term per- formance results. For a successful commercialization of this concept, it is necessary to conduct developmental research in • improving the basic thermodynamic cycle • using brush less DC rootors for variable speed control • using microprocessor control In addition it is necessary that long term testing and performance evaluation of multiple units be conducted. This is needed for • establishing component and system reliability • ascertaining maintainability requirements These activities are independent of the work on-going in cell cost and perfor- mance improvement. The successful solution of the VCC t~chnolO'Jf and cell module performance will satisfy the need from an overall performance viewpoint. The significant reduc- tion in cell module cost and a favorable competitive cost of other fuels will be the additional factors for economic viability. Given the current status, a har- monious working of all factors favorable to PV/VCC appear to place it amongst the most viable technologies for solar applications. ACK NOWLEDG!1E NT Parts of this study were supported by the Department of Energy under contract DE-AC03-B4SF1l997. REFERENCE.S 1. Scholten, \~.fl. and i1orehouse, ,J.H., Active Program Research Requirements, SA! Report, DOE/SF/11573-Tl. 2. Sclater, Neil, Brushless DC llotors Caine of Age, Design Engin., Dec. 1980, pp, 41-44. 3. Appelbaum, J., Operation of DC 11otors Powered by Photovoltaic Converters, Electric i1achines and Electrom~chanics, Vol. 3-A, 1978-79, pp. 209-·220. 4. Green, A. and fllakers, A.W., Advantages of Metal Insulator-Semiconductor Structures for Silicon Solar Cells, Solar C~~. Vol. 8, 1983, pp. 3-15. 5. Hall, R.tl., Silicon Solar Cells, Solid State Electronics, Vol. 24, 1981, pp. 595·616. 6. Murgunsan, S., An Overview of Electric Motors for Space Applications, IEEE Trans. on Industrial Electronics & Control Instrumentation, Vol. IECl-=ra":· No.°"-ii";--ifov. 1981, pp, 260-265. -· 7. natsuo, llirofumi and Kurokawa, Fujio, New Solar Cell Power Supply System using a floost Type flidirectional DC-DC Converter, 1982 IEEE Power Elec. _fonf., pp. 14-19. 8. Schoeman, J.J. and Van Wyk, J.D., A Simplified Maximal Power Controller for Terrestrial Photovoltaic Panel Arrays, 1982 IEEE Power Elect. Conf_., pp. 361-·367. 381 Page 582 9. Longrigg, Paul, DC to AC Inverters for Photovoltaics, Solar Cells, Vol. 6, (1982) pp. 343-356. 10. Haq, A.!1., Photovoltaics Systems Considerations, Solar Cells, Vol. 6 (1982) pp. 317-322. 11. Field, Richard L., Carrasco, Peter and DeQuadros, Cir. A., Review of Photovoltaic-Powered Refrigeration for Medicines in Developing Countries, Solar Cells, Vol. 6 (1982) pp. 309-316. 12. Nonlan, Michael J., Design and Fabrication of Air- and Liquid Cooled Photovoltaic/Thermal Collectors, DOE/ET/2279-162, (September 1981). 13. Solar Photovoltaic Residential Project: Project Integration !1eeting Agenda and Abstracts, DOE/ET/20279-150 (June 24-25, 1981). 14. Final Report: J.F. Long Experimental Photovoltaic House (June 1982) DOE/ET/20279-201. 15. Jarvinen, Philip 0., A Flywheel Energy Storage and Conversion System for Photovoltaic Applications - Final Report, (March 1982) DOE/ET/20279-159. 16. tlaff, George J., Photovoltaic Array Field Optimization and Modularity Study, (March 1983) Contractor Report SAND 81-7193. 17. Lambarski, T.J., Irby, C.A., Collaros, G.J., Anderson, E.R., Sowa, P., Schwinkendorf, W.E. a11d Res11ik, W.M., Design Analysis of Advanced Photovoltaic Technologies (August 1983) Subcontract Report SERI/STR-214-1997. 18. Discussion with Solarex, BNL and General Electric Co. 19. Mehalick, E.M. et al. The Design of a Photovoltaic System for a Southeast All-Electric Residence, Sandia Report 80-7172 (January 1982). 20. International PV Program Plan, SERI/TR 353-361. 21. McNelis, B., Solar Refrigeration and Water Pumping for Developing Countries, Conference Proceedings of UK Section of the International Solar Ene!:_91'._ Society, London (January 1982). 22. Meckler, M., Solar Powered Rankine Cycle, Dual Stage Chiller/Regenerator Improves Combined Cycle Efficiency, Proceedin~Solar Cooling and Dehumidifying Conference_, Carakas, Venezuella (August 1980). 23. Vokaer, D.P., Development of an Autonomous Free Piston Refrigerating Unit Driven by Rankine Cycle, Proceedings of the EC Contractors' Meeting held in ~!_he!_!~_, Greece (November 1981). 24. Vandendael, Y and Vokaer, D., Development of an Autonomous Free Piston Refrigerating Unit Driven by Rankine Cycle, Proceedings of the EC Contractors' Meeting held _in Meersburg_. F.R.G., June 1982. 25. Haverhals, J., Solar-Driven Refrigeration, Conference Proceedings of UK Section of the International Solar Ener~y Society, London, January 1982. 26. Giri, N.K. and Barve, K.M., Solar Ammonia-Water Absorption System for Cold 382 Page 583 Storage Application, Proceedings of the International Solar Energy Society_ Congress, New Delhi, India, January 1978. 27. World Health Organization, Solar Refrigerators for Vaccine Storage and Icemaking, EPI/CCIS/81.5, 1981. 28. Worsoe-·Schmidt, P., Calcium Chloride/Ammonia Solar Absorption Refrigerator, Proceedings of UK Section of the International Solar Energy Society, London, January 1982. 29. Guilleminet, J.J., Meunier, F., Marsin, G. and Royer, D., Solar Cooling Through Zeolithe Cycles, Proceedings of the EC C~.!!~ractors' Meeti~Held in ~then~. Greece, November 1981. 30. Goldsmid, H.J., Thermoelectric Refrigeration, Plenum, New York, 1964. 31. Field, E.L., Photovollaic/Thermoelectric Refrigerator for Medicine Storage for Developing Countries, Solar Ener.91., Vol. 25, 1980. 32. McNelis, B. and Lloyd, J.S., Evaluation of Solar Refrigerators for Use in the Vaccine Cold Chain, Procee~of UK Section of the International Solar_ _E nergy Society, London, January 1982. 33. SERI PV Advanced Research and Development Program, An Overview, February 1984, SERI/SP-281-2235. 34. Sunworld, Vol. 7, No. 2, Summer 1983. 35. PV, International, April/May 1984. 36. Alternate Source of Energy, r1ay/June 1984. 37. Notes provided by \L Wilhelm, Createch, Inc., N.Y. 38. Anand, D.K., Photovoltaic Driven Vapor Compression Cycles, Final Report on Contract D[-AC03-84SF11997, March 1985. 383 Page 584 HOTEL ACCOMMODATIONS Hotel reservations should be made early. We recommend: Pittsburgh Hyatt Hotel Sheraton Hotel at SEVENTEENTH ANN UAL Chatham Center Station Square PITTSBURGH CONFERENCE Pittsburgh, PA 15230 7 Station Square Drive ON (412) 391-5000 Pittsburgh, PA 15219 MODELING AND SIMULATION (412) 261-2000 *Howard Johnson's Motor Lodge 3401 Blvd. of Allies APRIL 24 - APRIL 25, 1986 Pittsburgh, PA 15213 Benedum Engineering Hall (412) 683-6100 University of Pittsburgh *University Inn Forbes Ave, & McKee Place More Than 350 Papers On: Pittsburgh, PA 15213 • ENERGY SYSTEMS • BIOMEDICAL SYSTEMS (412) 683-6000 • REGIONAL SCIENCE • ECOSYSTEMS • GEOGRAPHY • TRANSPORTATION Pittsburgh Hilton Hotel 600 Commonwealth Place • ROBOTICS • EXPERT SYSTEMS Pittsburgh, PA 15222 • ECONOMIC MODELING • ARTIFICAL (412) 391-4600 • MODELING AND INTELLIGENCE ESTIMATION • AND MANY OTHER William Penn Hotel • POWER SYSTEMS SESSIONS iAn ll,<>m P,=mn Place Sponsored by 6 - M l :30 - 3:00 RM 720 Department of Electrical Engineering MECHANICAL SYSTEMS - I , Session Chairman, School of Engineering F. D. Chichester, New Jersey Ins~D.Q!_ogy University of Pittsburgh Pittsburgh, Pennsylvania Modeling and Simulation of Magnetic Bearing Forces, J. A. Kirk. D. K. Anand and R. ~ o_f_M_a_r'y-l_a_nd_ _______ In Cooperation With Simulation for Region Filling Operation for The Pittsburgh Sections Mobile Robots , Zuo L. Cao, Yu Y Huang and of the Ernest L. Hall, University of Cincinnati Institute of Elect rical and Electronic Engineers and Design and Prediction of the Static The Instrument Society of America Behaviour of the Bolted Joints, Gaber M. M. Sheba, Menoufia University and The Systems, Man and Cybernetics Society Stability Considerations in Simulating Waiting Mechanis,ms, University of The Society for Computer Simulation M. A S. Mohamed and H. name, aff ilia- The International Association for Mathematics T. Salem, Military Technical College, Cairo a copy of the and Computers in Simulation (formerly AICA) Development of Three-A1is Discrete Mass and all other Rotational Dynamics Models of Flexible Spacecraft, F. D. Chichester, New Jersey Institute Conference Committee of Technology ~LE L. Luo : RENCE M. L. Hsiao 6 - N 1:30 - 3:00 RM 722 Z. Zhang 1-'1 I I ;::,ounu, ,, ........ H.Q. Lu M.Mallik COMPLIMENTARY COCKTAIL PARTY - 4:30-6:00 PM Thursday, April 24, 1986 Conference Coordinator Jeff Marquis LUNCHES AND DINNERS No formal arrangements have been made. A list of restaurants will be Conference Co-Chairmen available at the Conference. William G. Vogt Marli n H. Mickle Page 585 ©U. of Pittsburgh , 1986 MODELING ANU SIMULATION OF MAGNETIC BEAKING FORCES James A. Kirk Davinder K. Anand Koyer Vieira Chaitanya P. Jayaraman Associate Professor Professor Research Assistants University of Maryland , Colleye Park , MD 29742 I. Introduction Maynetic bearinys (1) are attractive for space as well as many otl1er applications since they are caµable of lony life due to the noncontactiny nature of the beariny . Also, they reµre- sent excellent choices for eneryy storaye due to the possibility of very hiyh efficiency excursions of input/output power . This feature becomes particularly attractive when couµled with attitude control systems for low earth orbit aµplications. The analysis reported in this µaµer, althouyh yeneral , was performed in support of the "sandwich" confiyuration maynetically suspended flywheel system currently under development by reseachers from the University of Maryland and the Goddard Space Fl iyht Center . Tt1is con- fiyuration is illustrated in Fiy. 1 and Fiy. L The flywheel has its radial dynamics control'led by the maynetic suspension which is biased by four symmetrically located samarium-cobalt permanent maynets and by control windinys which compensate the displacement of the flywheel relative to its centered µosition . To each µair of radially aliyned permanent magnets corresponds a closed loop feedback control system which provides active control in each orthoyonal direction . In this paper , the maynetic forces used for stabiliziny the rotor are modeled and validated with exprimental data . The analytical approach in modeling of the magnetic forces depends upon the evaluation of the path permeance and operating point of the magnet itself . Several methods, including the Schwartz-Christofell approach of mapping the magnetic field are used to evaluate the maynetic force . II . Permeance Analysis A theoretical expression for the force on the maynetic bearing as a function of the radial displacement of the flywheel can be developed by considering the general case of two surfaces approachiny each other. The magnetic force for this case is yiven by 2 1 2 dPa 1 ~a dP a F = 21' a els 2-p-~ ( 1) = a where~ flux in the airyap between rotor and stator '!5a maynetomotive force in the ai ryap Pa a permeance in the airyap. This expression can be evaluated provided the chanye in permeance as a function of the displacement of the flywheel is known . Three methods are used for the permeance calcula- tions . The first method uses equations derived throuyh semi-empirical methods. The second is based on numerical integration of the air gap . The third method uses analytical inteyra- tion instead of the numerical approach of the second. Semi-empi ,i cal When the cross sectional area of the air path remains constant , it is possible to calculate the permeance of this air path by the use of equations derived through semi-empirical methods (2) . This well known method is also used to estimate the relationship between the permeances of the useful flux path a~d the fringing flux paths shown in Fig . 3. 639 Page 586 The introduction of nt1merica·1 va1ues Into the a.bove expressions for the range of variations of the ai ryap shows that the va·1ues of dP /ds ano dP /ds vary from 1.2 to 3.b. This is used to estimate the fri n,;i ng f1 ux when cal cul~fi ng th.e o~erat i ny point of the permdnent maynets. Numerical evaluation This method consists of the cal.culation ·of the permeance throuyh the whole cylindrical gap assuming that the cross-sectional area of the airyap remains constant for small sectors of the ,Jap. The permeance for an incremental element illustrated in Fig. 4 can be shown to be 2r+g +oCOSa p µ (2'" )( 0 )1 a o g +ocosa 0 So that the total permeance becomes 360/a p I p n=l a and which can be easily differentiated. Evaluation by integration This method is governea by the same assumptions as the numerical n~thod discussed previously. Using the parameters of Fig. 5 the differential permeance of a small element of the gap with angular width da can be defined as 2r+go 1 dP µO --2- da _g__+_6_C_O_S_a 0 Therefore, the permeance of an airyap section of angular extension a 2 - a 1 is given by p 1 -1 1-E [ tan ( / l+E tan (1-,:2) o = £Y 0 The final expression for the permeance in the airyap is obtained by substitutiny tne correspondiny values of a 1 and a for each of the sections of Fiy. 6. 2 The total per111eance is obtained by the addition of the four sections r +P +2P wt1icn amounts to 1 3 2 and 2r+g ) 0 (g 2_62)1/2 0 again this can be easily differentiated to give Magnetic force The above three methods have been compared and it is found that the numerical approach is tne 640 Page 587 n10st accurate. Hm~ever, for an initial desiyn check, the ana1ytica1 expression is con- venient. Usiny this the force becomes F = _ _1;: _ j:2 µ nlo(Zr+g) o o (2) 4 a (g 2_ 62)3/2 0 The only unknown is the magnetomotive force (or the flux that is usefu1) which depends upon the operatiny point of the maynet. In order to obtain the operating point of the magnet, the flux paths and permeances of the magnetic circuit must be identified. Usiny a maynetic impedence ana1oyy (3) a schematic magnetic circuit of the bearing inc1udin'cl both conservative and lossy effects can be derived. To do this, "the conservative effect is related to the maynetomotive force by T = ~/P. The lossy effect is :F = Gd~/dt where G is the conductance of the eddy current path. The resultiny circuits of the maynetic suspension system are shown and analyzect in ref. 4. The permanent magnets are shown as a magnetomot i ve force source in series with a permeance a nct a conductance. The maynet i c f1 u x pro ~ 1 dw = - ,. (l-w2}1/2 Tne final expression for the radial force F per unit length becomes f (4) where K = complete elliptic integral of first kind. Tne total force per unit length actiny on the bearing is obtained by applying E4. (4) for each of the components of the force. g =Yo+ o for FA and g = Yo - o for Fs y0 is the ini- tial airyaµ and o is the radial disµlacement of the flywheel. To calculate the total force on the beariny due to the contribution of all maynetic sectors, reference is made to Fiy. 8 to obtain _ P = -ocose + PA ( l -(L}2 s,·n2e )1/2 Pr where Pr= inner radius of the rotor o = radial displacement of the flywheel. Including the contribution of all magnetic sectors, the limits Oto,. are used to integrate Fr= FA - Fs and obtain the force on the bearing. Integration yields the total force on the bearing as 11 oPf2[( l ,rt )•(-1-+ ,rt )J (5) FT= -2- go+o + 2{yo+6)2 Yo-o 2(yo-0)2 where pis the average radius of the airgap. The evaluation of the radial magnetic force in this case requires the evaluation of the ope rat i ny point of the permanent magnets and its correspondent magnetomot i ve force as done t>ef ore. IV. Analytical and Experimental Results The magnetic force is completely defined by Eq. (2) provided the flux output is known. Analytically this is obtained by the procedure outlined in section II. The resulting magnetic force as a function of the displacement of the flywheel is now calcu- lcted and is shown in fig. 9. This figure shows the graphic relationship between radial force and raaial _displacement of the flywheel after the evaluation of the change in permeance and magnetomotive force. The parameter which is varied is the operating point of the magnet so that the predicted force increases with flux output as expected. Also shown in Fig. 9 is the experimental results reported in Ref. 6. It appears that the magnet is operatiny at a 642 Page 589 relatively low value of the oµeratiny point. Tne radial maynetic force usiny the Scnwartz-Cnristoffel transformation of £4. (!:>) is identical to tnat shown in Fiy. 9 indi- catiny the excellent ayreement between the two analytical µrocectures. The prediction of the axial force is imµortant since it determines the weiyht carrying capa- bility of the bearing. The axial force is calculated usiny the Schwartz-Christoffel trans- formation (4). The maynetomotive force was obtained followiny the ~rocecture discussed earlier. The results are shown in Fiy. lU. This figure compares tne axial force as a func- tion of the radial displacement of the flywheel with experimental results obtained by Mac Bar Mechanisms, (ref. 5). The computations and experimental validation is for the condition where the flywheel is vertically offset a fixed distance from the pole faces on tne stator. Althouyh this offset is an important parameter it was not investigated. This is the subject of ongoing activity and will be incorporated into the final simulation. V. Canel us I ans The yood a~reement between the theoretical values obtained and the existiny experimental results verify the validity of the analysis developed. The results show that the effects of the value of the oµeratiny point of the permanent maynets on tne maynitude of the maynetic force can be siynificant. The values of the operatin9 points are yoverned by the leakaye and frinyiny of the magnetic flux and frinyiny factors varied from 1 to 3.5. These values correspond to leakaye factors varyiny from 1 to 5. While the leakage can be calculated and reduced by desiyn efforts, the fringiny flux is inherent to the yeometry of the airyap and should be evaluated as accura~ely as possible. VI. Keferences 1. Studer, P.: "Maynetic 13eariny for Instruments in the Space Environment", NASA Technical Memorandum 78048, Goddard Space Fl iyht Center, Greenbelt, 1Y78. 2. Raters, H.C: "Electromagnetic Devices", John Wiley & Sons, 1941, p. 197. 3. Buttenbach, R.: "Improved Circuit Models for Inductors Wound on Dissipative Cores", Proceedinys of the Second Asilomar Conference on Circuits and Systems, 1969. 4. Vieira, R.: "Analysis of a Ma\jnetic Bearing with·Two deydrees of Freedon", M.S. Thesis, 1985, The University of Maryla.nd.' 5. Zaremba, J.G.: "Control System Implementation Technology", TRW Technical Memorandum IRAD 78, TRW, Redondo Beach, 1978. 6. Machlanski, H.: "Final Report-Magnetic Bearing", Mac Bar Mechanisms, Inc., New York, 1976. 7. Bangham, M.L.: "Simulation and Design of a Maynetic Flywheel Bearing", M.S. Thesis, 1985, The University of Maryland. VII. Nomenclature A cross sectional area of the magnets B magnetic flux density E incomplete elliptic integral of the second kind £' complete elliptic integral of the second kind F maynetic force G conductance of the eddy-current paths H magnetic field K complete elliptic inteyral of the first kind P penneance of a magnetic path y gap lenyth between the rotor and the stator k Schwartz-Christoffel coefficient 1 axial length of the poles t maynet lenyth r radius s displacement t thickness of the iron ring t time w W-plane x coordinate y coordinate z coordinate f" magnetomotive force 4> magnetic flux v stream function :-643 Page 590 flux potential airgap sector anyle increment radial displacement of the flywheel £ normalized radial displacement 1-l permeat>i l ity p radius Subscripts A,B diametrical locations in rotor a airyap or axial displacement u useful j path i a anyular section t leakaye l per inch lenyth m maynet 0 initial conaitions 0 permeability in vacuum r rotor s stator T total X ,,y,, Z coordinates component Acknowledgements This research was supported by NASA/GSFC under Grant NAG5-396. The technical input into this research of E. Rodriguez and P. Studer is greatly appreciated. Jl.SSSSSS'i Figure l. -=-,_ _ ,CONTROL FLUX PLATE Figure 2. Figure 3. 644 Page 591 Figure 4 Figure 5 Figure 6 Figure 8 Figure 7 CXP£RIMENTAL RCSULTS EX.P£i\l01£NT>.L RC SUL TS T r (lb} O.P. • t (ll:)) O.P. • ( O.P. • 6.S 25 o:P. • 10.7 25 O.P. • 6.8 O.P. ,. 10.7 • 20 ,o 15 ~: lS I :~: 10 i .0/ 10 , I ~'.~ ~:1/ • ~·= ~ 0 1 0 0 .001 .002 .001 diepl Un) .005 ll..4di411 Fore• X R•di.41 D1s_plac•••nt Figure 9 Figure 10 645 Page 592 .~.,. e 21st Intersociety_ Energy Conversion Engineering Coiiference FINAL PROGRAM e August 25-29) 1986 Town and Country_ Hot-el e e e San Diego> California e e e e Page 593 869184 Review of the Characterization of Molten Nitrate Salt for Solar Thursday Afternoon Central Receiver Applications R. W. Carling, R. W. Bradshaw, Sandia National Laboratories Space Reactor Technology Development-2:00 PM 869185 San Diego Room Conceptual Design Study of a Solar Ammonia/Nitric Acid Co-Organizers: M. Swerdling, TRW, D. Buden, Science Production System Applications International S. F. Wu, G. Carli, R. J. Zoschak, Foster Wheeler Solar Development Corporation, D. J. Allen, Risk Research Group Chairperson: J. Angelo Jr., Florida Institute of Technology 869452 Magnetohydrodynamics-9:00 AM Post-Operational Disposal of Space Nuclear Reactors Esquire Room J. A. Angelo Jr., Florida Institute of Technology, D. Buden, Science Organizer: J. B. Dicks, University of Tennessee Space Applications International Corporation Institute Chairperson: L. C. Farrar, Mountain States Energy 869453 Some Thoughts on the Commercial Use of Reactors in Space Division J. Lee, Sandia National Laboratories, D. Buden, Science Applications International Corporation 869138 The MHD Development Corporation's Current Role in the 869454 Commercialization of Magetohydrodynamics (MHD) Extended Brayton Cycle, Radiator Investigation for Future G. Staats, W. Owens, J. McElwain, MDC Technical Advisory ARIAN-5 Space Nuclear Power Applications Committee Z. P. 7illiette, Commissariat a l'Energie Atomique J. Cacheux, Centre National d'Etudes Spatiales 869139 The Triple Cycle-MH:>, Gas Turbines and Steam 869456 J. B. Dicks, L. W. Crawford, University of Tennessee Space Institute Heat Pipe Design for Space Power Heat Rejection Applications M. Merrigan, Los Alamos National Laboratory 869140 The Metal-Ammonia Solution as a Pulsed and Continuous Power Source M. R. Johnson, University of Texas, W. R. Kallman, Reed Energy Advanced Space Power Concepts-2:00 PM Associates Golden West Room Organizer: E. VanLandingham, NASA Headquarters 869141 Chairperson: P. Pierce, RCA Astra-Electronics Experimental Studies of Two-Phase Liquid Metal Gas Flow in Vertical Pipes 869419 Y. Unger, H. Branover, A. El-Baher, S. Lessin, D. J. Ritz, Ben-Gurion Inertial Fusion Power for Space Applications University of the Negev W. Hogan, W. Meier, Lawrence Livermore National Laboratory, R. E. Olsen, Sandia National Laboratories, K. Murray, N. J. Hoffman, 869142 Energy Technology Engineering Center Explosive MHD-An Assessment H. J. Schmidt, Y. C. L. Wu, University of Tennessee Space Institute 869420 Use of Nuclear Energy for Bi-Modal Applications in Space 869146 F. L. Horn, J. R. Powell, H. Ludewig, Brookhaven National Laboratory Slagging Coal Combustors for MHD Applications M. Bauer, R. Braswell, H. Iwata, TRW Space and Technology Group 869421 Electrostatic Low Weight AC Generator for Aerospace Uses F. Cap, University of Innsbruck Thermoelectric and Dynamic Power Systems: Terrestrial I -9:00 AM 869422 Towne Room The Pegasus Drive: A Multi-Megawatt Nuclear Electric Propulsion System Organizer: J. E. Boretz, TRW E. P. Coomes, J. M. Cuta, B. J. Webb, D. Q. King, Battelle Pacific Northwest Laboratories 869306 Fabrication of Advanced Technology Silicon Germanium 869423 Thermoelectric Devices Solar Pumped Laser Technology Options for Space Power B. Heshmatpour, Thermo Electron Corporation Transmission E. J. Conway, NASA Langley Research Center 869308 Two-Dimensional Resistance Analysis in a Thermoelectric 869424 Multicouple Design of Superconducting Alternator for Space-Based Power P. J. Drivas, Thermo Ele9tron Corporation Generation- R. E. Dodge Jr., E. P. Coomes, Battelle Pacific Northwest 869309 Laboratories, J. L. Kirtley Jr., S. J. McCabe, Massachusetts Institute Testing of Thermoelectrics for the PU238 Special Applications of Technology RTG D. S. Trimmer, Teledyne Energy Systems 869310 Development of a 0.1 kW Thermoelectric Power Generator for Military Applications W. R. Menchen, Teledyne Energy Systems 25 Page 594 869418 Stirling Engines: Concepts & Applications-2:00 PM Development of Regenerable Energy Storage for Space California Room Multimegawatt Applications Organizer: W Martini, Martini Associates M. Olszewski, Oak Ridge National Laboratory Chairperson: R. J. Meijer, Stirling Thermal Motors Co-Chairperson: M.A. White, University of Washington Industrial Heat Pumps-2:00 PM 869131 Forum Room Fluidyne Pumping Engine with Minimal Tuning Line Organizer: J. Wurm, Institute of Gas Technology C. D. West, Martin Marietta Energy Systems Chairperson: A. R. Maret, Gas Research Institute 869132 869092 Ross-Stirling Engines: Variations on a Theme Industrial Heat Pumps: A Novel Approach to Their Placement, G. Walker, R. Fauvel, University of Calgary Sizing and Selection S. M. Ranade, A. Niha/ani, E. Hindmarsh, D. Boland, TENSA 869133 Technology An Assessment of the Concept of a Stirling Powered Torpedo G. T. Reader, C. Barnes, T. M. Dannatt, Royal Naval Engineering 869093 College Heat Pumping versus Heat Integration: A New Challenge G. J. Maffia, ARCO Chemical Company 869134 The V4-275R Stirling Engine in Underwater Application H. 869094 Nilsson, Sub Power AB, C. Bratt, United Stirling AB A Comparative Economic Evaluation of Industrial Heat Pumps C. J. Bliem, J. I. Mills, Idaho National Engineering Laboratory 869136 Field Performance of Dish Stirling Solar Electric System G. C. Coleman, J. E. Raetz, McDonnell Douglas Energy Systems 869095 Heat Pump for Subzero Climates Using Vacuum Freezing Process A. Koren, Israel Desalination Engineering Space Solar Dynamic Power Systems 11-2:00 PM Council/Chamber Room Solar Conversion/Solar Heating/Cooling-2:00 PM Organizer: J. H. Ambrus, NASA Headquarters Committee Room Chairperson: S. W Silverman, Boeing Aerospace Organizers: T. C. Min, North Carolina A&T University, G. Co-Chairperson: E. F. Binz, Rockwell International Meckler, Meckler Associates Corporation Chairperson: G. Meckler, Meckler Associates 869474 869264 Super Critical Organic Rankine Engines (SCORE) The Operation and Heat Extraction Experience of EMRO's Solar J. E. Boretz, TRW Space and Technology Group Pond J. Y. Lin, L. J. Fang, H. Yeh, Industrial Technology Research Institute 869475 Free-Piston Stirling Engines for Terrestrial Solar Electric Power 869265 Conversion The Performance of a Hybrid Solar Industrial Pre-Heat System in G. Dochat, N. Vitale, Mechanical Technology Taiwan D. T. Chen, L. J. Fang, H. Yeh, Industrial Technology Research 869476 Institute Solar Dynamic Power System Heat Rejection A. W. Carlson, E. Gustafson, Grumman Space Systems, 869266 K. L. McLallin, NASA Lewis Research Center Solar Cooling System Reduces Summer Utility Demand and HVAC System Life-Cycle Cost in Commercial and Institutional Buildings 869477 G. Meckler, Meckler Associates Solar Dynamic Power for Space State IOC E. F. Binz, J. Hartung, Rockwell International Corporation Fuel C~lls 111-2:00 PM Inertial Energy Storage for Space Applications- Sunset Room 2:00 PM Organizer and Chairperson: J. B. O'Sullivan, Institute of Cabinet Room Gas Technology Organizer and Chairperson: R. T. Bechtel, NASA Organizer and Co-Chairperson: H. Maru, Energy Marshall Space Flight Center Research Corporation Co-Organizer and Co-Chairperson: D. B. Eisenhaure, 869251 SatCon Technology Corporation DOE Molten Carbonate Fuel Cell Program Technology Issues and Plans 869414 F. D. Gmeindl, U.S. Department of Energy, V. M. Kolba, Argonne Advances in Flywheel Technology for Space Power Applications National Laboratory M. Olszewski, D. U. O'Kain, Oak Ridge National Laboratory .... 869258 869416 Molten Carbonate Fuel Cell Component Design Requirements .::, System Considerations for a Magnetically Suspended Flywheel T. G. Benjamin, R. Petri, Institute of Gas Technology D. K. Anand, J. A. Kirk, University of Maryland, R. B. Zmood, Royal Melbourne Institute of Technology G. E. Rodriquez, P. A. Studer, 869244 NASA Goddard Space Flight Center Molten Carbonate Fuel Cell Development and System Analysis T. Tanaka, M. Matsumura, E. Nishiyama, I. Hirata, Mitsubishi Electric 869417 Corporation Integrated Power and Attitude Control System (IPACS) Technology R. E. Oglevie, Rockwell International Corporation, D. B. Eisenhaure, SatCon Technology Corporation 26 Page 595 SYSTEM CONSIDERATIONS FOR A MAGNETICALLY SUSPENDED FLYWHEEL D. K. Anand, Professor, J. A. Kirk, Associate Professor Department of Mechanical Engineering University of Maryland, College Park, MD 20742, USA R. B. Zmooct, Senior Lecturer Department of Electrical Engineering, Royal Melbourne Institute of Technology Melbourne, Vic 3000, Australia P. A. Studer, G. E. Rodriguez, Goddard Space Flight Center National Aeronautics and Space Administration Greenbelt, MD 20771, USA ABSTRACT This paper discusses the system considerations of a magnetically suspended flywheel energy storage This paper presents the system considerations of system for spacecraft application. Key technologies a magnetically suspended energy storage system. The are identified and their influence on overall system key technologies for system success are presented in a design is discussed. Particular attention is technology flowchart. The key areas identified and addressed to the active bearing control system, the discussed include: the active bearing control system, touch down bearings and the dynamic performance and the back-up touchdown bearings, and the flywheel dyna- balancing requirements for the flywheel. Finally, a mic performance and balancing. Two possible hardware matrix of the key technologies versus the prototype designs are described which have been identified as designs is presented to show the current status of having characteristics suitable for energy storage in inertial energy storage research at the University of low earth orbit spacecraft. Finally, a matrix of the Maryland and to indicate directions for future work. key technologies versus the various prototype designs is presented to show the current progress of inertial THE KEY TECHNOLOGIES energy storage, and to show the direction of future work. A flowchart of the key technologies required in the development of a flywheel energy system for spa- cecraft power ~pp_l_ica~i9ns is shown in Fi • 1 LOW EARTH ORBIT SATELLITES place onerous performance CRITICAL TECHNOLOGIES - FLOW CHART requirements on their energy storage systems. Typically, of a ninety minute total orbit period the satellite operates for 60 minutes in sunlight during which energy from the photovoltaic arrays must be stored for use during the remaining 30 minute period of darkness. Up to the present time this energy storage requirement has been satisfied by electro-chemical batteries. However, there is continuous pressure to increase the reliability and lifetime of satellites, which is reflected in similar needs for the energy storage systems. In addition the steady increase in PERM MAG FIELD installed electrical load on these spacecraft together 3PHASE ---.../ with the fact that the energy storage elements consti- tute a significant proportion of the payload has led to the need to increase their specific energy density. ~:-~ -1 Ii These factors have led to the investigation of alter- CONVERSION £FFIC/£NCY'~I natives such as flywheel energy storage systems. CONVERSION EFFICIENCr"' This approach has been investigated by a number of BUS REGULA notl researchers (1-5], and has been shown to offer great AC$ REOMTS SPEED CONTROL 11 --+-------' P.W.M. ----, potential. Rodriguez, Studer and Baen [2] have con- STOBY'----~ cooe. cluded that magnetically suspended flywheel energy UNOERLINCO KNOWN storage systems for spacecraft offer the possibility l,INKNOWN !DATA REffDl of longer life by the elimination of intrinsic failure Fig, 1 Flowchart showing key technologies and the mechanisms, together with higher specific energy den- essential parameters relating to these sities (Wh/kg) and high peak power capabilities. A technologies. key conclusion of their discussion is that to achieve these possibilities for flywheel energy storage it In this figure the main subsystems are shown as being will be neces~ary to use fibre composite material the composite rotor, the motor/generator, the magnetic technol9gy for the flywheel, perm.9nerit magnet brush- suspension system, and the electronic control system. .1 ess motor/generators- of ironless construction for The underlined parameters are those which have been energyctrartSfer-to and frem the system arrd magnetic determined by external requirements or by previous bearings for flywheel suspension. studies (2,4,5,6] while the parameters marked with an Page 596 asterisk have yet to be deten11ined or require further control loops consisting of the electromagnetic study. For instance the flywheel configuration has control winaings that are driven by error signals been determined by extens l ve work by Kirk and- others generated tiy radial position sensors. These sensors [7,8], while the manufacturing process for the are positioned at right angles from each other in a flywheel has been addressed by Kirk and Huntington plane normal to the flywheel axis of rotation, but are [9]. co-linear with the respective control field generated For parameters marked by an asterisk, either in each quadrant. further study needs to be made, such as in the case of This system has been tested at speeds up to 2500 the effects of the gyroscopic loads, or additional rpm in air and 3800 rpm in vacuum with satisfactory experimental work needs to be performed, as in the results, and it is currently being prepared for case of the flywheel rotational run down losses. The testing at speeds up to 10,000 rpm in vacuum. The problem of run down losses will be addressed in a experimental testing of the flywheel has shown that it future paper. is sensitive to angular disturbances at high speeds, In the present work the three key areas which have which indicates that control of additional degrees of been identified and are discussed, include: freedom is required. This has led to the development * the active bearing control system, of the second configuration discussed below. * the backup touchdown bearings, and In the stack arrangement shown in Fig. 2 two * the flywheel dynamic performance and magnetic bearings are placed at the top and bottom balancing. surfaces of the flywheel rotor and the motor/generator is interposed between them in the inner bore of the HARDWARE DESIGNS flywheel. Since the bearings are separated by a distance of at least 2 inches (50 rrm) it will be ~ Two possible hardware configurations which have possible to sense and control the pitch and roll acceptable characteristics for application to energy motions as well as the translational motions, thus storage in low earth orbits have been studied. The overcoming the angular instability that was a problem first utilizes a single magnetic bearing discussed in earlier models. in ref, 3. The second utilizes a two bearing stack The successful fabrication and testing of the arrangement as illustrated in Fig. 2. single bearing flywheel has provided sufficient con- fidence for the project to progress to the 300 Wh flywheel energy system. In the development of this STATOR STACK design the stack arrangement discussed above has been adopted. These studies have also shown that the system characteristics given in Table 1 should be achievable. This table indicates that for applications in low earth orbits, the system can deliver 300 Wh of energy, with a round trip efficiency of 80%, as the flywheel speed runs down from 60,000 rpm to 30,000 rpm. The power budget indicates that of the total loss of 60W the maximum spin loss at 60,000 rpm is 32W with the balance being allocated to armature losses and to the power required for the suspension and power electronics. Table 1. Perfon11ance Specifications for 300 Wh Flywheel Energy System Orbit: LEO (90 minutes) Average Delivered Power 600 W Average Generator Power 660 W Energy Delivered 300 Wh Energy Generated 330 Wh Burst Speed 75,000 rpm Upper Operating Speed 60,000 rpm BEARING RING Lower Operating Speed 30,000 rpm Generator Voltage Const. 3 V/1000 rpm Fig. 2. Sectioned view of a two bearing stack Charge cycle 60 min arrangement for a magnetically suspended Discharge cycle 30 min (variable) flywheel. Load profile 1125 W for 9 min 374 Wf or 21 min In the first configuration a motor/generator is Round trip n 80% embedded in the flywheel which is stabilized around a stator that also houses the magnetic bearing and the electronics, The motor/generator is based on brush- The design of the flywheel is discussed in Ref. less DC-permanent magnet/ironless technology using [7]. It will weigh 18 lb, (8.16 kg}, have a 10 inch electronic commutation. Stabilization of the flywheel (254 11111) outside diameter, and will consist of 5 is provided by a magnetic bearing which has been graphite/epoxy rings that have a total thickness of 4 discussed extensively in earlier papers. inches (101,6 11111). It is proposed to interference The axial load of the flywheel ~otor is supported assemble the rings so as to overcome the limited by the static airgap field generated by~!he permanent radial tensile strength of fibre composite materials. magnets. In adctttton, the magnetic bearing stabilizes Ttis technique has-been shown to increase the specific the rotor rac,iically-. TMs is achi-eved by two position energy density by a factor of more than two. A sum- Page 597 mary of the specifications for the flywheel are given down (backup) bearings in the mechanical package. in Table 2. Shown in Figure 3 is a modification of the stack arrangement which includes these mechanical backup Table 2. Specification of 300 Wh Flywheel bearings. Inner Diameter 4 inch (101.6 mm) Outer Diameter 10 inch (254 mm) Thickness 4 inch (101.6 rrm) Configuration Multi-ring MAGNETIC BEARING 1 iron inner ring 5 graphite/epoxy rings Burst Speed 79,000 rpm Maximum Operating Speed 60,000 rpm Weight 18 lb (8.16 kg) ROTOR Usable Energy Density 16 Wh/lb (38 Wh/kg) Burst Energy Density 39 Wh/lb (86 Wh/kg) It will be noted from this table that the working energy density should be 38 Wh/kg and even when the mass of all the ancillary systems are taken into con- sideration the net energy density will compare more than favourably with electro-chemical energy storage which typically has an energy density of 14 Wh/kg. The design of the magnetic bearings for the 300 Wh flywheel is discussed in Ref. 10. To assist in the design of the bearings a computer proyram MAGBER has been developed, Using this program a number of stu- dies have been performed, from which it has been found that the most critical characteristic is the axial Fig. 3. Sectioned view of stack arrangement with load carrying capacity. For the bearings to be able touchdown bearings. to support a mass of 18 lb. (8.6 kg) under a 2g acce- leration it has been determined that the smallest The arrangement for touchdown bearings in a single suitable bearing stator must have a diameter of 4 magnetic bearing supported flywheel is illustrated in inches (101.6 rrm). For this sized bearing MAGBER Fig. 4. shows that the axial stiffness is 3330 lbf/in which indicates an axial sag of 0,011 inch (0.28 mm) under a 2g acceleration load. The findings of these design studies are shown in Table 3, where the principal parameters of the magne- tic bearing are summarized. Table 3, Summary of principal parameters for 4 inch magnetic bearing ~-:.::;::..-.:=::::;:::: ·- ----------~-- ~ ---------- ----~---·------- l ten i~equl re:1e11t Sour\.-.! E.ner,Jy 3J1J ,latt-itour St.urd'.Jt;! Ca.µ~l.Jility Requir~m~nt Total ?ower Gu Uatts Coos11:iµtion Total Eneruy 30 :l;-;i.tt-:loi.1r Jes.lgo Par.1,.1<.!tcr Consu,.1µtiun fly,ilh?!.!l J~SiJn i{~.~ulrei.~nt Statvr ;)izi; J in to 5 iu l:J Fly,,race 1 ui1,1~11s iun Jdn;j~ (1l, . .i: to 127 :),d ,.:c-.tuire11cnt Fig. 4. Sectioned view of single bearing arrangement Suuility Staole 5ystt:,:i urHlcr 2-~ rta.ui,11 with touchdown bearings. LOdU Std.tor uia. 4.0 in (lUl.o :.,.1) Based upon the MAGBER analysis and control system 0.U3S iro (v.JJ'I :,1.1) calculations, an envelope of allowable displacements 2 for the magnetic bearing is defined. Typically, with 1.4!> in (!135.4 :.,}) Si11ul,1tioo ,tl.!s1.1lt the flywheel in the centered position, the control :1agnct .i.3 in (7.o2 rm) Simuhtion ~esult system is capable of maintaining rotor stability for Lengtll up to +0.008 (:;:0,2 rrm) in rotor displacement. The Pole Face O.O(i5 in (l.l>S ,xi) Sir.tulation :tcsul t touchdown bearing configuration shown in Figure 5 is. Thickness ______ normally not in contact with the rotor except when __,_ _ starting the system from rest, If the flywheel move- ment exceeds +0,008 inches, (+0,2 lllll) then these TOUCH DOWN BEARINGS bearings come into operation to limit flywheel excur- sions until the magnetic bearing -re-establishes In order to have the magnetic bearing stack - suspension of the flywheel.- operate as required it-js-necessary to in(:lude touch- Conceptually, the touchdown bearings can be thought of as a pair, of thrust bearings with axial and Page 598 radial clearances designed to allow for the normal to be constantly applied to keep the rotor centered on excursions of the flywheel. The stationary portion of the stator. This is quite unacceptable in space the bearing set is composed of two high pr.ec~s ion ba 11 applications where bias power represents a significant bearings with fittings attached to their outer rings. penalty, The elimination of this penalty requires These fittings are designed to mate with rings that the magnetic circuit and/or the mechanical design attached to the flywheel. The axial separation of the must be modified to ensure that the static field is ball bearing sets, as well as the axial and radial uniformly distributed around the airgap, clearances between the stationary and rotating mem- Work is now proceeding on the development of a bers, defines the range of motion through which the computer program for automating the control system flywheel will move before mechanical contact occurs. design for these magnetic bearings. The approach being taken is to make it interactive so that the ACTIVE BEARING CONTROL SYSTEMS program user plays an integral part in optimizing the final design, As well work is proceeding on the A detailed discussion of the control system design design of the control system for the 4 inch bearings for active radial bearings is given in Ref. 11. to be used in the stack arrangement shown in Fig. 5. Initially considerable difficulty was experienced in This includes a study of methods of stabilizing the magnetically suspending the experimental bearings, In presently lightly damped roll and pitch angular modes. Ref, 12 this was attributed to the limited control In addition methods of damping these modes while using authority of the control windings and was corrected by a single bearing as shown in Fig. 2 are being con- decreasing the size of the permanent magnets. sidered. From an equivalent magnetic circuit for the It was found that the system performance was very bearing actuator it has been possible to show, for sensitive to sensor location due to coupling of the ~ small displacements of the rotor, that the radial two orthogonal directions. In the new design for the force, Fx, along the x-axis can be approximated by the 300 Wh flywheel, the sensors are to be mounted on the relation stator, and the eddy-current sensor currently used are to be replaced by capacitive sensors so as to limit Fx Kxx+Kii the effects of magnetic interference. It will then be possible to mount these devices in close proximity to where xis the displacement of the rotor from the the bearing actuators, which is not possible at pre- equilibrium point and i is the control winding sent, current. A linearized analysis shows that Ki and Kx are related by DYNAMIC PERFORMANCE /2 µ N 0 Dynamic instabilities of high-speed flywheels are 8 B Kx ,often caused 11 by rotor mass unbalance. Mass unbalance 0 is expected to cause pulsation of a magnetically suspended flywheel, which leads to dissipation of the where µ0 411 x 10-7 H/m, N is the number of turns on rotor spin energy due to the damping forces of the the control winding and 80 is the average radial flux suspension. The amount of influence of rotor unba- density in the airgap. For the experimental 3 inch lance on the dynamic response will depend on several bearing it has been determined from MAGBER and experi- parameters such as the radial stiffness of the magne- mentally that Kx = 105 N/mm and Ki = 29 N/amp. tic bearings, magnitude of mass unbalance and damping, It will be observed that the bearing actuator is and the rotational speed of the rotor. open loop unstable with a real axis pole in the right The suspension system of a conventional rotor hand half of the s plane, so a lead compensator has system customarily consists of a rotor mounted on a been used to stabilize the closed loop system, A root shaft, supported by some conventional type of mechani- loci plot for the final design shows that the system cal bearing such as roller or journal bearings. The is stable for loop gains, k, lying in the range UM/GSFC flywheel being developed can be construed as being a non-conventional rotor system in the sense 0.15 < k < 2.72. that it is magnetically suspended and has no shaft or hub. An analysis of system response to the effects of step An analytical investigation is being conducted to and impulse force disturbances on the control system determine the dynamic response of a magnetically were studied. It was seen that the system is well suspended flywheel with mass unbalance. behaved for small disturbances, and that an impulsive Inertia forces and moments, resulting from rotor force of 0.66N sec will just cause the bearing rotor unbalance, will tend to cause the geometrical spin to contact the stator, Also, the static stiffness of axis of the magnetically suspended flywheel to undergo the bearing was calculated to be 437N/mm (2494 translation and rotation with respect to the cen- lb/inch). terline of the magnetic bearings, The experimental 3 inch magnetic bearing and its A computer program is being written to determine control system was constructed and it was then stabi- the dynamic response, viz., the translational and lized so as to maintain a constant airgap. It was rotational displacements of the flywheel rotor when it found that this control system gave good transient and is subjected to mass unbalance. The following are static performance, although at a somewhat lower gain some of the parameters that can be varied in the com- than the· design value. Recent investigations of this puter program, which dictates the dynamic response of discrepancy appear to attribute this to the effects of the rotor: induced eddy currents in the iron magnetic structure which occur under transient conditions. The results • mass unbalance' of this investigation will be discussed in a forth- coming publication. • rotational speed of rotor As part of the investigation of thi:! bearing radfal forces versus lfoari n9 gap it was observed thJ this problem by providing force vs. displace- ment curves for each of the four quadrants. The curves can be obtained with the rotor at the nominal gap posi- tion or with the rotor at some prespecified eccentric displacement. Preliminary analysis has shown that the radial 10 10 RUN NUMBER RUN NUMBER control system will be effective for rotational distur- bances if the translational and rotational frequency 'Fig. 5. Summary of Design Run 4 Page 604 Fig. 6 shows axial stiffness, the most critical AXIAL OISP (mm) - parameter for the design. It is so critical that all 0 00 0 254 0 508 0761 I 015 1269 1523 1777 of the other parameters are of secondary importance. 30 It was observed in earlier simulation runs that a 3 inch (76 mm) diameter system was of insufficient size to support an 18 lb (80 N) wheel with a reasonable fac- 20 tor of safety. A 4 inch (101 mm) stator is the 89 O smallest stator which can satisfactorily support the AXIAL AXIAL FORCE FORCE desired weight. From Fig. 6 the maximum axial force is (lbs) (NJ - 30 lbs (-133 N) and the axial stiffness over small 10 445 displacements is 1667 lbs/in (292 N/rnm). Due to sym- metry the axial force vs. displacement for each of the four separate quadrants with no radial eccentricity is identical and each quadrant supports one-quarter of the -+.~-rl-~~h.~+.~-+~-c-+~~-l-~oo total rotor weight. Fig. 7 shows the axial stiffness 0 00 0 01 0 02 0 03 O 04 0 05 0 06 O 07 under a radial eccentricity of 0.003" (0.076 mm). AXIAL OISP (INCHES)- Quadrant 3 will not support as much weight as quadrant 1. However, the increased weight carrying ability of quadrant 1 tends to cancel the effect of the decreased weight carrying ability of quad rant 3, and the effects Fig. 6. Resultant Axial Stiffness/Radial Bias O are not seen in the resultant plot. Figs. 8-9 are the performance curves for radial stiffness for the 300 Watt-Hour (108 kJ) ~ystem. AXIAL DISP (mm)--+ 000 0254 0508 0761 1015 1269 1523 1777 15 66 7 RADIAL DISP (mm) -----+ TI 0 000 0 051 0 I 02 0 52 0 203 0 254 0.305 40 177 9 I 10 44 5 1 30-l---+---f--+--+-cK'-f----j 133 4 l AXIAL AXIAL FORCE FORCE RADIAL RADIAL {lbs) (N) FORCE FORCE (N) /~v ( lbs) 20+---J----+--+"----J----+-----i 89 0 22 2 ~ 1/ 44 0 00 0 O 00 0 01 O 02 0 03 0 04 0 05 0 06 0 07 --~-+--,-+~ ---+-~-+~-+--r-------1000 ::>•QUAD 3 AXIAL DISP (IN) -----+ '!k•QUA0 2 4 0000 0002 0004 0006 0008 0010 0012 X•QUAD I RADIAL DISP ( INCHES) ---+ Fig. 7. Quadrant Axial Stiffness/ Radial Bias 0.003 in Fig. 8. Resultant Radial Stiffness/ Axial Bias 0 Table 2. Simulation Results (See Nomenclature for units) RADIAL OISP (mm)------+ 0 000 0 051 0 102 0 152 0 203 0 254 0 305 60 266 9 50 222 4 RUN AM DEL KR AVE FAMAX@H RADS/AXF RADIAL FORCE 40 RADIAL 1779 FORCE 1 3500 0 0000 3001 o 26706 112363 (lbs) IN) 1 5000 00090 35320 30 824 114575 1 4500 00100 33520 29 419 113955 ,0 133 4 14500 0 100 32530 29419 110564 o•QUAD 3 *" QUAD2 4 29 454 96 436 X• QUAD I 14500 0 0090 2840 0 20 89 0 0 000 0 002 0004 0 006 0 008 0 010 0 012 RADIAL DISP(•n) FOR ALL RUNS LM: 0 3000 T=O 0650 RI= 2000 PLEAK=1 6~0 BSAT =1 500 H = 0 0650 Fig. 9. Quadrant Radial Stiffness/Axial Bias 0 GZERO = 0 03500 Fig. 8 gives the radial stiffness under no axial bias and Fig. 9 gives the radial stiffness for the four 5 Page 605 quadrants with no axial bias. Note that the contribu- as a stack, is shown in Figure 4. In order to have the tion to radial stiffness by quadrants 2 and 4 remain magnetic bearing stack operate as required it is almost uneffected by the radial motion. Table 2 gives necessary to include back up (touchdown) bearings in the recommended dimensions for the 300 WH (108 kJ) the mechanical package. Shown in Figure 12 is a modi- system based on many iterations simi 1 ar to those per- fication of the stack arrangement which includes mecha- formed above. nical back up bearings. CONTROL SYSTEM The control system for stabilizing the magnetic bearing is shown in Figs. 10 and 11. Basically, an MAGNETIC BEARING -15 Fig. 12. Back up Bearing Arrangement for Stator-Stack Fig. 10. Control System for Laboratory Prototype Based upon the MAGBER analysis and cont ro 1 system calrnlations, an envelope of allowable displacement for r-------, the magnetic bearing is defined. Typically, with the I Mechanical System I flywhe,el in the centered position, the control system I I I is capable of maintaining rotor stability for up to I ±0.008 in (±0.203 mm) of rotor displacement. The back I I up bearing configuration shown in Figure 12 is normally f Fdltl I not in contact with the rotor except when starting the feedback signal '----- _J system from rest. If the flywheel movement exceeds Eddy Current ±0.008 inches (±0.20.3 mm), then the back up bearings '------,-1 Compensation Displacement Network come into operation to limit flywheel excursions until Transducers the magnetic bearing re-establishes suspension of the flywheel. Conceptually, the back up bearings can be Functional Block Diagram thought of as a pair of thrust bearings with axial and radial clearances designed to allow for the normal excursions of the flywheel [±0.008 inches (0.20.3 mm)]. Fig. 11. Functional Block Diagram for Laboratory The stationary portion of the bearing set is composed Prototype of two high precision ball bearings with fittings attached to their outer rings. These fittings are designed to mate with rings attached to the fly~heel. eddy current transducer provides the radial position of The axial separation of the ball bearing sets, as well the flywheel. The transducer signal produces an error as the axial and radial clearances between stationary signal that drives a current thru four electromagnets. and rotating members, define the range of motion The magnetic flux of the electromagnets adds on one through which the flywheel will move before mechanical side and subtracts the permanent magnetic f1 ux on the contact occurs. other side, producing a corrective differential force. Geometric considerations require that the touchdown The control system is a nonlinear bang-bang system and bearing sets should be separated by as large an axial is discussed in detail in reference 20. The governing spacing as possible. This locates the bearings adja- equations of the control system were analyzed using a cent and between the magnetic bearings. In addition, program called CONTRL. This was written specifically the rotating and non-rotating portions of the flywheel for this application to study response and stability. should contact at as large a diameter as possible. By Details are given in reference 20. The system shown in locating the back up bearing sets adjacent to the Figs. 10 and 11 was fabricated, tested and used to sta- magnetic bearings, making the contact diameter 3.005 bilize the magnetic bearing. inches (76.269 mm), and the axial and radial clearance yaps equal to 0.006 inches (0.152 mm), the radial MECHANICAL DESIGN motion of the flywheel at the suspension rings is 0.008 inches (D.203 mm). The results of the MAGBER simulation are shown in The back up mechanical package shown in Figure 12 Table 2, and the mechanical configuration, referred to has been fabricated without the motor/generator and is 6 Page 606 currently undergoing testing, 6. Kirk, J.A., Anand, D,K. and Khan, A.A., "Rotor Stresses in a Magnetically Suspended Flywheel CONCLUSIONS System", Proceedings of the 20th Intersociety Energy Conversion EngTneerfngConference, August Results from the system parametric design, and the 18-23, 1985, Miami Beachg, Florida, pp. control system analysis, show that a 300 WH (108 kJ) 2,454-2.462. energy storage flywheel can be built by incorporating characteristics of a previously built magnetic bearing 7. Anand, D.K., Kirk, J,A. and Frommer, D.A., "Design into a stack arrangement. The major conclusions of Considerations for a Magnetically Suspended this study ar~: Flywheel System", Proceedings of the 20th Intersociety Energy ConversionEng,nemng 1. The system consisting of a stack arrangement Conference, August 18-23, 1985, M1am1 Beach, of two bearings similar to the earlier proto- F1or1da, pp. 2.449-2,453, type is a viable approach in designing a 300 WH (108 kJ) system. 8. Evans, H.E., and Kirk, J,A., "Inertial Ener\jy Storage Magnetically Levitated Ring-Rotor", 2. Some method of reducing permanent magnet unba- Proceedings ~ the 20th Intersoci ety Ener9y lance must be incorporated. Flux reduction Conversion. Engineering Conference, August 18-23, and flux shunting of the permanents are 1985, Miami Beach, Florida. appropriate methods. 9, Studer, Philip A., "Magnetic Bearings for 3, A control ~ystem identical to the prototype Instruments in the Space Environment", NASA system provides sufficient response to exter- TM-78048,1978, nal disturbances if the feedback gain is tuned, Improved response can be obtained if 10, Robinson, A.A., "Magnetic Bearings-The Ultimate a small amount of integral control is incor- Means of Support for Moving Parts in Space", porated. Spacecraft Tech. Dept., ESA Tech, Directorate, ESTEC, Noordwijk, Netherlands. 4. The effects of nonlinearities, particularly those leading to limit ~ycles need further 11. Anand, D.K., Kirk, J.A. and Anjanappa, M., evaluation. "Magnetic Bearing Spindles for Enhancing Tool Path Accuracy", Advanced Manufacturing Processes, Vol, 5, Capacitive, saturation, and hysteresis effects 1, No, 2, April 1986. of the iron should be included in the model but avoided in the operating range of the bearing. 12. Moskowitz, Lester R., Permanent Magnet Design and Application Handbook, Cahners Books International, 6, Back up bearings are conveniently included in Inc,,© 1976, the stack arrangement and are required to maintain flywheel excursions in the operating 13. Braver, J.R., Larkin, L.A., and Overbye, V.D., range of magnetic bearing control systems. "Finite Element Modeling of Permanent May net Devices", Magnetism and Magnetic Materials Conf., ACKNOWLEDGEMENT Pittsburyh PA Nov, 8-11, 1983. The work reported on in this paper has been 14, Colonias, John S., "Calculation of Magnetic Fields sponsored by the National Aeronautics and Space for Engineering Devices", IEEE Trans. Magnetics, Administration, Goddard Space Flight Center, under Vol. MAG-12, No.6, Nov. 1976, pp.1030-1035, grant NAG5-396. 15. Rotors, Herbert C., Electromagnetic Devices, New REFERENCES York, Wiley, © 1941. 1. Kirk, J.A., Studer, Philip A, and Evans, Harold E., 16. Hayt, William H. Jr., En\)ineering Electromagnetics, "Mechanical Capacitor", NASA TN D-8185, 1976. McGraw-Hill, Inc,,© 1981. 2. Kirk, J.A., and Huntington, R.A., "Energy 17. Kraus, John W., Electromagnetics, McGraw-Hill, Storage-An Interference Assembled Multiring Inc., © 1953. Superflywheel ",12th Intersociety Energy Conv. Engin. Conf., Aug. 28th-,Sept, 5, 1977, pp,517-524. 18. Downer, J,R., "Analysis of a Single Axis Magnetic Suspension System", Masters Thesis, MIT, Jan. 1980. 3. Kirk, J.A., "Flywheel Energy Storage-I: Basic Concepts", Int. J, Mech. Sci., Vol. 19,1977, pp. 19. Vieira, Rogerio de Azeucdo, "Analysis of a Magnetic 223-231. Bearing with Two Degrees of Freedom", Masters Thesis, University of Maryland, College Park, 1985, 4. Kirk, J.A., and Studer, P.A., "Flywheel Energy Storage-I I: Magnetically Suspended Superflywhee l", 20, Banyham, M.L., "Simulation and Design of a Flywheel Int, J, Mech. Sci., Vol, 19, 1977, pp. 233-245. Magnetic Bearing", M.S. Thesis, University of Maryland, College Park, 1985, 5, Kirk, J.A., Anand, D.K., Evans, H.E., and Rodriguez, E.G., "Magnetically Suspended Flywheel System Study", Presented at the Integrated Flywheel Tech. 1984 Workshop, NASA Marshal Space Flight Center, Huntsville, Alabama, Feb, 7-9, 1984. 7 Page 607 Page 608 1 9 8 6 N .S F M A N U F A C T U R I N 'G S Y ·S T E M S R E S E A R C H C O N F E R E N C E N O V . 1 8 - 2 1 , 1 9 8 6 T E C H N I C A L S E S S I O N S A N D P R O G R A M N o o n - 1 : 1 5 p . m . 6 . N O N D E S T R U C T I V E M E T H O D F O R Q U A L I T Y C O N T R O L T U E S D A Y , N O V E M B E R 1 8 L U N C H E O N O F G L A S S R E I N F O R C E D P L A S T I C S S . A f s h a r i , M . S q u i l l a n t e , a n d G e r a l d E n t i n e , R a d i a t i o n M o n i - 8 : 0 0 - 9 : 0 0 a . m . 1 : 1 5 - 3 : 0 0 p . m . t o r i n g D e v i c e s R E G I S T R A T I O N S E S S I O N 3 : F O R M I N G I 1 . A N A P P R O A C H T O T E C H N O L O G Y S Y S T E M S F O R I N - D I N N E R O N Y O U R O W N 8 : 3 0 - 9 : 1 5 a . m . P R O C E S S M A T E R I A L S P R O P E R T Y E V A L U A T I O N O P E N I N G S E S S I O N 8 : 0 0 - 1 0 : 0 0 p . m . C . R u u d a n d C . V i k r a m , T h e P e n n s y l v a n i a S t a t e U n i v e r s i t y . 1 . W E L C O M I N G A D D R E S S , D e a n W a y n e C h e n , C o l l e g e o f W O R K S H O P O N M A N U F A C T U R I N G R E S E A R C H N E E D S 2 . 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I N G P R O C E S S E S W E D N E S D A Y , N O V E M B E R 1 9 S E S S I O N 1 : W E L D I N G I H . K u h n a n d J . T i " a s o r r a s , U n i v e r s i t y o f P i t t s b u r g h 1 . M I N O R E L E M E N T E F F E C T S O N G A S T U N G S T E N A R C 8 : 1 5 - 1 0 : 0 0 a . m . 5 . E N G I N E E R I N G R E S E A R C H C E N T E R F O R N E T S H A P E W E L D P E N E T R A T I O N S E S S I O N 5 : M A C H I N E T O O L S , C O N T R O L , S E N S O R S M A N U F A C T U R I N G R . S u n d e l l , H . S o l o m o n , L . H a r r i s , a n d S . C o r r e a , G e n e r a l 1 . A D V A N C E D C O N T R O L A N D S I G N A L P R O C E S S I N G F O R T . A / t a n a n d R . B a i l e y , O h i o S t a t e U n i v e r s i t y E l e c t r i c C o m p a n y . M A N U F A C T U R I N G 2 . C O N S U M A B L E E L E C T R O D E , A R C W E L D I N G S I G N A L 3 : 0 0 - 3 : 2 0 p . m . D . D o r n f i e l d a n d M . T o m i z u k a , U n i v e r s i t y o f C a l i f o r n i a - A N A L Y S I S R E F R E S H M E N T B R E A K B e r k e l e y . G . C o o k , M . R a n d a l l , a n d M . S h e p a r d , V a n d e r b i l t U n i v e r s i t y . 2 . C A D / C A M F O R M U L T I F A C E T D R I L L S 3 : 2 0 - 5 : 3 0 p . m . K . H . F u h a n d S . M . W u , U n i v e r s i t y o f W i s c o n s i n - M a d i s o n . S E S S I O N 4 : C O M P O S I T E S , P L A S T I C S 1 0 : 0 0 - 1 0 : 2 0 a . m . ~ 3 . M A G N E T I C B E A R I N G S P I N D L E C O N T R O L I N M A C H I N I N G 1 . M O D I F Y I N G T H E R E S I S T I V I T Y O F P O L Y M E R I C F I L M S F O R R E F R E S H M E N T B R E A K J . K i r k , D . A n a d , a n d M . A n j a n a p p a , U n i v e r s i t y o f M a r y l a n d . U S E I N E L E C T R O F O R M I N G O F S U R F A C E F E A T U R E S 4 . U N M A N N E D M A C H I N I N G , H I G H S P E E D M I L L I N G 1 0 : 2 0 - N o o n V . L a n d a u , D . D i F r a n c o , a n d J . A n g u s , C a s e W e s t e r n R e - J . T l u s t y ; S . S m i t h , I . H e r n a n d e z , a n d Y . T a r n g , U n i v e r s i t y o f S E S S I O N 2 : W E L D I N G I I s e r v e U n i v e r s i t y . F l o r i d a . 1 . A D A P T I V E W E L D I N G U S I N G I N F R A R E D S E N S I N G T E C H · 2 . M E C H A N I C A L I M P E D A N C E A N A L Y S I S ( M I A ) : A N E W 5 . T H E R M A L S T R E S S A N A L Y S I S O F L A Y E R E D P R E S S U R E N I Q U E S T E C H N I Q U E F O R C U R E M O N I T O R I N G A N D C O N T R O L V E S S E L S T . L i n , K . G r o o m , Y . W a n g , J . G o o d l i n g , a n d 8 . C h i n , A u b u r n O F C O M P O S I T E S T R U C T U R E F A B R I C A T I O N G . B l a n f o r d , D . L e i g h , T . T a u c h e r t , a n d M . T i " a c y ; U n i v e r s i t y o f B . J a n g , H . H s i e h , a n d M . R a o , A u b u r n U n i v e r s i t y . U n i v e r s i t y K e n t u c k y . 2 . I N N O V A T I O N S I N E L E C T R O S L A G W E L D I N G 3 . I N T E G R A T I O N O F C A D / C A M F O R I N J E C T I O N - M O L D E D S . L i u a n d C . S u , T h e P e n n s y l v a n i a S t a t e U n i v e r s i t y . P L A S T I C P A R T S 1 0 : 0 0 - 1 0 : 2 0 a . m . 3 . B A L L F O R M A T I O N P R O C E S S E S I N W I R E B O N D I N G A P · K . W a n g , S . S h e n , C . H i e b e r , R . R i c k e t s o n , V . W a n g , S . R E F R E S H M E N T B R E A K P A R A T U S : S O M E R E C E N T D E V E L O P M E N T S E m e r m a n , a n d C . C o h e n , C o r n e l l U n i v e r s i t y . 1 0 : 2 0 - N O O N / . C o h e n a n d P A y y a s w a m y ; U n i v e r s i t y o f P e n n s y l v a n i a . 4 . P R O C E S S I N G - S T R U C T U R E P R E D I C T I O N S F O R S H O R T S E S S I O N 6 : F O R M I N G I I , M E T A L L U R G Y 4 . D E V E L O P M E N T O F T H R O U G H - T H E - M U L T I P L E - A R C F I B E R C O M P O S I T E S 1 . P R E F O R M D E S I G N I N M E T A L F O R M I N G S E A M T R A C K I N G S Y S T E M C . T u c k e r I l l , T . O s s w a l d , a n d S . A d v a n i , U n i v e r s i t y o f I l l i n o i s - S . K o b a y a s h i , U n i v e r s i t y o f C a l i f o r n i a - B e r k e l e y . U . T s a c h , T . S o c h o r , a n d C . L u , T h e P e n n s y l v a n i a S t a t e U n i - U r b a n a C a m p a g n e . 2 . M O D E L L I N G O F P L A S T I C F L O W I N M I C R O S T R U C T U R E 5 . S O L I D P H A S E P R O C E S S I N G O F T H E R M O P L A S T I C M A T E - v e r s i t y . D E V E L O P M E N T 5 . M I C R O P R O C E S S O R C O N T R O L O F A R C L E N G T H D U R - R I A L S P D a w s o n , C o r n e l l U n i v e r s i t y I N G G A S M E T A L A R C W E L D I N G D . L e e , J . A m o e d o , a n d J . V o g e l , R e n s s e l a i r P o l y t e c h n i c I n - 3 . M E A S U R E M E N T O F T H E I N T E R F A C I A L S T R E S S E S I N E . K a n n a t e y - A s i b u , J r . , U n i v e r s i t y o f M i c h i g a n . s t i t u t e . MAGNETIC BEARING SPINDLE CONTRDL IN MACHINING J. A. KIRK, Professor D. K. ANAND, Professor M. ANJANAPPA, Assistant Professor Department of Mechanical Engineering, University of Maryland, College Park, MD 20742 ABSTRACT. The use of a magnetic bearing spindle can not only successfully provide the benefits of high speed mach1n1ng but, more importantly, minimize tool path errors. In this paper the various sources of tool path error are discussed as functions of machine tool positioning errors and cutting force errors which are characterized as static, dynamic and stochastic. The operation of high speed magnetic bearing spindles is described and a control scheme whereby the spindle may be translated and tilted for minimizing tool path errors is discussed. This overall research activity funded by the National Science Foundation is a cooperative effort between the University of Maryland, Cincinnati Milacron, Magnetic Bearings, Inc., The Westinghouse Corporation, and The National Bureau of Standards. INTRODUCTION. To improve production efficiency of thin and in the cutting process itself. All the errors are r16 components, and to eliminate the secondary further discussed in ref. 20. deburring operation, it is desirable to increase spindle speeds and table feeds {i.e., to move toward MAGNETICALLY CONTROLLED SPINDLES. The magnetic high speed machining) while maintaining part tolerances spindles for use on machine tools are fairly experimen- and surface finish within acceptable limits. In tal at this time. The only spindles currently discussions with Westinghouse, Cincinnati Milacron, available for use on machine tools are developed and Magnetic Bearings Incorporated, and the National Bureau Duilt by Societe Mecanique Magnetique (S2M) of France. of Standards we have concluded that a magnetic bearing In 1984 Magnetic Bearings Inc. (MB!) of Radford, spindle can be retrofitted to existing machine tools Virginia (a division of Kollmorgan) obtained the and, with modification in feed rate, provide a solution patents from S2M and is currently distributing the S2M to the accuracy, deburring and MRR problems in thin rib spindle in the United States. At present there are machining. Experience by Westinghouse has shown that three models of magnetic spindles available for milling the deburring operation can be eliminated if the part purposes. These 3 models cover the speed range between is machined at higher surface speeds (i.e., higher 30,000, and 60,000 rpm with a rated horsepower between spindle speeds) provided that part accuracy is main- 20 and 34 [16,17]. tained. To achieve this goal control of the tool path error via a magnetic bearing spindle is required. Magnetic spindles consist of a spindle shaft sup- ported Dy contactless, active radial and thrust magne- During high speed machining the forces at the tic bearings, as is shown in Figure 3. In operation, interface of the cutting tool and workpiece can cause the spindle shaft is magnetically suspended with no the tool to chatter. When chatter occurs the effect mechanical contact with the spindle housing. Position can not only degrade surface finish and part tolerance sensors placed around the shaft continuously monitor but can also damage the tool. Generally, tool chatter the displacement of shaft in three orthogonal direc- is avoided by controlling. Doth the feed rate and tions. The sensor information is processed by a spindle speeds of the tool and does not appear to be a control unit and any variation in the position of the limiting factor in improving the metal removal rates in shaft are corrected by varying the current level in thin rib machining. This paper addresses the specific electro-magnetic coils, thereby forcing the spindle problem of identifying and controlling tool path error shaft to its original position. The magnetically as it effects dimensional accuracy and surface finish floating spindle shaft can be rotated freely about its in thin rib machining. Specifically, interest is cen- mass center even if the mass center deviates from the tered around high speed end milling operations with geometric axis. Conventional ball bearings (called particular interest on the use of a magnetically touchdown bearings) are also provided on both ends of suspended spindle for controlling the tool path error. the spindle for supporting the shaft when the spindle is stopped and for serving as the touchdown bearings in TOOL PATH ERRORS. Tool path error in two-dimensional case of a power failure. cutting can be represented as shown in Figure 1. The tool path error in computer numerical control machine It is particularly important to note that the tools is defined as the distance-difference between the spindle shaft can be translated up to ±.005 inches and required and actual tool path. In the more general tilled up to o.s· with no effect on the performance of case of 3-dimensional cutting (i.e., end milling), the the spindle system. This unique feature of magneti- tool path error includes the deviation in the z- cally controlled spindles can have significant impact direction in addition to that shown in Figure 1. in correcting tool path errors. Tool path error (in the absence of chatter) can be The unique design of magnetic spindles provides classified into the following four categories, based on significant advantages over conventional spindles with the source (1-20) or the error for each category; regard to tool path error correction. These advantages are: e deterministic position errors o deformation due to heat sources 1. Built-in 3-dimensional force sensors are e deformation due to weight forces available for adaptive control of the cutting ., deformation due to cutting forces. process. These four· error sources can cause three types oJ tool path errors, viz: static deterministic, dynamic deter- 2. Built-in 3-dimensional position sensors are ministic and stochastic. Shown in Figure 2 is a available for adaptive control of cutting pro- listing of the errors which are applicable to end cess. milling, in general, and the machining of thin rib structures in particular. Deterministic position 3. Ability to translate and tilt the spindle errors {both static and dynamic) are defined as those shaft (within air gap restrictions) for tool repeatable errors which will reoccur when an identical path error minimization. ApplicaDle for mini- set of input parameters exist on a given machine tool mizing Doth deterministic compliance error and structure. Stochastic errors, on the other hand, are stochastic errors due to variation in depth of defined as those errors which occur when a random input cut and machine tool dynamics in thin rib is presented to the machine tool. The main sources of machining. stochastic error are due to surface roughness of blank Page 609 4. High rotational speeds with reduction in generate static and dynamic tool path error cutting. forces and improved surface finish maps in end milling operations (i.e., burr free cutting). .. Expert system for deterministic tool path 5. Ability to control the stiffness of the errors spindle which can be particularly beneficial for chatter control. .. develop an expert system for stochastic error correction 6. High material removal rate (MRR) available with increased table feed rates. • develop and implement control algorithms for controlling magnetically suspended spindles to Additional advantages of the magnetic bearing spindle minimize tool path errors include no lubrication requirements and high thermal stability due to the absence of friction. • experimentally test and validate models and algorithms using a CNC vertical machining In the United States two manufacturers have imple- center fitted with a magnetically suspended mented magnetic bearing spindles in machine tools, spindle. Turchan and TMI-Forest, Inc. The inability to deal with different cutting tools made them unsatisfactory The current work is intended to fill a void in the for universal machines while somewhat satisfactory state-of-the-art in end milling machining. In a recent operation was obtained using them on dedicated machi- report [19] MTTF recommended research to "develop data nes. Currently manufacturers of machine tools are con- on cutting forces and deflections and their effect on cerned with the excessive cost and sophisticated accuracy of machined surface in end milling. Include electronics involved in terms of reliability and main- web flexibility. Assume input from the NC program and tenance. However, numerous manufacturers appreciate consider the feasibility of input from cutting force the definite advantages that magnetic bearings have measurement and analysis". The current cooperative over conventional ones and would encourage their use effort will address the task suggested in the MTTF should the technology become feasible. report. Several investigators have used magnetic spindles CONCLUSIONS. The present cooperative research direc- [8,9,10] by retrofitting them on existing machine tion of the authors and engineers from Cincinnati tools. Their primary focus was to use the magnetic Milacron, Magnetic Bearings Inc., Westinghouse and the bearing spindle to improve metal removal rate. In the National Bureau of Standards has been presented. The approach suggested in this paper, the many other advan- long term research work is in its early stages and tages of using magnetically controlled spindles to involves tool path error minimization through the use improve tool path errors can take precedence over the of magnetic bearing spindles. advantage of high metal removal rate. This approach exploits the full capabilities of the magnetic spindles Tool path errors have been characterized as static and will be useful for retrofitting existing machine deterministic, dynamic deterministic and stochastic. tools for tool path error minimization. The source of each of these errors is either in the machine tool itself or in the nature of the cutting ERROR MINIMIZATION. In general, tool path error con- process. Based on the ability of a magnetic bearing sists of machine tool errors and cutting force errors. spindle to both translate and tilt an initial control These errors can be static and dynamic deterministic scheme for the magnetic bearing has been presented. and/or stochastic. The machine tool static and dynamic Furthermore, it is expected that the long term benefits deterministic errors can be quantified using a laser of this cooperative research will be: metrology system and put in the form of an error map for use in software correction. Cutting force errors • Fundamental understanding of the dynamics and are both static deterministic i!Tld stochastic and can be performance of magnetically suspended spindles minimized by utilizing a magnetically controlled in a high speed machining environment. spindle and a control strategy which takes advantage of the spindles ability to tilt and translate, while con- e Generation of a body of fundamental, analyti- tinuing to rotate at high speeds. The current state of cal and experimental knowledge in the high the art of tool path error correction is discussed in speed machining of parts. detail in ref. 20. • The enhancement of accuracy by quantifying and ERROR MINIMIZATION METHODOLOGY. The benefits of using controlling tool path error. a magnetic bearing spindle for error correction in thin rib machining include the inherent advantages of high • Contribution to the basic knowledge of burr- speed machining and the implementation of error correc- free machining of thin ribbed microwave guide- tion methodologies for improving part shape and surface like parts. finish. • Development of a control stratecy for tool The University of Maryland in cooperation with path error minimization in end-milling that is Magnetic Bearings Incorporated, Cincinnati Milacron, machine independent. Westinghouse, and the National Bureau of Standards has undertaken a program to implement an error correction • Potential for increased MRR. methodology in a vertical machining center. The stra- tegy is to utilize an experimentally determined error matrix of a test machine, along with models of cutting ACKNOWLEDGMENT. The research discussed here represents force errors, and to implement a corrective control a cooperative activity started among engineers from the scheme to significantly reduce overall part errors in University of Maryland, the National Bureau of thin rib machining. Standards, The Cincinnati Milacron Corporation, Magnetic Bearings Inc., and the Manufacturing Group A control scheme as shown in Figure 4, is the pro- (Columbis, MD) of Westinghouse Corporation. Input from posed block diagram for control of a magnetic bearing a 11 these sources is greatly appreciated. The Na ti ona 1 spindle. This scheme, although still being refined, Science Foundation has funded this research work will take the overall machine error matrix and cutting through grant NSF 85-16218 and their support is grate- force model data .and adjust the spindle location (both fully acknowledged. translation and tilt) in order to minimize the instan- taneous overall tool path errors. The work currently involves the following tasks: Page 610 REFERENCES 19. "Technology of Machine Tools", Volume 1-5, MTTF Report, October 1980. 1. Anand, D.K., Kirk, J.A., McKindra, C.O., "Matrix Representation and Prediction of Three Dimensional 20. Anand, D.K., Kirk, J.A., Anjanappa, M., "Magnetic Cutting Forces", Transactions of ASME, Vol. 99, Bearing Spindles for Enhancing Tool Path Accuracy", Series B, Nov. 1977, pp. 828-834. Advanced Manufacturing Processes, Vol. 1, No. 1, Apri 1 1986. 2. Gillespie, L.K. "Advances in Deburring", Society of Manufacturing Engineers, Dearborn, Michigan 1978. 3. Hacken, R.J., Nanzetta, P., "Research in Automated Manufacturing at NBS", Manufacturing Engineering, REGUIREC PATH October 1983, p. 68-69. ACTUAi.. PATH 4. Kline, W.A., Devor, R.E., Lindberg, J.R., "The Prediction of Cutting Forces in End Milling with tool path error at 0 Application to Cornering Cuts", Int. Journal of = {x0 -xC: ) = Ex in x-coord. MTDR, Vol. 22, NO, 1, 1982, p. 722. - {y0 -y.; } - E, in y-coord. 5. Kline, W.A., OeVor, R.E., "The Effect of Runout on Cutting Geometry and Forces in End Milling", Int. FIG. 1 TOOL PATH ERROR Journal of MTDR, Vo. 23, No, 2/3, 1983, p. 123-140. 6. Koren, Y., "Cross-Coupled Biaxial Computer Cntrol for Manufacturing Systems", Journal of Dynamic Systems, Measurement and Control, Treans. of ASME, STATIC/ OYNAMlC/ SIBS Research Facility Addresses Problems in Set-ups for Small Batch Manufacturing", Industrial Engineering, June 1984, THERMAL pp. 68-73. DEFORMATION 8. Nimphius, J.J., "A New Machine Tool Specially POSITIONAL Designed for Ultra High Speed Machining of Aluminum Alloys", High Speed Machining, WAM of the ASME, New Orleans, Louisiana, December 9-14, 1984, pp. CUTnNG 321-328. FORCE 9. Raj Aggarwal, T., "Research in Practical Aspects of ~i THEORY ANO OR High Speed Mi 11 i ng of Aluminum", Techni ca 1 Report, METHODOLOGY ~ RESEARCH NEEDS PA"RTIA.LLY Cincinnati Milacron 1984. DEVEi.OPE~ FIG. 2 ENO MILLING ERRORS 10. Schultz, H., "High-Speed Milling of Aluminum Alloys", High Speed Machining, WAM of the ASME, New Orleans, Louisiana, December 9-14, 1984, pp. 241-244. 11. Simpson, J.A., Hocken, R.J., Albus, J. S., "The Flear Ball Seering Automated Manufacturing Research Facility of the (Thtust and .-.111al) National Bureau of Standards", Journal of Manufacturing System, Vol. 1, NO. 1, 1982, p. 17-32. 12. Tlusty, J., "Criteria for Static and Dynamic Stiffness of Structures", Section 8.5, Volume 3, MTTF Report, October 1980. 13. Tlusty, J., Macneil, P., "Dynamics of Cutting Forces in End Milling", Annals of CIRP, Vol. 24, 1975. 14. Truncale, J.F., "Production High Speed Machining in Aerospace", High Speed Machining, WAM of the ASME, New Orleans, Lousiana, December 9-14, 1984, pp. 231-240. 15. Watanabe, T., Iwai, S., "A Control System to Improve the Accuracy of Finished Surface in Milling", Journal of Dynamic Systems, Measurement, and Control, Trans. of ASME, Vol. 105, September 1983, p. 192-199. 16. "Application of Active Magnetic Bearing to Machine FIG. 3 MAGNETIC SPINDLE CONFIGURATION Tool Industry", S2M Literature. (REF.1 7) 17. "Active Magnetic Bearing Spindle Systems for Machine Tools", SKF Technology Services, June 1981. 18. "Measurement of Straightness of Travel" Laser Measurement System, Application note 156-5, Hewlett Packard Literature, 1976. Page 611 Page 612 F I G . 4 E X P E R I M E N T A L S E T U P F O R T O O L P A T H E R R O R M I N I M I Z A T I O N I N E N D M I L L I N G A PRELIMINARY PROGRAM IASTED Second IASTED International Conference APPLIED CONTROL AND IDENTIFICATION December 10-12, 1986 Los Angeles, California, U.S.A. Sponsors International Association of Science and Technology for Development - IASTED . Technical Committee on Control. Locaiion The Century Plaza Hmei , Los Angeles. California, U.S.A. INTERNATIONAL PROGRAM COMMITTEE F. Conrad Denmark L.J. Grujic Yugoslavia G.K.F. Lee U.S.A. S. Dormido Spain M.H . Hamza Canada P. Luh U .S.A. T. Dwyerlll U.SA. G. Jumarie Canada D. Moldovan U.S.A. S. Fadali U .S .A. N. Karim U.S.A. SYMPOSIUM Wednesday, December 10, 1986 8:00 Registration 9:00 Welcome 9: 15 Session 1 - Control I Chairmen: G.K.F. Lee (U.S.A.) and P.B. Luh (U.S.A.) • Adaptive controls for systems with unknown step inputs - H .-G. Y ch (U .S.A .) • Pole placement of separable 2-D systems- M. Shafiee (U.S.A.) • Optimal control for a class of interconnected systems with parameteruncertainty - R. Chai loo , M. E. Sa wan (U.S.A.) Dynamic decoupling based on state feedback- J. Y. Juang (U.S.A.) Sensitivity-constrained controller design for multi-parameter systems - W. Hafez, K. Loparo, M. Hashish , E. Rasrny (U.S.A .) Digital control algorithm with multi rate sampling- J.L. Aravena, X. Wei ping (U.S.A.) Fast tracking for time varying parameters - F. N. Chowdhury, J. L. Aravcna (U.S.A.) Multiobjcctive dynamic programming beyond Eigenvalue assignment-A.F. Sakr, Y.Y. Haimes (U .S A.) Parallel solution of nonlinear unconstrained optimization problems- P .B. Luh. X. Miao (U.S.A.) • Design of discrete-time robust controllers for multi variable systems - G. K. F. Lee , A. Barnani (U.S. A.) 1:30 Session 2- Control II Chairmen: A.S.C. Sinha(U.S .A.)andJ .C.S. Yang(U.S.A.) • Optimal stochastic control of linear systems with multiplicative and additive noise. a survey- H. V. Panossian (U.S.A.) • A recursive criterion for controllability of linear retarded systems - A .S.C. Sinha (U .S .A.) • Moving-horizon, certainty equivalent control of stochastic nonlinear systems - E. Yaz (U.S .A.) • Application of the Karhunen-Loeve expansion to the reduced order control of distributed parameter systems - J.B. Burl (U.S .A .) • Digitalization of existing continuous control systems into multi rate digital control systems - K.S. Rattan (U.S.A.) • Conditionally optimal stochastic control - L. W. Bezanson (U S .A.) • The application of adaptive control theory to man-machine systems - D. W . Repperger (U.S.A.) • An open- loop digital controller for the glucoregulatory system by insulin therapy - S. M. EI-Shal (U.S. A.) • Coordination study for out-of-step protection of a high voltage transmission line - M. Etczadi-Amoli (U.S.A.) Thursday, December 11, 1986 8:30 Session 3 - Control III Chairmen: R.E. Rink (Canada) and F. Conrad (Denmark) Minimum cost control of heat-pump/heat storage system with time-of-day energy price incentive - R. E. Rink, V. Gourishankar, M. Z ahceruddin (Canada) Sate I Ii te tracking station control with application to signal i nte1fcrcnce analysis - D. C. Carpenter ( Canada) A bidirectional servo controlled dynamomctcr system for hydraulic pumps and motors - F. Conrad , E. Trostmann (Denmark) • Computer based level controller- J. Purviance. T. Hcnon, M. Young (U.S.A.) • Robust adaptive control of a large flexible structure - J. Sun , P. Toannou, E. Falangas. H. Woo (U.S.A.) • Independent modal space control of nonuniformly distributed large flexible space structures - C.C. Nguyen. A. Baz, J . V. Fedor (U .S.A.) • Optimal control of a class of tandem queueing systems - B. Pourbabai (U.S. A.) • Implementation of a flexible manufacturing protocol - D. K. Anand, J.A. Kirk, R. Uppal (Canada) An application of control theory for the study of stability of a simple linear economic model - G . V .L. Narasimham (U.S. A.) Automatic train control systems- D.E. Ycntzas (Greece) Page 613 Implementation of a Flexible Manufacturing Protocol J,A, Kirk, Professor D.K. Anand, Professor M. Anjsnappa, Assistant Professor R. Uppal, Research Assistant Department of Mechanical Engineering and The Systems Research Center University of Maryland, College Park, MD 20742 Keywords: IGES, Manufacturing Automation Protocol, FMS, FMC ABSTRACT To adequately meet the wide range of system applica- tions, manufacturing systems have been divided into three This paper is concerned with the development and types as shown in Fig, 1, The three types are Special implementation of a flexible manufacturing protocol for Systems, Flexible Manufacturing Systems (FMS), and the automated machining. Of specific interest is the Flexible Manufacturing Cells (FMC), The degree of produc- machining of prismatic parts in a flexible manufacturing tion flexibility is the major difference between the cell. system types, The flexible manufacturing protocol involves providing SPECIAL SYSTEMS - Of the three systems, special design input via a computer aided design (CAD) environ- systems are the most 'process dedicated' but the least ment, an expert system for establishing manufacturability flexible, Typically, they produce only a few part numbers of the design, an intelligent process planning module for at a relatively high production rate, Special systems optimal component machining, design data base in an IGES incorporate many advantages of transfer line techniques format, automatic generation of machining codes, and with a well balanced degree of flexibility, A special finally, the downloading of machine data to the computer system obtains it's flexibility by the use of numerically numerical control (CNC) machine, where the manufacture of controlled special machine tools. Their mechanical design the designed part occurs. promotes process specialization while numerical control ailows random automatic tool changing, variable spindle The flexibility of work reported in this paper is speeds, and feed rates, and multiple axis movements enhanced by the use of standardization of design data base without manual intervention. This system is capable of and the standardization of machine control codes. By machining any one of the several parts simultaneously, using standardization it will also be shown that commer- However, each of the workpieces is machined in a sequen- cial CAD software can be interfaced directly with the tial order as it moves from station to station along a flexible manufacturing protocol discussed in this paper, fixed path on the material handling system, This paper also addresses the hardware interfacing FLEXIBLE MANUFACTURING SYSTEM - Flexible manufacturing issues inherent in the flexible manufacturing cell, An systems are designed for mid-volume manufacturing of a example of the flexible manufacturing protocol is pre- small number of different parts, Being at the midpoint sented and a machine-generated P.art .is discussed, of production techniques, this system type possesses advantages from both high and low production concepts. In INTRODUCTION an FMS, various types of workpieces are randomly and simultaneously transported between and processed at Automation was first introduced for mass production various machine tools and other workstations, according to due to its positive cost performance effect on investment, individual processing and production requirements, The After most shops were automated by the mid 1960's, it was unique characteristic of FMS relates to its bringing realized that mass production accounted for only 25% of together the following elements: material handling and the total production in the United States [7]. The other computer control to function as integrated automated manu- 75% of production is batch type which imposed difficulties facturing systems and in the system's random processing for automation because of lack of flexibility of the auto- capability with each workpiece, having it's own unique set mation practice, The need to automate batch production, of processing steps which are being carried out in however, was essential to improving productivity and parallel with the processing of other parts, flexible manufacturing was the logical approach, FLEXIBLE MANUFACTURING CELLS - Flexible manufacturing Numerical Controlled (NC) machines were installed at cells are the most flexible of the three types and viewed various factories in the early 1960's to achieve flexibi- as being effective when applied to the production of many lity in automation, These NC machines accepted programmed different workpieces, each being produced at a com- tool paths in the form of punched paper tapes prepared on paratively low production rate, The three types of manu- computers, and hence a different part only needed a new facturing systems do overlap one another in their punched tape. Later versions of these machines, called applications. Direct Numerical Controlled (DNC) machines and Computer Numerically Controlled (CNC) machines, allowed direct part It is helpful to draw a distinction between FMS and programming on the machine controller. as well as FMC, An FMS can be defined [1,4) as a computer controlled downloading of a part program through serial interface, configuration of semi-independent work stations and a Coupled with automatic tool changing mechanisms, Automated material handling system designed to efficiently manufac- Guided Vehicles (AGV), and Robots, these machines for the ture more than one part number at a low to medium volume«, first time allowed complete unmanned, but limited, An FMC (2,4] on the other hand is a group of machines and machining, In the early 1980's several such systems were associated material handling equipment that ls managed by installed to machine parts such as engine blocks, jet a supervisory computer or the cell host. These cells may engine parts, etc, (3), Many of these manufacturing be independent units or may be tied together to a central systems were specially developed by industrial giants, in computer to form an FMS, Fig. 2 shows the conceptual an effort to introduce automation, arrangement of FMS and Fig, 3 shows an FMC. FMC is gaining popularity among small to medium size manufac- Page 614 turers due to its comparatively small initial investment dization must exist throughout the system, specifically and yet be able to upgrade to a full scale FMS at a later this includes the use of IGES for geometric part represen- time. tation, the generation of standard machine tool control \ codes [i.e. M & G codes], and the use of the Feature This paper is concerned with a particular type of FMC Extractor and Expert Systems in a fully automated system, currently under research and development at the University of Maryland, The FMC, shown in Fig. 3, is a flexible The implementation of the protocol requires the deve- milling cell which is primarily intended for the produc- lopment of software packages for purposes of establishing tion of prismatic parts, A similar cell for producing manufacturability, intelligent process planning, cell parts on a turning center is also under development but is control and interfacing, In addition, it is necessary to not discussed in this paper, establish database standardization using NBS procedures. These issues are discussed first and followed by an example using the new protocol. THE FLEXIBLE MANUFACTURING PROTOCOL DATABASE STANDARDIZATION A protocol for automated machining in a cell is con- cerned with a standardized methodology used for automated The usefulness of a protocol depends on how general it production within a cell, This includes all processes is. If it is used for a very specific purpose under very from design to part production including AGV and robot specific conditions then it is of very limited use. In control, In this paper, our concern is primarily with the present work major emphasis was placed on making the automated machining. To simplify the process we have protocol as general as possible, Towards achieving this restricted the development, reported in this paper, to goal, the data base standardization is introduced at two prismatic parts in which machining takes place without positions in this proposed protocol. At the design stage, reorienting the part on the machine tool, Efforts are the IGES format is introduced to store part design infor- underway to implement a more general protocol (including mation so that this protocol will not be limited to its axi-symmetric parts) and these results will be reported in own CAD capabilities, but also be able to accept part the future, design data file created by any commercial IGES compatible CAD system, The second stage at which the standardization Shown in Fig, 4 is a schematic diagram of the is introduced is at the CAM data generation. the output suggested protocol for implementing user-to-part automa- of process planning is compatible with the US standard M & tion, It is assumed that the user in Fig, 4 is a designer G cutting codes as per EIA RS-274D, This standardization who will interact with a CAD system in order to obtain a allows that the proposed protocol is machine independent. suitable design for their requirements, In our current work we have taken the approach that the designer can IGES is a standard being developed at the National design a part by using either a commercial CAD system or Bureau of Standards for the exchange of graphics data, It one that is specifically developed for enhanced graphics establishes information structures to be used for the capability, digital representatlon and ~ommunication of product defi- nition data. It allows the compatible exchange of product Typically the deslgner will sketch a part ·on a com- definition data used by various CAD/CAM systems. The IGES puter terminal in 21/2D with the aid of entities such as version 2.0 specifies a file structure format, a language line, arc, rectangular pocket, circular pocket etc. Once format and the representation of geometric, topological the design is acceptable a design data base which is spe- and non-geometric product definition data. The methodo- cific to each CAD system is generated, The design data logy for representing the product definition data is inde- base is then converted to Inltial Graphics Exchange pendent of the geometric modeling method being used. In Specification (IGES) format through an IGES processor. At IGES, the product is described in terms of geometric this point, as shown in figure 4, the user can instead informatlon and non-geometric information with the non- bring in a design data base created by any commercial CAD geometric information being divided into annotations, system provided it is IGES compatible, definitions and organizations, The geometric category consists of elements such as points, lines, arcs, cubic After the design data base is converted to standard splines and parametric surfaces that model the product, IGES format a feature extracter is used to decompose the The annotation category consists of those elements which part into a library of standard solid primitives. These are used to clarify or enhance the geometry, including primitives include cylinders, pockets and slots, etc, The dimensions, drafting notat.ions and text. The definition part features are then presented to the user and the user category provides the ability to define specific proper- must input part material and tolerance information for ties or characteristics of individual or collections of each of the features, The informatlon, along with the data entities, The structure category identifies the IGES geometrical representation of the part, is sufficient grouping of elements from geometric, annotations or pro- to completely represent the part for subsequent pro- perty data which are to be evaluated and manipulated as cessing. single items. The next step is to evaluate the part and tolerance M & G Codes are the standard for cutting codes for all data in order to determlne if production is compatible numerically controlled machines and are specified in EIA with the cells available to the user, Once the part has RS-274D, The G codes are known as the preparatory func- been evaluated as belng compatible with an existing cell tions and they define the actual machining moves and the part is then checked for manufacturability, Thls cutter tool movement such as point to point positioning, includes a check for tolerances, geo~etrical machinability linear interpolation, (CW/CCW), axls selection, thread and fixture constraints, cutting, cutter compensation etc, The M codes are known as miscellaneous function control codes such as the Next the design data base is converted to M & G program stop, spindle ON/OFF, coolant ON/OFF, cutting codes (as per EIA RS 274 D) which are the U.S. clamp/unclamp, tool change etc. In both the standard M standard for cutting codes for NC/CNC machines. These codes and the G codes there are some codes which are codes are then downloaded to the CNC machine through a unassigned and left for the user to assign them for any serial RS 232 port and the manufacturing of the part takes special function not listed in the standard M & G codes, place as per the specification of the designer. For auto- mation, parallel data for cell control is also downloaded. In addition to the standard M & G codes, F function This includes specific instructions for fixture placement, which defines the feed rate in the x, y, z axes, T func- tion which defines the tool and S function which defines It is clear that for the Flexible Manufacturing the surface speed of cutter have been used in this soft- Protocol to operate efficiently a high degree of standar- ware. Page 615 MANUFACTURABILITY fined patterns which may exist within this linked list. The faces corresponding to the recognized feature will The manufacturability module consists of a 3-D feature then be removed from the data base and set aside. extractor and a knowledge base on manufacturability. The Proceeding on a surface by surface basis, the above steps feature extractor 1is discussed in depth under the section will be recursively applied until there are no more sur- of process planning. The manufacturability tests will be faces left. Before finalizing the feature extractor, an conducted by applying knowledge base on each feature of iterative procedure will be carried out to ensure that the the output of feature extractor, This includes testing selected primitive features are the optimum ones. for manufacturability of sharp corners, tolerance, surface finish, interference between tool holders and workpiece, Once all the features have been identified, the expert and materials encountered while drilling a hole, etc, If system for process planning will outline a sequence of any of the above tests fail to qualify, then the manufac- processes that need to be carried out to manufacture the turability module will generate a message outlining the part, A translator can then be used to generate the reason for failure. The user will have to change the necessary NC tool path which can be downloaded to the design of the part iteratively until the design passes the automated machining center, manufacturability tests. When the process plan has been completed the IGES PROCESS PLANNING database is reduced to a single CAM database, as indicated in Fig. 4, In essence the CAM database consists of a Process planning can be defined as the process of reordering of the part geometry information, with tool determining the methods and the sequence of machining a size requirements and tool change pause information workpiece to produce a finished part or component to included in the CAM file, design specifications. Process planning typically con- sists of the following activities - At this stage the CAM file is processed to prepare • Selection of processes and tools standard machine tool driver codes, known as Mand G • Sequencing the processes codes, Then Mand G codes are then further post-processed • Identification of all non machining elements and to prepare a data file of machine specific Mand G codes. estimating the non machining times. • Selection of workpiece holding devices PART MACHINING • Determination of proper cutting conditions and cutting times to machine the workpiece to spe- In the post-processed form the part data is now ready cified dimensions to be loaded directly to the machine tool. Prior to doing this step it is advantageous to perform a software A good process planner must have a detailed graphics simulation of the cell action, The emulation understanding of the different manufacturing processes and will check for fixture interrupts, code accuracy, and pro- select the order of processing based upon a given perfor- vide an estimate of the actual mach.ining time. If any mance index, In the current protocol there are two errors are observed in the cell behavior then the user can parallel paths which can be followed in producing the pro- make corrections as may be ~,equired. cess plan, On the left side of figure 4 the user must supply specific information, in the form of machinery Finally the data is downloaded to the cell and the data, as to how the part will be produced. The path on part is processed as follows: th~ right side of figure 4 is an intelligent process planner using expert system techniques. 1, The AGV delivers the raw material to the cell 2, The robot loads the raw material to the machine The ordered process planning uses a well established tool, approach and is not discussed, The unique feature of the 3. The cutters are loaded in the correct magazine present protocol is the intelligent process planner based slots on the machine tool upon an "expert system approach", 4. The machining codes are downloaded to the machlne tool and machining occurs An expert system is defined as a computer system that 5, The robot moves the completed part from the "emulates human expertise by applying the techniques of machine tool to the AGV. inference to a knowledge base" [SJ, Most importantly the 6. The AGV leaves the cell boundary system must be designed such that it can be easily updated or enhanced periodically. Although most expert systems CELL CONTROL are constructed for use in a particular domain, there are domain independent expert systems called "shells" [ 6). The software package dealing with cell control has the They have empty data bases and knowledge bases and so may following objectives: be used for a variety of applications. Such an approach is used here, • Transport the raw material into the cell via the AGV. The intelligent process planning consists of a 3-D feature extractor which uses the given data on part e Transfer the material from the AGV to the intelli- geometry to decompose the workpiece into a set of primi- gent fixture on the machining center. tive geometric features. The output from the feature extractor becomes the input to an expert system which o Use the robot and unload the finished part from outlines the required machining processes. The knowledge the machining center to the AGV. base for this expert system will include manufacturability information regarding each machinable primitive geometric • Transfer the finished part out of the cell via the feature and it will generate a set of processes for AGV, machining these primitive features on an automated machining center. To accomplish these goals the software package produces interwoven control codes which mesh with the Mand G coded To carry out the above steps, one would start with a CAM database, The cell command codes are sin,gle entity part drawing file (prepared by the designer by using a CAD instruction codes which are used to initiate an activity. package) represented in the standard IGES format. The Once the activity is completed a cell signal is sent to feature extractor would read this file and create a linked the cell host computer and cell operation continues. list of faces, edges and vortices which will represent the Typically the CAM database is loaded to the machining complete topology of the part. The 3-D features will center in the cell and then activity on the machining then be recognized by applying rules that test for prede- center is placed on hold until the raw material is in Page 616 ..... proper position. At this time machining starts and will ci. continue uninterrupted until the intelligent part fixture .. 0 must relocate to avoid a cutter intercept condition. When (.) this condition is predicted the machining center pauses 1 and the intelligent part fixture relocates the manner in which it holds the part, Machining then reinitiates and continues until a new fixture intercept is predicted, at which point the fixture movement occurs again, When machining is complete the part is removed from the fix- c,j II.'" ~ ture, placed on the AGV and the AGV is commanded to exit :liu t,;..; the cell, Once the cell boundary has been crossed, the "' cell is then free to initiate its next task. :.:.; "a:' AN EXAMPLE .w. :,; :, 0 z The part shown in Fig. 5 was generated using the ... a: PC-based UOM CAD software. The output of the CAD system : which is IGES compatible, becomes the input to the ordered process planner which generates the standard Mand G codes as shown in Fig. 5. It is further postprocessed to obtain machine specific code, The part was manufactured by downloading the code from the PC to a machine controller ~ N .J on the CNC machine. 3Nll HHSNWlH a: 0 As an alternate approach the above part was also manu- ::;; factured by downloading an IGES compatible design data § a ~ rl w file to PC, created from ANVIL-4000 residing on VAX 11/750 ,; UJQV.ON lUVd U3d NOll:JOOOUd Computer. CONCLUSIONS r--;:::::::::::::::::::.: := = = J A flexible manufacturing protocol has been suggested for user-to-part automation. The protocol has been enhanced by data and machine control code standardization z 0 and Al techniques in the process planner. An example z v,i: v,O illustrating the use of the protocol establishes its ~.: "W'"N u" o u--' viability as a flexible test bed, o':! a:" a:o "-w ~~ 0 ACKNOWLEDGMENT - This work was partly supported by NSF Grant CDR-85-00108 through The System Research Center. -RE-FE-RE-N-CE-S r :::;i I h I l. Anand, D,K., Kirk, J,A., Anjanappa, M,, Pecht, M,G., t f I "Supercomputers and Hierarchial Control: A Systems 8 I 8 I Viewpoint", Proceedings, NSF Conference on L._. __ ::::!J Supercomputers in Mechanical Systems Research, Lawrence Livermore National Laboratory, California, 1984. :le .w... 2. Anand, D,K,, Kirk, J.A., Anjanappa, M,, "Research in fl) the Flexible Manufacturing Laboratory", The Systems >-fl) Research Center, University of Maryland, College Park, Cl 1986, SRC-TR-86-61. ,--·------, z 0:: 3, "Computers in Manufacturing", By the Editors of j I :::> l- American Machinist, McGraw-Hill Publications, New . I o York, April 1983. J I E <( l IE u. :::> 4, Cutkowsky, M,, Fussel, P., "Precision Flexible I z Machining Cells within Flexible Manufacturing I I < ~ Systems", Carnegie Mellon University, Technical L _______ _l Report, CMU-RI-TR-83-2, 1983. UI ..I Ill 5. "Expert Systems 1986-Volume 1: USA & Canada", OVUM x Limited, London, 1986. w ..I LI. 6, Rychener, M,D., "Expert Systems for Engineering i::' --il Design", Expert Systems, Volume l, No. 1, pp, 30-44, h. :,:: . 1985. .i:.: ' ."...' I ;;:21 ;.;;,; h 7, Sata, T,, "Technology of the Unmanned Operations of :e .. j )OqOij i: FMS", Computers in Industry, Volume!:._, No, 2, pp. s Ii;: 127-137, 1983. ~ s. L. I Ja)Ui>J 6u1u1~>~1 I - - ::J Page 617 , ___ j _________ c C_•_H_ B o_und ary 5 ALL DIMENSIONS ARE IN INCHES TURNING CENTER '-1 3 ROBOT I 2 > M ACHINING CENTER I .C., ------- ---------·~~~---- C .!! 0 ;; ~o---+---+2---+3---+Y---s•---16f----,,r----s1----19 0. i: Raw Mat•rlal In E E 0 0 FIG. 5 TYPICAL PART USER FIG. 3 FLEXIBLE MANUFACTURING CELL M g, B CODES U II llC Ill NOOl TOI O • 125 M06 ;DEFINES TOOL Dil't NU02 S 100 FX 8 FY 8 FZ 8 ; SURFAl.E Sf'EED AND FEED NUO"":: GUO X 1 • 5 Y 1. 5 ;r.;I\F'JD MOVE fR0t1 OHl(iN TO I.DC N004 GOl Z .01 ; LOltlEH lOOL • 01 INf:H IN10 THE W/F' t.1005 GO:' X :'.5 Y 1.5 1--1 J 0 ; MOVE FRON I_ DC-· I ro l oc- CoMM•rolal u. o. "· Nf•06 G02 X ~. • 5 Y 2.5 I n J-l ; HOVE FROM LDC - 10 LDC CAD Bol'tw.a..,.. CAD &or twa:re N007 GO:: X :'.5 Y 3.5 1 J {_I ;MOVE FHOM LOE> - 10 I.UC- 4 tJI.H)H G02 X 1. 5 Y 2. 5 0 ,} 1 ;HOVE FROM LOC- 4 TO LOC- N009 Got z 0.5 ;RAISE TOOL .5 lt.JCH ABOVE W/P NOJO GOO X 2 V 2 tAF'ID HOVE W/0 CUTl ING NOil GOI - .01 ,.,, LOWER THE TOOL .01 INCH IN10 11/E W/P NOt~ G02 X 2 y 2.5 I 0 J-_ 5 ;MrJVE FROM LOC- 6 TO LDC- 7 N013 G02 X 2.5 y .3 I-.5 J 0 ;MOVE FROM LOC- 7 TO LDC- 8 N014 G02 X 3 V 2,5 I 0 J .5 ;MOVE FHUM LDC- 8 TO LDC- 9 N015 G02 2.5 V 2 I .5 J 0 ;MOVE FROM LOC- 9 ro LDC- 1(1 N016 GOI 0.5 ;RAISE Tool .5 ltJCH ABOVE W/P N017 GOO X t.75 y 1.75 ;RAPID MOVE W/0 CUTTING C Jt L L NOlB 801 - .01 ;LOWER THE TOOL .01 lNCH JNTO THE W/P Dat.a D••• N019 801 X 1.75 Y 3.25 ;MOVE tROM LDC- II TO LDC- 12 N020 G01 3.25 y 3.25 JMOVE FROM LDC- I:.' TO LDC- J;'. N021 GOI 3.25 y L75 ;MOVE FROM LOC- 13 TO LDC- 14 N022 GOI 1. 75 y l.75 ;HOVE FROM LDC- 14 TO LDC- 15 N0.23 GOI o.s ;rat:a. To C.11 C1t1.J... AOOUS'a,011 BCnhanoeM4tnt: PA RT FIG. 4 FLEXIBLE MANUFACTURING PROTOCOL Page 618 ADVANCED MANUFACTURING PROCESSES, 1(2), 245-268 (1986) MAGNETIC BEARING SPINDLES FOR ENHANCING TOOL PATH ACCURACY D.K. Anand, Professor J. A. Kirk, Associate Professor M. Anjanappa, Westinghouse Research Fellow Department of Mechanical Engineering University of Maryl and College Park, MD 20742 ABSTRACT Thin rib machining of electronic components or airframe structures can benefit from high speed ma chining for burr free cutting, improved surface quality and increased metal removal rate. It is suggested that the use of a magnetic bearing spindle can not only successfully provide the benefits of high speed machining but, more importantly, minimize tool path errors. In this paper the various sources of tool path error are discussed as functions of machine tool positioning errors and cutting force errors which are characterized as static, dynamic and stochastic. The operation of high speed magnetic bearing spindles is described and a control scheme whereby the spindle may be translated and tilted for minimizing tool path errors is discussed. This overall research activity is a cooperative effort between the University of Maryland, Cincinnati Milacron, Magnetic Bearings, Inc., The Westinghouse Corporation, and The National Bureau of Standards. INTRODUCTION One area of ma chining which can benefit from improvements in accuracy and higher spindle speeds is the production of thin rib electronic components or airframe structures. Shown in Figure 1 is a typical aluminum microwave guide vJhich is used in mobile radar applications. The path shape is composed of repeating 245 Copyright© 1986 by Marcel Dekker, Inc. 0884-2588/86/0102-0245$3.50/0 Page 619 246 ANAND AND KIRK sections of extremely tllin ribs v.iith "X" shaped openings which go completely through the part base. The economical production of thin ribs has proven troublesome because of the difficulty of controlling part tolerances and surface finish while maintaining high metal removal rates (MRR). A particularly troublesome area has been caused by burrs on the "X" shaped openings. These burrs require the finished piece to undergo a secondary deburring operation resulting in increased production time and costs. Studies have shown that the cost for cleaning and deburring can be quite high and is often unaccounted for in process planning for part production [2]. To improve production efficiency of thin rib components, and to eliminate the secondary deburring operation, it is desirable to increase spindle speeds and table feeds (i.e., to raove toward high speed machining) while maintaining part tolerances and surface finish within acceptable limits. In discussions with Westinghouse, Cincinnati Milacron, Magnetic Bearings Incorporated, and the National Bureau of Standards we have concluded that a magnetic bearing spindle can be retrofitted to existing machine tools and, with modification in feed rate, provide a solution to the accuracy, deburring and MRR problems in thin rib machining. Experience by Hestinghouse has shown that the deburring operation can be eliminated if the part is machined at higher surface speeds (i.e., higher spindle speeds) provided that part accuracy is maintained. To achieve this goal control of the tool path error via a magnetic bearing spindle is required. During high speed machining the forces at the interface of the cutting tool and workpiece can cause the tool to chatter. When chatter occurs the effect can not only degrade surface finish and part tolerance but can also damage tile tool. Generally, tool chatter is avoided by controlling both the feed rate and spindle speeds of the tool and does not appear to be a limiting factor in improving the metal removal rates in thin rib machining. Page 620 ENHANCING TOOL PATH ACCURACY 247 ---h--~~ 0 0 10 >l) N -; 0 -.c~· "' ~~ .i.. ~ 0 ---L-- 0 0 -+i "0 ' 0 - 0 0 N Cl) 0 -----~ ci w CD _l I m () :::, z 0 I I <(- s::. a <(~ .e l{) -------- "- 0 m w -0 ZCI) a: oz CD 0 +i ... . 0 0 -0 ~ "' "' f- -() Cl) 0 l l wZ -Cl)w 2: >,. -m 0 C..D. ....J :::, -....J - -----(-\J < - ----- - ~ 0 X a: 0... . ~ :E ------- -. S2 LL Page 621 248 ANAND AND KIRK In the absence of chatter, dimensional accuracy and the surface finish of the machined part control metal removal rate and, thus, production efficiency. 80th effects can be considered as the result of tool path errors. The tool path error in computer numerical control machine tools is defined as the distance-difference between the required and actual tool path. The magnitude of too 1 pa th error is both de termini s tic and stochastic in nature since it depends on both repeatable static and dynamic errors and randomly varying dynamic parameters. This paper addresses the specific problem of identifying and controlling tool path error as it effects dimensional accuracy and surface finish in thin rib machining. Specifically, interest is centered around higl1 speed end milling operations with particular interest on the use of a magnetically suspended spindle for controlling the tool path error. TOOL PATH ERRORS Tool path error in two-dimensional cutting can be represented as shown in Figure 2. In the more general case of 3-dimensi ona 1 cutting (i.e., end milling), the tool path error includes the deviation in the z-direction in addition to that sho1vn in Figure 2. Tool path error (in the absence of chatter) can be classified into the following four categories, based on the source or the error for each category; ~ deterministic position errors • defori.1ation due to heat sources II') deformation due to weight forces ~ deformation due to cutting forces. These four error sources can cause three types of tool path errors, viz: static deterministic, dynamic deterministic and stochastic. Shown in Figure 3 is a listing of the errors which are applicable to end milling, in general, and the machining of thin rib structures in particular. Deterministic position errors (both static and dynamic) are defined as those repeatable errors Page 622 ENHANCING TOOL PATH ACCURACY 249 y ,,,__ __ REGUIREO ACTUAL PATH tool path error at O - (x 0 -x~ ) = 2x in x-coord. = (y O -y ~ ) = 2y in y-coord. (z) X FIG. 2 TOOL PATH ERROR ,1hicl1 v1ill reoccur 11hen an identical set ,)f input paranet,~rs exist on a Jiv.~n ,.iachi11e tool struct·Jr•=· Stochastic errors, on t'1e other hand, ,ff,:! defined ,:i.·:; t!1ose ,~rrors v1l1i ch occur wi1en a r:i.nJoq input is pr<:!s,~nted to tlie mc\1ine t-)ol. The ma i '1 source ,)f stochastic error ,1ill occur ·in the cutting process itself. 1\11 the errors ctre furti1er di·;c,tssed br~low. Oeter1ninistic Position Errors Static det•-=r1ninistic position errors are reproducible mc'lin-= dr~penclent ;)OS i ti oni ng erro1·s dh·i ct1 sho11 U\J as tf1e difference !JeNe,~n tl1e d!):;olut,~ position t)1at tr1e r;i.:i.chine is co1,1n1an:1ed t-J (]': to (e.g. 4.0000 inche'.,) an•i ,1her2 it actuil.lly arrives at (e.g. 4.0002 inches), in the absence of cutting chips. Oynamic det2rninistic position errors are reproducible ~achine dependent ,~rrors ,1hict1 si1ov1 up as the (1ifference in pati1 i)et1i12t:n ,1her2 a 1nacl1i,1e is co1;irna1ded t,) go (ie., ,nab~ 1 90 de9ree t,1rn) and where it actually trctnsverses. Thes,~ errors ·t1ill deriend 011 table feed rate l)ut :10t on tirne. One tee fin i que for t,1e r,iec\ ;,1re:1ent of deter1ni ni sti c position errors involve usi·1g cl. l1iJt1 precision laser 111ec1surement system (such as Page 623 250 ANAND AND KIRK STATIC/ DYNAMIC/ STOCHASTIC DETERMINISTIC DETERMINISTIC WEIGHT DEFORMATION THERMAL DEFORMATION POSITIONAL CUTTING FORCE ~ THEORY AND OR METHODOLOGY ~ RESEARCH NEEDS PARTIALLY DEVELOPED 3 END MILLING ERRORS the H::,,,lett-Packar,j 1dser m2vology systern) dnd calibrctting t:1e individual .nac'.·1i,1e t:Jol. In using t:1is technique t'.1e rnachine tool t1\Jl,~ is treat,.:d as .c, rigid body 'vith 6 degr,jes of freedrm. The 1~rrors of tile rigi<1 tJody (in translation and rotation) as the t:i.ble :ioves along ti1e tfiree coordinat,: directions is then experi11ent.:1.lly deter1:iine1j, As an example of applying this techni,1ue :locken and tlanzetta of the rlational Bureau of Standards reports on its successful implementation on a precision coordinate nea·:;,1ring systein [3], il.nd lat,:r on a 111ac'.1ining center [7,11]. Once tl1e ,~rror rnea::;:ire:nents for a cii v,:n rnac'·1i ne tool are obtained they must 'Je used to correct the ,nachine tool move·~2nt. Baser\ Page 624 ENHANCING TOOL PATH ACCURACY 251 upon discussions with Ci nci nna ti i•li l acron and other ,,iachi ne tool man,.1fd.cturers no rnc\1ine tool •nanuf:1cturer at present incorporates provisions for position error correction to be included in their controll,2r. Deformation Due To Heat Sources Heat source errors are reproducii)le thermal ·ieformation errors due to r1e.1 t sources ,~h·i ch are both internal l'Hl ext2rna l to the r~a chi n e tool • Thesr~ 2rrors show u::, as position differences in s1Ji,1dle/tahle ,)osition a·; a fJnction of t2mperatt1re 1.nd time. In typiol applications t'le 1:ia,chine tool structure i; t:10rouiJhly 1,Jar,,1eti ,,1p and tile spi<1dl,~ itself is t 11e ina.jor source of tr1is Heat sour,.:e 1Jrrors cc111 l)e quantified by ,1ss.~ssi,1g tf1c: :iossible ::,)nst1nt and v:iria,)le :1eat sources of a mac'1ine tool an,! ex,wr·irnenta.lly det,~r,11i,1i1g t\1e effect ,if their ther,,ial cycles on At pr,2sent ,10 rnJnui·1ation of Clltting ,fl imperf2ct :Jl,rnk shape, ancl t;1,~ i1fluenc,:; of nac'1ine dyria.rnics on t;1c> c,H.ti<1lJ pr0ces·;. Dept:1 of cut 1 '.rr0rs cc1.n br~ :n1ie.:rst,)O,j by cJnsij':'ring the c.1·;,, of ,::nd ,Ji11in!J ,\·; ;1;11 i ,1 Fi gu r2 5. T',e imperf2ct ;>Lrnk si1ap2 consi·,ts of :1 non1i,1c1l iept'1 of ~llt ·,1hi:h has superpos,~·i on it rand(Wl v,1ridti 1Jn<, h tiik'<.n,::·;s (x,), The nonbal dept:1 of cut Jiv,2s rise t,) s1:2a.dy st,1t,~ r,,1ttin') fJr,:;r2s .1\li,:11 act on t'le toolh1or:q1i,;ce struct,we to c,1:.1se :1efori:iasi,Jns. These dr~f)r1n.1t.ions c,u1 be consi:Jer2d so.tic ,Jet,:r1ni:1istic a.n.J 11d.y f.le :)rcdicted lJy '\)plying chip cutting 11ec:1d,1ics [1]. T1e r.rn,io!l variations in rough mac'lined blank thi,:kness giv'c.: rise t•J svichastic vctria.tions in cuttiilg forces 11h·ich, i1 turn, ']ive rise to stJchastic v,:1riations i'l part shap~ or, alternativ<:ly, ca.us,: stochastic tool pat~ error. Page 628 ENHANCING TOOL PATH ACCURACY 255 The t.Jol pat'l err,Jrs Jue to v,:i.riati:)ns i1 depth of cut ,1re t.en,1ed "copyi:1g error's" and occ1ir as follo·,1s. The r.rndo1.1 11:,1,1' error (x) is 'co1,Ji,:!d 1 on to the rnc'1ine<1 surface~ (as x ) to r1 Cl 1 red1JC 0 '.:1 sc,-i.le. Tile 'rate of copyiilg' of for111 err0r can be 1ffi tten as i = x/x , 11/herc: i ;aries frorn Cl t,J 1. The resultant cutting 0 f.Jrce Fat the inst:rnt ,Jf generating a fi11i,l1ed surface ,iith a ·,trai 3ht t,J(Jt,1 cutt·~r can be ,ir·itten as, F = r ( 1' a Xa proportionality constant <>tlled cutti!lg stiffness and dept:1 of cut in the 1iir2ction normal to finis:1e(l s:irface. T11e c:Jtting force F acti11g i11 any plane .iill prodiJc·~ ,1 ,ieflection of t!1e t:)ol·-,rnr(z~liec,~ systern. Let < ~le t,12 ,:o::)1Jone:1t .Jf t:ie dr:!F"lection nor:,1al to the finisl1e:i s:1rf1ce "1rrict1 affects t:1e 1i i :n1,· n s i ,J 11 • Tne c.Jtting force i11 ter1,1s of tr1e 1ieflection is, F=kx (2) ct ,,:--ier~ k = stiffness :)etv1e•2n ool ,rnii ,icwr-;;iece called r1<',c'1i11,2 a stiffness. Fro1,1 e:i:wtions (1) and C2); ( 3) The d,~flection x at. iny i·1st1nt ca11 also be ,ff·i t.ten a.:; X = s-x ( i) a x - actual 1epth of cut. a Subs ti t11ting e,1uati )n (3) "i:-1 equation (4), Page 629 256 ANAND AND KIRK F::ir an incre1i1entdl case, equation (5) b,=cones /\X = hs [µ/(l+µ)] ()) 1~her2 /\s = increr:-ientdl req,li reel deµth of cut and !1x incre1.1ental deflection normal to finishe,1 surface. From Figure 4, /\s = x0 and /\x x1• Thus xl/xo = i µ/(1+)1} In 11¥JSt ;,1ac1i ni ng oper::iti ons p « 1 so tint _ ;1, and the copyi :19 error rJoes not ;:wopa9a te betvH:1:n :)iiSS•=S. End nilling does not follo,1 t'1e nor,nal bei1avior and a tJpical val,H! of µ for end milling is about 2.67 for cutti'1g stael [12], 1·Jhic\1 gives a. va.lu2 of i = 0,73. Therefore for ev<2:ry cons2c11tive µass, the error only reduces by '.l fa.ctor ,Jf ilbout L4. The cutc.,~r teetl1 are i,elical in practice ,Hid tnerefore ina.ke the relationships more corapli:ated [12.13]. t~o met!1od of correcting the stochastic errors is currently available but, through the use of a magnetic bearing spfodle, it will be possfole to translate tf1e rntting tool to ninimize tiles,~ errors. are c,irrently under stwiy and ,Jill be reported ;n, 'l. hter time. :1AGHETICALLY cminou.rn SP IiJDLES The rmg1e tic spi ridles for us,~ on mchi n::: t,)ol s 3.r2 f,1i rly experi11enta.l at this ti::1e. The only spindl(~S currently aHilable for use on ,Hc!ifoe tools are develo;Jed and built :1y Societ,~ '\ecanique :1agrH,tiqut:> (S2ii) of France. In U84 ia,pe tic Gearings Inc. (MBI) of ~adford, Virginia (a division of Koll~or~1n) obtai '1ed tr1e patents fro1,1 SZM and is rnrrently di stri buti ng ti1e S2'.l spindle in the United States. At 1iresent there ar2 chree models of 1nagrietic spiwjl,:,s available for 1.1illing p1Jrposes. These 3 nodels cover the s;)eed range betvJeen 30,000, and 60,000 rpm l'Jitr1 a rated horsepOl'Jer 0et\Je,~n 20 a.nd 34 [16,17]. Page 630 ENHANCING TOOL PATH ACCURACY 257 i1agnetic spindles consist ')fa spindle shaft supported by contactless, active radial and tfirust :nagnetic bearings, :i.s is shmm i11 Figure 6. In operation, the spindle s!1aft is r~ag·1eticc1lly suspended ·,1it'.1 no riechanical contact with the spindle I • ,lOll SI ng. Position sc~nsors pl aced ,1round the shaft continuously monitor ti1e displacernent of shaft in three orthogonal directions. The s,~nsor infor1na ti :)n is processi~d by a control unit :i.nd anJ variation in the position of ti1e shaft are corrected by varying ti1e c,1rre11t level in elec:tro-rnag·1etic coils, thereby forcing the spindle shaft to its original position. The tilagnetic,;1,lly floatin0 spi 1 dle shaft can be rotat1~11 freely about its :~ass center even if ti1e mass center deviates from tl1e geornet,··ic axis. Conventional ')a 11 bearings (called touchdo-.vn be11ri ngs) are al so provided on both ends of tt1e spindle for supporting ti1e shaft when t:1e S\Ji11dl!2 is stopped and f:)r servi 19 as the t·)uchdovm bearings in case of a po·,ier fa. i lure. It is particularly irnpol"tant to note that the spindle shaft can be translated up to ±.005 inches and tilled up to 0,5° with no !)ffect on tiie performance of the spindle systern. This uni ,we feat:ire of ,nagnetically controlh~d spindles can hav2 siJnificant i 1npact in correcting tJol pa th en·ors. Tl1e uni.~ue design of :nag:ietic spindles provijes significant ddvanta0es over conve:1tional spindl 0,~s vlith regarJ to to 1)l !)ath error correction. These advantages are: l. Built-i,1 ]-dimensional force sc~nsors ar2 a1ailable for adrtpti ve control of the cutting process. 2. Bui 1 t-in 3-cti;;12nsional position s<~nsors are available for d.iiapti ve. control of cutting process. 3. Ability to tl"anslat(~ and tilt the spi11dle shaft (\~ithin air gap restrictions) for tool path error ,nini,niz,ition. .11,pplical)le for minimizing i)oth deterministic cor~pliance error and stochastic errors due to vari a. ti on i 1 dept 11 of cut and machine tool dync1mics in thin ri,) nachining. 4. High rotational speeds .'/ith reduction in cutting forces and improved surface finish (i.e., burr free c:ttting). Page 631 258 ANAND AND KIRK Rear Ball Bearing (Thrust and Axial) Magnetic Thrust Bearing Rear Axial Bearing Rear Axial Magnetic Rotor Motor Stator \ Front Ball Bearing (Axial) Tapered (Thrust and Axial) Sensor Front Axial Bearing Sensor Front Tapered Magnetic Bearing Front Axial Magnetic Bearing - FIG. 6 MAGNETIC SPINDLE CONFIGURATION {REF.1 7) Page 632 ENHANCING TOOL PATH ACCURACY 259 :i. Ability to control the stiffness of the spi11dhi ;J~l"ich cctn be particularly beneficial for cilatter control. 6 . Hi g h mat•:: r i al removal r :1 t•= (i mR ) av a i l ab 1 e ,vi t r1 i q c re as r~ d Additional :idvantages of the 1-;i,;1.g1etic l)e,1ring spindle inclu:le no lubrication require1;ients ilnd hi]h t 11erlilal st1i)ility duet,) r.:1e absence of friction. ln tile United States tvrn nan:.tfacturcrs hav-2 ·i;npl,2:~t2nt(~r1 nagn= tic bearing spindles in mach i n-e t,)o ls, Turciian an,i TIU-Forest, Irie. Tr1e inability to deal ,vith different c,1tting tools :na(1,:: t:1en unsatisfactory for universal mac~ines ~hile some,11:1.3.t :;;i.tisf,3,ctory operation ~1as obtained using ti1er:i on faclicc1ted r:iac'1ines. Curr2ntly rnan-.,1fact1Jrers of ,nachinc: t0ols 3-re conc(~rned ,,Ji th t'1e excessi V?. cost 1nd sophi sti ca t,::d •':'lectroni cs involv2d in terms of reliability anct mai1tenance. nunet·ous ma11,.1f,3.cturers appreciate the definite advantages t 11at ;1agnetic be,1rings hav,:: over conventional ones and vwuld encourdge their use should the technology become feasible. Several investi']ators :1ave used magnetic spindles [8,9,10] r2trofitting ti1e11 on existing irucr1ine tools. Their primary focus ,ns t,J ,1se the mgrietic bearing spindle to improve ,netdl 1~21,10v.1l rat,:'!. In t\1.:: approach suggested in this paper, tile 1.any otr1er at1Vil.:ltrlges of •Jsing 1:iag12t-ically control12d spindles to i1:i;.iruve tool path err0rs can take prec2dence over the advanuge of l1iJt1 11et.1l r'=11oval rat,~. This approach exploits the foll capabilities of the r~agnetic spindles and will be useful f::lr retrofitting exi:;ting nachine tools for tool path error ,,1inimization. '::RROR. 1\IlH:iIV\TION In general, tool path er-ror- consists of mac'1in,:: tool c~rrors an,1 c,1tti rig force error-s. These errors can be static and dynamic deterministic and/or st0chastic. The machine tool st,ttic anrJ dynamic deterministic errors can be quantified using a laser rnetr;Jlogy system and put i11 the form of an error map for use i:1 software correction. Cutting force errors are botl1 static Page 633 260 ANAND AND KIRK deterministic a.nd stochastic and cdn be minimized by utilizing a magnetically controlled spindle and a control strcttegy which takes ,irlvantage of trie spindles ability to tilt and trctnsl.1te, ,'/h'ile continuing t<) rotd1::i:~ at high spee,is. In this section the ciJrrcnt stctte of the art of tool pat~ error correction is discussed. Hocken, et al. [3] ha·,.~ sho1•rn that .,_ l-iser meVology syst,~n [13] can be used to ev1luat~ static positioning errors ctnd de1:nn-:;trau~ their repeat.ability. Use of ti1e las0.r i nvol ·12s instrunenting a 1w1c 11ine tonl ,,ith optical r~le,-nents atuched to the s;1i1clle ,and ta.ble as is sho·,1r1 'in Figun~ 7. '.Jith proper optical ele,;1ents th·e l1ser position 11ea:,.1re:~ent system is adaptable to 11ea;tre all st1tic and dyrninic errors .~h·ich occ,Jr ,·litf10ut ,v1y c,Jtt i ng t1k i rig pl ,ice. One,= the errors hav:=.! been det,=rr,1i netj it is possii)le to gen~r,it,'..) (~rror ,naps (i.e., error 111atri><) in ,1hi•:h ti1e trc1e p,)sition beco@~::; t:1e input to the map and tr,e out;rnt (i.e., looke1i up v1lue) is the :;ictchine controller coordinat~s ;1hi::h Error 1nap correction can l)1; i:,1ple·,1(,nt.~,i i:1 eitner t:1e inrt progra:n software or in t~ie r:iac:,i,L tool ,:ontrolL~r itself. At ;wesent neither iinple;;ientation exists c 01,1rne r .: i a 11 y • \/hen t:1e 1:t:J.ct1ine L>ol is cutting chips the laser lilet:""ology syste:1 i:; not ,:t,hptcJ.ble to iil!~as:ire the ad(htional tool patl1 errors cau s,~d by c~t tti ng forces. Current work has concentr1tet1 on ,ninimizing t'1e chip c,1tting error 'uy ,:!ither impr,Jving 11ac'1ine t:iol :; true t,ire dynctini cs or co11pensa ting the error tfirougil software correction at ti1e p,1rt prograrnrniag st,1ge. One ,:ir:thod 1)f ir:1provi:1g tile det.~rmini :;tic tool pat\1 error fo cor1,1en ti ona l speed cldci1 i ni ng has been di sc11ssed by Koren [6] ·,1\10 sho1,2:i that, cross-coupled bi,Hhl control :)et;,ier~n mchine t'JOl .1xes is ;JreF,~rable instei-l.d ,"Jf individual-axis control ot G:i,-: rriachines. In conventional machines each axis has a separate close,j loop control, so that tr1e control bop of one axis received no infor1na:ion re:iarJing the other. However, any load distiJrbance error in one of tile axes is corrected only by its O\'l!l loop, vJhile the ot:1er loop experiences no change resulting ill path error or Page 634 ENHANCING TOOL PATH ACCURACY 261 Interferometer Reflector/Mount ~ FIG. 7 LASER POSITION MEASUR MENT cont,Jur ,2rror. Hence, l(oren has found ti1at ::ross-coupli ng the dXis ,,ill improv,~ t:ie accuracy of t:1e t:Jol path in contrJ:Jr cutting. The dra.1,back of this approach is tr1e reduced velocity response ,,hich might rnab~ it difficult for l1igh speecj ri.:i.chining applications. This approach, however, has no i~pact on stochastic tool path error. Kline, et al [4] developed a mecl1anistic ;nodel f:Jr ti1e predic- tion of feed rate on the force systein characteristics in end nilling. The rndel \,as developed :Jase:i on the ex;;erirnentally obtained average force data. for a given cutter geometry and 1'/0r,(- piece :;iaterial. The co::1puter model gives the force distribution Page 635 262 ANAND AND KIRK as a function of axial depth of cut and rotation of cutter. The program developed for end milling gives as output, such characteristics as, force profiles as a function of rotation, force center profiles, force distribution along the axis of cutter, cutter deflection profiles, etc. The model is verified on cornering cuts in end milling as shown in Fig. 8. During cornering the radi a 1 depth of cut varies and hence the cutting force. The model has been reported to be successful in predicting the forces during cornering to within 5-20% of the actual cutting force. The mechanistic model is therefore useful in programming the feed rate variation required during cornering to limit the cutting force within a threshold value. However, this method does not account for workpiece deflection under cutting forces, on for dynamic deterministic position errors. In addition this algorithm is not designed to account for stochastic variation in blank thickness. Kline, et al [5] later did work on the effect of runout of cutters held in set screw type tool holders in end milling. It was shown that cutter runout in end milling leads to changes in the amplitude and frequency of cutting force. A mathematical model was developed to include this effect into the previously developed mechanistic model [4]. Successful experimentation of the above model has been carried out for 7075 Aluminum. Watanabe and Iwai [15] have reported successful application of adaptive control to increase the accuracy of finished surface in conventional end milling. The deflection of the spindle nose is used to compute the cutting force and tool deflection at the tool-vwrkpiece interface, The tool position normal to the cutting surface is shifted to compensate for the tool deflection. The cutting force is also used to alter the feed rate to maintain the error within limits in the direction parallel to the depth of cut. The feed rate contro1 is achieved by the interpolation program of the machine control 1er. The motion normal to the cutting surface is, however, obtained by servo-programs since they need less compilation compared to interpolation programs. However, this Page 636 ENHANCING TOOL PATH ACCURACY 263 Workpiece -- -,", "IP-- .... / '\. Cutter \ I feed ) ., I Roughing Cutter -..----+-1I Radius Initial l Radial - 1--Depth 1 I Cutter l I Fx I I Feed FIG.8 CORNERING CUTS IN END MILLING (REF. 4 ) method is not designed to account for vmrkpiece deflection, stochastic variation in blank thickness and thermal deformation. In the ,~ork done at General Dynamics-Convair Division [14] a technique ca 11 ed 'Net Machining' is used to minimize the ramp error in thin rib machining. Using this technique, multiple cutting passes are made on each side of a free standing rib with each pass a 1 terna ting the side of the rib on which deeper amounts of material are removed. This technique is reported to have successfully reduced the ramp error due to deflection of thin ribs but v,ith the penalty of greatly increased part machining time. The review of the 1 i tera ture suggests that a systems approach to quantification and control of tool path errors will yield extremely beneficial results. For the most part it appears that Page 637 264 ANAND AND KIRK although the positioning errors of a machine tool can be measured with a laser metrology system, the minimization of these errors in an actual machine tool has not been carried out in practice, ERROR MINIMIZATION METHODOLOGY The benefits of using a magnetic bearing spindle for error correction in thin rib machining include the inherent advantages of high speed machining and the imlementation of error correction methodologies for improving part shape and surface finish. The University of Maryland in cooperation with Magnetic Bearings Incorporated, Cincinnati Milacron, Hestinghouse, and the National Bureau of Standards has undertaken a program to implement an error correction methodology in a vertical machining center. The strategy is to utilize an experimentally determined error matrix of a test machine, along with models of cutting force errors, and to implement a corrective control scheme to significantly reduce overall part errors in thin rib machining. A control scheme as shown in Figure 9, is the proposed block diagram for control of a magnetic bearing spindle. This scheme, although still being refined, will take the overall machine error matrix and cutting force model data and adjust the spindle location (both translation and tilt) in order to minimize the instantaneous overall tool path errors. The work currently involves the following tasks: (l(I generate static and dynamic tool path error maps in end milling operations • develop an expert system for stochastic error correction ~ develop and implement control algorithms for controlling magnetically suspended spindles to minimize tool path errors $ experimentally test and validate models and algorithms using a CNC vertical machining center fitted with a magnetically suspended spindle. The current work is intended to fill a void in the state-of-the-art in end milling machining. In a recent report Page 638 Page 639 ~ D I A i : . t _ - : : : . . . - : : : . _ - _ - - : _ - _ - _ - _ - _ - M A G N E T I C ~ i : : : : : : : : : : : : j 1. . . - - - - - I C O N V E R T E R ~ : = = = : : : : : : : : : : : : : : - - - ~ M I C R O P R O C E S S O R I B A S E D C O N T R O L I S Y S T E M P R O C E S S A I D C O N T R O L L E R C O N V E R T : : - : : : : . : : : _ - _ ~ _ : - - _ u 1 . 6 . X . 6 . Y A I D C O N V E R T f : = : ; : t i t : : P O M P A R A T O D A T A S T O R A G E S Y S T E M T A B L E 9 266 ANAND AND KIRK [19] MTTF recommended research to "develop data on cutting forces and deflections and their effect on accuracy of machined surface in end milling. Include web flexibility, Assume input from the tlC program and consider the feasibility of input from cutting force measurement and analysis". The current cooperative effort will address the task suggested in the MTTF report. CONCLUSIONS The present cooperative research direction of the authors and engineers from Cincinnati Milacron, Magnetic Bearings Inc., Westinghouse and the National Bureau of Standards has been presented. The long term research work is in its early stages and involves tool path error minimization through the use of magnetic bearing spindles. Tool path errors have been characterized as static deterministic, dynamic deterministic and stochastic. The source of each of these errors is either in the machine tool itself or in the nature of the cutting process. Based on the ability of a magnetic bearing spindle to both translate and tilt an initial control scl1eme for the magnetic bearing has been presented. Furthermore, it is expected that the long term benefits of tt1is cooperative research will be: Fun<1amental understanding of tl1e dynamics and performance of magnetically suspended spindles in a high speed machining environment. Generation of a body of fundamental, analytical and experi men ta 1 kn owl edge in the high speed rnachining of parts. The enhancement of accuracy by quantifying and controlling tool path error. Contribution to the basic knowledge of burr-free machining of thin ribbed microwave guide-like parts. ~ Development of a control stratecy for tool path error mini mi za tion in end-milling that is machine independent. ~ Potential for increased MRR. Page 640 ENHANCING TOOL PATH ACCURACY 267 ACKNO\:JLE0Gt1ENT The research discussed here represents a cooperative activity started among engineers from the University of Maryland, the National Bureau of Standards, The Cincinnati Milacron Corporation, Magnetic Bearings Inc., and the Manufacturing Group (Columbis, MD) of vJestinghouse Corporation. Input from all these sources is greatly appreciated, Special thanks to Ken Bone (Cincinnati Milacron), Henry McFadden (MBI), Arne Rasmussen (Westinghouse) and John Simpson (NBS) in discussing the technical ideas presented in tl1i s paper. REFERENCES 1. Anand, D.K., Kirk, J.A., McKindra, C.D., "Matrix Representation and Prediction of Three Dimensional Cutting Forces", Trans,icti ons of ASME, Vol. 99, Series B, Nov. 1977, pp. 828-334. 2. Gillespie, L.K. "Advances in Deburring", Society of Manufacturing Engineers, Dearborn, Michigan 1978. 3. Hocken, R.J., Nanzetta, P., "Research in Autoroated Manufacturing at trns", Manufacturing Engineering, October 1983, p. 68-69. 4. Kline, vJ.A., OeVor, R.E., Lindberg, J.R., "The Prediction of Cutting Forces in End Mi 11 i ng 1~i th Application to Cornering Cuts", Int. ,Journal of MTOR, Vol. 22, NO. 1, 1982, p. 722. 5. Kline, \LA., DeVor, R.E., "The Effect of Runout on Cutting Geometry and Forces in End Milling", Int. Journal of MTDR, Vo. 23, No. 2/3, 1983, p. 123-140. 6. Koren, Y., "Cross-Coupled Biaxial Computer Cntrol for Manufacturing Systems", Journal of Dynamic Systems, Measurement and Control, Treans. of ASflE, Dec. 80, Vol. 102, pp. 265-272. 7. Nanzetta, P.. "Update: NBS Research Facility Addresses Problems in Set-ups for Small Batch Manufacturing", Industrial Engineering, June 1984, pp. 68-73. 8. Nimphius, J.J., "A New Machine Tool Specially Designed for Ultra High Speed Machining of Aluminum Alloys", High Speed r,1achining. 11AM of the ASME, New Orleans, Louisiana, December 9-14, 1984, pp. 321-328. Page 641 268 ANAND AND KIRK 9. Raj Aggarwal, T., "Research in Practical Aspects of High Speed Mi 11 i ng of Aluminum", Techni ca 1 Report, Ci nci nna ti Mi 1 acron 1984. 10. Schultz, H., "High-Speed Milling of Aluminum Alloys", High Speed Machining, WAM of the ASME, New Orleans, Louisiana, December 9-14, 1984, pp. 241-244. 11. Simpson, J.A., Hocken, R.J., Albus, J.S., "The Automated Manufacturing Research Facility of the National Bureau of Standards", Journal of Manufacturing System, Vol. 1, NO. 1, 1982, p. 17-32. 12. Tlusty, J., "Criteria for Static and Dynamic Stiffness of Structures", Section 8.5, Volume 3, MTTF Report, October 1980. 13, Tlusty, J., Macneil, P., "Dynamics of Cutting Forces in End Milling", Annals of CIRP, Vol. 24, 1975. 14. Truncale, J,F., "Production High Speed l·1achining in Aerospace", High Speed Machining, IJA1,1 of the ASME, New Orleans, Lousiana, December 9-14, 1984, pp. 231-240. 15. \~atanabe, T., Iwai, S., "A Control System to Improve the Accuracy of Finished Surface in :v!illing", Journal of Dynamic Systems, t1easurement, and Control, Trans. of ASME, Vol. 105, September 1983, p. 192-199. 16. "Application of Active Magnetic Bearing to Machine Tool Industry", S2r1 Literature. 17. "Active f1agnetic Bearing Spindle Systems for Machine Tools", SKF Technology Services, June 1981. 18. "f1easurement of Straightness of Travel" Laser Measurement System, Application note 156-5, Hewlett Packard Literature, 1976. 19. "Technology of Machine Tools", Volume 1-5, MTTF Report, October 1980. Page 642 VALIDATION OF A RELATIONSHIP BETWEEN CUTTING FORCE AND SURFACE FINISH FOR OPTIMAL CONTROL OF END MILLING J. A. Kirk, Professor M. Anjanappa, Assistant Professor D. K. Anand, Professor Department of f,lechanical Engineering and The Systems Research Center llniversi ty of Maryland College Park, f,ID 20742 ABSTRACT it is the most practical and reliable parameter which follows the dynamics of cutting process faithfully and An understanding of the relationship between this parameter is readily available in a magnetic cutting force and surface texture is essential for bearing spindle. designing an optimal controller for enhanced accuracy of the machining processes. This paper deals with Villa et al [1] discusses the building of a model establishing the relationship between the two parame- relating surface texture to machining parameters. The ters, at higher frequencies, after the removal of the surface texture is considered to have predominantly fundamental tooth passing frequency components. geometric-kinematic components and that the stochasti- Experiments were conducted by machining thin rib com- city due to process dynamics is negligible. ponents on a low horsepower computer numerically controlled milling machine. A specially designed high Kline et al [2] have developed a model to accura- frequency force dynamometer was used to record cutting tely predict surface error based on their mechanistic force data, and surface texture of the machined surface cutting force model. The model assumes negligible was measured using a Talysurf-4 profilometer. The effect of dynamics on the surface texture generated. analysis of the cutting force and surface texture Several other investigators [3-7] have addressed this showed a reasonable correlation between the two parame- problem with the assumption that the effect of tool ters. The results are used to obtain a parameter dynamics, blank imperfections and workpiece dynamics on matrix suitable for use in digital optimal controller. surface texture generated is negligible. Hence these methods cannot be applied if the dynamics are signifi- I NTRODUCT l ON cant. Thin rib components, such as complex wave guides In machining thin rib components it is shown in [8] and microwave array plates, are machined from a solid that the stochastic components, due to the dynamics, block of material. Figure 1 shows a microwave array may not negligible and should be incorporated in plate used in mobile radar equipment. Typically, modeling and optimal control design. Rakhit et al [9] complex wave guides and array plates have many free- in their model included the effect of dynamics and standing thin ribs, require tight tolerance, have odd showed that the relationship between the probablistic contours, needs almost 95% of material removal from bar cutting force fluctuation and surface roughness along stock and must be burr-free to avoid microwave atte- the lay is linear for turning. nuation. High production rates, with such stringent machining requirements, can only be achieved if an In this investigation, the cutting force and accurate controller is available to maintain required resulting surface texture are considered to be made-up tolerance. Explicit knowledge of the relationship bet- of two components, one component consists of a deter- ween cutting force and surface finish can be very use- ministic part due to geometric and kinematic factors ful in designing such a controller. and the second component is a stochastic part attribu- table to dynamics. This paper focuses on the latter It should however be mentioned that, if the goal is high frequency components of cutting force and surface to control surface finish, then there are other texture in developing a relationship between the two machining parameters, such as feedrate, cutting speed, parameters. and tool geometry, which can be used to predict surface finish. However, for the purpose of this work cutting THEORETICAL CUTTING FORCE force is chosen as the only parameter to predict the surface finish. This choice is based on the fact that The theoretical cutting force in end milling con- Page 643 sists of both steady state and transient state effects, cutting force (i.e. vector sum of x and y forces) over with the transient state occurring when the cutter is four revolutions of cutter obtained for down milling of either entering or leaving the workpiece. The theore- a thin rib at a feedrate of 1 ipm (25.4 mm per minute) tical cutting force equations for end milling opera- and setting the remaining cutting parameters as listed tions are presented by Tlusty et al [10]. In a similar in Table 1. The cutting force increases from O lb to manner consider the case of a thin rib machining under 5.2 lb during zone A and remain constant at 5.2 lb in steady state conditions using an helical tooth end zone Band then drops to O lb in zone C. The cutting milling cutter. The length of cutting edge that is force is zero for the remaining part of one half rota- actually engaged in cutting varies and can be tion of the cutter, until the second flute engages in classified into three zones, as shown in Fig. 2. The cutting. The resultant cutting force profile for sub- length of cutting edge varies from zero to maximum in sequent teeth are identical. zone A, remains at the maximum value in zone Band tapers back down to zero in zone C. The cutting force TABLE 1 THIN RIB MACHINING PARAMETERS at various points along the length of the cutting edge also varies. The radial and tangential forces at any point on the cutting edge is, 1. Axial depth of cut 'da' 0.15 in. (3.81mm) 2. Radial depth of cut 'd ' 0.02 in. (.508mm) ( l) 3. Diameter of cutter 'dcr 3/16 in. (4.7625mm) 4. Tool material High Speed Steel 5. Number of flutes 'z' 2 (2) 6. Helix angle's' 300(Right Hand) 7. Spindle speed 'N' 5600 rpm where da is the axial depth of cut, ft is the feed per 8. Nominal feed rate 'f' 1.0 ipm (25.4mm) tooth, q, is the corresponding angular position and k is 9. Feed per tooth 'ft' 0.00009 ipt (.0023 the specific force whose magnitude depends on the work mm) piece material, tool geometry and average chip 10. Work piece material AL 6061 T6 thickness. 11. Type of machining Down milling 12. Coolant used None The theoretical cutting force in the x and y direc- tion, acting at the center of the tool, can be written as (see [10, 11] for more details), EXPERIMENTAL CUTTING FORCE F (sin\, - 0.15sin2a + 0.3a} in zone A u A simple thin rib machining experiment was designed - - F)sin 2 q, + 0.3¢ 22 2 - 0.15sin q,2) in zone B for a low horsepower three axis CNC vertical milling machine and the experimental setup is shown in Fig. 4. - - Fu[sin 2 ¢2 sin 2 (a-6) + 0.15sin 2 ¢2 A force dynamometer, capable of following high fre- ( a-6)-0.15sin 2 q,2 + 0.3( q,2-a+o}] in zone C quency cutting force signal, was designed and built. The Kistler 9067 quartz transducer was chosen as the (3) force sensor due to its unique features of high rigi- dity along with high sensitivity. Figure 5 shows a Fy F ( a-0.5sin 2 a - 0.3sin 2 a) in zone A cross sectional view of the dynamorneter. The natural u frequency of the force dynarnometer in the x, y and z Fu 2 2 ( ct, . - 0.5sin ¢ - O. 3s in q, in zone B axis was found to be equal to 6500 Hz, 6800 Hz, 13,500 2 2 2 Hz respectively. Fu [ 1 = -- tanh ab (4) of the above types of actuators have been discussed by many ab authors [3]-(5]. More recently, numerical and analytical techniques where A= 4ab is the core cross-sectional area. From Ampere's cir- (6]-[8] have been developed for the study of transient eddy cur- cuital law, the surface magnetizing force H, can be shown to be rents. Ni H =-1 II. THE TOTAL Flux (5) IN THE MAGNETIC CIRCUIT AND ITS TRANSFER s £.ff(x) FUNCTION where f,,11(x) is the effective length of the magnetic circuit. Con- Consider the simple electromagnetic actuator shown in Fig. 1. sequently, we finally obtain the flux in the magnetic core as It will be assumed that it is constructed from a solid core of linear ferromagnetic material having width 2a and height 2b, where tanh ab 1(s) = Cf'(x)N ~ [ i4 aµb2) 1+s ~ I·' 2a ·I :j X ~ \_ Armature mass :: M + (14 aµb2) + . . .J 1.,(s ). (7) Fig. 1. View of magnetic actuator. 9+s -- 1r2 a >> b. The winding about the core is excited by a current source. For transient disturbances the time response due to the first term The usual assumption, when considering eddy currents in con- in the infinite sum dominates the effect of all the higher order terms ductors, of neglecting the displacement current is made. so that we can approximate (7) by Since a >> b the actuator can be approximately analyzed using the semi-infinite plate shown in Fig. 2. Following Stoll (3, p. 10] it can be shown that the magnetic intensity H2 satisfies the diffusion 1(s) = Cf'(x)N ;8z [ (14 aµb2) equation 1 +s -- a2H, aH, 1r2 a?"= 1 (x, i1) = is a function of the air gap x, and f(i)(t) is a convolutional oper- function model of the effects of eddy currents on the transient per- ation on the current i. It will be noted from (9) that if the current formance of magnetic actuators. The method is currently being i1(t) = i0 , a constant, then extended to represent the higher order effects of eddy currents for lim f (i1)(t) = i (11) actuators which cannot be represented by semi-infinite plates. It ,-~ 0 has been found that lumped-parameter transformer models can and if Ji(t)J is small then I f(i)(t)J will also be small for all t. be used for this purpose. Considering small perturbations of the armature position and coil current about an operating point (x0 , i0 ), (10) can be written in REFERENCES functional form as [1] D. Anand et al., "Design considerations for magnetically sus- + io + Ai1)(t) = 1(Xo .:ix, 0 Lii<)N f(i0 1 Conversion Engineering Conf. (Aug. 18-23, 1985), pp. 2.449- Recalling the assumption that the armature position is changing 2.453. slowly compared with the response time of the eddy currents, and [2] C. Dawson and H. R. Bolton, "Design of a class of wide~angle expanding (12) using Taylor's theorem we obtain limited-rotation rotary actuators," Proc. Inst. Elec. Eng., vol. 126, no. 4, pp. 345-350, Apr. 1979. . . (x + .:ix, 1 + A1 )(t) = -(xo) N' l 1 Jaiix(t) [3] R. L. Stoll, The Analysis of Eddy Currents. Oxford, England: 1 0 0 1 0 0 L 0x Clarendon Press, 1974. + [(x0)N] f(Ai1)(t) (15) Proc. Inst. Elec. Eng., vol. 112, no. 8, pp. 1589-1594, Aug. 1965. [9] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series hence the perturbation force Af(Ax, Ai1)A is and Products. Orlando, FL: Academic Press, 1980. Af(AX, Ai1) = KxAX(t) + K;f(Ai1)(t) (16) [10] J. Meisel, Principles of Electromechanical-Energy Conversion. where New York, NY: McGraw-Hill, 1966. and On the Resolution and Contrast of K1 = 2I collector's capacitance, Cc, is the effective thermal 'i1 1 I I I I I capacitance of the fluid. i /Tc (1,0 .....,J ' ,...... I Assumption CS: The thermal coupling between the plate and the ~ fluid is infinite, so that the plate and fluid can be coalesced i~ I I into a single medium, 11. I I I Assumption C6: Under no-flow conditions, there is no heat diffusion in the x • direction along the collector (transport pipe) tubes. (a) without interface region model. 2.2. Model of the Interface Regjon Between Two Components. T In order to use an analytical solution for each component when r 11 simulating the solar collector loop shown in Fig. 1, it is necessary to , I l '-Tc: (a,O : examine what happens at the interfaces between the various • I I I components in the loop (e.g., between collectors and pipes) under 'T I I u I I flow and no flow conditions: • I I r I I I I m I I FJow condjtjons fpump js op}. Clearly, under flow I I X9I I conditions the fluid exiting from the downstream component enters the upstream component and thus establishes the same fluid .x., AXu1 temperature across the boundary. That is, at the boundary x = X 8 , (b) with interface region model. the following condition holds Fig. 3 Predicted ot simulated spatial temperature profile under no flow condition. At I;= Tl -1: TfI( 11 ·1, t) = Tm( 11 ·l, t); where x+ 8 and x· 8denote the points infinitesimally upstream and x [ clT fI( Tl • l, t)/clx ] = [ clT m( Tl -1, t)/clx ] downstream from 8 , respectively. For example, consider the interface between the cold pipe and the inlet of the collector located at where T fl• Tr u, and T fD denotes the temperature in the interface x = L1. Under flow, the fluid temperature at the collector inlet region, the upstream component, and the downstream component, Tc(L1,t) = TP1(L1,t), the fluid temperature at the outlet of the cold respectively; I; and 11 are normalized distances with respect to the pipe, Pt· total interface region length, LlX1 = AX0 + AXu, namely: (jj) Stagnant condjtjops fpump js o[O Under stagnant conditions (i.e. when the pump is ofO a temperature difference I; = ( X • Xa ) / ( AXo + liXu ) ' (3) develops between the adjacent components of the solar collection loop because the dynamics of these components differ in their thenna.l time 11 = AXu I ( AXo + AXu ) constants and solar absorbance as shown in Fig. 3a. This figure shows a typical fluid temperature profile predicted by the component Remark: 1. The third order polynomial of equation (2) was selected models of equation (A.6) at some time t. The temperatures profiles to model the interface region instead of the solution of the diffusion Tp l (x,t), Tc(x,t), and Tp z(x,t). are the cold pipe, collector, and hot equation of equation proposed by (6) because: (a) it gives the pipe temperatures, respectively computed using equation (A.6). The temperature profile rather than a differential equation which needs to temperature gradient across the collector and pipes reflect the be solved; (b) it can be looked upon as an approximate solution of the temperature profile at the instant the pump was shut off, i.e. the initial diffusion equation since it has the form of the solution given by the condition for equation (A.6). Note that since the spatial temperature separation of variables; and (c) attempts to use diffusions equations to profile across the boundaries between the components has not been simulate temperature profiles which are not monotonic over the modeled, discontinuities occur at the boundaries x and x ."Since interface region (as shown in Fig. 3) were not successfull. 81 82 in actual systems the transition across the boundary is smooth as Remark: 2. The polynomial model of equation (2) guarantees shown in Fig 3b, one needs to model this phenomena. In this study continuity of the temperature T f(x,t) and its spatial derivatives up to we use the following third order polynomial proposed by Herczfeld the third order at the boundary point x = Xa, i.e. [2] to represent the temperature profile T(l;,t) across the Interface Region (IR) under stagnant condition: Tf( x+8 , t) = Tr( x-8 , t) 3 Tn xi. Figure 5 shows typical u 0 ~ 42 L data used to determine the transit time, llljj . That is ii~j is obtained A T "c I by measuring the delay between the temperature pulses Tm f (xi, t), 40 l-c----l-1----l----------l'f----+------ic\----+ 0 N measured at point xi, and Tm f (xj, t),and xj respectively. The time (w/rrf delay between these two temperature responses is obtained using r-, r-, r---, 900 crosscorrelation technique, that is ll¼j = "C* where "C* is value of 'C for L_..J L _ _j L_.J L-.o which Rij ("C) = maximum, where 2s1 soo 1sa 10111 12se 1s011 11s11 2000 22s0 Tl t1t ( S(CONDS l t0 +T Fig. 6. Measured temperature response of sensors T15, T16. and Tl7 as collector Rij ( "C) = f Tm tl dependence implies that the optimizatio~ problef!l is nonli~ear. r C 1 The details of the optimization procedure 1s given m Appendix B. 11 60 0 INTlll\l'OLAT l!D p E - 1'1\1:DICTe.O YI{<,) Toe results of the estimation of the interface region parameters are R 50 Fl summarized in Table 3. The first col_umn gives t1:e region nur:iber T (for example Region #1 denotes the interface region between mlet u 40 R cold pipe and collector #p-Aa.s defined above). TI:e se.cond E: column designates the location where the component Junction 1s 50 located. The third and fourth columns give "best" values for the boundary lengths which minimize the performance index of 20 ~ equation (B.l). The fifth column gives the instant of time. The values entered in the "error" column of Table 3 represent the 10 11.U ll,H u.u n.u 11.H u .•• maximum, absolute deviation between the measured and Tr Tli" Tyl trJ '1t' flt I••.,... predicted values at each instant of time. Note that this value equals the value of J(.6.X 0 , .6.Xu) of equation (B.l) at the optimum boundary length values. A comparison between the l ,A=in~dw~- predicted temperatures Tn(x,t) and measured temperature Trm to and for the {9) second equation t >to. The generaior outlet tem- perature is T - tiT aMd the evaporator outlet tem- perature is Tg - tiTg. The equation for 6T and ti T can be co~pactlY expressed as e g where QE and Q are obtained by averaging over a spe- cified time pe~iod. .,, The control problem consists of two different types of ~T =Al+ 8.!!!_ + C~ (5) problems. One is concerned with the dynamics of the collector whereas the other is that of the conditioned ~=DH+_! (6) space. The storage decouples these to a very large degree. Consider a conditioned space whose internal energy change QR{k) is due to room air and structural where A. B, Care constant matrices and the D matrix mass so that represents the transient term I is the initial con- dition and T, S, mare the temperature and flow rate vectors described-by Q(k) = ~eCplTe1Ck+l) - Te0(k-l)j + QR(k) This equation can be used to specify Te 0(k) for simu- .lating the dynamic behavior of the chiller. Generally the difficulty is in identifying QR(k). In this study the load is not considered a parameter and instead T. ti,\ ;., .,.,.,,1 tn c:im11l;:itP tho r1vn:,mil" hPh:.vir,r nf thP Page 667 III. EXPERIMENTAL DATA This is sufficient information to determine the unknown constant matrices via least squares fitting There are three sets of experiments that need to for both the steady state and transient performance, be conducted for evaluating the constants in the The experimental data generated was used to deter- models developed. The first set is designed to study mine the coefficient matrices A, B. C and O already the transient and steady state performance of the derived and described earlier. It was assumed that system. The second and third sets are designed to all the cooling developed at the evaporator is used, evaluate the dynamic behavior and upgrade earlier i.e •• the load is considered infinite for the purposes estimates of constants obtained from set 1. For both of this experiment, This assumption coupled with the sets the following data are recorded: fixing of the generator inlet temperature allows for Measurements as functions of time: A\• ATg• TA the decoupling of the chiller from the entire system. The resulting experimental data, therefore, yielos Controlled parameters (over a the chiller•s dynamic performance considered as an independent component, Additionally, since the inlet small range) and outlet temperatures at the hot water storage tank are measured, the thermal losses of the piping can be Controlled parameters (over the estimated for purposes of evaluating overall system performance, dynamic rarige of performance) : Te' Tg The first set of experiments requires the rreasure- Table 1 Experimental Conditions ments of Ale• AT and TA for a mix of the controlled parameters. Eaci experiment is generally conducted System Status - to cover operating range parametric for approximately 45 minutes after which the equipment variations is allowed to settle to an equilibrium state before the next experiment is conducted, The data obtained Approximate allows the computation of the system constants A. B, Length of Run - 15 minutes for experiments 1-25 and C, D, Kand L to a first estimate. 45 minutes to steady state for experi- In the second set of experiments, a sudden pertur- ments 26-32 bation in Te, Tg, me and 111q is introduced once the system is under steady state, in order to simulate Sensors the behavior shown in Eq. 4. Location - See Schematic Each perturbation is approximately ±10% of the steady state value of the particular variable. In Samp 1i ng order to contain experimental complexity, initially Period - 20 or 30 seconds only one perturbation is introduced. In order to con- serve time, each of these experiments was conducted Sequence of after completing the experiments in the first set. Sensor - Convenient The time allotted to each of these experiments did not Samp 1i ng exceed one half hour. This information when used in conjunction with Eq. 5 allows a finer estimate of the Repeatability - 3 or 4 days constants already obtained by data of the previous set. Special In the last set of experiments the introduction of Procedure - control of evaporator and generator a perturbation while the system is in the transient input temperatures mode is desirable. What happens is that the system moves from one transient mode or line to another. When the system is in the transient state and has IV. PARAMETER IDENTIFICATION reached approximately half the rise time, a pertur- bation in one of the parameters Te, Tg, me and mg is The coefficients in the model equations for the introduced and maintained. This perturbation was at steady state temperature drops across the evaporator least ±10% of the value set at the beginning of the and the generator were evaluated using standard least- experiment. Once the perturbation is introduced it square techniques as employed in the computer program should be maintained and the experiment conducted for SHAZAM (9), The resulting expressions for the tem- one half hour to settle to steady state. For simpli- peratures are fication only one perturbation was introduced ini- tially with two introduced simultaneously in later . experiments. Some of the experiments were conducted ATg = -0.0276 Tg; - 0.023 Te; - 8,658 mg 0 in conjunction with those of set l during the period of spin-down. Information gathered in this set was • 2 useful in refining the matrices 1n Eq. 5. - 0.154 me+ 0,00201 r91 The necessary requirements for the experiment are listed in Table 1. The parametric variation of the temperatures and flow rates were selected to cover the . operating range of the chiller. Each experiment was ATe = 0,9272 T91 - 0.9850 Te; + 2.823 m0 9 conducted three or four times. The duration of each experiment was approximately 10 minutes for • 2 experiments 1-25 and 45 minutes for experiments 26-32. + 12.448 me+ 0.00216 lg; Page 668 values of Te within+ .504°C of the experimental where a= 1/Tg and a' = 1/Te appear as slopes in a • data. Figuris 2 and 3 show the preaictea values of linear equation, and the intercepts b anct b' involve the exit evaporator and generator temperatures versus the constant steady state temperature drops. In this the measured values, and show the accuracy of the pre- stucty. the time constants were found by least-square dictions. fitting the transient temperature drop rate {estimated The determination of the delays and time constants using a centered finite difference approxi ma ti on) to a which appear in the transient model of the evaporator linear function of the temperature drops using the ana generator temperature drops was performed using measured data for time delineated approximate constant the following procedure. For a given input pertur- steady state indicated in Figure 4. bation the time delay is read directly from the The delay times and time constants obtained using experi men ta 1 data. The exponential form of the tran- the method outlined above are given in Table 3, for sient equations are valid for a pure step input per- four different input perturbations, i.e., generator turbation. Many of the transient experiments had inlet temperature ana flow rate evaporator inlet tem- input perturbations with a significant rise time; thus perature and flow rate. It was found that changes in the equations expressed in section II are not the evaporator inlet temperature and evaporator flow appropriate for these events. For any input pertur- rate had no measurable effect on the generator tem- bation, assuming that the events may be linearly perature drop, and that the experiments were insuf- superimposed, the transient equations may be rewritten ficient to determine the effects of generator flow in differential form as rates on the evaporator temperature drop, V. RESULTS AND CONCLUSIONS A comparison of the steady state predictions to those measured are shown in Figs. 2-3. The transient performance is characterized by the time constant given in Table 2 and vary from 22,3 sec to 42.1 sec for generator and 43.4 sec to 61.9 sec for evaporator. A comparison of a random selection of measured and predicted temperatures is shown in Figs. 5-7. For where{·) indicates a time derivative. In this form, heat transfer calculations and correlations this the transient equations may be applied to the data degree of accuracy in the steady state results is con- measured from tests where the input perturbations are siderea to be very gooct. More importantly, the ther- of arbitrary form, assuming that the steady state tem- mal mass of the system is such that the indicated perature drops are known for all input states, The deviations in transient performance will have a mini- steady state temperature drops may be obtained for all mal effect on percent solar or average system COP. It system states by using equations (1) and (2), and the is therefore concluded that the equations are in a transient data fit to the differential form of the form that is useful for control simulation work. transient equations. using a finite difference Also, these models possess a sufficient amount of approximation for the time derivative and a least- accuracy to provide system coefficient of performance square estimation procedure to obtain the time (to within a few percent) that can be used for a com- constants Tg and Te• For some of the transient .Parative analysis in order to identify optimum control measurements, however. the temperature drops measured strategies. were relatively small compared to the accuracy with which the steady state temperature drops are predicted VI. ACKNOWLEDGEMENTS by equations (1) and (2). This is particularly true during the initial transient. To avoid these errors This work was performed unaer contract that this would cause. an alternate procedure was 0£-AC03-83SF11950 for the Department of Energy under applied. A typical transient experiment is charac- the project and technical management of Robert terized in Figure 4. From the experimental data, the LeChevalier. Particular thanks are due K. Lindler, M. time at which the input perturbation stops changing to Palmer and J. A. Kirk for many helpful discussions within a specified tolerance (.1° for temperature, .01 and suggestions. for flow rates) may be directly read, along with the delay time as mentioned above. In all cases it was VII, R£F£R£NC£S found that the perturbations in flow rate were suf- ficiently fast that the rise time was zero. After the 1. Blinn, J.C., Mitchell, J.W. and Duffie, J.A., initial rise time of the input quantity. the input may "Mode 1i ng of Transient Performance of Resi dentia 1 then be consiaerea as constant and the resulting Solar Absorption Air Conditioning System", steady state temperature drops may also be considered Proceedings of the 1979 International Solar constant. Because of the delay involved, this appears Energy Congress, May 1979. as a constant in the differential form of the 2. Auh, P.C •• "Development of Hardware Simulators for equations after one time delay, as inaicated in Figure Tests of Solar Cooling/Heating Subsystems and 4. At times past this point. the differential Systemsu, Phase I. Residential Subsystem Hardware equations may be rewritten as Simulator and Steady State Simulation, Brookhaven National Laboratory, September, 1979. 3. Auh, P,C., •0evelopment of Hardware Simulators for Tests of Solar Cooling/Heating Subsystems and Systems•. Phase II. Unsteady State Hardware Simulation of Residential Absorption Chiller. Brookhaven National Laboratory. September 1979, Page 669 Absorption Chiller·. Proceedings of the 1980 Annual Meeting of AS/ISES, Phoen1x. Arizona, p. m:- EVAPORATOR TEMPERATURE PREDICTION 5. Froemming, J •• Wooa, B.D. and Guertin, J., ASHRAE Transactions, 1979, pp. 777-786. 6. Anana, D.K., Allen, R,W,, and Kumar, B., 14 ·Transient Simulation of Absorption Machines", 0 Journal of Solar Energy, pp. 197-203, August 1982. p .. 7. Karaki, S., "Performance Evaluation of an Active l 12 0 0 Solar Cooling System Utilizing Low Cost Plastic i dlb Collectors ana an Evaporatively Cooled Absorption !.. " 10 0 Chiller", CSU Final Report SAN-30569-30, February ,- Q 0 a 1984. o" 0 0 8. Helferty, J., et al., "On the Selection of • 0 Distributed Parameter Models for Control Studies 0 of Solar Energy Systems", Solar Energy Conference, Hawaii, March 1987. " 10 12 14 16 9. White, K.J •• An Econometric Computer Program, Rice Tt (m.aat.1r.d) ~C University, Houston, TX, August 1980. Fig. 3 Comparl111on between predlct•d and m•,uurod ••••dy •t•t• ovapontor ••mpuatur• output app;rnx. const.lnt stt!ady st.1.tt: I """'"1 :-... 1.,1,, ti•• I I .--;-----------input I STORAGE TAN ( ,1. . AIR am Fig. 4 Characterization and nomenclature of a typical Fig. 1 CSU Experimental ayatem transient experiment GENERATOR TEMPERATURE PREDICTION GENERATOR TEMPERATURE PREDICTION .0 2---------------------,,. Run •2.7 D/13/8.5 .9, •.. 0 • OOo IC• 87 0 ! ..•.,• , f 77 .0,2 i 76 ! e,o 70 ,. l. ,. . 77 ,~ e ,7.f . ! 74 ~ •••. .-,,....,,....,FTn-.-r..-.-T+~.~.~.-.~+~+~+~+-+_+_+_+_+-, 72 73 71 72 jf o 11 70 70 70 72 74 70 74 ao 100 400 TC (..,.....,rod)'c; ......p F,g. 2 Co~ariton betwe•n predicted al\Q nMaeured ateady atste O-MH'alor t•llPt4>-•fahue Fig. S 'Tunalent oertorrnanc• comparlaon of th• oen•retot ovtl•t temp«atur• f0< a •••P drop In lnl•I te,np•rature Page 670 GENERATOR TEMPERATURE PREDICTION Run •25 8/2./(5 90 .•,• •• o 00000000 aaoooaooa 0 ooaoooooo 0 00 ! .•• 0 , ,r .04 0 e , l 000°000 02 £. ., + + e ao 71 .', 70 77 76 7' 200 300 400 500 eoo Time (-c) temp m•o•ur.d ••It temp F,g. 6 Trans1en1 performance comparison ol lhe generator outlet temperature 101" a atep rise in inlet temperature EVAPORATOR TEMPERATURE PREDICTION 26-,--------Ru-n -•3-0 8-/2-7 /-85- ---------, 24 22 0 00 ° o 0000 ooo0ooooooooooc r 20 ~ 18 r, 16 1.. 14 0 .. ······~·~·~=_....... ............... ~ 00000000000000 l 12 10 e~ l • ! • o+---,---,---,---,---,--,---,---.----1 100 200 300 Tlm• ( ..c ) moo•ur'9d ••H temp pr.dk:-tod e,dl ig. 7 Transient performance comparison of the evaporator outlet temperature for • step rise In Inlet temperature Table 2 Transient Results (1.pedwnt, 1., •• 1., .. Input hrburtw.tton O,t, 2S.8/l9 10 42.l 80 43.2 ,, ZS,8/29 10 JS.8 80 49.8 ,, 2).8/2 30 2).2 90 il.O ,, 2S.8/2 30 )l.4 90 46.9 ,, ll,8/Z 30 37.8 100 Sl.2 gt •~r.a9~ 22.0 "-' 88.0 so.a ( ll.0) (S.B) (B.4) (I.SI JZ,1/27 )0 48.2 , C - N E 03 ~ uJ (.) c,, >, - 0 ¢I:::; o O C:, :J :J -Q) - 0 0 ..c. 0 ,._ E 0 Q) a2 l - - ,._ II) C -,._ en C - ·- 0 0 C a. ::, -C - ·-0 C 0 a,.....; 0 ..c. Q) - Q) ·- 0 0 -Q) 0 a. <.) u u I U) (/) Q.. u ao J I 2 (/) 0 uJ 79 ~ HT Parameter 3 3 3 3 2 3 2 3 3 3 3 4 7S - I '.' - • '. I Phys. Model 2 2 2 3 I 4 2 3 3 3 -..,..:, 4 771 715 .....1 System Trans. 3 2 3 6 I 6 2 6 6 3 4 6 175------------------~---i 200 300 -400 500 eoo Steady State 2 I 2 2 I 3 3 4 4 2 2 4 Tlrn• (••c) m•o•ur•d o:idt t•mp Weather 5 5 5 4 5 5 5 4 4 4 5 4 FlG.3 Transient performance comparison of the generator outlet temperature for o step rise in outJet temperature. Legend: I as accurate as possible,2 better than 5% accuracy, 3 better than 10% accuracy,4 gross or stochastic information,5 test function, 6 not need- ed. GENERATOR TEMPERATURE PREDICTION 02 ----------------------,, ., J 00 70 777 75 ,.LQD /. 73 I 72. 71 1 j •--- h~uot \<>1.,, lhH~ dl ---. • .....---., ,,...u,>),ol6;-H. .. >I a •~---- ~,.n . f..""~~ 70 I •--- ~~~11 • 1. ..~ ,1 70 72 74 7& 7~ 0 ~-""•o=v-~c,~c- -,.-.-~,~,.~~.=...,,~~,.~"--'" TG {,neosvred) MONJH Of hCATIH!. Sl"-SOH FIG. I Comparison between predicted and measured FI GA. Washington, D.C. - Percent solo r and steady stole generator temperature. collector efficiency. 1092 Page 706 MAGNETICALLY SUSPENDED STACKS FOR INERTIAL ENERGY STORAGE FLYWHEEL by Davinder K. Anand Professor James A. Kirk Professor and Peter Iwaskiw Research Assistant University of Maryland Mechanical Engineering Department and The Systems Research Center College Park, MD 20742 This paper discusses the concept of a magneti- type of power conditioning must be incorporated to cally suspended flywheel stack as it applies to a maintain the required output voltage. In addition, 500 Watt-hour energy storage system. The proposed energy losses in the electronics associated with system is currently under hardware development and the charge and discharge cycles must be minimized. is based upon a "pancake" design reported earlier. For the 300 WH design, an efficiency of 90% for Also included in the system configuration are back- each cycle is desired. This was also assumed for up ball bearings which prevent damage to the system the 500 WH design. Therefore to supply 500 WH, a whenever there is a loss of magnetic suspension due 550 WH capacity flywheel was sized. to excessive outside disturbances. The back-up bearings also insure that the flywheel stays within Other design goals of the system include modu- the linear control range. A summary of the design larity, suitability to withstand outside load tools that have been developed to access perfor- disturbances and protection of equipment when mance of the control system and magnetic circuits failure of flywheel material or suspension occur. are included. An additional design criteria specifies that the rotor remain magnetically suspended under a 2-G INTRODUCTION radial load. This criteria is used in the 500 WH design. To protect the magnetic bearing, suspen- To effectively design a 500 WH flywheel energy sion ring and motor/generator when failure of the storage device usiny magnetically suspended stacks, magnetic suspension occurs, back-up ball bearings several parameters concerned with the specifica- are used. The outside portion of the ball bearing tions, design goals, and applications of the device (see Fig. 2) is set just beyond the gap operating have to be known apriori. For spacecraft applica- range of the magnetic bearing (typically± .01"). tions, it is important to minimize the mass and The ba 11 bearings support the flywheel when the size of the device without sacrificing its energy flywheel deflection due to outside disturbances storage capacity. Therefore, one design goal of exceeds this operating range. They protect the the system is to maximize the SED (specific energy magnetic bearing and motor/generator materials from density). This SED should exceed that of collision. A detailed discussion on magnetic electrochemical systems which is typically 14 bearing back-up ball bearings is given in a paper WH/kg. A system SED goal for a past 300 WH by Frommer [2,8]. For protection of satellite flywheel design [2-5] has been to exceed a value of equipment if the flywheel material fails under high 20 WH/kg or 9 WH/lb. This was the design goal used speeds (burst condition), it is necessary to design for the 500 WH energy storage system. the flywheel for separation of the outermost rings from the remainder of the flyweel [as was done in The proposed stacks for energy storage system reference 9-14]. Doing this makes the containment is based on a "pancake" magnetic bearing stack as of failed flywheels easier. shown in Figure 1. The magnetic bearings used in the stack have been Jiscussed by Kirk and Studer PROPOSED FLYWHEEL DESIGN [6,7] and are a required element for a viable and efficient energy storage system. The acceleration The 500 WH capacity flywheel was analyzed of the flywheel or charge cycle (motor mode) must using the FLYANS2/FLYSIZE software developed by occur during a 60 minute interval when the UMCP [11-13] and modified by TPI. The computer satellite is exposed to sunlight. The spindown of program FLYANS2 performs a stress analysis on a the flywheel or discharge cycle (generator mode) multi-ring flywheel arrangement given material pro- must occur during a 30 minute interval when the perties and inner radius ratios (inner radius of satellite is exposed to darkness. fhe energy ring/outer radius of entire flywheel). Other storage system during discharge must supply power inputs include the inner radius displacement ratio at a constant voltage of 150 ±2% volts DC. limit and the ring interference (in assembly) ratio However, to design a flywheel with suitable size limit. The inner radius displacement ratio input and capacity, operating speeds 1~hich are directly limits the gap growth (between the suspension ring proportional to generator output voltages must vary of the flywheel and the magnetic bearing) of the by 50% (the high operating speed being twice as suspension system due to the centrifugal forces much as the low operating speed). Therefore, some generated by the spinning flywheel. Gap growth Page 707 effects the suspension control system in a detri- system performance similar to past UMCP magnetic mental way by reducing the control system active bearings. stiffness, KA. The rin~ interference limit i~ the limit on the amount of interference between rings. Based on the UMCP 3" (7.6 cm) laboratory model, FLYANS2 performs a stress analysis for both nonin- Kr was taken to be one hundredth the value of Kx in terference fitted and interference-fitted rings. lb/amp. Thus, for the 500 WH design, Kr was chosen For interference fitted rings, it computes ring to be 56 lb/amp, while the value of Kx was chosen interface pressures that maximize SEO while staying as 5600 lb/in (1002 kg/cm) with a flywheel linear within a prescribed limit (typically 0.6%). The excursion range [around a uniform air gap] of ±.01 data from FLYANS2 is used for the FLYSIZE computer inches (±0.254 mm). program to actually size the flywheel. The FLYSIZE output for the 500 WH flywheel is shown in Table 1 Knowing the desired system axial-load carrying with the upper and lower operating speed ratio, capability, Kx, Kr, and minimum current, the selected as .375 and .75 of the burst speed. following physical and magnetic properties of the bearing are then determined using the MAGBER design It is assumed that the flywheel has a weight of program: half the total energy storage system. Therefore its SEO must be twice the system SEO. Through Stator radius, Air gap, Permanent magnet repeated simulations, it was determined that a (PM) area, PM thickness, PM operating flywheel configuration with an inner return ring point, Leakage Permeance, Air gap made of segmented iron and 5 composite (Celion 6000 Permeance, Air gap Flux and flux density, graphite/epoxy) outer rings, interferenced fitted Coil turns, Coil wire size and Axial Drop. and having inner radius ratios (inner radius of ring/outer radius of outer ring of flywheel) of The sizing of the magnetic bearing involved an .48, .5, .6, .7, .8 and .9, yielded high SEOs that iterative process via computer simulation using the exceeded twice the system SEO. The inner radius program MAGBER. Magnetic circuit permeances, displacement ratio limit and the ring interference fluxes, and flux densities were computed for trial limit value used was .006. Repeated computer runs physical dimensions (i.e., pole face thickness. gap for a 500 WH flywheel with a high SEO have yielded distance, axial drop, magnet area, magnet length) a flywheel configuration weighing approximately 30 and material magnetic properties of the bearing. lbs. The operating flux density of the permanent magnets was also derived. Kx, Kr, coil turns (N), and The stack bearing consists of 2 magnetic axial-load carrying capability (Wal could then be bearings, a motor/generator and 2 back-up ball determined using the computed magnetic circuit bearings as shown in Fig. 1 •• One requirement for parameters. the flywheel is that it must have a large enough height to house the components shown in Figure 1. Based upon the trial dimensions pole face Based on the sizing of the 300 WH flywheel system, the minimum component heights for the 500 WH system thickness and air gap distance was increased to is 4.50 inches (11.4 cm). avoid saturation in the iron material (which limits the amount of useful flux that crosses the suspen- Flywheels incorporating 4", 5" and 6" (10.2 cm, sion air gap). The flux density within the Fe 12.7 cm and 15.2 cm) magnetic bearings were ana- material should not exceed the value of 1.5 teslas lyzed and designed using the FLYANS2, FLYSIZE, and or saturation will occur. The maximum flux density MAGBER computer programs. MAGBER developed at UMCP of the iron material was determined by computing was used to determine the bearing's axial-load the flux density at the thinnest portion of the carrying capability. The results of design runs flux plates - i.e., at the pole faces. MAGDESIGN for flywheels using 4", 5" and 6" (10.2 cm, 12.7 cm (a program developed at TPI for this project) was and 15.2 cm) diameter magnetic bearings is sum- used to determine saturation conditions for various marized in ref. 1. displacements of the flywheel. The object was to remain at an unsaturated condition within the As mentioned before, centrifugal forces cause operating gap range of the suspension control system. the inner radius of the flywheel to expand at high speeds (called air gap growth). FLYSIZE determines SUSPENSION CONTROL SYSfEM DESIGN this expansion at the low and high operating speeds of the flywheel and reports there numbers to the user. Through iterative design runs using FLYANS2 The design goal for the suspension control and FLYSIZE, one can meet the air gap condition as system for the 500 WH energy storage system was to well as achieve a high SEO. The 500 WH design design a control system which would keep the yielded a SEO value of 19 WH/LB (42 WH/Kg) and an flywheel suspended under static and dynamic loads. air gap growth between lower and upper operating To withstand static loads (in this case a 2-G speeds of .015 inches (0.381 mm). radial load), a system gain was selected which pro-vided a steady state active stiffness sufficient to MAGNETIC BEARING TECHNOLOGY satisfy the required operating excursion range of the flywheel. The magnetic bearing for a 500 WH energy storage system was designed to support a 2-g axial Nearly all of the electronic component values load without loss of suspension. An additional from previous UMCP laboratory suspension control goal was to achieve a certain permanent magnet systems were used in the design of the 500 WH radial stiffness, Kx, and current-force sen- control system. A schematic of the control system sitivity, K1. Design values for Kx and Kr were for the magnetic bearing is shown in Figure 3. assumed based on maintaining suspension control The input reference voltage was determined to be within the range of Oto +15V, which was the Page 708 range used in past systems. The maximum operating: cycle was assumed such that over 21 minutes, the current was used to size the coil wire and the generator discharges at a low power of 625 watts power amplifiers. To minimize the control current and over the remaining nine minutes the generator and yet maintain the same steady state active discharges at a high power of 1875 watts. All stiffness the current-force sensitivity Kr was together, the generator delivers 1100 watts over increased and the adjustable reference voltage was 1/2 hour equal to 550 WH. 500 WH actually gets to reduced by the same proportion. By increasing Kr the satellite power system due to energy losses in the amount of coil turns needed for design was the power electronics. (This was a previously men- increased. For a value of R17 = 11 kQ and Kr= 56 tioned design goal). The voltage variation of the lb/amp (25.5 kg/amp), N was computed to have a generator is linear from 140V to 70V, but it varies value of 825 turns/coil with a maximum operating at two different rates due to the change in power current of 10.12 amps. Ki was then increased by a delivered. It was determined that the maximum factor of 2.5 to reduce the coil amperage to 4.05 current in the armature per phase is 8.93 amps and reduce the variable resistance to 4360 Q. amps/phase. This resulted in a K1 value of 140 lb/in (25 kg/cm) and a turns/coil value, N, of 2100 turns. The modified values were used for the 500 WH design. This maximum current (which exceeds that of the motor) is used to design the coils in the armature, The final parameter that was determined for the In the proposed motor/generator, the rotating ring suspension control system was the compensation net- will be replaced by a stationary ferrite ring glued work time constant, T. This parameter influences onto the inside periphery of a stationary ironless the damping of the system. For the 500 WH system, armature. The outside rotating ring assembly is it was desirable to maximize the damping so as to made up of PM magnets and is attached to a soft limit the flywheel excursions due to mass unba- iron backing ring. An 8-pole machine is proposed lance. To maximize system damping and minimize using a delta-connected winding operating at 4000 dynamic loading effects, an optimum value of Twas Hz maximum frequency. The dimensions of the device selected. To optimize T, root locus plots and Bode are constrained by the size of the flywheel and the plots were used and the results are shown in Ref. magnetic bearing. For the 500 WH design, the out- 1. side radius of the soft iron backing ring could not exceed the inner radius of the first composite ring For the 500 WH system, a value of T = .0016 sec of the flywheel. A 2 in. packaging height was a was chosen to minimize the amplitude of response design goal. The gap distance between PM's and and maximize damping. This called for a capaci- armature coils needed also to exceed the gap tance value of .016 µFin the compensation network distance of the magnetic bearing. Based on these of the control system (keeping the resistance the constraints, PM size and armature coil con- same as previous values of past systems). figuration and size were determined. Based upon experience gained in designing the Of further interest is the determination of control system shown in Figure 3, a modified ver- energy losses within the armature and also within sion of the control system, as shown in Fig. 4, is the power electronics of the device. Armature loss being currently investigated for use in the 500 WH (3I 2maxR) was computed to be 2.11 watts while the system. loss due to the ferrite ring was determined to be negligible (less than one watt). Most of the other MOTOR/GENERATOR DESIGN losses for the 500 WH energy storage system were kept the same as or scaled up from the 300 WH The motor/generator design for the 500 WH design. system is based upon a permanent magnet, electroni- cally commutated, 3 phase machine, shown concep- 500 WH DESIGN tually in Fig. 5. Several improvements in the conceptual design have been incorporated into the The proposed design of the 500 WH magnetically 500 WH system, and these are shown in Fig. 6. suspended flywheel energy storage system is shown in Fig, 7. The specifications of the entire system The first step in design was to determine is summarized in Tables 1 and 2. The design metho- power, voltage, and armature current variation dology flow chart for flywheel energy storage during the charge cycle of the motor and the system is shown in Fig. 8. discharge cycle of the generator. It was assumed that the bus of the motor receives a constant power Table 1 summarizes flywheel specifications com- of 650 watts from the solar array at 150V + 2% DC. puted using the FLYSIZE/FLYANS2 software. Table 2 This happens during the time span of an hour. gives magnetic bearing specifications which were Since motor voltage is proportional to flywheel determined using magnetic circuit theory and the speed and flywheel speed was chosen to vary by 50%, design programs previously discussed. a motor voltage profile varying from 70V to 140V was used in the design. (This assumed a voltage CONCLUSIONS/RECOMMENDATIONS drop of lOV during transfer of energy from PV array to flywheel motor). Based upon the state-of-the-art review and the proposed design of the 500 WH system, it can be Armature current variation (per phase) was concluded that determined by dividing the time equation of power by the time equation of voltage. At the beginning • Magnetically suspended flywheel energy of the charge cycle, the armature current/phase was storage systems are a viable and superior computed to be 3.1 amps and at the end it was com- alternative to batteries puted to be 1.4 amps. A proportional discharge Page 709 • System issues of attitude control and 6. Kirk, J .A., "Flywhee 1 Energy Storage - Part I, power transfer are manageable Basic Concepts", International Journal of Mechanical Sciences, Vol. 19, 1977, pp.- o The magnetically suspended flywheel system 223-231. can be designed using current knowledge in modules varying in size from 100 WH to 7. Kirk, J.A. and Studer, P.A., "Flywheel Energy 1000 WH. Storage - Part II, Magnetically Suspended Superflywheel", International Journal of Consistent with these conclusions, the following Mechanical Sciences, Vol. 19, 1977, pp. activities are currently underway: 233-245. • Construct Prototype 500 WH Energy Storage 8. Frommer, D.A., "Mechani ca 1 Design System using proposed design. Considerations for a Magnetically Suspended Flywheel", University of Maryland, M.S. Thesis, August 1986. • Bench test prototype to 20,000 RPM. 9. Kirk, J.A., Anand, D.K. and Khan, A.A., "Rotor • Enhance robustness of control electronics Stresses in a Magnetically Suspended Flywheel based on bench test. System", Proceedings of the 20th Intersoci ety ~ Conversion Engineering Conference, • Design a test program to cycle energy August 18-23, 1985, Miami Beach, Florida, pgs. storage wheel through operating range. 2.454-2.462. • Construct Spin Test Facility for cyclic 10. Evans, H.E. and Kirk, J.A., "Inertial Energy testing at design speeds. Storage Magnetically Levitated Ring-Rotor", Proceedings of the 20th Intersociety Energy • Test and evaluate prototype operation Conversion Engineering conference, August under design conditions. Incorporate test 18-23. 1985, Miami Beach, Florida. pgs. results in final design. 2.372-2.377. • Construct flight hardware experiment. 11. Kirk, J.A. and Huntington, R.A., "Stress Analysis and Maximization of Energy Density for ACKNOWLEDGMENTS a Magnetically Suspended Flywheel", ASME ~ 77-WA/DE-24, presented at 1977 ASME Winter This work was supported in part under NASA Annual Meeting. Grant NAG-5-396. The helpful discussions with E. Rodriguez and P. Studer of NASA/GSFC are appre- 12. Kirk, J.A. and Huntington, R.A., "Stress ciated. Redistribution for the Multi ring Flywheel", ASME ~!:. 77-WA/DE-26, presented at 1977 ASME REFERENCES Winter Annual Meeting. 1. SBIR Report "Design of a 500 Wh Magnetically Suspended Flywheel Energy Storage System, 11 13. Kirk, J.A. and Huntington, R.A., "Energy Contract NAS 5-29272, TPI, Inc., August 1986. Storage - An Interference Assembled Multi ring Superflywheel", Proceedings of the 12th IECEC 2. Anand, D.K., Kirk, J.A. and Frommer, D.A., Conference, Washington. D.C., September 2, "Design Considerations for a Magnetically 1977, pp. 517-524. Suspended Flywheel System", Proceedings of the 20th Intersociety Energy Conversion . 14, Kirk, J.A. and Anand, D.K., et al, trig°fneeri ng Conference, August 18--23, 1985, "Magnetically Suspended Flywheel System Study", Miami Beach, Florida, pgs. 2.449-2.453. NASA Conference Publication 2346, "An Assessment of Integrated Flywheel System 3. Anand, D.K., Kirk, J.A., Zmood, R.8., et al, Technology", Dec. 1984, pgs. 307-328. "System Consideratins for a Magnetically Suspended Flywheel", Proceedings of the 21st 15. Kirk, J.A. and Anand, D.K., "The Magnetically lntersociety Energy Conversion Engineering Suspended Flywheel as an Energy Storage Conference, Aug. 25-29, 1986, San Diego, CA System," NASA Lewis Research Center, Apri 1 pgs. 1829-1833. 1987. 4. Anand, D.K., Kirk, J.A. and Bangham, M.L., TABLE 1 FLYWHEEL SPECIFICATIONS FOR 500 WH "Simulation, Design and Construction of a ENERGY STORAGE SYSTEM Flywheel Magnetic Bearing", ASME Paper 86-DET-41, Presented at the Design Engineering Technical Conference, Columbus, Ohio, Oct. 5-8, Inner Diameter 5.760 in. (14.630 cm) 1986. Outer Diameter 12.000 in. {30.480 cm) Thickness 5.474 in. ( 13. 904 cm) 5. Anand, D.K., Kirk, J.A. and Bangham, M.L., "Design, Analysis and Testing of a Magnetic Configuration Multiring + 1 seg. iron ring Bearing for Flywheel Energy Storage", ASME 5 graphite/epoxy Paper 85-WA/DE-8, presented at 1985 ASME Winter rings Annual Meeting. Burst Speed 70 k rpm Max. Oper. Speed 52 k rpm Page 710 Low Oper, Speed 26 k rpm Weight 29 lbs, (13,2 kg) Usable Energy Density 18,96 WH/lb, (41,71 WH/kg) I. .. ,~~~' Burst Energy Density 44,95 WH/lb, (98,91 WH/kg) Air Gap Growth @ ,0353 in, (0,8966 mm) Burst Speed Air Gap Growth @ ,0199 in. (0,5055 mm) 52 k rpm Air Gap Growth @ ,0050 in. (0,1270 mm) l_J~ 26 k rpm TABLE 2 MAGNETIC BEARING SPECIFICATIONS FOR 500 WH ENERGY STORAGE SYSTEM FIGURE 2- FLYWHEEL TOUCHDOWN FOR A DOUBLE MAGNETIC BEARING STACK Radial Stiffness, Kx : 5600 lb/in, (1002 kg/cm) Current-Force Sensitivity, KI 140 lb/in, (25,1 kg/cm) Turns/Electromagnetic Coil, N 2100 turns Maximum Operating Current, i max 4,05 ~-.,1,;amps ... ,. . Q,1 ,1 ,, Eir:1,.<,:.1,.1dc. ._.." , '....,. , Gap Operating Range ± ,01 in, ( ±0. 254 mm) Nominal Gap Distance, g ,038 in. (0,965 mm) Sta£or Radius 2,88 in, (7,32 cm) Pole Face Thickness 0,15 in, (0,38 cm) FIGURE 3- CONTROL SYSTEM FOR MAGNETIC Magnet Diameter 1,8 in, (4,57 cm) SUSPENSION Magnet Length 0,3 in. (0,76 cm) FIGURE 4- CONTROL SYSTEM FOR 500 WR DESIGN FIGURE 1- MAGNETIC BEARING STACK FOR 500 WH SYSTEM FIGURE 5- LABORATORY MODEL OF PERMANENT MAGNET MOTOR/GENERATOR Page 711 ,.. .... ,e-e ROTM BACKNO PEMAp,ENT RON MAQHETS OPTICAL POSITION - IE'NSOA8 FEARffE ST ATOR COf-tE FIGURE 7- CROSS-SECTION OF 500 Wll FLYWHEEL ENERGY STORAGE SYSTEM FIGURE 6- MOTOR/GENERATOR DESIGN FOR 500 WI! SYSTEM lJilllT...J. Q!lI£l!'.L1 Material specs, inner radius, 1------l Flywheel ring sized, operating speeds, inner radius ratios, gap growth SEO, gap growth, flywheel weights, limit, interference limit maximu-m -s-tr.-·es-s-es- --.----------~ _...,._ _________N _. .,. --SPEaOck aa deinq uahtet?. sufficient? y !!:!fl!:Ll -stator t·ad and nom. Pole face thick11ess, min gap of bearing set by drop, coil turns, PH spe1.;s, flywheel ring sizes ..... FLYWHEEi, variable resistance Rl7, ·-suspension operating SIZED pln dimensions, static t·ange set by gap and radial load conditions -Gap growth INPUT l -- Wa C Ima>< N \ ·-Load conditions met? -Operating speeds '-------------..; ·Satut·ation prevented -Motor/Generator dng sizes within opernting range? constrained by fly, ring sizes HI\GNE·rrc BEARING----------! SIZED y ltlJ:!IT....i- --~CL~I\SSICA -Gap gt·owth Ifil!!1__]. Past control system ciI'cuitry CONTROLS -·Opet , speeds Power schedule pat·ameters, mass unbalance SOFTWARE -Fly .. weight and budget INPUT INPUT N y -System stable?~ Q!l'.tJ:lIT._1, Q!ITJ?!CT _} -Damping optimized Bode plots, root Max armature current, -Power losses~ @operating speeds? plots, compensator Ann .. resistance, power· too r·cat? _ constant 'l' losses, PM slze, coil size-. ---"---·-- N CON'l HUL SYS I f:;M MO l'OH/GENEHA'I O, is completely observable, using a single sensor located at x~x' (i.e., y(t) = c· T(x',t)), it is necessary that the observation time interval u(t) =(c!Y'WCc)·m(t) is the effective fluid velocity, V(t) = [(1:c.UUL)l(t)+ [to, t1l be chosen so that t1 2. t', where t' satisfies: T a(t}] is a disturbance function due to the solar insolation and ambient temperature, and the parameter a = (F'UUCc) is related to the collectors t * themal time constant, i.e. a= li,C' where Tc is the collectors thermal time x' = J u( cr) dcr. constant. ]';ote that u(t) is related to the flow rate and thus is the control to variable. In addition, u(t) is also a function of the thermal capacitance Cc, and is therefore not the real fluid velocity but an "effective" velocity of a This fact is proven using the method of characteristics to solve Eq. (]) for slug of hot fluid as it travels through the collector. T(x,t) and then reconstructing the initial temperature profile, along each characteristic curves of Eq. (1). The characteristic curves give the From the experimental validation studies of [31 and it was detennined relation between space, x, and time, t, and are the set of solutions to the [4], differential equation that the control variable, u(t), is linearly related to the fluid fiow rate m(t). On the other hand, it was found that the thermal time constant, 'c= Ila, dxldt = u(t), x(t0 ) = x0 . (3} depends on the location of the sensor and the flow rate (i.e. a= a(x,u(t)) ) This must be taken into account when designing the state estimator for a That is, solar collector. Specifically, if the estimator uses more than o.ne measurement sensor. then in designing the estimator, one must use t different gains to take into account the variations in the model parameters x(t) = x0 + j u( cr) dcr, x(t0 ) = x0 (4) as a function of sensor location and fluid flow rate. to III.OBSERVABILITY OF THE OTPF MODEL Their importance is that along each characteristic curve, Eq. (I), when V(t) = 0, reduces to an ordinary differential equation which has the solution In order to consid2.r the observability of the temperature profile across the solar collector described by the OTPF model of Eq. (l) one needs to define T(x(t), t) = exp!-a(t - toll T(x ,t ) (5) the output equation. The measured output, y(l), is a weighted spatial 0 0 temperature average across the collector, namely Figure 2 illustrates a set of characteristic curves in the (x,t) - plane, along L with the sensor path at x = x'. Note that for each value of x0 , there is a y(t) = f c(x) T(x,t) dx (2) unique characteristic curve, so that by varying the initial point x0 between 0 0 and x', the characteristic curves sweep out a closed region in the (x,t)- plane bounded by the lines X= 0, x = x·, and where c(x) is some scalar function of x. Note that when measuring the t* temperature using a single sensor located at x~xi, then c(x) = cio(x - x;), x( i") = i u(cr) dcr. where 8(x - xi) is a Dirac delta function, and ci is a constant sensor gain. to Definition DI: The OTPF and measurement models, given by Eqs. (I) and (2), respectively, is said to be observable at time t0 and point x0 , where x0 E 10, L], if the spatial temperature profile at time t0 , Characteristic curves T(x0 ,t0 ), can be determined from the output y(t), t E [t0 ,t1 ]. If this is true t* for all t0 and x0 E \0, L] (i.e. any T(x0 ,t0 ) ), the system is said to be x(t*) = f u(cr) do completely observable. (x',t ) Next we investigate the observability problem for several different sensor configurations using the above definition. 1. Singh: sensor measurement. If the output y(t), is measured via a sensor single sensor located at x = x', then c(x) = c'O(x - x'}, and y(t) = c'T(x',t). lt position should be noted that for the single sensor measurement y(t), the ,., () L observability of the system defined by Eq. (I) depends on the flow rate. x' That is, if the collector fluid is stagnant (i.e. u(t)=O), then the temperature, Distance in the direction of fluid flow T(x0 ,to), which can be reconstructed from the output y(t) of the sensor x- located at x=x' is oo.l:I. the time history at the point x', and it is impossible to reconstruct the spatial temperature profile at any other point along the Fig. 2. Characteristic curve and sensor position in the co11ector. Furthermore under flow conditions (i.e. u(t) > 0), one can (x,t)-plane. 1094 Page 714 In order to determine the value of T(x0 ,t0 ) at a point x and t from a 0 0 x E [O, x 1], can be reconstructed from the information provided from 0 sensor output y(t) located at x', we need to determine the specific point x 0 either one of the two sensors. = x(t0 ) which will be identified when retracing the characteristic curve of Eq. (4) starting at the point (x',t) shown in Fig. 2. From Eq. (4), the point This redundancy can be used to obtain parity checks on the accuracy of the x0 observed at time t0 as a function of observation time t, is given by: sensor measurements. For example, from Eq. (7), for the two sensor problem, T(x0 , t0 J at point (x0 ,t0 ) can be reconstructed from either point t (x,t1) or (L,t2), as shown in Fig. 3. That is: x 0 = x' - f u(c r)dcr (6) to Substituting Eq. (6) for x0 in Eq. (5) and solving for the initial state or T(x0 ,t0 ) we obtain: t T(x 0 , fo) = exp[ a (t 1-t0 )] exp[ a (t2 - t 1 )l T(L,t) (10) T[x0 ,t0 ] = T[ x' -J u(cr} dcr, t0 ] = exp[a(t - t0 )J y(t) (7) to where t2 is obtained from t2 This expression relates the initial state T(x0 ,fo) to the measured value y(t) f u(a) dcr = Llxi = L- XJ, as a function of time, i.e., the reconstruction equation. Note from Fig. 2 t I that if t Lt*, then the initial temperature profile, T(x 0 ,t 0 ), can be reconstructed, using Eq. (7), for any x0 over the entire interval [0, x']. Note that if u(t) = u (i.e. a constant), then Llx = u .'.It, and Eq. (10) becomes 2 Multiple sensor measurements, If the output y(t) of Eq. (2) is T(x0 , fo) = exp[ a (ti- fo)] exp[ a"1x I u] T(L,tl based on m - sensors located at the poinL, {xi, i = I, 2, ... , m}, then c(x) in Eq. (2) is c(x) = L Ci 6(x - Xj), so that Eq. (2) becomes m l~==:l Obsen:abie region by sens.or located a.t x = x during t -s:.. t < t' y(t) = L Ci T(xi,t) (8) r 1 O -i= I nm Observable region by sensor .located at X : L during t O "S_ t 2. t' Without Joss of generality, we assume that the sensors are located along the direction of fluid flow so that x l < x2 < ··· < Xj < ··· < xm. The ='0 Redundancy region by both sensors. ·co t" condition for the complete observability of Eq. (2) using m sensors is: fatl..l;_ The OTPF system of Eq. (I) is completely observable for all t0 and x0 E [O, L]. using the measurement y(t) of Eq. (8) from m distinct sensors located at x I < x2 < ... < Xi < ··· < xm, if: ·r (l) The mth sensor is located at the point Xm = L, and (2} The length of observation time, Llt = (t' - t0 ) is greater than Llt e'. 61min = (t' - fo) 0 0 where i* = max { t'i, i = l, 2, ... , m - l J with t'i evaluated from t'i Distance in the direction of fluid !low x ______.. f u(a) da = Llxi = Xi+ t - Xi, i = 1, 2, ... , m - 1 (9) Fig. 3. Regions of observability and redundancy for two sensor positions in the (x,t)-plane. The first condition guarantees that no portion of the initial temperature profile near the collector outlet (i.e. x = L) will be missed, and the second condition implies that the observation interval, Llt, is greater than the IV. SEQUENTIAL STATE ESTIMATOR longest transit time that is necessary for a slug of hot fluid to travel FOR THE OTPF MODEL. between any two adjacent sensors or between the inlet point and the first sensor position. Fact 2 is an extension of Fact I for the multiple sensor This section gives a sequential state estimator equations, and a solution case, and can be proved by determining the ti for each pair of sensors using technique based on the method of characteristics. The estimator presented the characteristic curves. in this section is an extension of the work done by Sugisaka et al. [8], where a state estimator was developed for the case when the parameters of For example, Fig. 3 shows the region of observability in the (x,t)-plane the OTPF model are assumed constant. The estimator presented here takes for two sensors located at x = x , and x = L over the time interval t .s:. t .s:. into account the case when the thermal time constant of the OTPF model 1 0 is a function of both distance x and flow rate u(t). t'. The region shaded by the horizontal lines gives the observable area for the sensor located at x = x 1, while the region marked by the vertical lines The OTPF model ofEq, (I) considered for the state estimator is: gives the observable area for the sensor located at x = L. The dotted region shows the area in which the continuous time measurements from both clT(x,t) dT(x,t) sensors are redundant (i.e. overlap). This occurs when t>t = t' - to> Lltmin· _d_t_ =-u(t) a;-+ f(T(x,t), x, t) ( II) Note that if the interval of observation Llt ~ (t" - fo), the sensors are fully redundant which means that the initial temperature profile T(x0 , t0 ), for all 1095 Page 715 where f(T(x,t),x,t) = a(x,u(t))(V(t) - T(x,t)) see Eq. A.3, Appendix A. The subject to the initial condition measurement system consists of m sensors, and their output as an m-dimensional vector y(t) : T( O)=T0 ; P( O)=P0 (16) m Note that Eqs. (15a-b) are the standard extented Kalman Filter equations x---5~,0--1~00-,0--1-s~0-0--2-0_0_0_2~0-0--3-0~0-©--3~a-0_0_4~0©0 TI ME c-,...::::,1=,=0=0--2"'0~0~0-2=0~0,--~3""0""0-c0--=-3"~--=-0-=-0-4=0 0 0 the U. S. Department Of Energy under contract No. DE-AC03-86 SF TIME (SECONDS) 16132. In addition, we are thankful to Dr. C. Rorres for his helpful discussions on the observability results, and Thieny Jurand for his help Fig. 6. Covariance function, P17(t), when the measurement with implementing the estimator equations on the digital computer. noise variance, 0 = 3. Finally we are grateful to both Ellen and Estell Smuda for their assistance in preparing this document. 1097 Page 717 REFERENCES Recent experimental validation studies [3], [4] has showed that the thermal time constant, 'c' depends on the distance along the collector, and the 11] Herczfeld, P.R., R. Fischl, G. Vardakas, and R. L. Wolfson. 'Experimental Validation of Dynamic Control Models.' Proc. of the effective flow rate through the collector.This implies that the OTPF model ASl,!E Solar Energy Division 3rd Annual Conference, Solar ofEq. (A.2) is Engineering, Reno, Nevada, 1981. 12) Klein, S. A. The Effects of Thermal Capacitance Upon the [aT (x,t) lilt]+ u [iJT (x,t) 1axJ + a(x,u) T (x,t) a(x,u) V(t) (A.3) Performance of Flat-plate Solar Collectors.' M.S. Thesis, University ofWisconsin, 1979. - where a(x,u), and hence TC' depend upon position, x, and flow rate, u. [3] Helferty, J., R. Fischl, P. R. Herczfeld, and T. Brisbane, 'Solar Collector Loop Modeling and Experimental Validation for NOMENCLATURE Distributed Parameter Models from Experimental Data.' Proc. of the 41h IFAC Symposium on Control of Distribuied Parameter Systems, Los Angelis, California, June 30 - July 2, 1986. A = Collector area ( m2) [41 Helferty, J. J., R. Fischl, P. R. Herczfeld, T. Brisbane, D, K. L = Collector length (m) Anand, \1. Sugisaka. 'On the Selection of Distributed Parameter W Collector width (m) Models for Control Studies of Solar Energy Systems,' Proc.of the F' Collector geometry efficiency factor 1987 ASlHE-JSME-JSES Solar Energy Conference, Honolulu, UL Overall collector heat Joss coefficient (kg/m2 °c -sec) Hawaii, March 22-27, 1987. Cc = Total collect0r thermal capacitance per unit area (kj/m2 °C) 15] Yu, T.K., and J. 1-1. Seinfeld. 'Observability of a Class of cp = Specific heat of collection fluid (kjlkg - oC) Hyperbolic Distributed Parameter Systems.'/.E.E.E. Trans. on Auto. (,a) Transmittance-absorption product Con1rol, Vol. AC-16, pp. 495-496, 1971. I 6 I m(t) = collector t1ow rate (litre/sec)· the control variable Thowson, A., and W.R. Perkins. ' Observability Conditions for J(t) = Solar radiation per unit area on a tilted collector plate (W/m.2) Two General Classes of Linear Flow Processes.' IE.EE. Trans. on Auto. Coniro/, Vol. AC-19, pp. 603-604, 1974. T (t) = Ambiem temperature (°C) 3 (7] Yu, T.K., J.H. Seinfeld, and W.H. Ray. 'Filtering in Nonlinear Time Delay Systems.' l.E.E.E. Trans. on Auto, Control, Vol. AC-19, pp. 324, 1974. [8] Sugisaka, M., R. Fischl, P.R. Herczfeld, P. Kalata, C. Rorres.' On Estimating the Fluid Temperature Profile in a Solar Collection System.' 12th PillSburgh Conf on Modeling and Simulation, 1981. [9] Seinfeld, J.H., G.R. Gavalas, and M. Hwang. 'Nonlinear Filtering in Distributed Parameter Systems', 1. Dyn. Syst., Meas .. Control, Vol 93D, pp. 157-163, 1971. APPENDIX A: THE ONE TEMPERATURE PLUG FLOW SOLAR COLLECTOR MODEL. The simplest distributed parameter model which describes the short term dynamics of the solar collector is Klein's One Temperature Plug-Flow (OTPF) model given by: WCc[iJT(x,t)lat] = WF(m)l(t) - cpm(t)[aT(x,t)lclx] · WF'UL(T(x,t) - Ta(tl) (A.l) subject to boundary and initial conditions: where T(x,t) is the fluid temperature profile across the collector, as a function of space and time, Tin(t) is the inlet fluid temperature at the collector inlet, and Tx(x) is the initial t1uid temperature profile across the collector at time t = lo· The other symbols used in Eq. (A. I) are explained at the end of this appendix. The OTPF model gives the rate of accumulation of internal energy of the fluid in terms of the rates of absorbed energy, energy gained by the t1uid, and energy losses which are given by the first, second and third terms on the right-hand side of Eq. (A.l), respectively, Eq. (A. I) can be rewritten as: aTf(x,t)/clt + u(t) [,ffr(x,t)/clx! + a Tf(x,t) = a V(t) (A.2) where a= (F'Ur,!Ccl, u = (cp'WCc)·m, and v(t) [(1:a/UL)l(t)+ T a(t)]. The parameter a is related to the thermal time constant of the collector, 'c• i.e. ,:c = 1/a. 1098 Page 718 PROTOTYPE TESTING OF MAGNETIC BEARINGS David P. Plant, Chaitanya P. Jayaraman, and David A. Frommer Research Assistants James A. Kirk and Davinder K. Anand Professors Mechanical Engineering Department University of Maryland College Park, MD 20742 Abstract and current sensitivity of the coils, Kr.[8,9] These parameters yield important performance infor- The work presented in this paper covers the mation such as the maximum weight capacity of the testing and evaluation of the performance of a magnetic bearing and the operating range under magnetic bearing assembly for flywheel energy which the system is stable. storage applications. A description of the experi- mental apparatus which collected the performance Theoretical formulation of the above parameters data is presented. It is shown that useful bearing have been developed at the University of 'Maryland. characteristics in the form of axi~l and passive Therefore there existed a need to verify the theory stiffness can be determined. The evaluation and with experiment. The goal that would be analysis of the performance data yielded important accomplished with the experimental performance data information explaining the variations between would be to bridge the gap between theory and theoretical expectations and experimental values. actuality. Resulting from this goal would be an improved understanding of magnetic bearings. Nomenclature Collection of Experimental Performance Data FA active radial force FI current force The determination of passive radial stiffness, Fx passive radial force active radial stiffness, and current force sen- KA active radial stiffness sitivity of the coils through experiment can be Kr current force sensitivity accomplished via an experimental apparatus deve- Kx passive radial stiffness loped by Frorrmer.[10-12] The experimental appara- tus is shown in Fig. 3. The strain ring is Introduction designed to be attached to the flywheel, via the mounting plate, to measure the resulting force upon An active pancake magnetic bearing succe_ssfully it. The rotor is free to move along the axis of developed at the University of Maryland is shown in measurement by mounting it to an aluminum plate Fig. 1.[1-4] "Pancake" refers to the sandwiching of which is free to slide on a set of linear bearings. permanent magnets between ferromagnetic plates. A The magnetic bearing is mounted to the stationary cross section of the bearing is shown in Fig. 2. portion of the system, along with accommodations The flux distribution from the permanent magnets, for relative displacement measurement. The test which support the bulk of the rotors weight is system is actuated by the lead screw attached b~t- shown in path A. Four electromagnetic coils are ween the strain ring and support bracket. It 1s located near the permanent magnets to control the used to move the mounting plate relative to the rotor about its unstable equilibrium point, i.e., magnetic bearing. The changing magnetic bearing the point at which the air gap is constant around force can be measured on the strain ring. The the stator. When the rotor displaces radially, the relative dis-placement of the plate and rotor is motion is sensed by a position transducer at the measured at the opposite end from the strain ring periphery of the rotor. The control system and is independent of the spring constant of the responds by sending a control current through the ring. The displacement is designed to be measured coils which results in an additional corrective with a eddy current proximity transducer. The eddy flux distribution (path B). This flux adds to the current transducer voltage output along with the permanent magnet flux on the large gap side and voltage output for the strain indicator yield the subtracts from the permanent magnet flux on the force versus displacement curves. In this case the small gap side. The net result is a corrective force versus displacement curves were displayed on force which moves the rotor back to the center an X-Y recorder. (nominal) position. An identical radial control system exists for the other orthogonal direction. The procedure for the experimental set up and The control in the axial direction is passive.[5-7] data collection for the passive radial stiffness, Kx, is as follows. First the magnetic bearing is The performance of a magnetic bearing can be bolted to the base fixture of the experimental characterized by a force versus displacement of the apparatus. Next the rotor is clamped to the mount- rotor (flywheel) relative to the stator (magnetic ing plate so that the iron return ring on the rotor bearing). This force results from magnetic flux is level in height with the magnetic bearing and produced by either the permanent magnets, electro- the magnetic bearing is centered with respe~t to magnetic coils, or a combination of the permanent the rotor, i.e., the gap between the magnetic magnets and electromagnetic coils. The ratio of bearing and rotor is a constant. By turning the these forces versus displacement of the rotor rela- actuating lead screw the rotor is displaced rela- tive to the stator can be classified as the passive tive to the magnetic bearing and force versus dis- radial stiffness, Kx, actiie radial stiffness, KA, placement curve is plotted on the X-Y recorder. A Page 719 variation of this experiment is to change the B) Current force sensitivity height level of the iron return ring on the rotor with respect to the magnetic bearing and record The current force sensitivity, K1 in lbs/inch, this height variation with the passive radial can be determined by making use of the family of stiffness. curves in figure 4. They represent the radial force exerted on the flywheel when a certain direct The experimental set up and data collection for current is applied to the control coils of the the active radial stiffness, KA, is very similar to bearing. K1 is the slope of the curve that is the experimental set up and data collection for the created by plotting the difference in the force, passive radial stiffness except for the following. F1, between the curves for non-zero current and The control system is active and power is supplied zero-current, with the current associated with each to the electromagnetic coils to provide control curve at zero displacement. The control coil restoring force, whereas the passive radial stiff- force, F1 v/s current curves for the 3" and the 4" ness measurement is performed with the control bearings are shown in Figure 5. system not active. The variations of the active radial stiffness include observing the effects of The curves show that a nonlinear relationship changing the control system gain and effects of exists between F1 and the current. Linearity varying the current saturation limit. The method (constant K1) occurred over a small range of the for changing the control system gain is simply current (+/-0.5 amps) after which it diminished in accomplished by varying the resistance level of a value. This nonlinearity is due to the saturation resistor in the control circuit. Variations of in the material in the control flux path. the current saturation limit are achieved by adjusting the power supply input voltage to the K1 for the 3" bearing was found to be around 5 power amplifiers of the control circuit. lbs/amp and about 10 lbs/amp for the 4" bearing. The procedure for extracting performance data Theoretical predictions for the K1 values were for the current force sensitivity of the coils, K1, almost three times the actual values. This discre- is quite different then for Kx and KA. The magne- pancy was mainly due to the saturation in the Ni-Fe tic bearing and flywheel are attached to the material at critical sections. A better and larger experimental apparatus in the same manner as for choice of flux paths further helped to close the the Kx and KA experiments. A power supply is gap between actual and theoretical predictions. directly connected to the electromagnetic coils and a bias current is fed to the coils. At each of the C) Active radial stiffness current levels the actuating lead screw of the experimental apparatus is turned so that the fly- The active radial stiffness, KA, describes the wheel is displaced relative to the magnetic bearing combined working of the bias flux and the control and these actions are recorded on the X-Y recorder. flux. KA in lbs/inch represents the slope of the From these plots a force versus current curve can curve of the active radial force FA v/s displace- be generated. K1 is the slope of the curve on the ment. force versus current plot. This curve may be thought of to be a combina- Analysis of Experimental Data tion of two curves, Fx v/s displacement and F1 v/s displacement as shown in the Figure 6. FA= F1-Fx A) Passive radial stiffness may then be plotted from these two curves. An identical curve may then be plotted by using the The passive radial stiffness, Kx, of the experimental apparatus with the magnetic bearing bearing may be obtained from a curve of the passive control system turned on. force (in the radial direction), Fx, v/s displace- ment of the rotor. The control system remains The resultant curve is nonlinear mainly due to inactive during this experiment. the nonlinearity of the F1 v/s displacement curve. F1 is affected by saturation in the Ni-Fe material Sample plots of radial passive force v/s and also by current limiting in the power ampli- displacement are shown in Figure 4. The slope of fiers found in the bearing's suspension control this graph in lb/inch, is the passive radial stiff- system. Repeated tests have shown that saturation ness, Kx, of the bearing. For the 3" and the 4" effects occur before the onset of current limit (rotor diameter) prototype bearings, Kx was found (for the 3" and 4" bearing). Figure 6 shows the to be constant over a fairly large range of the curve divided into 3 regions, the linear region, gap. It was therefore concluded that saturation the saturation region and the current limit region, did not occur in the flux path within this range The slope of the linear region gives the KA of the due to the permanent magnets since Ni-Fe saturation bearing. would have introduced nonlinearities in the Fx v/s displacement curves. It would be favorable to design magnetic bearings so that no saturation or current limiting The 3" (rotor diameter) bearing was found to occurs in the desired operating range so that the have a Kx of 950 lbs/inch and the 4" bearing had a complete system is linear. A larger linear range Kx of 1100 lbs/inch. The corresponding theoretical assures a larger range of controllability leading predictions for the 3" and the 4" bearings were to a more stable magnetic bearing. 1200 lbs/inch and 1800 lbs/inch. Further theoreti- cal investigation led to an introduction of more Conclusions and Recommendations extensive flux paths to account for leakage flux. The result of this was an acceptable correlation The extensive data obtained from the experimen- between actual and theoretical predictions. tal apparatus described in this paper resulted in improved understanding of the theoretical analyses. Page 720 The result of this is a design algorithm that pro- 8. Kirk, J.A., Anand, D.K., Vieira, R. and duces superior theoretical predictions. A highly Jayaraman, C.P., "Modeling and simulation of interactive design computer program is currently Magnetic Bearing Forces", Proceedings of the under development which will incorporate all of the 17th Annual Pittsburgh conference on Modelling improvements. and Simulation, Univ. of Pittsburgh, April 24-25, 1986, pps. 639-645. Continuing work includes the use of Vanadium Permendur which is a material with an extremely 9. Bangham, M.L., "Simulation and Design of a high saturation level (2.3 Teslas) as compared to Flywheel Magnetic Bearing", University of Nickel Iron {1.5 Teslas). Also the constraints Maryland, M.S. Thesis, Dec. 1985. of current limit is alleviated with an improved power amplifier system to provide adequate current 10. Anand, D.K., Kirk, J.A. and Frommer, D.A., to the electromagnetic coils. "Design Considerations for a Magnetically Suspended Flywheel system", Proceedings of the Acknowledgement 20th Intersociety Energy Conversion Engineering Conference, August 18-23, 1985, This work was supported, in part, under NASA Miami Beach, Florida, pps. 2.449-2.453. Grant NAG5-396. The helpful discussions with Ernie Rodriguez and Phil Studer of NASA/GSFC are appre- 11. Anand, D.K., Kirk, J.A. and Bangham, M.L., ciated. "Design, Analysis and Testing of a Magnetic Bearing for Flywhee 1 Energy Storage", ASME References Paper 85-WA/DE-8, presented at 1985 ASME Winter Annual Meeting. 1. Kirk, J.A., "Flywheel Energy Storage - Part I, Basic Concepts", International Journal of 12. Frommer, D.A., "Mechanical Design Mechanical Sciences, Vol. 19, 1977, pp. Considerations for a Magnetically Suspended 223-231. Flywheel", University of Maryland, M.S. Thesis, August 1986. 2. Kirk, J.A. and Studer, P.A., "Flywheel Energy Storage - Part II, Magnetically Suspended Superflywheel", International Journal of Mechanical Sciences, Vol. 19, 1977, pp. 233-245. 3. Kirk, J.A. and Huntington, R.A., "Energy Storage - An Interference Assembled Multiring Superflywheel", Proceedings of the 12th IECEC Conference, Washington, D.C., September 2, 1977, pp. 517-524. 4. Kirk, J.A. and Anand, D.K., et al., "Magnetically Suspended Flywheel System Study", NASA Conference Publication 2346, "An Assessment of Integrated Flywheel System Technology", Dec. 1984, pps. 307-328. 5. Evans, H.E. and Kirk, J.A., "Inertial Energy Storage Magnetically Levitated Ring-Rotor", Proceedings of the 20th Intersociety Energy Conversion Engineering Conference, August 18-23, 1985, Miami Beach, Florida, pps. 2.372-2.377. 6. Anand, D.K., Kirk, J.A., Zmood, R.B., et al., "System considerations for a Magnetically Suspended Flywheel", Proceedings of the 21st Intersociety Energy Conversion Engineering Conference, Aug. 25-29, 1986, San Diego, CA pps. 1829-1833. 7. Anand, D.K., Kirk, J.A. and Bangham, M.L., "Simulation, Design and Construction of a Flywheel Magnetic Bearing", ASME Paper 86-DET-41, Presented at the Design Engineering Technical conference, Columbus, Ohio, Oct. 5-8, 1986. Page 721 LYWHEEL Figure 1. Pancake Magnetic Bearing STATOR ROTOR NF NF Figure 2. Cross Section of Pancake Bearing Figure 3. Prototype Testing Apparatus Page 722 Fx@ 13 empa Fx@ 12 amp• Fx@ 11 emp• 't<:""--"'-:::-------_.,::""J.~--------..:::::,...,~~ ~~;;~~~~ENT (IN) Figure 4. Radial Force VS. Flywheel Displacement CURRENT FORCE VS CURRENT 5----------------------------- --------- .,..._.3· Bg. Kx= 950 IB/ in 4 ·---------, ·-·----"--------,,c'!'.---,,..c::::____ __ ;,1a---114" Bg. Kx=l!JOO IB/in i t'J 1 ---1 ~ 0 ___ j as-1./...--------i-----.....: ::___--I----------I--------I ~ 0-2 -5 -6./...------l-------+-------+-------1 -2 -1 0 CURRENT Figure 5. Coil Bias Force VS. Current BEARING LINEAR REGION SATURATION CURRENT LIMIT RADIAL REGION FORCE,Fa (LBS) Fa= Fl- Fx Fa FLYWHEEL CENTERED ~:._-----li---1-----J-_::::,,..,_ ___ _:FLYWHEEL POSITION DISPLACEMENT (IN) Figure 6. Restoring Forces VS. Flywheel Displacement Page 723 THE DESIGN OF A MAGNETIC BEARING FOR HIGH SPEED SHAFT DRIVEN APPLICATIONS R.B. Zmood, Senior Lecturer, Department o:f Electrical Engineering, Royal Melbourne Institute o:f Technology, Melbourne, Victoria, Australia D.K. Anand, Pro:fessor, J .A. Kirk, Pro:fessor, Department o:f Mechanical Engineering, University o:f Maryland, College Park, MD 20742, USA Abstract rotor position error is sensed by a transducer and its output is used to regulate the current in the control Because o:f their many unique attributes, windings o:f the bearing actuator. Active magnetic bearings are being developed :for bearings using electro-magnets (EM) alone both space and terrestial applications. or using permanent- and electro-magnets This paper describes work on an active (EM/PM) in combination have been electromagnet/permanent-magnet bearing :for constructed. a high speed sha:ft driven centri:fuge. The principles o:f operation o:f both the This paper describes recent work on an actuator and the bearing control system are act! ve radial EM/PM magnetic bearing ;for a described. Measurements o:f the high speed sha:ft driven centri:fuge. The experimental bearing static and dynamic principle o:f operation and test results :for per:formance are presented. The . the magnetic bearing actuator are di:f:ficulties experie·nced in achieving the presented. This is :followed by a speci:fied per:formance are discussed and the description o:f the bearing control system sources of these problems are suggested. together with results on the static per:formance when the sha:ft is not rotating. Di:f:ficulties experienced in stabilizing the control system and in achieving adequate Introduction closed loop static sti:ffness are examined and the source o:f these problems Magnetic bearings have unlimited 11:fe identi:fied. This led to modifications to expectancy and very low drag torques at the control system design, which high speeds. 'fhese characteristics have compromised the closed loop bandwidth, but encouraged their intensive development :for signi:ficantly improved the static space applications, over the last fifteen sti:f:fness. Finally the experience years [1J. In this :field, their use in obtained, when the motor was energized and flywheel energy storage systems and in rotation speeds up to 3000 rpm achieved, is satellite attitude control systems has been described. investigated by a number o:f researchers [2- 6J. Other unique attributes, including the ability to control the rota ting sha:ft Bearing Mechanical Con:figuration position, and to damp external vibrations have encouraged their consideration for use A sectioned view o:f the EM/PH radial in scienti:fic and industrial applications, magnetic bearing is shown in Fig. 1. The such as magnetic spindles :for high speed _design consists o:f a circular aluminium machining of' aluminium alloys [7,8J and housing which retains the touch-down turbomolecular vacuum pumps [9]. bearings at each end. The housing is split in the middle so that it may be separated Over the period that these devices have into two halves :for easy access to the been studied many different types have been. interior components. devised. These may be conveniently classi:fied into two main categories: The rotor shaft, which passes through the Passive magnetic bearings normally use the bearing housing, is fitted with a soft iron interaction between two permanent magnet, sleeve that brings its overall diameter to or in some cases constant- or alternating- approximately 30 mm. Two position current, :fields to establish stable transducers, o:f which the North-South (H-S) equilibrium points. In this case a one is shown, are located at right angles positive restoring :force is generated when to each other in the centre o:f the bearing the suspended part is displaced away :from structure by a cent·ral aluminium ring. The the equilibrium point. The second type is interior construction o:f the bearing the active magnetic bearing which generally consists of two mild-steel flux rings uses a closed loop :feedback system :for separated by a circular row o:f permanent controlling the position o:f the suspended magnets which £1 t into holes drilled in the shaft or rotor. In these bearings the ce.ntral ring. These permanent magnets Page 724 supply the magnetic bias flux necessary- :for relative air-gap, de-fined by e=x/g 0 • correct operation o:f the bearing. Fitted The e:f:fecti ve pole-:face · thicKness and radius is te£:f and R, respectively, and the armature radius is r. The air-gap ·flux density is B0 tesla, and. µ 0 :41fx1o-7 H/m. It will be noted :from the above equation that the -:force Fx(X) is a nonlinear :function o-:f the displacement x as shown in Fig. 3, E--W AXIS Fig, 1. Sectioned View of' Experimental Magnetic Bearing. to each f'lux ring are f'our mild steel pole pieces. These are wound with multi-turn coils to which the control current is Fig, 2. View o:f Magnetic Bearing Showing applied, Permanent Magnet and control Field Magnetic Flux Paths. The principle o:f operation o:f the actuator :for the N-S direction is illustrated in Fig. 2. The permanent magnet flux is Armature Force N 1600r-----------------~ uniformly distributed around the periphery o:f the air-gap with a typical path being shown by line '1', In the absence of' 1000 current in the control windings, the armature, assuming it is centred in the air-gap, will be in a state of' unstable 600 equilibrium. When the armature is displaced upwards, say, :from this position, an upward magnetic reluctance f'orce will be 0 exerted causing it to move :further in this direction, and in the absence o:f any restoring :forces it would ultimately -600 contact the touch-down bearings. I:f current is passed through tl1.e control windings then additional magnetic fluxes -1000 are generated along paths '2' and '3', where their directions are reversed i:f the current direction is reversed. It will be -1600 '-----'-------'-------'----...J observed, :for the :flux directions shown, -1 -0.6 0 0.6 that the fluxes in the air-gap at the top x/go combine additively while those at the bottom subtract. Since the magnetic Fig. 3. Actuator Static Spring Force. reluctance -force is proportional to the flux density squared it is easy to see that the net :force acting on the armature in It Can also be Shown that the-armature this case is upwards. Reversal o:f the :force is a linear :function o:f tl,e control control current will reverse the :flux current, 1, and -for small displacements, x, directions and the resultant net force. the total -force, Fx(X,i), is Analysis shows that the static force Fx(X) generated by the permanent magnet :field is given by where 1fB2t (RH') F (K) o eff K and 2 Boteff 8 i~0(Ncoi11+Ncoil2l(R+r) where x is the armature displacement, g0 is the average air-gap, and e is the go Page 725 The number o:f turns on the coils o:f the top ·to the current i=0.25 amp. This - e:ffect is . and bot tom pole pieces nearest the reader, attributable to the pole-:face flux· density in Fig. 1, are Mcoili and Ncoi12 B0 =0.3 T being considerably lower than respect! vely. The angle subtended at the expected. This is believed to be pole-:face is 20 , and t11.e remaining principally due to the magnitude of the 0 terms are as de:fined above. The linearity leakage :flux from the permanent magnets o:f the armature :force as a :function o:f the being greater than was assumed in the control current is a direct result o:f the design. :flux generated by the permanent magnets, and yields a high current sensitivity :for currents of small magnitude. This should Control System Description be compared with actuators not :fitted with permanent magnets where the :force is a non- The bearing is controlled by two uncoupled linear :function o:f current and the but identical control systems one of whose sensitivity is almost zero :for small block diagram is shown in Fig. 5. A currents. variable reluctance position sensor provides the radial pos! t!on of the shaft, Tl1.is signal is compared w! th an internal Actuator Test Results reference signal to give the pos! tion error, which is used to dr! ve a current A:fter assembly, the bearing actuator was ampli:fier that in turn feeds the associated mounted on a specially constructed test co':ltrol windings o:f the bearing actuator. rig, where the static armature :force as a As shown in the above :figure the control :function o:f its position and control system has been designed using an internal current was measured. The per:formance stabilization loop and an outer :feedback results :for the E-W axis are plotted in loop for stiffness control. The discussion Fig. 4- :for control currents varying in the below shows that this approach allows the range -0.75 to +0,75 amp. optim!za tion o:f both the transient performance and the static stiffness of the It will be observed :for zero control bearing. current that the variation in the armature :force as a :function o:f its position :follows In Fig. 5 the magnetic bearing actuator is a law similar to the one shown in Fig. 3. represented by an undamped mass-spring Tl1.e static sti:ffness, Kx, about the null system with a negative spring constant. position is seen to be 196 N/mm while the Consequently the actuator transfer function current sensitivity, K1, :for x=0.3 mm is has two real poles arranged symmetrically 175 N/amp. These should be compared with about the imaginary axis. As this system the design values o:f 300 N/mm and 184 N/amp is open loop unstable a lead compensator respectively. · has been used to stabilize the inner (stabilization) loop. It was found in the Armature force F (kgf) design studies that the optimum time 16 .--------------------, constant for the lead network was 0.0067 sec. Further analysis of the inner loop :feedback system showed that the closed loop 10 bandwidth was 90 Hz and the static stiffness was 1065 N/mm. As the design 0.75 objective was to reach a bandwidth of 400 5 0.5 Hz and a stiffness of 17500 N/mm the use of a simple lead compensator was deemed 0.25 unsa tis:factory. ---------------·· 0 0 .... ,, 1_1.e01_6Hi _e,eh_ +t + -6 e.e01m.+1t1,11+1 L£AI11UGC01!PENSATOR -0.7 LUII (OHP£HSAJOII POWER AIIP 1. ................................., BEARINGACtUA10R -10 -16 StAIUL12ATIOM LOOP 0 Q1 02 Q3 Q4 0.6 Armature position x (mm) J'OSIIIOMLOOP Fig. 4. Actuator Force vs Control Current as a Function of Armature Fig. 5. Magnetic Bearing Control System Position. E-W Axis. Block Diagram. It will be observed :for non-zero control Various means of improving the performance currents that the armature force versus of the actuator control system were pos! tion curves !ni ti ally follow the one considered. Of these, the add! tion of an :for zero current until the motion of the outer feedback loop seemed to offer the armature approaches its extremities, when clearest possib111 ties for improvement. To _they droop toward the values corresponding meet the requirements mentioned above it Page 726 was also found. necessary to use a lead/lag transient performance and static stiffness compensator in the outer (position) loop as could be achieved. shown in Fig. 5. The design studies showed that with this compensator and a loop Bearing Fitted to Centrifuge Drive Motor sensitivity K = 40 the bandwidth and static stiffness would . exceed 500 Hz and Following the above investigation the 20000 N/mm. A plot of the stiffness as a bearing was installed on the centrifuge · function of frequency for the bearing drive motor and a simulated centrifuge design is shown in Fig. 6. It will be rotor was fitted to the top of the noted that the bearing stiffness remains cantilever shaft which extended vertically constant at the static value for upwards from the top of the motor. frequencies up to about 10 rad/sec when it Initially the bearing control system was decreases to a minimum value at operated with the outer position loop 100 rad/sec. Above this frequency the disabled. apparent stiffness increases rapidly due to the shaft inertia. After adjustment of the stabilization loop gain, measurement of the closed loop frequency response indicated that there Control System Performance were three principal resonant modes at 20, 45, and 150 Hz. The lowest frequency Bearing Fitted to Test Rig corresponds to the first order bending mode of the cantilever shaft combined with the The bearing actuator was fitted to the same rotor mass. As shown in Reference 10 this test rig used for the static measurments, frequency also corresponds to the first but arranged to have a single degree of order critical speed of rotation of the freedom, and only one of the bearing motor. It is believed the other two control loops was activated at a time. frequencies correspond to mechanical Initially only the stabilization loop, in resonances of the non-rotating parts of the each case, was closed and its loop gain was motor. adjusted for good response to small scale disturbances. It was found that the bandwidth of the stabilization loop feedbacK systems were The response of the stabilization feedbacK approximately 90 Hz. With the same gain loop to sinusoidal inputs was settings the static stiffness in the E-W experimentally investigated, and it was and N-S direction were measured, and found found that the closed loop frequency to be 1400 and 1090 H/mm respect! vely, response had a number of resonances at which should be compared with the design frequencies in the range 120 to 500 Hz. value static stiffness of 1065 H/mm. Closer examination showed that these arose from structural resonances, and in After completion of the tests on the inner particular the one at 120 Hz was due to the loop the outer loops were closed with the first order bending mode of the test rig lead/lag compensators shown in Fig, 5 swinging beam to which the armature was present. It was found that both axes, of attached. the bearing control system, were unstable for all non-zero values of the loop gains. Attempts to close the outer loop and After experimentation with the transfer maintain stable operation with the lead/lag functions of the compensators they were compensator shown in Fig. 5 proved futile, replaced by integrators, and it was found for even small values of the loop that the loop gains could be easily sens! ti vi ty led to poor transient response. adjusted for good transient performance. With the lead/lag compensator replaced by a Frequency response measurements of the lag networK it was found that acceptable bearing control systems indicated however, that the closed loop bandwidth was reduced M 197 ----.-----.----..---~-----.-. to between 20 and 25 Hz. With the same a r (jw)/x(jw) loop gains the static stiffness of each g axis was measured, and, within the accuracy n i & Static stiffness : 55670 HIMM of the measurement technique, was found to ~ be infinite. In addition, the pullout 106 i,,----+----+----1----1-----.'-< d forces for the E-W and H-S axes were measured to be 6.37 and 6.27 Kg respectively. Once the tuning of the control loops, and the testing described above, was completed the centrifuge motor was satisfactorily run at speeds up to 3000 rpm. This meant that the centrifuge was able to successfully 104 traverse the critical speeds at 1000 and L.-J...J..1.J..U.W........L...1...1..L.1.U.U..-.L..J..U..J.J:Y,j....::Jc...UU.WW......J...J..J...U.WJ irl 100 101 102 103 104 2220 rpm, which correspond to the Frmencq (!'ad/m) principal resonant modes at 20 and 45 Hz. It was noted as the rotor traversed the Fig. 6. Magnetic Bearing Stiffness lower of t11.ese two speeds that the position Fn(Jw)/x(jw) as a transducer output developed a small Function of Excitation Frequency. Page 727 ampl! t ude ripple at the frequency corresponding to this speed. 8. M. Brunet, "Contribution of Active Magnetic Bearing Spindles to Very High Speed Machining", from High Speed Conclusions Machining, presented at ASME Winter Meeting, New Orleans, Louisiana, PED, A spindle EM/PM active magnetic bearing has Vol 12, Dec 9-14, 1984. been successfully demonstrated for a 9, ,Technical Literature: STP centrifuge at speeds up to 3000 rpm. ~~Turbomolecular Pumps, Edwards During the commissioning phase o:f this High Vacuum, England. bearing a number o:f problems were 10. T. Bevan, The Theory of Machines, encountered, both with the actuator and Longmans, Green and co Inc, New Yori<, its control system. While measures were talurs) THFN l:lley represent a straight bole A: POCKET-2 HAS THE FOLLOWING ATI'RIBUTES: - IT CONTAINS 5 SURFACES CODI: (SURFACE-7 SURFACE-8 SURFACE-9 SURFACE-to Recursively test the following condition: SURFACE- I I) (COND ( (AND (PARALLEL CIRCLE-I CIRCLE-]) - SURFACE-7 IS BOUND BY CONTOUR-7 (NEGATIVE PLANE) (EQUAL (RADIUS CIRCLE-I) (RADIUS CIRCLE-])) - REMAINING SURFACES (ODD-NUMBERS (CONTAINS CIRCLB-1)) (SURFACE-8 SURFACE-9 SURFACE- IO SURFACE- I I) (ODD-NUMBERS (CONTAINS CIRCI.B-J))) FORM ANOTHER CONTOUR NAMED CONTOUR- I I CT NIL)) - CONTOUR-11 REPRESENTS A POSITIVE PLANE THEREFORE, ACCORDING TO RUI.B P I, POCKET-2 IS A-POCm L---------------------- Figure 5. Representation code for a specific rule for holes Figure 6. Portions of a sample session with the intelligent feature extractor 240 Page 740 Dpto. de lngenieria Mecimica Avda. Reina Mercedes, sin E.T.S.1.1. Universidad de Sevilla // // Page 741 Monday Sep. 21, 10.30 -12.30 251 MACHINE AND SYSTEM DESIGN 3406 DESIGN OF ARTOBOLEVSKY'S LEVER-GEAR PISTON MECHANISM BY CURVE MATCHING T. E. Shoup 2614 MERIT PARAMETERS OF TRANSMISSION OF MECHANISMS DESIGN Hong-Liang Yin, Fu-Bang Wu 1511 DEVELOPMENT OF AUTOMATIC LET-OFF MECHANISM FOR SHUTTLE LOOM P. B. Jhala, S. R. Joshi 1510 HYPOTHESIS FOR QUANTITATIVE FUNCTIONAL ANO ECONOMIC TYPE SYNTHESIS FOR MECHANISMS H. T. Thorat, J. P. Modak 0413 EKSTREMALNYJ SINTEZ MEHANIZMOV K. C. Encev DESIGN AND ANALYSIS OF MAGNETIC BEARINGS D. K. Anand, J. A. Kirk, G. E. Rodrfguez, Ph. A. Studer Tuesday Sep. 22, 16.10-17.50 463 CONTROL SYSTEMS 0501 LOW COST ELECTRONIC FUEL CONTROL CONCEPT FOR SMALL GAS TURBINE ENGINES . T. Krepec, M. Krepec, A. I. Georgantas 2401 COMMENSURATE POSITIONING OF A STEPMOTOR ACTUATED STEWART PLATFORM G. P. Rathbun, G. R. Dunlop 415 TOOL PATH ERROR CONTROL FOR END MILLING OF MICROWAVE GUIDES D. K. Anand, J. A. Kirk, M. Anjanappa 3534 THE STOCHASTIC ANALYSIS OF 'MACHINES MAIN PARAMETERS FLUCTUATIONS N. Salenieks, V. Sergejev, G. Upitis 0419 MECHATRONICS M. S. Konstantinov, S. P. Patarinski, Z. M. Sotirov, L. G. Markov Thursday Sep. 17, 11.00-13.00 511 ROBOTS AND MANIPULATORS 0401 APPLICATION OF POINT MASS MODELS IN DYNAMICS OF ROBOTS P. I. Genova - 37 Page 742 ~(ili_ ~ ANALYSIS OF MAGNETIC BEARINGS Davinder K. Anand, Professor James A, Kirk, Professor Mechanical Engineering Department University of Maryland College Park, MD 29742 G. Ernest Rodriquez, Program Manager Philip A, Studer, Senior Engineer NASA/GSFC Greenbelt, MD 20771 The current research utilizes the approach of radially supporting a single rotor using permanent and electromagnetic in a parallel magnetic path, Static stabilization in all three translational coordinates is achieved via electromagnets that are driven by an error signal generated by radial position sensors, These sensors are located orthogonal to each other in order to obtain decoupling between motion in the x and y directions, The motor/generator is based on brushless DC-permanent magnet/ironless technology using electronic commutation, The system has been tested at over 9500 rpm with satisfactory results, The successful fabrication and testing of this has provided the necessary confidence to proceed to a larger size. More importantly it has indicated the necessity of controlling additional degrees of freedom in order to obtain stable dynamic suspension at higher rpm, A matrix of key technologies versus various prototype designs is presented to show the current status and emphasize future directions. Keywords: Energy storage, magnetic suspension, composite flywheel, brushless d.c. motors INTRODUCTION plates, The flux distribution from the permanent magnets support the bulk of the rotor weight. Four Magnetic bearings have many advantages over conven- electromagnetic coils are located•near the per- tional ball bearings and therefore present unique manent magnets to control the rotor about its opportunities in rotating machinery, Magnetic unstable equilibrium point, i.e., the point at suspension is particularly attractive in conjuction which the air gap is constant around the stator, with the use of high-strength composites for the When the rotor displaces radially, the motion is flywheel design (Anand, Kirk and Frommer, 1985; sensed by a position transducer at the periphery of Evans and Kirk, 1985; Kirk, Studer and Evans, 1976; the rotor. The control system responds by sending Kirk and Huntington, 1977; Kirk, 1977; Kirk and a control current through the coils which results Studer, 1977; Kirk, Anand, Evans and Rodriguez, in an additional corrective flux distribution, 1984; Kirk, Anand and Khan, 1985), Composites This flux adds to the permanent magnet flux on the allow the attainment of very high speeds and con- large gap side and subtracts from the permanent sequently high energy to weight ratios. The weight magnet flux on the small gap side, The net result penalty due to magnetic suspension is small since is a corrective force which moves the rotor back to the flywheel uses a relatively light flux return the center (nominal) position, An ldent1cal radial ring, which is a small fraction (typically 0.1 to control system exists for the orthogonal direction, 0,01) of the flywheel weight, The control in the axial direction is passive. A magnetically supported bearing could theoreti- cally have a reliable lifetime on the order.of 20 DESIGN OF A 300 WATT-HOUR MAGNETIC BEARING years. This extraordinary lifespan is attributed to the total elimination of bearing friction. The Design Considerations lifetime, in fact, should be governed only by the life of the control and motor electronics, The requirements for the 300 WH (108 kJ) energy storage system are given in Table l along with the Magnetic bearings have been considered for a wide simulation results, Geometrically, an ideal 300 WH variety of applications. Recently, magnetic (108 kJ) system should be as compact as possible, bearings have been considered for applications in thus the proposed system is a stack arrangement of supporting space telescopes, vibration damping, and two magnetic bearings similar to the prototype machine tools (Anand, Kirk and Anjanappa, 1986; shown in Fig. 3, Due to the 18 lb (80 N) rotor, Robinson, 1984; Studer, 1978), each bearing must carry 18 lbs, (80 N) for a factor of safety of two, The center section, between the The purpose of this work is to simulate the opera- two magnetic bearings, contains a high efficiency tion of a magnetic bearing, and apply the results ironless armature, electronically commutated of the simulation to the design and construction of motor/generator, The motor/generator system is a 300 WH (108 kJ) spokeless flywheel energy storage described in Anand, Kirk and Anjanappa (1985), system, Kirk, Studer and Evans (1976), Kirk and Studer (1977), and is not discussed further in this paper. BEARING CONFIGURATION It is assumed that, in general, the stack arrange- ment can be designed as two separate bearings, An active pancake magnetic bearing successfully This arrangement allows for the control of rocking developed at The University of Maryland is shown in motion by independently controlling the two radial Figs, l and 2. "Pancake" refers to the sandwiching control systems. In order to have the magnetic of permanent magnets (PM) between ferromagnetic bearing stack operate as required it is necessary Page 743 to include back up (touchdown) bearings in the presented and discussed. mechanical package. Figures 4-6 are the result of a typical design run The approach to designing the 300 WR (108 k.J) to determine the geometry of the 300 WR (108 kJ) system is to compute magnetic stiffness based upon design. Figure 4 lists a summary of the results permeance modeling. The detailed modeling of the and the parameters of the designs attempted. permeance are presented in Bangham (1985) and Figure 5 shows axial stiffness, the most critical Vieira (1985). The most important characteristic parameter for the design. It is so critical that is the total axial force carrying ability. Both all of the other parameters are of secondary impor- the maximum axial force, and the curve shape (axial tance. It was observed in earlier simulation runs force vs. displacement) are important parameters. that a 3 inch (76 mm) diameter system was of insuf- To prevent excessive sag, it is desireable to have ficient size to support an 18 lb (80 N) wheel with a large slope over lower displacements. Also, a a reasonable factor of safety. A 4 inch (101 mm) large peak axial force prevents the loss of suspen- stator is the smallest stator which can satisfac- sion under external and axial force overloads. torily support the desired weight. From Fig. 6 the maximum axial force is - 30 lbs (-133 N) and the The overall axial performance can be increased by axial stiffness over small displacements is 1667 altering a variety of parameters. The parameters lbs/in (292 N/mm). Due to symmetry the axial force which primarily affect the axial force in order of vs. displacement for each of the four separate importance are permanent magnet size, rotor and quadrants with no radial eccentricity is identical stator diameter, and pole face size. Increasing and each quadrant supports one-quarter of the total magnet size is the easiest method to increase the rotor weight. Figure 6 shows the axial stiffness axial force. However, magnet size is restricted by under a radial eccentricity of 0.003" (0.076 mm). saturation effects. Saturation can be tolerated to Quadrant 3 will not support as much weight as some extent, so long as it does no.t occur within quadrant 1. However, the increased weight carrying the range of radial motion; i.e., the range of ability of quadrant ,1 tends to cancel the effect of operation. The range of operation is not equiva- the decreased weight carrying ability of quadrant lent to the actual nominal air gap since the actual 3, and the effects are not seen in the resultant air gap is constrained by touchdown bearings to plot, Table l gives the recommended dimensions for prevent saturation and retain alignment. The the 300 WR (108 k.J) system based on many iterations operating range must be sufficiently large to allow similar to those performed above, the control system to correct for any external disturbances. Control System The total axial force is also altered by increasing the rotor and stator diameters. These dimensional The control system for stabilizing the magnetic changes create a larger pole face area, and thus bearing is shown in Fig. 7. Basically, an eddy facilitate the use of larger magnets without current transducer provides the radial position of causing saturation to occur prematurely. the flywheel, The transducer signal produces an error signal that drives a current thru four Increasing the pole face size similarly increases electromagnets. The magnetic flux of the electro- the bearing's ability to stall the occurrance of magnets adds on one side and subtracts the per- saturation. However, attention should be paid to manent magnetic flux on the other side, producing a the role of pole face area. As area is increased corrective differential force. The control system the flux density in the air gap will decrease. is a nonlinear bang-bang system and is discussed in Since the flux term is squared in the force detail in Bangham (1985), The governing equations equation, the overall force ·will decrease if the of the control system were analyzed using a program pole face area is increased without correspondingly called CONTRL, This was written specifically for increasing the magnet size. this application to study response and stability, Details are given in Bangham (1985). The system The beneficial effects of a large radial stiffness shown in Fig. 3 was fabricated, tested and used to is seen by perturbing the flywheel position and stabilize the magnetic bearing, introducing 6B from the control coil. The correc- tion force current about the nominal position is, Mechanical Design K = constant Based upon the MAGBER analysis and control system calculations, an envelope of allowable displacement Simplifying, for the magnetic bearing is defined. Typically, with the flywheel in the centered position, the F = 4K( 6B)B control system is capable of maintaining rotor sta- bility for up to ±0,008 in (±0.203 mm) of rotor This shows that a large radial flux (B) is benefi- displacement. The back up bearing configuration cial for providing a large correcting force. This shown in Fig. 3 is normally not in contact with is an important and somewhat unexpected point. A the rotor except when starting the system from large radial flux indicates the presence of a large rest. If the flywheel movement exceeds ±0.008 destabilizing force. However, the nature of the inches (±0,203 mm), then the back up bearings come control system is such that the destabilizing force into operation to limit flywheel excursions until is harnessed beneficially. The above procedure is the magnetic bearing re-establishes suspension of also applicable when the rotor is not in the cen- the flywheel. Conceptually, the back up bearings tered position. In this case the flux density will can be thought of as a pair of thrust bearings with not be equivalent on both sides of the rotor, and axial and radial clearances designed to allow for the resulting expression is more complex. the normal excursions of the flywheel (±0.008 inches (0.203 mm)]. The stationary portion of the bearing set is composed of two high precision ball Simulation Results bearings with fittings attached to their outer rings. These fittings are designed to mate with The program MAGBER was run over a wide range of rings attached to the flywheel, The axial separa- parameters of interest, The input values were tion of the ball bearing sets, as well as the axial obtained either by iteration, experience or con- and radial clearances between stationary and siderations discussed in the previous section. In rotating members, define the range of motion this section the final results of the design are through which the flywheel will move before mecha- Page 744 nical contact occurs, Alabama, Feb, 7-9, 1984. Geometric considerations require that the touchdown Kirk, J,A,, Anand, D,K, and Khan, A,A., "Rotor bearing sets should be separated by as large an Stresses in a Magnetically Suspended Flywheel axial spacing as possible, This locates the System", Proceedings of the .™ Intersociety bearings adjacent and between the magnetic Energy Conversion Engineering Conference, bearings. In addition, tthe rotating and non- August 18-23, 1985, Miami Beachg, Florida, pp, rotating portions of the flywheel should contact at 2.454-2,462. as large a diameter as possible, By locating the back up bearing sets adjacent to the magnetic Kirk, J,A., and Huntington, R,A,, "Energy bearings, making the contact diameter 3.005 inches Storage-An Interference Assembled Multiring (76,269 mm), and the axial and radial clearance Superflywheel", 12th Intersociety Energy Conv, gaps equal to 0,006 inches (0.152 UDU), the radial Engin. Conf., Aug, 28th-Sept, 5, 1977, motion of the flywheel at the suspension rings is pp.517-524, 0.008 inches (0,203 UDU), To avoid status of all key technologies is shown in Fig, 8, Kirk, J,A., and Studer, P.A., "Flywheel Energy Storage-II: Magnetically Suspended The back up mechanical package shown in Fig, 3 Superflywheel", Intl. J, Mech. Sci., Vol. 19, has been fabricated without the motor/generator and 1977, pp. 233-245. is currently undergoing testing, Kirk, J,A,, Studer, Philip A, and Evans, Harold E,, "Mechanic.al Capacitor", NASA TN I>-8185, CONCLUSIONS 1976. Results from the system parametric design, and the Robinson, A.A., "Magnetic Bearings-The Ultimate control system analysis, show that a 300 WR (108 Means of Support for Moving Parts in Space", k.J) energy storage flywheel can be built by incor- Spacecraft Tech. Dept,, ESA Tech. Directorate, porating characteristics of a previously built ESTEC, Noordwijk, Netherlands, magnetic bearing into a stack arrangement, The study also indicates that a method of reducing per- Studer, Philip A., "Magnetic Bearings for manent magnet unbalance must be incorporated; the Instruments in the Space Environment", NASA effects of nonlinearities, particularly those TM-78048,1978, leading to limit cycles, need further evaluation; capacitive, saturation, and hysteresis effects of Viei rs, Rogerio de Azeucdo, "Analysis of a the iron should be included in the model but Magnetic Bearing with Two Degrees of Freedom", avoided in the operating range of the bearing; and Masters Thesis, University of ·Maryland, College finally back up bearings are required to maintain Park, 1985. flywheel excursions in the linear operating range of the magnetic bearing control syste,n, Zusammenfassung: In dem hier beschriebenen Forschungs Projekt wird ein radial gelagerter Rotor mit Permanentmagnet und Electromsgneten parallel ACKNOWLEDGEMENT unterstutzt, Sstische Stabilitaet wird durch Electromagneten, welche durch radisle The work reported on in this paper has been spon- Positionssensoren kontrolliert wreden, erreicht, sored by the National Aeronautics and Space Der Motor/Generator bssiert suf dem burstenlosen Administration, Goddard Space Flight Center, under Gleichstrom-Permanentmsgnet-Prinzip, Das System grant NAGS-396, wurde bei uber 9500 Umdrehungen pro Minute zufriedenstellend getested, Eine Zussmmenstellung der wichtigsten Technologien mit verschiedenen REFERENCES Prototypensusfurungen ist dsrgestellt um den Stand der Entwicklung zu dokumentieren and zukunftige Anand, D,K,, Kirk, J,A. and Anjanappa, M., Enwicklungen aufzuzeigen, "Magnetic Bearing Spindles for Enhancing Tool Path Accuracy", Advanced Manufacturing Processes, Vol. 1, No. 2, April 1986. Anand, D,K,, Kirk, J,A. and Frommer, D,A,, "Design Considerations for a Magnetically Suspended Flywheel System", Proceedings ~ the 20th Intersociety Energy Conversion Engineecing Conference, August 18-23, 1985, Miami Beach, Florida, pp, 2,449-2,453, Bangham, M,L., "Simulation and Design of a Flywheel Magnetic Bearing", M,S, Thesis, University of Maryland, College Park, 1985, Evans, H,E., and Kirk, J ,A,, "Inertial Energy Storage Magnetically Levitated Ring-Rotor", Proceedings of ~ 20th Intersociety Energy Conversion Engineering Conference, August 18-23, 1985, Miami Beach, Florida. Kirk, J.A., "Flywheel Energy Storage-I: Basic Concepts", Int. J. Mech, Sci,, Vol. 19, 1977, pp. 223-231, Kirk, J.A., Anand, D,K,, Evans, H,E,, and Rodriguez, E.G., "Magnetically Suspended Fiyure l. Pancake Ma':Jnetic Bearin':;1 Flywheel System Study", Presented at the Integrated Flywheel Tech, 1984 Workshop, NASA Marshal Space Flight Center, Huntsville, Page 745 "~'""- ~-.---·r T I W' r" , -, b 02 0 0) 0 04 0 0~ 0 Of, Fig, s. Resultant Axial Stiffness/Radial Bias U Fig. 2. Exploded View of Stator for Pancake Bearing Fig. 6. Quadrant Axial Stiftness/ Radial Bias o.OU3 in :-~<;;-;.:;:,-.;.;;. . ~ I ' 'I I L ____ I _! fig, 3, Back up Bearing Arrangement for Stator-Stack F11ncUonal Bloek Diagram Fiy. 7. Functional Block Oiayram for Labordtory Table 1. Requirements for 300 WHR (108 kJ) Prototype Energy Storage System --------.-----,--,--,-,-,-----.-----,---, [>1(,001 ,OfQU0,0[ .. f>ll ,o,H •owt,o t0NIUWP110>1 l lncnUUIC.U 1 Q l Al [>If IIOY CONSU .. PllON SH.Cl OCSl~II l}tnchl ,,. 10 i,.,o flYWIH[l 0!"{1<5101< A[OUlll[ .. fNT '51.0TOiYPC 1...,1e-nu.llon O 111,,.,,.10111t .. ml (4 1nch Gellnr•bl,d .,.,<1.er .,., STAUlf SY'l{" Uly, as shown in Fig, 6. Y - cy(x)-cY(y)+cy(z)+ax•Z+Z[EX(x)+s:x(y)J-X•Ez(x) Analytical Model: The modeling of a three axis, flat Z - cz(x)-cz(y)Hz(z)-Y[ EX(x)+EX(y) J+X•Et(x) bed, vertical spindle CNC machining center (made up of links and joints) requires the simplifying assumptions shown below: The last column in equation 4, E, represents the 1. The machine table and the workpiece are assumed to actual position of the tool tip with respect to the be rigid bodies which are rigidly connected, table coordinate system after motions in the x, y and 2, The tool is assumed to be a point in space rigidly z directions of the respective slides, atached to the spindle nose, 3. Each carriage is for linear motion along one The error term is found by taking the vector direct ion only and there is a measuring device to difference between the commanded position and the measure its position, actual position arrived at, represented by the last column of equation 4, The machine tool-workpiece system is considered as a chain of linkages and this relationship can be Experimental Work: A careful inspection of (4) shows described using homogeneous coordinate transformation that the error vector is composed of 18 individual matrices, The correlation of the error terms require error components, In order to prepare an error map at the measurement of the error terms to be made with any location in the work zone all the 18 error terms respect to the same reference system. The machine must be measured. These error terms were grouped consists of three linear carriages viz. longitudinal, together as linear, angular, straightness and square- transverse and vertical, ness. The nominal tool position is selected as the The accuracy and repeatability of the measurement reference point. Four orthogonal coordinate systems system and the machining center is important for error Page 754 correction. To measure the above error terms a commands, disturbances and noise. Hewlett-Packard 5528A laser measurement system was 3. Robustness: stability and performance maintained in used. This system is specificallly designed to the presence of model uncertainties. measure all the above error terms, except the roll about the motion axis, very accurately in a machine Classical control theory with such design tools as tool environment [10], Nyquist criteria, Bode plots and root locus, has many methods available to determine performance robustness. All the "linear measurements", ox(x), oy(y) and Doyle and Stein [11] have shown however, that these oz(z), were obtained using a linear interferometer and methods can fail to provide adequate robustness retroreflectors. margins. The "angular measurements" , cy(x), e:x(y), e:z(x), Modern state space system analysis, including the e:z(y), was obtained using a similar setup. linear quadratic Gaussian (LQG) [12] control design methodology, have provided a strong theoretical foun- The "straightness measurements" , oy(x), oz(x), dation for modern analysis. However, there has been a ox(y), oz(y), ax(z), and oy(z), were done with the considerable gap between theory and practice, in straightness interferometer and the straightness situations such as determination of quadratic cost reflector. functions. The "squareness measurements", ax, ey, and oz, Reassement of the LQG quadratic cost function were carried out using an optical square. using Singular Value Decomposition (SVD) analysis allows frequency domain Multi-Input Multi-Output For all the above experiments, care was taken to (MIMO) loop shaping and removes the excessive number attain thermal stability by collecting all the data of free parameters (weights). This forms the basis of after the machine and environment temperature were LQG loop transfer recovery (LQG/LTR) as developed by stable. In addition, the experiments were conducted Doyle and Stein [13]. Application of SVD analysis to at various machine feedrates so that the effect of model uncertainties by Lehtomaki et al [14,15] allows machine motion on the above errors [i.e. dynamic guaranteed (stability) robustness. A number of deterministic errors] could be obtained. theoretial LQG/LTR designs have been reported cen- tering on vehicle control, gas turbine control and Error Correction Methodologies: The strategy of tool process control. path error correction, for cutting force-independent deterministic errors, is based on nullifying the Pole placement (assignment) techniques have effect of the error itself by algebraic summation of recently been extended to include robustness [16]. the programmed position input with the output of the Davison, et al [17,18] have proposed a multivariable process model. robust servomechanism methodology based on minimiza- tion of a given quadratic performance index subject to Two methodologies of implementing the above stra- arbitrary constraints. tegy are discussed in this paper and are shown in Fig. 8. In path-A, the M&G machine tool motion codes are Controller Development, Numerous metal cutting modified before feeding into the machine controller, control strategies have been employed to provide and all the correction is achieved by attaining constant tool life, constant cutting force, tool path machine tool table movements only. In path-B, the error reduction and chatter suppression. For best error correction is superimpos.ed over the nominal results a systems approach should be taken. table movements by taking advantage of magnetic Concurrently, much fundamental progress has been made bearing spindle technology. In the later approach all in the development of useful, robust, mul.tivariable the errors are corrected by the incremental transla- control system design methodologies and tools, This tional and tilt movements of the spindle rotor within research effort includes the synthesis of recent the air gap. theoretical developments with traditional milling pro- cess control experience. System identification will The error correction via table movement method be required to experimentally determine the machine (path-A) is currently near completion and the results dynamics. It is proposed that analysis, design and will be reported in detailed paper shortly. simulation of the milling system will be performed in an integrated, VAX based, simulation and Computer An expert system is being developed as part of the Aided Control System Design (CACSD) environment. The methodology in following path-A [9]. Included in this control system will be implemented and validated using expert system are provisions to produce the required high performance microprocessor technology. information which is needed to implement the methodo- logy for path-B. The methdology following path-B will CONCLUSIONS: A theoretical methodology has been deve- be implemented as soon as the magnetic spindle faci- loped to show that the cutting force independent posi- lity becomes operational. This methdology of tioning errors, for a CNC vertical machining center, correcting errors by spindle movements, when consist of 18 error terms, These 18 error terms completed, will overcome the restriction placed on the depend only on the position of the cutting tool in the table movement methodology. The table movement metho- tool working volume and these errors are both dology assumes the point of cutting is just a point repeatable and measurable, using a Hewlett-Packard and has no orientation requirements. However, in Laser metrology system. After measurement the errors practice such as end milling, the orientation of the are prepared in a matrix look-up talbe, termed as tool is very important. This can very eas!ly be error map. corrected for, via path-B, since the spindle rotor can be both tilted and translated. Two methodologies of implementing the error map for correcting cutting force independent tool path ROBUST CONTROLLER TO MINIMIZE TOOL PATH ERROR: A errors have been presented. The first error correc- systematic approach to develop and build a robust tion methodology intercepts the control codes to the controller to minimize tool path errors is under machine tool controller and corrects them per the progress. Following is a brief discussion of the information stored in the error map, The second error approach taken. correction methodology uses tilt and translation of the magnetic bearing spindle to perform real time Literature Survey. The objectives of feedback control error correction. An approach to develop a robust systems can be summarized as [11]: controller has been identified and work is proceeding. This controller will handle the magnetic spindle error 1. Stability: bounded inputs generate bounded outputs. correction methodology as outlined in the paper. 2. Performance: small errors in the presence of input Page 755 ACKNOWLEDGEMENT: The research work reported in this Annual Allerton Conference on Communication, paper represents a cooperative activity of the person- Control, and Computing, October 1978. nel from the University of Maryland, the National Bureau of Standards, the Westinghouse Corporation and 17. "The Robust Control of a Servomechanism Problem Magnetic Bearing, Inc. This work has been supported for Linear Time-Invariant Multivariable Systems," by the National Science Foundation through grant Davison, E.J., IEEE Transactions, Vol. AC-21-34, NSF 8516218 and was partly supported by NSF grant February, 1976. CDR 8500108 through The Systems Research Center. 18. "The Design of Controllers for the Multivariable REFERENCES Robust Servomechanism Problem Using Parameter Optimization Methods," Davison, E.J., Ferguson, 1. "Magnetic Bearing Spindles for Enchancing Tool I.J., IEEE Transactions, Vol. AC-26, PP• 93-110, Path Accuracy," Anand, D. K., Kirk, J .A., February 1981. Anjanappa, M., Advanced Manufacturing Processes, Vol. 1, pp. 245-268, 1986. 2. "Magnetic Bearing Spindle Control in Machining," Kirk, J.A., Anand, D.K., Anjanappa, M., Proceedings of 13th Conference on Manufacturin_g_ Research and Technology, November 1986. 3. "Tool Path Error Control in Thin Rib Machining," Anjanappa, M., Kirk, J.A., Anand, D.K., Proceedings of 15th NAMRC, pp. 485-492, May 1987. 4. "Three Dimensional Metrology," Hocken, R., Simpson, J.A., et. al., Annals of the CIRP, 26/2, 1977. 5. "The Automated Manufacturing Research Facility of the National Bureau of Standards," Simpson, J.A., r--- .940 REF-, Hocken, R.J., Albus, J.S., Jour. of Manufacturing lr-----,900+.001--------jf- .020•.002 I System, Vol. 1, 1982. L~ ~ . ~o•.001 ~ 1t I 6. "Statistical Analysis of Positioning Error of a t.,09 .020+.002 CNC Milling Machine," Donmez, A., Liu, C.R., Section AA {All dimensions in inches) Barash, M., Mirski, F., Jour. of Manuf. Systems, Vol. 1, No. 1, pp. 33 , 1982. Fig, 1 Microwave Guide (Courtesy of 7. "A New On-Line Measurement System for Machine Westinghouse Corp.) Tool Errors," Ni, J., Wu, S.M., 15th NAMRC, Lehigh Univ., pp. 573-577, 1987. 8. "Technology of Machine Tools," MTTF, Vol. 5, 1980. CUTTING FORCE-INDEPENonn ERRORS CUTTING FORCE-INDUCED ERRORS 9. "Error Compensation for Accuracy EnhancemEPt [11 Precision Machining," Shyam, s., M.S. the,' University of Maryland, College Park, '"!'"st TYPE OF ERROR POSITION I THERMAL IW E I GIIT CUTTING FORCE Ii\:, ERROR DEFORMATION DEFORMATION DEFORMATION 1987. NATURE OF ERROR OETERtHNISTIC DETERMINISTIC STOCMASTIC 10. "5528A Laser Measurement System," User's Guide, FUNCTIOtlAL POSITION I TEMPERATURE 'MASS COMPLIANCE DEPTH OF CUT OEPENDEtlCY FEEORATE (T) (M) (k) PROCESS Hewlett-Packard. (P,f) DYNAMICS 11. The LQG/LTR Procedure for Multivariable Feedback Control Design," Stein, G., and Athans, M., IEEE Transactions, Vol. AC-32, pp. 105-114, February Fig.2 Tool Path Error Classification 1987. 12. "The Role and Use of the Stochastic Linear- Quadratic-Gaussian Problem in Control System Design," Athans, M., IEEE Transactions, Vol. AC-16, pp. 529-552, December 1971. 13. "Multivariable Feedback Design: Concepts for a Classical/Modern Synthesis," Doyle, J.C. and Stein, G., IEEE Transactions, Vol. AC-26, No. 1, February 1981. 14. "Robustness Results in Linear-Quadratic Gaussian Based Multi variable Control Designs," Lehtomaki, W.A., Sandell, N.R., Athans, M., IEEE ·--.......~ Direct~on Transactions, Vol. AC-26, pp. 75-92, February of Motion 1981. Fig. 3 Linear carriage for X-Motion 15. Robustness and Modelling Error Characterization," Lehtomaki, N.A., et al, IEEE Transactions, Vol. AC-29, pp. 212-220, March 1984. 16. "On Robust Eigenvalue/Eigenvector Assignment," Seppo, P., Koivo, H., Proceedings Sixteenth Page 756 ""· '--·"-...Direction of Motion Fig. 4 Angular Errors Actual Position Fig. 7 Assignment of Coordinate Systems for a 3-Axis Vertical Machining Center 6x(x) Fig. 5 Linear Errors y H y , - Theoretical Y Axis I Motion Axis 'az y I X - Reference Axis I I X zi z z , - Theoretical z Axis I I z Motion Axis ay\ xy - Reference X-Y Plane I I xy z , z z - Theoretical Z-Axis I z Motion Axis I I '2x yx - Reference X-Y Plane I I yx Fig. 6 Non-Orthogonality of Axes Fig. 8 Two Methodologies of Implementation Page 757 AN ALliOR !THl1IC RELATIONSHIP BETI1EEN THE curnnG FORCE AIIO SURFACE TEXTURE IN MACHINrNG PROCESSES M, Anjanappa, Assistant Professor J.A. Kirk, Professor O.K. Anand, Professor t1ec11a11 i ca I Engineering Department University of Maryland, College Park, 110 20742 KEY\IOROS: r:utt i ng process dynatni cs, Surface texture, Model 1 i ng of cutting process, end r.ii 11 i ng AllSTRAcr optimal control design. Rakhit et al (7] in their model, for turning, included the affect of dynamics and showed Explicit Knowledge of the relationship between the that the re I at i onshi p between the probao list i c cutting cutting force and 5Urface texture generated, including force fluctuation and surface roughness along the lay is the effects of cutting process dynamics, will lea1 to linear. r.tore accurate modelling of ,:iachining processes. Tots could allow the material rei:ioval rate to be increased In this investigation, the cutting force and thereby ir.iproving the productivity. This paper presents resulting surface texture are considered to be r.iade-up of a nethod of establishing an algorithmic relationship bet- two components, consisting of a deterministic part due to ween the two parameters in r.iachining thin rib components. geometric and kinematic factors and a stochastic part where the dynamics of the cutting process are signifi- att:ri but able to dynamics. This paper focuses on tne cant. The relationship, represented hy a parameter latter high frequency components of cutting force and matrix, is develooed based on experir.iental ly obtained surface texture in developing a relationship between the data of thin rib r.iachining. This approach provides a two parameters. practical way of predicting the surface accuracy in thin rib r.iachining. STEAOY STATE CUTTING FORCE O!STR!BUT!mt !tlTROOUCTl Ofl The steady state theoretical cutting force equations for end r.ii 11 i ng operations are presented by n usty et al End r.ii 11 i ng, to produce th In rib coraponents, is one [8]. [n a similar manner consider the case of a thin rib of tile riajor operations in the electronic and aerospace machining under steady state conditions using an helical industries. Traditionally, the stock removal is achieved tooth end milling cutter, The length of cutting edge by taking several rough .cuts and one or more finish cuts that Is actually engaged in cutting varies and can he fror.1 d sol id block of r..aterial. The ,iumber of passes and classifiea into 3 zones. The length of cuttin9 edge hence ,:iachi ni ng cost depends on the dir.iens i ona l accuracy increases from n to 1:iaximum in zone A, stays at :'lilximun and surface finish. Components sucn as complex wave ! n zone B and tapers down to zero in zone C. rn add i - guides ano array plates, typically, have many free- tion, the cutting force at various points along the standing thin ribs, require tight tolerance, have odd length of the cutting e1i ng high fre- shape are considered as uncontrollable inputs. For a quency cutting force signal, was ocsigned and built usin'I cutting process which is linear, stationary and ergodic, Kistler 9067 quartz transducer. The natural frequency of the relationship between cutting force force and the sur- the force: dynarnometer in the x, y and z axis was found to face profile can be written as, be equal to 6500 Hz, 6800 Hz, 13,'iOO hz respectively. y(n) = !!(n) for all n £ LO, L) ( 3) The l'IOrkpiece was mounted on the ctynamometer platforr.i and the experiment was conduct en hy oo,m r:ii 11 i ng the where,!' (n) • cutting force vector [x x ] rough surface of the v10rkpiece with a high speed steel cutting force variation] 1 2 two flute t.e 1 i cal end mi 11 i ng cutter. y(n) • scaler uutput [surface profile height] K = system parameter matrix of appropriate dimen- 11,t: output of charge amplifiers representing the sion and units cutting force in x and y axis were recorder! on a magnetic L • workpiece length tape rerorder. The experimental resultant cutting force ot,ta1net1 hy tJown milling the specimen is shown in Fig. 4. Equation (3) is essentially a perturbation equation s i nee the cutting force and surf ace profile parameters Conparison of the theoretical and experimental plots are considered as perturbations over tne nonimal sho.m 111 Fig. 2 and 4 shows that the experimental pro- values. file, unlike tn~ theoretical profile, includes frequen- : i es other than the tooth passing fret1uency. The The system parameter matrix K must be obtained for experimental resultant cutting force 11as ft I tered through relating y and x. The approach taken in this paper is a ni 911 pass filter to remove the components of tne s i gna 1 to apply correlation techniques on the experimentally at frequencies of the fundamental tooth passing frequency obtained data. dnd lower. The resultant cutting force is further µro- cesseu tnrough a lo,i pass filter to r1:111ove high frequency Post multiply Eq. (3) by x'(n\ on both sides, and c.:.,:i;,onents oreater than 5,000 llz, wh1cn L chos1,n as the taking tile estimate of product variables, upper limit for Chi$ research. E (y !.' J = .:;! ( 4) lr,c r~sultar,T :utting forcr after tne filtering, ;1,. ..- ,,, in rig. ~. cr,,1tains hoth stochastic and hi911er urucr njr~onics of the tooth passing frequency and i\ where X • covariance of x(n) t>e1ny investigate1ncontrol l.1ble lnput~. The •incontrollable lnputs are error Jue to the assumption of linearity of the pro- represented as white noise input to the system. For cess, etc.. As a flrst approximation the rnagnltude of the purpose of this work, the cuttlng process ls the variance of \ (n) are chosen to be equal. The further assumed to be a linear, statlonary and ergodic actual magnitude-however, will be caluculated using the stochastic process. Tots assumption will be verified experimental data. With the above assumption, there later ln the paper. Figure 2 shows the block diagram are three unknowns whose values can now be obtained. of the system. The stochastic linear difference equation of the cutting process ls written as, Now consider the output Eq, (2), which when post multiplied by x'(n) and taking the estimate of product !,(n+l) • Ax(n) + !!_u(n) + ~(n) (l) vsrlables yields, y(n) • Kx(n) for all n c (O,LI (2) E (y !,'} • KX (6) where,! (n) • state vector (2 x l) (cutting force where Xis covariance matrix of !!_(n), This estimate variation in pounds) can be-used to obtain K, u (n) • scalar input [feedrate variation ln inches per minute) Expelmental Evaluation ). (n) • white noise vector (2 x l) y (n) • scalar output [surface profile height) Cutting Force, The methodology developed for L • Length of the workpiece or duration of system parameter identification, calls for a data set cutting free of deterministic tool path errors, To attain this ~,!,!.•system parameter matrices of appropriate goal, care was taken to ensure either the absence or dimension and units compensation of determlnistlc tool path errors in all the ensuing experiments, All thin rib machining Equations (l) and (2) are essentially perturbation experiments were conducted on a low horse power Dyna equations since the state, control and output parame- CNC vertical milling machine by finish milling the thin ters can be considered as perturbations over the nomi- rib of the specimen to its final thickness as shown in nal values. The whlte nolse ls assumed to have zero Fig, 3, The feed rates are varied from 0.5 inch per mean and that it ls uncorrelated. Also we assume that minute (ipm) to 1,5 1pm while maintaining other cutting the cutting force variation from the nominal value ls parameters as listed in Table l, The nominal feed rate zero mean. The assumption of zero mean of state vector of 1 1pm was chosen based on the past experience with ls not a llmitatlon for the proposed procedure. the machine, A specially designed and built high fre- quency force dynamometer ls used to obtain the three In order to use Eq. (l) and (2) for compensatory orthogonal force components, The x and y axis cutting control, the system parameter matrices A, B, and K must force signals were recorded on a magnetic tape be obtained. The approach taken in thie paper is-to recorder, apply correalation techniques on experimentally obtained data. TABLE 1 THIN RIB MACHINING PARAMETERS Noting that the white noise is uncorrelated to either x(n) or u(n) and that u(n) is deterministic, the state equation can be expressed as, l, Axial depth of cut 'd ' 0,15 in, (3,81mm) X •A-X- -A' + -B U B' + r (3) 2, Radial depth of cut •9 ' 0,02 in, (,508mm) 3, Diameter of cutter 'd f 3/16 in, (4,7625mm) where, X, U and r represent the covariance matrices of 4, Tool material c High Speed Steel !_(n), u(n) and ~(n) 5, Number of flutes 'z' ,2 6, Helix angle 'fl' 300(Rlght Hand) Similarly, the post nultlpllcatlon of Eq. (1) with 7, Spindle speed 'N' 5600 rpm its transpose yields, 8. Nominal feed rate 'f' 1,0 ipm (25,4mm) 9. Feed per tooth 'ft' 0,00009 ipt (,0023 _!(p) • AX(p+l) for p • 0,1,,,P, (4) mm) 10 Work piece material AL 6061T6 where, X(p) ia the autocorrelation of x(n) and p la the 11, Type of machining Down milling number of discrete steps required before the correla- 12 Coolant used None tion function goes to zero, By defining, (5) Figure 3 also shows the schematic diagram of the the coefficients of A can be obtained by least square experimental setup used for cutting force data genera- fltt ing, tion and further signal processing, Further the x and y axis cutting force signals were fed through a low Equation (3) now has four unknowns which la more pass filter followed by a high pass fllter into the than the number of unique equations, In situations digitizer, The digitizer ls a 'CDC Cambridge' data like these, the normal practice la to select the GJSgnl- acquisition system fitted with a 'Cipher' magnetic tude of white noise intensity matrix, Since there la digital tape recorder and a 16 channel, 12 bit analog no generally acceptable procedure available, the judi- to digital converter, cious choice depends on the designers past experience and understanding of the physical problem at hand, A digitization rate of 10,000 samples per second Some of the factors that need to be considered in such was chosen since the maximum frequency of interest la a selection are, the bandwidth of noise, the modeling about 5,000 Hz, To aid in synchronization of cutting 16 Page 774 force sl~nal~ ·.1lth ~urf:tce profile ~lgnals, the flnal that the data ls not purely random. lt ls~ combina- 20 seconds ,if d!lt.l was JLgltlzeJ, The falling edge of tion of periodic slnusldal wave ,md r,rndom sl3nals, cutting force q[gnals and the f3lling edge of surf3ce From the definition of [71 it c:in be loosely called prof Lle signal 'Jas used as the reference point for stochastic, The presence of periodic signal l, due to synchronlzatlon purposes. The magnetic tape contalnlng the high order harmonics of tooth passing frequency the dlgltal data of cutting force Ln blocked format Ls after filtering only the fundamental tooth passing fre- then r.1ounted on UNIVAC 1190 for use wlth system Lden- quency, This work ls intended to hlghllght the role 50%). Penning- volved in the cycle. The degree of rigor desired in ton's[17] data was obtained by the "direct static the analysis dictates the range of the required ther- method" which involves the direct measurement of modynamic properties and the accuracy needed. At vapor pressures. Greely[l9] and McNeely[20] used the minimum, the equilibrium properties, either in the "dew-point" method in conjunction with steam tabulations or in the form of correlations, must be tables. available. For a more careful and detailed analysis, the effect of hardware configuration must be in- Enthalpy data cluded and the knowledge of some transport prop- The data on the heat of dilution for aqueous LiBr erties, i.e. viscosity and thermal conductivity, were published by Lange and Schwartz[21]. Some might be necessary. Fortunately, the transport data also appeared in a NBS circular[14]. The latter properties are not needed for simple first and sec- source was used by the authors of the IGT bulle- ond law analyses of an absorption cycle. tin[ll] to establish h-T-x charts for aqueous-LiBr The most desirable way to include the thermo- solutions. In order to develop various isotherms, dynamic properties of a substance would be the for- they made use of the isobaric heat capacity pre- mulation of a fundamental equation in any one of sented in the International Critical Tables[l6] and the four standard forms. An equivalent represen- a private communication obtained from Pennington tation would be an equation of state together with at Carrier Corp. ideal-gas state properties. Both the formulations In 1939, Haltenberger[22] outlined a method to have the advantage of built-in thermodynamic con- estimate the heat of dilution from P-T-x data. When sistency. For water substance, such fundamental McNeely[l2] presented his Duhring charts, he used equations exist and are internationally agreed upon. a similar procedure to verify the values reported by Unfortunately, for the aqueous solutions of LiBr, Lange and Schwartz[20]. He made use of the iso- there are no such widely accepted formulations. baric heat capacity data reported by Loewer[13] to The thermodynamic properties of ammonia- establish isotherms in the h-x plane. These are the water systems have been investigated in detail and most recent enthalpy values currently in use for the results are reported[l, 2, 4-10]. Among these, aqueous LiBr. the data reported by IGT[ 4] contain the most recent information. The only source of entropy tables is a Entropy data paper by Scatchard et al.[5]. Currently, the only available source of aqueous- The properties of aqueous-LiBr solutions, ear- LiBr entropy data is the doctoral thesis of lier available in scattered form, were compiled to- Loewer[13]. For the purposes of our analysis, these gether in an IGT report[ll]. Some of this data was were recalculated. The reasons for these recalcu- published by ASHRAE[3] and later updated by lations and the procedure that was used is detailed McNeely[12]. The latter is considered to be the in the next section. most current data. Some entropy tables for LiBr- water solutions have been calculated by Loewer[13]. These will be discussed in greater de- 3. ENTROPY CALCULATIONS FOR AQUEOUS LiBr tail in the next section. Some additional thermo- SOLUTIONS dynamic property data are available in an NBS cir- cular[l 4], in Lewis and Randall[15] and in From the point of view of thermodynamic com- International Critical Tables[16]. patibility, the best way to estimate the specific en- For aqueous LiBr, or, for any binary solution tropy of a substance is to use a fundamental equa- with only one volatile constituent (here, water), the tion. Unfortunately, fundamental equations are not measurement of the vapor pressure is the key to the available for the aqueous solutions of LiBr and an evaluation of thermodynamic properties. alternative must be found. A particularly desirable Page 783 Absorption machine irreversibility 245 method would be one making use of the available vapor to the fugacity in pure water state P-T-x data and compatible enthalpy data for each solution. (13) The range of concentration of the LiBr solutions which is encountered in practical absorption cycles However, in the range of pressures encountered can be as high as 0.6-0. 7 fraction basis. This is by the fugacity can be replaced by the absolute pres- no means a dilute solution. Consequently, the equa- sure tions for diluted solutions may not be applicable. The procedure to calculate the specific entropy (14) of aqueous-LiBr salts by making use of available property data is outlined in this section. From first The value of 'Y ± has been investigated earlier. It principles, and using the relations for the Gibbs' is related to the activity a2 of the solute as follows: free energy and Helmholtz function for binary sys- tems, the entropy of an aqueous solution can be derived as For a binary solution, the two activities a 1 and li 1 (ah) (av) a2 are not independent but related by the Gibbs-rt - - dT - LPt - dP T; T aT P,x P; aT P,x Dehem equation + R { (xf (In a 1 _ In a2 ) ctx} . () n1 d In a1 + n2 d In a2 = 0. (16) Jx, 7M 1 M2 This is strictly true when both the pressure and The data for the specific enthalpy of the solution the temperature are constant. However, for solu- and the relationships for its specific volume are tions, the pressure alone has little effect on the ac- available from McNeely[12] and IGT[l 1] and can tivity coefficient and constant temperature is a suf- be used to numerically evaluate the first two inte- ficient criterion for equation (16) to apply. grals. The last term on the right-hand side, how- Therefore, it is standard procedure (e.g. Robinson ever, is recognized as the entropy of mixing and Stokes[27]) to experimentally measure the ac- (As mix). The procedure for evaluating it is outlined tivity of one constituent (the solvent or solute) and in Rant[23], Bosnjakovic[24] and Haase[25]. It is estimate that of the other constituent by the Gibbs- also explained by Loewer[l3]. The principal steps Duhem equation. Thus, it is possible to estimate 'Y± are as follows: either by direct experiments (usually by measuring the potential of suitable cells with or without liquid Asmix = (1 - x)As1 + (8) junction) or, indirectly, by knowing the activity of XAS2, the solvent (which can be found either from the (1- vapor pressures or from changes in the freezing or As;= Riln a1), (9) boiling points). The vapor pressure, as stated earlier, can be S2 = s20 - 2R2 ln(m±'Y±) + c-2- _T i2-0) ' (10) either measured directly (the "direct static" method) or by successively passing it through des- S20 = lim S2, (11) iccants (the "dynamic" method) or by letting the x---->O solution come into equilibrium with a reference so- lution (the "isopiestic" method), among others. and, for ideal solutions At low concentrations, it is possible to theo- retically predict the activity coefficients of the sol- As= -R(n1 + n2) ute by the limiting law of Debye-Huckel (discussed in many books, including Lewis[15]). This is con- [x In x + (I - x) ln(l - x)]. (12) venient because the numerical integration of the Gibbs-Duhem equation is difficult for very low con- From the above, it is clear that in order to estimate centrations. At times, the 'Y± data from e.m.f. mea- the specific entropy of the aqueous LiBr, the spe- surements is used to overcome this difficulty in- cific entropies of the water (available from steam stead of the theoretical value. tables), of solid LiBr (available from Latimer[26] In 1947, Robinson and McCoach[28], published and the enthalpy data should all be known. In ad- data on the values of 'Y ± in the form of a technical dition, the "activity" a 1 of the water in the aqueous note. It was also published as part of a more com- solution and the "mean ionic activity coefficient" prehensive paper[29] in 1949 and later incorporated 'Y ± of the LiBr ions in the electrolytic solution must in their book published in 1958. These were the val- be known. ues used by Loewer[13] in calculations of entropy The "activity" a 1 of the solvent (water) can be values. expressed as the ratio of the fugacity of the water The above data on 'Y ± of aqueous LiBr were ob- Page 784 246 D. K. ANAND and B. KUMAR tained by using the Gibbs-Duhem equation on the c Results of property value calculations vapor-pressure data obtained from isopiestic mea- • Results of second law analyses. surements. The vapor pressures themselves were not reported directly. Results of property value calculations In order to maintain thermodynamic consis- As stated earlier, the only property value that tency, the activity coefficients 'Y ± of the solute needed to be recalculated for this work was the spe- should be measured from the same vapor-pressure cific entropy of the aqueous-LiBr solution. How- data that is used to estimate the activity of the sol- ever, it is necessary to incorporate the most recent vent. With this consideration, the most recent P-T-x data and the corresponding specific enthal- vapor-pressure values reported by McNeely[12] pies in order to obtain thermodynamically consis- were used in conjunction with the Gibbs-Duhem tent values of specific entropy. equation to recalculate the values of 'Y ± . Because The Duhring coefficients A and B supplied by the vapor pressures at lower concentration are not McNeely[12] were used to generate P-T-x equations significantly different as reported by different for this work. sources, the value of 'Y ± at the molality of 2 was McNeely[12] had used a method proposed by matched with that reported by Robinson and Haltenberger[22] to generate h-T,x data for McCoach[28]. (The authors had verified the value aqueous-LiBr solutions. This method is explained of 'Y ± at this concentration from ·other sources.) in detail in [12] and involves the use of the follow- While the actual results will be presented in the next ing: section it is sufficient to point out here that the re- • P-T-x data calculated values of 'Y ± differ significantly from • Clausius Clapeyron equation to obtain the latent those reported by Robinson et al.[27-29] and used heat of solution of aqueous LiBr by Loewer[l3], in his calculations. Therefore, it • Use of steam tables for water vapor data was considered necessary to recalculate the en- • Numerical integration of the partial enthalpy of tropy tables of aqueous LiBr by using the most re- water in solution, over the concentration range. cent P-T-x data, the most recent enthalpy data of In addition, the specific enthalpy of the solution McNeely[12] and the revised "I± data, in eqns (7)- at the base concentration (50% LiBr) is also re- (12). The results of these calculations are presented quired. McNeely provided a simplified table of in the next section. steam table equations and constants which are used here for the sake of consistency. The authors repeated the procedure suggested 4. RESULTS by Haltenberger[22] and explained by McNeely[12] The results of the analysis are presented as fol- and recalculated the h-T-x curves. The results are lows: given in Table 1 and also plotted in Fig. 1. The com- Table 1. h-T-x tables for aqueous-LiBr solutions s2ecific Enthal2ies of Agueous LiBr Solutions (Btu/lb) X T(°F) .oo .10 .20 .30 .35 .40 .45 .50 .55 .60 .65 .70 40.0 8.0 5.3 2.3 .o -.7 -.7 .3 3.5 10.2 21.8 60.0 27.9 22.2 16.8 12.4 10.8 10.0 10.3 12.8 18.9 29.7 80.0 47.9 39.4 31.6 25.2 22.9 21.3 20.9 22.8 28.3 38.4 100.0 67.9 56.6 46.6 38.3 35.1 32.8 31.7 33.0 37.9 47.4 120.0 87.8 73.9 61.8 51.6 47.6 44.5 42.8 43.5 47.7 56.5 69.2 140.0 107 .8 91.3 77.0 65.0 60.1 56.3 54.0 54.0 57.7 65.8 77.8 160.0 127.8 108. 7 92.3 78.4 72.7 68.2 65.2 64.6 67.6 75.1 86.4 180.0 147.8 126.1 107.8 91.9 85.4 80.1 76.4 75.2 77.6 84.4 95.1 200.0 167.7 143.3 123.0 105.4 98.1 92.l 87.7 85.9 87.6 93.7 103. 7 220.0 187.7 161.2 138.4 119.0 110.8 104.0 98.9 96.5 97.5 102 .9 112.2 123.4 240.0 207.7 178.8 154.0 132.6 123.6 116.0 110.2 107.1 107 .5 112.1 120. 7 131.4 260.0 227.7 196.5 169.7 146.4 136.6 128.1 121.5 117. 7 117 .3 121.3 129.1 139.2 280.0 247.7 214.5 185.6 160.5 149.6 140.4 132.9 128.3 127.2 130.3 137 .4 146.9 300.0 267.7 232.7 201.9 174.8 163.0 152.7 144.4 138.9 136.9 139.2 145.5 154.3 320.0 287.7 251.2 218.6 189.5 176. 7 165.4 156.0 149.5 146.5 147.9 153.3 161.3 340.0 307 .8 270.3 236.0 204.8 190.8 178.3 167.8 160.1 156.0 156.2 160.5 167.7 360.0 327.8 290.1 254.2 220.9 205.6 191.8 179.8 170. 7 165.2 154.1 167.2 173.4 380.0 348.0 310.8 273.7 238.0 221.3 205.8 192.2 181.3 174.1 171.3 172.9 177 .9 400.0 368.2 332.9 294.8 256.7 238.2 220.7 204.9 191. 9 182.6 177. 7 177 .4 180.9 Page 785 Absorption machine irreversibility 247 Specific Enthalpy of Aqueous-Li Br (Btu/lb) 400 300 200 T("F) h 400 (Btu/lb) 320 240 100 160 80 40 0 -100 -200 0 0·2 0-4 0·6 0·8 1·00 - X ( Fractional Concentrotrotion of Lithium Bromide) Fig. 1. Enthalopy plots for aqueous-LiBr solutions. parison between this data and McNeely's val- The computer algorithm created from the above ues[12] will be discussed in the next section. procedure was used to generate the tables of spe- The authors carried out the numerical integra- cific entropy over the temperature range of 0-130°C tion of the Gibbs-Duhem equation on the P-T-x data and the concentration range of 0-70% LiBr. The based on Duhring constants to generate the activity results are shown in Table 3 and also plotted in Fig- coefficient of LiBr. Above the molality of 1.8, the ure 4. P-T-x data of McNeely are used. Below that value, the osmotic coefficients measured by Robinson and Results of second law analysis McCoach[28] yielded the P-T-x data. The calcu- The equations presented in the previous section lated values of the activity coefficients (at 25°C), were used to calculate the results detailed in Tables along with the values reported by Robinson and 4-8. McCoach[28] are presented in Table 2. This com- Table 5 shows the values of the mass flow rates parison is plotted in Fig. 2. and the thermodynamic properties (temperature, The procedure for enthalpy calculations dis- enthalpy and entropy) at various stages of the single cussed in detail in Loewer[13] was then carried out effect LiBr/water absorption cycle. A schematic to recalculate the specific entropy values of diagram of the corresponding single effect cycle is aqueous LiBr. For this purpose, the P-T-x and h- shown in Fig. 5. The sink temperature of 45°F is T-x data based on the Duhring charts and the re- selected to match with the lowest temperature in calculated activity coefficients were used. A com- the cycle (evaporator temperature). Table 6 shows parison of the specific entropy (at 25°C) with the the values for the cases of a double effect LiBr/ values reported by Loewer[l3] is shown in Fig. 3. water cycle. The schematic diagram of the corre- Page 786 248 D. K. ANAND and B. KUMAR Table 2. Comparison of aqueous-LiBr activity coefficients at 25°C (77°F) (Comparison of the values reported by Robinson and McCoach [28] with values calculated from Gibbs-Duhem equation) Activity Coefficient (~±) Molality Robinson and Gibbs-Duhem m Mccoach (28] Equation 0.1 0.796 0.796 0.2 0.766 0.766 0.3 0.756 0.756 0.4 0.752 0.753 0.5 0.753 0.754 0.6 0.758 0.759 0.7 0.767 0.767 0.8 o. 777 0.778 0.9 0.789 0.790 1.0 0.803 0.804 1.2 0.837 0.838 1.4 0.874 0.875 1.6 0.917 0.917 1.8 0.964 0.965 2.0 1.015 1.015 2.5 1.161 1.282 3.0 1.341 1.469 3.5 1.584 1.752 4.0 1.897 2.062 4.5 2.28 2.465 5.0 2.74 2.89 6.0 3.92 4.34 7.0 5.76 6.46 8.0 8.61 9.40 9.0 12.92 13.85 10.0 19.92 21.57 11.0 31.0 33.70 12.0 46.3 50.11 13.0 70.6 74.59 14.0 104.7 107.1 15.0 146.0 149.6 16.0 198.0 200.3 17.0 260.0 260.0 18.0 331.0 328.1 19.0 411.0 398.0 20.0 485.0 474.0 Page 787 Absorption machine irreversibility 249 Activity Coefficient for Aqueous Li Br 6 5 4 - Gibbs Duh em Equation In (Y±) -e-- Robinson and Mc Coach [28] 3 2 O-+-----~----~----~---~-- 0 5 10 15 20 - m (molality) Fig. 2. Plots of aqueous-LiBr activity coefficients at 25°C (77°F). Page 788 250 D. K. ANAND and B. KUMAR Table 3. s-T-x tables for aqueous-LiBr solutions Specific Entropy _c,.!, Aqueous Li Br Solution (kCal/ky°C) T ---> (DEG. C) X .o 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 130.0 .0000 .8114 .8473 .8819 .9154 .9478 .9792 1.0096 1.0391 1.0678 1.0957 1. 1228 1.1492 1.1749 1. 2000 .0500 .7940 .8271 .8592 .8901 .9200 .9490 .9771 1.0044 1.0309 1.0567 1.0817 1. 1061 1.1299 1. 1530 .1000 .7719 .8028 .8325 .8613 .8891 .9160 .9422 .9675 .9921 1.0161 1.0393 1.0620 1.0841 1. 1056 .1500 .7468 .7755 .8032 .8299 .8558 .8809 .9052 .9288 .9517 .9740 .9956 1.0167 1.0373 1.0573 • 2000 • 7 208 .7475 .7732 .7981 .8222 .8455 .8682 .8901 .9114 .9322 .9523 .9719 .9911 1.0097 • 2500 .6932 .7181 .7420 .7652 .7876 .8093 .8304 .8508 .8707 .8899 .9087 .9270 .9448 .9621 .3000 .6642 .6874 .7097 .7313 .7522 .77 24 .7920 .8110 .8295 .8475 .8650 .8820 .8986 .9147 .3500 .6338 .6553 .6762 .6963 .7158 .7347 .7530 .7708 .7880 .8048 .8211 .8370 .8524 .8675 .4000 .6017 .6219 .6414 .6603 .6785 .6962 .7133 .7300 .7461 .7618 .7771 • 7920 .8065 .8206 .4500 .5683 .5873 .6057 .6 234 .6406 .657 2 .6733 .6889 • 7041 .7189 • 7332 • 747 2 .7608 .7741 .5000 .5346 .5525 .5697 .5864 .6026 .6182 .6333 .8481 .6623 .6762 .6897 .7029 .71~7 .7 282 .5500 .5025 .5192 .5354 .5510 .5661 .5008 .5949 .6887 .6 221 .6.351 .6478 .6681 .67 21 .6838 .6000 .4886 .5036 .5180 .5320 .5456 .5587 .5714 .5838 .5%9 .6076 .6198 .6301 .6409 .6500 .4861 .4990 .5114 .5235 .5352 .5466 .5577 .5684 .5789 .5891 .5991 .7000 .4880 .4987 .5091 .5192 .5 291 .5387 .5480 Table 4. Tabulation of LiBr/water absorption cycle parameters mhw 2,495 kg/hr (5,500 lb/hr) mew 2,720 kg/hr (6,000 lb/hr) mchw 1,633 kg/hr (3,600 lb/hr) UAgen 1,633 kCal/hr. °C (3,600 Btu/hr. °F) UACW 3,265 kCal/hr. °C (7,200 Btu/hr. °F) 0 UAchw 1,633 kCal/hr. c (3,600 Btu/hr. °F) TGEN 87.8°C (190°F), for single effect cycle 140.6°C (285°F) and 87.8°C (190°F) for double effect cycle TCUND 37 .8°C ( 100°F) TABS 37.8°C (100°F) TEVAP 7. 2°C (45°F) Effectiveness of all solution heat exchangers: 0.7 Page 789 Absorption machine irreversibility 251 1.0 Specific Entropy of Aqueous Li Br at 25°C - Recalculated ' --a.- Loewer Data[13J 0.8 ig' ' fJ ' s ( Btu) 0.6 lb°F ' ' n ' 's 0.4 0.2 0 0.2 0.4 0.6 0.8 1.0 X(Wt.froction of LiBr in aqueous solutions) Fig. 3. Plots of aqueous-LiBr specific entropies at 25°C (77°F). Table 5. Tabulations for a single effect LiBr/water cycle Summary of LiBr/Water Cycle (by section) -----------·----·---------- Section m T X h s b --------~-----------~------------------·--------- l 9.008 100.00 .55362 -71.51 ,560274 68.5634 2 9.008 100.00 .55362 -71.51 .560274 68,5634 3 9.008 151.00 .55362 -46.48 ,600576 71. 6409 4 8.008 190.00 .62275 -30.34 .575976 101. 1806 5 8.008 127.20 .62275 -58.49 .533836 95.9842 6 8.008 127.20 .62275 -58.49 .533836 95.9842 7 1.000 190.00 0 1145.74 2.861557 32.3046 8 1.000 100.00 0 67.68 .940697 0,537 10 1.000 45.00 0 67.68 .946228 -2.4759 11 l ,000 45.00 0 1080.90 2.953788 -82.7736 20 154.740 207.78 0 175.31 1. 116482 12.4169 21 154.740 199.24 0 166.78 1.103628 10.8885 22 168.808 80.21 0 47.93 .904767 0,3581 23 168.808 87 .66 0 55,36 ,918435 0.3441 24 168.808 94.04 0 61. 73 .930010 0.4082 25 101.285 60.82 0 28.57 .868258 0.8846 26 101.285 50.82 0 18.59 .848895 1.4516 ---------· ·----------·- m n:iass flow rate/refrigerant flow rate T temperature (°F) X weight fraction of LiBr h specific enthalpy (Btu/lb) after converting to IGT [11] datum s specific entropy (Btu/lb°F) b specific availability (Btu/lb) Page 790 252 D. K. ANAND and B. KUMAR Table 6. Tabulations for a double effect LiBr/water cycle Summary of LiBr/Water Cycle (by section) Section m T X h s b ------ 1 9,008 100.00 .55362 -71.51 .560274 68,5634 2 9.008 100.00 .55362 -71,51 .560274 68,5634 3 9.008 150.86 .55362 -46,48 .600575 71.6409 4 8.008 190.00 .62275 -30.34 ,575976 101. 1806 5 8.008 127.20 .62275 -58.49 .533836 95.9842 6 8.008 127.20 ,62275 -58.49 ,533836 95.9842 7 0,470 190.00 0 1145.74 2.861557 32,3046 8 1,000 100.00 0 67.68 ,940697 0,5370 10 1.000 45,00 0 67.68 .946228 -2.4759 11 1.000 45,00 0 1080.90 2,953783 -82, 7736 13 9,008 234.44 .55362 - 5.04 .660022 80.7007 14 8,479 285.00 ,58821 14,68 .662295 99.1826 15 8.479 190. 71 .58821 -29.35 .602809 87.5446 16 8.479 190.71 .58821 -29,36 .602809 87.5446 17 .530 285.00 0 1186.76 2,661273 182,4193 18 .530 190.00 0 158, 14 1.089532 9,9266 19 .530 100,00 0 158.14 1.102317 2,9626 20 154.740 295.74 0 263.22 1.240048 33.0205 21 154.740 290.58 0 258.06 1.233208 31.5863 22 168.808 84.65 0 52.35 .912932 0.3306 23 168.808 92.09 0 59,78 .926490 0,3756 24 168.808 95.38 0 63.06 .932415 0.4282 25 101.285 60.82 0 28.57 .862258 4.1528 26 101.285 50.82 0 18.59 .848895 1.4516 m mass flow rate/refrigerant flow rate T temperature (°F) X LiBr weight fraction h specific enthalpy (Btu/lb) after converting to IGT [11) datum s specific entropy (Btu/lb°F) b specific availability (Btu/lb) Table 7. Second law analysis results for a single effect LiBr/water cycle q !lb I Component kCal/kg kCal/kg kCal/kg (Btu/lb) (Btu/lb) (Btu/lb) Generator 734(1321) 109.6 (197.2) 22.7 (40.8) Condenser -599(-1078) -17.7 (-31.8) 10 (18.1) Evaporator 563(1013) -44.6 (-80.3) 14 (25.3) Absorber -698(-1257) -37.9 (-68.3) 38 (68,4) Solution Heat ±125(±225) -7.8 (-13,9) 7.8 (13.9) Exchanger Pump 0 0 0 Throttles 0 - 1.7 (-3) 1.7 (3) Total 0 0 94.2 (169) Page 791 Absorption machine irreversibility 253 Specif i c Entropy of A q u e o us Li Br So I u t ions 1-4 S 1·2 KCol) ( Kg°C 1·0 0·8 0·6 100 80 60 40 20 0·4 L----+----+-----+----+------+----+ 0 0.1 0.2 03 0.4 0.5 0.6 - X Fig. 4. Entropy plots for aqueous-LiBr solutions. Table 8. Second law analysis results for a double effect LiBr/water cycle q bb I Component kCal/kg kCal/kg kCal/kg (Btu/lb) (Btu/lb) (Btu/lb) Generator I 444(798) 117 (210.7) 6 (10.8) Generator II ±:_303(±:_545) -4.6 (-8.3) 4.5 (8.2) Condenser -308(-555) -9 (-16.2) 3.3 (6) Evaporator 563(1013) -44.6 (-80.3) 14 (25.3) Absorber -698(-1257) -37.9 (-68.3) 32.4 (58.2) Solution Heat ±:_125(±:_225) -9.4 (-17) 9.4 (16.9) Exchanger A Solution Heat ±:_207(±:_373) -7.7 (-13.9) 7.7 (13.9) Exchanger B Pump 0 0 0 Throttles 0 -3.7 (-6. 7) 3.7 (6. 7) Total 0 0 81.1 (146) Page 792 254 D. K. ANAND and B. KUMAR Tc -100 •p 14--+-....., TG-190"F VII eak Solution (3) Condenser (7) Generator m• w (3) Solution Heat EI changer (6) (2) TE-45•p TA-lOO"F Evaporator Absorber Fig. 5. Single effect LiBr/water absorption cycle. fc;1-211'5"F Generator- I Solution Heat Exchanger 'A' (8) Solution Heat Exchanger 'B' (6) ('5) m TE-45"F TA-IOO"F 1-1...-1....,. Evaporator Absorber Fig. 6. Double effect LiBr/water absorption cycle. Page 793 Absorption machine irreversibility 255 sponding double effect cycle appears in Fig. 6. Duhring equations[12] to calculate the values of all Cycle parameters are identified in Table 4. thermodynamic properties. Based on the property values of Tables 1 and 3, The values of the LiBr activity coefficients re- the second law analysis of a single effect LiBr/water ported by Robinson and McCoach[28] and those cycle is carried out and the results are shown in calculated by the authors are very close to each Table 7. As a check, the sum of individual heat in- other, but there is a systematic difference (Robin- puts, work outputs and the availability increases son's values are mostly lower than those calculated over individual components must add up to zero by the authors). Although the difference is small, (over the cycle) and they are seen to do that. The it can still add up during the process of numerical individual irreversibility values must be non-nega- integration which has to be done to calculate the tive, as is evidenced. specific entropy over a range of concentrations. Table 8 contains results analogous to Table 7, Consequently, a systematically higher value of so- except that the cycle is a double effect LiBr/water lution entropy is reported (as compared to the val- cycle. ues of Loewer[13]). However, the trend of entropy curves is quite similar to the results of Loewer. Because the values of specific entropy reported 5. DISCUSSIONS AND CONCLUSIONS here are based on one constant and the most recent P-T-x data, they will be useful for any future second The P-T-x curves from the Duhring constants law analyses involving aqueous-LiBr cycles. specified by McNeely[12] were successfully repro- duced in the calculation of the h-T-x data. Mc- Acknowledgements-The early part of this work was sup- Neely's enthalpy versus temperature curve at the ported by DOE Contract No. DE-AC03-79CS30204. Com- puter funds for this work were supported by the Computer base concentration (50% LiBr), over the tempera- Science Center at the University of Maryland. ture range of 0-180°C was also reproduced. The same procedure (including the simplified steam table equations), was used to obtain good compar- isons for the enthalpy of the solution over the 0- NOMENCLATURE 1400C temperature range. Above this temperature, a I solvent activity at concentrations away from the base concentration a 2 solute activity (50% LiBr), a significant difference was observed b availability (kcal/kg) between the solution enthalpy calculated and those b; availability of the "i"th incoming stream (kcal/ kg) reported by McNeely. The reason for this discrep- bj availability of the "}"th outgoing stream (kcal/ ancy is not known but it is suspected that the dif- kg) ferent schemes for numerical integration (graphical (!lb ls change in availability for cycle (kcal/kg) method based on 5% steps on the concentration cv control volume scale, as used by McNeely, versus digital computer f1 solvent fugacity (Pa) Ji solvent fugacity in pure state (Pa) program based on a 1% step on the concentration h general notation for enthalpy (kcal/kg) scale, as used by the authors) may be the cause. I general notation for irreversibility (kcal/kg) Fortunately, the range of temperature concentra- i2 partial molal enthalpy of solute (kcal/kmole) tion encountered for the first and second law anal- i20 partial molal enthalpy of solute at infinite dilu- tion (kcal/kmole) yses for the thermodynamic cycles here is such that m molality there is no significant difference in the solution en- 11lhw mass flow rate of hot water (kg/hr) thalpy from the two sources. mew mass flow rate of cooling water (kg/hr) In order to calculate the value of the specific 11lchw mass flow rate of chilled water (kg/hr) entropy of aqueous LiBr, it is useful to first cal- m ± mean ionic molality m; mass flow ratio for the ith material stream en- culate the enthalpy values, which were obtained tering the cycle from the Duhring plots of P-T-x curves, as dis- mj mass flow ratio for thejth material stream leav- cussed earlier. In addition, one also needs to know ing the cycle the activity coefficient of the salt for all concentra- n 1 number of solvent moles n2 number of solute moles tion at a given temperature. The activity coefficient P general notation for vapor pressure (Pa) is not independent of the P-T-x data and can be P 1 vapor pressure of solution (Pa) obtained from it by carrying out the numerical in- Pi vapor pressure for pure solvent (Pa) tegration of the Gibbs-Duhem equation. The en- Q heat input (kcal/kg) tropy values reported by Loewer[13] use the activ- qd differential heat of dilution (kcal/kmole) ity coefficient reported by Robinson and R universal gas constant (kcal/K kmole) R 1 gas constant for the solvent substance (kcal/K McCoach[28] which, in turn, was calculated by the kmole) use of the Gibbs-Duhem equation on their own P- Rz gas constant for the solute substance (kcal/K T-x data. In order to be consistent in the calculation kmole) of entropy, it is necessary that the same P-T-x data s general notation for entropy (kcal/K kg) sw specific entropy of water (kcal/K kg) be used both for the calculation of the enthalpy val- SLrnr specific entropy of LiBr (kcal/K kg) ues, as well as to obtain the activity coefficient. The s 20 partial molal entropy of LiBr at infinite dilution authors have consistently used the P-T-x data from (kcal/K kmole) Page 794 256 D. K. ANAND and B. KUMAR As mix entropy of mixing (kcaVK kg) 9. A. B. Stickney, Graphs help to solve ammonia ab- T temperature (K, cq sorption system problems. Ref. Eng. 54, 451-57 To ambient temperature (K, cc) (1947). TABS absorber temperature (cC) 10. B. E. Eakin and R. A. Macriss, ASHRAE Trans. 70, T coND condenser temprature (cC) 319-327 (1964). T EVAP evaporator temperature (cC) 11. Institute of Gas Technology, Research Bulletin 14, T GEN generator temperature (cC) The absorption cooling process. ITG, IIT, Technology UAcw heat transfer rate per unit temperature for the Center, August 1957. cooling water (kcal/hr cq 12. L. A. McNeeley, Thermodynamic properties of UAchw heat transfer rate per unit temperature for the aqueous solutions of lithium bromide. ASHRAE chilled water (kcal/hr °C) Trans. 85, 413-434 (1979). UAgen heat transfer rate per unit temperature for the 13. H. Loewer, Ph.D. thesis, University of Karlsruhe generator hot water (kcal/hr 0 C) (1960). w u useful work (kcal/kg) 14. NBS Circular No. 500. Wx useful work over cycle (kcal/kg) 15. G. N. Lewis and M. Randall, Thermodynamics. x concentration of LiBr (percent weight) McGraw-Hill, New York (1961). 'Y ± mean ionic activity coefficient 16. International Critical Tables. McGraw-Hill, New York (1929). REFERENCES 17. W. Pennington, Refrig. Eng. 63, 57-61 (1959). 18. ACG Data Book, A-10-5, Dow Chemical Co. 1. S. W. Briggs, Second law analysis of absorption re- 19. E. M. Greeley, Carrier Corporation Report (1959). frigeration. AGA and IGT Conference on Natural Gas 20. L. A. McNeely et al., Carrier Corporation Report Research and Technology, Chicago, 1971. (1964). 2. D. K. Anand, K. W. Lindler, S. Schweitzer and W. 21. E. Lange and E. Schwartz, Z. Physik Chem. 133, 129- J. Kennish, Second law analysis of solar powered ab- 130 (1928). sorption cooling cycles and systems. J. Solar Energy 22. W. Haltenberger, Ind. Eng. Chem. 31, 783-786 (1939). Engng 106, 291-298 (1984). 23. Z. Rant, Forsch. Ing. Wes. 26, 1 (1960). 3. ASHR AE Handbook ofFundame ntals, Chap. I, (1985). 24. F. Bosajakovic, Technische Thermodynamik. Stein- 4. Institute of Gas Technology, Research Bulletin 34 kopf-Verlag, Dresden (1937). (1964). 25. R. Haase, Thermodynamics ofI rreversible Processes. 5. G. Scatchard et al., Thermodynamic properties-Sat- Addison-Wesley, Reading, Mass. (1969). urated liquid and vapor of ammonia-water mixtures. 26. W. Latimer, J. Am. Chem. Soc. 43, 818-826 (1921). Refrig. Eng. 53, 413-419 (1947). 27. R. A. Robinson and R.H. Stokes, Electrolyte Solns., 6. HVAC Guide, Vol. 31. (ASHVE, New York, 1953). 1958. 7. B. H. Jennings, New investigations in absorption re- 28. R. A. Robinson and H.J. Mccoach, J. Am. Chem. frigeration. Refrig. Eng. 30, 87-93 (1935). Soc. 69, 22-44 (1947). 8. Kyes, F. G., Renaissance of absorption refrigeration 29. R. A. Robinson and R. H. Stokes, Trans. Far. Soc. cycle. Ind. Eng. Chem. 21, 477-480 (1929). 45, 612-624 (1949). Page 795 16TH NAMRC May 24-27, 1988 University of Illinois Urbana, Illinois Page 796 .. 294 , Ci / ~pervisotyi~i~,~~;pef-Or Machining Systems ctit.d. l~Widpment of Software Modules for a Flexible Manufacturing System for Sheet Metal Parts By M. Geiger. U. Geissler ................. , ... , ........................................... 316 and Testing of an Intelligent Feature Extractor Within a Manufacturing Protocol /3. Kumar. D. K. Anand, J.A. Kirk . . ........................... 320 Collision Avoidance by Dynamic Programming Cesarone; Kornel F, Eman. ,,ii1it>.;;L, •••......••......•...............•.••......... 328 ,.<4,. ... ,.u. ." Servo System drawing. The cylindrical surfaces present In response, the intelligent feature extractor within the drawing are also recognized. The lists out everything it knows at that instant procedure for that is slightly more compli- regarding the particular entity that was named. cated, because the feature extractor has to The listed information can include (1) the type guess the cylindrical surface from the presence of entity (2) the parameters of the entity (3) of circular and/or elliptical arcs. The the attributes of the entity. The intelligent intelligent feature extractor attempts to guess feature extractor accesses the attributes of the stock shape from the drawing data. the entity by examining each of the associated Currently, the processed stock shapes are facts present in the 'associated-facts' slot of either rectangular (for the vertical machining the data structure for the entity. center) or cylindrical (for the turning The second important module that facili- center). In order to guess the stock shape, tites user enquiry is triggered by a command of the feature extractor, after searching for all the form planar and cylindrical surfaces present, picks (why-is ) out the outermost ones. If the part is found In this case, the intelligent feature extractor confined within at least two pairs of orthogo- examines the associated facts for this entity nal planar surfaces, it is classified as rec- until it finds one that indeed states that the tangular. If one cylindrical surface encloses entity has the specified attribute. It exami - all entities within it, the stock is classified nes that fact variable to test if it has a as cyl i ndri cal. parent rule and a parent fact. If that is the (v) The Recognition of Features. The recognition case, the parent fact is examined in turn, to of features starts with locating the outermost check if it also has a parent fact. This pro- surfaces of the part. If the stock shape is cess is continued till a parent fact pointer rectangular, the outermost surfaces lie within value of 'nil' is returned (denoting a seed the three pairs of parallel planes that are fact). The datils of each intermediate facts farthest apart. For cylindrical stock shapes, are listed out, thereby explaining the the outermost surfaces lie on (1) the cylindri- reasoning in concluding now a particular attri- cal surface that encompasses all geometric bute is recognized to be valid for the named entities and (2) the pair of planes farthest entity. apart that are normal to the axis of this (vii) Redirection of the Outhut File. After the user cylindrical surface. Next, for each outermost has been sat1sf1ed wit the outcome of the pro- surface, the outermost contour is located. The cessing by the intelligent feature extractor, a outermost contour contains all points on every request can be made to generate the entity for that plane within it. After this, corresponding PMF file. Essentially, the an attempt is made to simplify the outermost generated file contains several sections in the contour. A typical attempt to simplify the header format, including (1) a header section, outermost contour would involve supplying (2) a features section, (3) a topology section missing lines (or arcs) between aligned (but and (4) a geometry section. The features sec- non-adjacent) lines (or arcs). The addition of tion is intended to define several types of these missing elements would simplify the features, collections of faces, either as outermost contour to a rectangle or a complete 'simple' feature (naming individual faces) or circle. It will also generate additional as 'pattern' features (collections of other closed contours - those including the newly functional features). The faces can be defined supplied line (or arc) entities. Next, the in terms of a set of topological entities, nesting levels of the individual closed con- which are, in turn, defined in terms of tours for the given surface is determined. A geometrical entities. closed contour is nested within another closed A set of canned procedured can be used contour if its components all lie within the (within a post processor) to generate the other contour (or share edges with it). The necessary 7&G code for each feature. levels of nesting for a particular contour is significant because contours with an even (or THE ADDITION OF NEW KNOWLEDGE. The new knowledge can zero) levels of nesting contain material within consist of either (1) new facts or (2) new rules. The them whereas contours with odd levels of facts are always updated whenever a new input file is nesting contain void within them. specified. The sequence of steps necessary to add a The cross sections of slots are new rule is shown schematically (figure 10). It recognized next. Such a cross section belongs requires one to define all non-standard vocabulary to a hollow (odd leveled) contour on an outer- terms, at the levels of features, contours and primi- most surface that shares an edge with its tive geometrical entities. Next, any non-standard enclosing solid (even leveled) contour. The geometrical relationships are specified. The construc- remaining hollow contours on the outermost sur- tion of the code for a new rule then reduces to the face represent the cross sections of either a task of expressing the preconditions in terms of the pocket or a hole. Further testing, including testing of these relationships, with proper arguments. the analysis of the contours on the non- Currently, this sequence of steps is being followed 323 Page 802 manually for adding new rules to the feature extractor this part are also recognized and listed by the knowledge base. An interface is also under development intelligent feature extractor. which will lead to user automatically through these At this point, the user may enquire the intelligent steps and assist in the generation of the necessary feature extractor regarding the reasoning used by it to code that form the production rules. arrive at a particular conclusion. In this instance, the user wishes to find out why the feature named RESULTS OF A SAMPLE SESSION. The results of a sample 'pocket-2' has been identified as such. The feature session with the intelligent feature extractor are pre- extractor comes up with an explanation of which rules sented (figure 11). The interaction between the user were applied. Eventually, when the user is satisfied, and the feature extractor is in a question and answer he/she puts in the necessary material and tolerance format. data. A post processor then generates the necessary At the beginning of this sample session, the user feature file in the PMF format. While generating this requests that an IGES file be processed. After the file, certain rules are applied towards the sequencing complete path name for the IGES file is specified, the of the features. For example, features that correspond feature extractor processes this file. The feature to the same tool diameter would be grouped together (to extractor reads the file on a character-by-character minimize the tool change time). Portions of the basis. The directory section, which contains a catalog resulting PMF file are shown (figure 14). For the pur- of all the entities present in the drawing is read poses of this validation, a set of canned routines are first. As a particular entity is encountered, an used to generate the necessary M&G code that will be instance of its type is generated. The actual name eventually downloaded to the machine tool. depends on the type of the entity. The most encoun- tered geometrical entities include lines, circles, DISCUSSIONS AND CONCLUSIONS. The feature extractor transformation matrices and views. The data structure described here is an important component of a complete, assigned to an entity contains information on what type working, automated CAD/CAM link. It is capable of of entity it is as well as information regarding the accepting CAD files generated by any commercial CAD directory and parameter section record number pointers tool that contains an IGES interface. It has been for this entity. Next, the records of the parameter tested with two commercial CAD tools (Anvil-5000 and section are read. The data structures that were cadkey). One of them (the Anvil-5000 package) runs on generated to represent the individual entities are the mainframe whereas the other one (cadkey) primarily augmented by inserting the parameter values as occuring runs on microcomputers. The feature extractor can be in the parameter record into their respective slots. used with either type of CAD tool. This process continues till all the parameter section The input data for the feature extractor contains records are exhausted. Because it can take a signifi- evaluated, wire-frame representations for the part cant amount of time to read and process the IGES file, drawing. Even though, ideally speaking, wireframe especially for the more complex drawings, a mechanism representations cannot describe a solid object with is provided to inform the user regarding the progress certainty, the application of a set of rules to this of the IGES file processing as it takes place. A set data can help identify the morphological features for a of fact variables are also generated. They represent number of simpler shapes. As the rules are refined and the seed declarative information regarding these enti- the rule-base expanded, this feature extractor will be ties. able to handle more complicated part geometries. After the stock shape is guessed, the outermost Examples of such geometries include conical and spheri- surfaces are considered. All the planar contours that cal surfaces. Even though the IGES format has facili- are present in the outermost planes are identified and ties for representing the general conic surfaces, many data structures are generated to describe these in commercial CAD tools do not take advantage of that. terms of the individual entities that are linked in a Instead, they tend to use simpler techniques like closed chain. Next the outermost contour is located. solids of revolution. If the angular steps during The outermost contour is one which meets the criterion creation of a solid of revolution is kept small, the that every point on every entity within the plane lies generated profile will closely approximate the actual inside it (subtending a total of 2*3.1415 radians profile. However, the size of the resulting IGES file angle, as compared to O radians that would be subtended may become unmanageable because a large number of tiny at a point outside the contour). Next, an attempt is geometrical entities have to be generated where only a made to simplify the outermost contour, by attempting few conic surface entities would have sufficed. to supply missing entities, such as lines between Although the Flexible Manufacturing Protocol, of aligned lines. As an example (figure 12), the surfaces which this feature extractor is a part, deals with a 1, 3 and 5 contain outermost contours that can be variety of data files, the feature extractor itself simplified into rectangles by supplying lines that are deals with only two of these: the ascii drawing (IGES) shown with a hatched pattern. The addition of these file and the ascii features (PMF) file. The standar- lines creates additional contours. The process is dization of these two types of files as input and out- repeated for the inside contours and any other contours put mediums was the most important issue related to the that these might enclose, in turn. Once all the con- integration of the feature extractor into the FMP. tours within this plane are exhausted, it is seen that After these two formats were selected and agreed upon, contour 1 encloses contour 2 within the face 1 (figure the development of the feature extractor continued 13a), and they share a common line. Because contour 1 independent of the development of the other blocks of is not contained by any other contour, it must contain the FMP. It also enabled the use of very different material, and the contour 2, enclosed by it, must development systems and programming languages within represent hollow. Also, since they share part of their different parts of the protocol. boundary, from the application of another rule, it Examples of such languages include C, Pascal, Lisp appears that contour 2 represents the cross section for and FORTRAN, among others. a slot. On the other hand, for the face 2 (figure The PMF format is found adequate for representing 13b), the contour 1 encloses contour 2 but shares no the results from the feature extractor. part of the boundary with it, Since the contour 1 con- Future work will be directed towards the further tains material and contour 2 contains void, from the testing of the feature extractor with additional application of one of the rules, it appears that the geometries. Additional work in the area of improving contour 2 represents the cross section of either a the user interface is also planned. This would enable pocket or a hole. In order to classify it any further, the user to pose simple English like sentences to the it is necessary to consider the adjacent surfaces. feature extractor, both for the purposes of explanation rurther analysis reveals that its companion contour as well as for expanding the rule base. (figure 13c) indeed contains material and therefore the contour 2 on the face 2 (figure 13b) represents an ACKNOWLEDGEMENTS. This research was supported by the entrance cross section for a pocket. In a similar Systems Research Center at the University of Maryland. fashion, the other morphological features present in Computer time for this work was partially supported by 324 Page 803 the Computer Science Center at the University of Maryland. The assistance of Thelma Miller in the preparation of the final mats is appreciated. r=:cJ POCKET REFERENCES. HOLE (1) "CAD: The Big Picture for Micros", G. Hart, PC • Magazine, March 11, 1986. () ( 2) "The Automatic Production of Machined Components Starting From a Stored Geometric Description", ~::~ A.R. Grayer, Advances in Computer Aided PART SLOT Manufacturing, North Holland, 137-151, 1977. (3) "Shape Classification in Computer Aided Design", L.K. Kypryanou, Ph.D. Thesis, University of Cambridge, 1980. (4) "Shape Features in Geometric Modeling", G.E.M. Jared, Solid Modeling by Computers from Theory to Applications, Edited by M.S. Picket, General Motors Research Laboratory, 1984. Figure 1: A sample part containing machinable features (5) "Extraction of Feature Information from Three- dimensional CAD Data", M.R. Henderson, Ph.D. Thesis, Department of Industrial Engineering, Purdue University, West Lafayette, Indiana, USA, May 1984. (6) "Automated Group Technology Part Coding From a Three-dimensional CAD Database", M.R. Henderson, Knowledge-Based Expert Systems for Manufacturing, published by the American Society of Mechanical Conr,crcio.l C A D Soit= Engineers, New York, USA, 1987. (7) "Automated Recognition of Machined Surfaces from a 3-D Solid Model", B.K. Choi, M.M. Barash and D.C. @=HEFil.E Anderson, Computer Aided Design, 16(2), 81, 1984. (8) "Feature Extraction by Volume Decomposition", T.C. Woo, Proceedings of the Conference on CAD/CAM in Mechanical Engineering, MIT, Cambridge, G) = FEAllJIE Ftl.E Massachusetts, USA, 1982. Flxti.ring (9) "The use of IGES for Automated N/C Machining", W. Constraints Rickert, Masters Thesis, Mechanical Engineering /GLIEAL -, Department, University of Maryland, College Park, ( Ootco. © = JNTERIElllATE Fll.E Bo.!!e © Maryl and, USA, 1987. ' - - _/ (10) "Initial Graphics Exchange Specifications (IGES), Version 3.0", B. Smith and J. Wellington, Report NBSIR 86-3359, National Bureau of Standards, Gaithersburg, Maryland, USA, 1986. (11) "A Flexible Manufacturing System Protocol", R. Uppal, Masters Thesis, Mechanical Engineering Department, University of Maryland, College Park, Maryland, USA, 1987. ® :l'ROCESSPUNF[LE ( 12) "AMRF Database Report Format" T. H. Hopp, Automatic Manufacturing Research Facility Report, National Bureau of Standards, Gaithersburg, Maryland, USA, 1987. ® ~ 10. ,0.; 000000331'00000) 9 ,o ,so : gettable-instance-variables 110,0 ,50 ,50.,0; 0000003:,P0000020 : gettable-instance-variables : inittable-instance-variables) IOO,O. ,40. ,35 .• 4S. ,3S. ,4S. ,35.; 00000 l 07P0000056 100,50. ,40. ,35. ,45 .• 35 .• 45 .• 35. 00000 l09P0000057 S0000001i)(l()()()()()200000110POOOOOS7 T0000001 Figure 7: The Data Structure for the General Fact Entity Figure 3: Sample IGES file Sample Feature Rules USl!ll (1) IF (there exist two parallel circles of equal radii with aligned axes IIIFE!lEIICE EIIGIIIE and both are contained within an odd nesting of closed contours) DATA l'IU!S THEN they represent a straight hole. ACCESS lllJII/STOP Jl!U!S (2) IF (there exist two elliptical arcs of equal axes on parallel planes) THEN they represent an inclined hole through the parallel surfaces. CREATE APPLY fflOWU!OOI! (3) IF {there exist two elliptical arcs satisfying Pythegorean relationship llUU!S RUU!S DASI! on perpendicular planes) THEN they represent an inclined hole through the perpendicular surfaces. (1) IF (a contour bounds a negative surface AND its enclosing contour shares no edge with it AND its adjacent contours all bound positive surfaces AND the companion contour bounds a positive surtace) Figure 4: Components of the Intelligent Feature Extractor THEN this contour represents the entrance face for a pocket. (1) IF (a contour bounds a negative surface AND one or more of its non-enclosing adjacent contours bounds a positive surface) THEN Fenture this contour represents the entrance face for a slot. ~. Depression Protrusion Figure 8: Sample rules used by the Intelligent Feature Extractor Figure 5: The hierarchical taxonomy for features 326 Page 805 Sample Rule FE, The valid commands are: IF (a contour bounds a negative surface . USER: (read-lGES.file) shares no edge with it AND its ad· AND rts enclosing contour surfaces AND the companion co~::n~ contours all bound positive FE: Please specify the IGES lite name THEN this contour represent s th e entrr anocuen dfasc ea fpoor sait ipvoec skuertf.a ce) USER: FE: The folloLwininegs: entilies were generated: 37 (line-1, ... , line-37) Circles: (cirde·1,circle-2) Sample Code ~~==~ormation matrices: {tr.ans·matr-1, ... ) (v1ew·1, ... ,view-8) (make-rule rule-p-l Notali~ns· (nole-1, ... ,note-S) (IF (<= (send ?canto . rt USER: {what-is view-5) . (not (shared-edges ¥~o~~o~~e-area) 0.0) t!!~~ FE vlew-5 is a view (for-all (send ;.~ ~~rf} oouurr .;eandJ~aJcoesnintg-c-oconntotouursr)) )) It was read from. th I Its ~ssocialed tran:to~!S .data base. (> {send (send ?c i5u ~ce-area) > 0.0) Its hst of parameters is (;tn matrix is trans·matr-5. THEN :surl~~~~\e~)~.g)inion-contour) USER: (draw-part) (:= (next-pocket-name) (mak~:~!~ance 'pocket FE: .... Completed. (append USER: {extract-contours) (f\nd-faces ?contour} (f!nd-faces {send ?cont . . FE The following planar contours were obi . (find-faces (send ?. con t o°uurr .:acdoJmapcaennti-ocno-nctoonutros)u)r ] USER: (extract-surfaces) a1ned ... FE, The following surfaces were obtained USER: (extract-features) .. FE: The folloHwoilnegs :m orpholo 91. cal features were extracted. Slots: 1 (hole--l) Pockets: 1 (slot-1) (pockel-1) Figure 9: Equivalent Lisp cod e f or a sample rule USER: {Why-is pocket· 1 a-pocket) FE: The featu(1r)e Itesn ctiotyn tpaoincekde lc· 1o hal s the following attributes· (2) Adjacent conto:rsour, contour-6, bounds a ~e . The,er (3) The compan;on c~~ji; all bound pos;t;,e surt2:~·;• surtace, surtaca-9. ore, according to th e rule P-1r,, cpoonctkoeutr·· 19 ,a pbpoeuanrds st~ :s~.; ·~. ;~7~ce, surface-11. Figure 11: Asamp ie sessi.o n with the intelligent feature e xt ractor IIUUi PAI 1116 LISP COD!i Figure 10: Sequence of steps for add'i ng new rules 0 0 Companion Face- I Face-2 ~ contour 2· DQ _____ .11I []11 2' 1~ D , 0 0 0 (al (bl (c) DCJ Figure 12: Contours within the o u te rmost surfaces of a sample part Figure 13: (a) Contours within the (c) Contours ~/~~~~~u:~;;-pitahrinn oth1 n e s usrufratace~ ~to~ athcee S1,u rface 2 327 Page 806 THIRD INTERNATIONAL CONFERENCE ON COMPUTER-AIDED PROOOCTION ENGINEERING - University of Michigan College of Engineering Ann Arbor, Michigan June 1-3, 1988 : Conference Proceedings Edited by Professor Shyam K. Samanta Published by Society of Manufacturing Engineers One SME Drive. P 0. Box 930 Dearborn. Michigan 48121 Page 807 THE USE OF IGES IN AUTOMATED CNC MACHINING J. A. Kirk, Professor M. Anjanappa, Assistant Professor D. K. Anand,Professor W. K. Rickert, Jr., Research Assistant University of Maryland Mechanical Engineering Department Systems Research Center College Park, MD 20742 ABSTRACT The introduction of the Initial Graphic Exchange Specification (IGES) and the EIA standard Mand G Code~ for Numerically Controlled machines (N/C) allows for a standar- dized automated interface between existing computer aided design systems and N/C manu- facturing systems. The Flexible Manufacturing Protocol, developed at the University of Maryland, outlines such an interface to control automated manufacturing cells. This paper demonstrates the feasibility of the protocol by developing an automated IGES to CNC interface to control a 3 axis CNC machining center given the geometric representation of the part in IGES format. Wireframe representations of 2-1/2 dimen- sional parts, composed of linear elements, are the primary focus of this work. The automated production of the samp1e part, presented in the paper, demonstrates that direct control of N/C machine is possible using an IGES design data file as input to the protocol. INTRODUCTION The need for standardization of communications between CAD systems has brought about an effort, led by the National Bureau of Standards, to create a neutral file for geometric data transfer [l, 2]. The result was the first version of the Initial Grap hi cs Exchange Specification ( IGES) completed in 1979. IGES was subsequently accepted by the American Nationa 1 Standards Institute (ANS I) in 1981 [3]. With the IGES standard available the concept of a standardized automated manufacturing system is within reach. The Computer Integrated Manufacturing and Design Group at the University of Maryland is currently developing a standardized automated manufacturing system which accepts IGES compatible design file as input. To accomplish this objective the Flexible Manufacturing Protocol, shown in Fig. 1, has been developed. Following is a brief discussion of the protocol. The reader is referred to [4] for more details of the pro to col • The user begins by generating a 3 dimensional representation of the part on a CAD system. The type of system used to create this representation is not important as long as the data is transferred to the manufacturing system in IGES format. After the part data is transferred to the manufacturing system, the geometric representation is decomposed into the features that need to be machined. This is accomplished in the feature extractor portion of the protocol. Since the IGES format does not contain a uniform format for tolerance information, the user must supply this information interactively after the features has been identified. 243 Page 808 The system must decide at this point if the part can be machined by any of the automated manufacturing cells available. A cell data based containing all the func- tions, achievable tolerances and tools available in the cells will be made available to achieve this objective. If the part is incompatible or unmachinable with these cells then the system returns the user to the design stage. Parts that are compatible and manufacturable are then earmarked for the appropriate cell and the necessary machine codes are developed as discussed below. The first step in developing the machine codes is process planning. A process planner takes the feature and tolerance information developed earlier in the protocol and develops a plan to accomplish the production of the part. Two types of process planners are envisioned by the protocol. The first type of planner is the ordered process planner. In this type the user interactively enters the necessary machining information to accomplish the production of the part. Typical information would be mac hi ni ng parameters such as cutter diameter, speeds and feedra tes for each feature. The second type of planner is the intelligent process planner. This process requires no user input, producing the plan automatically using expert system techniques. In either case, the output is a CAM database which is used to create the necessary machine codes to produce the part. After the machine codes are generated, the fixtures for transporting and ma chining the part are developed. This is accomplished with interactive input from cell control. The controlling data along with machine codes are then downloaded to the cell and the part is produced. One method of enhancing the accuracy of the part is by using software error mapping techniques similar to those developed at the National Bureau of Standards [SJ. The automated IGES to CNC interface reported in this paper was designed as a path- finder for portions of this protocol as shown by heavy lines in Figure 1. The most prominent common aspects are the feature extractor and ordered process planner (feature planner). Since these aspects are basic to the protocol, a demonstration of the feasibility of the IGES to CNC interface demonstrates the overa 11 concept of the protocol. The objective of this work is to demonstrate the feasibility of the Flexible Manufacturing Protocol by developing an automated interface to control a 3 axis CNC vertical milling machine, given a geometric representation of the part in IGES format. SYSTEM OVERVIEW The automated IGES to CNC interface takes graphical input data, in the form of an IGES file, along with minimal machining data input provided by the user, and creates the machine codes necessary to produce the part on a CNC machining center. Since most commercial CAD systems can generate IGES files, an interface that uses an IGES input is CAD system independent, thereby resulting in a standardized CAD/CAM link. The interface is made up of four parts. The first part of IGES to CNC design interface is the 11 IGES interface". An IGES file in its standard format contains not only geometric data but also innovation information and other non-geometric data as well. Since, for the purposes of machining, only the geometric information is required, the file needs to be simplified. This is accomplished by the IGES interface program IGINT [6]. The second part of the design interface is the "feature extractor 11 • The feature extractor takes the geometric representaton of the part, condensed from the IGES file, and extracts the features to be machined. This procedure is carried out by eight programs, PROGl through PROGS [6]. 244 Page 809 The third part of the design interface is the "feature planner 11 which generates tool paths to accomplish the machining of each feature. To do this, various machining parameters such as tool diameters and feed rates are provided interactively by the user. Since the user is involved at this point. all additional machining parameters used by the CNC interface are also input at this time. There are two interactive programs in the feature planner called PROG9 and PROGlO [6]. The final part of the design interface, the "CNC interface", takes the tool paths generated in the feature planner, along with the user provided information and genera- tes machine codes to produce the part. The CNC interface generates machine codes in two formats. One is the machine dependent DYNALAN [7] language code which is used to control a DYNA DM2200 CNC milling machine, and the other is the M&G codes of Electronic Industries Association (EIA) Standard RS-274-D which are compatible with many N/C and CNC machining centers [8]. Two programs are used for this, the DYNA program and the M&G program [6]. The programs that make up the design interface are written in BASIC language and have been implemented on an IBM AT. The IGES files are obtained from an ANVIL 5000 CAD program residing on the VAX 11/750 computer system. The IGES files are trans- ferred to the IBM vi a a phone modem using the KERMIT protocol. The machine codes are transferred to the machining center via an RS-232 cable using the program DOWN [6]. Some simplifying assumptions were necessary to make the project feasible, with the available resources. These assumptions include that the part must be 2-1/2 dimen- sional, machinable, presented as a wireframe model, and made up of only line segments. Each one of the four constituents, that make up the design interface, is discussed in detail in the following sections. The IGES Interface IGES was developed to allow CAD systems, from various vendors, to exchange graphic information in a uniform.manner. IGES is a three dimensional standard based on wire frames and simple surfaces [l]. An IGES ASCII file has five sections, which appear in the following order - start section, global section, directory section, parameter data section, and the terminate section. Each section is made up of a number of 80 column records. The complete file has many features that are beyond the needs and capabili- ties of the IGES to CNC interface. The IGES file is therefore processed through an IGES interface program, IGINT, which creates a simple file consisting of only geometric information. After the IGES file is downloaded from the VAX system to the IBM AT, the IGINT program begins the analysis with the directory section of the file. Line entities are found by checking the identification number in the first field. When a line entity is located the status number is checked to see if the line is part of the geometry. If the line is part of the geometry then the parameter data pointer is noted. After all the directory entries have been checked the program proceeds to the parameter data section. The program then reads the coordinate data from the parameter data entries that coincide with the pointers noted in the analysis of the directory section. This data is written to file, preceeded by the number of geometric lines that make up the representation of the part, in X-Y-Z coordinate pairs. The resulting file is used as 1n put to the feature extrac~or. Feature Extractor The part to be produced is geometrically represented by a wireframe model made up of line segments. The function of the feature extractor 1s to take the wire frame representation and extract the features to be machined. The features identified in the feature extractor fall into two general categories. Depressions in the surface of 245 Page 810 the part, referred to as "pockets". and raised surfaces contained within these pockets, referred to as "posts". For the limited case of 2-1/2 dimensional milling on one side of a workpiece, the identification of these two types of features provides an adequate basis for manufacturing of the part. The procedure of identifying features begins at the top of the part, then moves down through the part redefining all the features wherever a change in cross-section occurs. Each set of features defined in this manner constitutes what will be referred to as a "level". The final product of the feature extractor is a collection of pockets and posts formed into groups that are referred to as pocket groups. Each pocket group is made up of a pocket and any posts that provide an internal boundary to the pocket. The feature extractor designed for this work is complf!tely automatic and consists of eight programs [6]. The sequence of feature extraction by these eight programs can be best understood by considering an example. Figure 2, shows the wireframe represen- tation of a sample part. The input for the first program is the simplified IGES file of the part, consisting of information on line segments. The first program (PROGl) begins by eliminating vertical line segments and ramp 1i ne segments. The program then finds the maximum and minimum X, Y and Z coordinates of the line segments. The minimum X and Y values and the maximum Z value are then subtracted from all the line segment coordinates. In this fashion a datum is established as shown in Fig. 3, on the top face of the block in the lower left hand corner of the X-Y plane. The size of the workpiece needed is al so known from the minimum and maximum values. The PROGl now finds the various Z levels on which the line segments reside. These levels are then sorted top to bottom. Finally, all the line segments are sorted according to level, and placed in a file in a level by level fashion. This information is used as input to PROG2 for implementing the level comparisons that result in the plan views of each level. The program begins with the first level. Since this level is already complete, it is transferred in its entirety to a new file. The second level is then read in, one line segment at a time, and compared with the lines that make up the first level. If a match is not found then the segment is added to this collection of line segments. If a match is found then both the new line segment and the one it matches are deleted. After all of the line segments of the second level are checked in this manner this collection of line segments is saved in the new file as the plan view of the second level. These line segments are then com- pared with those of the third level and so on until the the last level before the bot- tom of the part is reached. The information produced by PROG2 is used as input to both PROG3 and PROGS programs. The PROG3 takes the plan views produced in PROG2 and eliminates the edge line segments while adding line segments for the edge gaps. This is accomplished by deleting the edge line segments while saving their endpoints. These endpoints are then reconstituted into Hne Sc:gments that close the edge gaps thereby creating new plan views. The new plan views generated by PROG3 are fed to PROG4 where the line segments are formed into features. This is done by simply forming closed loops out of the segments and saving these ordered loops to file. Note that the separation by level is still maintained. The PROGS uses the information produced by the PROG2 to identify the features defined by the PROG4 program. The PROGS begins by checking the feature to see if it includes an edge line. If an edge line is included then the feature is a pocket. Otherwise the program assumes that it is a nested feature. 246 Page 811 A nested feature is approached in the following manner. An imaginary line segment is drawn from one of the vertices of the feature to the boundary of the workpiece. This line segment, referred to as a "definition line". is then checked against the original plan view of the level developed by PROG2 to determine the number of inter- sections. Line segments that make up the feature are eliminated from consideration. If the number of intersections is an odd value then the feature is a pocket. If the number of intersections is an even value or zero then the feature is a post. This procedure is illustrated in Figure 4. Once the features are sorted in this fashion, they are saved in a file for further processing. It should be noted that a horizontal line segment is used as the definition line and that only line segments with an endpoint below this line are considered. Also, horizontal lines are ignored. This approach eliminates inconsistencies that arise from segment endpoints positioned on the definition line. The PROG6 program takes the information provided by the PROGS and orders the 1i ne segments that make up the features. Pockets are ordered in a counterclockwise fashion, and posts are ordered in a clockwise fashion. This is done for two reasons, the procedure for computing offsets in the feature planner is simplified and the finishing cuts made on the part will be climb cuts which conform to the directions mentioned. The program accomplishes this by determining the area of the feature, using a method of breaking the feature up into triangles and then finding the areas of these triangles using the cross product approach. Since these areas carry a sign with them, after they are summed the sign of the to ta 1 area of the feature determines its sense. A negative area denotes a clockwise sense, and a positive area denotes a counterclock- wise sense. Once the segments making up the features are ordered in this manner, they are saved in files with the pockets and posts separated into different files. The PROG7 program takes the pocket file generated in the PROG6 and orders the pockets on each level so that a nested pocket appears before the pocket that surrounds it. This is accomplished using a definition line scheme similar to the one used in PROGS. If a pocket's definition line intersects another pocket an odd number of times then the pocket is inside that pocket, otherwise it is outside. The pockets are then saved in a file in this order. The PROG8 program takes the pocket file generated in PROG7 and the post file generated ~Y PROG6 as input and groups the pockets and posts into pocket groups. This is accomplished using the same definition line scheme used in PROG7. The pocket groups are then saved to file for further processing. Note that since the pockets are already ordered there is no danger of a post being grouped with the wrong pocket. At this point all the features are defined and sorted into pocket groups. This infor- mation is used as input to the feature planner. Feature Planner Once the pocket groups have been determined by the feature extractor, a coherent plan is developed to produce them, using the feature planning portion of the IGES to CNC interface system. The input to the feature planner includes the geometric defi ni- ti on of the pocket groups and limited user input concerning machining parameters. The output of the feature planner is a tool path for the machining center to follow. The feature planner consists of the interactive program PROG9 and the automatic PROGlO program. The feature planner begins with PROG9. Since each pocket group inpl'Jt 1s con- sidered to be independent, the user must provide machining parameters for each pocket 247 Page 812 group on each level. Five mac hi ni ng parameters are required for each group, vi 2:: cutter diameter, number of Z-steps, feedrate for the cutter, and plunge rate of the cutter. These parameters are interactively input by the user who is presented with a diagram of the pocket group along with level data associated with the group. The PROG9 then produces a new pocket group made up of line segments, offset half a too'l diameter inwards from the pocket and outwards from the posts. A pocket group's tool paths are set up in the following manner. If the pocketing mode was on, the first cuts are the pocketing cuts followed by the final finishing cuts. If the pocketing mode was off, the only cuts are the finishing cuts. If more than one Z-step,was indicated 1n the machining parameters the pocket group will be machined in increments. The finishing cut offset tool paths developed in PROG9 is fed to PROGlO. The prograr,1 reads in the first pocket group and checks to see if the pocketing mode is on. If the pocketing mode is off, the group is saved as is in a new file. If the pocketing mode is on, the pocketing tool paths are developed. The program then moves on to the next group, unti 1 all the groups are exhausted. CNC Interface The tool paths, along with the machining parameters, generated by the feature planner is then processed through the CNC interface to generate the ma chine-specific codes. The sequence of machine code generation for each pocket group is given below. The depth of the first cut on a pocket group is determined by the depth of the group and the number of Z-steps entered in the PROG9 program for this group. If the pocketing mode was used, the pocket group is cleaned out in the following manner: A rapid move to .1 inch above the surface is performed to allow free movement to the beginning of the first pocketing tool path, which is also accomplished with a rapid move. The spindle is now moved into the workpiece using the plunge rate defined in PROG9. Following this, a move in the X-Y plane to the tool path's endpoint is accomplished using the feedrate defined in PROG9. The process is then repeated for the next pocketing tool path and so on. After the pocketing is finished, or if the pocketing mode was turned off in PROG9, the program begins the finishing cuts. These are accomplished in a manner similar to that of the pocketing cuts except the tool follows the pocket or offsets all the way around to the beginning before the tool is retracted from the workpiece. When these procedures have been accomplished, the first pass on the group is finished. If only one Z-step was specified then a tool change is performed and the next group is machined. If more than one Z-step was used then the procedure is repeated at the next depth and so on until the bottom of the group is reached. Finally, the program sets up a tool change at the end of each packet group and spindle off at the end of the last pocket group. The above machine codes, in two kinds, are generated by the CNC interface. One is the machine-specific DYNALAN compatible code and the other is the standard M&G codes confirming to EIA RS-274-D standards. For the purpose of demonstrating the feasibi- lity of the automated IGES to CNC interface, DYNLAN compatible codes were used. RESULTS A 3-D wireframe representation of the pa.rt used to test the IGES to CNC design interface 1s shown 1n Figure 2. The part was designed on the VAX computer using the 248 Page 813 ANVIL 5000 program. The resulting IGES file was downloaded from the VAX to an IBM AT disk file using the KERMIT program. At this point the user enters machining infor- mation for each feature. This information, along with the feature information a)ready available, are then processed into tool paths. After the tool paths were developed the form of postprocessing is chosen. If a DYNALAN program was desired, the DYNA program is run. If M&G codes were desired the M&G program is run. To illustrate the dual capabilities of the interface, both types of codes were produced and the resulting codes were in agreement [6]. The DYNALAN program produced by the interface was then downloaded via RS-232 interface to a DYNA 1)12200 CNC vertical milling machine using the program DOWN. The DYNALAN was then executed and the part was produced successfully. The IGINT program and the PROGl through PROG8 programs took a combined total of 9-1/2 minutes to process the part. After the machining parameters were input, the system created the tool paths in less than three minutes. The M&G code took an addi- tional two minutes, and the DYNALAN program was generated in a little under three minutes. Total processing time, including machining parameter entry by the user, for a part of ·this complexity takes less than half an hour. CONCLUSIONS One particular path thru the Flexible Manufacturing Protocol (FMP) has been deve- loped. This path involves an automated IGES to CNC interface to control a 3 axis machining center, given the geometric representation of a part in standard IGES for- mat. A method of extracting features from an IGES representation of a part has been described and it has been shown that the feature extraction technique, and subsequent generation of standard control codes for machine tools is easily generated. The automated production of the sample part demonstrated the feasibility of auto- mated IGES to CNC interface, which is critical to the successful implementation of the FMP currently under installation at the University of Maryland. ACKNOWLEDGEMENT This research was partially supported by NSF Grant CDR-85-00108 through The Systems Research Center. REFERENCES 1. "Initial Graphic Exchange Specification (IGES)", Version 2.0, National Technical Information Services, U.S. Department of Conunerce, Springfield, VA, February 1983. 2. Hordeski, M.F., CAD/CAM Techniques, Reston Publishing Company, Inc., Reston, VA, 1986. 3. Fallon, M., "Standard C!'"aphics'i. The DEC Professional, Vol. 5, No. 1, July 1986, pp 22-27. 4. Kirk, J.A., Anand, D.K., Anjanappa, M., and Uppal, R., "Implementation of a Flexible Manufacturing Protocol•, Proceedings of the 2nd IASTED International Conference, Los Angeles, CA, 1986, pp. 71-75. 5. Simpson, J.A., et al, "The Automated Manufacturing Research Facility of the National Bureau of Standards•, Journal of Manufacturing Systems, Vol. 1, No. 1, 1982, pp 17-32. 249 Page 814 6. Rickert Jr., W.K., "The Use of IGES in Automated CNC Machining 11 , M.S. Thesis, University of Maryland, College Park, March 1987. 7. "DM2400/2200 Programming Manual''. DYNA Electronics Inc., Santa Clara, CA, 1984. 8. "RS-274-D Interchangeable Variable Block Data Format for Positioning, Contouring, and Contouring/Positioning Numerically Controlled i·lachines", Electronic Industries Association, Washington, DC, February 1979. I. G, E. I, r -cnt'..111~, I Firl..... I I Plcrining /~2 ,,___::===:r-L_-_-_. - - _. ,_ / ry,,_ I I 91ni'l I 1'1-ocass I ~. .......e =~~Lf-=1,2"1W'::i- _. r----, CB.i. /lalror.y I &t-cawei41 L - - - - ..J PART FIG.l FLEXIELE MAAl.FACTI.RING PRIJTIXJJ.. 250 Page 815 FIG.2 SAMPLE PART z y POCKET FIG.3 BLOCK DATUM FIG.4 FEATURE IDENTIFICATION 251 Page 816 Page 817 SB-ROBOTIC ASSEMBLY SESSION 6 Bin-Picking of Curved Objed Using Range Finder. TAKEHIRO FUJITA, KOSUKE SATO, and SEIJI INOKUCHI (Osaka Uuiversity, Toyonaka, Osaka, JAPAN). Wednesday, July 20 Knowledge-Based Scheduling Method for Automatic Multi-Item Assembly. 9:10-12:30 a.m. YASUHIRO KAJIHARA and HIROKAZU OSAKI (Okayama University, Okayama, JAPAN). 6A Robot Motion Control 6B Mobile Robots A New Method of Inserting Operation Applied by Ultra-Sonic Vibration in 6C Sensor Based Manufacturing Process Control-I Assembly Process. NAOTAKE MOHR!, NAGAO SAITO (Toyota Technological In- stitute, Tempaku-ku, Nagoya, JAPAN), and MASARU TAKIGUCHI (Koito Cutting and Bending Manufacturing Co., Ltd., Shimizu, Shizuoka, JAPAN). 6D CAD/CAM 6E Accuracy Measurement and Identification of Robot Parameters SC-SIMULATION Simulator for Design and Operation of Flexible Manufacturing Systems. HIDEO FUJIMOTO (Nagoya Institute of Technology, Showa-ku, Nagoya, JAPAN). 6A-ROB0T MOTION CONTROL NAL Flight Simulator for Research and Development. AKIRA WATANABE, Sensor Feedback Using Approximate Jacobian. FUMIO MIYAZAKI (Department of TOSHIO BANDOW, HIROYASU KAWAHARA, and KAORU WAKAIRO (Na- Mechanical Engineering, Osaka University, Toyonaka, Osaka, JAPAN; Currently at tional Aerospace Laboratory in Japan, Chofu-shi, Tokyo, JAPAN). the Center for Robotic Systems in Microelectronics, University of California-Santa A Collision Detection Algorithm for Geometric Simulation. KENJI SHIMADA, Barbara, Santa Barbara, California, USA), YASUHIRO MASUTANI and SUGURU AKIRA OKANO, SHINJI KAWABE, and HIDEO MATSUKA (IBM Japan Co. ARIMOTO (Department of Mechanical Engineering, Faculty of Engineering Science, Ltd., Chiyoda-ku, Tokyo, JAPAN). Osaka University, Toyonaka, Osaka, JAPAN). Curved Surface Locator for Robot Simulator. TETSUO SHIMADA (Industrial In- Robot Controller with Digital Signal Processor for the Resolved-Acceleration Con- stitute of Hyogo Prefecture, Suma, Kobe, JAPAN), and YUKIO TADA (Kobe trol. HIROKAZU MAYEDA, KAZUO KUSAMOTO, and KAZUNORI OHASHI University, Kobe, JAPAN). (Osaka University, Toyonaka, Osaka, JAPAN). PD-Type Two-Stage Robust Tracking Control for Robot Manipulators. KOICHI OSUKA, TOSHIHARU SUGIE, and TOSHIRO ONO (University of Osaka Prefec- SD-VISION SYSTEMS AND IMAGE PROCESSING-2 ture, Sakai, Osaka, JAPAN). Development of Visnal Feedback Robots, Designed to Assemble Complex V. S.S. Sliding Mode Control with Joint Acceleration Feedback for Robot Automotive Components. MICHIHARU OSADA (Nippondenso Co., Ltd., Anjo, Manipulators. TOHRU WATANABE (Ritsumeikan University, Kyoto, JAPAN), Aichi, JAPAN). HISAO NAKAJIMA, HISANORI KAINO (Kyoto University, Kyoto, JAPAN), and KENICHI KAWATA (Daikin Industries Ltd., Settsu, Osaka, JAPAN). Digital Image Decomposition by Data Dependent Systems. SUDHAKAR M. PAN- DIT and CHRISTOPHER R. WEBER (Department of Mechanical Engineering and Motion Control of a Robot Arm Using Variable Structure System. K. KOSUGE and Engineering Mechanics, Michigan Technological University, Houghton, Michigan, K. FURUTA (Tokyo Institute of Technology, Megro, Tokyo, JAPAN). USA). Proposal of a Hierarchical Feedback Control Scheme for Pneumatic Robot Systems. Visual Inspection System of Printed Circuit Boards by Multislit Light Method. N. SADAO KAWAMURA, KEIITIROU MIYATA, HIDEO HANAFUSA, KIMINARI KAKIMORI, T. MORIMOTO, S. KISHIMOTO, Y. TAKAHASHI, M. OHSAKI, ISHIDA (Ritsumeikan University, Kyoto, JAPAN). and T. NAKAO (Sharp Corporation, Tenri-shi, Nara, JAPAN). A New Design Method for a Robust Servomechanism Using Continuously Variable Structure Control. H. HIKITA, H. KUBO, and K. KIKUCHI (Muroran Institute of Technology, Muroran, Hokkaido, JAPAN). SE-ROBOT PATH CONTROL A Study of Isotropic and Anisotropic GIE Robot Manipulators Under Optimal Path Control. STELIOS C. A. THOMOPOULOS and RICKY Y. J. TAM (Department of Electrical Engineering, Southern Illinois University at Carbondale, Carbondale, Il- 6B-M0BILE ROBOTS linois, USA). Automatic Lawn Mower Gnidance Using a Vision System. MASAHIKO HAYASHI Optimal Trajectories of Robotic Manipulators. JAMES T. PRITCHARD and YASUO FUJII (KUBOTA, LTD., Sakai, Osaka, JAPAN). (Westinghouse Corporation, Baltimore, Maryland, USA) and D. K. ANAND (Department of Mechanical Engineering and The Systems Research Center, University A Knowledge Based Navigation Controller for a Robotic Vehicle. YO SHIKUNI of Maryland, College Park, Maryland, USA). OKA WA (Osaka University, Suita, Osaka, JAPAN) and MASARU TERAMOTO (Brother Industries, Ltd., Mizuho-ku, Nagoya, JAPAN). Optimal Polynomial Trajectories for Robot Manipulators. SUNIL K. SINGH (Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New Vehicle FoUowing System Using Vehicle-to-Vehicle Communication-Its Concept, York, USA) and M. C. LEU (Mechanical Engineering Department, New Jersey In- Control Algorithm, and Communication System. SADAYUKJ TSUGA WA, stitute of Technology, Newark, New Jersey, USA). SATOSHI MURATA, TERUO YATABE, TAKESHI HIROSE (Mechanical Engineering Laboratory, Ministry of International Trade and Industry, Tskukuba, Tracking of Sharp Corners Using a Robot and a Table Manipulator. M. JOUANEH, JAPAN). Z.-X. WANG and D. DORNFELD (Department of Mechanical Engineering, Univer- sity of California-Berkeley, Berkeley, California, USA). Routing Control of Automated Guided Vehicles in FMS. SUSUMU FUJII, HIROAKI SANDOH, RYUSUKE HOHZAKI (Kobe University, Kobe, JAPAN). Path Planning of Mobile Robot Based on Visual Information. HIDEKI HASHIMOTO, TAKASHI KUBOTA, FUMIO HARASHIMA (University of Tokyo, Bunkyo-ku, Tokyo, JAPAN). Development of Mobile Maintenance Robot System "AIMARS." RYOICHI NAKAYAMA, KATSUHIKO SATO, SATOSHI OKADA, HISASHI HOZUMI, AKIRA ABE, HIDEHARU OKANO (Toshiba Corp., Kawasaki, Kanagawa, JAPAN). Practical Course Follow Performance of an AGV without Fixed Guide Ways. GUN- JI SUGIMOTO, KEIICHI WATANABE, YOSHIKI NINOMIYA, TAKERO HONGO, HIDEO ARAKAWA (Toyota Central Research & Development Labs., Inc., Aichi-gun, Aichi, JAPAN). 9 Page 818 Optimal Trajectories of Robotic Manipulators James T. Pritchard Fellow Engineer Westinghouse Corporation Baltimore, MD Dave K. Anand Professor Department of Mechanical Engineering and The Systems Research Center University of Maryland College Park, MD 20742 implicitly planned path, the program planner supplies ABSTRACT position, velocity, and acceleration knots (or constraint points) in Cartesian space and then This research investigates a generalized technique interpolates paths between the knots in joint space. for determining the optimal trajectories of robotic An explicitly defined path describes the path with a manipulators. The method is computationally fast and function, or set of functions, and then finds the robust while allowing for generalized optimization trajectory which approximates the function(s). criteria. It can also handle mixed boundary conditions The criteria for good trajectories and trajectory specified at both the beginning and end of the planning has been described as being efficient to trajectory, and allow for the definition of static and compute and execute. It should yield predictable and dynamic constraint equations. The approach uses accurate results, and not degenerate unacceptably near temporal finite elements to discretize the optimization singularities. In addition, the position, velocity, functional. and acceleration should be smooth functions of time. The results indicate that the temporal finite Finally, the path must be realizable, and it must be element method offers a superior technique for the easy to determine if the path is realizable. solution of optimal control problems. In particular, Trajectory planning typically uses a parameterized the method has advantages for the solution of the class of functions to satisfy constraints on the robotic manipulator optimal trajectory problem, or any position, velocity, and acceleration. These functions other problem that has highly nonlinear dynamic may be polynomials, exponentials, splines, or any other equations which may cause divergence with traditional function satisfying the necessary constraints. techniques. This paper develops a generalized technique for determining the optimal trajectories of a robotic mani- I NT ROD UC TI ON pulator. Temporal finite elements, which are defined in terms of time rather than position, are used to The process of defining the path and the resultant discretize the optimization functional. position, velocity, and acceleration that the The finite element approach is first applied to a manipulator must follow is called trajectory or path two point boundary value problem (TPBVP) resulting from planning. (The reader is referred to a total of 81 the variational formulation of an optima' robotic tra- references that are listed in ref. 1 and used in the jectory problem. The technique is then extended to an course of this research). Trajectory planning is optimal three point boundary value problem, and it is accomplished by converting the description of a desired shown how to apply the technique to a genera 1 multi- motion to a trajectory by defining the time sequence of point boundary problem (MPBVP). The method presented intermediate configurations of a robot arm between the allows the solution of the optimal trajectory problem start and finish of a path. The path planning can be for a variety of different optimization criteria. accomplished at the joint level or in Cartesian space, Candidate criteria include minimum time and minimum but it is typically best executed at the joint level, energy expenditure, Minimum inertia and mixed criteria because control is much easier to accomplish at this can also be defined. level. Path planning is to be distinguished from path tracking in that the path planning stage may be done 2 ROBOTIC MANIPULATOR SYSTEM DESCRIPTION off line while path tracking must be done on line in real time. In a typical cylindrical robot of Fig. 1, the ver- The path planning of a trajectory is a difficult tical axis provides the first degree of freedom. problem at best, involving as it does the inverse Azimuth rotation about the vertical axis provides the kinematics problem and the high rates of new arm second degree of freedom, and the radial motion of the configurations. The approaches to path planning are either the implicit or explicit types. To define an Page 819 arm provides the third degree of freedom. Additional and it is recognized that a new performance index has degrees of freedom are contained in the end effector, been defined and the variation in Jon the extremal for but they will be ignored in the present study except the optimal control u* is oJ(u*) = 0 for the effect of their mass and inertia. The azimuth The search for a constrained optimal solution to and radial degrees of freedom are driven by torque the control problem is simplified by the minimum limited and force limited actuators, respectively. principle of Pontryagin. The minimum principle establishes the local necessary conditions that the Definition of Kinematic Equations optimal control u*(t) must satisfy and The Denavit-Hartenberg (D-H) representation for mechanical links provide a framework for defining the H = (x, u, l , t) = A ( x, u, t) + >.. T( t) f ( x, u, t) ( 7) kinematic equations. This leads to a 4x4 homogeneous transformation matrix in which each links orientation leads to a redefinition of the necessary con di ti ons to will be described relative to the previous link's coor- dinate frame. Four parameters, a, a, a, and s comple- tely describe the shape of the link and its relative x* = aH TI"( x*, u*, >.., t) (8) motion with respect to the previous link in the kinema- tic chain. Once the manipulator coordinate systems are defined, a transformation matrix is defined as >.* = :~(x*, u*, >., t) (9) ( 1) 0 = lalui ( x* • u* • >.. * • t) (10) Based on the definition of the A matrix, a homoge- neous matrix which describes the location of the ith coordinate frame with respect to the jth link coor- with the boundary conditions as dinate frame is expressed as [H(x*, u*, >..*, tf) + a:r (*, tf)]otf ( 2) ( 11) Specifically, for a 6 degree of freedom (dof) manipula- tor, the location of the hand with respect to the base is given by The minimum principle states that if u*(t) is an optimal control, and x*(t) and l*(t) the corresponding (3) trajectory and adjoint vectors respectively, then the optimal control u*(t) minimizes the Hamiltonian at Now, a point q can be defined in terms of the hand or every instant in the trajectory. That is end effector coordinate system which can be related to the base coordinate system through the transformation. H(x*,u*,l*,t) < H(x*,u,l*,t) t 0 dto ( 13) system to follow the admissible trajectory x* that minimizes the performance index. Appending the system dynamics as an equality subject to x = f(x,u,t) becomes constraint leads to the performance index J = 11J 1 <1> dt (14) 0 t . J(u) = Jt64 >(x(t),x(t),u(t),>.(t),t)dt (5) . subject to x = 11f(x,u,r). Note that 11, must be substi- where tuted for explicit values oft. If the terminal time is unspecified (as in a mini- mum time problem), p becomes a parameter to be deter- ..,t) H + E!! (x,t)]T ~(t) + !!(x,t) (6) mined in the optimization process such that: Page 820 J = 6(x,11,T) + j 1 c and a2 > c2. Using the law of cosines Optimal Two Point Boundary Value Problem yields the state inequality constraint equation. For the problem considered h~re, it is necessary to As with the simple state constraint, seven include the terminal constraints additional variables have been introduced into the augmented problem to account for a simple obstacle. i/J(X,11,T)l = 0 ( 16) One limiting factor using this technique is that the constraint must be mathematically describable in the and the nondifferential control constraints problem coordinates. It might be necessary to approximate a square, for instance, by four ellipses, S(x,u,rr ,T) = 0 ( 17) thus adding 28 additional variables. It can be clearly seen that with even a few obstacles, the problem size where slack variables are introduced to convert the could get prohibitively large. For this reason a inequality constraints to equality constraints. Using multi-point boundary value approach is taken in the the slack variables a(T) and fl(T), and the Lagrange next section. multipliers v, 11(T), and p(T), the minimum time problem becomes a fixed time problem of minimizing the para- Optimal Multi-Point Boundary Value Problem meter rr. That is If interior boundary conditions are added to the TPBVP of the previous section, a boundary value problem J = 1T (18) with interior point constraints is obtained. These boundary conditions can be expressed as R(x,11,ti) = 0 ( 21) w~ere t 0 < ti < tf. and R is ?f d~mension q. If only a single interior point constraint is added, a three The Hamiltonian of this problem is point boundary problem is obtained. However the method can be generalized to an N-point or multi-point H = PTf +pTs (20) problem. Taking the variations of Ja (i.e. 011, ox, op, au, av, Sequential Gradient-Restoration Algorithm (SGRA) op) yields the necessary conditions. The Hamiltonian The actual algorithmic technique used in the finite for the Automelec robot is used to write the explicit element solution of the robotic optimal control problem equations in time normalized form [l]. Thus one has a is based on the sequential gradient-restoration TPBVP with the following necessary conditions: four algorithm of Miele. An important property of the state differential equations, four adjoint differential sequential gradient-restoration algorithm is that, due equations, eight boundary conditions, six nonlinear to the constraint satisfaction that must occur in each simultaneous equations that must be satisfied at all iteration, it generates a sequence of feasible subop- times, and one additional isoparametric equation to timal solutions on its way to determining an optimal account for the parameter rr which is the minimum time solution. This result is a marked improvement over solution. This set of equations must be solved to results obtained using other techniques for solving determine the minimum time optimal control solution optimal control problems. These other techniques, such which consists of the minimum time 11, the optimal tra- as the gradient and variation of extremals methods, try jectories x(t) along the minimum time path, and the to solve the total problem at one time and thus give control history u(t) needed to achieve the optimal either the optimal answer or no answer at all. solution. It is possible to convert an optimal control 4 FINITE ELEMENT FORMULATION OF THE OPTIMIZATION problem with state inequality constraints (bounds) into PROBLEM an unbounded TPBVP using the appropriate transformations •. In the present study, state Since opt\:lllal control problems considered in this constraints are handled in an indirect manner. That study have been normalized in time, it is a simple is, the extremal arc is considered a single subarc even matter to discretize the time continuum. All that is though it may be infinitesimally close to the state necessary is to divide the time interval from t=O to constraint boundary. t=l into N elements with N+l nodal points where the The introduction of a single state constraint first and last nodal points coincide with time t=O and equation in this manner increases the problem size by time t=l, respectively. two additional state variables, one additional control To satisfy compatibility and completeness variable, two adjoint equations to balance the state requirements in the variational formulation of the equations, one nondifferential constraint equation and optimal control problem, the polynomial of the shape its associated Lagrange multiplier. These seven functions of the state variable must be at least first equations must be added to the overall problem size to order with respect to time, while the adjoint and account for one state constraint, and each of these control variable shape functions must be at least variables must exist at all times. Each state constant. This selection of shape functions guarantees constraint must be handled in a similar manner which convergence as the elements become small. implies that, for a highly constrained problem, the As noted earlier, an interpolation function must be size will grow rapidly even for a few initial states. selected to describe the distribution of the field Using the techniques of the last section, it is variable over the continuum. In the context of this possible to pose the time optimal control/trajectory study, the field variables are all of the state, problem with obstacle avoidance as a TPBVP with state control, and lagrange multipliers used in the Page 821 variational formulation of the augmented functional. matrix yet to be constructed will be due to the Polynomial interpolation functions of the form variable z that affects each of the other superelements. It should be noted that for a fixed x = a0 + ai ti time problem there would be no variations of the functional elements as 11 would be a constant. In that are used where i defines the degree of the polynomial case, a straight symmetric superelement would be approximation. In this study, a particular linear obtained. In this situation z is represented by the version of the interpolation function is used. In the one isoperametric equation that passes through all the formulation of the approximating element~= 2t/Dt, points of the finite element mesh. The indefiniteness where Dt is the difference between two nodes i and j, is caused by the constraint equations augmented to the and ~ is defined with 1; = 0 at the center of the functional, and is evidence by the zeroes on the element, and~= -1 and~= 1 at nodes i and j element diagonal. If one can represent the form of z respectively. The interpolation function then becomes in some other manner, it may be possible to get rid of the isoperimetric equation and make the superelement x = a + a ~ symmetric. One method that is used in traditional 0 1 approaches (such as the gradient method with shooting) for the element. Evaluating this function at each for handling isoperimetric equations is to include a node, solving for the constants a and al' and new state variable equation. Using this technique 0 performing the appropriate substitutions allows the increases the number of equations by two times the nondimensional or natural approximating element to be number of elements (state and adjoint), but does not written as eliminate z. Thus the equations are still unsymmetric. Upon close inspection of the isoperimetric x = "12" (1 - ~)xli "12" + (1 + ~)lj = N1xi + N2xj = N T (E;)x equation, it can be shown that the equation can be (22) rewritten as the derivative of x is found by taking partial n t. T derivatives of the element. The integration of a g,r + 2 J J - N Ep dt 0 (25) function, for example the matrix product NTAN, can then e=l t; be simplified by a transformation from the time domain to a natural coordinate system. which is symmetric with respect to K over all the superelements with the exception of~ 5 which is not a Finite Element Representation of the Quasilinearized part of the stiffness matrix. This s~mmetry implies (TPBVP) that the global stiffness matrix equations are indeed The quasilinearized problem is now approached from completely symmetric indefinite for time indefinite the standpoint of a finite element problem. To problems, and have a structure that can be exploited accomplish this, the continuous variables are replaced for efficient solution. It can be also shown how the by finite elements between two time increments. global matrix can be constructed to use a symmetric Letting: indefinite banded matrix routine to solve the linearized equations in an efficient robust manner. e11 = NTp , ex = NT x, eu = NT u, er = NTr, C = r The Application of the FEA technique to the augmented performance index yields the following (x-f) T = F(t), fx = A(t), f u = B(t) , f = E discretized functional ,r and e" 1a!t! x = MTx (23) n t. T T T T J = 1T + l ) JP N[F + M x - AN x - BN u - Ez]dt Descretizing J into n elements and using the e=l ti independent boundary con di ti ons at time t=l for the deletion of m and v, yields n t. T T T + L J Jr [NS N u + NS N x + NS]dt (26) n e=l t; U X J = ( g + g Z) 1 + J 6 L PT [ ( NM T - NAN T) x 11 e=l NBNTu - NEz + NF]dt (24) and the new necesssary matrix equations for the sequen- tial gradient restoration formulation are used to Now for the variation of J to be stationary over the obtain the time indefinite case. The superelement can entire domain, the follow expressions must be satisfied be written as _ aJ _ aJ _ aJ _ aJ _ aJ 0 ax au a z a p a r Kll O K13 K14 I O X 0 Also the equivalent variations must be satisfied over each element, as is made up of multiple O K22 -K23 K24 I O u 0 J elements. It should be noted that the parameter z in the isoperametric equation contributes to each element K31 -K32 O O I -K35 p NF even though it is only a single term. This seems to violate the symmetry desired in the superelement K41 K42 O o I o r NS matrix. In reality, however, symmetry is still 1T preserved as the final row in the global stiffness 0 Page 822 where Ku = 1: ~ K ltt.j (MNT - NANT)dt 13 = l l + \,ToA + u TQB ( 31) tj t. T 1 1 K14 = 1t . K22 = 1 t NN dt + l 12 AT A + BT B dt + CT C dt l l '2" 0 t. T where NB NTdt, K2 4 = l t J NS u N dt NE dt and and where Kij = Kii, and the isoparametric equation is ,,TQB 1 = vTl I j -I J[ u1_ J ( 32) ul+ n t. T I I I I I I Making the same substitutions that were made in the [ O O -e~l 1t i E N dt 1 ] [ x u P 11 TPBVP case, and descretizing the augmented MPBVP functional into n = n1 + n2 elements yields J. + [1] = 0 (28) A typical global matrix representation of a three node, linear, fixed time, TPBVP has the form shown in Generation of Finite Elements Fig. 4. The same system, with an interior point The robot manipulator analyzed in this study has constraint and the resultant discontinuity in the two degrees of freedom or four states. The finite adjoint variable, is shown in shown in Fig. 5. Not~ elements for a four state dynamic system assuming a that both of these representations are shown before the linear variation in each of the elements will be end point boundary conditions have been applied, Both described below. A linear functional approximation of sets of equations are singular until the application of a state vector wi 11 be of the fo 11 owing form the known boundary values. It is only then that the system is made indefinite. -ex = [NJ T-X ( 29) Comparing Figs. 4 and 5, it can be seen that each interior point constraint adds 2nq - n + n variables such that !x is a 4 x 1 vector ~nd ~- is s_ x 1. . The finite element formulat1on w1th t1me varying where n is the number of continuous vRriabTes per matrix coefficients was the form used throughout this node, nq is the number of adjoint variables per node, study as it supplies a better representation of the and nc ~s the number of interior point constraints. finite element field at no additional complexity for Thus each interior point constraint adds the equivalent optimal control/trajectory problems considered here, of approximately two temporal nodes to the problem and the coefficients were readily available. For yielding a significant reduction in problem size another type of problem, this additional complexity may compared to defining obstacles explicitly. not be appropriate. 5 NUMERICAL EXAMPLES Finite Element Re resentation of the Quasilinearized MPBVP) Both the unconstrained and the constrained two The quasilinearized MPBVP functional with one point boundary value problems are solved using a interior point constraint at time t=l can be written as computer program developed as part of this research. This program implements a temporal finite element = 12 pTbO(f - ~) A - fxA - fuB - f C]}dt application of the sequential gradient restoration J j + 11 algorithm discussed previously. The same technique was applied to a two state problem with a single control to prove that the concept and the technique are valid for (30) the multi-point boundary value problem. In order to preserve the banded symmetric indefinite The TPBVP Without Nondifferential Constraints characteristics of the matrix and to allow for the discontinuity in p at time t=l, it is necessary have Solving the minimum time problem in an to unconstrained work space involves minimizing the all continuous variables defined on both sides of the interior point. In the functional described, there quasilinearized functional presented earlier for the must exist variables at x x u u p and quasilinearized dynamic equations of the ACR Automelec 1_, +, -, +, -, p1 • The continuity of tile sta 1te an1d co1ntrol 1. two degree of freedom robot arm. vafiables, at time t=l, is enforced by augment1ng the For the case studied, the boundary C<'nditions on functional with equality constraint equations and their the states were associated Lagrange multipliers. The new augmented . x ( O) functional with the addition of the SGRA isoparametr1c 1 0.7 m x1 ( l) 0.7 m constraint is then x2(o) 0.0 m/s x2( 1) 0.0 m/s J = 11-1 pT[O(f - ~) + A - f A - f B - f C]}dt 0 X U 11 x3(0) = 0,0 r x3(1) p/2 r 0 + 12 l+ j pT(O(f - x) A x (0) 0.0 r/s x ( 1) 0.0 r/s + lI f A - f B - f C]}dt 4 4X U 11 and the initial trajectory guesses were intentionally poor. They were Page 823 (p/2)t r a region in the middle of the trajectory where there is zero actuation force while actually at the state constraint. The system is unable to achieve a better x4(t) = 0.0 r/s, u1(t) = o.o N, u2(t) = 0.0 Nm representation of the control force because there are not enough finite elements in the system, and the The minimum time to move between the two end points control must be continuous. Optimization criteria was found to be 1,937 seconds. This occurred at the other than minimum time, would not affect the control end of seven gradient cycles. The minimum time to move so significantly. rr/2 radians with the arm held at 0.7 m was calculated to be 2,69 seconds. Using the minimum time trajectory The MPBVP resulted in a time savings of 28%, Figure 6 shows the Even though the formulation of the solution of initial and optimal trajectory and that, in order to boundary problems with interior point constraints was minimize the time between two points for a polar mani- straightforward, difficulties were encountered in pulator with bounded controls, it is necessary to extending the computer program developed to solve the reduce the inertia of the manipulator. MPBVP. For this reason, a simple linear quadratic Figures 7 and 8 show the state and control problem was set up to verify that the technique variables as functions of time for different iterations actually would perform as expected. The problem con- of the problem, From these figures, it can be seen sists of minimizing the quadratic functional subject to that at the end of the first restoration cycle (N=l), the state equation constraints and the boundary con- and before the optimization criteria has been applied, ditions xl(O) = 0, x2(0) = 0, xl(l) = 1, and xl(2) the trajectories and their associated controls have o. already begun to converge to the optimum. This fact The temporal finite element solution of the MPBVP occurs because the differential equation constraints is shown in Fig. 11, along with the analytic solution. must be satisfied, while at the same time, minimizing It can be seen that the agreement at the nodal points the deviations from the initial state and control is excellent. In fact, it is impossible to see the dif- histories. Observing the control histories (Fig. 8), ference in the accelerations because the optimal acce- it is noted that the radial control force is not leration is a linear function that is exactly modeled saturated, most of the time, as would be expected. by the finite element approximation. Both the state This is due to the fact that the control is variables x1 and x2 match the trajectories at the node approximated as a continuous function, and can not points. The states have appreciable error between the achieve the discontinuities present in a bang-bang nodal points, but this error could be minimized if system, The angular control torque for this case is either more nodal points were selected, or a higher saturated most of the time, except near the midpoint, order approximating function were used. The primary where it must reverse direction. point to make, however, is that the temporal finite The values of the parameter rr, which is also the element method is an effective tool in the solution of minimum time, are listed in table 1 which shows that the MPBVP which has previously been considered extre- the optimization criteria (Q < 0.01) is satisfied after mely difficult to solve. seven gradient cycles, It is also noted that after the first restoration cycle, and before any optimality 6 SUMMARY AND CONCLUSIONS conditions are satisfied, the calculated trajectory can be traversed in 2.32 seconds, This results in a time The results of this research have shown that the savings of almost 14% over the fixed arm trajectory, temporal finite element method offers a superior tech- It should be emphasized that each of these nique for the solution of optimal control problems. In intermediate trajectories is a realizable suboptimal particular, because the method obtains a global solu- trajectory, because the sa ti sfacti on of the state tion at each iteration, it avoids the divergence constraint equations is enforced at each iteration. problems associated with conventional methods that must From a practical engineering standpoint this is very perform multiple forward and backward integrations of important as it may be acceptable or even wise to use a the differential necessary equations while simulta- suboptimal trajectory. A case in point is to avoid the neously satisfying the nondifferential necessary con- bang-bang operations of the system actuators. ditions. The method presented in this paper has the One point that is clear from the plots of control further advantage that it can be formulated to solve force is that it is difficult to reproduce the the multipoint boundary value problem in a straightfor- discontinuities of actual optimal control variables for ward manner. This is of special importance in robotics bang-bang control systems. The state variable problems where a typical approach to path generation is trajectories, however, are very accurate. to define way points that the manipulator must pass through. TPBVP with state constraints A lower bound state inequality constraint was 7 REFERENCES defined for the previous problem in which rmin was defined to be 0,3 meters. The minimum time trajectory 1. Pritchard, James T., "Optimal Trajectories of was found to be 2.093 seconds which is only slightly Robotic Manipulators," Ph.D. Dissertation, University above the unconstrained problem. The small difference of Maryland, College Park, MD, June 1987. in the final time is attributed to the fact that the state constraint is only active over a small segment of the trajectory. The controls and trajectories for this problem are given in Figs. 9 and 10. In Fig. 9 is seen that once the manipulator reached the constraint, the velocity went to zero. The radial control force plot of Fig. 10 shows that the system is trying to achieve bang-bang actuation at the beginning and ending segments of the manipulator trajectory. There is also Page 824 Figure 1: Cylindrical Robot Schematic Figure 2: Two Axis Robot Schematic (,) (I) K K q " ' (,) (1) (•) <•l K K .. • q 0 ;., ·[ : :I ' (I) •(K ,J q ' Figure 4: Global Matrix of a Three Node TPBVP Figure J: Obstacle Representation I I I I II II ., 0 ] {I) Kt I II 1 (I) I ., 0 ' 12 I \ ----------1-----------1-----------1-----------1--- l---1--- ., I (,) I (1) II II I R I I I 1--•1---1--- ., - •,, I •,, I 1---1---1-~- ., - ----------- ----------1----------- -----------11- ----------1,-----!1---, 1 •,- --- Table l: Robot Trajectory Convergence Properties 1 I R 1--r ., . Ij {t) (2) 1 KI t K1 2 ___I__ -- ---_ ! -__I _ ..,, . . N p Q J=,r ----------1---------- ---------- -----------1---1---1--- 1 II I I ., 0 4. 3e-5 2. 326 I <•) {•) I I l 1. 4e-5 • 2197 2 .137 II • • I I .., 21 u , 2 6. 9e-5 .1093 2. 045 3 2. 9e-5 . 0623 1. 997 •, 3. 6e-5 . 0395 1. 971 2. 7e-5 . 0264 1.954 _:_:::::::I::·:: I-:::: I_:· :I -I=: ===i ==========+l+= 6 1. 9e-5 , 0181 1.944 7 3. 2e-s • 0097 l.937 Figure 5: Global Matrix of a Three Node MPBVP Page 825 1.r - · - - - · ·: ·· · · - - - - ; - - - - · - -:- · - - - ii : JS------~--- ', I I 5-------+-------~------~ ' I ' ~------,'- ------~' ------4' I ' ' -.75L - - - . -- - - rI - - - - - - l 1 ' -1- - - - - - - T - - - - - - - , ·1.-- __ J.__ ---1 a.a 0.1 0.2 OJ 0.4 0.5 0.5 0.: 0. .1 .4 .6 .I -lized Tioe C aec J Figure 6: Polar Robot Optiaal Trajectory Figuu 7: Rad.bl Velocity (xi} I. -------,-- ----r-·-- -····1··--·--···-·r·-·-·-----·-··1 J_ --- --j _- -----~ --.. ---_: _- ----_l _-- ---_: •, I I I ! I ' ' I .51- - - ---- ~' ------ -:'- ------ ~' --- • I I I .Zi~' - - - - - - -,' - - - - - - - rI - - - - - ' ' ' ' j I '' I ~,-------1--- ---:------~-------r------~ -.)Sr- ------:- ------~ -------:- ------t-------: -1. L ~ : - ---~-- - ~ - ~ 0. .1 .4 .6 .8 I. -llzed Hoe (sec) -lized Tiae Cs ec l Figure a: Nonnalized Radial Control Force (u1) Figure 9: Radial Velocity (x2) 2. ··--y-·---, ----i-----r--- r----,-- - ' ' I 1.5 -L' ----L' .sj------- ·- - - - .J - - - - -1- - ----J-----1 '- ----1 'I ' I. ---~-----:- ---~----i----~ .Zi~------ '! I 'I 'I .5 +----~-----:--- ~----~----~-----1-----i E O.t- M:=O 0. ___ L ____ L ____ J ---~-- --,-- --r--- f----~ r ! ; I ! : : : I I I l I ~ -.Zi ~-------~-------1-------~ - 1 I I I ;-/ I ! I 1 I I I 5 '! '1 I' 'l l :; _- _ -_ -_ --~--_ -_-_-_ 1---_ -_-_ T-~ ----T---_ -_/\-_1 ---_-_-_-r_ _______J 'JI -.5 - - - - -T-------1-------,-------~- ' ' ' I -~-------r' -------,' -------~I -1.5 : I : I ~--- : - - - ·- T - - - - -, - - - - -1- - - - - ~ -, - ::'f---.::._::--=--: -1. ' 1. l' J' _~ __ J -2. L 0. .1 .4 .6 .8 0. .25 .5 .75 I. 1.25 1.5 1.75 2. Nor.all zed Ti111e (sec) lime(sec) !-J (I) l a;, a,•. a,• - RotaUonaa 811'• ...• a,. o, -111,etforenoe 8tr••••• FIG 4- Interference and Rotationa 1 Stress.es for a FIG 7- Cross section of Pancake Magnetic Bearing 2 ring assembly =sss1.issssssi P. M. MOTOR DESIGN FIG 5- A single pancake magnetic bearing MAGNETIC SUSPENSION ASSEMBLY MULTI RING FIG a~ Original concept of a Permanent Magnet motor/generator design MAGNET PLATES FIG 9- Improved concept of a Permanent Magnet motor/generator design FIG 6-·- Exploded view of the Pancake Magnetic Bearing 30 Page 833 Single Domain Methods for Modeling Objects in the Round for Engineering and Manufacturing Applications J.J. COX, H. FERGUSON and K. KOHKONEN, Brigham Young University, Provo, UT A Network Implementation or Real-Time Dynamic Simulation with Interactive Animated Graphics M.W. DUBETZ, J.G. KUHL and E.J. HAUG, The University of Iowa, Iowa City, IA The Evaluation or Moments or Bounded Regions Using Spline Approximations of the Boundary J. ANGELES, McGill University, Montreal, CANADA, and Z. CHAOMING, R. DUARTE and H. NING, National Autonomous University or Mexico, Mexico City, MEXICO The Use or IGES in Rapid and Automated Design Prototyping J.A. KIRK, D.K. ANAND, M. ANJANAPPA and W.K. RICKERT, JR., University of Maryland, College Park, MD Computer Aided Design or Internal Involute Spur Gears C.-B. TSAY, National Chiao Tung University, Hsinchu, Taiwan, REPUBLIC OF CHINA MONDAY, SEPTEMBER 26 SESSION D3 2:00 P .M. - 3:40 P .M. KEY WEST ROOM OPTIMAL DESIGN OF MECHANICAL SYSTEMS AND ELEMENTS Chairman: R.W. MAYNE, State University of New York at Buffalo, NY Vice Chairman: E. SANDGREN, Purdue University, West Lafayette, IN Automated Design of a Turbocharged, Gasoline Fueled Four-Stroke Engine for Minimum Fuel Consumption J.K. WOODWARD, JR., Sverdrup Technology, Tullahoma, TN, and G.E. JOHNSON and R.L. LOTT, JR., Vanderbilt University, Nashville, TN Design for Latitude Using Topt K.L. D'ENTREMONT, Missouri Public Service Commission, Jefferson City, and K.M. RAGSDELL, University of Missouri, Columbia, MO Optimal Design of Wind Turbines Using BIAs, A Method of Multipliers Code B.D. VICK, McDonnell-Douglas Aircrart Co., Long Beach, CA, W. WRIGGLESWORTII, Hughes Aircraft, Tucson, AZ, L.B. SCOTT, University or Arizona, Tucson, AZ, and K.M. RAGSDELL, University of Missouri, Columbia, MO A New Algorithm for Inverse Design or Flow Headers R. ARAYA, Universidad de Chile, Santiago, CIIILE, and V. MODI, Columbia University, New York, NY 15 Page 834 DE-Vol. 14 ADVANCES IN DESIGN AUTOMATION - 1988 presented at THE 1988 ASME DESIGN TECHNOLOGY CONFERENCES - THE DESIGN AUTOMATION CONFERENCE KISSIMMEE, FLORIDA SEPTEMBER 25 - 28, 1988 sponsored by THE DESIGN AUTOMATION COMMITTEE OF THE DESIGN ENGINEERING DIVISION, ASME edited by S.S. RAO SCHOOL OF MECHANICAL ENGINEERING PURDUE UNIVERSITY THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS United Engineering Center 345 East 47th Street New York, N.Y. 10017 Page 835 THE USE OF IGES IN RAPID AND AUTOMATED DESIGN PROTOTYPING J. A. Kirk, D. K. Anand, Professors, M. Anjanappa, Assistant Professor, and W. K. Rickert, Jr. Research Assistant University of Maryland Mechanical Engineering Department Systems Research Center College Park, Maryland ABSTRACT To obtain full automation between design and com- ponent production a Flexible Manufacturing Protocol The Initial Graphic Exchange Specification (IGES) [FMP] has been developed at the University of Maryland. for design data and the EIA standard M and G Codes for This protocol is shown in Figure 1 and the d-i scussion Numerically Controlled machines (N/C} is used to deve- will be restricted to the automated machining of lop an automated interface between existing computer prismatic parts. The FMP consists of a number of aided design systems and N/C manufacturing systems. integrated software modules which produce the required The Flexible Manufacturing Protocol, developed at the drivers to control an automated and flexible machining University of Maryland, outlines such an interface to [i.e. chip formingl cell. Of particular interest in control automated manufacturing cells used for proto- this paper is a manufacturing cell consisting of a: typing quick design changes. This paper demonstrates one application of the protocol, developing an auto- Vertical Machining Center mated IGES to CNC interface to control a 3 axis CNC Automated Guided Vehicle machining center given the geometric representation of Loading/Unloading Robot the part in IGES format. Wireframe representations of 2-1/2 dimensional parts, composed of linear elements, The purpose of the FMP is to provide a she 11 in are the primary tools used for design representation. which a mechanical designer creates a component [at the The automated production of the sample part, presented top of the FMP flowchart] and then has the component in this paper, demonstrates that rapid prototyping manufactured [at the bottom of the FMP flowchart], The is possible using an IGES design data file as input to class of components currently under consideration are the protocol. prisraatic parts in which the raw material starts out as solid rectangular raw stock and the designer's com- INTRODUCTION ponent is produced by machining operations which subtract features from the raw stock, thereby producing One of the major goals of the design process is to the desired component. obtain raTid prototype production of a designer's com- ponent, he current procedure typically entail 's a Clearly, the task of developing and implerr~nting a designer interacting with a Computer Aided Design (CAD) FMP is broad based and interdisciplinary and cannot be System, to produce his component, and then the transfer covered completely in any one paper. This paper will of the CAD database information to machining facilities address a particular path thru the protocol in which where the component is manufactured. This transfer of the designer interacts with a "Commercial Computer data to the machining facilities is currently handled Aided Design System" and produces an IGES file which in a variety of ways, ranging from hand coding of a describes his component. "blueprint" to semi -'automated data transfer to computer numerical controlled machine tools (CNC). The need for standardization of communications bet- ween CAD systems has brought about an effort, led by For purposes of this paper we are concerned with a the National Bureau of Standards, to create a neutral class of parts which are loosely termed "components". file for geometric data transfer [1,2). The result was Components are considered to be building blocks of a the first version of the Initial Graphics Exchange mechanical system and, specifically, are prepared by Specification (IGES) completed in 1979. IGES was sub- the removal· of material from solid raw stock using CNC sequently accepted by the American National Standards machine tools. · One such machine tool is a "machining Institute (ANSI) in 1981 [3]. With the IGES standard center" which has the capability of automated tool available the concept of standardizing the rapid and changing and can, by means of this ability, create a automated production of a mechanical prototype becomes variety of features in the raw stock. feasible. 27 Page 836 The IGES path thru the FMP has extremely important tically using expert system techniques. In either industrial applications since it relies upon existing case, the output of the planner is an ordered database standard formats for data representation •. The Initial which is contained in the process plan file [file 5 in Graphic Exchange Specification [ IGES] by the National Figure 1]. Bureau of Standards and the EIA RS-274-D data format for numerical controlled machines [M & G codes] allows At this point a CAM database is produced which con- for a standardized and automated interface to be deve- tains standard M & G machining codes and the fixture loped between existing CAD system outputs and Flexible requirements for holding the part. This information is Manufacturing Cells [or, in the case of our contained in an M & G code file which is shown as File discussions. flexible machining centers]. 5 in Figure 1. The controlling data, along with machine codes, are then post processed to become speci- In this paper the blocks of the FMP will be briefly fic to the machine tool which is physically in the · discussed and the various file formats [shown by cell. circles to the right of the flowchart in Figure 1] which are currently standardized will be outlined. In the FMP shown in Figure 1 the machine specific Given an IGES representation of a component it will be file is termed the "N/C Code File" and is indicated as demonstrated that an automated interface to control a File 7. At this point in the FMP, cell control infor- 3-axis numerical controlled machining center [following mation is required if the cell is to operate in a fully the FMP] is feasible. autonomous mode. This information would consist of the necessary commands to transport the raw material into FMP OVERVIEW the cell, load the material into the machine tool, tell the machine tool to accept the N/C code file, initiate The user begins operation of the FMP by generating machining, unload the part after machining is complete a 3 dimensional representation of the part on a CAD [ or rotate the part if additional feature machining is system. The type of system used to create this repre- required] and transport the part out of the cell. This sentation is not important as·long as the data is portion of the FMP is currently under development and transferred to the manufacturing system in IGES format. will be reported in latter papers. For the present After the part data is transferred to the manufacturing paper the N/C code file is downloaded directly to a system, the geometric representation is decomposed into vertical machining center in which the tool library has the features that need to be machined. This decom- been previously set to agree with the tooling require- positions is accomplished in the feature extractor por- ments set forth in the process plan. One additional tion of the protocol and has been described elsewhere block, "Cell Accuracy Enhancement" is shown as - [4]. Since the IGES format does not contain a uniform affecting cell control. In this block a variety of description for tolerance information, the user must accuracy enhancement methodologies, such as using soft- supply this information interactively after the ware error mapping techniques similar to those deve- features have been identified. This information loped at the National Bureau of Standards [5], are results in the conversion of a drawing file [file 1 in being developed. These are discussed in more detail in Figure 1] to a feature file [ fi 1e 3 in Figure 1]. references [6-10]. After creating the feature file the protocol is The automated IGES to CNC design interface used to evaluate any fixturing constraints which apply reported in this paper will demonstrate that an IGES to the part. This software module is currently under design data file can be used to directly control an N/C development and, at present, it is used to provide machine tool. The work reported in the present paper information for part fixturing which is appended to the will concentrate on the development and validation of part Feature File, thus forming an intermediate file an automated interface to control a 3 axis CNC vertical [file 4 in Fig. 1]. The FMP must decide at this point milling machine, given a geometric representation of if the pa rt can be machined by any of the automated the part in IGES format. This interface is a manufacturing cells available. A cell data base con- simplified version of the FMP which is currently being taining all the functions, achievable tolerances and expanded upon to a chi eve the full FMP goa 1s set forth tools available in the cells is used to evaluate this above. objective. If the part is incompatible or unmachinable with existing cells then the system returns the user to SYSTEM OVERVIEW the design stage. Parts that are compatible and manu- facturable are then earmarked for the appropriate cell The automated IGES to CNC interface takes graphical and the FMP continues to develop necessary machine input data, in the form of an IGES file, along with codes as discussed below. minimal machining data input provided by the user, and creates the machine codes necessary to produce the part The first step in developing the machine codes is on a CNC machining center. Since most commercial CAD process planning. A process planner takes the feature systems can generate IGES files, an interface that uses and tolerance information developed earlier in the pro- an IGES input is CAD system independent, thereby tocol and develops a plan to accomplish the production resulting in a standardized CAD/CAM link. The inter- of the part. Two types of process planners are under face reported in this paper, consists of four segments. development in the protocol. The first type of planner is termed the ordered process planner. Here the user The first segment is the "IGES interface". An IGES interactively enters the necessary machining infor- file in its standard.format contains not only geometric mation to accomplish the production for each feature in data but also innovation information and other non- the part. Typical information would be machining para- geometric data as well. Since, for the purposes of meters such as cutter diameter, speeds and feedrates machining, only the geometric information is required, for each feature. The second type of planner is the file needs to be simplified. This is accomplished currently under development and is called the intelli- by the IGES interface program IGINT [11]. The second gent process planner. This process planner requires no segment of the design interface is the "feature user input and produces an optimal process plan automa- extractor". The feature extractor takes .the geometric 28 Page 837 representaton of the part, condensed from the IGES the parameter data entries that coincide with the poin- file, and.extracts the features to be machined. This ters note.d in the analysis of the directory section. procedure- is carried out by eight programs, PROGl This data is written to file, preceeded by the number through PROG8 [11). of geometric lines that make up the representation of the part, in X-Y-Z coordinate pairs. The resulting The "feature planner", which make up the third file is used as input to the feature extractor. segment, generates tool paths to accomplish the machining of each feature. To do this, various Features machining parameters such as tool diameters and feed Central to the design of the part to be produced, rates are provided interactively by the user. Since is a wireframe model geometrically represented by line the user is involved at this point, all additional segments. The function of the feature extractor is to machining parameters used by the CNC interface are also take the wireframe representation and extract the input at this time. There are two interactive programs features to be machined. The features identified in in the feature planner called PROG9 and PROGlO [11]. the feature extractor fall into two general catagories. Depressions in the surface of the part, referred to as The fourth segment "CNC interface", takes the tool "pockets", and raised surfaces contained within these paths generated in the feature planner along with the pockets, referred to as "posts". Further work which user provided information and generates machine codes has expanded the feature extractor is included in to produce the part. The CNC interface generates reference [4]. For the limited case of 2-1/2 dimen- machine codes in two formats. One is the machine sional milling on one side of a workpiece, the iden- dependent DYNALAN [12] language code which is used to tification of these two types of features provides an control a DYNA 1),12200 CNC milling machine, and the adequate basis for manufacturing of the part. The pro- other is the M&G codes of Electronic Industries cedure of identifying features begins at the top of the Association (EIA) Standard RS-274-D which are com-. part, then moves down through the part redefining all patible with many N/C and CNC machining centers. Two the features wherever a change in cross-section occurs. programs are used for this, the DYNA program and the Each set of features defined in this manner constitutes M&G program [11). what will be referred to as a "level" [11). The programs that make up the design interface are The final product of the feature extractor is a written in BASIC language and have been implemented on collection of pockets and posts formed into groups that an IBM AT and a Sun workstation. The IGES files are are referred to as pocket groups. Each pocket group is obtained from an ANVIL 5000 CAD program residing on the made up of a pocket and any posts that provide an VAX 11/750 computer system. The IGES files are trans- internal boundary to the pocket. ferred to the IBM and Sun via a phone modem using the KERMIT protocol. The machine codes are then downloaded The feature extractor designed for this work is to the machining center via RS-232 line. completely automatic and consists of eight programs [ 11]. The sequence of feature extraction by these Some simplifying assumptions were necessary to make eight programs can be best understood by considering an the project feasible, with the available resources. example. Figure 2, shows the wireframe representation These assumptions include that the part must be 2-1/2 of a sample part. The input for the first program is dimensional, machinable, presented as a wireframe the simplified IGES file of the part, consisting of model, and made up of only line segments. information on line segments. Each one of the four segments that make up the The first program (PROGl) begins by eliminating design interface, is discussed in detail in the vertical line segments and ramp line segments. The following sections. program then finds the maximum and minimum X, Y and Z coordinates of the line segments. The minimum X and Y The IGES Design Interface values and the maximum Z value are then subtracted from IGES was developed to allow CAD systems, from all the line segment coordinates. In this fashion a various vendors, to exchange graphic information in a datum is established as shown in Fig. 3, on the top uniform manner. IGES is a three dimensional standard face of the block in the lower left hand corner of the based on wire frames and simple surfaces [l]. An IGES X-Y plane. The size of the workpiece needed is also ASCII file has five sections, which appear in the known from the minimum and maximum values. The PROGl following order - start section, global section, direc- now finds the various Z levels on which the line tory section, parameter data section, and the terminate segments reside. These levels are then sorted top to section. Each section is made up of a number of 80 bottom. Finally, all the line segments are sorted column records. The complete file has many features according to level, and placed in a file in a level by that are beyond the needs and capabilities of the IGES level fashion. to CNC interface. The IGES file is therefore processed through an IGES interface program, IGINT, which creates This information is used as input to PROG2 for a simple file consisting of only geometric information. implementing the level comparisons that result in the . . plan ·views of each leveL Ttie program begins with the After the IGES file is downloaded from the VAX first level. Since this level is already complete, it system to the IBM AT or Sun system, the IGINT program is· transferred in its entirety to a new file. The begins the analysis with the directory section of the second level is then read in, one line segment at a file. Line entities are found by checking the iden- time, and compared with the lines that make up the tification number in the first field. When a line first level. If a match is not found then the segment entity is located the status number is checked to see is added to this collection of line segments. If a if the 1i ne is part of the geometry. If the line is match is found then both the new line segment and the part of the geometry then the parameter data pointer is one it matches are deleted. After all of the line noted. After all the directory entries have been segments of the second level are checked in this manner checked the program proceeds to the parameter data sec- this collection of line segments is saved in the new tion. The program then reads the coordinate data from 29 Page 838 file as the plan view of the second level. These line that a nested pocket appears before the pocket that segments are then compared with those _of the third surrounds it.· This is accomplished using a definition level and so on until the the last level before the· line scheme similar to ttie one used in PROGS. If a bottom of the part is reached. pocket's definition line intersects another pocket an odd number of times then the pocket is inside that The information produced by PROG2 is used as input pocket, otherwise it is outside. The pockets are then to both PROG3 and PROGS programs. The PROG3 takes the saved in a file in this order. plan views produced in PROG2 and eliminates the edge line segments while adding line segments for the edge The PROG8 program takes the pocket file generated gaps. This is accomplished by deleting the edge line in PROG7 and the post file generated by PROG6 as input segments while saving their endpoints. These endpoints and groups the pockets and posts into pocket groups. are then reconstituted into line segments that close This is accomplished using the same definition line the edge gaps thereby creating new plan views. scheme used in PROG7. The pocket groups are then saved to file for further processing. Note that since the The new plan views generated by PROG3 are fed to pockets are already ordered there is no danger of a PROG4 where the line segments are formed into features. post being grouped with the wrong pocket. At this This is done by simply forming closed loops out of the point all the features are defined and sorted into segments and saving these ordered loops to file. Note pocket groups. This information is used as input to that the separation by level is still maintained. the feature planner. The PROGS uses the information produced by the PROG2 to identify the features defined by the PROG4 Feature Planner program. The PROGS begins by checking the feature to Once the pocket groups have been determined by the see if it includes an edge line. If an edge line is feature extractor, a coherent plan is developed to pro- included then the feature is a pocket. Otherwise the duce them, using the feature planning portion of the program assumes that it is a nested feature. IGES to CNC interface system. The input to the feature planner includes the geometric definition of the pocket A nested feature is approached in the following groups and limited user input concerning machining manner. An imaginary line segment is drawn from one of parameters. The output of the feature planner is a the vertices of the feature to the boundary of the tool path for the machining center to follow. The workpiece. This line segment, referred to as a feature planner consists of the interactive program "definition line", is then checked against the original PROG9 and the automatic PROGlO program. plan view of the level developed by PROG2 to determine the number of intersections. Line segments that make The feature planner begins with PROG9. Since each up the feature are eliminated from consideration. If pocket group input is considered to be independent. the the number of intersections is an odd value then the user must provide machining parameters for each pocket feature is a pocket. If the number of intersections group on each level. Five machining parameters are is an even value or zero then the feature is a post. required for each group, viz: cutter diameter, number This procedure is illustrated in Figure 4. Once the of z-steps, feedrate for the cutter, and plunge rate of features are sorted in this fashion, they are saved in the cutter. These parameters are interactively input a file for further processing. by the user who is presented with a diagram of the pocket group along with level data associated with the It should be noted that a horizontal line segment group. The PROG9 then produces a new pocket group made is used as the definition line and that only line up of line segments, offset half a tool diameter segments with an endpoint below this line are con- inwards from the pocket and outwards from the posts. sidered. Also, horizontal lines are ignored. This approach eliminates inconsistencies that arise from A pocket group's tool paths are set up in the segment endpoints positioned on the definition line. following manner. If the pocketing mode was on. the first cuts are the pocketing cuts followed by the final The PROG6 program takes the information provided by finishing cuts. If the pocketing mode was off, the the PROGS and orders the line segments that make up the only cuts are the finishing cuts. If more than one Z- features. Pockets are ordered in a counterclockwise step was indicated in the machining parameters the fashion, and posts are ordered in a clockwise fashion. pocket group will be machined in increments. This is done for two reasons, the procedure for com- puting offsets in the feature planner is simplified and The finishing cut offset tool paths developed in the finishing cuts made on the part will be climb cuts PROG9 is fed to PROGlO. The program reads in the first which conform to the directions mentioned. pocket group and checks to see if the pocketing mode is on. If the pocketing mode is off, the group is saved The program accomplishes this by determining the as is in a new file. If the pocketing mode is on, the area of the feature, using a method of breaking the pocketing tool paths are developed. The program then feature up into triangles and then finding the areas of moves on to the next group, until a 11 the groups are these triangles using the cross product approach.· exhausted. Since these areas carry a sign with them, after they are summed the sign of the total area of the feature determines its sense. A negative area denotes a clock- CNC Interface wise sense, and a positive area denotes a .counterclock- The tool paths, along with the machining parame- wise sense. Once the segments making up the features ters, generated by the feature planner is then pro- are ordered in this manner, they are saved in files cessed through the CNC interface to generate the with the pockets and posts separated into different machine-specific codes. The sequence of machine code files. generation for each pocket group is given below. The PROG7 program takes the pocket file generated The depth of the first cut on a pocket group is in the PROG6 and orders the pockets on each level so determined by the depth of the group and the number of 30 Page 839 z-steps entered in the PROG9 program for this group. CONCLUSIONS If the pocketing mode was used, the pocket group is cleaned out in the following manner: A rapid move to A Plan for Rapid and Automated Production of Design .1 inch above the surface is performed to allow free Prototyping has been described in this paper. The plan movement to the beginning of the first pocketing tool is termed a Flexible Manufacturing Protocol [FMP] and path. which is also accomplished with a rapid move. consists of a number of software modules which produce The spindle is now moved into the workpiece using the standard file formats containing both geometric and plunge rate defined in PROG9. Following this, a move machining information·. in the X-Y plane to the tool pa th' s endpoint is · accomplished using the feedrate defined in PROG9. The One particular path thru the. FMP _has been described .. process is ttien repeated for the .next· pocketing tool in detail in this paper. This path involves an· auto-· path and so on. mated IGES to CNC interface to control a 3 axis machining center. given the geometric representation .of After the pocketing is finished, or if the a part is standard IGES format. A method of exracting pocketing mode was turned off in PROG9. the program features from an IGES representation of a part has been begins the finishing cuts. These are accomplished in a described and it has been shown that the feature manner similar to that of the pocketing cuts except the extraction technique, and subsequent generation of tool follows the pocket or offsets all the way around standard control codes for machine tools is easily to the beginning before the tool is retracted from the generated. workpiece. A sample part, consisting of a prismatic block con- When these procedures have been accomplished, the taining a number of pockets and posts, has been used to first pass on the group is finished. If only one z- validate the use of IGES to CNC interface for rapid step was specified then a tool change is performed and prototyping purposes. Preliminary results demonstrated the next group is machined. If more than one Z-step that the IGES to CNC interface functions will ultima- was used then the procedure is repeated at the next tely provide for excellent integration between CAD and depth and so on until the bottom of the group is automated/rapid part production. reached. ACKNOWLEDGEMENT Finally, the program sets up a tool change at the end of each packet group and spindle off at the end of This research was partially supported by NSF Grant the last pocket group. CDR-85-00108 through The Systems Research Center. The above machine codes, in two kinds, are REFERENCES generated by the CNC interface. One is the machine- specific DYNALAN compatible code and the other is the 1. "Initial Graphic Exchange Specification (IGES)", standard M&G codes confirming to EIA RS-274-D stan- Version 2.0, National Technical Information dards. For the purpose of demonstrating the feasibi- Services, U.S. Department of Commerce, Springfield, lity of the automated IGES to CNC interface, DYNLAN VA, February 1983. compatible codes were used. 2. Hordeski, M.F., CAD/CAM Techniques, Reston RESULTS- Publishing Company, Inc., Reston, VA, 1986. Figure 2 shows a 3-D wireframe representation of 3. Fallon, M• • "Standard Graphics", The DEC the part used to test the IGES to CNC design interface. Professional, Vol. 5, No. 1, July 1986, pp 22-27. This part was designed using the ANVIL 5000 CAD system residing on VAX 11/750 computer. The resulting IGES 4. Kumar, B.J., Anand, O.K. and Kirk, J.A., "An file was downloaded from the VAX to an IBM AT disk file Intelligent Feature Extractor for Automated using the KERMIT program. At this point the user Machining". Proceedings of the Fifth International enters machining information for each feature. This Conference on Systems E,ineer1ng, September 9-11, information. along with the feature information already 1987, Dayton, OH, pgs. 2 7-240. available, are then processed into tool paths. After the tool paths were developed the form of postpro- 5. Simpson, J.A., et al, "The Automated Manufacturing cessing is chosen. If a DYNALAN program was desired, Research Facility of the Nationa 1 Bureau of the DYNA program is run. If M&G codes were desired the Standards", Journal of Manufacturing Systems, Vol. M&G program is run. To illustrate the dual capabili- 1, No. 1, 1982, pp 17-32. ties of the interface, both types of codes were pro- duced and the resulting codes were in agreement [11). 6. Kirk, J.A •• Anand, D.K., and Anjanappa, M., "Accuracy Enhancement Methodologies in Thin Rib. The OYNALAN program produced by the interface was Machining", Proceedings of the NSF Manufac- then downloaded via RS-232 interface to a DYNA DM2200 turing Systems Researc Conference, 1987, Ann CNC vertical milling machine. The DYNALAN was then Arbor, MI., pp. 9-14. executed and the part was produced successfully. 7. Anjanappa, M., Kirk, J.A., and Anand, D.K., "Tool The IGINT program and the PROGl through PROG8 Path Error Control in Thin Rib Machining", programs took a combined total of 9-1/2 minutes to pro- Proceedings of 15th NAMRC, Bethleham, PA, 1987, cess the part. After the machining parameters were pp. 485-4 2. input, the system created the tool paths in less than three minutes. The M&G code took an additional two minutes, and the DYNALAN program was generated in a little under three minutes. Total processing time, including machining parameter entry by the user, for a part of this complexity takes less than half an hour. 31 Page 840 8. Anand, D.K., Kirk, J.A., and Anjanappa, M., "Tool Path Error Control for End Milling of Microwave Guides", Proceedin~s of the 7th World Con~ress on the Theor~ of Mach1nes and Mechanisms, Vo. 3, Sevilla, pain, 1987, pp. 1499-1502. 9. Kirk, J.A., Anjanappa, M., and Anand, D.K., "Validation of a Relationship Between Cutting Force and Surface Finish for Optimal Control of End Milling", ASME Publication DSC-Vol. 6 ASME Winter Annuel Meeting, 1987, Boston, MA. pp. 15-24. 10. Anjanappa, M., Anand, D.K., and Kirk, J.A., "Identification and Optimal Control of Thin Rib Machining", ASME Publication DSC - Vol. 6, ASME Winter Annual Meeting, 1987, Boston, MA, pp. 15-24. 11. Rickert Jr., W.K., "The Use of IGES in Automated CNC Machining". M.S. Thesis, University of Maryland, College Park, March 1987. FIG.2 SAMPLE PART 12. "DM2400/2200 Programming Manua 1 ". DYNA Electronics Inc., Santa Clara, CA, 1984. z y Ccurclol CAD 8oltv_.. (j) = IRllfINl FILE @=!BES FILE G) = FE.11\IE FILE r1.;f;11iiFot-, I ~l::i"".I I L -,- -..J 0 • INTB1Ell!ATE FILE FIG.3 BLOCK DATUM ® =PIO'.ElSPUNFILE ® = HMl aIE FILE POST 0 = lilt ClIE FILE POCKET FIG.4 FEATURE IDENTIFICATION FIG . I R.fXlllf IWlf/,CllJUMj fmltXll. 32 Page 841 CONTROL METHODS FOR MANUFACTURING PROCESSES Page 842 DSC-Vol. 9 COT ETH 0 ANUFACTURI G ROCE SES presented at THE WINTER ANNUAL MEETING OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS CHICAGO, ILLINOIS NOVEMBER 27-DECEMBER 2, 1988 sponsored by THE DYNAMIC SYSTEMS AND CONTROLS DIVISION, ASME edited by D. E. HARDT MASSACHUSETTS INSTITUTE OF TECHNOLOGY THE .Ai"MERICAN SOCIETY OF MECHANICAL ENGINEERS United Engineering Center 345 East 47th Street New York, N.Y. 10017 Page 843 Library of Congress Catalog Number 88-82843 Statement from By-Laws: The Society shall not be responsible for statements or opinions advanced in papers ... or printed in its publications (7 .1.3) Copyright © 1988 by THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS All Rights Reserved Printed in U.S.A. Page 844 ERROR CORRECTION METHODOLOGIES AND CONTROL STRATEGIES FOR NUMERICAL CONTROLLED MACHINING M. Anjanappa, Assistant Professor, D. K. Anand, J. A. Kirk, Professors and S. Shyam, Research Assistant Department of Mechanical Engineering University of Maryland College Park, Maryland ABSTRACT: feed rate, "Thermal deformations" due to heat sources in a machine tool are reproducible errors which causes Tool path error, defined as the distance dif- a change in the required position of the machine due ference between the required and actual tool path, is to spindle heat up, room temperature variation, fric- classified as cutting force-independent and cutting tion between various moving elements of the machine force-induced errors, This paper deals with the deve- tool etc, "Weight deformations" are caused by changes lopment and experimental validation of a comprehensive in the weight of stationary objects which are firmly cut ti rTg force~independent tool ·path error cbrrection · positioned on the machine tool table, These errors methodology, Also, in this paper, a brief discussion show up as reproducible static position difference in of the methodology to control cutting force-_induced the spindle/table position and occur in addition to errors is presented, Two methodologies of the .cutting deterministic position errors. force-independent error compensation are ·aeveloped, In the first method, the machining codes to machine The "cutting force deformations" can be considered controller are intercepted and changed to obtain com- as (i) deterministic .tool path errors due to pensated slide movements, In the second approach, the compliance between the tool and the workpiece and (ii) unique feature of tilt and translation of a magnetic stochastic tool path errors due to variations in the spindle rotor is used to perform error correction, depth. of cut and process dynamics. The errors due ·to ·without affecting the slide movements: ·----the experimen- cutting force show up ftS position differences between tal validation of thE:? first methodology, ilnplemented the required and actual tool/workpiece ·position and on a vertical CNC machtn·ing center, showed enhancement results in workpiece shapes which_are not perfect, in the accuracy of part. Various researc.hers have dealt·with the problem of INTRODUCTION minimizing these errors in various machine tools and coordinate measuring machines, Cal _ibration techniques The productivity. 9f precision parts can only be using three ·dimensional metrology on a coordinate improved if the tolerance and surface finish are main- measuring machine 1CMM) has been presented by Hocken tained within acceptable limits, at high metal removal [3], The static positioning error terms a~e measured rates, The dimensional accuracy of a machined part is and are stored as _matrices and used to correct the a function of the tool path error, Tt:ie tool path data during a measurement, In. the moael used for error in machining is defined [1,2] as the distance transformation the variation of the angular errors difference between the required/programmed and the with the machine -axis is not taken into account. actua 1 tool pa th, A statistical analysis for the characteristics of Tool path error is classified, as shown in Fig, 1, 'Positioning Error' or 'Scale Error' of a CNC milling according to the source-and the nature of the error as machine was done by Donmez [4], It was found that the cutting force-independent errors, and cutting force- mean of the error is significantly affected ~Y the induced errors. table position and that the feedrate has no signifi- cant effect_ on the posi ti oni ng error. However, the Static deterministic "position errors" are those study is based just on one of the many geometric com- repeatable errors which are a function of machine ponents of the position errors, The feedrate used (3 slide position. The cause for these errors are ipm and 18 ipm) appears to be too ·small to cause any geometric inacc~racies of )he slideways and the misa- dynamic errors. Much higher feedrates, up to 300 ipm, lignment in the str~ral element assemblies, . are used on CNC machines for end milling of thin ribs, Dynamic deterministic j1o-s:lt!,?n errors" are those reproducible errors which are a.function of the table The results and methods for error compensation of 41 Page 845 a three axis coordinate measuring machine at NBS is Linear Errors presented by Zhang [SJ. Compensation for static posi- tioning errors and some thermal effects are incor- The translational error terms are further divided porated in the technique. Minimization of errors due into a "positioning error" (also called "scale error") to cutting forces is discussed by Anjanappa et.al. and two "straightness of motion" terms [10). The scale [6]. The cutting process is modeled as a discrete error is the difference between the actual carriage stochastic system and the system parameters were position in the motion direction and the scale reading obtained using a methodology developed to identify represented by dx(x). Slide straightness errors, system parameters based on experimentally obtained ~y(x) and dz(x), are the nonlinear movement that an data. An on-line microprocessor based optimal control 1ndicator senses when it is stationary and reading was developed and used for maintaining surface rough- against a perfect straightedge supported on a moving ness within specified values. slide or moved by the slide along a perfect straightedge which is stationary. The errors are A real-time compensation scheme for static posi- shown in Fig. 4. tion errors and thermal errors of a CNC turning center at NBS is described by Donmez, et al.[7]. The errors Orthogonality Errors are predicted by the compensation system and adjust- ments made to the control loops of the machine tool "Orthogonality Errors" account for the angular controller in real-time. However , the compensation orientation of two or more axes with respect to each system used requires additional hardware and access to other. Definition of orthogonality is dependent upon builders controller. [BJ and [9] also addresses the the way the motion axis itself defined. One method is problem or error minimization via adjustments made to to measure the straightness in two dimensions and slide movements. · define the motion axis such that the straightnesses with respect to this are minimum. For the carriage In all the reported work, dynamic deterministic shown in Fig. 2, the motion axis will be a line such errors are not included and these can be a major error that source in machining at high feedrates. In addition the methodologies used in the reported work assume 2 2 that the machining is single point cutting. The S= dYi(x) + dZi(x) (1) assumption is essential since it is not possible to change the orientation of the tool in conventional machines. For three orthogonal motion axes the X-axis is selected as the reference motion axis. The deviation The work reported in this paper, represents a from orthogonality of the Y~motion axis with respect comprehensive approach to include dynamic deter- to the X-axis is defined by q , as shown in Fig. 5., ministic error in the error map. In addition this where the X and y axes form azplane. The deviation paper presents a methodology to overcome the restri c- from orthogonality of the z-motion axis with respect ti on of single point cutting in implementing error to the X-Y plane is defined by two angles o,x and a.y. map. This method uses a magnetic· magnetic bearing spindle where the tool system can be tilted within the air gap, to include multi-point cutting as is the ANALYTICAL MODEL case in end milling operations. Reader is referred to [1] for more information on magnetic bearing spindle The modeling of a 3-axis, flat-bed, vertical CNC operation. machining center as shown in Fig. 6 requires the following simplifying assumptions: CUTTING FORCE-INDEPENDENT ERROR TERMS 1. the machine table and the workpiece are Machine errors due to static and dynamic deter- assumed to be rigid bodies which are rigidly ministic deformation can be represented in terms of connected. geometry of the links and joints. For the purpose of 2. only cutting force independent errors are defining the errors a linear carriage is chosen (Fig. considered. 2) with the following assumptions: 3. the tool is assumed to be a point in space rigidly attached to the spindle nose. 1. The carriage is for linear motion along X - 4. each carriage is for linear motion along one axis direction only and there is a measuring 2. The carriage is a rigid body device to measure its position. 3. There is a measuring device for X - position Since part accuracy is determined by the relative Each motion direction is associated with six position of the tool and the workpiece, the vector degrees of freedom. These errors are discussed under describing this is sought. The machine tool-workpiece the title of angular errors, linear errors and orthe- system is considered as a chain of linkages and this gonality errors. relationship can be described using homogeneous coor- dinate transformation matrices. Angular Errors The correlation of the error terms re qui re the The angles are defined as rotations about mutually measurement of the error terms to be made with respect perpendicular axes, which are the machine axes, and to the same reference system. The machine consists of are functions of the slide position. e;x(x), e;x(y), three linear carriages - a table connected to the and e;x(z) represents the rotation about the X-axis, Y- cross-slide through a prismatic joint, the cross-slide axis, and Z-axis respectively. Rotations about the X, connected to the bed by a prismatic joint, and the Y, and Z axes are al so kno~.rr"as roll, pitch, and yaw vertical slide connected to the column by a prismatic respectively. The errors are shown in Fig. 3. 42 Page 846 joint. The cutting tool is rigid1y connected to the vertical slide. -(z(z) -(y(z) Rr [ (z1(z ) -(x(z) llx(z) ] = 1 lly(z) (8) The nominal tool (spindle) position is selected as 2 -(y(z) -(x(z) 1 oztz)+Z the reference point. Four right-handed orthogonal 0 0 0 coordinate systems are selected for the purpose of defining the error, one assigned to the reference point which is fixed in space ard the other three are where llx(z) = o (z) + (J. .z (9) assigned to each of the three slides, as shown in Fig. X y 6. The transformatiqn matrices representing these and lly(z) = oy(z) + (J.x.z (10) slides are given by 1Tj where i and j can be any one of R, X, Y, and Z representing the coordinate systems. The schematic chain of linkages is shown in Fig. 7. By taking the inverse of equations (5) and (7) and substituting in equation (4) we get the required The homogeneous transformation describing the transformation matrix Xrz : relative translation and rotation of the cross-slide with respect to the reference coordinate system is given by Rry. The position and orientation of the e:z(x,y)-e:z(z) -e:y(x,y )+e:y{z) table with respect to the reference system Rrx is -e:z(x,yi+e:z(z) 1 e:x(x,y)+e:x(z) given by the equation; [ e:y(x,y)-e:y{z) -e:x(x,y)+e:x(z) l ,, J R R Y 0 0 0 TX = Ty• TX (2) ( 11) where K = Similarly, the position and orientation of the tool with respect to the reference system is given by; X-ox(x )-ox (y)+ox( z)+(J.z. Yffiy. Z+Y .e: z(x,y) R R Y X -Z[(y{x)+e:x(y)] Tz = Ty. TX. Tz (3) Y-oy(x)-oy(Y)+oy(z)+(J.x.Z+Z.e:x(x,y)-X.e:z(x) [ Z-oz(x)-oz(y)+oz(z)-Y.e:x(x,y)+X.e:y(x) The position and orientation of the tool with respect 1 to the tab 1e , on which the workpiece mounts, can be J written as; where the term i{j,k) = i(j)+i{k). Xr z-- Yr - l RT - l RT X • Y • Z (4) The last column in equation (11) represents the Carriage transformation matrices actual position of the tool tip with respect to the table coordinate system after motions of the X, Y, and When the cross-slide moves a di stance Y the trans- Z directions of the respective slides. formation matrix of the cross-slide in the reference system is given as, The tool path error is found by taking the vector difference between the commanded positions and the actual position arrived at. Hence, the tool path - z(y) -e:y(y) l error (El is given by; E = 1 -e:x(y) o lyx((yx))- YJ (5) -e:x(y) 1 oz(y) 0 0 1 -ox(x )-o x(y )+ox( z) +(J. z. Yffiy .Z+Y .e: z(x,y )-Z[e: x(y )+e:y(x )J -oy(x )-oy(y )+oy( z )ffix.Z+Z.e: x(x,y )-X.e: z(x) [ -o z(x )-o z(y )+oz( z)-Y .e: x(x,y )+X.e:y(x) where llx(y) = ox(y) + (J. .Y (6) (13 2 EXPERIMENTAL WORK The second term in equation (6) arises due to the squareness error of the Y-axis with respect to the X- A careful inspection of equation ( 13), shows that axis. the tool path error vector (E) is composed of 18 indi- vidual error components which is listed in Table 1. Similarly the transformation matrix for the table, In order to prepare an error map at any location in which moves a di stance X with respect to the nomi na 1 the work zone a 11 the 18 error terms should be position of Y-slide, is given as, measured. The 18 error terms are grouped under linear, angular, straightness and squareness category. -e:z(x) e:y(x) ox(x)-1 Static Error Term Measurement y TX = [ e:z1(x ) 1 -e:x(x) oy(xl (7) -e:y(x) e:x(x) 1 oz(x) To measure the above error terms a Hewlett-Packard 0 0 0 1 5528A Laser Measurement System was utilized. This system is specially designed to measure all the above error terms, except the roll about the motion axis, The transformation matrix for the tool slide very accurately in a machine tool environment [11]. moving a distance Z with respect to the reference system is given by, 43 Page 847 Table 1 Li st of Error Terms Dynamic Error Term Measurement The dynamic errors can be very significant under Error Term Descri etion high feedrates which are common in highspeed machining (HSM). The HP system has provisions to measure 0 (xl X - axis sea le error straightness dynamic errors only. Hence, only ox (y) y - axis scale error straightness errors, are measured and included in the oy (z) z - axis seal e error map. The dynamic straightness error measurement was oz (x) y straightness of X axis conducted at various feed rates ranging from 10 oy (x) z straightness of X axis inch/minute to 200 inch/minute. However, the creation oz (y) X straightness of Y axis of error map including all dynamic terms, require some ox (y) z straightness of Y axis minor hardware modification in both the machine tool oz (z) X straightness of z axis controller and the measurement system. The error ox (z) Y straightness of Z axis terms thus generated will encompass both static and gy (x) Roll of table dynamic deterministic errors (i.e., all cutting-force gX (y) Roll of cross-slide independent errors). Following is a brief discussion gy (x) Pitch of table of such an error map generation. gy (y) Pitch of cross-slide X Ez (x) Yaw of table The machine tool controller generates a velocity Ez (y) Yaw of cross-slide profile with respect to time depending on the CXX Squareness of Z in Z-Y plane programmed feedrate. The velocity curve exponentially ex Squareness of Zin Z-X plane increases with time to the programmed feedrate and Cly z Squareness of Y in X-Y plane remains constant for some time before exponentially dropping to zero. Therefore to relate any dynamic error measurement to the position of the machine with The measurement of the linear terms ox(x), oy(Yl, respect to the reference coordinate system the velo- and oz(Z) was done by a linear interferometer ana city profile has to be determined. For this purpose a retroreflectors. The interferometer/retroreflector microprocessor based system can be used which can assembly is mounted on the spindle in position of the collect both the machine position display signal from tool and one retroreflector is fixed on the table, in the controller and the time. The laser measurement position of the workpiece. For complete details on system has to be synchronized with the machine start- how to make measurements refer [11]. Measurements up to record error data. Error measurement can be were made at 1 inch increments. The test conditions automatically done at certain time intervals so as to were as shown in Table 2. relate the error terms to the machine position and feedrate. The error matrix developed by this method The measurement set-up similar to X-axis is used has error terms as a function of table position and for Y and Z axes, except for Z-axis the interferometer feedrate. was mounted on the table and the retroreflector was mounted on the spindle. The measurement of the pitch The error map including dynamic errors is £y(x), £x(Yl and the yaw E:z(x), Ez(Yl was done currently under investigation at the University of following the set-up given in 11 • The measurement Maryland. However, the methodology of implementation of straightness errors lly(x), oz(x), llx(Yl, 0z(Yl, presented in this paper is applicable to both static 'i' \ \; ~: ._ ·-.,.., . ,,.f1 ', \ 01236; -0.001 ' A . - -f+---&-R- - -FI \ G40 G49 060 G20; I G91 028 ZO; \ G91 G26 XO YO; j G52; -·0.()'J~ · · · ·r--· · 1- - 1-1·- ,·--1 ·-·r-· r--1-,---,-1 · -,---~ G92 XO YO ZO; o 2 .3 4 5 t> 7 a · g 10 ,, 12 13 1-1 ~s ,s GlO 02 Pl X -14.0 Y -10,0; G54 T 3 H6; FIG. 13 DYNAMlC STRAIGHTNESS ERROR IN Z DIRECTION GOO G90 XO YO S 1500. H3; FOR X MOTION G4 3 Zl. 0 H 3 ; GOO Z 1.0; GOO X 2.3 Y 2.3; GOl Z-1.2 F 4.0; GOl X 4.7 F 12 . 5 PATH a FIG. 16 UNCOMPENSATED M&G CODES VA8NAC N)(:I oontrol l•r ...., 01236; G40 G49 GBO G20; G91 G28 ZO; G91 G26 XO YO; G52; G92 XO YO ZO; GlO 02 Pl X -14 . 0 Y -1 0 . 0; G54 T 3 H6; GOO 090 X -0 . 0364 Y -0.0228 Z 0.0029 S 1500. H3; G43 Zl.O H 3 GOO X - 0.041' 1 y -0.0256 z 1.0046 GOO X 2,2fl5 y 2 . 2732 2 1.0057 GOl X 2.2659 y 2.2764 2 -1.1944 F 4. 0; Gill X 4 . 6620 y 2.2712 z -1.1911 F l.2. 5 FIG . 17 COMPENSATED M&G CODES FIG.14 TWO METHODOLOGifs OF ERROR CORRECTION 49 Page 853 Journal of Power Sources, 22 (1988) 301 - 311 301 SATELLITE POWER USING A MAGNETICALLY SUSPENDED FLYWHEEL STACK* JAMES A. KIRK and DAVINDER K. ANAND University of Maryland, Mechanical Engineering Department and The Systems Research Center, College Park, MD 20742 (U.S.A.) Summary This paper reports upon research activities, with magnetically suspended flywheels, that are being cooperatively conducted by TPI, Inc. and the University of Maryland for GSFC. The purpose of the effort is to critically examine and further the development of all the key technologies which impact the inertial energy storage system. The results presented in this paper discuss the concept of a magnetically suspended flywheel as it applies to a 500 W h energy storage system. The proposed system is currently under hardware development and is based upon two "pancake" magnetic bearings arranged in a vertical stack. Introduction To effectively design a 500 W h flywheel energy storage device, several parameters concerned with the specifications, design goals, and applications of the device have to be known a priori. For spacecraft applications, it is important to minimize the mass and size of the device without sacrificing its energy storage capacity. Therefore, one design goal of the system is to max- imize the SED (specific energy density). This SED should exceed that of electrochemical systems, which are, typically, 14 W h kg- 1 . A system SED goal for a past 300 W h flywheel design [2 - 5] has been to exceed a value of 20 W h kg-1 or 9 W h lb-1 . This was the design goal used for the 500 W h energy storage system. The proposed energy storage system is based on a "pancake" magnetic bearing stack as shown in Fig. 1. The magnetic bearings used in the stack have been discussed by Kirk and Studer [ 6, 7] and are a required element for a viable and efficient energy storage system. The acceleration of the flywheel or charge cycle (motor mode) must occur during a 60 min interval when the satellite is exposed to sunlight. The spindown of the flywheel or discharge *A portion of the work reported in this paper was performed under NASA contract NAS5-29272 [l]. 037 8-77 53/88/$3.50 © Elsevier Sequoia/Printed in The Netherlands Page 854 11 302 I MAGNETIC BEARING Fig. 1. Magnetic bearing stack for 500 W h system. cycle (generator mode) must occur during a 30 min interval when the satellite is exposed to darkness. The energy storage system during discharge must supply power at a constant voltage of 150 ± 2% volts d.c. However, to design a flywheel with suitable size and capacity, operating speeds which are directly proportional to generator output voltages must vary by 50% (the high operating speed being twice as much as the low operating speed). Therefore, some type of power conditioning must be incorporated to maintain the required output voltage. In addition, energy losses in the electronics associated with the charge and discharge cycles must be minimized. For the .300 W h design, an efficiency of 90% for each cycle is desired. This was also assumed for the 500 W h design. Therefore to supply 500 W h, a 550 W h capacity flywheel was sized. Other design goals of the system include modularity, suitability to withstand outside load disturbances, and protection of equipment when failure of flywheel material or suspension occur. An additional design criterion specifies that the rotor remain magnetically suspended under a 2 g radial load. This criterion is used in the 500 W h design. To protect the magnetic bearing, suspension ring, and motor/generator when failure of the magnetic suspension occurs, back-up ball bearings are used. The outside portion of the ball bearing (see Fig. 2) is set just beyond the gap operating range of the magnetic bearing (typically ±0.01 in.). The ball bearings support the flywheel when the flywheel deflection due to outside disturbances exceeds this operating range. They protect the magnetic bearing and motor/ generator materials from collision. A detailed discussion on magnetic bearing back-up ball bearings is given in a paper by Frommer [2, 8]. For protection of satellite equipment if the flywheel material fails under high speeds (burst condition), it is necessary to design the flywheel for separation of the Page 855 303 z Quadrant 1 I Stator,Center + X Fig. 2. Flywheel touchdown for a double magnetic bearing stack. outermost rings from the remainder of the flywheel (as was done in refs. ,9,_ 14). Doing this makes the containment of failed flywheels easier. Proposed flywheel design The 500 W h capacity flywheel was analyzed using the FLYANS~/ FL YSIZE software developed by UMCP [11 - 13] and modified by TP.I. TJ;1e computer program FLY ANS2 performs a stress analysis on a multi-ring flywheel arrangement, given material properties and inner radius ratios (inner radius of ring/outer radius of entire flywheel). Other inputs include the inner radius displacement ratio limit and the ring interference (in assembly) ratio limit. The inner radius displacement ratio input limits the gap growth (between the suspension ring of the flywheel and the magnetic bearing) of the suspension system due to the. centrifugal forces generated by the spin- ning flywheel. Gap growth affects the suspension control system in a detrimental way by reducing the control system active stiffness, KA- The ring interference limit is the limit on the amount of interference between rings. FLY ANS2 performs a stress analysis for both non-interference fitted and interference-fitted rings. For interference fitted rings, it computes ring interface pressures that maximize SED while staying within a prescribed limit ( typically O. 6%). The data from FLY ANS2 are used for the FL YSIZE computer program to actually .size the flywheel. The FL YSIZE output for the 500 W h flywheel Page 856 304 is shown in Table 1 with the upper and lower operating speed ratio, selected as 0.375 and 0.75 of the burst speed. It is assumed that the flywheel has a weight of half the total energy storage system. Therefore its SED must be twice the system SED. Through repeated simulations, it was determined that a flywheel configuration with an inner return ring made of segmented iron and 5 composite (Celion 6000 graphite/epoxy) outer rings, interferenced fitted and having inner radius ratios (inner radius of ring/outer radius of outer ring of flywheel) of 0.48, 0.5, 0.6, 0.7, 0.8 and 0.9, yielded high SEDs that exceeded twice the system SED. The inner radius displacement ratio limit and the ring interference limit value used was 0.006. Repeated computer runs for a 500 W h flywheel with a high SED have yielded a flywheel configuration weighing approximately 29 lb. The stack bearing consists of 2 magnetic bearings, a motor/generator, and 2 back-up ball bearings as shown in Fig. 1. One requirement for the flywheel is that it must have a large enough height to house the compo- nents shown in Fig. 1. Based on the sizing of the 300 W h flywheel system, the minimum component height for the 500 W h system is 4.50 in. (11.4 cm). Flywheels incorporating 4 in., 5 in. and 6 in. (10.2 cm, 12.7 cm and 15.2 cm) magnetic bearings were analyzed and designed using the FL YANS2, FLYSIZE, and MAGBER computer programs. MAGBER, developed at UMCP, was used to determine the bearing's axial-load carrying capability. The results of design runs for flywheels using 4, 5 and 6 in. (10.2, 12.7 and 15.2 cm) dia. magnetic bearings are summarized in ref. 1. As mentioned before, centrifugal forces cause the inner radius of the flywheel to expand at high speeds ( called air gap growth). FL YSIZE deter- TABLE 1 Flywheel specifications for 500 W h energy storage system Inner diameter 5.760 in. (14.630 cm) Outer diameter 12.000 in. (30.480 cm) Thickness 5.474 in. (13.904 cm) Configuration Multiring ~ 1 seg. iron ring 5 graphite/epoxy rings Burst speed 70k r.p.m. Max. oper. speed 52k r.p.m. Low oper. speed 26k r.p.m. Weight 29 lb (13.2 kg) Usable energy density 18.96 W h lb- 1 (41.71 W h kg- 1) Burst energy density 44.95 W h lb- 1 (98.89 W h kg-1) Air gap growth @ burst speed 0.0353 in. (0.8966 mm) Air gap growth@ 52k r.p.m. 0.0199 in. (0.5055 mm) Air gap growth @ 26k r.p.m. 0.0050 in. (0.1270 mm) Page 857 305 mines this expansion at the low and high operating speeds of the flywheel and reports these numbers to the user. Through iterative design runs using FL YANS2 and FL YSIZE, one can meet the air gap condition as well as achieve at high SED. The 500 W h design yielded an SED value of 19 W h lb- 1 ( 42 W h kg- 1) and an air gap growth between lower and upper operating speeds of 0.015 in. (0.381 mm). Magnetic bearing technology The magnetic bearing for a 500 W h energy storage system was designed to support a 2 g axial load without loss of suspension. An additional goal was to achieve a certain permanent magnet radial stiffness, Kx, and current-force sensitivity, K 1 . Design values for Kx and K 1 were assumed based on main- taining suspension control system performance similar to past UMCP magnetic bearings. Based on the UMCP 3 in. (7.6 cm) laboratory model, Kr was taken to be one hundredth the value of Kx in lb A- 1 . Thus, for the 500 W h design, Kr was chosen to be 56 lb A- 1, while the value of Kx was chosen as 5600 lb in.- 1 (1002 kg cm-1) with a flywheel linear excursion range (around a uni- form air gap) of ±0.01 in. (±0.254 mm). Knowing the desired system axial-load carrying capability, Kx, K1, and maximum current, the following physical and magnetic properties of the bearing are then determined using the MAGBER design program: Stator radius, air gap, permanent magnet (PM) area, PM thickness, PM operating point, leakage permeance, air gap permeance, air gap flux and flux density, coil turns, coil wire size and axial drop. The sizing of the magnetic bearing involved an iterative process via computer simulation using the program MAGBER. Magnetic circuit perme- ances, fluxes, and flux densities were computed for trial physical dimensions (i.e., pole face thickness, gap distance, axial drop, magnet area, magnet length) and material magnetic properties of the bearing. The operating flux density of the permanent magnets was also derived. Kx, K1, coil turns (N), and axial-load carrying capability (Wa) could then be determined using the computed magnetic circuit parameters. Based upon the trial dimensions, pole face thickness and air gap distance were increased to avoid saturation in the iron material ( which limits the amount of useful flux that crosses the suspension air gap). The flux density within the Fe material should not exceed the value of 1.5 T or saturation will occur. The maximum flux density of the iron material was determined by computing the flux density at the thinnest portion of the flux plates, i.e., at the pole faces. MAGDESIGN (a program developed at TPI for this project) was used to determine saturation conditions for various displacements of the flywheel. The object was to remain at an unsaturated condition within the operating gap range of the suspension control system. Page 858 306 Suspension control system design The design goal for the suspension control system for the 500 W h energy storage system was to design a control system which would keep the flywheel suspended under static and dynamic loads. To withstand static loads (in this case a 2 g radial load), a system gain was selected which provided a steady state active stiffness sufficient to satisfy the required operating excursion range of the flywheel. Nearly all of the electronic component values from previous UMCP laboratory suspension control systems were used in the design of the 500 W h control system. A schematic of the control system for the magnetic bear- ing is shown in Fig. 3. The input reference voltage was determined to be within the range O - +15 V, which was the range used in past systems. The maximum operating current was used to size the coil wire and the power amplifiers. To minimize the control current and yet maintain the same steady state active stiffness the current-force sensitivity K1 was increased and the adjustable reference voltage was reduced by the same proportion. By increasing K1 the amount of coil turns needed for design was increased. For a value of R 17 = 11 k.Q and K 1 = 56 lb A- 1 (25.5 kg A- 1), N was computed to have a value of 825 turns/ coil, with a maximum operating current of 10.12 A. K 1 was then increased by a factor of 2.5 to reduce the coil amperage to 4.05 A and reduce the variable resistance to 4360 n. This resulted in a K 1 value of 140 lb in.- 1 (25 kg cm- 1) and a turns/coil value, N, of 2100 turns. The modified values were used for the 500 W h design. The final parameter that was determined for the suspension control system was the compensation network time constant, T. This parameter influences the damping of the system. For the 500 W h system, it was desirable to maximize the damping so as to limit the flywheel excursions due to mass unbalance. To maximize system damping and minimize dynamic loading effects, an optimum value of T was selected. To optimize T, root locus plots and Bode plots were used, and the results are given in ref. 1. Linear Gain Low Pas Power Adjust Filter Amplifier Coils X Summing Amplifier Compensation Eddy Current Network Transducer A(Ts + 1J_~} V X (o(ST+_U~- Fig. 3. Control system for magnetic suspension. Page 859 307 For the 500 W h system, a value of T = 0.0016 s was chosen to mini- mize the amplitude of response and maximize damping. This called for a capacitance value of 0.016 µF in the compensation network of the control system (keeping the resistance the same as previous values of past systems). Based upon experience gained in designing the control system shown in Fig. 3, a modified version of the control system, as shown in Fig. 4, is being currently investigated for use in the 500 W h system. i - - - Fd I MAG. BEAR. MODE'L I POWER COMPEN K AMPLll'IER Kl 1/Ma2 3ATOA #2 Go Kx I- POSITION COMPEN TRAN8D. SATOR #1 Ho POSITION LOOP Fig. 4. Control system for 500 W h design. Motor/generator design The motor/generator design for the 500 W h system is based upon a permanent magnet, electronically commutated, 3-phase machine, shown conceptually in Fig. 5. Several improvements in the conceptual design have been incorporated into the 500 W h system, and these are shown in Fig. 6. MULTI RING Fig. 5. Laboratory model of permanent magnet motor/generator. Page 860 308 NI-FE-8 ROTOR BACKING PEMANENT ------../ IRON MAGNETS OPTICAL POSITION SENSORS FERRITE ST A TOR CORE ARMATURE WINDING A TT ACHED(MOLDED) TO ST A TOR CORE Fig. 6. Motor/generator design for 500 W h system. The first step in design was to determine power, voltage, and armature current variation during the charge cycle of the motor and the discharge cycle of the generator. It was assumed that the bus of the motor receives a constant power of 650 W from the solar array at 150 V ± 2% d.c. This happens durring the time span of an hour. Since motor voltage is propor- tional to flywheel speed and flywheel speed was chosen to vary by 50%, a motor voltage profile varying from 70 V to 140 V was used in the design. (This assumed a voltage drop of 10 V during transfer of energy from PV array to flywheel motor.) Armature current variation (per phase) was determined by dividing the time equation of power by the time equation of voltage. At the beginning of the charge cycle, the armature current/phase was computed to be 3.1 A and at the end it was computed to be 1.4 A. A proportional discharge cycle was assumed such that over 21 min, the generator discharges at a low power of 625 W and over the remaining 9 min the generator discharges at a high power of 1875 W. Altogether, the generator delivers 1100 W over 0.5 h, equal to 550 W h. 500 W h actually gets to the satellite power system due to energy losses in the power electronics. (This was a previously mentioned design goal.) The voltage variation of the generator is linear from 140 V to 70 V, but it varies at two different rates due to the change in power delivered. It was determined that the maximum current in the armature per phase is 8.93 A/phase. This maximum current (which exceeds that of the motor) is used to design the coils in the armature. In the proposed motor/generator, the rotating ring will be replaced by a stationary ferrite ring glued onto the inside periphery of a stationary ironless armature. The outside rotating ring assembly is made up of PM and is attached to a soft iron backing ring. An 8-pole machine is proposed using a delta-connected winding operating at 4000 Hz maximum frequency. The dimensions of the device are constrained by the size of the flywheel and the magnetic bearing. For the 500 W h Page 861 309 design, the outside radius of the soft iron backing ring could not exceed the inner radius of the first composite ring of the flywheel. A 2 in. packaging height was a design goal. The gap distance between PM's and armature coils needed also to exceed the gap distance of the magnetic bearing. Based on these constraints, PM size, and armature coil configuration and size were determined. Of further interest is the determination of energy losses within the armature and also within the power electronics of the device. Armature loss (312 m,,_xR) was computed to be 2.11 W, while the loss due to the ferrite ring was determined to be negligible (less than 1 W). Most of the other losses for the 500 W h energy storage system were kept the same as, or scaled up from, the 300 W h design. 500 W h design The proposed design of the 500 W h magnetically suspended flywheel energy storage system is shown in Fig. 7. The specifications of the entire system are summarized in Tables 1 and 2. Table 1 summarizes flywheel specifications computed using the FLY- SIZE/FLY ANS2 software. Table 2 gives magnetic bearing specifications which were determined using magnetic circuit theory and the design programs previously discussed. MA NETIC BEARING ,uoNETIC BEARINO ELE TRONIC MODULE SUPPORT STRUCTURE COMPOSITE COMPOSITE MATERIAL MATERIAL FLYWHEEL FLYWHEEL SUPPORT STRUCTURE " BACK-UP BALL BEARINOS Fig. 7. Cross-section of 500 W h flywheel energy storage system. Page 862 310 TABLE 2 Magnetic bearing specifications for 500 W h energy storage system Radial stiffness, Kx 5600 lb in.- 1 (1002 kg cm- 1) Current-force sensitivity, K1 140 lb in.- 1 (25.1 kg cm- 1) Turns/electromagnetic coil, N 2100 turns Maximum operating current, imax 4.05 A Gap operating range ±0.01 in. (±0.254 mm) Nominal gap distance, g 0 0.038 in. (0.965 mm) Stator radius 2.88 in. (7.32 cm) Pole face thickness 0.15 in. (0.38 cm) Magnet diameter 1.8 in. (4.57 cm) Magnet length 0.3 in. (0.76 cm) Conclusions/recommendations Based upon the state-of-the-art review and the proposed design of the 500 W h system, it can be concluded that: • Magnetically suspended flywheel energy storage systems are a viable and potentially superior alternative to batteries. • System issues of attitude control and power transfer are manageable. • The magnetically suspended flywheel system can be designed, using current knowledge, in modules varying in size from 100 W h to 1000 W h. Consistent with these conclusions, the following activities are currently underway: • Construct a Prototype 500 W h Energy Storage System using the pro- posed design. • Bench test prototype to 20 000 r.p.m. • Enhance robustness of control electronics based on bench testing. • Design a test program to cycle energy storage wheel through opera- ting range. • Construct a Spin Test Facility for cyclic testing at design speeds. • Test and evaluate prototype operation under design conditions. Incorporate test results in final design. • Construct a flight hardware experiment. References l SBIR Rep. Design of a 500 W h magnetically suspended flywheel energy storage system, Contract NAS 5-29272, August, 1986. 2 D. K. Anand, J. A. Kirk and D. A. Frommer, Design considerations for a magnetically suspended flywheel system, Proc. 20th Intersoc. Energy Conv. E'l~i,ponf., Miami Beach, FL, Aug. 18 - 23, 1985, pp. 2.449 - 2.453. 3 D. K. Anand, J. A. Kirk, R. B. Zmood et al., System considerations-for a magnet- ically suspended flywheel, Proc. 21st Intersoc. Energy Conv. Eng. Conf., San Diego, CA, Aug. 25- 29, 1986, pp. 1829 - 1833. Page 863 311 4 D. K. Anand, J. A. Kirk and M. L Bangham, Simulation, design and construction of a flywheel magnetic bearing, ASME Paper 86-DET-41, presented at the Design Eng. Tech. Conf., Columbus, OH, Oct. 5 - 8, 1986. 5 D. K. Anand, J. A. Kirk and M. L. Bangham, Design, analysis and testing of a mag- netic bearing for flywheel energy storage, ASME Paper 85-WA/DE-8, presented at 1985 ASME Winter Annual Meeting. 6 J. A. Kirk, Flywheel energy storage - Part I, Basic concepts, Int. J. Mech. Sci., 19 (1977) 223 - 231. 7 J. A. Kirk and P. A. Studer, Flywheel energy storage - Part II, Magnetically sus- pended superflywheel, Int. J. Mech. Sci., 19 (1977) 233 - 245. 8 D. A. Frommer, Mechanical design considerations for a magnetically suspended flywheel, M.S. Thesis, Univ. Maryland, August, 1986. 9 J. A. Kirk, D. K. Anand and A. A. Khan, Rotor stresses in a magnetically suspended flywheel system, Proc. 20th Intersoc. Energy Canu. Eng. Conf., Miami Beach, FL, August 18 - 23, 1985, pp. 2.454 - 2.462. 10 H. E. Evans and J. A. Kirk, Inertial energy storage magnetically levitated ring-rotor, Proc. 20th Intersoc. Energy Canu. Eng. Conf, Miami Beach, FL, August 18 - 23, 1985, pp. 2.372 - 2.377. 11 J. A. Kirk and R. A. Huntington, Stress analysis and maximization of energy density for a magnetically suspended flywheel, ASME paper 77-WA/DE-24, presented at 1977 ASME Winter Annual Meeting. 12 J. A. Kirk and R. A. Huntington, Stress redistribution for the multiring flywheel, ASME paper 77-WA/DE-26, presented at 1977 ASME Winter Annual Meeting. 13 J. A. Kirk and R. A. Huntington, Energy storage - an interference assembled multi- ring superflywheel, Proc. 12th JECEC Conf., Washington, DC, September 2, 1977, pp. 517 - 524. 14 J. A. Kirk and D. K. Anand et al., Magnetically suspended flywheel system study, NASA Con{. Pub/. 2346, An Assessment of lntergrated Flywheel System Technol- ogy, Dec. 1984, pp. 307 - 328. Page 864 Page 865 CELL CONTROL STRUCTURE OF FMP FOR RAPID PROTOTYPING D. K. Anand, J. A. Kirk, Professors M. Anjanappa, Assistant Professor and S. Chen, Research Assistant Department of Mechanical Engineering and Systems Research Center University of Maryland College Park, Maryland ABSTRACT This paper presents the development and successful demonstration of a Flexible Manufacturing Protoco l (FMP) for rapid prototyping of prismatic parts. The cell control structure is defined to suit rapid prototyping of quick design changes. ·The software modu l e input/output formats and their interfacing issues are discussed. An example of how the FMP for rapid prototyping works with aver- tical machining cell is included. The successful demonstration of the protocol verifies the smooth information flow through the control structure. INTRODUCTION To be successful in today's marketplace, it is essential to meet conflicting demands such as greater product diversification, improved quality and lower costs. On top of the above requirements, in many cases, it is imperative to 'shorten' the time needed from 'concept to product' to make the product a suc- cess. Hence, one of the major goals of taday's design process is to obtain ra¥id prototype ~roduction of a designer's component. The current procedure typical y entails a esigner interacting with a Computer Aided Design (CAD) System, to pro- duce his component, and then the transfer of the CAD databas ,~ information to machining facilities where the component is manufactured. This transfer of data to the machining facilities is currently handled in a variety of ways, ranging from hand coding of a "blueprint" to semi-automated data transfer to computer numerical controlled machine tools (CNC). To obtain full automation between design and production a Flexible Manufacturing Protocol (FMP) has been developed at the University of Maryland. Reader is referred to [1,2,3,4] for more details on FMP. Rapid Prototyping, using FMP, discussed in this paper, is a natural outgrowth of FMP with emphasis on reducing concept to product time. For purposes of this paper we are concerned with a class of parts which are loosely termed "components". Components are considered to be building blocks of a product and, specifically, are prepared by the removal of material from solid raw stock using CNC machine tools. One such machine tool is a "machini ng center" which has the capabi 1 ity of automated tool changing and can, by means of this ability, create a variety of features in the raw stock. Figure 1 shows the FMP for Rapid Prototyping and the discussion in this paper will be restricted to automated machining of prismatic parts. The FMP con- sists-" of a number of integrated software modules that produce required drivers to 89 Page 866 control an automated and flexible machining cell. Of particular interest in this paper is a manufacturing cell consisting of a vertical machining center, an auto- mated guided vehicle and material handling robot. The purpose of developing FMP for rapid prototyping is to provide a shell in which a mechanical designer creates a component (at the top of the flowchart) and that has the component manufactured Cat the bottom of the flowchart). The class of components currently under consideration are prismatic parts in which the raw material starts out as sol id rectangular raw stock and the' designers' component is produced by machining operations which subtract features from the raw stock, thereby producing the desired component. This paper presents a flexible manufacturing protocol (FMP) for rapid proto- typing of prismatic parts. The various file formats (shown in circles to the right of flowchart in Fig. l) which are currently standardized will be discussed. Given an IGES (Initial Graphics Exchange Specification) representation of a com- ponent, it will be demonstrated that an automated rapid prototyping (following the FMP for rapid prototyping) is feasible. THE FMP FOR RAPID PROTOTYPING OVERVIEW Although the focus of this paper is the control structures it is worthwhile to give a brief overview of the FMP for rapid prototyping as to its functionability. Shown in Fig 1 is the FMP for rapid prototyping within a cell. This inclu- des all processes from design to part production including AGV and robot control. Following is a brief description of various stages of FMP for rapid prototyping namely, part design, manufacturability, process planning and cell control. For more detailed information the reader is referred to [1,5]. Part Desi ~n At t e top of the flowchart the user can design parts by two different approaches. In the first approach a commercial CAD system is used to create the design and store the design in an Initial Graphics Exchange Specification (IGES) format, which in file 2 in Fig. l. The FMP for rapid prototyping then decomposes the IGES file by a feature extractor into a collection of features such as grooves, pockets, slots, holes, etc. The user at this stage can interactively add information, such as toleran- ces, materials, and surface finish thereby creating the feature file (file-3 in Fig. 1). Feature file at this point consists of the geometry, topology, features, and manufacturing information of a component. In the other alternative approach the component is designed by using a spe- cial feature-based CAD system [4]. In this path the feature file (file-3 in Fig. l) is created directly. Manufacturabilitt Manufactura ility by definition could conceivably encompass a wide variety of functions. One such example is to check for tolerances and geometrical machi- nability, sharp corners, surface finish, interference between tool holders and workpiece. However, in this work, at the current stage, no manufacturability checks are made. Since only one eel l (vertical machining eel 1) does exist, in this work, no cell identification is required either. Process Planning Process planning can be defined as the process of determining the methods and the sequence of machining a workpiece to produce a finished part or component to satisfy the design specifications. In the FMP for rapid prototyping there are two parallel paths that can be followed in producing the process plan as shown in Fig. l. On the left side is the ordered process plan which uses a well established approach of user interac- tion. The intelligent process planner, on the other hand takes the feature file as the input and outlines the required machining processes automatically. This is discussed in more depth in references [4]. 90 Page 867 NC Code Generation The output of the process planner is processed through a pre-processor to generate EIA RS 244 standard M & G codes. A post-processor then translates the standard M & G codes into the machine specific codes. Cell Control Based on the process pl an gfmerated by the process planner, the cell host will coordinate the activities in the shop floor to machine the part. Tasks involved during the m~r.ufacturirg processes include: Trunsport the raw mata~ial into the cell via AGV. Transfer the material from AGV to the machining center. Unload finished part from the machining center to the AGV. Transfer the finished part out of the cell via the AGV. STANDARDIZATION AND FLEXIBILITY The FMP for rapid prototyping can operate efficiently if high degree of standardization exists throughout the system. Notice in Fig. 1 that there are seven different types of files exist at different stages in the FMP. The most important feature of the FMP is that the standardization is introduced in four of these seven file types. They are #2 - IGES file, #3 - feature file, #5 - pro- cess plan file, and #6 - M & G code file, and are described below. The IGES file is consistant with the IGES Version 3.0 which specifies file structure format, a language format, the representation of geometric, topologi- cal, and non-geometric product definition data. Although IGES has addressed the need for data exchange, it cannot handle tolerances, materials and surface finish information. The Product Data Exchange Specification (PDES), currently under development at NBS, fully supports the needs for a con,,ilete product model [6]. Another alternative to PDES is the Part Model Format (PMF). PMF is the format currently being used by NBS as the part model to transfer part information. Unlike PDES, it deals only with machinable parts, and it supports only a boundary representation solid modeler. At present, there is still some latitude in choosing the feature file format so that either PDES or PMF can be selected as the format to be attached to the FMP for rapid prototyping in the near future. The process plan file describes the manufacturing activities to be carried out at the system level and eel l level to accornpl i sh the manufacturing tasks. Although there is no standard in the process plan file format, the Process Plan Format (PPF) used by NBS is selected to be the process plan file format for the FMP for rapid prototyping. The process plan file format will be discussed in depth in later sections. M & G Codes, as specified in EIA RS-2740, are the standard for cutting codes for all NC/CNC machines and is chosen for FMP for rapid prototyping. CONTROL STRUCTURE From the functional point of view, the FMP for rapid prototyping can be represented by two different blocks as shown in Fig. 2. The top block represents the FMP/D (Part Design) that prepares all the required manufacturing related data, such as feature file, process plan file, and NC code file for a particular part. The lower one is FMP/M (Manufacturing} where the manufacturing processes take place, such as transportation of workpiece, loading/unloading of the part, and machining. The philosopies of the FMP/D have been partially validated by previous works [1,2,7,8,9], however, the link between the FMP/0 as well as the structure of the FMP/M remains unexplored. The work reported in this paper addresses this issue. Specifically the cell attributes, the cell configuration and system hierarchy, the cell capability and user environment will be discussed. 91 Page 868 The Cel 1 Attributes In order to achieve high flexibility and tractability the following two attributes must be satisfied [10]: 1. The cell and its component parts and pieces must be modular. 2. The cell and its components fit into a structured hierarchy. The modular approach allows the user to distribute the investments over a long period of time, to gain experience, to refine the software and to proceed towards complete automation. The hierarchical concept which consists of several control levels, has been generally accepted as the control structure of a flexible automation system. It provides a method for partitioning the control problem into modules so that each module can be implemented as a finite-state automation. Cell Configuration and System Hierarchy Based on the concept of modularity and hierarchical control [12] for rapid prototyping, the system configuration is defined as shown in Fig. 3. The cell, in our system as shown in Fig. 4 consists of a robot for workpiece transportation inside the cell and a machining center. Other components include a gripper and advise that work together with the robot arm and machining center, respectively. The dashed line represents the cell boundary with the AGV traveling through the cell boundary and delivering the workpiece. The user accesses the cell facility either by the direct link or by using the FMP for rapid prototyping where the user can design the part and manufacture the part immediately. At the top level of the hierarchy is a system manager that manages the cell level components, distributes and schedules the production tasks. The cell hosts reside at the second level from the top. An equipment controller is placed bet- ween the cell host and the shop floor components to access the intermediate operation information of the cell. Notice that the AGV control module is at the same level as cell host in order to serve as a material transportation cell deli- vering parts between cells. The relationship between parent and child modules is a master-slave relationship. No direct handshaking is allowed between any two modules at the same level of hierarchy. The information path between modules at the same level is controlled and handled by parent module or modules at a higher 1 eve l • Cell Capability and User Environment The vertica1 machining cell is designed for automated machining with the following capabilities and limitations: o The cell will handle prismatic blanks. o Tools limited to the tool magazine. o The cell will machine without fixture intercepts. o Equipment status is always known. o One part for each AGV run. The FMP for rapid prototyping is designed to be a multi-user system, and can be accessed from the system workstation or console (system context), or from a remote PC as a terminal (system context), or computer (remote computer context). For each level of cell hierarchy, there will be manual mode, automode, and help mode. With the manual mode, the user will be able to access the status of components in the next level of hierarchy as well as control these components. When in au.tomode, thf, control is then returned to the upper hierarchy. These modes will help the user in setting up the cell, controlling individual com- ponents, diagnosing the cell, and recovery from failures. Since the intelHgent vise, gripper, and AGV are not available at the current stage of development of the cell, the control of these components is simulated by several personal computers together with human intervention, thereby providing a dynamic ,nodel. The personal computer takes in the command from the parent module of the simulated component and shows it on the screen. The human reads the command from the screen, executes it. and responds to the PC with the current status of the component or the status of execution. The PC then converts 92 Page 869 the status into a specific format and returns the information to the commanding module. SOFTWARE STRUCTURE The software structures are defined as shown in Fig. 5. Functions performed by each module are described in the following paragraphs. User Interface Program (UIP) module is the program through which the user will access the utilities of the system. More than one user will be allowed to log in and run this program. UIP provides optional entries in the FMP/D for the user to select from. It is also the program through which the user can enter the System Control Program (SCP) of FMP/M in order to carry out the manufacturing tasks. The System Control Program (SCP) module manages, controls, and monitors all of the cells. It will accept system level process plans as input in the automa- tic mode. It will also accept system level work elements (e.g. command AGV to go to a target location) in manual mode. Only one SCP can run at a time. Cell Control Program (CCP) module will accept and execute the eel l level process plan. CCP first decomposes the process plan into a collection of cell level commands, relay these commands one at a time to the equipment controller and assures that the status of the command is in the correct status. It also accepts cell level command in the manual mode. The major responsibility of the Equipment Control Program (ECP} module is to accept cell level commands issued from cell host and execute those commands on the appropriate piece of equipment. All the software modules inside the cell boundary have been developed and implemented [11]. Interfaces of each module are under development and are discussed in later sections. The hardware available for this work is mapped on to software as shown in Fig. 6. FMP/0 ~ FMP/M INTERFACE ISSUES Although discussion of all the interfacing issues are beyond the scope of any one paper, following is a brief description of some of the interfacting issues that needed to be addressed in order to develop the protocol. The SCP needs a driver which defines the sequence and procedures to be carried out to accomplish the manufacturing task. This includes the control of system level components, such as control of AGV to travel through cell boundary and control of ce 11 components. such as the vise, gripper, robot. and VMC. which can not be seen by SCP. The SCP also needs the NC codes for the specific machining tool to cut the part. The process plan file in FMP should provide the former infor- mation while the postprocessor provides the NC code file. The information required for the SCP is thus defined as the process plan files and the NC code file. There are two types of process plan files: the system level process plan files (PP SCP), which are used to drive the SCP, and the cell level process plan files (PP-CCP), which are used to drive the cell host (CCP). Each manufacturing task of a-particular design consists of a SCP process plan file and one or more CCP process plan files generated by the processor planner in FMP/D. The rela- tionship between PP SCP and PP CCP is parent-child relationship. The general structure of a process plan file consists of 4 different sec- tions: the header section, the parameters section, the requirements section, and the procedure section. The header section defines the general information about the file such as the plan ID, plan version, plan type, and plan name. The para- meters section declares undefined parameters which will be defined at run time. The requirements section declares required child process plan files and hardware components. The procedure section describes the procedure for accomplishing the given task. The PP CCP procedure section consists of cell level work elements which will be decomposed into cell level commands by the cell host. The work element is defined as the lowest level of manufacturing commands that are recognized by the process planner. 93 Page 870 SOFTWARE I/0 TYPES Shown in Fig. 7 is the software 1/0 types between various software modules. Input/Output (I/0) of each software module in FMP/M is classified according to three major types of information: request type, status type, and NC code data type. The request type of information encompasses all the requests that need hardware service. Status type of information covers all the status reports as the result of status requests. NC code data type includes all the files that are to be used in the manufacturing processes such as PP SCP, PP CCP, CCFILE, and NC code file. - - The communication between CCP and SCP is done through the use of a mailbox. This increases the flexibility of the cell so that in case the SCP is idle or down, the cell utility is still available for some other system. All software modules are activated by request type of information. Because this is a closed loop system, every request type of 1/0 will be associated with a status type of 1/0. To simplify the complexity and increase the flexibility of the system, the I/0 format is unified except for data type of information. Each data type has its own natural format that can not be changed. The fundamental 1/0 format consists of 64 characters, as shown in Fig. 8. Based on this fundamental format, we first define the cell level command format. Every work element in PP CCP is a task to be completed by one or more cell com- ponents. This implies that the target field can be filled in with one of the four components: VISE, GRIPPER, ROBOT, and VMC. The parameter field is divided into 3 sub-fields with 15 digits for each sub-field. The parameter can be the contents of the command, numerical values that shows the target point to be reached, or just blanks. Another type of information that needs to be formated in the lowest level of hierarchy is the status type. Similarly, the format described previously for eel 1 level commands can be applied to the status type of information. For the link between CCP and ECP, the format for request type and status type are exactly the same as those at the lowest level. respectively, except there is one more target (ECP) for both. The format for the link between SCP and CCP is also similar to that discussed previously. More details can be obtained from reference [11]. IMPLEMENTATION All the software modules from CCP and down (see Fig. 5) of the vertical machining cell have been developed and integrated. However, at the current stage of development SCP and UIP are not available. To overcome this problem, the user at this stage of development is advised to place the PP CCP filename in the TEMPFILE. When the user turns the control of CCP to auto mode, the cell will first check out the cell status and, if the cell is in the READY status, it will receive this prepared command from TEMPFILE and starts executing the PP CCP. In order to validate the FMP for rapid prototyping a prismatic part was designed and then manufactured. This part, shown in Fig. 9, was designed on the SUN workstation. A "VMC SETUP" file which serves as a library of the vise setup at the machine table is used to help the CCP decide the loading target point of the part in a world coordinates. During the manufacturing process, the computers interact with each other based on the control hierarchy and the cell level commands in the CCFILE. The whole process took about twenty minutes after the part was designed and the part was successfully manufactured. This demonstration shows that enough manufac- turing information flows smoothly through the control structure for rapid prototyping. CONCLUSIONS The Flexible Manufacturing Protocol {FMP) for rapid prototyping presented in this paper proposes a way to make efficient use of information resources for computer-integrated production method. Software structure for eel l control is defined and functions to be achieved by each software module are discussed. The 94 Page 871 demonstration of successful automated and rapid manufacturing of the sample part shows that enough information flows smoothly through the protocol structure. REFERENCES 1. J.A. Kirk, D.K. Anand, M. Anjanappa. and R. Uppal. "Implementation of a Flexible Manufacturing Protocol", ProLeedings of the TASTED Applied Control and Identification Conference, December 1986, Los Angeles, CA. 2. B. Kumar. D.K. Anand and J.A. Kirk, "Integration and Testing of a Intelligent Feature Extractor within a Flexible Manufacturing Protocol", Proceedings of the 16th NAMRC, May 1988, Urbanan, IL. 3. Walter Kellner Rickert, Jr., "The Use of IGES in Automated CNC Machining", M.S. Thesis, Mechanical Engineering, College Park. University of Maryland, Feburary 1987. 4. B. Kumar, D.K. Anand and J.A. Kirk, "An Intelligent Feature Extractor for Automated Machining". Proceedings of the 5th International Conference on System Engineering, September 1987, Dayton, Ohio. 5. Mark R. Cutkosky, Paul S. Fussell and Robert Milligan, Jr, "Precision Flexible Manufacturing Cells within a Manufacturing System", Technical Report, Carnegie-Mellon University, 1983, Pittsburgh, PA. 6. Bradford M. Smith, "Product Data Exchange Specification - The PDES Project - Objectives, Plans and Schedules", National Bureau of Standards, June 1986, Gaithersburg, MD. 7. H. Hammer, "Flexible Manufacturing Cells and Systems with Computer Intelligience", Robotics and Computer-Integrated Manufacturing, Vol. 3, No. 1, PP. 39-54, 1987. 8. Y. Ono, "Cell Control Systems", Robotics & Computer-Integrated Manufacturing, Vol. 3, No. 4, PP. 389-393, 1987. 9. D. K. Anand, J.A. Kirk, E. Magrab. M. Anjanappa and D. Nau, "Protocol for Flexible Manufacturing Automation with Heuristics and Intelligence", Manufacturing International, April 1988, Atlanta, Georgia. 10. M. Weck, G.Kiratli, "Applicability of Expert Systems to Flexible Manufacturing", Robotics & Computer-Integrated Manufacturing, Vol. 3, No. 1, PP. 97-103, 1987. 11. Sujen Chen, "Structure of a Flexible Manufacturing Protocol for Design and Control of a Vertical Machining Cell", M.S. Thesis, Mechanical Engineering, College Park, University of Maryland, May 1988. 12. Mclean, C.R., "The Vertical Workstation of the AMRF: Software Integration", ASME Symposium on Intelligent and Integrated Manufacturing, Chicago, IL, 1986. 95 Page 872 C.Oa....-cial Feature Saeed C A O Soft_..o C ~ O CD G) = CflA',II!«J FJLE 0 • IGES HLE USER C1ol. Hetll CD = FEAlll'E FILE Intel l lgont Fixture Plonnlr,g ri_oo-'l. -, < Oeta a.,,., 0 U I ' I CELL II CCHELLLL H12O ST AGV • C!D .__ __, CELL HOST • WIUYACTIJRABILITY • FllTIJII!IG • PROCESS PUii • !IC CODE CE/100 TI ON EQUIPIIENT .___...,...__, CONTROLLER CELL COIIPONENTS FMP/M GRIPPER VtfC VJSE ROBOT Figure 3 System Configuration 4 ll>JIUFACTURING > • CELL CONTROL PART Figure 2 F~IP/D and F~1P/M L Cell Boundary I- - - - - - - - - - - - - - - - - - - - - ROBOT I PART VACHINING CENTER I Raw llaterial In USER Figure 4 Th,, Cell 97 Page 874 U m ( ) ( O i e r • I - S { J / ( - - - - - - - 1 - - - - - U l P U l P U m I m I n t e r i m h l t r f a c e P r o c r U I P r o c r 1 1 1 S p l e a S y 1 l t 1 1 I K m c e r I c 1 1 1 1 p u l e r S C P S C P S y 1 l e a S y 1 l r . l l C o 1 L r o l C o a l r o l P r o c u a P r e e r • I I • I t • ' C C P C C P m A G Y C t l l I I C e l l c o o l r o l l e r C e l l I I C e l l C e l l 1 2 c o o l r o l l e r i o s l C o a l r o l , i 1 t l 1 L i 0 D ( 0 ~ 0 1 1 C H l r t l 1 ( 1 1 ' 1 l a l i 0 D C 0 P r o c n • P n c r i • D . _ _ _ _ _ I - r - - - + - - - , - - - - - I C P r " , , o , , , 1 e 1 1 E C P f . q u i i - e o l I F . q u i i - e 1 L F . q u i i - e a l ~ 1 i i - e 1 L m l r o l l e r C o a l r o l I C o a l r e l l m l n l l e r P r o c r U I P r t c r • I I I I I I I ' V I C v » C G r i p p e r R e i o ! V i s e C r i p p u m t r o l l e r I m l r o l l e r c o a l r o l l e r c o o l r o l l e r m t r o l l e r c o a l r o l l e r 1 i 1 1 1 1 i 1 i 0 D 1 i 1 d 1 L i n 1 i 1 1 1 l 1 l i n 1 i n l 1 L i n 1 i 1 1 l 1 l i o D s i a u h l i o a _ I I . \ _ - j 1 6 1 4 T . J - J ' - - _ . . . . . . . _ _ _ _ . _ " - ' - " . . . ; c . ; . ~ f F - - I I m . . . . m 1 1 1 1 n ) : ( l J T S I / U R J S / O V F i g u r e 6 H a r d w a r e M a p F i g u r e 5 S o f t w a r e S t r u c t u r e P a g e 8 7 5 C ll•tr ) Jalorm1tion type Sp,ce .S.1.1l.e ,1.1, Tarret field t 't t = Cell 12 CCP "' Shlus fi,ld .-- D j -.:;; u -'-' JC cot, 4ah ECP - Par>m.tas field - u ~ ~ ~ ~ "' c:! "' ~ "' ~ "' lise Cripper 1,,1,ot TIC End .r ,.,,,.,, ! EON) cbar>der conlroll,r contrcll,r coolroll,r eontrolltr siauhlion eiauhlion 1iauhli•• sinhlio• Figure 8 Fundamental I/0 format )1 - lt - ...-... lf - _ flC '--- - - - - - - _ J '" _.,, Figure 7 Software 1/0 Types Figur~ 9 Demonstration Part 99 Page 876 A CAD APPROACH TO MAGNETIC BEARING DESIGN M. Jeyaseelan, Research Assistant D. K. Anand, Professor J, A, Kirk, Professor University of Maryland Mechanical Engineering Department and the Systems Research Center College Park, MD 20742 ABSTRACT predictions and the experimental findings of charac- teristic parameters of the hearing such as Kx and Ki A design methodology has been developed at the Magnetic due to neglecting the three dimensional charac- Bearing Research Laboratory for designing magnetic teristics. Improving the flux computations by making bearings using a CAD approach, This is used in the better approximations of flux paths, with more probable algorithm of an interactive design software package. paths to account for the total flux, minimizes the The package is a design tool developed to enable the discrepancies. An additional factor was the occurrence desl.gner to simulate the entire process of design and of saturation at some critical sections in the ferro- analysis of the system. Its capabilities include magnetic bearing material. As saturation limits interactive input/modification of geometry, finding further generntion of control flux, it has to be any possible saturation at critical sections of the corrected. An interactive CAD program has been deve- system and the design and analysis of a control system loped incorporating the above improvements, In addi- that stabilizes and maintains magnetic suspension. tion, it enables the designer to design and analyze a linear control system for stabilizing the bearing [11]. INTRODUCTION SOLUTION METHODOLOGY Several researchers have conceptually designed and fabricated magnetically suspended flywheels and Determining the distribution of magnetic flux in free bearings since the late 1960's (1-10]. The system space ls a complex process and it is the key issue in being studied at the University of Maryland consists permeance computation. This air space is reduced into of a flywheel suspended by a magnetic bearing which is a network of simply shaped flux paths as shown in radially active and axially passive; It provides figure 1. The volume of each of these paths is then constraint in two orthogonal radial directions by means computed to obtain the permeance. of actively controlled electromagnetic coils, whereas axial movements and all other degrees of freedom Once the network of all probable flux paths is .laid (except flywheel spin) are constrained by means of out, the permeance computation p:rocess starts with permanent magnets only. Details of this "pancake" breaking each path down to very simple shapes (for bearing design have been discussed previously [5]. The example, paths 3. 1, 3, 2 and 3. 3 in figure 1) for which performance of such a magnetic bearing can be charac- the cross sectional areas are either readily known or terized by a force versus displacement of the rotor can be calculated fairly easily. Since the geometry of relative to the stator. This force results from magne- the bearing is symmetrical about the horizontal and tic flux produced by either the permanent magnets, vertical axes and each magnetic plate has been slotted electromagnetic coils, or a combination of the per- to yield four independent quadrants for control, per- manent magnets and electromagnetic coils [7]. Hence, meances may be computed for one quadrant and this can in evaluating this flux, it is important that all pro- be applied for the entire bearing. For this analysis a bable flux paths are considered and the leakage flux is total of six major paths are defined in order to accounted for. This process 1 of course, starts with account for the useful, fringing and leakage permeance the calculation of permeances in all the flux paths. around the bearing. Among the above permeances, only In choosing the flux paths that are probable, con- permeance in path 1 (in the air gap) constitutes the siderable knowledge and experience is necessary on the useful flux while those in paths 2, 3, 4 and 6 consti- designer's part. For the problem under study, a net- tute the fringing flux. Finally, permeance in path 5 work of probable paths (9] was developed for flux flow constitutes leakage flux of the bearing system, between the permanent magnets in the magnetic bearing and the return ring. The approximate calculations Once all the permeances are computed, the total of revealed some discrepancies between the theoretical these permeances, Pt, cs calculated by summing up all Page 877 the 6 values, Then, a quantity S,., the operating flux After seventeen parameters are entered in this manner, density of the magnet, is computed from the hysteresis program control is transferred to another phase called curve (B-H curve) for the permanent magnet. the 'parameter modification phase', In this phase, Computation of $m, the total flux contributed by the all the parameters that have been input thus far are magnet, 4>u, the useful flux across suspension air gap, summarized and displayed. The user is asked to enter $f, the fringing flux, and K,c, the passive radial the number corresponding to the item that he wishes to stiffness of the bearing, follow this. Permeances modify, After all modifications are done interac- discussed so far are those due to the permanent tively, pressing the Sat, love): 1.58 T. "Simulation, Design and Construction of a Flywheel Flux Densit1J B at section S = 1.88 Teslas. ==> Sat, level: 1,58 T. Magnetic Bearing", ASME paper 86-DET-41, presented at the Design Engineering Technical Conference, Press IIJN k8ll to continue , , , Columbus, Ohio, Oct, 5-8, 1986, Figure 2: Critical sections for saturation check: Bias flux and control flux. 6, Anand, D,K,, Kirk, J,A,, and Frommer, D,A., "Design Considerations for Magnetically Suspended Flywheel Systems", Presented at IECE Conference, Miaml. Beach, Fla, Aug. 18-23, 1985. 7, Plant, D, P,, et al,, "Prototype Testing of Magnetic Bearings", Presented at IECE Conference, Philadelphia, PA. Aug. 10-14, 1987, COHl'IIOL SVSl'El1 BLOCM D1AG1W1 8, Rotors, Herbert C,, 11Electromagnetic Devices", John Wiley and Sons, Inc,, 1941. 9, Downer, James R,, "Analysis of a Single Axis Magne- tic Suspension System", M, S, Thesis, Massachusetts Institute of Technology, January 1980, 10, Iwaskiw, Peter A,, "Design of a 50.0 WH Magnetically Suspended Flywheel Energy Storage System", M, S, MJu.•t..lde 9•ln Jln•l•t.on l17, 112 1117/Jll Thesis, University of Maryland, College Park, 1987. Law,. .. filter ltaht.on 116, Jrl: Cap,u:it.or CJ J/(0,,R(,,o(s+O,.R'?}) 1'.-r Alllpllfler !1.11idDN Rl'J, RZl, 112? (RZ2'+R2ll/ (U91tltZZ) CDlla tlectrc..tigreb ICi Pl•nt "-•· aiaper.-lon with Fl.,.,.Mel (t,11)/(1 .. Z-.b,,.,) 11. Jeyaseelan, M., "A CAD Approach to Magnetic Bearing Trtnsill~MI E.li1JCur~nl tullUu.cen H8 Cimpensttor Res. RI.R2,RJ,R4: Cap. Cl 1'..«s+(il'J'J)l(s+(V(ANTD) Design", M,S, Thesis, University of Maryland, L..Uln..._-1!rut!9rt....~RH=••~t2-_____ ,uRtl"'il""'I"-\ ___ College Park, 1988, Figure 3: Control system block diagram with components and transfer functions. Page 880 MAGNETIC BEARING DESIGN CONTROL SYSTEM DESIGN Introduction Modify St;i.bi\ity 11naly5l1 and R17 n,nge romput1tion Compute reference voltage, Ka. and natural frequency recompute limiting mmfand control flux Ym Ya Compute max. control flux, redesign current at saturation &flwo:den!lty Root locus plot, Time respolHle plot and Bode ploti go back lo Introduction return to main menu Figure 5: Flow diagram for Control Figure 4: Flow diagram for Magnetic Bearing System Design. Design. Page 881 FLUH PATHS; Variation of Ka_unsat & Ka_sat CROSS SECT IDNA.L U IEM v Figure 6: Graphical output of the design program showing cross sectional view of flux paths. Air G•p II») Figure 9: Plots of active stjffness k vs. air gap width g • a 0 Variation of Kx with Air Gap Width TREND CHART OBTAINED FROM PROGRAM RESULT~ Kx Ka inc dee inc dee inc dee Magnet inc Thickness lm dee Magnet inc Diameter Dm dee Air Gap (In) Pole Face inc Figure 7: Plot of passive stiffness kx vs. air gap Thickness widtn g • lpf dee . 0 X ' Coil inc Turns N dee Variation of Ki_unsat & Ki_sat Pin inc With Air Gap Width Diameter Dpin dee Air Gap inc Width g0 dee inc: increase dee: decrease Figure 10; Trend chart obtained. from program results. ACKNOWLEDGEMENT Figure 8: Plots of curren~ force sensitivity ki vs. Th.ic--; work was supported in part under NASA e;rant NAGS- air gap width g • 396, T!Je helpful discussions of G,E. Rodriguez of 0 NASA/GSFC and P. Studer of TPI, Inc. are greatly appre~ ciated. Page 882 Knowledge Representation Scheme for an Intelligent Feature Extractor B. Kumar, D. K. Anand and J. A Kirk Mechanical Engineering Department University of Maryland College Park, Maryland 20742 Abstract generation of machine tool paths. In such applications, usually all the parameters corresponding to the A Flexible Manufacturing Protocol (FMP) recently individual machining processes, e.g., the particular implemented at the University of Maryland, attempts to machine, the fixture, the operational speed, the feed rate, link the user to a finished part. As part of this etc., are known in advance and the computer tool implementation, an intelligent feature extractor has been incorporates them into a complete NC code file. developed which is sensitive to the needs of the other blocks within the FMP. The intelligent feature extractor However, by themselves, neither CAD nor CAM accepts input part drawing files represented in the NBS tools possess the necessary 'intelligence' that is standard IGES (Initial Graphics Exchange Specifications) represented by the human process planner, who reviews format. On the output side, the feature files are the engineering drawing created by means of the CAD represented in a Part Model Format (PMF), also currently tool, interprets it and extracts a set of machinable used at NBS. A set of basic rules have been devised to 'features'. While a feature can be defined in a more represent the geometrical, topological and feature-specific general manner, (e.g., [Hirschtick 1986]), for our purposes, knowledge. The actual implementation of the feature each feature represents one set of interconnected extractor was done by using the Flavors package in Franz machinable surfaces corresponding to one finishing Lisp on a Sun. workstation. machining operation. As an example, the somewhat simple part shown here (figure 1) would be identified by the process planner as comprising of three separate Introduction features: a circular hole, a rectangular slot and a rectangular pocket. The process planner wouid use his Traditionally, the human process-planner has own experience and knowledge about machining provided a link between the design and machining aspects operations to identify a suitable set of processes that would of product manufacture. Subsequently, mainframe and generate each individual feature and create the desired microcomputer based CAD tools were developed. A part on a feature by feature basis. Therefore, the feature survey of selected CAD tools appears in [Hart 1986]. The extractor is a prerequisite for automatic process planning. varying degrees of sophistication for these tools include entity drawing, editing, inquiry and help facilities. Within Earlier work on feature extractors includes that of every CAD system, as a first step, certain 'primitives' or [Grayer 1977], who obtains NC tool paths from a stored 'entities' are entered into the CAD database. The entities part representation for 2.5-D pockets and holes; of may be simple items like lines, arcs, circles, points, [Kyprianou 1980] (also [Jared 1984]), that is concerned with rectangles, ellipses, polygons, parallel lines, free forms or the procedure for the automatic classification of generic they may be higher level groupings of these. Most depressions and protrusions within a part; and of mainframe based CAD tools have true 3-D capabilities, [Henderson 1984], who uses a cavity,-volume approach for including the ability to specify three dimensional swept features, using the technique of subtracting the coordinates for individual entities and to carry out three feature volumes from the cavity volume until no cavity dimensional operations on these. On the CAM side, volume remains. In a later work, [Henderson 1987] uses a computers have been used extensively for the automatic bottom-up algorithm, first searching for small form 1 Page 883 features and then constructing macro-features from the underway. At the beginning point in this protocol, the small elements. [Choi 1984] use an algorithmic approach user, who is a designer, interacts with a CAD system in for the syntactic pattern recognition of machined surfaces. order to finalize a suitable design that meets certain [Woo 1982] uses a 'convex-hull' technique to represent the requirements. The designer can use either a commercial part geometry as a series expansion of the object in terms CAD package or a feature-based design tool developed in- of convex components with alternating signs. [Rickert house and containing enhanced graphics capabilities. The 1987], uses a level-by-level search procedure for 2.5-D part desi~ is displayed on a CRT screen and after it is found descriptions in the Initial Graphics Exchange acceptable, a design data base, in a format specific to that Specifications (IGES) format, described in detail by [Smith CAD tool, is generated. An Initial Graphics Exchange 1986], to generate the NC code for a vertical milling Specifications module, that may either be a part of the machine. [Hirschtick 1986] use a set of production rules CAD package or a separate model altogether, can then developed by using the YAPS rule interpreter to create a convert this data base into the IGES format. At this point design advisory system, called the Extrusion Advisor, within the protocol, the user can choose to bring in which defines generic features in terms of certain another data base created by a different CAD system, characteristic pattern sets. Most existing feature extractors provided that it is also represented in the IGES format. have either not been developed and tested as an integral, The feature extractor decomposes the part into a set of part of a complete CAD/CAM link or tested in a limited standard morphological features. The primitive features way only. The emphasis often happens to be on one or include faces, holes, slots, pockets, etc. The user is required two of the following four required areas: (1) CAD to specify material and tolerance information, which is tool/ solid modeler (2) feature, recognition, (3) process1 not present in the original IGES file; The resulting file is a planning and (4) NC code generation. ' 'feature file' which is represented in a Part Model Format (PMF) also currently in use at NBS [Hopp 1987]. If the user A flexible manufacturing protocol (FMP), described has decided, at the very outset, to use a feature-based later, recently implemented at the ·university of design tool instead of a commercial CAD tool, an Maryland, attempts to link the user .t o the finished part. appropriate file in the PMF format is automatically As part of this implementation, a feature extractor has generated by this tool. At this point, the fixturing been developed which accepts part description files created requirements for the given shape are determined, and by any CAD tool equipped with the US National Bureau incorporated into an intermediate file. The next step is to of Standards prescribed IGES interface and creates a map of evaluate the part and toierance data in order to determine the individual morphological features for subsequent if the specifications are compatible with the capabilities of processing by the other blocks of the FMP. It is expected the machine cells that are available. If that is the case, the that the feature extractor described here will (1) take tolerance, geometrical machinability and the fixturing advantage of the standardization obtained from the use of constraints are compared with the available resources to the IGES format (thereby becoming independent of the verify the manufacturability of the part. specific CAD tool used), and (2) will be more sensitive to the needs of the other blocks within the FMP, having been Once the part is found machinable, a process plan file developed as an integral part of it. is generated, either manually (as currently implemented) or by an intelligent process planner (as planned in future). A short introduction to the feature extractor appears Once the process plan has been generated, a file containing in [Kumar 1987] and a discussion of some of the issues the necessary M&G code (as per EIA RS 274D) is created. related to the integration of the feature extractor into the This file has the necessary low-level commands in a FMP appear in [Kumar 1988]. The present work attempts relatively machine-independent format. If the particular to emphasize on the knowledge representation scheme machine tool that is to be used does not support the M&G used by the feature extractor. codes, a converter module creates another file that contains the native NC code for the specific machine tool. These codes are then downloaded into the machine tool The Flexible Manufacturing Protocol (FMP) through its RS232 serial port and the actual machining is carried out. For the purposes of automation, a file Flexible manufacturing systems are concerned with containing the commands for automatic cell control is small to moderate lot sizes of parts for which the turn- downloaded in parallel. A detailed description of this around time involved in going from the conceptual stage protocol_ is provided in [Uppal 1987] and [Chen 1988]. to the finished product stage is relatively small. In such a system, there exists a sequence of steps that links the user The Flexible Manufacturing Protocol described above to the finished part. This sequence of steps is called the uses a specific degree of standardization within the Flexible Manufacturing Protocol (FMP). One illustration complete CAD/CAM link. Several feedback loops are of such a protocol, recently implemented at the University provided that enable the user to check the design and of Maryland, is shown (figure 2), by means of a flow chart. product prior to the actual machining. The intelligent In the current implementation of this protocol, the part feature extractor described here occupies an important part shapes are restricted to prismatic parts in which the within the protocol in the sense that it is one of the three machining takes place without reorienting the part on the places within the FMP where AI techniques can be used to machine tool. Efforts to implement a more general advantage. protocol that includes axisymmetric parts are currently 2 Page 884 Requirements of the feature extractor As the feature extractor processes an input IGES file, it generates a number of data structures corresponding to In order to function successfully within the FMP, the the entities that are read in. The data structures used to feature extractor must possess a minimum set of represent the individual geometrical entities are instances capabilities. These include the ability (I) to process of different flavored objects. The Flavors object used to drawing files presented in the prespecified (ICES) format, represent the low level geometric entities contain (2) to represent the raw drawing data into a set of initial parameter slots to accommodate values that are unique to facts, (3) to represent a set of rules pertaining to the that object. An example of a line-entity object is shown recognition of morphological features, (4) to apply these (figure 4) which itself, in turn, descends from the parent rules to the current facts, possibly generating new facts, (5) class called geometric-entity object. As an instance of a to draw conclusions from the known facts, (6) tp take particular type of geometric entity is generated, a 'seed' certain actions based on some of these conclusions, (7) to fact is also generated to assert the existence of this entity. facilitate enquiries from the user, (8) to create an output The Flavors object used to represent the general fact entity file that describes the machinable features in another is shown (figure 5). The general fact entity contains four prespecified output (PMF) format, and (9) to incorporate slots- (1) a parent rule, (2) a parent fact, (3) the attributes of new knowledge from the user. Among these, the the current fact, and (4) the arguments of the current fact. requirements (2) through (5) are directly related to the In the case of seed facts, the first two fields contain the knowledge representation scheme. The other issues have 'nil' pointer. In general, the parent fact slot contains a been discussed in a separate work [Kumar 1988]. pointer to an earlier generated fact and the parent rule slot points to a rule that successfully operated on this parent The feature extractor primarily consists of an inference fact, resulting in the discovery of the current fact. The fact engine and a knowledge base (figure 3). Most of the attribute slot contains the address of a list data structure interaction with the user takes place by means of the whose elements summarize the attributes related to the inference engine. As the feature extractor attempts to current fact. For the,case of the fact that a particular line, carry out its required functions, it encounters different entity (e.g., line-5) exists, this field may contain the first types of information. The inference engine attempts to element of the form organize this information into meaningful facts which can be processed later. The knowledge base of the feature (is-a line) extractor, at any given time, contains: (1) a set of facts that describe the current state of affairs regarding the entity The fact arguments field contains the necessary data, (2) a set of feature related rules that the inference arguments to define the fact accurately. In the above engine can apply to the existing facts, possibly generating example, this field would contain a list containing a single new facts. Initially, a set of rules have been already element, 'line-5'. established, and the fact base is empty. When the user The data structures for higher level geometric entities specifies a particular ICES file for processing, the inference are similar .t o those for low level geometric entities. engine reads it in and generates a set of 'seed' facts. However, most of these are recognized and generated as a Thereafter, when the user requests that a particular result of operations carried out on other existing facts and feature be searched for, it attempts to pick up the rules therefore, contain distinct pointers within the parent rule related to that features (in a top down fashion) and applies and the parent fact slots. The existence of attributes it to the existing facts. Every time a rule 'fires', some new pertaining to an individual entity (either low level or facts are generated and added to the beginning of the fact higher level) is denoted by a list of two elements, pointed base (essentially creating a depth first approach to problem to by an element of the attributes slot of the current fact. solving). The knowledge describing the features (and the The existence of a binary relationship between two entities existing facts) is implemented as a set of Flavors objects is also represented similarly except that the second [Franz 1987] and the knowledge regarding the procedure member of this list usually refers to the other entity that for recognizing these features is implemented as a set of this relationship affects. production rules. The specific data structures used to represent the facts and the rules are described next. The representation of rules The representation of facts The production rules used by the feature extractor can During its operation, the feature extractor may be divided into five categories- encounter the following types of (declared or inferred) • rules to guess non-planar surfaces facts: • rules to guess the stock shape • the existence of low level geometric entities • rules to guess enclosures • the existence of higher level geometric entities • rules to guess concavity and convexity • the existence of an attribute pertaining to a particular • rules to guess morphological features entity Because it is necessary that the concavity and convexity • the existence of a relationship that links two or more information be available prior to the guessing of features, of the existing entities and the enclosing of the surfaces be known before guessing the concavity and convexity, and so on, the rules 3 Page 885 of the above categories have to be applied in the order Operations carried out by the feature extractor shown. It is necessary to exhaust all the rules for guessing non-planar (e.g., cylindrical or conical) surfaces prior to The feature extractor takes the following actions in attempting to guess the stock shape. The rules to guess response to specific user requests. enclosures essentially establish which side of a physical surface contains material and which side contains void. (1) Input file selection- When a new IGES file is selected Based on that, it is possible to identify the concave and for input, all existing facts are reset. The IGES file is read convex edges. The rules to guess the morphological in on a character by character basis. The names and features make use of this knowledge. empty frames for the individual entities are generated during the processing of the directory section and the The general rule data structure is an object that c~ntains slots are filled during the processing of the parameter four slots- section. (2) Graphical display- The feature extractor uses the • the rule name Suncore graphics package to display the part that was • a text string to convey the intent of the rule in plain read in. If the IGES file has specified any 'view' entities, language these are used for display, otherwise, a set of standard • a field to specify the input code for the rule views are used. Zero length lines and other physically • a field to specify the generated code for the rule trivial entities are neither created nor displayed. Be.cause the IGES representation is wire-frame in The first three fields are supplied by the (expert) user at nature, no attempt is made to 'hide' any physical lines. 1 the time the rule is specified. The name of the rule is used Since the feature extractor is not intended to duplicate for identification purposes. It is also used to define. the the functions of any commercial CAD tools, there are names of the procedures that have to be executed if the no elaborate methods to view cross-sections or to rule 'fires' (or 'fails'). The rule-text field contains dimension the patt. information regarding the intent of the rule in plain language. Its purpose is to communicate to the user, at the (3) Extraction of planes and contours- Up_on displaying a user's request at a later time, the purpose of the rule in new drawing, the feature extractor searches the list of plain language. The rule code field (specified by the user) geometrical entities that are present (mostly lines) to is a list structure of the form identify all the planar surfaces. After all the planar surfaces are extracted, the feature extractor looks for all. (IF AND AND ..... . the closed contours that are present within each plane, each contour representing a linked chain of lines and THEN arcs which start and end at the same point in space. AND AND ..... ELSE (4) Stock shape determination- The information regarding AND AND ..... ) the stock shape is not provided within the IGES file which is only concerned with the finished product. The The predicates and~ the action items can themselves be feature extractor determines cylindrical surfaces from list structures each of whose elements is one of the the presence of circular or elliptical arcs. It also picks out following the outermost cylindrical and planar surfaces. If the part is found confined within at least two pairs of • a valid s-expression in Franz Lisp orthogonal planar surfaces, it is classified as rectangular. • a term that belongs within the rule vocabulary If there is one cylindrical surface that encloses all the • a term that has some meaning within the context of entities within it, the stock is considered cylindrical. an earlier appearing term which belongs within the rule vocabulary (5) Feature recognition- For each outermost surface of the • a list structure whose elements satisfy one of these part, the outermost contour, i.e., the contour that four criteria encloses all the points of every entity present on the plane, is located. An attempt is next made to simplify The predicates are constructed in a form similar to the the outermost contour, typically by supplying missing well-formed formulae (wff) of predicate calculus. When lines (or arcs) between aligned but non-adjacent pairs of a rule is first specified, the inference engine examines each entities. This results in the generation of new contours, term appearing within each wff. Depending on what the with a common edge with the enclosing contour. Next, term is, it may process the subsequent terms in a the nesting level of the individual closed contours is particular fashion. Eventually, the inference engine determined. Contour with an even or zero level of generates the necessary Lisp code that would perform the nestings contain material within them while the tests and the actions intended by the rule. This generated contours with an odd level of nestings contain no code is then attached to the fourth field of the rule data material. The cross sections of slots, pockets ar.d holes structure. At execution time, it is the generated code field are recognized by applying the appropriate rules. of the rule that is actually evaluated to test if the rule should apply or not. (6) User enquiries- User enquiries are generally facilitated in one of two ways. The first type of enquiry has the format 4 Page 886 (what-is ) At the beginning of this sample session, the user requests that an IGES file be processed. After the complete In response, the feature extractor listrs out every thing it path name for the IGES file is specified, the feature knows about the named variable at the given instsnt. extractor processes this file. The IGES file format can vary Th~ infor_1:1~tion listed may include (i) the type of from record to record. Therefore, it is necessary for the variable, (u) its parameters, if any, (iii) its attributes. The feat_ure extra_ctor to read the file on a character-by-character featu~e :xtractor accesses the attributes of the variable by basis, T?: directory section, which contains a catalog of all exammmg each of- the associated facts present within the _entitles ~res_ent in the drawing is read first. As a 1 the 'associated-facts' slot of its data structure. The particular entity is encountered, an instance of its type is', second type of user enquiry takes the form ge1:erated. The actual name depends on the type of the ~ntity. _The most encountered geometrical entities include (why-is ) Imes, orcles, trz.nsformation matrices and views. The data structure assigned to an entity contains information on In this case, the feature extractor first verifies that the what ~ype of entity it is as well as information regarding sug_gested attribute indeed applies to the particular . the directory and parameter section record number variable (by examining the 'associated facts' field). If poi~ters for this entity. Next, the records of the parameter that is the case, it examines the associated fact to see if a sect10n are read. The data structures that were generated to pare1:t fact a~d a I:'arent rule is present. If so, the parent represent the individual entities are augmented by adding fact is exammed m turn. This process continues until the_ parameter values as occuring in the parameter record. no parent facts or rules are indicated. The details of each This process continues till all the parameter section intermediate facts are listed out, essentially providing a records are exhausted. A set of fact variables are also summary of how the feature extractor made a particular generated. They represent the seed declarative conclusion. information regarding these entities. (7) Output file selection- After the features have been recog~~ed, a PMF file consistent with [Hopp 1987] and After the stock shape is guessed, the outermost contammg several sections in the header format can be surfaces are considered. All the planar contours that are generated. These include (i) a header section, (ii) a present in the outermost planes are identified and data features section, (iii) a topology section and (iv) a structures are· generated to describe these in terms of the individual entities that are linked in a closed chain. Next geometry s_ecti?1:· The features can be either 'simple' features (mdividual faces) or 'pattern' features the outermost contour is located. The outermost contour (collection of these). The faces can be defined in terms of is ~ne w~~h meets the criterion that every point on every a set of topological entities, which are, in turn defined entity within the plane lies inside it (subtending a total of in terms of geometric entities. A set of canned 2*3.1415 radians angle, as compared to O radians that procedures is used to generate the necessary M&G code would b_e subtended at a point outside the contour). Next, for each feature. an atte~pt is made to simplify the outermost contour, by attemptmg to supply missing entities, such as Jines (8) The addition of new knov,rledge- The new knowledge between aligned lines. As an example (figure 8), the can consist of either (1) new facts or (2) new rules. The surfaces 1, 3 and 5 contain outermost contours that can be facts are always updated whenever a new input file is simplified into rectangles by supplying lines that are specified. The sequence of steps necessary to add a new shown with a hatched pattern. The addition of these lines rule is shown schematically (figure 6). It requires one to creates additional contours. The process is repeated for the define all the non-standard vocabulary terms, at the inside contours and any other contours that these might lev~l~ of features, contours and primitive geometric enclose, in turn. Once all the contours within this plane entities. Next, any .non-standard geometric are exhausted, it is seen that contour 1 encloses contour 2 relationships are specified. As the feature extractor is within the face 1 (figure 9a), and they share a common refined more, the standard vocabulary will itself line. Because contour 1 is not contained by any other become sufficiently powerful to accommodate a large contour, it must contain material, and the contour 2, variety of rules. The specification of a new rule enclosed by it, must represent hollow. Also, since they involves composing the wff for the rule structure share part of their boundary, from the application of explained above by using the elements of the rule another rule, it appears that contour 2 represents the cross vocabulary. So far, new rules have been manually section for a slot. On the other hand, for the face 2 (figure 9b), the contour 1 encloses contour 2 but shares no part of added to the rule base. Eventually, an interface will be the boundary with it. Since the contour 1 contains developed to automatically guide the user through the material and contour 2 contains void, from the new rule creation process. application of one of the rules, it appears that the contour 2 represents the cross section of either a pocket or a hole. Results of a Sample Session with the Intelligent Feature In order to classify it any further, it is necessary to consider Extractor the adjacent surfaces. Further analysis reveals that its companion contour (figure 9c) indeed contains material The results of a sample session with the intelligent and therefore the contour 2 on the face 2 (figure 9b) feature extractor are presented (figure 7). The interaction represents an entrance cross section for a pocket. In a between the user and the feature extractor is in a question similar fashion, the other morphological features present and answer format. 5 Page 887 in this part are also recognized and listed by the intelligent References feature extractor. [Chen 1988] Chen, Sujen, "The design and At this point, the user may enquire the intelligent implementation of a flexible manufacturing feature extractor regarding the reasoning used by it to protocol with a vertical machining center", Masters arrive at a particular conclusion. In this instance, the user. thesis, Mechanical Engineering Department, wishes to find out why the feature named 'pocket-2' has . University of Maryland, College Park, Maryland,: been identified as such. The feature extractor comes up May 1988 with an explanation of which rules were applied. [Choi 1984] Choi, B.K., Barash, M.M., and Anderson, D.C., Eventually, when the user is satisfied, he/she puts in the "Automated Recognition of Machined Surfaces necessary material and tolerance data. A post processor from a 3-d Solid Model", Computer Aided Design, then generates the necessary feature file in the PMF 16(2), 81 format. While generating this file, certain rules are [Franz 1987] Franz Lisp Reference Manual, Franz Inc., applied towards the sequencing of the features. For Alameda, California example, features that correspond to the same tool [Grayer 1977] Grayer, A.R., "The Automatic Production of diameter would be grouped together (to minimize the Machined Components Starting From a Stored tool change time.) Portions of the resulting PMF file are Geometric Description", Advances in Computer shown (figure 10). For the purposes of this validation, a Aided Manufacturing, North Holland, 137-151, 1977 set of canned routines are used to generate the necessary [Hart 1986] Hart, G., "CAD: The Big Picture for Micros", PC M&G code that will be eventually downloaded to the Magazine,March, 1986 machine tool. [Henderson 1984] Henderson, M.R., "Extraction of Feature Information from three-dimensional CAD data", Discussions Ph.D. Thesis, Department of Industrial Engineering, Purdue University, West Lafayette, Indiana, May, The feature extractor described here is an important 1984 component of a real-life, working, automated CAD/CAM [Henderson 1987] Henderson, M.R., "Automated Group link. It is capable of accepting CAD files generated by any Technology Part Coding From a Three-dimensional commercial CAD tool that contains an IGES interface. CAD Database", Knowledge-Based Expert Systems Even though, ideally speaking, wirefra:me representations for Manufacturing, . published by the American cannot describe a solid object with certainty, the Society of Mechanical Engineers, New York, 1987 application of a set of rules to this data can help identify [Hirschtick 1986] Hirschtick, J.K. and Gossard, D. C., the morphological features for a number of simpler· "Geometric Reasoning for Design Advisory shapes. As the rules are refined and the rule-base Systems", Proceedings of the ASME Computers in expanded, this feature extractor will be able to handle Engineering Conference, Chicago, Illinois, 1986 more complicated part geometries. [Hopp 1987] Hopp, T.H., AMRF Database Report Format, Automatic Manufacturing Research Facility Report, Although the Flexible Manufacturing Protocol, of National Bureau of Standards, Gaithersburg, which this feature extractor is a part, deals with a variety Maryland, 1987 of data files, the feature extractor itself deals with only two' ijared 1984] Jared, G. E. M., "Shape Features in Geometric of these: the ascii drawing (IGES) file and the ascii features· Modeling", Solid Modeling by Computers from (PMF) file. The standardization of these two types of files Theory to Applications, Edited by M. S. Picket, as input and output mediums was the most important General Motors Research Laboratory, 1984 issue related to the integration of the feature extractor into (Kumar 1987] Kumar, B., Anand, D.K., and Kirk, J.A., "An the FMP. After these two formats were selected and Intelligent Feature Extractor for Automated agreeed upon, the development of the feature extractor Machining", Proceedings of the Fifth International continued independent of the development of the other Conference on Systems Engineering, Dayton, Ohio, blocks of the FMP. It also enabled the use of very different September, 1987 deveiopment systems and programming languages [Kumar 1988] Kumar, B., Anand, D.K., and Kirk, J.A., within different parts of the protocol. "Integration and Testing of An Intelligent Feature Extractor within a Flexible Manufacturing Future work will be directed towards the further Protocol", The Sixteenth NAMRC conference, testing of the feature extractor. Additional work in the University of Illinois, Urbana, Champaign, Illinois, area of improving the user interface is also planned. This May, 1988 would enable the user to pose simple English like [Kyprianou 1980] Kyprianou, L.K., "Shape Classification sentences to the feature extractor, both for the purposes of in Computer Aided Design", Ph.D. Thesis, explanation as well as for expanding the rule base. University of Cambridge, 1980 (Rickert 1987] Rickert, W., "The use of IGES for automated Acknowledgements N JC Machining", Masters Thesis, Mechanical Engineering Department, University of Maryland~ This research was supported by the Systems Research College Park, Maryland, 1987 Center at the University of Maryland. Computer time for [Smith 1986] Smith, B. and Wellington, J., Initial Graphics this work was partially supported by the Computer Exchange Specifications (IGES), Version 3.0, Report Science Center at the University of Maryland. 6 Page 888 NBSIR 86-3359, National Bureau of Standards, POCKET Gaithersburg, Maryland, 1986 [Uppal 1987) Uppal, R, "A Flexible Manufacturing System Protocol Driver for a Vertical CNC Machining Center", Masters Thesis, Mechanical Engineering HOLE Department, University of Maryland, College Park, Maryland, 1987 0 +( .____~() [Woo 1982] Woo, T.C., "Feature Extraction by Volume SLOT Decomposition", Proceedings of the Conference on CAD/CAM in Mechanical Engineering, MIT, +== 5-=--;;;=--;;;=--;;;;;~=__,2Jp Cambridge, Massachusetts, 1982 Figure 1: A sample part with machinable features ;-----+----- 0 ;',OOAWit-0 FILE C-rciel Feattni Based USER C A O Soft,era C A 0 @ = IllcS FILE INFERENCE ENGINE 0 = FEATI..RE FILE RUN/STOP , , ACCESS FILES /USER-\ \ [Toi. Hatll, CREATE APPLY RULES RULES 0 FJ,turing 1 = r Iirt~Uig;,,t INTEMOIATE FILE . ConstrIa ints I F1,turo I j© Planning 'ti:'OOAL~-._ <>- L.,. - ' - --' < Oata Basa/_ _____ ,..., . 4 Figure 3: Components of the intelligent feature extractor '--· __/ - CE.L-.... --1 ursl)ili t~ ....._ ooilitt,.- Mooulo : gettable-instance-variables L - _J : gettable-instance-va~iable~ : inittable-instance-vanables) ® = PIIOCESS Pl.AN FlLE (deflavor line-entity _J (x-1 y-1 z-1 x-2 y-2 z-2) (geometric-entity) : gettable-instance-variables : gettable-instance-variables ® : inittable-instance-variables) = MI.G COCf FlLt Figure 4: The data structure for a line entity 0 = Nit Ctn: FILE (defflavor fact (parent-rule parent-fact fact-attribute fact-arguments) : gettable-instance-variables : gettable-instance-variables : inittable-instance-variables) Figure 2: A Flexible Manufacturing Protocol (FMP) Figure 5: The data structure for the general fact entity 7 Page 889 CREATE NEW-RULE NON NON NON STANDARD STANDARD 1---lllllo! STANDARD ENTITIES CONTOURS FEATURES CJ [J NON ( LI s~u L~ODE) ........- --iL--P-A_R_s_I_N_G_..J STANDARD RELATIONS Figure 6: The sequence of steps for adding new rules 0 0 0 FE: The valid commands are: USER: (read-lGES-file) DGJQLJ FE: Please specify the IGES file name 0 0 0 USER: FE: The following entities were generated: Lines: 37 DLJD Circles: 2 Transformation matrices: 8 Figure 8: The outermost surface contours for a sample part Views: 8 Notations: 5 USER: (what-is view-5) FACE-1 FACE-2 COMPANION CONTOUR 2' FE: view-5 is a view. It was read from the IGES data base. Its associated transformation matrix is trans-matr-5. Its list of parameters is (5). USER: (draw-part) (a) (b) (c) FE: .... Completed. Figure 9: (a) Contours within surface 1 USER: (extract-contours) (b) Contours within the surface 2 FE: The following planar contours were obtained ...... (c) Contours within the companion to surface 2 /PART_MODEL /HEADER USER: (extract-surfaces) PART_NAME = 'SAMPLE PART /END_HEADER FE: The following surfaces were obtained ..... . /TOPOLOGY /SHELLS . ' USER: (extract-features) SHE001; FAC001, FAC002, FAC'.003, FAC004, FACOOS, FE: The following morphological features were extracted. FAC006, FAC007, FAC008, FAC009, FAC010. Holes: 1 (hole-1) /END_SHELLS Slots: 1 (slot-1) Pockets: (pocket-1) /FEATURES FEAT1; SIMPLE; FACES FACOOS . FEAT2; SIMPLE; FACES FAC006; USER: (Why-is pocket-1 a-pocket) FEAT3; PATTERN; FACES FEAT1 FE: The feature entity pocket-1 has the following attributes: . (1) Its contained contour, contour-6, bounds a negative /END _FEATURES surface, surface-9. /FUNCTIONALITY /TOLERANCES (2) Adjacent contours, ..... , all bound positive surfaces. TOL001; FEAT3; PLUS_MINUS; 0.06200 0.00000. (3) The companion contour, contour-9, bounds a positive surface, surface-11. /END_T OLERANCES Therefore, according to the rule P-1, pocket-1 appears to be a-pocket. /END_ FUNCTIONALITY /END PART MODEL Figure 7: A sample session with the feature extractor Figure 10: Sample PMF file 8 Page 890 Page 891 PROTOCOL FOR FLEXIBLE MANUFACTURING AUTOMATION WITH HEURISTICS AND INTELLIGENCE 0. K. Anand and J. A. Kirk, Professors of Mechanical Engineering M. Anjanappa, Assistant Professor of Mechanical Engineering 0. Nau, Associate Professor of Computer Science E. Magrab, Professor of Mechanical Engineering The Systems Research Center University of Maryland College Park. Maryland INTRODUCTION first is the absolute optimum plan which is generated by ignoring all constraints. The second, and more The approach to successful computer automation useful optimum strategy, is based upon equipment capa- ( l-7) of the deslgn procedure and subsequent manufac- bility and fixturing/material handling constraints, ture initially depends on whether the product under · Prior to manufacture a process plan must be consideration is a component or system. The latter generated which includes the establishment of manufac- can introduce a level of complexity that is several turing constraints on manufacturability, The process orders of magnitude larger than that of a component, plan includes selection of an appropriate machine tool Even for a component it is appropriate to initially based upon dimensions, tolerances and surface finish speak about a class of components aggregated by the requirements of the design, The ideal plan would have group technology approach, In this paper, we are considered the interface structure, tooling; control interested in limiting our consideration to components and the performance of each manufacturing operation, that can be manufactured on a CNC · machining center and The process plan chooses an optimal set of recom- adequately represented by 2 l/2D geometry. Such manufac- mendations for a specific machine tool, These recom- turing of parts in smn 11 batches represents approxima- mendations may include type of work holding device, tely 75% of the manufacturing effort in the U.S. its location, cutting tool, sequence of cutting opera- Specifically, we are concerned with flexible manufac- tions and cutting parameters for each machining opera- t1,rlng in a cell where we incorporate expert or tion, To further aid process planning group knowledge-based systems to the fullest extent technology will allow the grouping of parts in accor- possible, Also, it is important that we incorporate dance with their processing requirements, heuristic reasoning in addition to the algorithmic Although not considered here, the issue of timing approach -throughout the process from design to manu- and scheduling as well as data base handling including facture [ l-19]. data collection, updating and use is a very important The manufacture of goods requires seven steps, element of factory automation and crosses all boun- viz. specification, product design including process daries, A schematic of our approach is illustrated in planning, scheduling, raw material aquisitlon, produc- Fig, 1, The figure has the following four important t ion, qua 11 ty assurance and monl tor ing, and and, often, overlapping phases: Design, Process shipping/distribution. The automation studied here is Planning, Machining, Interfacing, To achieve flexible concerned with steps one, two, five and six, The pro- automation of components, each of the phases raise posed approach utilizes AI techniques and interface specific issues, A few of these are listed below, standardization and, as such, it is both intelligent Design: The particular part must satisfy design and integrated, The for mer implies expertness, while axioms of independent functional requirements the latter implies a standard communication format and minimum information content. Important such as the Manufacturing Automation Protocol (MAP). issues being addressed include: reasoning by The tools used for design, optimization and manufac- analogy, innovation via heuristics, algorith- ture of the part are typically CAD/CAM, AI, GT, etc, mic computation, quality versus cost, range Although there ls no general computation theory of design and scale, manufacturability, and for design, a procedural methodology aided by the maintenance of an iterative design algorithms and reasoning does exist, CAD/CAM is environment, and special attention to Feature simply a design methodology aided by a relational and Based Design to overcome IGES limitations, heuristic data base, To optimize the design for manu- Process Planning: One of the most important issues is facture (DFM), it ts important that the design be com- that of geometrical representation and patible with new technology available in feature extraction from the finalized design, manufacturing, There are two optimal strategies, The Other issues for purposes of planning the 209 Page 892 machining process are: qualitative versus turing process· by which the component is to be pro- heuristic rules, spatial and temporal duced. reasoning, lnterference avoidance, ·intelli- The University of Maryland's approach to the gent fixturlng, maintanence of accuracy, hard above problem is to give the designer access to the physics versus soft expert advice and cell manufacturing (machining) process with the assistance dynamics. · bf a series of programs that provide for both graphi- Interfacing: This phase prlmarily deals with the need cal displays and "expert advice." The first step has for a standard approach to communication; been to expand and improve upon feature-based design that is, the ~llty to translate within the (FBD) system originally used at NBS [8-10). The FBD design- to-manufacture path. Important issues system uses as its primatlve a host of machinable include: lGES data representation, M/G Codes features, in our case those features obtainable from a for rnachlninr,, ans the feAture database in the same cutting tool magazine is loaded to be in agreement order ln which the df'signer has sketched hls part. with the tool library. The tool length offsets and ~hlle this orderlnr. ls taking place the user is pre- cutter compensations are entered for each tool and sented with ench ff'nture nnd ls requested to enter the then cutting is initiated, At the end of all cutting machining pnrnmetern for lhe fenture. Before lnl- the finished part iB currently manually unloaded, A tl11tlng feature r<'orderlng and machining input, the typical sample part is shown in Figure 8. This part user ls presented with a tool library containing consists of 2 pockets and a number of holes with the information on the type, n df'f 1 ned the first feature ls pre- current development for automated component manufac- sented to the user, along with its dimensions, and the turing at the University of Maryland. The protocol is user ls prompted for machine tool parameters. For the concerned with creating an environment whereby the rertangular pocket the dimensions of the pocket design engineer becomes involved in the manufacturing length, width, depth and the coordinate of one loca- process of the component being developed, The input tion point are displayed on the top half of the format to the FMP is either an ICES representation of computer screen. The bottom half of the screen has the designer's part or a feature based representation, prompts for the m.1chlne parameters which include - Either type of input is analyzed with algorithmic, tool library number for the rough cut tool, tool heuristic, or artificial intelligence based software, l t brnry number for the ftntsh cut tool, feed rate and and control codes required to produce the part are type of cut (finish/rough). automatically generated, An initial version has been Once machine data input for al I the features is develojped and validated on a vertical CNC machining suppl led a C/\H d11ta base is generated. This database center. contains the geometric data of the part combined with The flexible manufacturing cell has been the machining datn. The C/\H dntabase contains all the established to validate the element of the FHP, This information that is needed to machine the part and an cell consists of a CNC vertical machining center, a example of the database is shown in Figure 7. simulated material handling robot and automated guided The next step in the Implemented FHP is to pro- vehicle. A version of the FHP has been implemented in cess the CAM database into standard cutting codes the flexible manufacturing cell and ~ number of parts, capable of driving the machining center, These stan- represented in lGES data format, have been produced in dard codes are called Hand G codes and are specified the cell, in F.l/1 RS-27q. The C codes are known as preparatory Although the FHP has been developed and is being functions and they define machining moves and cutter demonstrated in a machining application, the overall tool movement such ,i,,; polnt to point positioning And concept and module integration is equally applicable 1lne:ir interpolation. The H code~ are known as to other sreas such as flexible automation for Printed mlscel laneous funct Ion control codes and include Circuit Board assembly, program stop, spindle on/off, clamp/unclamp, tool change, etc. ACKNOWLEDGEMENTS In the present work only four banic C codes (i,e, GOO, COi, CO2, GO)) lrnve been used for defining all This work is supported in part by the Engineering cutting operations, Specific routines have been writ- Research Center, Systems Research Center, National ten to generate al I fen tores in terms of these 4 basic Science Foundation and The National Bureau of G codes. 11,ese G codes are standard and found in all Standards, CNC machines accepting M & G codes, thus insuring that the II & G codes gen('rnted by the FHP are machine Inde- REFERENCES pendent. However, besides these four G codes other G codes have also been used, These C codes are for 1, Anand, D.K,, "Research in Flexible Manufacturing," def lnlng the dl ff erent coordinate systems, tool length Second Annual SRC,Conference, September 1986, College compensation, cutter radius compensation, plane selec- Park, tion, etc, A list of the H & G codes used in the FMP can be found in reference (3), 2. Anand, D,K,, Kirk, J,A., Anjanappa, M., and Pecht, M,G,, "Supercomputers and Hierarchical Control: A 213 Page 896 SystemR Viewpoint," Lawrence Livermore Laboratory - 17. Anand, D.K., Kirk, J.A., Anjanappa, M., ''Magnetic NSF Proceedings, September 1984, Livermore, CA. Bearing Spindles for Enhancing Tool Path Accuracy," Advanced Manufacturing Processes, Vol. 1, No. l, PP• 3. Uppal, R. "Flexible Manufacturing Protocol Driver 245-268, 1986. For a Vertical Machining Center", M.S. Thesis, University of Maryland, Aug. 1987. ""' ts. Anjanappa, ti., Kirk, J.A., Anand, D.K., '.'Tool Path Error Control in Thin Rib Machining," Proceedings of 4. Gershwin, S.B. "A Central Perspective on Recent 15th NAMRC, PP• 485-492, Hay 1987. Trends in Manufacturing Systems';, Conference on Decision and Control, December 1984, Las Vegas, 19. Anjanappa, M., "Error Minimization in Machining", Nevada. Ph.D. Dissertation, Univ. of Maryland, 1986. 5. Baer, T., "Simulating The Factory," Mechanical Engineering, December 1986. 6. Anand, D.K., Kirk, J.A., and Anjanappa, M., "Tool Path Error Control of End Hilling of Microwave Guides", Proceedings of 7th World Congress on the Theory of Machines and Mechanisms, September 1987, Universidad de Sevilla, Sevilla, Spain. 7. Francis, P.H., "To..,ar::1 a Science of Manufactur- ing", Mechanical Engineering, Vol. 108, No. 5, 1986, PP• 32-37. 8. Kramer, T. R. ancl Jun, J., "Software for an Auto- mated Machining Workstation", Proceedings of the 3rd Biennial International Machine Tool Technical Conference, Sept. 1986. Heurletlc ,_._ __ , Manulectureblllty ReHonlng 9. Magrab, E.B., "The Vertical Machining Workstation of the AMRF: Sof tw11 re Integration", Integrated and Intelligent Hnnufnc-t11rlng, C.R. Un nnd T. C. Chong, Eds., ASHE DED - Vol. 21 (Dec. 1986), PP• 83-100. 10. McLean, C.R., "The Vertical Machining Workstation of the AMRF: Software Integration", Integrated and Intelligent Manufacturing, C.R. Lin and T.C. Chang, Eds., ASHE DED - Vol. 21 (Dec. ·1986), pp. 101-116. 11. P. Brown and S. Ray, "Research Issues in Process Planning . at the National Bureau of Standards," Proc. 19th CIRP International Seminar on Manufacturing Flxhn,g Systems, June 1987, pp. 111-119. 12. N.C. Ide, "InteRration of Process Planning and Solid Modeling thro11!'(h Design by Features," Master's thesis, Computer Science Dept., University of Maryland, 1987. Emulation 13. D.S. Nau, "Hierarchical Abstraction for Process Planning," Proc. Second Internati. Cont. Applications of Artificial Intelligence in Engineering, June 1987. VerHlcetlon 14. D.S. Nau and H. Gray, "SIPS: An Application of Hierarchical Knowledge Clustering to Process Planning," Jroc. Symposium on Integrated and MACHl~O i---------' Intelligent Manufacturing at ASHE Winter Annual Meeting, Anaheim, CA, Dec. 1986, pp. 219-225. 15. H.B. Voelcker, A.A.G. Requicha, E.E. Hartquist, W.B. Fisher, J. Metzger, R.B. Tilove, N.K. Birrell, Figure 1 Approach tor Autometed Mec'*11ng W~A. Hunt, G.T. Armstrong, T.F. Check, R. Moote, and J. McSweeney, "The PADLl.0/2 S;stem for Defining and Displaying Solid OhJects," ACM Computer Graphics 12:3, Aug. 1978, 257-263. 16. Kirk, J.A., Anand, D.K., Anjanappa, H., "Magnetic Bearing Spindle Control in Machining," Proceedings of 13th Conference on Production Research and Technology, November 1986, pp. 127-l)ff . 214 Page 897 Feature B•••d CAD eyatem • (lJ z (lJ : z u :i :i e 0. -------------------- "( w "( a: w a: r r 1 :c :I: :I: lnttllloont 0) (lJ i ::, OI i LI F ixture I i •E ii: 0 Planning ___ J a: ii'. (lJ (lJ ,'~-;-e-;·\ z z P A R T ii z~ 0 r--- --"' , _( _T_oL_ _M_a l.,.l .. )., , / m a: ii .w.. aw: (lJ ... (lJ z z a) ,' GLOBAL \----------- z z i 0.. \.~~TA '!_A_!!§/ B ::, ii "( ;; 0 0 m 0 w 0 a: ,.5, ,•,,. .:; r .5 I :! OI • w OI •E 0 w 0a: 0 ,•:: 0 0.. I If r M-;n-;;i.;,: 1 w • a: il, f (Machlnlny urablllty 1 i:! ~ Data) "( L~~d~•- __ 1 a: w 0.. II. :s • J, ..I i i ..I :: 0 Ordered :x: 0 • J: C: Proceu "( Planner ., C A M j Data BaH OI a) IU (J 0 Generate EIA RS 244 a: II. Standard M & G Codn Poetproceuor (Tranalate M & O to CNC Mic codu) Download Data To CNC Machine r-------1 C E L L I CELL 1 Accuracy I 1 Enhancement I ----- _J PART Figure 2 Implemented Flexible Manufacturing Protocol 215 Page 898 CUTTING FORCE -INDEPENDENT ERRORS CUTTING FORCE-INDUCED ERRORS -- POSITION THERMAL WEIGHT CUTTING FORCE TYPE OF ERROR ERROR DEFORMATION DEFORMATION DEFORMATION NATURE OF ERROR DETERMINISTIC DETERMINISTIC STOCHASTIC POSITION, TEMPERATURE MASS COMPLIANCE DEPTH OF CUT , FUNCTIONAL FEEDRATE ( T) (Ml ( kl PROCESS DEPENDENCY ( P,1 ) DYNAMICS Figure 4 Tool Path Error Cluelllcatlon Poet proceooed MIG codee of the part PATH A PATH B Expert ayetem YASNAC MX3 110,4. 7,2. ,o. ,2. 3,2. ,o. H Line for cutting controller force Inde- pendent error l00,0.,2.3,2.J,2.,2.J,2.J,2. IS Arc correction Motion· comm- ands to X,Y&Z 110,4. 7,2. ,-1. 2,2. 3,2. ,-1. 2 19 Line feed motora Modified M& G I 00, - I • 2, 2. 3, 2. 3, 2. , 2. 3, 2. 3, 2. codee of the '24 Arc part Expert eyatem for cutting force Inde- pendent error Figure 8 IOES data for a rectangular pockek correction Moll9n comm- Incremental ands to X,Y&Z motion algnal for X,Y,Z & 0 feed motore BLANK 6 , , -2 Magnetic Spindle controllor RPF 1.9)75 , l.9Jn , 5.9J7S, 5.0625 ,-.J, .5 , 4 , J , 6.5 ,Y + Introduce RPF current-blaa to tranelate & 2.5, 2.S, S.4375 , 4.5 ,-.5, .J, J, 2 , 5.5 ,N 1111 eplndle- tool ayetem CPK 3.125 , 3.875 , .3499999 ,-.C , J , 5.5 ,CL,Y Accuracy Enhanced DRILL Part J.125, 3, .3499999 ,-.8, 2, 4.S, 2 Figure II Error Correctlo.11, Methodologlu Figura 1 CAM databau 216 Page 899 SAMPLE PART Figure 8 Sample part machined on a Matsuura 510 V machining center 217 Page 900 Page 901 Magnetic Bearing Spindle Control D.K. Anand M. Anjanappa Department of Mechanical Engineering Department of Mechanical Engineering The University of Maryland . The University of Maryland J.A. Kirk E. Zovi Department of Mechanical Engineering Department of Mechanical Engineering The University of Maryland The University of Maryland M. Woytowitz Department of Mechanical Engineering The University of Maryland ABSTRACT. The use of magnetic bearing spindle in machining thin rib components, such as microwave guides, can not only provide the benefits of high speed machining but, can also minimize tool path errors . Tool path errors are classified as cuttinq force independent and cuttinc force dependent errors and are characterized as static, dynamic and stochastic in· nature . This paper deals with the retrofitting of a vertical . machining center with an S2M - 825/500 macnetic spindle includi ng the interfacing of various controllers. In addition, this paper discusses the selection of a test part to validate the on-line error minimization controller . INTRODUCTION. A Magnetic bearing spindle and coordinate measurements controller, with its unique features, retrofitted to existinc machine tools, can provide a solution to Experimental validation of control minimize the tool oath error while maintaininq hiqh methodologies developed earlier. metal removal rate· in thin rib machining. The current research prc._ject investigates this approach by the use of error maps and soindle control of a Matsuura-S2M TOOL PATH ERROR. The accuracy and surface finish of a sys tem developed at the University of Maryland. The machined part 1s a function of tool path error which is following tasks defines the complete scope of the defined as the distance difference between the actual project; and the required tool path . Tool path error is classified , as shown in Fig. 1, according to the source Generate static and dynamic tool path error map and the nature of the error as cutting fo r end mil li ng operations. force-independent and cutting force-dependent errors. Develop a control system for cfe terministic tool Static deterministic aposition errors" are those oath error correction. repeatable errors which are a function of 111qchine slide posit ion. The cause for these errors are geometric Deve lC'C and impl el'lent a methodology for inaccuracies of the slideways and the misalignment in controlling a magnetically suspended spindle to the structural element assemblies. Dynamic mini mize tool path error . deterministic "position errors" are those reproducible errors which are a function of the table feed rate . Exoerimenta]ly test and validate the control a Thermal Deformations" due to heat sources, both svs t em and aloorithm usi~~ a CNC vertica l internal and external to machine tool system, are r~c~ininq cente r fitted ..-it:> a rnaoneticaJly reproducible errors which causes a change in the · suspended spindle. · recuired position of the tool relative to the workpiece. Thermal cycles of the spindle system, Earli er work has already presented details of the ambient temperature variation and friction are some analytical development of the l'lethodolooies used for example of the heat sources . "Weight deformations" are correction anc control of deterministic and stochastic caused by changes in the weight of stationary objects errors. which are firmly positioned on the machine tool table . These errors show up as reproducible static position This paper presents a brief discuss Ion of the errors and occur in addition to position errors. procress made, since the last report, in the following speci fie research tasks; · The a cutting force deformations" are classified as (i) deterministic tool path errors due to compliance The retrofitt inq of a vertical machining between the tool and the workpiece and (ii) stochastic center with an S2M soindle . tool path errors due to cutting process dynamics. The errors due to cutting force show up as position Interfacinq and control of the spindle for differences between the required and actual tool~· ~~ safety and -use in con j unction with the relative to the workpiece and results i,n workpiece Yasnac controller . shapes which are not perfect. Development of a samcle test oart for error oeternination ant# measurement via 31 Page 902 In surrmary, all the deterministic errors, both While the existing Matsuura MC500 Yasnac CNC 3000G static and dynamic, are those errors that reoccur when controller was retained, the latter three controllers an identical set of input parameters exist on a oiven were installed as part of the active maonetic bearino machine tool structure. Stochastic errors, on the , retrofit. - ·· other hand, are defined as those errors which occur when a random input is presented to the machine tool. Derivation and implementation of the overall ff: J~ese errors are discussed in detail in reference controller coordination scheme has accounted for the 9 largest portion of the AMB retrofit. The functional reouirements can he summarized as: MECHANICAL INTERFACING. The retrofit of a Matsuura MC-500V mach1n1ng center with a high speed, l. Providino the operational control necessary to magnetically suspended spindle required several operate the CNC mill, modifications to the original machininq center. The L. Implementation of safety interlock measures, basic plan was to remove the z-axis head from' the 3. Interfacing necessary for communication of machine, cut off the existing spindle casting, and real-time process monitorina and control data mount the new magnetic spindle in its place. ~. Coordination necessary to irnnlement the error' correction scheme. Before the head could be removed, it was necessary to disconnect and remove the tool changer and spindle The nature and satisfaction of these requirements will motor. Moreover, all control lines to the original be briefly reviewed in the following paragraphs. spindle drive system were re-configured to allow machine operation once the spindle was removed. The first objective, of the AMB retrofit process, was to provide the operational control necessary to Once all unnecessary equipment was removed from the support conventional milling functions. This effort head, it was found that the spindle housing was too involved the coordination of the CNC, AMB, and spindle thin to allow the mounting of the magnetic spindle. To drive controllers. This phase, which is now complete, mount the new spindle, a riser block was designed to allows for the operation of CNC, AMB, and spindle func- serve as an interface between the head and the new tions from the suitably modified CNC operator console. spindle. Due to mounting constraints on the spindle, In addition, monitoring of AMB and spindle status, the riser block would be bolted to the head and then spindle speed, and spindle torque information has been the spindle bolted to the riser. provided on the operator console. Before any machining occurred, all of the original For CNC operation of a 25KW, 30,000 rpm active components of the head were cataloged and weighed; any magnetic bearing spindle, safety is a critical concern. deviation in weight between the original head and the Although each of the CNC, AMB, and spindle drive modified magnetic spindle head could be compensated for cont:ollers provide internal safety features, at the counter weight. considerable effort has been invested into inteoration of various fault, interlock and error handling - To preserve the rigidity of the head, some of the procedures. Levitation of the AMB system has been spindle housing was left intact, and the riser was interlocked to satisfactory CNC operational status. designed to conform around the remaining portion of the Similarly, spindle rotation is interlocked to housing. The spindle housing was cut and the head's satisfactory AMB status. The S2M AMB controller mounting surface was rrachined flat. provides a comprehensive set of monitoring functions including cooling, excessive spindle bearing load or The riser was designed to provide a rigid and displacement, and spindle drive faults, as reported by accurate mounting surface for the new spindle. The the spindle drive unit. AMB controller faults, in major design considera.tions were rigidity and the turn, invoke dynamic braking of spindle rotation and preservation of the original tool position. The final assert a table stop request signal. Table stop request design of the riser resembled an open box with the ~as been impleme~ted such that l• Y, and z axis motion bottom side serving as the magnetic spindle's mounting is frozen an9 a SPIN:lLE ERROR message displayed on surface and the open end enclosing the original spindle the operators display console CRT. Both the spindle housing. To provide maximum rigidity it was decided fault and table stop request conditions must be reset to make the spacer from one piece of stock. by the operator, before operation is allowed to resume. Availability and machinability dictated the use of Multiple spindle stop push bottoms, as well as the CNC 6061-T6 aluminum as the spacer material. emergency stop, are available to stop spindle rotation. After the riser was completed, the head was drilled Central to this research, is the implementation of and tapped and assembled with the riser. The spindle the error minimization controller. The basic elements mounting surface was face milled flat relative to the of the accuracy enhancement retrofit are depicted below slide ways of the head. To minimize the new spindle's the dotted line of the simplified control system block alignment error, the spindle mounting bolt pattern was diagram given in Figure 2. As indicated, various also aligned with the same slide ways. online process parameters are provided to the error minimization controller as inputs to the control The new head/riser assembly was then weighed. The algorithm. Based on these inputs, the error careful design of the spacer produced a negligible five minimization control will use the predetermined error pound difference between the original spindle head and characterization to generate perturbational control the modified magnetic spindle head. signals to translate and tilt the AMB spindle to correct for dimensional errors. The theoretical After hanging the new spindle, the alignment was development necessary to support the derivation of the verified. Any misalignment errors can be compensated robust, multivariable ~OQtroller has been previously by tilting the spindle in the air gap. reported in Reference l5J. The input parameters currently under investigation include, ELECTRICAL INTERFACING AND CONTROL. Implementation of the active magnetic bearing (AMB) error correction 1. X, Y, Z axis position, methodology involves the interaction and coordination 2. X, Y, Z axis velocity commands, of four independent controllers, 3. X, Y, Z axis servo lag, 4. Spindle displacement and bearino forces, 1. Existing CNC controller, 5. Thermal conditions. - 2. Active magnetic bearing controller, 3. Variable speed spindle drive, 4. Online error minimization controller. 32 Page 903 Extraction of realtime x, Y, Z axis position, and The inner and outer surfaces of the boundary will potentially servo lag, data from the Yasnac 3000G CNC display errors made up of all of the CFI error terms controller has particularly problematic. This except linear interpolation. The straight sections information was not directly obtainable and very little display both the transient and steady state documentation was available to facilitate its straightness error; the inner and outer corners display extraction. 5jnce the desired information can be the cornerino error; and the curved section displays displayed on the Ci','C ooerator console CRT, various . the cir~0lar-interpolation error. Moreover, the hardware anrJ software debugging methods were applied to positioning error is superimposed over the errors that locate internal position data which could be extracted occur when ever the table stops along an axis. and provided to the error minimization controller. After several weeks of monitorino embedded Finally, the thin rib displays all the CFI errors microprocessor activity with a logic analyzer, a memory plus the work piece compliance erro·r. Due to the fact mapped, micron resolution, position interface was • that all the mentioned errors are present in the thin discovered within the CNC controller internals. After rib, its correction will signify the compensation of a complete disassembly of the embedded microprocessor all of the mentioned error terms. read-only m?.mory (ROM),. several surgical ROM mpdifications were implemented to provide position at a In order to measure the test part, and hence the predictable (8ms) update rate. A digital hardware errors, a coordinate measuring machine will be used. position interface, modelled as a finite state machine, To minimize the use of this expensive piece of has been developed to capture, buffer and transmit the equipment, preliminary measurements of the test parts axis position data to the error minimization will be done using digital micrometers and calipers to controller. The remaining error minimization obtain a rough estimate of the errors present and their controller inputs are comparatively straight forward source. analog signals. Due to the high levels of electro- magnetic interference (EMI) and potential for ground FUTURE WORK. With the experimental facility fully loops, all digital signals are opto-isolated and analog operational, remaining efforts involve implementation signals differentially buffered. of the actual error minimization methodology. These activities include, Implementation of the error compensation methodology also reouires mechanisms to coordinate and Generation of the complete error maps, sequence CNC and error minimization controller Completion of CNC machine dynamics operations. The present approach involves the down identification, loading of the part program, in M G codes, to both Control system implementation and validation. the CNC and error minimization controllers. In this scenario, the CNC and error minimization controller Codification of the ongoing dimensional error execute the same part program simultaneously. This investigation into error map representations will begin allows the error minimization controller to cooperate with fairly simple error representations and with the existing CNC controller and completely defines progressively increase in sophistication. the desired tool trajectory. Existing CNC support for optional M-codes M21 through M28 is currently being Accurate identification of the AMS spindle and CNC interfaced to the error minimization controller to machine dynamics is crucial to the development of the provide seouencing and handshaking functions. dynamical system oodels required for the control system design process. The spindle calibration and SAMPLE PART. In order to validate error correction, identification process is essentially complete. using the magnetic spindle, a sample test part was Identification of the CNC machine dynamics will proceed designed as shown in Fig. 3. The m,ijor problem asso- pending completion of the previously described ciated with using a part to quantify machining errors real-time axis position interface. is that several types of errors may be coupled and pro- duce a resultant error in the feature. Hence, the Control system 111'.)delling ls currently underway individual errors can not be separated and quantified. using a VAXbased computer-aided control system design The features incorporated into the test part should be (CACSO) environment composed principally of the ACSL, chosen such that only one class of error is displayed MATLAB and MACSYMA software packages. This environment in the feature. supports the robust, multivariable control design methodologies which will be applied, once the system The principle errors under observation in this identification phase is complete. Trial error research are associated with the X-Y plane of a minimization controller designs will also be evaluated, vertical milling machine. The errors,sproduced have in this environment, using mixed continuous and been classified as cutting force independent (CFI) and discrete simulation, prior to microprocessor cuttino force dependent (CFO). The specific CFI error implementation. terms under investigation at this time are: point to point positioning, transient and steady state The error minimization controller implementation straightness, cornering, and circular and linear will be performed using an IEEE 796 (Multibus) based interpolation. Work piece compliance is the principle coirputer system. This system utilizes an Intel 386/387 aco error being studied. processor pair and executes the Intel RMX II operating system. High performance interface boards will be The present test part incorporates three distinct incorporated to ensure adequate real-time performance. features in an atteirpt to isolate the above error In addition, the Oatel ST-701 analog input board has terms: holes placed around the perimeter, a boundary, been hardware and firmware oodified to provide and a thin rib in a pocket. This part by no means sufficient throughput. This error minimization isolates all the individual errors, but it contains computer system, currently being assembled, is similar features that show a progression of the influ,nce of to a system presently providing highspeed system the error terms. identification data acquisition services. The holes drilled in the boundary sectiori of the Evaluation of the error minimization capabilities part are features that will only display the point to of the magnetic spindle retrofitted Matsuura te500 will point positioning error induced when the machine's be performed by comparing the dimensional accuracy of a table 111'.)ves from one position to another and stops to sequ,nce of sample parts. This sequence will use the drill a hole. Several parameters associated with this MC500, with no error correction, as the baseline with error may be controlled, position, direction, and feed which to evaluate various error map formulations and rate. control system implementations. Dimensional accuracy will also be compared to a part milled on a conventional Matsuura IC510 vertical CNC mill. 33 Page 904 ACKNOWLEDGEMENT. The research work reported in this 5. Kirkl J.A., Anjanappa, M., Anand, D.K. and Shyam, paper represents a cooperatfve activity of the S., 'Accuracy Enhancement Methodoloaies in Thin Rib personnel from the University of Maryland, the National Machining," Proceedings of the 14th - NSF Bureau of Standards, the Westinghouse Corporation, the Manufacturina Conference-;-october 6-~1987, Ann David Taylor Naval Research Center and the Magnetic Arbor, MI. Bearing, Inc. This work has been supported by the National Science Foundation through grant NSF 8516218 6. Anjanapoa, J., Kirk, J•.A. and Anand, O.K., "An the Engineering Research Center at the University of P.lgori thmic Relationship Between the Cut tlno Force Maryland and ONR Program Element 61152N through the and Surface Texture in Machining Processes,•• David Taylor Research Center. Proceedings of the 17th TASTED International Conference, November 1987, New Or leans, LA. 7. Kirk, J.A., Anand, D.K. and Anjanappa, M., 1. Anand, D.K., Kirk, J.A. and Anjanappa, M.,. "Validation of a Relationship Between Cuttino Force "Magnetic Bearing Spindles for Enhancing Tool Path and Surface Finish for Optimal Control of End Accuracy," Advanced Manufacturing !..!.=== Milling," ASME Publication DSC- Vol.£,_ "Modeling Vol. 1, pp. 245-268, 1986. and Control of Robotic Manipulators and ManufacturingProcesses," ASME WinterAnnual 2. Kirk, J.A., Anand, D.K and Anjanappa, M., ''Magnetic Meeting, December 13-18, 1987 Boston, MA. Bearing Spindle Control in Machining," Proceedings of 13th NSF Conference .2!l Manufacturing Research 8. Anjanappa, M., Anand, D.K. and Kirk, J.A., and Technology, NoveMber 1986. "Identification and Optimal Control of Thin Rib Machining," ASME Publication DSC:;. Vol. £,_ Modelinq 3. Anjanappa, M., Kirk, J.A. and Anand, D.K.l "Tool and Control of Robotic Manipulators and Path Error Control in Thin Rib Machining,' Manufacturing Processes, ASME Winter Annual Proceedings of 15th NAMRC, pp. 485-492, May 1987. Meeting, December 13-18, 1987 Boston, MA. 4. Anand, O.K., Kirk, J.A. and Anjanappa, M., "Tool 9. Anjanappa, M., Anand, O.K., Kirk, J.A. and Shyam, Path Error Control for End Milling of Microwave S., "Error Correction Methodologies and Control Guides," Proceedings of the 7th ~ Congress .2!l Strategies for Numerical Controlled Machining," to the Theory of Machines and Mechanisms, September be presented at the 1988 ASME Winter Annual 17-22 Sevilla, Spain, Pp. 1499-1502. Meeting in Chicago, IL. OJTIIM> Rm-ltmemff Elim$ OJTTING RKE-IIWE Elim$ rtPE If 8ml POSITJ(N nmw.. EGiT OJTTil«l RHl: Elim fffiR1A1l(N IH(FJ1ATJ(N ~Tllli NAlUE If 8ml IITER!INISUC !Em1IHISUC STOCHASTIC RtCJllliAL POSITI!ll 10031Alt.lE l!A5'S ClffLIAICE 1lPlH If arr IEPEMBO ~TE m:nss ll\'IWUCS FIG.l 'IOOL PA1H ERROR CLASSIFICATION 34 Page 905 NOTE: wirt MI~ED ~----, FOR BREVITY h-AXIS OPTICAL • • • MOVEMENT ENCODER COMMANDED POSITION NUMERICAL COMPUTER. POSITION FEEDBACK CONTROL :',UMERICAL CODES CONTROL EXISTING ACTUAL POSITION MACHINE ACCURACY CUTTING ENHANCEMENT FORCES ERROR MAGNETIC MAG;,/ETIC MINIMIZATION BEARING SPINDLE CONTROLLER CONTROLLER FORCE & DISPLACEMENT CUTTING FEEDBACK COt----+-7 9____,tJ Space t---f----j Figure 8. Output selection menu. For each mass flowrate, enter the new effectiveness tor the regenerator (Min = a. 000 Max = 1. ooo) At this point, an accurately drawn LOW O. BOO* psychrometric chart depicting the syste~ Medium o. 750 performance at any timestep in the simulation could be presented by pressing "P" for High 0. 700 "Psychrometric Chart". Figure 9 shows typical results for a ventilation type desiccant Enter the new value for the highlighted parameter above: cooling system and Figure 10 shows typical results for a recirculation type system. (Hit the carriage return to keep the parameter as shown above.) Notice that a schematic of the desiccant system appears above the psychrometric charts Figure 7. Regenerator modification. in Figures 9 and 10. This allows an engineer using Destrol to easily visualize the location of each of the state points labeled on the The user would next enter a heat psychrometric chart. After viewing the exchanger effectiveness for each of three mass psychrometric chart, the user can press the flowrates (low, medium, and high). The actual "Shift-PrtSc" key combination to send a copy values of these flowrates in lbs/min is ot the diagram to his printer. Pressing any defined by the "control strategy" (choice 6 in other key will return the display to that Figure 6). Thus the program allows for a shown in Figure 8. control strategy in which the mass flowrate varies depending upon the temperature (as well as the air moisture content in advanced designs) of the conditioned space and/or the fci1 ~ r_._s_-.i--- Ii ambient. L-..J~Hti I r,, Conditioned I ---, 3 I After entering the new values for the Space .'['C--l.' l..J~ '- ----- heat exchanger effectiveness, the program Uen ti Ia t ion Hod, · HO!JS[J would prompt the user to press any key in order to return to the modification menu (shown in Figure 6). At this point, other components could be modified if desired. Once all of the necessary modifications have been made, the user would press "X" in order to return to the main menu shown in Figure 5. If future simulations would rely on data similar to that currently defined by the program, the user could enter 11 8 11 for "Save" in order to save the current set of data. After pressing "S" the program would allow the user to rename the data file if desired. Once }'jqure 9. Typical psychrometric chart for a the file has been saved on6tlisk, the display ventilation type desiccant cooling would again appear as shown in Figure 5. system. 73 Page 910 Figure 11 shows a sample display that is minimize the auxiliary energy requirements ot obtained by choosing "C" for "Comfort Chart". the desiccnnt cooling system. Obviously, As can be seen in this figure, humidity ratios there will be tradeoffs between system costs, in the conditioned space below 0.0043 pounds energy consumption and comfort. It is hoped of moisture per pound of air are considered that Destrol will be a useful tool for too dry while humidity ratios above 0.012 are arriving al optimal designs. considered too humid. Similarly lines representing the division between too cold, comfortable, and too hot (according to ASHRAE THE COMPUTER MODEL standards) appear in the figure. For the simulation shown in Figure 11, the program has The control strategy and the mathematical determined that the control strategy under model used lo simulate the components in consideration would cause the conditioned De:;trol wi 11 be briefly described in this space to be comfortable 83% of the time, to be section of the paper. For brevity only the too dry 3% of the time, to be too hot and dry ventilation cycle will be discussed. :Refer to 2% of the time, etc. Fiqure 9 tor a simple schematic of the deuiccant cooling system for the ventilation mode of operation. ea npu For cnch timestep of the simulation, Conditioned ------TI!- Destrol first, reads in the ambient conditions Space 1 (Ti, w1 , l~ and Ia). Next, the operating stutus of the cooling system is determined i.e. whether the system is on or off. This decision is based upon the operating status during the previous timestep and the current temperature and perhaps humidity ratio of the conditioned space (T6 and w6 ). For more advanced systems, the user can provide the control strategy to be used to determine the air flowrates through the system (m1 and m10 J. For example, the air flowrates can be increased during times requiring a large cooling capacity. If it is determined that the desiccant cooling system is to be off during the timestep, then the program calculates the new temperature and humidity ratio for the Figure 10. Typical psychrometric chart for a ~onditioned space (T6 and w6 ) based on the recirculation type desiccant internal and external heat and moisture gains cooling system. for the dwelling. 77 F If it is determined that cooling is : : needed during the timestep, then the prograc, I I COLD & HUMID : HUMID : HOT & HUMID calculates the system temperatures T2, T I I 3 , T4 , ( 0 \ ) : ( 1 \ ) l ( 2 \ ) T7, Ta, and Tg based on the known ambient : l temperature (T1) and current temperature of I I .. _________________,_ -----l------------------------- w -.012 the conditioned space (T5). An iterative solution is required due to the fact that T ( 83 \) \ 2 \) 6 (~ ~ -) ____________ I and w6 change during the timestep thus causing COMFORTABLE HOT a change in state points 2, 3, 4, 7, 8 and 9. . I I ---------------- l,,j' • • 004 3 Once convergence is obtained, the energy I I I I I : quantities (cooling provided, auxiliary heat ' I ( I ( 3 \ ( 2 \ ) I required, etc.) are calculated by assuming I COLD & DRY I : I DRY I HOT & DRY that each component of the system can be I I trented as a steady-state, steady-flow process 71.5 F BO F with inlet and exit conditions equal to the Press any key to continue . .. averaged value for the timestep. Figure 11. Typical display showing the performance of the control strategy in terms of comfort. The conditioned space is characterized bv an overall heat transfer coefficient, a - thermal capacitance, and an infiltration rate. If it was determined that these comfort Furthermore the user can specify the internal levels were unacceptable, then after studying heHl gain and the vapor generation rate for the psychrometric charts at various times in each of the 24 hours of the day. A moisture the simulations, the engineer could modify the balnnce and an energy balance are used to control strategy in order to increase the calculate the new dwelling temperature and comfort of the conditioned ~pace. Similarly humidity ratio for each timestep of the modifications could be made in order to simulation. 74 Page 911 The Evaporative Coolers CECl and EC2} fit s f or the Fl and F2 potent i a l s f o r silica gel in terms of temperatu re (K) and h umi d ity The process occurring in an evaporative ratio (kg/kg). The resul ts are: cooler is one of constant wet bulb. In the limit, the exit state of an evaporative cooler -2865 has the same wet bulb temperature as the inlet Fl + 4 . 24 4,,...0 . 8 624 ( 4) state and is saturated. Thus for the Tl. 490 evaporative cooler, ECl, the effectiveness is defined as the ratio of the actual moisture gain by the air to the maximum amount of moisture that could theoretically be gained by Tl. 490 the air. F2 - 1 _127 ..., 0 .07 969 ( 5) 6360 (1) Two effectivenesses of th e Fl and F2 potentials are used to determine th e o u t let (State 4 1 represents the state that would be state (state 2) of the d e hu midi f i er . Tnese achieved if sufficient moisture was added in effectivenesses are defined as: the evaporative cooler in order to obtain a saturation condition at the e xit.) Similarly F12 - Fl1 for evaporative cooler EC2. eFl ( 6) Fl9 - Fl 1 (2) F2 2 - F2 1 eF2 = ( 7 ) The values of eECl and eEc2 are F29 - F21 determined by the control strategy as defined by the program user. Jurinak and Beckman Thus for given inlet states 1 and 9 , equ a tions (1980) recommend a low and high value of 0.80 (4) and (5) are used to solve f or F li, F1 9 , and 0.96 for the evaporative cooler F2 1 and F2g. Next, for known effecti v e ne sses effectiveness. eFl and eF2, equations (6) and (7) are solved f or Fl 2 and F2 2 . Finally, equations (4) and (5) are solved for the dehumidifier ex it state The Heat Exchanger CHE} (T2 and w2)• Assuming that the mass flowrates of the The values of eFl and eF 2 are determined process stream and regeneration stream are by the control strategy as defined b y the equal, the temperature of the cooled air program user. Jurinak and Beckman (198 0) leaving the heat exchanger (state 3) can recommend a low and high value of 0. 07 and theoretically approach the inlet temperature 0.05 for eFl and 0.80 and 0.95 f or e F2 . of the air to be heated (state 7). The heat exchanger effectiveness can then be defined as the actual heat transferred in the heat CONCLUSION exchanger to the theoretically maximum heat that can be transferred. This is identical to The computer program Destrol is~ a s the definition of effectiveness found in most sophisticated as many of the desiccant heat transfer texts e.g. Holman (1981). computer models that are currently in use today. Its accuracy is dependent upon the accuracy of the parameters chosen to represent ( 3) the various components of the systeo. f or example, Destrol will not calculate the effectiveness of a given type of regenerator ; The program does allow for eHE to vary that effectiveness must be supplied by the with air flowrate. Jurinak and Beckman (1980) person using the program . However, because o f recommend a low and high value of 0.80 and its ease in use and because the progra~ 0.95 for the heat exchanger effectiveness. readily provides a visual display of th e system's performance (e.g. in the fo rn o f psychrometric charts), it is believed that The Rotary Dehumidifier (DH} Destrol can be a valuable design too l especially for analyzing various contro l Destrol assumes that the desiccant used s trategies employing advanced controllers. If is silica-gel whose properties have been outstanding performance can be predicted by extensively tested. The rotary dehumidifier the use of a "smart" controller which i s not is modeled using the theory introduced by currently commercially available, then t he Banks, Close, and Maclaine-Cross (1970 and program could be used to provide the 1972) . By defining two dimensionless justification for developing this "smart" potentials, Fl and F2, they reduced the c ontroller. analysis of heat and mass transfer in the rotary dehumidifier to the known solution of heat transfer in rotary s t nsible heat exchangers. Jurinak (1982) developed curve 75 Page 912 ACKNOWLEDGMENT This work was supported by the Division of Solar Heat Technologies, Department of Energy, under contract DE-AC03-86SF16132. REFERENCES ASHRAE, 1977, Handbook of Fundamentals. Banks, P.J., Close, D.J., and Maclaine-Cross, I.L., 1970, "Coupled Heat and Mass Transfer in Fluid Flow Through Porous Media - An Analogy with Heat Transfer," Proceedings of the 4th International Heat Transfer Conference, Elsevier, Amsterdam, VII, CT3 .'l. Holman, J.P., 1981, Heat Transfer, McGraw-Hill Book Company, New York, New York, pp. 454-456. Jurinak, J.J., and Beckman, W.A., 1980, "A Comparison of the Performance of Open Cycle 'Air Conditioners Utilizing Rotary Desiccant Dehumidifiers," Proceedings of the AS/ISES Annual Meeting, Phoenix, Arizona, pp. 215-219. Jurinak, J.J., 1982, Open Cycle Desiccant Cooling - Component Models and System Simulations, Ph. D. thesis, University of Wisconsin - Madison. Maclaine-Cross, I.L., and Banks, P.J., 1972, "Coupled Heat and Mass Transfer in Regenerators - Prediction Using an Analogy with Heat Transfer," International Journal of Heat and Mass Transfer, Vol. 15; pp. 1225-1241. 76 Page 913 ·IECEC-89 August 6-11, 1989 Washington, D.C. PROCEEDINGS OF THE 24th INTERSOCIETY ENERGY CONVERSION ENGINEERING CONFERENCE Paaicipating Societies VOLUME 3 Flow Batteries High Temperature Batteries Batteries for Space Power Key Issues in Space Energy Storage Magnetic Bearings in Energy Storage Flywheel Sytems Fuel Cells Ambient Temperature Batteries Editor:· William D. Jackson ~!~.~fflit9f:: :, DorotµyiiJ.\·,i I-lull INSTITUTE OF ELECTRICAL AND ELECTRONICS ENGINEERS gineering Center • 345 East 47th Street • New York, NY 10017 Page 914 DYNAMICS CONSIDERATIONS FOR A MAGNETICALLY SUSPENDED FLYWHEEL bY C.M. Lashley, D.M. Ries, R.B. Zmood, J.A. Kirk and D.K. Anand Mechanical Engineering Department University of Maryland College Park, MD 20742 ABSTRACT this is not generally the case, and any structural resonances within the operating range of frequencies can The Advanced Design and Manufacturing Lab is have adverse effects on system stability. The results of involved in the design of a magnetically suspended this test were used to suggest possible design fl heel energy storage system for satellite applications. modifications to remove any such resonances. If this is T er d esign of the multiring composite flywheel was found to be impossible, they can be used to derive or optimized. An inner-ring interference of .006 was found verify a mathematical model of the system, including the to be greatly beneficial, while having an inner radius dynamic effects of the structure, which would allow growth of 8.7 mil at speed. The optimum amount of iron improved controller designs to be studied. present in the inner ring was shown to be 5.5 Ibs for this flywheel. Modal testing was used to obtain the natural FLYWHEEL OPTIMIZATION frequencies and mode shapes of a flywheel system prototype. These results were used to suggest design The optimization was implemented using two modifications to remove resonances from the operating computer pro rams[5], for stress analysis of composite range. If this is found to be impossible, the results can be fl heels FLf'ANSZ), and for eometric desi n used to verify a mathematical model which can be used to (KYSIZI!?), produced at the UkIVERSITY OF study improved control system designs. MARYLAND. Interference Assemblv INTRODUCTION When using FLYANS2 the user can specify the The Advanced Design and Manufacturing maximum interference allowed between the rings when Laboratory at the University of Maryland is involved in they are assembled into a flywheel. The interference is the design of a magnetically suspended flywheel energy defined by the equation, storage system for satellite applications. This system concept promises increased stored energy per unit mass, Interference = (r2 - rl) / rl, as well as greater reliability than batteries currently in use. Other potential advantages include high efficiency, where r and r2 are the nominal inner radius of the outer allowed by the near frictionless magnetic bearings, and ring and the nominal outer radius of the inner ring the availability of a large rotating inertia for attitude respectively. This interference results in favorable control [ 11. stresses in the rings of the flywheel. The stored energy, the operating speed range, and the flywheel thickness was A study was conducted to optimize certain held constant. parameters which can affect the design and performance of a magnetically suspended, multi-ring, uniform Figures 1 and 2 show the increases in the useable thickness, composite flywheel[2]. During flywheel design SED and maximum angular speed that can be obtained by the useable specific energy density (SED), and the designing the rings with increasing amounts of maximum flywheel angular speed (burst speed), should be interference. Figure 3 shows the flywheel weight maximized, while the flywheel weight, inner radius decreasing as the amount of interference increases. growth, and required assembly force should be minimized. These illustrate the advantages of increasing the The inner most ring of the flywheel must be made from maximum amount of interference in the rings. iron, the amount of iron present was optimized with respect to the stored energy and the useable SED. Figure 4 shows the increases in the growth of the flywheel inner radius as the amount of interference is A four inch prototype aluminum flywheel system increased. This growth should be kept to a minimum was recently designed and constructed (four inches refers because any growth must be compensated for in the to the outer diameter of the magnetic bearing) [3]. A magnetic bearing control system. Figure 5 shows the modal testing procedure was used to separately study the almost linear increase in the maximum required assembly dynamic characteristics of the flywheel and support structure. Previous control system designs [4] assumed that both of these elements are infinitely rigid. However, 1505 ~~278i-3/89/0000-15$015. 00 1989 IEEE Page 915 force. This is based on a coefficient of friction of .l. It while the hammer was applied at each grid point of the lubrication is used during assembly the force rPquired structure (including the reference). In this way a row or could be lowered. column of the symmetric FRF matrix was identified which Choosing the maximum amount of interference to is sufficient for the modal analysis program to identify a be .006 would be greatly beneficial to the design and complete set of natural frequencies and mode shapes. operation of the flywheel. The assembly can be achieved with as yet undetermined, but tolerable forces. These can Impact tests were carried out on the aluminium be realized as long as the magnetic bearing can tolerate a flywheel while freely suspended from the roof, and the inner radius growth of 8.7 mil. support structure mounted to the shaker table. Shaker Test Inner Radius Ratio Uniformly distributed random noise from the One user input to FLYSIZE is the inner radius analyzer was used to drive the electro-hydraulic shaker ratio (IRR) of the flywheel, table, to which the test piece was bolted. The FRF were produced between the output of a reference IRR = ri / ro, accelerometer, mounted on the base of the structure, and with ri and ro being the flywheel inner and a roving accelerometer, positioned in turn at each grid outer radii respectively. point. As in the impact test, these FRF were then used to deduce the natural frequencies and plot the mode shapes. The four inch support structure was tested in this manner. An inner most ring of segmented iron was used to simulate the motor/generator magnet structure and the flux return rings of the bearing. The amount of FOUR INCH FLYWHEEL IMPACT TEST segmented iron present is a function of the IRR. The amount of iron present approaches zero as the IRR approaches .45. An impact test of the freely suspended four inch aluminium flywheel clearly shows that the first natural frequency is 4.35 kHz (see fig. 8). This value is Figure 6 shows that at an IRR of .41 the stored substantially above the maximum operating frequency (1 energy is at a maximum, and figure 7 shows that at the a kHz) and the bandwidth of the control system (300 Hz). It same IRR the useable SED is at maximum. The total can therefore be concluded that the flywheel behaves as a weight of iron present is 5.5 Ibs and is 18.3% of the total rigid body over the frequency range of interest. No mode flywheel weight. The optimum IRR was found to be .41, this result allows a large amount of iron to be present in shapes were plotted for this experiment. the inner ring of the flywheel. FOUR INCH SUPPORT STRUCTURE MODAL TESTING IMPACT TEST Modal testing is an experimental method used to determine the natural frequencies and mode shapes of a The four inch support structure consists of a cubical aluminium box with sides approximately nine structure from measured force and response data. These inches in length. Visible through a view port, is the center- signals are first used to calculate the frequency response pillar, on which the magnetic bearings and the stator of a functions (FRF) between various marked grid points. A motodgenerator are mounted. When the system is modal analysis computer program is then used to curvefit assembled, the hollow lindrical aluminium flywheel fits a single degree of freedom model to each response peak over the center-pillar. 2 photograph of the assembly with on each FRF. These models directly give the natural the front plate and flywheel removed is given in fig. 9. frequencies and by plotting the relative magnitude and phase of each grid point, also yield the mode shapes [6]. As previously mentioned, the test was carried out A Hewlett Packard 3562A dynamic signal analyzer with the structure mounted on the shaker table. The results show that there are three natural frequencies was used to measure the required FRF as well as for overall control of the experiment. A frequency span of below 1 kHz,these being at 385,635 and 806 Hz. The 100 1.35 mode shapes for these frequencies are plotted in fig. 10, Hz to kHz was selected to include the range of with the two faces normal to the x-axis and the roof normal operating frequencies. The present design calls removed for clarity. It should be noted that additional for the flywheel to operate between rotational speeds of tests were performed which showed that these faces and 30,000 rpm (500 Hz) and 60,000 rpm (1 kHz). For the the roof show very little deflection for the modes given. experimental set-up used, excitation could be supplied This is to be expected, as the excitation provided was usin either an impact hammer or a shaker table. Entek always in the z-direction which is 90 degrees away. "EA!Y", running on an HP 9000 computer, was the modal analysis program used. The FRF measured appear to identify two other Impact Test modes between 1 kHz and 1.35 kHz. It was impossible, however, to plot the mode shapes accurately as the energy An instrumented impact hammer was used to of the impact pulse declined considerably beyond 1 kHz. supply a force pulse to the test structure and the response In addition, higher modes inherently contribute less to the measured with a light-weight accelerometer. These response and are more difficult to measure. signals were used by the analyzer to calculate the FRF between the force a plication and measurement points. The accelerometer preference) position was held constant 1506 Page 916 Mode Shape 1- 385 Hz transverse stiffness). This increase could have been provided by the increase in effective mounting stiffness The first mode shape appears to consist of rigid between the test. body motion of the entire structure accompanied by some bending of the center-post and rotation of the walls. This Mode Shape 2 - 747 Hz motion is primarily due to the flexibility of the interface between the sliding and fixed parts of the shaker table to Mode shape 2 is similar to mode shape 3 of the which the structure was fixed during the test. Modes such impact test, with changes in frequency and shape as this one will be found when the stiffness of the consistent with an increase in transverse mounting mounting arrangement cannot be considered to be zero stiffness. (free-free) or infinite (clamped). This situation is likely to be encountered during actual operation. Mode ShaDe 3 - 838 Hz Mode Shape 2 - 635 Hz This mode does not appear in the impact test at all. From the mode shape plot, it appears that there is a A great deal of bending in the center-pillar and great deal of deflection of in one element of the center- small vibration amplitudes elsewhere are characteristic of pillar, accompanied by rotation of the walls. Further the second mode. This suggests that the mode is primarily experimentation is necessary to completely describe this due to the flexibility of the center-post. In other words, it mode. appears that a model of the center-pillar alone, with boundary conditions of the correct flexibility,w ould give APPLICATION OF RESULTS similar results. This type of reasoning allows suggestions of design changes to be made to increase the natural Design Modifications frequency of this mode. The entire structure is, of course, made up of many coupled elements, it is not strictly It is evident from the differing results between correct to say that a mode is "due" to any one. impact and shaker testing, that it is possible to alter the dynamic characteristics of a structure by selectively Mode Shape 3 - 806 Hz changing mounting and attachment stiffness. This result can also be obtained by changing the effective stiffness of The third mode resists simple description. Close the structural elements. It is therefore theoretically examination reveals that the walls are pivoting about their possible to redesign the structure so that all of the natural bases, but bending very little. The center-pillar appears to frequencies are above 1 kHz. If this is achieved, the be vibrating in some combination of the first and second support structure could be considered infinitely rigid. This sinusoidal modes of a simply supported beam. It can would greatly simplify the analysis of the control system as therefore be argued that the flexibility of the hold-down only the controller and rotor dynamic effects would have bolts for the walls, in bending, contribute heavily to this to be included in the theoretical model. To this end, a mode. As previously mentioned, this is only a qualitative critical examination of the test results was performed to approach for examining the test results. None of the identify the necessary design modifications. modes can really be taken as independent. Both the impact and the shaker test identified the FOUR INCH SUPPORT STRUCTURE: center-pillar and the hold-down bolts of the walls as the SHAKER TEST most flexible elements of the design (apart from the mounting arrangement). The center-pillar, currently The shaker test also identified 3 natural many separate elements assembled with locational fits, frequencies below 1k Hz, these being at 565,747, and 838 could be redesigned as one continuous unit to increase Hz. The corresponding mode shapes are plotted in fig. stiffness. Off-center fasteners could be incorporated on 11. Mode shape 1f rom the impact test does not appear the ends to more closely approximate the clamped in these results. This is because the impact test included boundary condition which gives the highest natural the dynamic interaction between the stationary and frequency. In a similar way, an increase in the number or moving parts of the shaker table. In the shaker test, size of the bolts holding the walls to the base would however, the excitation is provided by the moving part probably increase the natural frequency associated with and the elements below are not included. Consequently, this motion. It is also important that the stiffness of the the first natural frequency and the effective mounting mounting be very high to restrict rigid body modes. stiffness increases significantly between the tests. Because of the coupled nature of the problem, however, it is not possible to predict the exact effects of these changes Mode Shape 1 - 565 Hz without some kind of mathematical model. As a result, further testing is necessary to gauge the effectiveness of This shape is very similar to mode shape 2 from the design modifications. the impact test except that it appears at a lower frequency and includes more bending of the walls. If, as before, it is One possible solution that has not been explored is assumed that the mode is largely due to flexibility of the to test the structure in its free-free state. In this condition, center-pillar, it is possible to easily explain the reduction ri 'd body modes will not appear and natural frequencies in natural fre uency. If the transverse, but not the opother modes may be increased. rotational stif%ess, of a beam supported at both ends is increased, the natural frequency will decrease. This It should be noted that it may not be possible to corresponds to an incremental movement on the path remove all the natural frequencies from the operating between free-free (zero transverse stiffness) and pinned- range while meeting weight constraints. In this case, the pinned (infinite 1507 Page 917 dynamics of the structure must be included in the model 5. Khan, A.A., "MaximizationO f Flywheel used to design the control system. Performance", M.S. Thesis, 1984 Mathematical Model 6. Ewins, D.J., Modal Testine: Theorv And Practice, Research Studies Press LGl.,Letchworth, Results of a modal test can be used to directly Hertfordshire, England, 1984. obtain a mathematical model of a structure. However, this requires that the entire FRF matrix be measured for a 7. Zmood, R.B., Anand D.K. and Kirk, J.A. ," Analysis, frequency range much greater than the operating range. Design, And Testing Of A Magnetic Bearing For A These requirements are very hard to meet. As a result, it Centrifuge", 12th Biennial ASME Conference on is better to derive a theoretical model, perhaps using the Mechamical Vibration And Noise, Montreal, finite element method, which can then be validated and Cananda, (to be presented Sept 1989) refined using the experimental data. This model, in state space form, can be combined with those of the flywheel and control system to give a model for the entire system. In this way, the performance of different controller options can be studied and optimized. This approach is called coupled structure analysis [7]. The overall model should also be experimentally verified. This could easily be done by measuring the response of the system to a sinusoidal current in the magnetic bearing, and comparing it with the output of the model. CONCLUSIONS Several conclusions can be drawn from this study. The four inch aluminium flywheel behaves as a rigid body for the entire operating range of the system. The natural frequencies and mode shapes of the support structure have been measured for different mounting conditions. In Figure 1. addition, several design modifications have been Useable SED as a Function of Interference, suggested to try to remove most of these resonances from 500Wh Flywheel. the operating frequency range of the system. If this is found to be impossible,the test data can be used to derive or verify a theoretical model of the structure which can be used as part of an improved system model. One important action to be carried out in the future is the testing of the support structure in its free-free state. ACKNOWLEDGEMENTS The use of the facilities of the Vibrations laboratory of the University of Maryland, as well as the he1 ful discussions with Dr. M. K. Abdelhamid and Michael Eurke, are nreatly appreciated. 0 0 002 am, 0 W6 0 0011 0 01 I"P..ER*NCC REFERENCES Figure 2. Maximum Angular Speed (burst) as a Function 1. Kirk, J.A. and Anand, D.K., "Satallite Power Using A of Interference. Magnetically Sus ended Flywheel Stack", Journal Of Power Sources, 12 (1988). 2. Huntin ton, R A , "Stress Analysis And Maximization Of Pegrmance For A Multiring Flywheel", M.S. Thesis, 1978. 3. Iwaskiw, A.P., "Desi Of A 500 Wh Magnetically Suspended Flywhee$Energy Storage System", M.S. Thesis, 1987. 4. Plant, D.P., "Prototype Of A Flywheel Energy Storage System", M.S. Thesis, 1988. Page 918 0 o m * o m , O W 6 0 WO IKTEllrrRrNCE Figure 3. Total Flywheel Weight as a Function of Intertm MY. Figure 6. Stored Energy as a Function of the Inner Radius Ratio. , 3 , , , , , , , , , I 0.001 0.00, 0.006 0.024 0.0, 11111"1LE,*CI Figure 4. Inner Radius Growth (at speed) as a Function of Figure 7 Useable SED as a Function o f the h e r R adius Interference. Ratio. 0 . 4 _. 7 M O 0 .. '--tr] ._ I: i0 on2 ODD, 0 0 % oooe 0 01 ,.T,k,,hr,, I Figure 5. Maximum Assembly Force as a Function of Figurc 8. FRF o f the 4 in. Flywheel. Interference. 1509 Page 919 Figure 9. 'K.e 4 in. Support Structurc. L i Figure 11. Mode Shapes 1 to 3 for the Shaker Tesi. Figure io. Mode Shapes 1 to 3 for the Impact Test. 1510 Page 920 A HIGH EFFICIENCY MOTOR/GENERATOR FOR MAGNETICALLY SUSPENDED FLYWHEEL ENERGY STORAGE SYSTEM W.L. Niemeyer+, P. Studerr , J.A. K i r kx , D.K. Anandx, R.B. Zmood*x + Goddard Space F1 ig ht Center, Greenbelt , Mary1 and , 20771-7313 * Department o f Mechanical Engineering, U n i v e r s i t y o f Maryland, Col lege Park, MD 20742 Department o f Communication and E l e c t r i c a l Engineering, RMIT, Melbourne V i c t o r i a 3000, Aus t ra l i a . T Consultant, TPI Inc. ABSTRACT To be compet i t ive, a FES system must maximize S p e c i f i c Energy Densi ty (SED) w h i l e ma in ta in ing a The research presented i n t h i s paper discusses t h e round t r i p e f f i c i e n c y i n excess o f 80 percent. t heo ry and des ign o f a brushless d i r e c t cu r ren t S p e c i f i c Energy Densi ty i s a measure o f t h e motor f o r use i n a f lywheel energy s torage system. f lywheel energy s torage c a p a b i l i t y , and i s The motor des ign i s opt imized f o r a nominal 4.5 t y p i c a l l y measured i n watt-hours pe r k i logram. The i n c h ou ts ide d iameter ope ra t i ng w i t h i n a speed e f f i c i e n c y i s maximized by e l i m i n a t i n g o r reducing range o f 33,000 - 66,000 r e v o l u t i o n s pe r minute sources o f energy l o s s throughout t h e system. I n w i t h a 140 v o l t maximum supply vo l tage. The t h e proposed energy s torage system, t h e suspension equations which govern t h e motor 's ope ra t i on a r e subsystem, t h e motor/generator, and windage a re t h e app l i ed t o compute a s e r i e s o f acceptable design p r i n c i p a l sources o f losses. parameter combinations f o r i d e a l operat ion. Engineer ing t r a d e - o f f s a re t h e n performed t o m minimize t h e i r r e c o v e r a b l e energy l o s s w h i l e remaining w i t h i n t h e des ign c o n s t r a i n t boundaries. A f i n a l i n t e g r a t e d s t r u c t u r a l des ign i s presented whose fea tu res a l l o w i t t o be i nco rpo ra ted w i t h t h e 500 watt-hour magne t i ca l l y suspended f lywheel . INTRODUCTION The motor/generator i s one o f t h r e e key elements i n a f lywheel energy s torage (FES) system, t h e o t h e r two being t h e f lywheel i t s e l f , and t h e magnetic suspension bear ings w i t h t h e i r assoc iated c o n t r o l c i r c u i t r y . The o b j e c t i v e o f t h e f lywheel system i s t o s t o r e and supply power i n spacec ra f t app l i ca t i ons . An a l t e r n a t i v e technology, and t h e f l y w h e e l ' s c h i e f compet i tor , i s t h e Fig. 1 Flywheel energy s torage system u s i n g e lect ro-chemical b a t t e r y s torage system, which has a motor /generator and two stacked been used e f f e c t i v e l y f o r many years. However, t h e magnetic bearings. e lect ro-chemical system has a l i m i t e d l i f e t i m e , even w i t h today 's advances i n b a t t e r y technology I n t h i s paper, t h e losses o f t h e motor /generator 111. The p r i n c i p a l advantages o f t h e f lywheel subsystem due t o t r a n s i s t o r sw i t ch ing losses, and energy storage system a re a p o t e n t i a l l y u n l i m i t e d p o s i t i o n sensor and commutation c i r c u i t r y l i f e t i m e and a comparat ive ly h i g h e f f i c i e n c y , due d i s s i p a t i o n w i l l be o f concern o n l y i n so f a r as t o t h e absence o f s l i d i n g and r o l l i n g surfaces. t hey r e l a t e d i r e c t l y t o t h e e l e c t r i c a l machine design. The system proposed by K i r k and Anand [2], i s i l l u s t r a t e d concep tua l l y i n F i g 1. The system MACHINE DESIGN OPTIONS u t i l i z e s a "pancake" magnetic bea r ing s tack which suspends a m u l t i - r i n g , i n t e r f e r e n c e - f i t , composite f lywheel . Nested between t h e magnetic bear ings i s Considerat ion o f spacecraf t performance t h e motor/generator f o r conve r t i ng mechanical requirements have shown t h a t t h e s torage capac i t y energy s to red i n t h e f lywheel t o e l e c t r i c a l energy should be 500 Wh. An e a r l i e r i n v e s t i g a t i o n [3 ] has and v i c e versa. Power c o n d i t i o n i n g c i r c u i t r y which shown t h a t t h e f lywheel system should operate over must be prov ided between t h e motor/generator and a speed range o f 33,000 t o 66,000 rpm (550 t o 1100 t h e spacecraf t e l e c t r i c a l loads t o ma in ta in a r p s ) w i t h an o v e r a l l round t r i p e f f i c i e n c y o f a t constant output vo l tage w i l l no t be discussed i n 1 east 80 percent. t h i s paper. 1511 CH2781-3/89/0000-1511 $1.00 ' 1989 IEEE Page 921 Whi 1 e t h e o p e r a t i n g p r i n c i p l e s o f e l e c t r ic a l r i g i d s t r u c t u r e f o r t h e permanent magnets and has a machines remain unchanged, t h e development o f h i g h e r i n e r t i a . An " i r o n l e s s armature" mechanical improved e l e c t r i c a l and magnet ic m a t e r i a l s , as w e l l arrangement, where t h e armature i s f r e e s t a n d i n g as major advances i n t h e f i e l d of power e l e c t r o n i c s and t o t a l l y detached f r o m t h e magnet ic i n n e r r e t u r n i n r e c e n t t i m e s have made t h e development o f r i n g [4], i s shown i n F ig . 2. I n t h i s arrangement, h i g h e r e f f i c i e n c y motor /genera tors p o s s i b l e . O f t h e i n n e r r e t u r n - r i n q i s a t t a c h e d t o t h e permanent p a r t i c u l a r i n t e r e s t a re t h e developments, i n t h e vagnet assembly and S O does no t exper ience a f luc- f i e l d o f permanent magnet m a t e r i a l s , such as t h e t u a t i n g magnet ic f i e l d a s t h e permqnent macjnets r a r e - e a r t h - c o b a l t and Nd-Fe-B a1 1 oys , and, i n t h e r o t a t e . f i e l d of s o f t magnet ic m a t e r i a l s such as t h e amorphous magnet ic a l l o y s . Aaferi als The development o f h i g h energy p r o d u c t permanent magnets has p e r m i t t e d t h e i r use i n p r o d u c i n g t h e main magnet ic f i e l d , t h e r e b y e l i m i n a t i n g t h e requ i rement f o r a f i e l d w i n d i n g w i t h two r e s u l t s . F i r s t l y , i t a l l o w s a " b r u s h l e s s " motor d e s i g n t o be developed. I n t h i s case t h e permanent magnets and t h e armature w i n d i n g a r e p l a c e d on t h e r o t a t i n g and s t a t i o n a r y members, r e s p e c t i v e l y . Th is , coup led w i t h commutation e l e c t r o n i c s a l l o w s t h e e l i m i n a t i o n o f s l i p r i n g s and brushes which a r e a source o f Y U C T l R I N G f r i c t i o n , e l e c t r o m a g n e t i c i n t e r f e r e n c e , and mechanical wear. Secondly, t h e permanent magnet F ig . 2 A m o t o r / g e n e r a t o r u s i n g i r o n l e s s f i e l d i n c r e a s e s e f f i c i e n c y by e l i m i n a t i n g t h e armature c o n s t r u c t i o n . r e s i s t i v e l o s s e s a s s o c i a t e d w i t h t h e f i e l d windings. The c u r r e n t permanent-magnet m a t e r i a l s Thus h y s t e r e s i s and eddy c u r r e n t l o s s e s i n t h e o f p r e f e r e n c e f o r h i g h performance a re t h e i r o n r e t u r n p a t h a re e l i m i n a t e d . I n a d d i t i o n t h e r e Nd-Fe-B a l l o y s . The h i g h c o e r c i v e f o r c e o f t h e s e a r e no p o l i n g f o r c e s p r e s e n t , due t o t h e magnet m a t e r i a l s a l l o w s des igns h a v i n g h i g h a i r g a p f l u x r i n g b e i n g n o n - c o n c e n t r i c w i t h t h e s t a t o r , because d e n s i t i e s w i t h l a r g e a i rgaps . Consequent ly t h e i n n e r r e t u r n r i n g and t h e magnet r i n g a r e p o s s i b i l i t i e s e x i s t f o r t h e armature w ind ings t o be s t r u c t u r a l l y coupled. T h i s can be i m p o r t a n t when designed t o e x i s t e n t i r e l y i n t h e a i r g a p , r a t h e r magnet ic b e a r i n g s a re used f o r suspension, as t h e s e t h a n b e i n g c o n f i n e d t o s l o t s i n t h e s t a t o r . d e s t a b i l i z i n g d i s t u r b a n c e f o r c e s must be c o n t r o l l e d by t h e b e a r i n g c o n t r o l system. I n s p i t e o f t h e s e Advances have a l s o been made i n m a t e r i a l s used f o r advantages, t h e o v e r a l l s t r u c t u r a l d e s i g n o f t h i s t h e s t a t o r magnet ic c i r c u i t r e t u r n path. As an motor f o r h i g h speed o p e r a t i o n would be q u i t e a l t e r n a t i v e t o i r o n l a m i n a t i o n s , b o t h powdered f o r m i d a b l e due t o t h e c a n t i l e v e r e d armature and meta ls and amorphous a l l o y s can reduce c o r e l o s s e s i n n e r r e t u r n r i n g . due t o b o t h h y s t e r e s i s and eddy c u r r e n t s . Amorphous m e t a l s o f f e r t h e p o t e n t i a l o f r e d u c i n g t h e c o r e l o s s e s o f motors and t r a n s f o r m e r s by more t h a n 70 p e r c e n t . For t h e m o t o r ' s a rmature w ind ing , s e v e r a l developments o f f e r a l t e r n a t i v e s t o c o n v e n t i o n a l magnet w i r e . One method f o r c r e a t i n g compact c o i l s which produce smal l motors and d e l i v e r more power i n l e s s space i s t o use square w i n d i n g w i r e . When o p e r a t i n g a t h i g h commutat ing f r e q u e n c i e s , L i t z w i r e can be used t o m i n i m i z e eddy c u r r e n t s . Rachine Mechanical Arrangements The new magnet ic m a t e r i a l s have opened up o p p o r t u n i t i e s f o r new mechanical des igns o f t h e e l e c t r i c a l machines. Th is p a r t i c u l a r l y a p p l i e s t o t h e permanent magnet m a t e r i a l s which a l l o w c o n s i d e r a b l y g r e a t e r freedom i n t h e d e s i g n o f t h e F ig . 3 Adopted m o t o r / g e n e r a t o r mechanical magnet ic f i e l d system. F o r a permanent magnet c o n f i g u r a t i o n . b r u s h l e s s DC motor, t h e magnets must be on t h e r o t a t i n g p o r t i o n o f t h e motor t o a v o i d t h e need t o As a consequence o f t h e s t r u c t u r a l d i f f i c u l t i e s t h e t r a n s m i t c u r r e n t across t h e a i r g a p . F o r t h e mechanical arrangement shown i n F ig . 3 has been f l y w h e e l a p p l i c a t i o n , i t i s conven ien t t o use an adopted. I n t h i s d e s i g n Nd-Fe-B magnets a re e x t e r n a l r o t o r c o n f i g u r a t i o n as i t p r o v i d e s a more a t t a c h e d t o an i r o n r i n g which i s f i t t e d t o t h e 1512 Page 922 i n t e r n a l sur face o f t h e f lywheel r i m . Th is r i n g , t h e d e t a i l e d aspects o f t h e machine design. It which prov ides t h e r e t u r n pa th f o r t h e a i rgap w i l l be seen i n a l a t e r sec t i on t h a t t h e major magnetic f l u x , must have s u f f i c i e n t s t reng th t o source o f losses i n t h e present des ign i s i n t h e w i ths tand t h e l a r g e hoop st resses experienced a t winding. L i t z w i r e can be used t o min imize eddy h i g h r o t a t i o n a l speeds. The 3-phase armature c u r r e n t and p r o x i m i t y e f f e c t losses i n t h e winding winding i s shown mounted i n t h e a i rgap, r a t h e r than and has been proposed f o r use i n h igh frequency i n s l o t s , and i s a t tached t o t h e s t a t o r power magnetic devices [5,6]. However, a heavy laminat ions. Th is arrangement i s a t t r a c t i v e f rom p r i c e , i n terms o f space u t i l i z a t i o n , i s p a i d by an e l e c t r i c a l s tandpoint , bu t necess i ta tes a l a r g e i t s use. a i rgap, and i s o n l y f e a s i b l e w i t h RECO and Nd-Fe-B permanent magnet m a t e r i a l s which have ext remely DESIGN CONSTRAINTS AND OBJECTIVES h i g h coe rc i ve forces. The s t a t o r l am ina t ions i n t h i s case need t o be made f rom a l ow l o s s m a t e r i a l Phys ica l c o n s t r a i n t s determine t h e bas i c geometric such as amorphous metal a l l oys . Not shown i n t h e s i z e o f t h e motor-generator and mandate c e r t a i n f i g u r e a re t h r e e p o s i t i o n sensors which a re used s t r u c t u r a l cons iderat ions. Fig. 4 shows t h e b a s i c f o r sensing and c o n t r o l l i n g t h e commutating geometry o f t h e f lywheel and magnetic bear ings as c i r c u i t r y so t h a t t h e cu r ren t i s switched t o t h e developed f rom prev ious s tud ies [3,18]. From t h e c o r r e c t s t a t o r wind ing a t any i n s t a n t . work on t h e s i z i n g o f t h e f lywheel i t has been determined t h a t t h e motor/generator needs t o f i t Control Logic and Switching Electronics w i t h i n a volume having a diameter o f 114.3 mm (4.5 i n c h ) and a h e i g h t o f 63.5 mm (2.5 i nch ) . Advances i n e l e c t r o n i c s have a f f e c t e d motor /generator des ign i n severa l ways. They have a l lowed t h e development o f compact designs, and w i t h t h e i n t r o d u c t i o n o f power f i e l d ' e f f e c t t r a n s i s t o r s (FET) they have pe rm i t ted power sw i t ch ing a t ra tes up t o a 1 MHz o r more. The power FET switches are c o n t r o l l e d by p o s i t i o n sensors which de tec t t h e l o c a t i o n o f t h e r o t o r magnetic po les w i t h respect t o t h e armature phases. Many a l t e r n a t i v e technologies e x i s t f o r these sensors, and they i nc lude : magneto-effect devices such as magneto-res is tor and h a l l e f f e c t switches, o p t i c a l sensors, and i n d u c t i v e sensors. Other types o f non-contact sensors can a l s o be used. SOURCES OF LOSSES The losses which occur i n t h e motor /generator a r i s e f rom f o u r p r i n c i p a l sources: t h e windings, t h e s t a t o r magnetic core, t h e e l e c t r o n i c commutating Fig. 4 Flywheel s tack showing motor space c i r c u i t r y and aerodynamic drag. The phys i ca l a1 1o cat ion. sources o f these losses toge the r w i t h formulae r e l a t i n g them t o t h e system parameters are I n a d d i t i o n t h e motor i s requ i red t o be a summarized i n Table 1. s t r u c t u r a l member sandwiched between t h e upper and lower magnetic bearings. An enc losure housing i s Table 1 t o be prov ided t o g i v e l a t e r a l and a x i a l r i g i d i t y I I I t o t h i s p i l l a r . The arrangement shown i n t h e above Loss Source Physical Source Remarks I f i g u r e prov ides t h e necessary s t i f f n e s s and spacing - between t h e bearings, as w e l l as ensur ing t h e two Resistance P I'ROC bear ing are c o n c e n t r i c a l l y al igned. Complex re la t ionship . D i f f i c u l t t o quant i fy a n a l y t i c a l l y I 1 I A schematic d i a gram o f t h e spacecraf t e l e c t r i c a l system i s shown i n Fig. 5. Here t h e e l e c t r i c a l S t a t o r Core Hysteresis P = mB1"Yf machine operates as a generator d u r i n g t h e Eddy current P = 30-minute darkness p e r i o d when i t discharges t h e f lywheel and as a motor d u r i n g t h e 60 minutes Electronics f lywheel charg ing pe r iod when t h e pho tovo la t i cs a re Resistance and Losses consist o f a constant component switching and a frequency dependent cmponent exposed t o sun l i gh t . The motor/generator i n p u t and ou tpu t power p r o f i l e s , t oge the r w i t h t h e machine Aerodynamic Windage (viscous) P = Const N' t e rm ina l vo l tage as a f u n c t i o n o f t ime, which were used by Iwaskiw [3], are shown i n Fig. 6. To achieve an o v e r a l l round t r i p e f f i c i e n c y o f 80 percent Iwaskiw has shown t h a t t h e maximum average The r e l a t i v e c o n t r i b u t i o n o f each o f these sources power l o s s i n t h e f lywheel energy s torage system t o t h e t o t a l motor/generator losses depends upon cannot exceed 28 watt. I n t h i s work, an average 20 1513 Page 923 w a t t l o s s has been budgeted f o r t h e machine T h i s w i n d i n g arrangement i s w e l l s u i t e d f o r d.c. FLYWHEEL I b r u s h l e s s o p e r a t i o n because each phase v o l t a g e i s I c o n s t a n t f o r 60 e l e c t r i c a l degrees so t h a t t h e t o r q u e and v o l t a g e r i p p l e i s minimized. T h i s w i l l l e a d t o smoother and more e f f i c i e n t o p e r a t i o n t h a n a s l o t wound c o n f i g u r a t i o n . Because o f t h e h i g h speed o p e r a t i o n t h e r e l a t i v e l y l o w t o r q u e s exper ienced by t h e a i rgap d i s t r i b u t e d w i n d i n g s h o u l d be e a s i l y t r a n s f e r r e d t o t h e s t a t o r s t r u c t u r e . The s u r f a c e wound armature i s o n l y p r a c t i c a b l e w i t h modern h i g h c o e r c i v e f o r c e permanent magnets such as t h e RECO and Nd-Fe-B F ig . 5 Schematic diagram o f p h o t o - v o l t a i c a l l o y s , as, i n t h i s case a c c e p t a b l e a i r g a p f l u x power supp ly f o r s p a c e - c r a f t u s i n g d e n s i t i e s can be e s t a b l i s h e d w i t h o u t d i f f i c u l t y . f l y w h e e l energy s t o r a g e system. r e s i s t a n c e l o s s e s d u r i n g t h e 30 m i n u t e g e n e r a t i n g phase, w i t h t h e remain ing 8 w a t t b e i n g a l l o w e d f o r t h e ba lance o f t h e l o s s e s shown i n Tab le 1. E q u a t i n g t h e armature energy l o s s o v e r t h e 30 m i n u t e d i s c h a r g e p e r i o d w i t h t h e budgeted v a l u e of 600 watt-min, r e q u i r e s t h a t t h e d e l t a connected armature r e s i s t a n c e be 0.173 ohm/phase. POW.. 8-up*".d TO UOlDl VdUa. &$#IIod HO lOl hw (-c 0m.l . . , . l . Q w w r * , D n 1 0 . O " l I . D W W n . * L " I ) 3 F ig . 7 ( a ) Developed v iew o f 3-phase armature w ind ing ; ( b ) T r a p e z o i d a l l y - shaped l i n e - l i n e armature vo l tages . :! 21' The d e s i g n c o n s t r a i n t s and parameters f o r t h e FES * . e I" ww ; a Im; a.. . - ;, * ; 1 system d iscussed above a re summarized i n Table 2. F ig . 6 Motor /genera tor i n p u t and o u t p u t v o l t a g e and power p r o f i l e s . Table 2 From Fig. 6, it can be seen t h a t t h e energy i n p u t 1) Volumetric l i m i t s d u r i n g t h e charge phase i s 2.15 MJ. I g n o r i n g l o s s e s , i t i s easy t o show t h a t t h i s i s more t h a n a. Outer diameter = 114.3 mn (4.5 inch) s u f f i c i e n t t o i n c r e a s e t h e f l y w h e e l ( w i t h J = b. Maximum he ight E 63.5 mn (2.5 inch) 0.0991 kgm2) speed f r o m 550 t o 1100 rps . I n t h e s e c i rcumstances t h e motor t o r q u e c o n s t a n t KT = 0.2025 2) Motor vo l tage and torque constants KB, KT N m/amp. a. Maximum supply vo l tage = 140 v o l t A developed view o f t h e 3-phase armature w i n d i n g b. Maximum speed = 80,000 rpm d e s i g n i s shown i n F ig . 7(a): Here t h e w i n d i n g C. Operating speed range = 550 t o 1.100 rps f o r each phase i s u n i f o r m l y d i s t r i b u t e d i n t h e (33,000 t o 66,000 rpm) a i r g a p o v e r a span o f o n e - t h i r d o f t h e p o l e p i t c h , S , r a t h e r t h a n b e i n g p l a c e d i n s l o t s . I n a d d i t i o n 3) Time t o reach max speed: 60 min. (from 112 speed) tRe c o i l s o f each phase a r e f u l l - p i t c h e d , w i t h a d o u b l e - l a y e r l a p - w i n d i n g b e i n g s e l e c t e d f o r ease of a. Flywheel i n e r t i a = 0.0991 kg m' assembly. S ince t h e w ind ings are u n i f o r m l y (0.877 l b f i n sec*) d i s t r i b u t e d o v e r a span o f 1 /3 Sp and t h e r o t o r permanent magnets have a span o f 2 /3 Sp t h e induced b. Supply power p r o f i l e (Fig. 6 ) e l e c t r o m o t i v e f o r c e s a re i d e a l l y t r a p e z o i d a l l y 4) E f f i c i e n c y goal o f BOX a t 500 Wh shaped waves as shown i n F ig . 7 (b) . I n p r a c t i c e t h e s e waveforms w i l l be s l i g h t l y rounded a t t h e c o r n e r s o f t h e wave-tops due t o f l u x f r i n g i n g . 1514 Page 924 PARAMETRIC TRADE-OFFS I n t h i s sec t ion , t h e bas ic motor equat ions a r e used t o eva lua te t h e competing e f f e c t s o f t h e number of po le -pa i rs and t h e motor s t a t o r leng th , upon var ious key system v a r i a b l e s such as t h e copper volume, machine weight, and t o t a l machine losses. Using t h e da ta g iven i n Table 2, t h e t o t a l copper volume requ i red i s p l o t t e d as a f u n c t i o n o f t h e \ number o f p o l e p a i r s and t h e motor s t a t o r l e n g t h i n F ig . 8. As can be seen, copper volume decreases f o r i n c r e a s i n g numbers o f p o l e - p a i r s and i n c r e a s i n g motor s t a t o r leng th . I n some cases, t h e armature 0 1 2 3 d 5 NUMBER OF POLE PAIRS copper volume w i l l n o t f i t i n t h e assumed airgap, e l i m i n a t i n g those combinations as p o s s i b l e design F ig. 9 V a r i a t i o n o f motor weight as a s o l u t ions . f u n c t i o n o f number o f po le -pa i rs and COPPER VOLUME (IN-3) s t a t o r length. 20 \ I - LO*.26’ +L ae.60’ Lp.76’ 8L O.1.; 1 a manner p r o p o r t i o n a l t o t h e square o f t h e o p e r a t i n g frequency, w h i l e t h e h y s t e r e s i s losses \ vary d i r e c t l y p r o p o r t i o n a l t o t h e opera t ing f requency [7]. Both losses vary as a d i r e c t 16: f u n c t i o n o f t h e m a t e r i a l weight i n f l u e n c e d by t h e 10 magnetic f i e l d s . The r e s u l t s o f t h i s ana lys is , which a r e p l o t t e d i n F ig . 10, a re normal ized f o r an o p e r a t i n g speed o f 60,000 rpm and f o r f o u r 5 po le-pa i rs . 0 0 2 4 E S 10 12 NUMBER OF POLE PAIRS Fig. 8 To ta l armature copper volume as a f u n c t i o n o f s t a t o r l e n g t h and number o f po l e-pai rs. I n Fig. 9 , t h e v a r i a t i o n o f t h e machine weight w i t h t h e number o f po le -pa i rs and t h e s t a t o r l e n g t h i s p l o t t e d . The machine weight i n t h i s contex t r e f e r s o n l y t o t h e weight o f t h e s t a t o r laminat ions , t h e copper armature windings, and t h e r o t o r i r o n , and does no t represent t h e e n t i r e weight o f t h e motor. The t o t a l weight would i n c l u d e t h e weight of t h e housing, t h e permanent magnets, and hardware. As can be seen, t h e machine weight decreases i n a l l cases f o r i n c r e a s i n g numbers o f po le -pa i rs . However, an optimum motor l e n g t h i s found w i t h i n t h e range 6.35 t o 22.23 0 . (0.25 t o 0.875 in.). Apart f rom r e s i s t i v e losses, i t was noted above t h a t t h e o t h e r major sources o f losses i n t h e motor a r e due t o h y s t e r e s i s and eddy currents. Hys teres is l o s s i s experienced i n t h e s t a t o r , and eddy c u r r e n t losses a re exper ienced i n bo th t h e armature w ind ing and t h e s t a t o r laminat ions . Although some e m p i r i c a l r e l a t i o n s e x i s t f o r e s t i m a t i n g these losses i n t h i n sheets, exper imentat ion i s more r e l i a b l e , e s p e c i a l l y f o r F ig . 10 R e l a t i v e machine losses as a f u n c t i o n q u a n t i f y i n g t h e eddy c u r r e n t losses i n t h e o f motor s t a t o r l e n g t h and number of armature. For t h i s reason, a normal ized t r e n d pol e-pai rs . a n a l y s i s i s employed f o r t r a d e - o f f purposes, f rom which an op t im ized cho ice can be made. Once t h e Examination o f Fig. 10 shows t h a t t o minimize t h e motor geometry i s selected, more r e f i n e d l o s s t o t a l losses t h e s t a t o r l e n g t h should be chosen t o est imates can be made, based on t h e m a t e r i a l da ta be 12.7 mn (0.5 i n ) . The choice o f t h e nurber o f sheets and e m p i r i c a l data. What i s known f rom po le -pa i rs i s no t so immediately apparent. F ig . 10 exper imenta t ion i s t h a t eddy c u r r e n t losses vary i n suggests t h a t a 2-pole machine should be se lect$d. 1515 Page 925 However, t h e volume o f copper r e q u i r e d f o r t h i s case would n o t f i t i n t o t h e a i rgap . A l so t h e magnet ic i r o n r e t u r n pa ths would be ex t reme ly wide f o r t h i s case making c o n s t r u c t i o n v e r y d i f f i c u l t . Thus, f o r p r a c t i c a l reasons t h e p r e f e r r e d c h o i c e f o r t h e machine i s 2 po le -pa i r s . Having s e l e c t e d t h e s e key parameters q u a n t i t a t i v e es t ima tes show t h e t o t a l l o s s e s i n c l u d i n g t h o s e due t o w i n d i n g r e s i s t a n c e , s t a t o r c o r e l osses , armature eddy c u r r e n t s , and secondary l osses , a r e app rox ima te l y 28.5 wat t . I n t h i s i n s t a n c e t h e o v e r a l l round t r i p e f f i c i e n c y would be 95 pe rcen t . CONCLUSION The motor des ign has now been completed and a s e t o f manu fac tu r ing drawings have been prepared. The mechanical packaging o f t h e H a l l - e f f e c t sensors posed some problems, b u t t h e s e have now been resolved. The c o n s t r u c t i o n o f t h e p r o t o t y p e motor i s soon t o begin. REFERENCES 1. Anand, D.K., K i r k , J.A., Z y o d , R.B. , Studer , P.A., and Rodrigues, G.E., System Cons ide ra t i ons f o r a M a g n e t i c a l l y Suspended Flywheel" , Proceedings o f t h e 21s t I n t e r s o c i e t y Energy Convers ion Eng ineer ing Conference, San Diego, CA, August 25-29, 1986, pp. 2.449 - 2.453. 2. K i r k , J.A., and Anand D.K., " S a t e l l i t e Power Us ing A M a g n e t i c a l l y Suspended Flywheel Stack" , Jou rna l o f Power Sources, 22 (1988) pp. 301-311. 3. Iwaskiw, A.P., "Design o f a 500 Watt-Hour Magnet!cal l y Suspended Flywheel Energy Storage System , M.S. Thesis , Univ. o f Maryland, Dept. o f Mech. Eng. Co l l ege Park, Maryland, 1987. 4. K i r k , J.A. and Studer, P.A., "Flywheel Energy Storage P a r t I 1 - M a g n e t i c a l l y Suspended Super f l ywhee l " , I n t . J. o f Mech. Science, Vol. 19, NO. 4, (1977) pp. 233-245. 5. R i c h t e r , A.N., " L i t z Wire Use I n High Frequency Power Convers ion Magnet ics" , Powertechnics Magazine, A p r i l 1987, pp. 31. 6. R i c h t e r , A.N., "Us ing L i t z Wire I n Magnet ics Design", E l e c t r o n i c s L i b e r t y v i l l e , I L , Lake P u b l i s h i n g Corp., August 1986. 7. Mark 's Standard Handbook Fo r Mechanical t;gine;rs, ed.. ii n c h ii e ff T.. Baumiiestterr,, 8 tt h e n., i n g s p o r t Press Inc., 1978. 1516 Page 926 PED-Vol. 37 Advances in Manufacturing Systems Engineering presented at THE WINTER ANNUAL MEETING OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS SAN FRANCISCO, CALIFORNIA DECEMBER 10-15, 1989 sponsored by THE PRODUCTION ENGINEERING DIVISION, ASME edited by M. ANJANAPPA D.K.ANAND UNIVERSITY OF MARYLAND THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS J#, United Engineering Center 3.45 East 47th Street New York, N.Y. 10017 Page 927 TOOL PATH ERROR ANALYSIS FOR HIGH PRECISION MILLING WITH A MAGNETIC BEARING SPINDLE M. A. Woytowitz, D. K. Anand. and J. A. Kirk Department of Mechanical Engineering The University of Maryland College Park, Maryland M. Anjanappa Department of Mechanical Engineering The University of Maryland Baltimore, Maryland ABSTRACT This paper is concerned with error mappin_g and increasing the accuracy of a CNC milling machine that is retrofitted with a magnetic beanng spindle. Three classes of errors, viz, thermal, ~ometric and ramp errors are identified and investigated. It is observed that the largest errors identified are ramp errors, in case of thin rib parts. and that all the deterministic errors identified could be compensated using a magnetic bearing spindle in conjunction with an error minimization controller. INTRODUCTION: The overall purpose of the research, underway at the University of Maryland, is to develop a methodology to increase the accuracy of a CNC ~ machine by using a magnetic bearing spindle to compensate for tool path errors. However, this paper focuses on the classification and quantification of tool J>ath error present in a machine fitted with a magnetic bearing spindle and means to compensate for them. Dimensional accuracy and surface finish of a machined part is a function of tool path error. The tool path error in machining is defined as the vector difference between the req_uired/ programmed and actual tool path [1]. The magnitude of the error is both deterministic and stochastic in nature since it depends on both repeatable (static and dynamic) and random (dynamic) parameters. Previous research s':._,,~ts separating errors as either cutting force independent (CFI) or cutting force dependent ( ;'!)). CFI errors are those errors that occur in the absence of metal cutting (i.e., dry run) while ci:D errors can be directly linked to the metal cutting. . CFI en.. ., can be further classified as deterministic position errors, error due to weight forces, and error due to beat sources . CFD errors, on the other hand is further classified as error due to workpiece/tool compliance and cuttin~ process dynamics. The errors are both static and dynamic in nature. These errors are discussed m detail in reference [2]. It is possible to minimize these errors, either by pre-compensating or by on-line correction, if they can be identified and quantified. This can be best achieved with a CNC machine fitted with 129 Page 928 a magnetic bearing spindle, since it has some unique features suitable for on-line adaptive control of tool position [3 J. Pre-compensation of tool path errors (primarily used to correct CFI errors) consists of determining the errors committed by the tool and imflementing compensation schemes which rely on data recorded off-line. For example, Tlusty [4 uses a semi-automatic master part (trace test) to measure errors. Suforer et.al., [5] use an error matrix of coordinate corrections to improve the accuracy of large NC machine tools. Donmez (6) refined this approach by implementing statistic principles to determine the characteristics of geometric positioning errors. This same methodology has been applied by Zhang et.al. [7] to improve the accura9 of coordinate measuring machines at the National Institute of Standards and Technology. In [8J it was shown that cutting force independent errors can be measured and pre-compensated on a vertical machining center reliably. The on-line correction (primarily used to correct CFO errors) involves, typically, an adaptive controller which can monitor the machining status and adaptively control the appropriate machin- ing {>arameters. For example, DeV or et al. [9] present a model descnbing the compliance due to cutting forces of a thin web work piece. Anjanappa et.al. [21 models the cutting process as a discrete stochastic system and an on-line microprocessor based optimal controller was developed and used for maintaining surface roughness within specified values. The on-line correction techniques discussed before are found effective for reducing machine tool errors. However, the requirement of attaching highly sensitive measuring instruments to moving machine elements in a manufacturing environment and dedicating metrology equipment to a machine indefinitely make this approach difficult, expensive, and hence, impractical for many applications. To overcome these limitations, a test facility has been setup, at the University of Maryland, by retrofitting a Matsuura MC500-V milling machining center with an S2M B25/500 magnetic bearing spindle and is discussed in detail in (10]. Use of the magnetically suspended spindle provides an additional level of control for error minimization. Two uruque features of the magnetic bearing spindle are: • Built-In 3-dimenslonal force and position sensors which allow force adaptive control in the cutting process with no limitation on the size and shape of the workpiece. • Ability to translate and tilt the spindle shaft within air gap restriction (+I- .005 inches of translation and + I- 0.5 degrees oft/It). Much research has been conducted in the area of error minimization of NC machine tools. However, this research focuses on a new promisin~ area of machines with magnetic bearing spin~es whose f.roblems are unique and needs special techniques to exploit their potential for adaptive contro . · ERROR CLASSIF1CATION AND QUANTIFICATION Deterministic tool path errors, for the purposes of this research, are classified as shown in Fig. 1. The non-detemnnistic errors (such as errors due to chatter) are not considered here. The CFI error classification has been reported before in [2] and it is very much similar. The CFO error classification, however, is chosen based on the most frequent errors in the machined part. Static loading produces CFI error resulting in static/Geometric Errors which show up as positional inaccuracies due to errors in production and assembly of the elements which are used m the machine consµ-uction. Dynamic loading results in CFI errors dependent on the acceleration and deceleration of machine components. It produces transient and steady state trajectory errors as well as feedrate dependent over-shoot and under-shoot errors. By including the effect of feedrate on positioning errors, it is possible to combine static geometric errors and over-shoot/ under-shoot errors into one error class called geometric position error. 130 Page 929 I Deterainiatic Error Classification I I I !cutting "Force Independent! !cutting Force Dependent! I I I I I I Theraal Loading static Loading Dynaaic Loading Static & (teaperature change (position, weight (acceleration• Dynamic Loading dependence) dspendence) retardation (cutting process dependanca) dependence) I I I I I I CONTROLLER TRANSIE!l'l' & THERMAL DEFORMATION STATIC/GEOMETRIC OVER-SHOOT & STEADY STATE RAMP ERROR ERROR UNDER-SHOOT TRAJECTORY ERROR ERRORS ERROR 1 GEOMETRIC POSITI0N ~ ERROR Fig. 1 Deterministic Error Classification Following the methodology of [81 it is possible to describe the errors of a three axis milling machine using 18 error terms. Since the majority of the machining operations to be encountered by the Matsuura/S2M are 2 1/2 dimensional, only the X-Y plane of the machine tool is considered for investigation. Therefore, only the seven terms associated with X-Y planar motion are necessary: 1. clx1i- Axial Position Error in X-axis 2. cly x - Y-Straightness Error of X-axis 3. cly - Axial Position Error in Y-axis 4. clx - X-Straightness Error of Y-axis 5. ez x) - Yaw of table (X-axis) about Z axis 6. ez ) - Yaw of cross slide (Y-axis) about Z axis 7. az - X-Y Axes Squareness Error Since in end milling operations, the cutter is generating finished surface only at one point on the work piece, e z(x) and e z(y) will not affect the part's final dimensions. Measurements of the angular errors are preformed to remove the axial and perpendicular motion of the table due to rotation about the tool from the straightness and axial position measurements. Squareness errors between the X and Y axis can be resolved into sine and cosine components and added to the axial position and straightness error terms. The CFI ~eometric position errors associated with the motion of the table by the drive system alon~ each ruos can be represented in the form of an error matrix followin~ the methodology in [8,llJ. This matrix consists of axial and straightness errors for each axis at different positions and several feedrates in both directions. Since error data at several feedrates is present, errors due to the servo drive and electronic control system are included in the map. The error map for motion of the table by the drive system consists of four matrices (two for each axis): Iox x] = !error, machine position, + /- feedratel clxy] = error, machine position, +/- feedrate oyx] = error, machine position, + /- feedrate clyy] = error, machine position, + /- feedrate The thermal deformation of the machine tool structure results in a net displacement of the tool relative to the workpiece. Thermal deformation was significant with the magnetic spindle since it has extensive cooling water circuits around the magnetic coils. In addition, air cooling is present which makes it more complicated thermally. Changes in temperature at different loca- tions on the headstock and machine frame can be measured using thermocouple and linked to the thermal deformation error by either a functional relationship or a 'look up' table. 131 Page 930 CFD errors result from the same loading conditions previously discussed. However, due to the complexity of the machi~ process, separation of the influence of each loading condition on errors imparted to the work piece is difficult. Moreover, stochastic errors begin to become a factor. Hence, CFD errors are traditionall:y minimized through error avoidance techniques. One deterministic CFD error encountered in thin rib machining is ramp error. Ramp error is the result of the deflection of a compliant work piece by cutting forces and is defined as the difference between the thickness at the top and the thickness at the bottom of a thin nb [2], which is often encountered in the manufacture of microwave guides (Fig. 2). Since the geometty of the work piece is known, it is possible to relate the ramp error to the forces imparted by the cutter• :. x x·. •• •• t I •• • I •, • I • s 1-- ....., --., I- ,---11-•eteloot I I I ...~I .+...2.. f-- SECTtON AA CALL DIMENSIONS IN INCHES) Fig. Microwave Guide (Courtesy of Westinghouse Corp.) In this study the geometric position error, thermal deformation error and ramp errors are investigated. The measurement and analysis of these errors are presented in the followtng sections. GEOMETRIC POSfflONING ERROR Experimental Work The net tool position displacement relative to the machine table for each axis is determined from seven error terms, listed in previous section, which are measured under static conditions using the HP 5528A-based laser measurement system. The water coolant system of the magnetic spindle remained off in order to minimize thermal effects. However, the bulk spindle and machine ambient thermocouple voltage outputs are monitored so that thermal effects due to the servo motors and ambient conditions can be removed from the geometric position error data. Four types of measurements were conducted, viz, Axial Position, Straightness, Angular, and Squareness to obtain all the seven error terms. Each error term was measured at one inch increments of table motion at five commonly used feed rates (10, 30, 50, and, 100 ipm. and Rapid) in positive and neiative directions. Six sets of data are recorded at each feed rate and the standard deviation of the first four sets and the full six sets are computed to assure that the averages of the errors represent a repeatable error. Since the error terms are measured at several feed rates in both directions, repeatable errors due to the machine's servo drive controller will also be accounted for in the final geometric position error map. Results Figure 3 shows the average Axial Position errors along the X-axis {bx(x)} for the traversing of the machine's table at five feed rates in the negative direction. The errors show a strong dependence on position and feed rate. The standard deviations of the errors at each position are approximately an order of magnitude less than the errors themselves. If one was to measure the errors at only one feedrate, the resulting information would not necessarily be valid at other feedrates. When the table moves from one position to another, the table sometimes overshoots or undershorts the target and must then readjust. Interestingly, this procedure is very repeatable with respe~ to table position and feed rate, as shown by the small standard deviation of the errors. 132 Page 931 II 100 ipa D 30 ipa llrror {lli1a) + 50 ip• 0 10 ipa * JtAP:ID .,.z Hacbina Position (Xnohes) Fig. 3 Axial Position Error of X-Axis (For Negetive Direction) A strong dependence on the direction of table motion was observed. This direction dependence is due to backlash errors in the geared drive trains and different geometric errors on each face of the lead screw threads. Since the data points are well behaved, linear interpolation between the data points is an acceptable method of calculating the Axial Position errors at positions between the data points The maximum error between points at a fired feed rate was approximately 0.6 mils when the table moves along the X-axis from -19 inch to -18 inch ~sitive direction) at 100 ipm. However, if one considers moving from -19 inch to -20 inch at 501pm (negative direction) and back to -19 inch (p_ositive direction), the data suggests that a larger total error of approximately 1.6 mils would be evident. The Axial position errors along the y-axis { dy(y)} were measured and evaluated in the same manner as above. Like the x-axis, the y-axis errors show a strong dependence on position and direction (Fig. 4). As for feed rate dependence, the error appears to become smaller as the table velocity increased for negative motion. In the positive direction, however, the errors appear to be less dependent on feedrate. 1110 ipa. 030 ip:a. Brror (Hi1a) +50 ip:a 0100 ip:a. *Rapid •O.H Machine Position (:Inohaa) Fig. 4 Axial Position Error of Y-Axis (For Positive Direction) 133 Page 932 The ¥-straightness error of X-axis {oy(x)} was measured at the same five feed rates in both directions (see FiJ. 5 for negative direction). The errors are small ( less than 0.1 mils) compared to the Axial Position errors . The errors showed little de{endence on feed rate or direction but do vary with position. The X-straightness error of Y-aru x(y) }, on the other hand, are slightly larger and show a larger dependence on feedrate and direction (Fig. 6). O.GS 1110 ipa 030 ip11 llrror (Kile) + 50 ipa <) 100 ip111 *Rapid Fig. 5 Y-Straightness Error of X-Axis Standard deviations of the Strai~htness errors at each position along both axes are of the same magnitude as those for the Axial Position errors. Due to the relative magnitude of the straightness errors compared with other errors measured, they will be neglected and assumed equal to zero in the final error map matrices. 1110 iplll 030 iplll Error (Hila) + 50 ipllll <) 100 ipa ..e.:aapid Machine Position (Xnchaa) Fig. 6 X-Straightness Error ofY-Axis (For Positive Direction) 134 Page 933 111110 ipm o,o ipm •I Brror (Aro-aeo) +so 1pm ·2 <> 100 ipm _, lkRapid ., Machine Position (Xnohea) Fig. 7 Angular Error of X-Axis about Z-Axis Figure 7 shows the angular error ofX -axis about Z-axis { ez(x)}. The angular errors are quite small (less than 1 arc-sec) for all feedrates except for 10 ipm. Examining the raw data revealed that lar~e changes in the bulk spindle and machine ambient temperatures occurred during the test. This is substantiated by the large standard deviations associated with the average errors. The main purpose of the measurement of Angular errors is to correct the Straightness and Axial Position measurements for angular rotation of the optics. Therefore, the An~lar errors should be of the same magnitude as the Straightness errors. Therefore, the 10 1pm angular error measurements are discounted on the basis of the data recorded at the other feedrates and the large standard deviation of the average errors at each position. Angulare"ors ofY -axis about Z-axis { ez(y)} is shown in Fig. 8. The Angular errors for positive motion are of the same magnitude as those encountered along the X-axis. There appears to be no reason to discount the An$Ular errors measured along the Y-axis durini the negative translation of the table. Therefore, their sine and cosine contributions to the Y -runs Straightness and Axial Position error terms will be calculated and included in the final Geometric Position error map. The largest contribution by the Angular errors to the straightness error measurements is -3 0.6 111110 ipm •4 -0.2 o,o ipm Error (Arc-aec) •0.4 +so ipm •0.6 ¢ 100 1pm .... .lRapid •I .,.a .,., Ka9hina Position (inch••I Fig. 8 Angular Error of Y-Axis about Z-Axis 135 Page 934 arc-seconds. This error is equivalent to a perpendicular displacement of the table of + 0.102 mils over the seven inch measurement range. The contribution to the Axial Position errors would be a negligible lE-9 mils. The Squareness error between the X-Ya xis { az} is determined by performing two strai~tness measurements using an optical square. The Sq.uareness error anp.e ( clockwise positive) is calculated to be -1.719E-3 degrees using the X-8X1S as reference. This error results in a contribu- tion to the Y-axis Straightness error and will be included in the final error map. The recorded error terms are then analyzed and reduced resulting in a geometric position error map following the methodol~ outlined in [8, 11 ]. The map contains the set of matrices Dxx, Dxy, Oyx, and Dyy of geometnc position errors (or the table motion relative to the tool position at five feed rates in both feed directions. For more details on the measurement results the reader ,s referred to (11]. THERMAL ERROR Ex.perimentaJ work Tests were performed to determine the 1herma1 Deformation errors along the X and Y axes. Errors due to changes in ambient conditions and servo motor heat sources proved negligible compared to the deformations experienced by spindle head due to the coohng water ilowing through the magnetic spindle. Since the spindfe bore/tool is centered about the x-axis of spindle housing, the deformation errors along the x-axis is symmetric with no effect on tool position. Hence, model was developed only for the y-axis thermal deformation errors. Also, although a model for thermal shock was derived it is not reported here since this problem, was eliminated by redesign of the spindle cooling system. Two tests (cool down and recovery from cool down) were initially designed to determine Thermal Deformation errors that could corrupt data gathered during the Geometric Position error term measurements. However, since the new spindle cooling system has eliminated thermal shock, the model desired here can be used to describe §;adual (quasistatic) thermal deformation of the machine tool. Several "recovery from cool down tests were conducted for the Y-axis and Fig. 9 shows a typical error plot obtained. In these tests the deformation of the headstock varied linearly with respect to temperature. Results from having only the servos on "warm up" is presented in Fig. 10. Interestingly, the bulk spindle temperature does not change; this is understandable, since the headstock is well removed from the servo motor heat sources. Ill Bulk Spindle 'l'eap. Deformation (inch••> 0 Alllb!ent Machine T-p • .•. oo. Fig. 9 Thermal Deformation along Y-Axis 136 Page 935 ll.41GOl6 II Blllk Spindle Teap. De~oraation •·- Cinohea) D Aabiant Machine T••P. ····-- H.• zs.a » ».z 16.4 26.6 u.a n 21.z 21., 21.• '1'-perature ( C) Fig. 10 Thermal Deformation Along Y-Axis (Warm-up Test) Modeling Using the data from these tests it is possible to construct a linear model of the Thermal Deformation error along the Y-axis based on the change in the Bulk Spindle temperature and the change in the Ambient Machine temperature. By modeling the headstock as a fixed beam a matrix equation can be developed to describe the thermal deformation [12]; dy = c1L\Ta where Ta is the initial temperature, Tb is the final temperature and c1 and C2 are constants. Let [TJ = rA~al L\7:11 IL\Tan L\Tbn Therefore A least square fit can be performed to solve for c1 and C2 • [TJT d y = [TJT [TJ C C = [TJ dy {[TJT[TJ.-1 The unbiased variance is given by: a1- = J(c )/(N-n), where N = the number of data sets and n = the number of parameters ( constants ) N Now, J(c) = L ei2 • where ei is the error of the least square fit and is given by; i=1 e=dy-(T]c 137 Page 936 Two hundred and eighty three data sets were used to evaluate the c vector. The manipulation of the T matrix and the dy vector was accomplished using the software package MAT I.AB. The following results were calculated: C = [0.2262 -0.4055f X 10 ·3 a= 1.1120x 10-4 inches (unbiased standard deviation) Therefore, the thermal deformation error of the Matsuura/S2M milling machine along the Y-axis in the absence of thermal shock is given by: lJy = (ATa Alb)~~~~~ k10·3 inches,whereTaisthecbangeinambientmachine temperature( deg), and Ti, is the ciiange in bulk spindle temperature( deg). The bulk spindle temperature, as used here, includes the thermal effects due to the heating of bearings on the spindle head. A magnetic bearing spindle error minimization controller, under development , can use the thermal deformation model oflinear deformation to correct for the errors produced by quasistatic temperature change. By monitoring the above two temperatures thermal error can be compen- sated by moving the tool inside the air gap of the magnetic spindle RAMPERROR Ramp error is the result of deflection o fa compliant workpiece/tool due to the cutting force. It is defined as the difference in the thickness of the rib at the top and bottom [2]. The ramp error considered here is similar to the profile errors in [13] and the surface error in [14J. In reality, the ramp error due to a helical teeth cutter is nonlinear, but for simplicity we will consider the strai$ht teeth cutter. The ramp error therefore can be considered as a linear approximation for a hehcal tooth cutter. As a first iteration of Ramp error identification, several thin rib test parts, as shown in Fig. 11, were produced on the Matsuura/S2M machine and on a conventional spmdle Matsuura MC-510V milling machine. When machining the thin rib test part, the part geometry, depth of cut, and tool remain fixed. Using a half inch two flute medium len~h end mill and an axial depth of cut of 0.500 inches, the rib is rough cut to a thickness of 0.100 mches. The same tool is then used to perform a finish of cut of 0.040 inches on each side. It should be noted, when machining a P.art having a high compliance, it is necessary to take relatively large finishing cuts. Else the part will not possess enough stiffness to allow for cutter engagement. The feed per RPM of the cutter is set at 0.001 inches/revolution, as recommended for a half inch end mill by the Machinist tT = tB = 0.020 inches desired ttTn=n-= tT =/:. tB ofter nochining tn=-\J-= I o.s· tT Ronp Error= tT - tB Fig. 11 Thin Rib Test Part 138 Page 937 Handbook [151. Parts were cut using up milling and down milling at feedrates of 30, 40, 50. 60, and 100 ipm. The errors produced by the two machines were compared on the basis of magnitude and scatter. Figures 12 and 13 present the results of the part metrology. The errors produced by the magnetic bearing spindle have a larger scatter than those produced b_y the conventional bearing spindle. This large scatter can be linked to the stiffness of the magnetic bearings. At present, the magnetic bearings in magnetic bearing spindle have a much lower stiffness compared to the conventional bearing spindle. Hence, cutting forces introduced to the spindle s_ystem result in large scatter and magnitude in Ramp error. These results highlight the need to improve the cutting performance characteristics of the Matsuura/S2M machine tool. Improving bearing stiffness may help bring the magnetic bearing Ramp errors in line with the errors produced by the conventional spindle. 0.011 0.01 D 0.009 D O.OOII D 0.007 1111~1-1 ..... , ... Error u:nob••> D 0.006 ti D CJ,,.,,,,.,. a....tna D ~ o.oos 11111 D D D o.- 1111 D 1111 D 111111 O.OOJ I I I •• O.OOl ,o zo JO 40 so 60 N 80 90 Peadrate (ipa.) - Fig. 12 Thin Rib Ramp Error (Up Milling) 0.01 D 0.009 D o.ooa Cl 0 0.007 D D B 0.006 D B Error (Xncbe•) o.005 ·""""'""'·-· ...,, .. 0..-ttc ..., ,.,. o.004 I D 11111 O.OOJ D I CJ 1111 O.OOl 1111 1111 I 0.001 1111 Ill 11111 0 0 10 zo JO ,o so 60 111 80 ,0 100 Jl'eedrate (ipa. > Fig. 13 Thin Rib Ramp Error (Down Milling) 139 Page 938 Due to the large scatter of the data, finding a correlation between Ramp error and feedrate is difficult. However, some trends can be concluded form the data The conventional bearing machine consistently produced a smaller Ramp error at all feedrates. The data scatter tends to be smaller for the conventional bearing spindle. Finally, down milling finishing cuts on both machines resulted in the smallest errors for each machine. Examining the magnitude of the errors produced by both machines reveals that these are the largest errors encountered in this study. Therefore, a more thorough study of the machining of compliant work pieces and the parameters affecting Ramp errors are suggested as future work. Fig. 14 Thick Rib Test Part In order to investigate the effect of tool deflection while machining non-thin rib parts ( thick rib parts), several test parts as shown in Fig. 14 were cut. The boundary features of test part provided information on the ramp error in thick rib (0.5 inch thickness) parts. Ramp errors were measured to be of the order of -0.5 mils. The negative ramp error is the result of tool deflection not work piece deflection. Interestingly, the mean of the errors in boundary thickness were comparable for both machines. The fact that a significant difference in errors IS only present in the thin rib parts leads one to conclude that more complex cutter/work piece interaction is present in thin rib machining. SUMMARY OF RESULTS Table !provides a summary of the errors examined in this study. Quasistatic thermal defor- mation errors (gradual temperature changes in the machine components) behave linearlY. with respect to temperature changes and thermal deformation errors along the x-axis proved negligible compared to those along the y-axis. Geometric position errors in the table movements show that axial position errors were consistently the largest of all error terms. These errors possess a position, direction, and feedrate dependence. All errors associated with a particular axis, had a small standard deviation but no apparent trend of the dependence on the above parameters. Therefore, compensation can be performed by using a matrix error map of the geometric position error associated with the input parameters. Ramp errors _produced when machining thin rib test {>arts dominated all classes of errors studied. Companson of the errors produced by a conventional bearing spindle Matsuura MC- 510B machining center with the magnetic bearing machine showed that the magnitude and scatter of the errors produced were consistently larger for the magnetic bering machine. Manufacture of thick rib parts resulted in negative ramp errors associated with tool deflection. The error map and the results of ramp error investigation is under implementation, at the University of Maryland, for error minimization (16] purposes and will be reported later. 140 Page 939 Table -1 Error Identification Summary srror ldentltloatlon auaaary Magnitude Niniaization strategy Y-axl• Tharaal Theraal Shock 3.0 ail• Error Avoidanca by Detoraation Error radaaign of apindla cooling •Y•t•a Quaaiatatic 2.0 ail• Error Coapenaation Theraal loading uaing linear aodel x-axi• Theraal Tharaal Shock• Negligible N/A Oeforaation Error Quaaiatatic Geoaetric Poaltion C•o-tric error• 1.5 ail• Error Coapenaation Error (X •Yax••> in aachine alaaent• using aatrix look-up • Servo Control tabla• error• Thin Rib Raap Error Work piece 6 . 0 ail• coapliance due to (with large N/A cutting forces acatter) Thick Rib Raap Error Tool compliance o. 5 ails due to cutting N/A fore•• CONCLUSION The study suggests that the machining characteristics of the magnetic bearing spindle require improvements. This might be accomplishes by increasing the stiffness of the beanngs at the cutter tooth passing frequency, making the spindle more robust for precision machining applications. Also, further study is warranted into the mechanisms involved in compliant work piece machining. Finally, investigation of using the ma~etic bering spindle's ability to tilt in the air gap to reduce ramp error requires investigation smce magnetic bearing spindles provide a vehicle for the addition of another level of control to existing machine tool technology and deserve consideration as a unique approach for increasing the capabilities of future machine tools. REFERENCES 1. Anand, D.I(., Kirk, J.A. Anjanappa. M .• "Magnetic Bearing Spindles for Enhancing Tool Path Accuracy",Advanced Manufactunng Processes. Vol. 1, No. 1, pp. 121-134, 1986. 2. Anjanappa. M .• Kirk. J.A, Anand, D.I(., "Tool Path Error Control in Thin Rib Machining". Proceedings oJ 15th NAMRC. Bethlehem, PA. 1987, pp.485-492. 3. Anand, D.I(., Kirk. J.A. Anjanappa, M .• Zivi, E .• Woytowitz, M.A. "Magnetic Bearing Spindle Control". Proceedings of 15th Conference on Production Research and Technology, pp.31- 35, January 1989. 4. Tiusty, J. • 'Techniques for Testing Accuracy of NC Machine Tools", Int. Journal ofM TDR. vol. 12, 1971. 5. Dufour, P .• Gm_P.petti, R., "Computer Aided Accuracy Improvements in Large NC Machine Tools", Int. Journal oJ MTDR. vol. 21, 1980. 6. Donmez, A. Llu, C.R.. Barash, M .• Mir, M., "Statistical Analysis of Positioning Errors of a CNC Milling Machine", Journal ofM anufacturing Systems, vol. 1, no. 1, 1982. 7. Zhang, G .• Veale, R., Charlton, T .• Borchardt, B .• Hocken, R., "Error Compensation of Coordinite Measuring Machines.Annals oft he CIRP. vol. 34/1/1985. 141 Page 940 8. Anjanappa, M., Anand, D.K., Kirk, JA., Shyam, S., "Error Correction Methodologies and Control Strategies for Numerical Controlled Machining", Control Methods for Manufacturing Processes, DSC-Vol. 7, 1988, pp.41-49. 9. DeVor, RE., Sutherland, J.W., Kline, W.A., "Control of Error in End Milling", 11th NAMRC, 1983. 10. Anjanappa, M., Anand, D.K., Kirk, JA., Zivi, E., Woytowitz, MA."Retrofitting a CNC Machining Center with a Magnetic Spindle for Tool Path Error Control", to be published in the proceedings of INCOM'89, September 1989, Spain. 11. Woytowitz, M.A., "Tool Path Error Classification and Identification for High Precision Milling with a Magnetic Bearing Spindle", M.S. Thesis, The University of Maryland, 1989. 12. lncropera, F.P., DeWitt, D.P., "Fundamentals of Heat and Mass Transfer", 2nd edition, John Wiley, NY, 1985. 13. Tlusty, J., "Criteria for Static and Dynamic Stiffness of Structures", Section 8.5, MITF Report, 1980 14. Kline, W.A., DeVor, RE., and Shareef, IA, "The Prediction of Surface Accuracy in End Milling",Joumal of Engineering for Industry, Vol. 104, August 1982, pp. 272-278. 15. Oberg, E., Jones, F., Horton, H., "Machinery Handbook", 23rd edition, Industrial Press. NY, 1988. 16. Zivi, E., " Robust Control of Magnetic Spindle for Error Compensation", Ph.D., Thesis, The University of Maryland, 1989. 142 Page 941 PREPRINTS I FAC Volume I INTERNATIONAL FEDERATION OF AUTOMATIC CONTROL ---- September-26-29, 1989 ' ~·--•-h,--~--.,..,...,-,_~--x-.,- .~., _ Page 942 INCOl\1'89 Manufacturing Automation and Prototyping for Printed Wiring Boards J.A. Kirk, D.K. Anand, J.D. Watts Dept. of Mechanical Engineering & Systems Research Center, University of Maryland, College Park, U.S.A. Abstract. This paper presents an improved method of manufacturing automation and prototyping for Printed Wiring Boards. The protocol requires that three data sources be present [circuit specifications, component specifications, and a circuit layout database], in computer interpretable form. The specifications for these three data stores is presented and a generic workcell, suitable for low volume high part mix prototyping. is discussed. In order for the protocol to control the generic workcell, the subtask orders which are required for proper function are also presented and discussed. Keywords. Assembling, automation, computer hardware, logic circuits, printed wiring board. INTRODUCTION After the assembly kit is complete, the board is assembled by hand and then subjected to an Work is currently under way at The University of iterative cycle of inspection and rework. After Maryland is into the development of a protocol for passing assembly, inspection and rework, the board rapid automated assembly of Printed Wiring Boards. is electrically tested (with appropriate reworking The aim of the protocol is to develop a and inspection), conformal coated, visually methodology for controlling the placement, inspected and electrically retested. The assembly soldering, and inspection of both, plated through is then given a final over-all visual inspection hole and surface mount components in a high part and placed in stock were it is made available for mix/low lot size production environment. delivery to the customer or use in a higher level Additionally, the results of this work must be assembly. integratable into an existing manufacturing environment. Figure 2 is shows schematic diagram for rapid prototype assembly of printed wiring boards. In Figure 1 shows a diagram· of the typical present rapid prototype assembly, the design information design and manual assembly operation for printed is used to both produce a drawing package wiring boards. Here the design engineer develops containing all the circuit layout drawings, and to an electrical schematic which is then used to directly control an automated assembly workcell. generate a computer database of the required A main component of the rapid prototype system is circuit layout. Taken by hand from the design the assembly protocol. This protocol provides the database is the component parts list, procurement important link to establish the methodology, via requirements, assembly work instructions, the use of existing industrial standards, or by electrical test parameters, and quality inspection developing in-house standards, which allows and acceptance criteria. electronic circuit assembly design information to be directly used in controlling a generic assembly Although some of the data interchange between workcell. functional groups in the process is automated, typically it is still administered manually. For The rapid prototyping assembly protocol provides instance, parts lists, which are created on a CAD interface definition and data links for the system, are manually transferred into the material operation of an automated production system for control/purchasing computer system through the the manufacture of electronic circuit assemblies. re-keying of the data. Additionally, tracking the Additionally, the protocol identifies the required transition from design to layout to manufacturing design information which must be available in is done either on paper (manually), or verbally. order to produce a functional assembly. By The final database Configuration Control Drawing identifying the information which is needed in Database in Figure 1 is then utilized to generate electronic assembly production, and then a circuit board drawing package (i.e., configuring an appropriate generic assembly photomaster) which is used to fabricate a bare workcell, it is possible to utilize the research circuit board. Once the bare circuit board is presented here in a wide variety of existing fabricated, it is returned to an assembly area commercial or military production facilities. where it is kitted with an assembly manual and the required parts. The assembly manual includes a BACKGROUND work order (a detailed set of assembly instructions), the required assembly drawings, and The Advanced Design and Manufacturing Laboratory the control documentation (which are used to trace (ADML) at The University of Maryland has been the assembly/inspection process and all subsequent actively involved with a local electronic systems rework of the board). contractor in developing a protocol for the automated assembly of printed wiring boards. This particular organization is currently utilizing 141 Page 943 manual assembly and soldering methods in their assembly workcell (showing all the available printed wiring board manufacturing process. They inputs and outputs from each software module] it are, however, in the process of developing is desireable to constrain the inputs and outputs products that will require the use of automated to coincide with information conmonly available in placement, soldering, and inspection processes. a typical manual assembly process. Following this These new designs will require the integration of line, each process in the design and manufacturing both, plated through hole (PTH) and surface mount process flowchart is depicted as a operation devices (SMD's). module with its required inputs and developed outputs. For such modules, where automation The manual production of electronic assemblies techniques are applicable, software drivers are diagram was developed for this work and is then needed to control the actual assembly abbreviated in Fig. 3. The diagram shows a equipment. For those modules where human abbreviated picture of the design and assembly involvement is a necessity, the guidelines and process, while remaining unencumbered by task definitions must provide sufficient detail to incorporation of the particular nuances of each control the operation in a production environment. process as performed by any specific entity or Furthermore, once computer terminals and screens manufacturer. are introduced to the assembly floor, the needed operator inputs to the system should not require The flowchart shows the development of the circuit typing text for data entry. Bar codes and voice design, the generation of the assembly recognition systems would be the preferred data instructions, the purchasing/ inspection paths for entry mechanisms. the bare boards and parts, and finally, the assembling and inspection of the completed Development of rapid prototyping assembly protocol hardware. ln short, the diagram expands upon the in this manner supplies additional benefits in information presented in Figure 1. that it reflects exactly what the requirements of the software are and what functions each software The goal for this project is to develop a rapid module must perform. This serves as a safeguard prototyping assembly system which links an against the protocol becoming too dependent upon automated factory for electronic assembly into the commercial or poorly designed software which, existing manual environment. Figure 4 shows the although adequately performing the designated flow of the system and how it is integrated into operations, requires cumbersome communications and this existing environment. The system, consisting information preparation modules to be generated so of both hardware and software, is discussed as to satisfactorily integrate it into the system. further in the following section. Such a dependency on commercial or poorly developed software drastically reduces the AUTOMATED PWB ASSEMBLY flexibility of the automated system, which was one of the initial driving factors in the development The rapid prototyping assembly system, must allow of the rapid prototyping assembly protocol. for short assembly workcell setup times and rapid downloading of CAO generated placement data. For the purposes of this research, it is assumed Additionally, the protocol must be capable of that the following restrictions apply: dealing with the placement, soldering, and inspection of both surface mount devices (SMD) and 1. The information available to the protocol plated through hole (PTH) components. A schematic is in a standardized format. diagram for the rapid prototyping assembly system is shown in Fig. 5. From Fig. S, it can be seen 2. The choice of components for use in new that the system inputs will consist of standard electronic assembly designs is limited to design information, inventory information, cell those on a preferred parts list and the status information, and system queuing, all of designer be made aware of these which must be presented in a defined standard limitations prior to the initial design. format. ln turn, the protocol will produce the cell control corrmands (standard output driver 3. The workcell is capable of placing all codes) to operate the assembly workce11 and components on the preferred pa~ts list provide status feedback to the designers and the onto the unpopulated substrate. inventory system. 4. An inventory system is available to supply To identify the locations of key data .necessary the workcell without increasing down times for protocol operation, the data flow requirements or reducing production through puts. The of a typical design/assembly process were supply of components into the workcell can analyzed. A Ganes and Sarson Dataflow format was be fully automated via an automated used in this analysis and has identified the material handling system, or can be design and manufacturing data parameter manually loaded into the workcell requirements for production of PWB's. This magazines and matrix trays prior to a information also includes the format and location production run. of the design data for access by the assembly protocol. Charting the dataflow of the current Interface drivers are required to convert the assembly process was mandatory to identify the proprietary design information into standardized final source of information used in the assembly formats, and then additional drivers are required process. The decision to define and chart the to convert the standardized protocol outputs into present design/assembly information paths was made "machine specific" driver codes. The restriction to ensure that the flexible assembly protocol that inputs and outputs of the rapid prototyping would utilize existing data in an efficient manner assembly system be standardized has an additional by accessing the needed information automatically benefit in that each driver is modularized and at the source. Accessing this data at the source becomes a distinct piece of software, while still will help eliminate errors of using outdated data, an integral part of the overall software plan. and it will help avoid the inefficiencies of Since the proper operation of these software creating and maintaining multiple data stores~ modules is conditional only upon the presence of the correct inputs (as it is the module itself Since the rapid prototyping assembly protocol will which generates the outputs), each module becomes generate the process plan for the automated interchangeable with any other module requiring 142 Page 944 the same inputs and producing similar outputs. As designer appear on a preferred parts list. There a collection of dedicated hardware drivers, the is no limitation on the parts individual rapid prototyping assembly system allows for the manufacturers place on their preferred parts introduction of a wide assortment of equipment and lists, just that the final workce11 be confi~ured easy system expansion. So long as the interface such that it is capable of handling and placing definition of the protocol is maintained, it may all the components on the preferred parts list • be adapted to a variety of specialized tasks within the production environment. This stipulation that the parts the designer uses must appear on the manufacturer's preferred parts Figure 6 shows a simplified flowchart of the list and further, that the part's specifications design and assembly flow for Printed Wiring Board and dimensions be entered into the components assemblies. This figure further defines the specifications datastore, introduces an additional process flow diagram shown in Figure 4 and its benefit. Currently, the costs involved in the primary use here is to illustrate the required entering new part information into the computer information (called the specifications stores) database is a hidden cost. With the use of the needed to develop the rapid prototyping assembly rapid prototyping assembly system, however, an system. At the present time, it is proposed that actual cost can be derived for this process. This three data stores should be available to the cost can then be assigned as a direct cost of not assembly system. The first specifications store, using parts already on the preferred parts list. CIRCUIT SPECIFICATIONS, is a data store containing all information pertaining to the operation of the The rapid prototyping assembly systems approach is completed assembly. This includes design consistent with just in time (JIT) inventory requirements, restrictions on component types, control. As the required design information is in component reliability, temperature requirements, computer intelligible form, purchase orders for currents and voltages at various test points, the required components for a scheduled production error analysis, margin of error, worst case run can be produced automatically at a set time analysis, reliability calculations, test period prior to the run initiation date. In this validations and diagnostic tree. way, components are brought in-house on a job basis, thereby reducing inventory storage and The second data store, COMPONENT SPECIFICATIONS, maintenance costs. is an integral part of the inventory database kept by the manufacturer, and must contain inventory In the final task, that of workcell control, it is part number, manufacturer part number, important to remember that the protocol accepts manufacturer identification, part function, part design information in a specified standardized reliability, part temperature considerations, part format, and produces cell control information, in package type, number of pins, Phase dimensions, a standardized output format. Hence, if the origin (pin l, center, other), placement offsets, manufacturer is configuring a new workcell, it is tool number to handle part, tool point offsets, desireable to purchase equipment that accepts location of tool, feeder type, location of feeder information in this format. If the protocol is to and relative rotation of feeder axes from assembly control a currently existing cell, interface axes. drivers that convert the protocol outputs to the machine specific driver codes are required. A third datastore is the CIRCUIT LAYOUT DATABASE. This database contains the necessary information If a new cell is being configured, it is important related to the assembly such as component to accurately estimate what the production demands rotation/orientation, X coordinate, Y coordinate, will be. Demands for low part mixes with little Z coordinate, logical placement order, placement or no dependence on mixed technology applications pressure, component lead configuration/length, will warrant the configuration of a workcell which feeder location, tool needed, tool location, and differs significantly from a cell configured by board based vision landmark. the demands for high part mixes with a higher dependence on mixed technology applications. In order for the rapid prototyping assembly system to become operational, the following functions In the present work, the production demands must be in place: imposed were high part mixes and small production runs. Based on these demands, the generic 1. Standard format information be declared workce11 shown in Fig. 7 was configured. The and made available to the protocol choice to utilize SCARA robots was based on the concerning component placement on the premise that short production run setup times are assembly substrate. more important than the shorter production run times attainable through the use of dedicated 2. A link to the inventory system be made placement machines. Additionally, as the cell which provides parts availability will be installing PTH components, one of the information. SCARA robots can easily be programed to pre-tin all PTH components prior to the production run. 3. Confirmation be given when parts are loaded into the workcell. For lower volume production, which is the emphasis in the rapid prototyping assembly system 4. The workcell be made controllable by the development, flexible pick and place machines, rapid prototyping assembly system for the such as SCARA robots, are preferred. These placement of the parts onto the substrate. machines are usually robotic manipulators which can perform a multitude of different tasks and can The first task, standard format information, stems be reprogrammed quickly. Typically, these from the requirement standardization. This task machines are not taught component placement sites. demands the installation of the proper translation Instead, the component placement locations, modules, or interface drivers, between the dictated by the designer's CAO drawing, in protocol and the specific design system. At conjunction with component databases, are used to present these standards are under review, but the drive the movement of the manipulator. initial work has involved both IGES and POES Additionally, since these systems usually standards. The second task, inventory control, incorporate vision systems, they are capable of requires that the components available to the correcting for variations in board to board layouts through board based bindmarks. 143 Page 945 The choice of utilizing printing type solder TO p,en: A?tX:~l•IT dispensing equipment is made based on the wide BOA~O PROO.Cll~P. .1 1 acceptance these systems have achieved in industry. As no reprogralTl!ling is needed to institute a new production run, the systems are highly flexible. Additionally, as the system down time is limited only by the loading of solder paste and the changing of solder screens, production through put is sufficient to meet the production volume requirements set previously. The pneumatic syringe indicated in.the post reflow robot envelop serves as a post reflow (post soldering) or rework device, allowing for the deposition of solder when screening or stenciling is not possible. Its primary purpose is to apply solder paste to the pads of SMD's which cannot 1=111,tc I PQESEN1 ASSErilLT F\?CCEOCRE undergo the conventional reflow operations due to the risks of thermal shock. ( i P:•2 CE~!~ Solder reflow is completed through a conveyor fed I! JN;:(JR!1AT!I), in-line vapor phase reflow system (VPS). Although VPS has attained the highest recognition and use in the industry, it is not a truly flexible nor economic system to use. Since the saturation temperature of the working fluid is a constant, PRQTOC!l. the only variables available for customizing the II soldering process are variations in the conveyor feed speeds and in changing the working fluid. As the working fluids commonly used produce relatively high operating costs ($600 per gallon), changing the fluid unnecessarily quickly proves to Ii be too costly. VPS was used inspite of this 1· drawback since it eliminates the need to format the placement of components on the board on the basis of component sizes and colors, a major m,ult 2 soomr 011GlAH !'!J1 drawback in the use of near infrared reflow FEEOBACt All) C[tlllE:o1 Ei.Ied as a part of the FMP described earlier, will be (l)sensitive to the needs of the other blocks withm the protocol, (2) provide a means to demonstrate a working link from a CAD drawing to the corresponding machmed part. Standard features Most researchers active within the feature extraction area (as well as the feature based design area) propose their own definitions of what a feature is. A summary of feature defmitions was compiled by Unger [11]. Essentially, there are two types of attributes that affect the classification of a feature, viz, boundary attributes and shape attributes. The boundary attributes pertain to the relationship of the bounding edges and faces of the feature with the bounding surfaces of the workpiece. The shape attributes pertain to the relationship of the bounding edges and faces of the feature among themselves. For the cur- rent research, a hybrid scheme for standardizing the features has been used. This scheme is illustrated in Fig. 2. The selected standard features are slots, pockets, holes, bosses, and bridges. The above features are defined based strictly on their boundary at- tributes in relation to the workpiece. For this research, we are concerned with only two types of stock shapes, viz prismatic and axisymmetric. This means that one can have upto five times two, i.e., ten combinations of edge-surface boundary attributes corresponding to the above features. In addition, each of the above feature is also classified ac- cording to its geometric shape. Current- ly, the shapes considered include a rec- tan$Ular, cylindrical, wedge shaped, conical, and spherical. Theoretically, one can have five different shapes for each of the above ten edge-surface- boundary-attributes combinations, i.e., upto fifty total combinations. In prac- tice, however, some of these combina- tions do not occur very frequently, e.g., a wedge-shaped hole within an axisym- metric stock. The input and output standardization It is one of the objectives of the FMP that it should not be restricted to any one CAD tool. Because of the fact that many commercial CAD tools do Fig. 1 Flexible Manufacturing Protocol (FMP) contain an Initial Graphics Exchange Specifications (IGES) interface [12], it 52 Page 950 was selected as the standard input format for the feature extractor described here. There are no predefined standard features agreed upon for the output. However, the part model format (PMF), developed at the National Institute of Standards and Technology, does appear to contain mechanisms for the required attributes of the features file such as geometry do.ta, connectivity (topology) do.ta, and groupings of surfaces into features. Because of these advantages, the PMF format is selected as one of the standard output formats for the feature extractor. Boundary edges on multiple adjacent faces one face ~l•l~ ~,~m Boundary edges on slngle face ~ Outermost edges lie on connected faces ~"'~ (11) Boundary edges on multlple nonadjacent faces ~~ ~(C)~ Fig. 2 Standard Features (a) Slots, (b) Pockets, (c) Holes, (d) Boss, (e) Bridge AI ~resentation e representation of the feature extraction as a knowledge engineering problem is shown by means of a block diagram in the Fig. 3. The IFEM con- tains a user interface, a knowledge base and an inference engine. Some of the issues related to the feature extraction problem and the knowledge repre- sentation scheme have been discussed in separate works [131. Among the re- quirements, two are directly related to the knowledge representat10n scheme discussed next. KNOWLEDGE REPRESENTATION SCHEME FOR THE IFEM As the feature extractor attempts to carry out its required functions, 1t en- FEATURE FILES counters different types of information. The inference engme attempts to or- Fig. 3 Feature Extractor as a Knowledge ganize this information into meaningful Engineering Problem facts which can be processed later. The 53 Page 951 knowledge base of the feature extractor, at any given time, contains a set of facts that describe the current state of affairs regarding the entity data and a set of feature related rules that the inference engine can apply to the existing facts, possibly generating new facts. Initially, a set of rules have already been established, and the fact base is empty. When the user specifies a particular IGES file for processing, the feature extractor reads it and generates a set of seed facts. At the same time, it also generates the necessary data structures to represent the geometric entities read from the IGES data base. Thereafter, when the user requests that a particular feature be searched for, it attempts to pick up the rules related to that features (in a top down fashion) and applies it to the existmg facts. Every time a rule fires, some new facts are generate-t and added to the beginning of the fact base ( essentially creating a depth first approach to probleM solving). The knowledge describing the features ( and the existing facts) is implemented as a set of Flavors objects [14) and the knowledge regarding the procedure for recogruzing these features is implemented as a set of production rules. The specific data structures used to represent the facts and the rules are described later in this paper. Data structures The standard data structures to represent some of the geometric entities are shown in Fig. 4. Every geometric entity is represented as a flavors object. A hierarchical taxonomy is used. Items like lines, circles, planes, etc are considered specializations of the hiiher level item called geometric entity and are defined as such. Consequently, a line entity would mherit all the attributes (as well as the procedures) of its parent class of geometric entity. A similar hierarchical taxonomy is used for features. Slots, pockets, holes are all special variations of the general feature. Conse- quently, the parameters corresponding to these, which result from their individual boundary attributes and their shape attributes can be described as flavors objects, each inheriting some parameters from the higher level generic feature parameters. (delllavo, llne-onllty jdelllnor IHlura (x-1 y-1 •·2 y-2} CIYP• parameter• componenta) la•omat rlc-•ntlt y} 0 :get ta bl• .in I tan c•-v a rla b I•• :gatta ble-1 na ta nee- va rla bl ea : sett ab I•· In a ta nc e-varla b lea :aalt a bl a-Ina tan ca. v arlable a :I nit ta ble-ln •tan••·•• rla b lao) :lnlltablo-lnelance-varlabl .. ) Fig. 4 Standard Data Structures Repre<,entation of facts During its operation, the feature extractor may encounter four types of ( declared or inferred) facts, namely, the existence of low level geometric entities, the existence of higher level geometric entities, the existence of an attribute pertaining to a particular entity, and the existence of a relationship that links two or more of the existing entities. The Flavors object used to represent the low level geometric entities contain parameter slots to accommodate values that are unique to that object. As an instance of a particular type of geometric entity is generated, a seed fact is also generated to assert the existence of this entity. The Flavors obJect used to represent the general fact entity contains four slots as shown in Fig.5. In the case of seed facts, the fust two fields contain the nil pointer. In general, the parent fact slot contains a pointer to an earlier generated fact and the parent rule slot points to a rule that successfully operated on this parent fact, resulting in the discovery of the current fact. The fact attribute slot contains the address of a list data structure whose elements summarize the attributes related to the current fact. For the case of the fact that a particular line entity ( e.g., line-5) exists, this field may contain the first element of the form < is a line > . 54 Page 952 The fact arguments field contains the necessary (delllavor fact arguments to define the fact accurately. In the above (perent-laot example, this field would contain a list containing a parant .. rule single element, line-5. The data structures for higher fact-attrlbutaa fact•argumonta) level geometric entities are similar to those for low () level geometric entities. However, most of the former : get tab I e-1 n •tan c e-va rl ab ta a are recognized and generated as a result of operations :aetta ble•lnata nce-varlablea :lnlltable-lnatanca-varla bleo) carried out on other existing facts and therefore, con- tain distinct pointers within the parent rule and the parent fact slots. The existence of attributes pertaining to an individual entity ( either low level or higher level) is denoted by a list of two elements, pointed to by an element of the attributes slot of the current fact. The existence of a binary relationship between two entities is also represented similarly except that the second member of this list refers to the other entity that this relationship affects. Representation of rules The production rules of the feature extractor can be divided into five categories as rules to guess non- Fig. 5 The General Fact Entity planar surfa ces, the stock shape, enclosures, con- cavity/convexity, and morphological features. It is necessary to exhaust all the rules in the proper order for guessing non-planar surfaces prior to attempting to guess the stock shape. The rules to guess enclosures establish which side of a physical surface contains material and which side contains void. Based on that, it is possible to identify the concave and convex edges. The rules to guess the morphological features make use o( this knowledge. The general rule data structure is an object that contains four slots (Fig. 6) namely, the rule name, a text (dalllavor rule (rule-number string to conve,>: the intent of the rule in plain language, rule-teat a field to specify the input code for the rule, and a field to specify the generated code for the rule. The first three generated-code) () fields are supplied by the (expert) user at the time the : g at tab I e-1 n at a nc •· v a rl ab la a rule is specified. The rule code field (specified by the :aett ab le-lnatance-varla blea user) is a list structure of the form : In Itta ble•tnatance•va rla blea) (IF < predicate-1 > AND < predicate-2 > AND ... < predicate-n > THEN < action-11 > AND < action-12 > AND .... ELSE < action-21 > AND < action-22 > AND ..... < action-2k) The predicates and the action items can themsel- ves be list structures each of whose elements is either a valid s-expression in Franz Lisp, or a term that belongs within the rule vocabulary, or a term that has some meaning within the context of an earlier appear- ing term which belongs within the rule vocabulary, or Fig. 6 The General Rule Entiry a list structure whose elements satisfy one of the above three criteria. The predicates are constructed in a form similar to the well-formed formulae (wff) of predicate calculus. When a rule is first specified, the inference engine examines each term appearing within each wff. Eventually, the inference engine generates the necessary Lisp code that would perform the tests and the actions intended by the rule. This ienerated code 1s then attached to the fourth field ofthe rule data structure. At execution time, 1t is the generated code field of the rule that is actually evaluated to test if the rule should apply or not. 55 Page 953 The feature extractor tasks and rule groups The feature extractor completes the seq_uence of going from an input IGES file to a resultant features file by executing the following cructal tasks in sequence: • read in an IGES file- - - - - - -(task-10) • draw part pictorial - - - - - - - (task-20) • extract planes - - - - - - - - -(task-30) • extract contours - - - - - - - - (task-40) • extract cylindrical surfaces - - -(task-SO) • extract faces - - - - - - - - -(task-60) • extract stock shape - - - - - -(task-70) • extract features - - - - - - - - (task-80) • create features file - - - - - - - (task-90) The set. of rules t~at pertain to a s~ecific task is ~lied a rule-group. The data structure for the rule-group IS shown m Fig. 7. At the time of execution (delflnor rule-group ofa task, the feature extractor seeks out the correspond- (rulo~-g:~,o~u=p-number ing rule-group data structure, sets its initial conditions ~:1 ~·;~~::. and then applies rules from this group to the known facts terminating-condition) repeatedly, until the termination condition is satisfied. < > This concludes the individual task. :gollable-lnatanco•verlobl .. : aett ab I•· In• t • nc e-v aria b la• ~In Itta bl •·I nata nee-variables) The buildintup of the fact base Upon t e specification of a particular IGES file for processing, the feature extractor reads it in and ~enerates a set of seed facts (Fig. 8). At the same time, It also generates the necessary data structures to repre- sent the geometric entities read from the IGES data base. The seed facts contain the nil pointers in their slots for the parent rule and the parent fact. When a par- ticular task is executed, the rules from its rule-group are repeatedly applied until its termination condition is satisfied. Some rules may apply (fire) successfully. Every time a rule fires, some new facts are ~enerated and added to the fact base . The generated (mferred) facts do indeed contain valid pointers in their parent fact and parent rule slots. Fig. 7 The General Rule-Group Entity Facts: .,.4_ ___ Seed facts: Rules .,.,_.. ___ Given rules Event , ually, the last task is executed. If features have been located, the latest members of the factbase cause a situation like the one shown in Fig. 9 to develop. The last few facts contain the value < is a feature> in their fact-attribute field, indicating that this fact denotes the nil existence of a particular feature. The name of the data nil structure that contains the parameters for this feature would appear within the fact-parameters field of the particular fact. Consequently, one ends up with a net- work of facts in which certain facts at the end, denoting the discovery of features, are linked through a set of intermediate facts to the seed facts. As a result of this linkage, the feature extractor is able to trace back the reasoning that it used in arriving at a certain feature. nil nil The current rule base During the execution of a specific task, the feature extractor first checks whether any prerequisite tasks have already been performed. If that happens to be the case, it then sets the initial conditions for that rule- Fig. 8 Initial Fact Buildup group. It then attempts to test the rules for that rule 56 Page 954 ~oup, starting with the rule-1. Prior to testing of a rule, Facts: <1114---- Seed facts + 1t checks whether the termination condition for that concluded facts task is already satisfied. If not, it evaluates the lisp code corresponding to the predicate portion of the rule. If Rules <11114---- Given rules that portion evaluates to a non-nil value, then the rule is said to fire and the action part of the code is then evaluated. If the rule does not ap,Ply or, alternately, the ELSE situation for the rule applies, the feature extrac- tor proceeds to the next rule within the rule group, after evaluating the portion of the code corresponding to the El.SE part. Every time a rule actually applies, the testing of rules would again begin with the rule-1, i.e., from the beginning. An example of the initial conditions, the termina- tion condition and the specific production rules cor- responding to the individual tasks is shown for task 10. ~t;~ ,:o _read in a CAD file in the IGES format ~u1sne· None. Initial condJtjons· • set the variable have read IGES file to false. • set the variable current-file to the path for the opened user speclFied file Fig. 9 Final Fact Base • set the variable reading IGES file to true. Tennjnatjon conditioO"The variable reading IGES file becomes false. B.ule:.l IF reading IGES file is true AND the end of current-file is false THEN set the current record to the next record from current-file AND set the current record type according to the 73rd character of string. Bw.e:2 IF reading IGES file is true AND the end of current-file is true THEN close the current-file AND set the variable reading IGES file to false. Ruk:3 IF the current record type is a start record OR the current record type is a global record OR the current record type is a terminate record THEN do nothing. ~ IF the current record type is a directory record THEN skip one record from the current file AND extract the directory record fields for the current record AND set the entity type according to the first field of the directory record fields AND create a data structure for this entity type AND assign the directory entry field of this data structure according to the tenth field of the directory record fields AND assign the transformation matrix field of this data structure according to the seventh field of the directory record fields AND assign the parameter entry field of this data structure according to the second field of the directory records fields. ~ IF the current record is a parameter record AND the entity type is a transformation matrix THEN read parameters from the current record AND set the fields- rll, r12, r13, tl, r21, r22, r23, t2, r31, r32, r33, t3 for its data structure. Ruk::n IF the current record is a parameter record AND the entity type is a line THEN read parameters from the current record AND set the fields x-1, y-1, z-1, x-2, y-2 and z-2 for its data structure. 57 Page 955 Buk.:1 IF the current record is a parameter record AND the entity type is a circle THEN read parameters from the current record AND set the fields zc, xc, ye, x 1, yl, x2, y2 for its data structure. B.ulc:8 IF the current record is a parameter record AND the entity type is a view lllEN read parameters from the current record AND set the field view-number for its data structure. B.ulc:2 IF the current record is a directory record lllEN create a fact asserting the existence of the current entity. A complete listing of rules for all the tasks is given in detail in reference [10]. IMPLEMENTATION ISSUES FOR THE IFEM Two different modes of operation, the automation mode and the interactive mode, for the feature extractor is provided. These two modes are described in detail in [10]. For each task. a set of production rules are specified. The feature extractor attempts to apply these rules to the current fact base. IT a particular rule fires, new fact data structures may be generated and added to the fact base. Rules are applied in a sequential order (the order in which they are specified in the rule base). They take the form: IF THEN < execute-action. During both the test as well as the action, the feature extractor may encounter terms for evaluation which are in turn defined by other lisp functions. In that case, these other functions (and any functions that these may be calling) are executed also, essentially creating a depth-first approach to problem-solving. Prominent vocabulary terms (representing Lisp functions that are invoked during the application of the rules) are summarized in reference [lOJ. ANEXAMPLE The example part, shown in Fig. 10, is a prismatic part containing six mor- phological features, namely a rectan- gular slot, a rectangular pocket, and (our cylindrical holes. Furthermore, all six features appear within a single face of the part. Although the feature extractor developed within this work is capable of handling more general three-dimen- sional shapes, the experimental facility to validate the feature extractor,is cur- rently set up to process parts only to the above simpler level of compleXIty. The user creates the part drawmg by using any one of the several commercially available CAD tools. The drawing data is then stored in the ASCII IGES for- Fig. 10 Example Part with Six Features mat. Execution of tasks On the SUN workstation, the feature extractor is invoked from within the Franz Lisp environment. The first request that a user would typically make is that the IGES file be processed. The directory section, which contains a cataJoi o( all the entities present in the drawmg is read first. As a particular entity is encountered, an mstance of its type IS generated. The actual name depends on the type of the entity. The most encountered geometrical entities include lines, circles, transformation matrices and views. The data structure assigned to an entity contains information on what type of entity it is as well as information regarding the directory and parameter section record number pointers for this entity. Next, the records of the parameter section are read. The data structures that were generated to represent the individual entities are augmented by adding the parameter values as occuring in the parameter record. This process continues till all the 58 Page 956 parameter section records are exhausted. A set of fact variables are also generated. They represent the seed declarative information regarding these entities. After the stock shape is guessed, the outermost surfaces are considered. All the planar contours that are present in the outermost planes are identified and data structures are generated to describe these in terms of the individual entities that are linked in a closed chain. Next the outermost contour is located. The outermost contour is one which meets the criterion that every point on every entity within the plane lies inside it (subtending a total of 2*3.1415 radians angle, as compared to Or adians that would be subtended at a point out- side the contour). Ne~t, an attempt is made to simplify the outermost contour, by attempting to supply missing entities, such as Imes between aligned lines. As an example (Fig. 11 ), the surfaces 1, 3 and 5 contain outermost contours that can be simplified into rectangles by sup- plying lines that are shown with a hatched pattern. The addition of these lines creates additional contours. The process is repeated for the inside con- tours and any other contours that these Fig. 11 Planes and Contours for the Example Part might enclose, in turn. FACE-1 FACE-2 COMPANION Once all the contours CONTOUR 2' within this plane are exhausted, TEJ it is seen that contour 1 encloses ·u;J w;J contour 2 within the face 1 (Fig. 12a), and they share a common line. Because contour 1 is not contained by any other contour, it must contain material, and the (a) (b) (c) contour 2, enclosed by it, must Fig. 12 Companion Contours for the Example Part represent hollow. Also, since they share part of their bound- ary, from the application of another rule, it appears that contour 2 represents the cross section for a slot. On the other hand, for the face 2 (Fig. 12b) , the contour 1 encloses contour 2 butshares no part of the boundary with it. Since the contour 1 contains material and contour 2 contains void, from the application of one of the rules, it appears that the contour 2 represents the cross section of either a pocket or a hole. In order to classify it any further, it is necessary to consider the adjacent surfaces. Further analysis reveals that its companion contour (Fig. 12c) indeed contains material and therefore the contour 2 on the face 2 (Fig. 12b) represents an entrance cross section for a pocket. In a similar fashion, the other morphological features present in this part are also recognized and listed by the feature extractor. At this point, the feature extractor has accumulated enough knowledge about the problem to attempt to recognize the shape features present within the part, (extract features). The corresponding interaction is shown (Fig. 13). After the individual features are recognized by the feature extractor, it is necessary to calculate the parameters for them for downstream processing and the eventual generation of the machine NC codes. This is the purpose of the create feature file task. Two types of files are typically generated, viz, .pd f onnat files and .pm/f onnat files. The .pd file is generated for a single (ace at a time and contains the feature parameters for that face. In order to create such files, the feature 59 Page 957 extractor first groups the individual features according to the faces that they lie on. The .pmf file contains the facility to represent the fea- Sep 27 Jt:10:IIJ; (USER:) rte ... ,.,.,ona ·tut-ao·. Sep 27 tt:U":19; tures in three dimensions and only one such file Sep 27 t 1:41:1'); The comm&n4 •. .t rot:t-f•etw-.1' b test-ID. Sep 2711:2111:42:16; Componenh: ...- 1S..,..-14~-ll lep 2111:42=16; Mne-J6Nae-53Nea-5t Miu-41 NIM-SS • The use of a commercial CAD Sep 2111:42:16; Now e1tkiactiat ..... _ iep 27 1 t:-42:16~ f••ture-J: tool to generate CAD file in IGES Sep 2111:42:16; lw-,: 1MtM Sep-27 fl:42:16; Componffh:drde-4drcht-1 format -kp 27 I l:r minimization controller. minlae for S2M B25!500 spindle] of the spindle. Following is a brief discussion of the tool path error and Currently, the- thrust of the overall project is to design the magnetic spindle. and develop an on-line error minimization controller to increase the productivity of end milling of thin -nb components. This controller, which is currently under TOOLPA1H ERROR development stage, when completed would use the cutting force information to tranSlate and tilt the spindle The accuracy and surface finish of a machined part is a rotor thereby compensating for tool path error. function of tool path error which is defined as the . distance difference between the actual and the required To accomplish this, first of al~ a CNC machine fitted tool path. Tool path error is classified, as shown in with a magnetic spindle is needed. In addition, such a Fig.1, according to the source and the nature· of the system must provide an user interface whereby the user error as cutting force-independent and cutting can tap into the current status and be able to command · force-dependent errors. the translation and tilt of the spindle rotor on-line in real time. Static deterministic positiou errors are those repeatable errors which are a function of machine slide position. Currently, to the best of the authors knowledge, MFL The cause for 1hese errors are geometric inaccuracies of Machine Tool Inc., is the only bwlder marketing a the slideways and the misalignment in the structural· -.. machining center fitted with a magnetic spindle. element assemblies. Dynamic deterministic position However, these machines do not provide the interface errors are those reproduab]e errors which are a function fouranslation and or ulting of the spindle rotor. of the table feed rate. Thermal Defo rmatwns due to heat Consiaering the situation, the decision was made to sources, both internal and external to machine toor- system, are reproduable errors which causes a change in the required position of the tool relative to the 1 workpiece. Thermal cycles of the spindle system, University of Maryland-UMBC, Baltimore, MD 21228 ambient temperature variation and friction are some 0 639 Page 961 example of the heat sources. Weight deformatiom are caused by changes in the weight of stationary objects which arc firmly positioned on the machine tool table. These errors show up as reproducible static position errors and occur in addition to position errors. ·-, Thruat . Beomg . Mag,ellc Thrust I. - ... _ Bearing CUTT!M:. F~E· llU."1)1:!) l'OS!TlOK error correction methodology involves the interaction and coordination of four independent contr01lers: Eristing CNC controller, Active magnetic bearing controller, Variable speed spindle drive, Online error minimizalion controller. While the existing Matsuura MC500 Yasnac CNC 3000G controller was retained, the latter three controllers were installed as pan of the active magnetic bearing retrofit. Derivation and· implementation of the overall controller coordination scheme has accounted for the largest . portion of the AMB retrofiL The functional · requirements can·be summarized as: - - 1. Providing the operational control necessary lO operate the CNC-mill, Jmplemcuat_ion of safety inlerwi:k measures, Fig. 3 Prototype rnultivariable control structure 641 Page 963 CRT. Both the spindle fault and table stop request · EXPERIMENTA L VALIDATION conditions must be reset by the operator, before operation is allowed to resume. Multiple spindle stop In order to validate the error correction using the push bottoms, as well as the CNC emergency stop, are magnetic spindle a simple end milling operation was available to .stop spindle rotation. designed. In this approach a straight surface was machined [i.e. ·end milled) ·to half the length with· no externaLcontrol input. During the machining of the Central to this research, is the implementation of the latter half portion, a sinusoidal bias voltage input was error minimization controller. The basic elements of given to the spindle controller interface unit. The the accuracy enhancement retrofit are depicted below resulting machined surface had a straight surface for the the dotted line of the simplified control system block half length and the remaining surface was sinusoidal. diagram given in . Fjg.3. As indicated, various online The frequency of the surface was same as the control process parameters are provided to the error input frequency as was predicted. · The surfaces of both minimization controller as inputs to the control halves showed the same degree of surface roughness. algorithm. Based on these inputs, the error This preliminary experiment proved that the spindle minimization control will use the predetermined error rotor [in turn the tool] can be both translated and tilted characterization to generate perturbational control in a controlled manner at required frequencies. signals to translate and tilt the AMB spindle to correct for dimensional errors. The theoretical development necessary to support the derivation of the robust, FU11JRE WORK multivariablc controller has been previously reported (Kirk and collcagues,1987). The input parameters With the experimental facility fully operational, currently under investigation include: remaining efforts involve implementation of the actual error minimization methodology. These activities x; Y, z axis posilion, include: X, Y, Z axis velocily commands, X, Y, Z axis servo lag, Completion of CNC machine dynamics Spindle displacemenl and bearing fore es, ideniification, Thermal conduions. Control system implementation and validation. Extraction of real time X, Y, Z axis position, and Accurate identification of the AMB spindle and CNC potentially servo lag, data from the Yasnac 3000G CNC machine dynamics is crucial to the development of the controller has particularly problematic. This information dynamical system models required for the control system was not directly obtainable and very little documentation design process. The spindle calibration and was available to facilitate its extraction. Since the identification process is essentially complete. desired information can be displayed on the CNC Identification of the CNC machine dynamics will operator console.CRT, various hardware and software proceed pending completion of the previously described debugging methods were applied to locate internal real-time axis position interface. position data which could be extracted and provided to the error minimization controller. After several weeks Control system modelling is currently underway using a of monitoring embedded microprocessor activity with a VAX based computer-aided control system design logic analyzer, a memory mapped, micron resolution, (CACSD) environment composed principally of the position interface was discovered within the CNC ACSL, MATLAB and MACSYMA software packages. controller internals. After a complete disassembly of the This environment supports the robust, multivariable embedded microprocessor read-only memory (ROM), control design methodologies which will be applied, several surgical ROM modifications were implemented once the system identification phase is complete. Trial to provide position at a predictable (8ms) update rate. error minimization controller designs will also be A digital hardware position interface, modelled as a evaluated, in this environment, using mixed continuous finite state machine, has been developed to capture, and discrete simulation, prior to microprocessor buffer and transmit the axis position data to the error implementation. minimization controller. The remaining error minimization controller inputs arc comparatively straight The · error minimization controller implementation will forward analog signals. Due to the high levels of be performed using an IEEE 796 (Mulubus) based electromagnetic interference (EMT) and potential for computer system. This system utilizes an Intel 386/387 ground loops, all digital 'signals arc opto-isolated and processor pair and executes the Intel RMX II operating analog signals differentially buffered. system. High performance interface boards will be incorporated to ensure adequate real-time performance. Implementation of the error compensation methodology 1n· addition, the Date! ST-701 analog input board has also requires mechanisms to coordinate and sequence been hardware and firmware modified to provide CNC and error minimization controller operations. The sufficient throughput. This error, minimization computer present approach involves the down loading of the part system, currently being assembled, is similar to .a system program, in M & G codes, to both the CNC and error presently providing high ·speed system identification data minimization controllers. In this scenario, the -CNC and acquisition services; · - error minimization controller execute the same part - - - program simultaneously. - This allows the error - _ Evaluation of the error minimization capabilities of the minimization controller to cooperate with the existing magnetic spindle r~trofitted Matsuuni_MC500 will be CNC controller and completely defines the desired tool performed-by comparing _thc aimensional accuracy of a trajectory. Existing CNC support for optional M-cooes _ - sequence of sample pans. This.-Sequence will use the M21 through M28 is currently being interfaced to the MC500, with no error correction, as die ~aseline with error minimization -controlleuci'provid~-sequc:J)cing and_ _ which to evaluate various error map formulations and handshaking functions. -- @n_trol system implementations. Dimensio·nal accuracy - · wi·n also be compared to a part milled- on~ conventional Matsuura MC5IO vertical CNC mill. 642 Page 964 ACKNO'WLEDGEMENT The research work reponed in this paper represents a cooperative activity of the personnel from the University of Maryland, the National Institute of Standards and Technology (formerly the National Bureau of Standards), the Westinghouse Corporation, the David Taylor Naval Research Center and the Magnetic Bearing, lnc. This work has been supponed by the National Science Foundation through grant NSF 8516218 the Engineering Research Center at the University of Maryland and ONR Program Element 61152N through the David Taylor Research Center. REFERENCES Anand, D.K., J.A Kirk and M. Anjanappa(1986). Magnetic Bearing Spindles for Enhancing Tool Path Accuracy. Advanced Manufacturing Processes, Vol.I. No.I, pp.121-134. Anand, D.K., J.A Kirk, and M. Anjanappa(1987). Tool Path Error Control for End Milling of Microwave Guides. Proceedings of the 7th World Congress on the Theory of Machines and Mechanisms, Vol.3, pp.1499-1502. Anjanappa, M., J.A Kirk, and DX Anand(1987). Tool Path Error Control in Thin Rtb Machining. Proceedings of 15Ilf NAMRC, pp. 485-492. Anjanappa, M, D.K. Anand, J.A Kirk, and S. Shyam(l988). Error Correction Methodologies and Control Strategies for Numerical Controlled Machining. Control Methods for Manufacturing Processes, DSC Vol. 9, pp. 41-49. Field, M., S.M. Harvey, J.R. K.ahles(1982). High Speed Machining Update, 1982: Production Experiences in the U.S.A. Metcu1 Research Associales Inc., Cincinnati, Ohio, USA Kirk, J.A, M. Anjanappa, D.K. Anand, and S. Shyam(1987). Accuracy Enhancement Methodologies in Thin Rib Machining. Proceedings of the 14th NSF Conference on Manufacturing Research and Technology, pp.9-14. MTfF(I980). Technology of Machine Tools. Machine Tool Task Force Repon, Vol.1-5. Nimphius, JJ.(1984). A New Machine Tool Specially, Designed for Ultra High Speed Machining of Aluminum Alloys. High Speed MachiniJ1g, pp. 321- 328. Raj Aggarwal, T.(1984). Research in Practical Aspects of High Speed Milling of Aluminum. Cincinnati Milacron Technical Repon. Schultz, H.(1984). High-Speed Milling of Aluminum Alloys. H",gh Speed Machining, pp.241-244. SKF (1981). Active Magnetic Bearing Spindle Systems for Machine Tools. SKF Technology Services Report. Tlusty, J.(1980). Criteria for Static and Dynamic Stiffness of Structures, Machine Tool Tssk Force Repon, Vol.3, Section 8.5. - 643 Page 965 THE EFFECT OF STRUCTURAL VIBRATIONS ON MAGNETIC BEARING OPERATION R.B. Zmood*+, D.K. Anand*, J.A. Kirk*, E. Zivi* * Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, U.S.A. + Department of Communication and Electrical Engineering, Royal Melbourne Institute of Technology, Melbourne, Victoria 3000, Australia. .. ABSTRACT of a machine tool magnetic spindle, similar Increasing interest in industrial and to the one installed at the University of aerospace applications of high performance Maryland, is considered. For simplicity magnetic bearings has led to a close study the bearings are assumed to be coupled to of their operation over recent years. the machine frame by flexible supports Characteristics such as the ability to having negligible damping. In the control the spindle position with high analysis, the operation of the magnetic accuracy, and to change the spindle dynamic bearings was investigated for changes in behaviour as a function of its speed have the support stiffnesses and the rotor led to the industrial use of these speed. bearings. In applying these bearings difficulties have been experienced with rotor and structural vibrations interfering DESCRIPTION OF MAGNETIC SPINDLE with the magnetic bearing control system operation. In this paper the effects of A.simplified diagram of the mechanical part non-infinite casing stiffness are examined of the magnetic spindle is shown in Fig. 1. for a machine tool magnetic spindle. It is It consists of upper and lower radial concluded that when the magnetic bearings bearings, each being controlled along the are coupled to the machine frame by x- and y~axes. In addition, although not flexible supports then additional stable, shown in.the diagram, the spindle contains but lightly damped, whirl frequencies are .a z-axis magnetic bearing.mounted above the introduced for,the range of spindle speeds top bearing, and a drive motor.mounted. and casing stiffnesses considered.· It is between· the upper and lower·. bearings. · The observed that these frequencies can be z-axis bearing is used to control.the . damped by using active damping in the vertical position of the spindle,,but as bearing control system. motion in this direction is not cross- coupled into the transverse'axes·it will INTRODUCTION not be considered in this study. similarly the influence·of the motor on the. actions Magnetic bearings are finding industrial of the bearings can be ignored excepting applications in situations where there is a for the gyroscopic cross-coupling component need to both control the position of a high speed spindle and to modify its dynamic behaviour as a function of spindle speed. Typical of such applications is the "magnetic spindle" which can be used for high speed precision machining of aluminium alloys on vertical machining centres. In applying these bearings in various situations the authors have found that structural vibrations of both the machine rotor and its casing can have a major effect on their operation (l]., The purpose of:this paper is to examine the.:effect of flexibly mounted magnetic bearing stators on the operation of the bearing contro1 system. To.study the effect of these structural Fig.1. Simplified mechanical arrangement vibrations on bearing d'peration, an example of magnetic spindle. 1499 CH2781°3/89/0000-1499 $1.00 © 1989 IEEE Page 966 caused by the rotation of the spindle about excess of 60,000 rpm, which is twice the the z-axis at speed nR. maximum recommended operating speed. As shown in Fig. 1 it is assumed that the The structure of the control system which bearing stators are coupled to the machine is used with the magnetic spindle is shown frame by springs and dampers, which in Fig. 2. The four outputs of the represent the compliant bearing supports position transducers are fed to PIO and are due to the combined flexibility ~f controllers whose outputs are then fed to the magnetic spindle casing and the machine their respective control winding inputs via tool column. For simplicity it has been power amplifiers. This control scheme 1 assumed that the spring stiffnesses Kc which has been widely used [3,4,5) for the Kcv1,.Kcx2, and Kcv2 all have the samexl• control of active magnetic bearings, is of nUlhericai value, and that the damping the type supplied by the manufacturer with coefficients Ccxi, Cc 1 , Ccx2 , and c can the magnetic spindle, and has been adopted be neglected. The patameters of thecy2 for the present investigation. Its magnetic spindle are given in Table 1. The successful operation in this application parameter Kcxl is not listed and will be appears to stem from the weak gyroscopic allowed to vary over a wide range as a part cross-coupling with this type of magnetic of our investigation. spindle when operated in the range of speeds mentioned above. Table 1 To investigate the operation of the Parameter Symbol Value magnetic bearing spindle and its control Rotor :mass mR 37 kg system a state variable model of the Z-axis moment of inertia 1zz 0.053 kg , 2 spindle and its PIO controllers was X- and y-axis moment of inertia IXf'IYY 1.13 kg m constructed. Using this representation, (=) Distance from CM to top bearing h3 0.1193 m Distance from CM to bottom bearing h4 0.166 m [~xll Top bearing spring constant 3141 N/mm 'ixy2l Bottom bearing spring constant Kxl•~l [f ~] ¾2, 2 5606 N/mm ';2 Top bearing current sensitivity MAGNETIC 4 Kixl• iy2 409 N/mm 4 X PIO Bottom bearing current 4 BEARING sensitivity Kix2,Kiy2 623 N/mm Radial position transducer 5 8 50 V/mm Controller sensitivity x1• y1 5 8 50 V/mm Top bearing stator mass x2• y2 mc:i 35 kg Bottom bearing stator mass mc2 35 kg 4 TRANSDUCER The interiors of the bearing stators Fig.2. Magnetic spindle control system contain electromagnets arranged to generate structure. magnetic fields along the x- and y-axes respectively, which in turn cause forces to the system eigenvalues and transient act upon the ferromagnetic rotor in the responses were computed using standard directions of the fields. These forces are numerical procedures. Even though the functions of the applied winding currents model used is relatively simple and and increase with increasing current consists of a rigid body representation for magnitudes. In addition inductive sensors the spindle and one-degree-of-freedom are mounted so as to measure the spindle models for the bearing stator to frame translational positions relative to the dynamics there are twenty state variables. interior bore of the bearing stators. The number of state variable will increase Signals from the sensors are fed to signal rapidly if higher order representations for conditioners in the control system which the spindle and casing dynamics are give analog ouput signals proportional to adopted, in which case the numerical the ~ha.ft.position in the x , y , x , and problems can become quite daunting. For 1 1 2 y directions. this situation alternative numerical 2 procedures, such as dynamic condensation [6], are being examined to keep the CONTROL SYSTEM numerical analysis tractable. Analysis of the spindle dynamics [2] show In this phase of the investigation it has that there is not only coupling between the been assumed that the casing stiffness is x 1- and x 2-axes, and the y - and y infinite, and the simulated responses 1 2-axes, but also between the x- and y-axes due to compared with those obtained gyroscopic cross-coupling. This might at experimentally. The simulated response to first sight suggest that the controller al volt step applied to the reference needs to be quite complex to accomodate input is shown in Fig 3(a) for the case this multivariable control system. However where nR=O. It will be noted that the peak it has been found that this is not the case time, settling time, and overshoot are 2.5 for this system as a comparatively simple msec, 13 msec, and 45 percent respectively, controller remains stable for speeds in and these values closely approximate those 1500 Page 967 casing stiffness, was examined. A I.!: comparison of the simulated and ~ ··xl experimentally determined transient responses shown in Fig. 3 suggests that the I casing for this magnetic spindle can be considered to have almost infinite T = 2.5 Msec stiffness. However it is the purpose in pk J this section to investigate what effect .-! : 1 KSeC non-infinite casing stiffness and non-zero s I spindle speeds will have on the operation Pment overshoot : 45 of the magnetic bearings and their control system • .... " As mentioned above it will be assumed that .02 .94 .es ' ,19 the casing damping is sufficiently close to TIME (sec.) zero for it to be neglected. Such an assumption in fact presents a worst.case Fig.J{a). Simulated response to a 1 volt when investigating the effects on stability step applied to the x1 reference input. of variations in spindle speed and casing OR=O. stiffness. obtained from· the experimentally recorded 200CI response shown in Fig J(b). The closed loop system eigenvalues were also computed g I as a function of spindle speed and their l• I 1500 damped natural frequencies are plotted in Fig. 4. It will be observed that the ;' closed loop damped natural frequencies only g change by a small amount as the spindle 8, 1000 speed varies from zero to 60,000 rpm. In f addition the damping of these frequencies remains almost unchanged over this speed range. As a consequence the dynamic I fl 5001 behaviour of the spindle only changes marginally as the spindle speed varies. I l This observation is confirmed by the ! simulated response to a step applied to the o~-~-~-~-~-~-~-o ;o 20 30 40 50 60 70 reference input which shows that for SPINDLE SPUD (x 103 rpm) spindle speeds, nR, up to 3161 rad/sec (30,000 rpm) there is little change in the Fig.4. Damped natural frequencies of transient response. magnetic spindle as a function of spindle speed with infinite casing stiffness. {MILS} (LBFJ 6. 00 500 ACTUATOR FORCE !i !'1 Tp-.. l.9 11sec Fig. 5 shows the variation of the damped 3. 60 ,! i JOO OV•risboot • 61 percel_l~t natural frequencies, wd, of the bearing I ; closed loop system eigenvalues as a ''.t function of the casing stiffness 1.20 100 ~ I coefficient, nc 2 , which is defined as ·-·-·-·-·INPUT STEP Ii' -1. 2-0 -100 : -~ n n 2 .,...,. ..i: --~----~--"'··===··' C ~ i : •. .•· mc1 -3 .=60 -300 ! [ : .: OUTPUT RESPONSE \j \ For large values of nc2 it will be observed that the natural frequencies wd are -6. 00 -soo essentially those of the casing resonant 0.1000 0 .1100 0 .1200 0.1300 0.1400 0 .1500 frequency TIME (sec.) Fig.J(b). Experimentally measured step response of magnetic spindle for nR=O. wdcase =~ " 0 c EFFECTS OF CASING FLEXIBILITY AND and the frequencies due to the closed loop SPINDLE SPEED UPON SPI~DLE OPERATION bearing control system with infinite casing stiffness. Ho!ever as the casing stiffness In the previous section the operation of coefficient fie decreases it will be the :magnetic bearings, ,~sswning infinite observed that the bearing control system 1501 Page 968 damped natural frequencies are strongly observation the general shape of the loci influenced by the casing dynamics. If is similar to those given in Fig. 6 for a typical values for the casing s~iffnes, stationary spindle. Again no whirl. coefficient lie in the range 10 to 10 instabilities are observed for this case, (rad/sec) 2 then it will be observed that al~ough the damping coefficients of the four critical frequencies would be excited lightly damped modes ,re !lightly de~reased by residual spindle forces as nR increases for:the case where nc =10 (rad/sec) • from zero to 3161 rad/sec (30,000 rpm). 108 108 100001 u •.. :.;.,- !! ~ ~ 1000 i El I 10• .. 0 ii! ~ o. 1 '---~~~_.__.._,_~..__,_._~~-'---'--'-'u.ilU 100 0.01 0.1 10 100 -2000 -1500 -1000 -500 0 DAMPING EXPONENT ( 1/sec) Fig.5. Damped natural frequenies wd of Fig.6. Bearing control system eigenvalues bearing control system as a function of as a function ~f the casing stiffness casing stiffness, nc2 , with nR=O. coefficient nc (shown as a parameter) for nR=O. The bearing control system eignevalues are r----------•-•= .:-r-;-10-=-•--i 10000 plotted on the complex plane as a funciion of the casing stiffness coefficient nc, in Fig. 6. Each loci in this plot, which is u for spindle speed nR=O, represents the path .~. fo½lowed by two coinc!dent e!genvalues ,s "'. .' !! nc increases from 10 to 10 (rad/sec) . It will be observed that, as nc2 decreases ~ toward the value 104 , two branches of the g loci approach the imaginary axis, thus 1000 yielding lightly damped modes, while the I remaining two branches remain well damped. ~ It will also be observed from Fig. 6 that the control system eigenvalues all have I 0 negative damping exponents, so that the 10• whirl motions are all stable. However, as i these critical frequencies are so lightly damped, they will pose considerable 100 problems as the spindle speed traverses -2500 -2000 -1500 -1000 -500 0 their•values. It is probable that DAMPING EXPONENT (1/se<:::) additional damping of the casing would be Fig.7. Bearing control system eigenvalues required for satisfactory operation. as a function ~f the casing stiffness coefficient nc (shown as a parameter) It is well known that the gyroscopic cross- coupling can induce whirl instabilities for nR=6238 rad/sec. under some operating conditions. To investigate this possibility for non- CONCLUDING REMARKS infinite casing stiffness the operation of the magnetic spindle was simulated at the It has been shown that the PIO controller, speed nR=6238 rad/sec (60,000 rpm). The which is commonly used for stabilizing plot of the eigenvalues for this case is shown in Fig. 7, where it will firstly be magnetic bearings, yields a satisfactory observed that the eJgenvalue loci for the simulated transient performance for the bearings in the magnetic spindle when the forward and backward whirl modes are now casing is assumed to have an infinite bifurcated, as compared with the loci shown in Fig. 6. However apart from this· stiffness. This simulated response was 1502 Page 969 found to compare. favourably with the experimentally recorded response. 6. J.R. Bielk, personal communication. This system was used as a baseline for 7. R.B. Zmood, "The Influence of Elastic investigating the effect of flexibly Rotors on the Performance of Magnetic mounted bearing stators. It was found that Bearings", Proc. 23rd Intersoc. Energy very lightly damped resonant modes were Conversion Conf., Jul. 31-Aug. 5, introduced by the compliant bearing 1988, Denver, Colorado, pp. 127-132. supports, which could pose problems when the spindle speed corresponded to one of these critical frequencies. In addition, while the analysis shows that all the modes are stable, this is only marginally so. Consequently, any excess phase within the bearing control loops is likely to cause whirling instabilities to occur. Experience has shown [7] that the robustness of magnetic bearing control systems can be improved by the use of actively damped controllers. One approach which has shown some success is the use of lossy notch-filters, where the zeros of the filter are judiciously positioned in the left half of the complex plane so that they are adjacent.to the modal frequencies to be damped. It has been found however that this approach can be rather tricky to apply, and further·work needs to be done on improving the design methods for these bearing control.• systems •. REFERENCES 1. R.B. Zmood, D.K. Anand, J.A. Kirk, "Analysis, Design, and Testing of a Magnetic Bearing for la:. Centrifuge". To be presented at the 12th Biennial ASME Conf •. on· Mech. Vibrations ,and Noise, Sept~·1989. 2. c. P. Jayaraman,· J .A. Kirk, D.K •.A nand, "The Effect·. of Rotor Dynamics on a ·Flywheel Stack Energy Storage System", Proc. 23rd··Intersoc. Energy·,eonversion Engrg. Conf; t Jul.· 31-Aug. · 5, 1988, Denver, Colorado; pp. 87-92. 3. F. Matsumura, K. Nakagawa, M. Kido, "Theory· and;:Experiment- of ·.Magnetic Bearing for,, Radial· and.-Thrust. , , Control'!, •Electrical'.Engineering in Japan, Vol.c 106B, ·No.1 .. 2 {feb,,,1986) ·pp. 135-42. . . 4. s. Fukata,· T~ ·,Shimomachi;:.H. rTamura, "Dynamics of Active Magnetic,Bearings Composed. of Solid Cores.· and Rotor" ,, Memoirs of Fae.· of Engrg.•,; Kyushu University, Vol., 46, ·'No. '.3, (Sep ,1986) pp. 279-295. : . ;:.-p:,~·:--1.~ \:·-t .;::. . 1i..,;;r, ... -,.;_;;:1.l?-\,\¼-J1r~~~::J ·>:,,,;rct-1.\z· 5. A.V. Sabnis,' J.B.-, Dendy; .1 F~Min)t('~T.f;;,;,;t/2 r• Schmitt,."Magnetically~Suspended,;Large_ Momentum Wheel II, .. J. :·Spacecraft ·and!· ,h;: . Rockets, Vol. 12, No. >7 (Jul ,1975)! pp~ 420 1503 Page 970 ANALYSIS, DESIGN, AND TESTING OF A MAGNETIC BEARING FOR A CENTRIFUGE R. B. Zmood Department of Communication and Electrical Engineering Royal Melbourne Institute of Technology Melbourne, Victoria, Australia D. K. Anand and J. A. Kirk Department of Mechanical Engineering The University of Maryland College Park, Maryland ABSTRACT INTRODUCTION Magnetic bearings have unique characteristics such as Magnetic bearings have unique characteristics such as unlimited life and very low drag torques which have unlimited life and very low drag torques, which have made their application in space technology very attrac- made their application in space technology very attrac- tive over the last fifteen years. More recently, other tive over the last fifteen years. Their uses for fly- attributes, have encouraged their consideration for wheel energy storage and satellite attitude applications in scientific and industrial fields. This stabilization systems have been seriously investigated paper describes the experimental radial permanent by many researchers and in recent years one such atti- magnet biased magnetic bearing developed for use on a tude control system has flown in the French SPOT centrifuge. The operation and design of the actuator satellite. More recently, other attributes, have led is presented, and a comparison between experimental to their application in diverse industrial fields, such measurements and predicted performance is drawn. The as turbo-compressors, turbo-molecular vacuum pumps, and dynamic performance limitations of the existing design centrifuges [1]. As well, a number of investigators are examined and it is conclud~d that the casing struc- have studied the use of magnetic bearings for vibration tural dynamics of the bearing are important in the ana- control of rotating shafts and for vibration isolation lysis of its controller. The coupled structure [2]. A more complete list of references is given in approach is proposed as a means of handling the more [ 4]. complex control system design problem introduced by the casing vibrations. This paper describes the experimental radial EM/PM magnetic bearing developed for use on a centrifuge. The NOMENCLATURE principle of operation of the radial bearing actuator is described. It is indicated that the use of a per- 80 = air-gap flux density manent magnet bias flux increases the sensitivity for CR,Cc = rotor and casing damping matrices currents of small magnitude and also results in the Fc(s) casing receptance matrix actuator force being a linear function of the control Fx(x,ix) = force on actuator armature current. Experimental measurements of the original and Fx,Fy forces on rotor in frame Cxyz modified actuator performance are presented and these g0 average armature air-gap are compared with the predicted performance of the Gxi(s) = actuator transfer function design. The control system design for the magnetic ix control current bearing is discussed and measurements of its static iRc control currents vector performance are presented. Difficulties experienced in Kx = actuator static stiffness achieving adequate closed loop static and dynamic per- K;x = actuator current sensitivity formance are examined and possible means of overcoming KR,Kc rotor and casing static stiffness matrices these problems are suggested. KxRC,KiRC = actuator static stiffness and current sen- sitivity matrices RADIAL MAGNETIC BEARING ACTUATOR rotor and casing inertia matrices number of coil turns A sectioned view of the EM/PM radial magnetic bearing generalized force vectors acting at rotor and is shown in Fig. 1. The design consists of a circular casing nodes aluminium housing retaining the touch-down bearing at qR,qC generalized coordinate vectors of rotor and each end. The housing is split at the middle so that it casing nodes may be separated into ~alve, for easy access to the R actuator pole radius interior components. The e\ploded view of the bearing r = actuator armature radius shown in Fig. 2 illustrates the interior construction teff = effective pole-face thickness of the actuator. It consists of two mild steel e 1/2 x pQle face an,9le flux rings separated by a row of permanent magnets Uo = 4nxl0 -/ H/m. ' 345 Page 971 tion becomes non-uniform so that the resultant force is non-zero and acts in the direction of the displacement. Superimposed on the permanent magnet flux is the flux generated along paths '2' and '3' by the current in the N-S coils. This flux combines with the flux from the permanent magnets to give rise to a controllable nett force which is a function of the armature displacement and the applied current. For a small armature displacement, x, and control current, ix, the total force Fx(x,ixl along the E-\1 direction can be shown to be approximately ( 1) where ,rBa2teff(R+r) Kx (2) J.Jogo and Fig. 1 Sectioned view of experimental magnetic 2Boteff sine Ncoil (R+r) Bearing Kix ( 3) go arranged in a circular pattern to fit into holes drilled in the aluminium central ring. These permanent with a similar expression for the force Fy(Y,iy) along magnets provide the magnetic bias flux which is nec- the N-S direction also applying. Here g0 is the cessary for correct operation of the bearing. Fitted average armature air-gap, teff is the effective pole- to each flux ring along two axes at right angles called face thickness, R is the pole radius, and r is the the North-South (N-S) and East-West (E-W) axes respec- armature radius. The air-gap flux density is denoted tively, are four mild steel pole pieces wound with by B0 and u0 =4,rx10-7 H/m. In equation (3), the control multi-turn control coils. The coils along each axis are winding has Ncoil turns and the pole face subtends an connected in series, and are independantly excited by angle of 20 degrees. It wi 11 be noted from equation Ohe E-W and N-S control currents, which are used for (3) that the current sensitivity Kix is directly pro- controlling the position of the rotor shaft. Two posi- portional to the air-gap flux density B0 established by tions transducers for sensing and providing electrical the permanent magnets and is independent of the control output signals proportional to the shaft positions relative to the bearing housing are located along the N-S and E-W axes by the central aluminium ring. E--W AXIS Fig. 3 View of magnetic bearing showing permanent magnet and control field magnetic flux paths l. central nng 7. .$0eket bead cap screw- 2. flux ring s. wave washer ). pole piece 9. touchdovn ball be11.ring current magnitude so long as the magnetic components 4. 11.lu11>iniu= houi-1,ng 10. position transducer sensor are unsaturated. These characteristics should be com- 5. drav rod ll. l!ECO pcniianent IM.gnet 6. electro111agnet coil 12. rotor spindle sleeve pared with those for actuators having no permanent magnets where the force is a non-linear function of the Fig. 2 Exploded view of experimental magnetic control current and the sensitivity is almost zero for bearing small current magnitudes unless a constant bias current is supplied. The principle of operation of the actuator for the N-S direction is illustrated in Fig. 3. With the armature ACTUATOR PERFORMANCE centered in the bore of the bearing actuator the per- manent magnet flux is uniformly distributed around the The bearing actuator was initally assembled with twenty periphery of the air gap so that the nett force acting permanent magnets. Subsequently it was fully loaded on the armature is zero. A typical route followed by with an additional twelve magnets. In each case the the flux is shown byc•path 'l'. For small displacements actuator was mounted in a test-rig and the armature from the central position, the air-gap flux distribu- force measured as a function of armature position and 346 Page 972 control current, with typical performance curves being insufficiently taken into c ~ount in the original obtained as shown in Fig. 4. Taking the neutral point design. Also the leakage fluxes in some of the regions as x=0.3,mm it will be observed that for small displa- external to the actuator were neglected because indivi- cements and for currents in the range -0.5 to 0.5 amp dually they were of small magnitude. However in aggre- equation (3) applies to a good approximation. gate they are significant and cannot be ignored. Upon the completion of this investigation it will be The static stiffness Kx and current sensitivity Kix• possible to accurately predict the flux densities at for the two cases, is given in Table 1, with the various positions in the actuator including the impor- design values included for comparison. tant pole-face air-gap region. As part of this work an interactive computer program is being written to carry Table 1. Static Stiffness and Current Sensitivities out a complete magnetic analysis of the actuator, together with an analysis of the actuator control coils. No. of Perm. Mags.· Design Values Parameter 20 32 (20 P.M.) CONTROL SYSTEM DESIGN It has become apparent that one of the most challenging 51 196 301 aspects of magnetic bearing design is the modeling of Kx (N/mm) the centrifuge rotor dynamics, and the mechanical reso- 98 176 184 nant modes of the centrifuge casing. The reason for Ki X (N/amp the importance of these modal frequencies is because they often lie within the frequency bandwidth of the bearing control system and as a consequence have a pro- The values of Kx and Kx; given in Table for the case found effect on its closed loop stability. 1 of 20 permanent magnets is consistent with B0=0.29 T The initial bearing design was based on a single- rather than the design value of B0 =0.7 T. Subsequent degree-of-freedom model for the centrifuge which effec- investigation indicates that leakage flux, particularly between the two flux rings, is much larger than antici- tively ignores the gyroscopic and vibrational effects pated, and as a consequence the air-gap bias flux den- other than the first order transverse mode [l]. Based sity is considerably reduced. The severe curvature of on these assumptions a multiple feedback path bearing control system, shown in Fig. 5, was designed the static characteristics is also explained by the low air-aap bias flux density, and is due to flux reversal to have a 500 Hz bandwidth and a static stiffness of 20,000 N/mm, as summarized in Table 2. Experimental when-the control current magnitude becomes large. work showed that while the inner loop control system The design of the actuator is currently being closely was stable and had a performance comparable with the design values, the outer loop performance was never investigated so as to establish an accura~e model 1?f: achieved. Investigation showed the single-degree-of-the magnetic components: The ap~r?ach being.used to freedom bearing mode1 was inadequate, as experiments experimental1y map the r1ux dens1t1es at various points demonstrated the presence of prominent resonant modes in the actuator and to compare them with the values at 20, 45, and 150 Hz, as we11 as well as many less obtained in the design computations. pronounced ones. The work in [1] showed that a lead/lag compensator in the outer loop fatled to give Armature force F (N) stable operation for all non-zero loop gains. However, 150 substitution of an integrator gave stable operation with infinite static stiffness, but at the price of a considerably reduced bandwidth of 25 Hz. 100 I(Amp) 0.75 50 0.5 0.25 '" 0 . 1.nt tMJt/lHW ,_, Mf I • 0 L.. .............................. J JurhcnW•»t -50 h1!tlo .. ~ .., ,t htt. -100 -150 c_-~'---..-J'------1----'----' 0 0.1 0.2 0.$ 0.4 0.6 Armature position x (mm) Fig. 5 Magnetic bearing control system b1 o ck di a gram Fig. 4 Force vs actuator current as a function of armature position - final design The effects of rotor dynamics and the empirical effects of machine casing structural dynamics have been further Because the air-gap flux density due to the permanent analyzed in [4], where it has been shown that more magnets is considerably lower than expected, close detailed models aid in the design of the bearing attention is being given to deve}oping a better ~odel control system. In this work a non-rotating bearing of the leakage fluxes in the actuator. Calculations was mounted on a test stand and its modal response show the leakage flux between the two flux rings was 347 Page 973 recorded for frequencies in the range 100 to 500 Hz. the previous design approaches; but in spite of these The mode shape for each modal frequency was determined advances it is felt that the robustness of the design from these measurements, as illustrated in Fig. 6 for still needs improvement. the mode at a frequency of 115.39 Hz. Independantly of the above measurements, the magnetic bearing frequency Table 2. Magnetic Bearing Performance response transfer function, shown in Fig. 7, was measured for frequencies in the range 10 Hz to 1 kHz. Two prominent modal frequencies, believed to be due to structural bending, can be observed in this figure at Bandwidth Static Pull ou1 143 and 232 Hz. At this juncture, the difference bet- Descriptior (Time Resp Stiffnes' Force Remarks ween the results obtained by these two methods have not EW N' EW N' been reconciled. The amplitude response has been approximated by the model transfer function A. Centrlfuoe ll uui-J llJ I multiple loop 2 Inner Loop Only 27 ;i( s +2.02x 6 2 510 c.s. ) ( s +6. 83x 10 ) --z----.--2_ ___"_ _2_ ___6 _ , ( ) (lead compensator) 4 (s -2.67x10 theoretical BW=90 Hz 1065 106! )(s +8.07xl0 )(s +2.14xl0 ) n/a experim'tl I N/mm N/mn BW.,90 Hz 1400 109( whose frequency response is superimposed on the experi- experiment a 11) I N/mm N/mn mental curve in Fig. 7 for comparison. This transfer determined Outer Loop Closed function was obtained using a least-squares curve modes: 20, 45, (lead/lag) I 150 Hz fitting routine with a three-degree-of-freedom model theoretical BW=500 Hz 20 000 for the magnetic bearing and test stand. . I N/mm experim'tl unstable n/a n/a (integr'tr~ experim'tl BW.,25 Hz 62,5 6I.5 . . . ,. . . . N N 15. t.xperimental lest R1g L4J 1 DOF Model not analyzed because prev- ious experi- ence showed Fig. 6 Mode shape for modal frequency: 115.39 Hz. inadequate Mode shape shown by full line, and reference 3 OOF Model grid shown by broken line ( 2x notch -t 2x lead) single theoret i cal TR=0.5 ms loop C.S. Ts=l2 ms experim'tl TR "4 ms Ts=14 ms r-~===-~f''.'.';,E;}URED COUPLED STRUCTURE ANALYSIS OF MAGNETIC BEARING / MODEL One of the main limitations of the present methods is that, even though the rotor can usually be adequately modelled mathematically, the centrifuge casing struc- ture is often extremely complex and therefore cannot be accurately modelled with ease. This results in the equations of motion having great uncertainty, -1,0'--~~~~"'-~~~~.......,_-~~~~ 10 100 1000 which in turn leads to difficulty in arriving at pre-l FREQUENCY (Hz) dictable and robust bearing controller designs. An alternative approach is the use of the Nyquist and Bode methods in conjunction with experimentally determined frequency response data. Wh i1 e this approach works Fig. 7 Frequency amplitude response for N-S axis well for specific situations the results are not trans- of magnetic bearing mounted on test stand. ferrable to new circumstances, because it is not easy to separate the dynamic effects of the bearing and Using the three-degree-of-freedom transfer function rotor from those of the casing. Coupled structure ana- model described above, a bearing control system having lysis of magnetic bearings, which will now be active damping of the resonant modes was designed. The discussed, provides a theoretical framework within controller adopted consisted of a cascade of two lead which experimental and analytically derived data can be networks and two notch filters, where the zeros of the integrated into a form suitable for the study of many notch filters were positioned in the left-hand half- diverse applications of these bearings. plane adjacent to the modal poles on the imaginary axis of the s-plane. The analysis showed that the gain and Rotor Equations of Motion phase margins are 23 dB and 67 degrees respectively. It is shown in Table 2 that the experimentally deter- A simplified diagram of the centrifuge showing the mined rise- and sett l i'illg-t i mes compare favourably with coordinate frames for the rotor is given in Fig. 8. the design values. The static stiffness was found to Here the non-rotating frame Cxyz has the axis Cz be noticeably increased over the values obtained using aligned along the local axis of rotation of the rotor 348 Page 974 and the axes Cx and Cy always lie in the plane of sym- metry of the rotor. The other frame of importance is 01x1Y1z1 where axis 01z1 is aligned through the . bearings. Using these reference frames, and assuming s2 r,,-,,,, ,,,, J the linear and angular displacements are small, it can be shown [4] that the rotor and armature equations of ["0' M°c l {'O 0 motion in matrix form are given by °] ' lK xRC Kc-KxRC ( 5) where MR, CR, and KR are the rotor inertia, damping, and stiffness matrices respectively, qR is the rotor generalized coordinate vector, and OR is a vector of the system generalized forces acting at rotor nodes. [ Krnc] (9) It should be noted that matrices MR and KR are sym- X = iRC • metric and CR is skew-symmetric because of gyroscopic [::] -Krnc effects. The above equation defines the response of the centri- fuge generalized coordinates to changes in the control current input iRc• It can be seen from (9) that the number of degrees-of-freedom has been increased con- siderably by the inclusion of the casing generalized coordinates. Often it can be assumed, as it will be here, that the casing stiffness is very large. Under these conditions considerable simplification in the representation of the system is possible. Fig. 8 Simplified layout of centrifuge rotor showing coordinate frames Casing Equations of Motion The magnetic bearing actuator is generally attached to the centrifuge casing, which experience has shown [1,4] contributes to the dynamic response of the bearing control system. The complexity of the casing design generally precludes simple analytical dynamic models being developed so that alterna~ive ~pproaches such as finite element and modal analysis [5J methods need to Fig. 9 Simplified arrangement of bearing actuator be considered. coupled to rotor and casing Either of the methods mentioned above leads to casing From (9) it can be shown that equations of motion of the form qc = - Fc(s)(KxRCqR + KiRciRc) ' (10) ( 6) 2where Fc(s)=(s Mc+Kc1)·1 is termed the receptance where Mc, Cc, and Kc are the ~asing ine~tia, damp~ng, matrix of the centrifuge casing, and Kc1=Kc-KxRC· and stiffness matrices respectively, qc 1s the casing Palazzolo [6] and Bielk [7] have shown that the generalized coordinate vector, and Qc is a vector of spectral representation of the receptance matrix is the generalized forces acting at the casing nodes. 2 4 Often the elements of the damping matrix Cc are suf- Fc(s) = - s Kc1·lMcKc1-l + Kc1-l + s R(s) , (11) ficiently small for the second term in (6) to be neglected. where R(s) is the modal residual term. Substituting (10) and (11) into (9) gives Coupled Structure Analysis [s 2(MR+KxRcKc1· 1McKc1- 1KxRCl + sCR + (KRl The centrifuge rotor and casing are coupled by means -KxRcKc1-1KxRc) - s4KxRcR(s)KxRcJqR = of the magnetic bearing actuator as shown in Fig. 9. It can be seen from (1) that the generalized forces (- s2Kc1-lMcKc1-l + Kc1-l + s4R(s) + I)KiRciRc (12) acting on the rotor and casing are given by ( 7) where KR1=KR-KxRC· Assuming the casing stiffness is and very large, it can be shown that the modal residual term is small in the frequency range of interest, so (8) that (12) simplifies to where KxRC, and Ki RC are the diag?n~l _beRring_actuator 2 1 1 static stiffness and current sens1t1v1ty matrices, [s (MR+KxRcKc1· McKc1- KxRcl + sCR + (KR1 respectively. Taking the Laplace transform of (5) and (6) and substituting (7) and (8) gives -KxRcKc1· 1KxRc)JqR = (- s2Kc1- 1McKc1·1 + Kc1- 1 + I)KiRCiRc (13) 349 Page 975 We have arrived at a reduced order model of the magnetic bearing system given by (13). It can be seen that (13) has a form similar to (5), but with modified inertia and stiffness matrices. The reduced order representation given in (13) is well suited for stabi- lity studies of magnetic bearings using dynamic con- densation techniques, as well as for the application of pole-placement methods to bearing controller design. Both aspects are being further considered in our work on systematic design methods for bearing control systems. CONCLUDING REMARKS The development of an experimental radial permanent magnet biased magnetic bearing for use in a centri- fuge has been discussed. The principle of operation of the actuator has been described and the limitations of its performance have been determined. It has been found that this is principally due to the inadequate allowance made for the leakage flux between the flux rings. Experience has shown that the centrifuge rotor dynamics and the resonant modes of the centrifuge casing strongly influence the operation of the magne- tic bearing controller. The inclusion of the casing structural dynamics considerably increases the complexity of the bearing control system design problem. In approaching this difficulty, the coupled structure method, discussed above provides a theoreti- cal framework within which both analytical and experi- mentally derived models of the bearing sub-structures can be integrated for further analysis. REFERENCES 1. Zmood, R, B, Anand, D.K, Kirk, J.A., "The Design of a Magnetic Bearing for High Speed Shaft Driven Applications", 22nd Intersoc. Energy Conv. Eng. Conf., August 10-14, 1987, Philadelphia, Pennsylvania, Paper 879148. 2. Schweitzer, G.,"Magnetic Bearings for Vibration Control", presented at Instabilities in Rotating Machinery Conf., June 10-14, 1985, Springfield, Virginia, pp. 317-326 (avail. NASA CP 2409). 3. Allaire, P.E., Lewis, O.W., Knight, J.D., "Feedback Control of a Simple Mass Rotor on Rigid Supports", J. Franklin Inst., Vol. 312, July 1981, pp. 1-11. 4. Zmood, R.B.,"The Influence of Elastic Rotors on the Performance of Magnetic Bearings", 23rd Intersoc. Energy Conv. Eng. Conf. Aug 1-5, 1988, Colorado, Paper 889469. 5. Ewins, D.J., Modal Testing: Theory and Practice, Research Studies Press, England, 1984. 6. Palazzolo, A.B., Wang, B.P., Pilkey, W.D.,"A Recept- ance Formula for General Second-Degree Square Lambda Matrices", Int. J. Numerical Methods in Eng. Vol. 18, No. 6, June, 1982, pp. 829-843. 7. Bielk, J.R., personal communication. 350 Page 976 PROTOTYPE OF A MAGNETICALLY SUSPENDED FLYWHEEL ENERGY STORAGE SYSTEM BY Mr. David P. Plant TPI, Inc. Bethesda, MD 20817 and Dr. J. A. Kirk, Dr. D. K. Anand University of Maryland, Mechanical En ineering Department College Park, MD 20742 furnishes the system with four degrees of freedom which are ABSTRACT actively controlled by the magnetic bearings. Control of the axial direction remains passive and rotation in the axial axes The work presented in this paper covers the recent is controlled by the brushless dc motor generator. developments at the University of Maryland and how these progressions apply to a 500 Watt-hour magnetically The objective of this paper was to design a prototype 500 suspended flywheel stack energy storage system. The work watt-hour stack energy storage system. This system will includes the design of such a flywheel stack energy storage make use of two four inch diameter pancake magnetic system and a critical study of the non-contacting bearings previously tested experimentally and validated displacement transducers and their placement in the stack using a computer aided design algorithm [2]. This system system. The flywheel stack energy storage system has been will also include a brushless dc motor generator which was designed, constructed, and is currently undergoing commercially available and purchased from an outside experimental analysis. The results acquired from the non- vendor. The flywheel, constructed of aluminum, is designed contacting displacement transducer study showed that to withstand rotational speeds of 30,000 rpm. currently available transducers will not function as desired and that further research is essential. The work was essentially divided into two parts. The first part was the mechanical design of the stack system. This 1. Introduction included dimensioning and tolerancing of all components and allowance for practical assembly of this stack. The A single magnetic bearing provides for control in three second part of the thesis was directed towards a critical degrees of freedom, actively in the radial degrees of study of the non-contacting displacement transducers and freedom and passively in the axial degree of freedom. To their placement in the stack system. remain competitive with electrochemical energy storage systems, flywheel energy storage systems must attain very 2. Stack Design high rotational speeds, on the order of 80,000 rpm[ 11. These high rotational speeds require strict control over the There are three main objectives in the design of the flywheel dynamic motions of the flywheel. At operating rotational energy storage project awarded by NASA/GSFC to the speed the flywheel experiences various degrees of motion, Magnetic Bearing Laboratory at the University of Maryland. such as precession and nutation. At these rotational speeds The first design objective states that the flywheel energy a single magnetic bearing flywheel system, with only two storage system must store 500 WH of energy. The second degrees of freedom controlled actively, would be design objective requires the complete flywheel energy inadequate. Therefore a stack magnetic bearing system was storage system to have a round trip efficiency of 80% or devised to resolve this problem of flywheel control. The greater. The third design goal is that the specific energy stack system consists of two pancake magnetic bearings density, SED, be at least 20 “/w The SED is the amount which are positioned at each end of the flywheel as shown in of energy that can be stored per unit weight. The value of figure 1. Also included in the stator portion of the stack 20 “/,was chosen because it far exceeds the SED of system is a brushless dc motor generator. This arrangement electrochemical energy storage systems currently used in 1485 CH2781-3/89/0000-1485 $1.00 0 1989 IEEE Page 977 LEO satellites. The goals of 20 "/& and 500 WH are generator include, no contacting brushes that limit the important because this determines the nominal size of the rotational speed and wear out, higher reliability, and long flywheel. The first prototype stack system will have an shelf life. In addition, brushless dc motors can sit idle for aluminum flywheel which will retain most of the dimensions many years with no loss of performance [6]. The brushless of the stack system design with a composite material dc motor generator selected for this stack system design, flywheel. The only difference of the current design and of was a commercially available motor purchased from BE1 the final stack system is the outside diameter of the Kimco Magnetics Division. This motor was selected aluminum flywheel which will be much smaller to allow the because, dimensionally it was small enough to fit inside the aluminum flywheel to have a burst speed of greater than stack system and for the cost it had the highest rated 30,000 rpm. rotational speed. This motor was able to accelerate the aluminum flywheel to a speed of 30,000 rpm in a vacuum. 2.1 Stack Design Parameters Before the motor was inserted into the stack system, it was tested in a separate test rig. Since the design and As discussed in the previous section, the SED and the construction of this test rig had to adhere to a strict time desired amount of energy storage determine the size of the limit, it made use of existing parts available in the magnetic flywheel and ultimately the size of the stack system. The bearing laboratory. Also this test rig included a designed SED is the stored kinetic energy divided by the flywheel part which could easily be interchanged between the test rig weight and is a function of the flywheel material properties and stack system. The motor was fully tested to a rotational and the shape of the flywheel. The equation for the SED is speed of 15,800 rpm. the following: SED = & x U U ' L lY 3. Non-Contacting Displacement Transducers where & is a shape factor, UUII. is the ultimate tensile strength of the composite material in the hoop direction of A vital element in the suspension of flywheels, via magnetic the flywheel, and y is the weight density of the flywheel bearings, are the non-contacting displacement transducers. material [3]. The FLYANS2 and FLYSIZE computer These transducers or sensors detect the displacement of the programs, which are available on the University of flywheel relative to the stator portion of the magnetic Maryland's mainframe computer, were used to size the bearing. This displacement is referred to as the measurand. flywheel. The computer programs were originally written by In practice, measurement systems seldom respond directly R. Huntington in 1978 and later modified by A. Kahn in to the measurand. More often, for ease in measuring, it is 1984 [4-51. These computer programs perform a stress desirable to convert from one physical quantity to another analysis and performance maximization procedure for a by means of a transducer. The conversion in this case is multiring, constant thickness flywheel. Some of the inputs to from displacement to a voltage level which is proportional the programs include, flywheel material properties, the to the physical displacement of the flywheel. Next this number of flywheel rings, the inner radius ratio of each ring, voltage signal is fedback through the control system and flywheel outer radius, the desired energy storage, the compared to a reference voltage. operational speed interval in percent of burst speed, and Some of the types of non-contacting displacement ring interference limits. Some the outputs include, the transducers presently accessible are inductive, capacitive, maximum or burst angular speed, the stresses developed in and optical transducers. Although there are other types of each ring, the radial growth of the flywheel at various non-contacting displacement transducers, such as radiation, speeds, the flywheel weight, the SED for the operational ultrasonic,and air gauging, only inductive, capacitive, and speed range, and the operational speed range. Figure 2 optical types were investigated. The general advantages and displays the final size of the flywheel and some other disadvantages of the inductive, capacitive, and optical important parameters. sensors are presented in figure 3. It shows that the inductive sensor has adequate frequency response (20 KHz), small 2.2 Brushless DC Motor Generator DesignlSelection size, and has a relatively large linear range (80 mils). The main disadvantage of the inductive sensor was uncertainty A brushless dc motor generator can be defined as having of operating in a strong magnetic field. Also the inductive three elements, a fixed wound armature or stator, a rotor sensor produced a sensing area that was the shape of a cone with permanent magnets attached to it, and a means of protruding from the sensor's probe tip. Any conducting sensing rotor position. Advantages of such a motor material that would intersect this conical sensing field would 1486 Page 978 affect the output of the sensor. The capacitive sensor could previous magnetic bearing systems built at the University of be custom sized to tailor fit the stack system. Problems of Maryland. The voltage output curve for this sensor is low frequency response (less than 6 KHz), very high cost, shown in figure 4. This sensor was able to meet all of the and stray capacitance fields basically prohibited the use of stack system’s sensor requirements except for the size capacitive sensors in the stack system. The optical sensors requirement. The sensor’s probe was too large to fit on the were quite promising with very high frequency responses inside of a magnetic bearing. This sensor was tested for the (100 KHz), large linear ranges (100 mils), very low cost (less reason that it was readily available and worked successfully than $loo),a nd very small probe size with the use of fiber in previous magnetic bearing systems. The other Kaman optics. The only disadvantage of the optical sensor was the sensor, KD-2300-1SU, passed all requirements for the stack problem of non-uniform surface reflectivity of the target system and proved to be very versatile. The voltage output surface. versus displacement curve is shown in figure 5. The sensitivity was easily adjustable to 60 volts per inch. The 3.1 Transducer Selection linear range for the KD-2300-1SU was only approximately 40 mils for an aluminum target and 35 mils for a stainless In the previous section displacement transducer steel target. An advantage of this sensor was that it did not performance requirements were defined. At this time it is detect ferromagnetic materials. necessary to determine these performance requirements of The last sensor tested was the SPOT optical sensor designed the displacement transducer for the stack system. For this and built at the Magnetic Bearing Laboratory. This sensor’s stack system the displacement transducers were to be voltage output versus displacement curve is shown in figure moved from sensing the outside periphery of the flywheel to 6. Optical sensors produce voltage output versus sensing the inside surface of the flywheel. Another displacement curves that have two linear portions, these requirement was that the displacement transducers were to portions are named the front slope and the back slope. be placed between the bias flux plates within the magnetic Since this sensor was built in-house it proved to be quite bearings. The offset distance has a range from 40 to 80 mils. flexible. The sensitivity and linear range were easily This offset distance can vary depending upon the target adjustable to match the required specifications of the stack surface desired. The target surface for the displacement system. transducer can be the return ring, producing an offset Once all the displacement transducer’s sensitivities were distance of 80 mils, or can be a non-magnetic material calibrated to 60 volts per inch, further experiments on the inserted within the return ring to reduce the offset distance sensors were performed to reveal if these sensors could to approximately 40 mils. The maximum diameter the function on the inside of a magnetic bearing. The first displacement transducer can have is equal to the height of experiment that was performed on all displacement the permanent magnets minus some nominal distance for transducers was to substitute one of the displacement mechanical fixturing. The permanent magnet height for the transducer being tested with an existing Kaman KD-2400 4“ magnetic bearing is 0.300 inches. Since the displacement inductive sensor in an existing magnetic bearing. All of the transducer will be lodged inside of the magnetic bearing, the displacement transducers passed this test except for the transducers must have the ability to withstand large SPOT optical transducer. The SPOT displacement magnetic fields. transducer failed the test because of the target’s non- uniform surface reflectivity. The target in this case was the 3.2 7’ransducer Testing outside surface of the magnetic bearing system’s flywheel which is constructed of aluminum. The problem of non- The experimental testing of each displacement transducer uniform surface reflectivity was documented in figure 7. was separated into two parts. The first consisted of voltage This figure displays the voltage output of the SPOT and output of the transducer versus target displacement testing Kaman KD-2400 transducers versus time for a flywheel and the second dealt with performing experimental tests speed of 100 rpm. The peak to peak displacement of the using the displacement transducer in an actively controlled Kaman KD-2400 sensor was approximately 0.05 volts, which magnetically suspended flywheel system. translates at 60 volts per inch to 0.8 mils. The peak to peak Two different model sensors (KD-2400 and the KD-2300- displacement of the SPOT sensor was approximately 0.14 1SU) were tested from Kaman Instrumentation volts or 2.3 mils. In an attempt to eliminate the non-uniform Corporation of Colorado Springs, CO. The KD-2400 sensor surface reflectivity problem, different colored target was an inductive type sensor and was the sensor used in all surfaces and polished target surfaces were utilized. All 1487 Page 979 these types of surfaces did not correct the problem. For this From the previous experimental work, it was concluded that reason the SPOT sensor was dropped from further the displacement transducers presently available could not consideration. be adapted to the inside of a magnetic bearing. Inductive All the inductive sensors passed the suspension test. To sensors will not work because of the alternating magnetic conduct further experiments it was necessary to design and fields, capacitive sensors have problems with static electric fabricate a mechanical fixture to house the displacement fields, and the optical sensors have problems with non- transducers within the magnetic bearing. Once the sensors uniform surface reflectivity. Optical sensors are relatively were placed in the magnetic bearing two experiments were new in the field of dynamic displacement sensing and with conducted, a voltage output versus displacement time could function on the inside of a magnetic bearing. experiment and a suspension test. The voltage output Presently at the University of Maryland, we are developing versus displacement test was conducted using both the two transducers, one an optical sensor and the other an Scientific Atlanta and Kaman KD-2300-1SU sensors. For inductive type sensor. Both of these sensors have overcome this experiment, an aluminum ring had to be placed on the the related problems, such as non-uniform surface inside of the return ring to provide the sensors with an reflectivity and varying magnetic fields. We have successfuly aluminum target to detect. Figure 8 shows the curves suspended a flywheel via a magnetic bearing with the optical created by the Scientific Atlanta sensor. There are three sensor and are in the process of proving the inductive curves in figure 8, one curve for no current applied to the sensor. Results of these sensors will be presented in the EM coils and two curves with different currents applied to near future. the E M coils. These three curves show that an inductive sensor can still function within a static magnetic field. For 3.3 Adaptation of Transducers to Stack System both the Kaman and Scientific Atlanta sensors the sensitivity of the sensor decreased once inside the magnetic The ultimate design of the 500 WH energy storage stack bearing. This change in sensitivityw as due to the large system requires flywheel rotational speeds of 80,OOO rpm. magnetic fields originating from the magnetic bearing. The At these rotational speeds, the flywheel will experience a sensors were recalibrated to 60 volts per inch for the next radial growth of 8 to 9 mils at the inner diameter of the test of suspension with the inside sensor. The flywheel was flywheel or at the air gaps of each magnetic bearing. rotated to a low speed of a few hundred revolutions per Current magnetic bearing designs utilize a single minute and the output signals from the Scientific Atlanta displacement transducer per axis. This arrangement and Kamna KD-2400 sensors were compared. The functions properly until the flywheel grows radially. Upon Scientific Atlanta sensor was tested on the inside of the radial growth the sensor detects a false displacement and magnetic bearing and the voltage output of this sensor was relays this deceitful displacement to the control system. compared to the voltage output of one of the Kaman KD- Therefore an arrangement of two displacement transducers 2400 sensors, which was used to suspend the flywheel. The per magnetic bearing axis is necessary. The two output signal of the Scientific Atlanta sensor did not match displacement transducers per magnetic bearing axis are the signal produced by the Kaman sensor. The reason why organized in a differential arrangement. This differential these two graph do not correspond was because the arrangement will also eliminate all environmental errors Scientific Atlanta sensor was affected by the dynamic produced, such as temperature, pressure, and radiation. magnetic fields produced when the magnetic bearing was The current stack system design will only experience actively suspending the flywheel. To confirm this hypothesis rotational speeds of 30,000 rpm and a maximum radial a second experiment was run. This experiment produced a growth of 5 to 6 mils. For these reasons this stack system strong alternating electromagnetic field directly in front of will only utilize one sensor per magnetic bearing axis. The the Scientific Atlanta sensor. The sensor was fixed relative compensation for radial growth of flywheel was to the target which was the iron pin at the center of the EM accomplished through an electronic circuit. A block coil. The output of the sensor was monitored and found to diagram of the circuit can be seen in figure 9. The vary although the sensor and target were fixed. This test displacement of the flywheel detected by the displacement concluded that inductive sensors were affected by varying transducer can be separated into two signals, one signal magnetic fields and could not be utilized within the represented by di and the other by the oscillatory signal dt. magnetic bearing. This test was also conducted on the The signal, di, is comprised of the radial growth, gi, of the Kaman and Bently Nevada sensors and similar results were flywheel plus the original offset distance which is equal to obtained. Vref. The oscillatory signal, dt, is first eliminated and then 1488 Page 980 the original offset, Vref, is substracted from di to eliminate 5. Khan, A.A., "Maximization of Flywheel Performance", the radial growth, gi, from the feedback signal of the control M.S. Thesis, University of Maryland, 1984. system. 6. Gauthier, M., and Roland, J.P., "State of the Works Performed by Aerospatiale in Kinetic Energy Storage 4. Conclusions and Recommendations and Associated Fields", Proceedings of the 23rd Intersociety Energy Conversion Engineering With all of the stack system's components, such as the motor Conference, July 31-August 5, 1988, Denver, Co., Vol. generator and touchdown bearings, designed and selected, 2, pp. 105-110. the final stack system design was completed. All of the STATOR STACK internal stack system parts, such as the motor generator and the touchdown bearings, are assembled with locational type fits. The two magnetic bearings are compressed via the outside structure. This compression stiffens the stator portion of the stack system and increases the robustness of the stack system. Several different technologies were brought together to construct this energy storage stack system. A brushless dc motor generator was incorporated into the stack system, enabling experimentation at high rotational speeds. The mechanical fixturing of the individual magnetic bearings and the stiffening of the overall structure provided for a stack system with increased robustness. Although the non-contacting displacement transducers would not operate on the inside of the magnetic Figure 1. Magnetic Bearing Stack System bearings, current work with optical and inductive sensors appears promising. Some of the future work on this stack flywhccl Material: 6(HI-T6A luminum system will include, dynamic balancing of the flywheel while flywheel ID: 4 5W suspended magnetically, energy storage cycle testing, and Flywhscl OD. 6.RW high speed testing. flywheel Height 6.414' flywheel Weight 12.83 Ibr 5. Acknowledgement Arr Gap GroMh'. 0.MIV @ 14,732 rpm Air Gap Growth'. 0.0057" @ 29,465 rpm This work was supported in part under NASA grant NAG- Alr Gap Growih.. 0.01111" @ 39.287 rpm 5-396. The helpful discussions of G.E. Rodriguez of * NASNGSFC and P. Studer of TPI, Inc. are greatly Au Gap Growth IS the amount of flywheel expansiona t the air gap. which IS the reparation berwccn the stator and rftum ring of the mapcric kanng. appreciated. Figure 2. Flywheel Parameters for Stack System 6. References Plant, D.P., "Prototype of a Flywheel Energy Storage System", M.S. Thesis, University of Maryland, 1988. ' I 'YIX of Sensor Advantnccr I>lci,d"elllnees Jeyaseelan, M., "A CAD Approach to Magnetic Bearing Design", M.S. Thesis, University of Maryland, 1988. Kirk, J.A., "Flywheel Energy Storage Part I - Basic Concepts", International Journal of Mechanical LDur Frequency Response Cost "Strry Cnpacllance Sciences, Vol. 19, No.4, 1977, pp. 223-231. Huntington, R.A., "Stress Analysis and Maximization Opltcal 100 K H z Frcl aucnzcey R crpanre Surface Rcflectiviry of Performance for a Multiring Flywheel", M.S. Thesis, LCl"oesat r University of Maryland, 1978. Figure 3. Sensor Advantagers and Disadvantages 1489 1 I Page 981 K a m a n KD-2400 S e n s o r 0.a 0.m - 0.76. - 0.72 -~ 0.7 - 0.68 - 0.66 - 0 M 40 60 M m.phccment (d.) 0 .1urmnumtu*t Figure 4. Kaman KD-2400 Sensor Figure 7. ReflectivityT esting of SPOT Sensor K a m a n KD-2300-1SU S e n s o r SC'II:N'I'IYIC A'I'LAN'I'A IN 4" volt.- output v. mmp.cc-mt a . U,,,R" - 3 0 -10 IO 30 DISPLACEMENT (mi ls) Figure 5. Kaman KD-2300-1SUS ensor Figure 8. Sensor Inside Magnetic Bearing I RI md; V ref o n 1 n o 6 o n 8 o r 0 1 2 O I I 0 1 s 0 1 8 0 2 RANGE DlSPUCEHENT (INCHES) Figure 6. SPOT Sensor Figure 9. Air Gap Growth Compensator 1490 Page 982 PROCEEDINGS OF NSF DESIGN AND MANUFACTURING SYSTEMS CONFERENCE Arizona State University Mechanical and Aerospace Engineering Department Tempe, Arizona January 8-12, 1990 Conference Organizer M. C. Shaw Professor of Engineering Arizona State University Sponsored by Published by National Science Foundation Society of Manufacturing Engineers Design and Manufacturing Systems One SME Drive Engineering Division PO Box 930 Washington. DC 20550 Dearborn, Michigan 48121 Page 983 MAGNETIC BEARING SPINDLE CONTROL IN MACHINING J.A.Kirk D.K.Anand M. Anjanappa E. Zivi M. Woytowitz Department of Mechanical Engineering The University of Maryland College Park, MD 20742 ABSTRACT This paper reports on the final year program of a three year grant to the University of Maryland to utilize a magnetic bearing spindle to minimize tool path error in machining. A Magnetic bearing spindle and controller, with its unique features, retrofitted to existing machine tools, has been shown to minimize tool path error while maintaining high metal removal rate. A general and flexible accuracy enhancement methodology has been formu- lated, implemented and demonstrated. It was shown that the hierarchical control structure, using active magnetic bearing spindle, is an effective method for compensation of tool path errors. This research work is a cooperative effort between the University of Maryland, Magnetic Bearing Incorporated, The Westinghouse Corporation, and the David Taylor Naval Research Center. INTRODUCTION A Magnetic bearing spindle, with its unique features, retrofitted to existing machine tools, provides a solution to minimize the tool path error while maintaining high metal removal rate in thin rib machining. The work reported in this paper shows that by using error maps and spindle control [o f a Matsuura-S2M system] that tool path error minimization is both practical and achievable. The following tasks defines the scope of the project: • Develop a test facility by retrofitting CNC Machining center with a magnetic bearing spindle. • Generate deterministic (static and dynamic) tool path error maps using laser metrology. • Develop and implement a methodology for controlling a magnetically suspended spindle to minimize tool path error. • Experimentally test and validate the control system and algorithm using the University of Maryland test facility. Page 984 Earlier work [1-10] has already reported the details of analytical development of the methodologies used for error map creation and control of deterministic and stochastic errors. This paper presents a brief discussion of the above tasks and the results obtained. TEST FACILITY In order to develop an error minimization controller, first of all, a CNC machine fitted with a magnetic spindle is needed. In addition, such a system must provide an user interface where the user can tap into the current status of the machine and be able to command the translation and tilt of the spindle rotor on-line and in real time. Since, no such system is available, the University of Maryland has retrofitted an S2M-B25/500 magnetic spindle to an existing Matsuura MC500 CNC machining center. · Mechanical retrofitting work required several modifications to the original machining center. It required disassembling the conventional spindle head from the machining center, cut off the existing spindle casting to leaving only the guide ways intact and then mount the new magnetic spindle in its place. Electrical interfacing required for the active magnetic bearing (AMB) error correction methodology involves the interaction and coordination of four independent controllers: • Existing CNC controller, • Active magnetic bearing controller, • Variable speed spindle drive, • Online error minimization controller. While the existing Matsuura MC500 Yasnac CNC 3000G controller was retained, the latter three controllers were installed as part of the active magnetic bearing retrofit. The details of this work is reported in (11,12]. DETERMINISTIC TOOL PATH ERROR MAP Previous research suggests separating errors as either cutting force independent (CFI) or cutting force dependent (CFD). CFI errors are those errors that occur in the absence of metal cutting (i.e., dry run) while CFD errors can be directly linked to the metal cutting. Determinis- tic tool path errors, for the purposes of this research, are classified as shown in Fig. 1. The non-deterministic errors (such as errors due to chatter) are not considered here. The CFI error classification has been reported before in [1] and it is very much similar. The CFD error classification, however, is chosen based on the most frequent errors in the machined part. Geometric Position Errors The CFI geometric position errors associated with the motion of the table by the drive system along each axis can be represented in the form of an error matrix following the methodology in [13]. Four types of measurements were conducted, viz, Axial Position, Straightness, Angular, and Squareness to obtain all the seven error terms. Each error term was measured at one inch increments of table motion at five commonly used feed rates (10, 30, 50, and, 100 ipm. and Rapid) in positive and negative directions. 2 Page 985 i Deterministic Error Classification~ I 1 1 !cutting Force Independent I !cutting Force Dependent! I I I 1 I I Thermal Loading static Loading Dynamic Loading Static & (temperature change (position & weight (acceleration & Dynamic Loading dependence) dependence) retardation (cutting process dependence) dependence) I I I I l I CONTROLLER TRANSIENT & THERMAL DEFORMATION STATIC/GEOMETRIC OVER-SHOOT & STEADY STATE RAMP ERROR ERROR UNDER-SHOOT TRAJECTORY ERROR ERRORS ERROR 1 GEOMETRIC POSITION ERROR ~ Fig. 1 Deterministic Error Classification II 100 ipm 0 JO ipm Error (Mils) + 50 1pm 0 10 ipm ;ii. RAPID ·1.Z Machine Position (Inches) Fig. 2 Axial Position Error of X-Axis 3 Page 986 Figure 2 shows a typical plot obtained for the average Axial Position errors along the X-axis { o x(x)} for the traversing of the machine's table at five feed rates in the negative direction. The errors show a strong dependence on position and feed rate. The standard deviations of the errors at each position are approximately an order of magnitude less than the errors themselves. If one was to measure the errors at only one feedrate, the resulting information would not necessarily be valid at other feedrates thereby corroborating the fact that dynamic error map is essential. The recorded error terms are then analyzed and reduced resulting in a geometric position error map. For more details on the measurement results the reader is referred to (11]. Thermal Error The thermal deformation of the machine tool structure results in a net displacement of the tool relative to the workpiece. The deformations experienced by spindle head due to thermal shock primarily due to cooling water and air circuits proved to be very large. However, the thermal study is not reported here since this problem, was eliminated by redesign of the spindle cooling system. The remaining thermal error is the gradual ( quasistatic) thermal deformation of the machine tool. Several "recovery from cool down" tests were conducted for the Y-axis and Fig. 3 shows a typical error plot obtained. In these tests the deformation of the headstock varied linearly with respect to temperature. A magnetic bearing spindle error minimization controller can use the thermal deforma- tion model of linear deformation to correct for the errors produced by quasistatic temperature change. -o.oooz ·0.0006 -o.oooa II Bulk Spindle Temp. oetorma.tion (inches) ·0.001 0 Ambient Machine Temp. -0.00IZ ·0.0014 ·0.0016 ·O ,0018 Temperature (Cl Fig. 3 Thermal Deformation along Y-Axis. 4 Page 987 Ramp Error One deterministic CFD error encountered in thin rib machining is ramp error. Ramp error is the result of the deflection of a compliant work piece by cutting forces and is defined as the difference between the thickness at the top and the thickness at the bottom of a thin rib (14], which is often encountered in the manufacture of microwave guides. Since the geometry of the work piece is known, it is possible to relate the ramp error to the forces imparted by the cutter. As a first iteration of Ramp error identification, several thin rib test parts were produced on the Matsuura/S2M machine and on a conventional spindle Matsuura MC-510V milling machine. Figure 4 presents the results of the part metrology. The errors produced by the magnetic bearing spindle have a larger scatter than those produced by the conventional bearing spindle. This large scatter can be linked to the stiffness of the magnetic bearings. Improving bearing stiffness is one way to improve the performance. Table 1 provides a summary of deterministic tool path errors examined and more details can be found in [14]. The error map and the results oframp error investigation is implemented for error minimization purposes. Ramp Error for 20 Mil Rib ( Down Milling. 1/2" endmill) 0,01 D -· 0.009 D O.OOB El D 0.007 D D El 0,006 D 8 lltonventlonol Bearing Error (Inches) o.oos 0Nagnetlc: Dearing 0.004 ! 11111 O.OOl 0 11111 0,002 l1lil ! 0.001 1111 11111 11111 0 0 10 20 30 40 50 60 TO 80 90 100 Feedrate (ipm.) Fig. 4 Thin Rib Ramp Error (Down Milling) 5 Page 988 t)agnitude l:Ll.n.imization Strategy Y-axis Thennal Thennal Shock 3.0 mils Error Avoidance by Deformation Error redesign of spindle cooling system Quasistatic 2.0 mils Error Compensation Thennal loading using linear model X-axis Thennal Thermal Shock & Negligible N/A Deformation Error Quasistatic Geometric Position Geometric errors 1.5 mils Error Compensation Error (X & Y axes) in machine elements using matrix look-up t Servo Control tables errors Thin Rib Ramp Error Work piece 6.0 mils compliance due to (with large N/A cutting forces scatter) Thick Rib Ramp Error Tool compliance 0.5 mils due to cutting N/A forces CONTROL METHODOLOGY AND IMPLEMENTATION The robust controller uses cutting force (from built-in sensors on the magnetic bearing spindle) and the error map as input, and generates a displacement bias for the magnetic bearing spindle as output. The bias, which is proportional to the tool path error at any given tool position, is used to translate and tilt the spindle to minimize the tool path error. Central to this research, is the implementation of the error minimization controller. The basic elements of the accuracy enhancement retrofit are depicted below the dotted line of the simplified control system block diagram given in Fig. 5. The theoretical development neces- sary to support the derivation of the robust, multivariable controller has been previously reported [1]. The input parameters investigated include: • X, Y, Z axis position, • X, Y, Z axis velocity commands, • X, Y, Z axis servo Jag, • Spindle displacement and bearing forces, • Thermal conditions. Implementation of the error compensation methodology also requires mechanisms to coordinate and sequence CNC and error minimization controller operations. The present approach involves the down loading of the part program, in M & G codes, to both the CNC and error minimization controllers. ln this scenario, the CNC and error minimization control- ler execute the same part program simultaneously. This allows the error minimization (, Page 989 NOTE: X ~ Y-AXIS LOOPS m!ITTED Fon BREVITY Z--AXIS DC Z--AXIS OPTICAL r- ,--- • • • SERVO/DRIVE .\10\T.\IE\'T ENCODER X, Y, Z, COllfMA:NDED POSJTIOX :'-T\IERJCAL CO.\IPUTER POSITIOK FEEDBACE co:,TnOL ----< Kl'MERICAL CODE E:\1STJ\ G \1.KHI\T ------ EA\CHC.;r\nC .. iD..cY!E :,T L ~---~ FORCE\"SG ERROR l\L.\G:NETIC 1IAG?\ETIC .\!I\I.\IJZATIO:N ==) BEARIKG ==) SPI\DLE - CO\TROLLER COKTROLLER /\ ERROR .\!AG\ETIC THER\l..\L ====::::.:::'i_,1 CORRECTIOJ\ SCSPE:\"SIOK D.-\T.-'. FORCES:. DISPLACD.JE\T CCTTI\G FEEDBACE COKDITIONS Fig. 5 Prototype Error minimization control structure controller to cooperate with the existing CNC controller and completely defines the desired tool trajectory. The error minimization controller implementation is performed using an IEEE 796 (Multibus) based computer system. This system utilizes an Intel 386/387 processor pair and executes the Intel RMX II operating system. EXPERIMENTAL VALIDATION Evaluation of the error minimization capabilities of the magnetic spindle retrofitted Matsuura MC500 has been performed by comparing the dimensional accuracy of a sequence of sample parts. This sequence uses the MC500, with no error correction, as the baseline with which to evaluate various error map formulations and control system implementations. The details of experimental results will be reported soon. 7 Page 990 CONCLUSION From the experimental results, the following conclusions could be drawn; • Three classes of errors, viz, thermal, geometric and ramp errors are identified and investigated. It is observed that the largest errors identified are ramp errors, in case of thin rib parts, and that all the deterministic errors identified could be compensated using a magnetic bearing spindle in conjunction with an error minimization controller. • Magnetic bearing spindles can provide simultaneous high speed, error compensation, and process monitoring capabilities. • A general and flexible accuracy enhancement methodology has been formulated, implemented and demonstra~d. • The hierarchical control structure, using a AMB spindle, is an effective method for compensation of machining dimensional errors. • The current spindle bandwidth of 125 Hz is adequate to compensate dynamic tool path errors. • At conventional cutting speeds, the low dynamic stiffness, of the S2M AMB spindle significantly limits accuracy and stability. • Based on the facility and control structure established herein, considerable future qualitative improvements should be possible with metrology and AMB spindle enhancements. • A second generation spindle design, which includes advanced control concepts could provide significant stability and performance improvements. ACKNOWLEDGEMENT The research work reported in this paper represents a cooperative activity of the personnel from the University of Maryland, the National Institute of Standards and Technology [formerly the National Bureau of Standards], the Westinghouse Corporation, the David Taylor Naval Research Center and the Magnetic Bearing, Inc. This work has been supported by the National Science Foundation through grant NSF 8516218 the Engineering Research Center at the University of Maryland and ONR Program Element 61152N through the David Taylor Research Center. REFERENCES 1. Anand, D.K., Kirk, J.A., Anjanappa, M., Zivi, E., and Woytowitz, M., "Magnetic Bearing Spindle Control", Proceedings of 15th Conference on Production Research and Technology, pp.31-35. 2. Anjanappa, M., Anand, D.K., Kirk, J.A., and Shyam, S., "Error Correction Methodologies and Control Strategies for Numerical Controlled Machining", Control Methods for Manufacturing Processes, ASME Publication DSC-Vol. 7, ASME WAM, 1988, pp.41-49. 3. Kirk, J.A., Anjanappa, M., and Anand, D.K., "Validation of a Relationship Between Cutting Force and Surface Finish for Optimal Control of End Milling", Modeling and Control ofR obotic Manipulators and Manufacturing Proce,\:s·es, ASME Publication DSC VOL.6, ASME WAM, 1987, pp.25-3'.:l 8 Page 991 4. Anjanappa, M., Anand, D.K., and Kirk, J .A., "ldentification and Optimal Control of Thin Rib Machining", Modeling and Control of Robotic Manipulators and Manufacturing Processes, ASME Publication DSC VOL.6, ASME WAM, 1987, pp.15-24. 5. Anjanappa, M., Kirk, J.A., and Anand, D.K., "An Algorithmic Relationship Between the Cutting Force and Surface Texture in Machining Processes",proceedings of 17th IASTED International Conj., pp.18-21, 1987, New Orleans, LA. 6. Anjanappa, M., Kirk, J.A., and Anand, D.K.,"Tool Path Error Control in Thin Rib Machining", Proceedings of 15th NAMRC, Bethlehem, PA, 1987, pp.485-492. 7. Kirk, J.A., Anand, D.K., Anjanappa, M., and Shyam, S., "Accuracy Enhancement Methodologies in Thin Rib Machining", proceedings of 14th NSF Conference on Production Research and Technology", Ann Arbor, MI, 1987, pp.9-14. 8. 'Tool Path Error Control for End Milling of Microwave Guides", Proceedings of 7th TVorld Congress on the The01y of Machines and Mechanisms, Sevilla, Spain, 1987, Vol.3, pp.1499-1502 (with D.K. Anand and J.A. Kirk). 9. Anand, D.K., Kirk, J.A., and Anjanappa, M., "Magnetic Bearing Spindles for Enhancing Tool Path Accuracy",Advanced Manufacturing Processes, Vol. 1, No. 1, pp. 121-134, 1986. 10. Kirk, J.A., Anand, D.K., Anjanappa, M.,"Magnetic Bearing Spindle Control in Machining", Proceedings of 13th NSF Conference on Production Research and Technology, Gainesville, Florida, 1986, pp.127-130. · 11. Woytowitz, M.A., ;'Tool Path Error Classification and Identification for High Precision Milling with a Magnetic Bearing Spindle", M.S. Thesis, The University of Maryland, 1989. 12. Zivi, E., "Robust Control of Magnetic Spindle for Error Compensation", Ph.D., Thesis, The University of Maryland, 1989. 13. Shyam, S., "Error Compensation for Accuracy Enhanced Precision Machining", Masters Thesis, University of Maryland, College Park, 1987. 14. Woytowitz, M., Anand, D.K., Kirk, J.A., and Anjanappa, M., 'Tool Path Error Analysis for High Precision Milling With a Magnetic Bearing Spindle", To be presented at the 1989 ASME-WAM. 9 Page 992 PROCEEDINGS OF THE SECOND INTERNATIONAL SYMPOSIUM ON MAGNETIC BEARINGS SEIKEN SYMPOSIUM JULY 12-14, 1990 TOKYO, JAPAN Edited by Prof. T. Higuchi Sponsored by Institute of Industrial Science, University of Tokyo Page 993 TABLE OF CONTENTS A Low Noise Magnetic Bearing Wheel for Space Application........................................ 1 U.J. Bichler Teldix GmbH(GERMANY) Development of Magnetically-suspended, Tetrahedron-shaped Antenna Pointing System··············································································································· 9 T. Higuchi*, H. Takahashi**, K. Takahara**, and S. Shingu** *University of Tokyo arid **Toshiba Corporation(JAPA N) A Digital Time Delay Controller for Active Magnetic Bearings...................................... 15 K. Youcef-Toumi, S. Reddy and I. Vithiananthan Massachusetts Institute of Technology(USA) Self-tuning Digital State Controller for Active Magnetic Bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 M. Brunet and J. Rioland S2M(FRANCE) Digital Control System for Magnetic Bearings with Automatic Balancing.................. . . . . . . 27 T. Higuchi*, T. Mizuno**, and M. Tsukamoto*** *University of Tokyo, **Saitama University and ***Asahi Chemical Industry Co., Ltd.(JAPAN) The Industrial Applications of the Active Magnetic Bearings Technology........................ 33 M. Dussaux Societe de Mecanique Magnetique(FRANCE) Testing of a Magnetic Bearing Equipped Canned Motor Pump for Installation in the Field .................................................................................................................. 39 J. Imlach*, R.R. Humphris••, B.J. Blair**, and P.E. Allaire** *Kingsbury Inc. and **University of Virginia(USA) Experience with Magnetic Bearings Supporting a Pipeline Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . 47 J. Schmied Sulzer Escher Uyss Ltd.(SWITZERLAND) Loading Test in an Air Turbine Borne by Active Magnetic Bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 T. Inoue, M. Takagi, 0. Matsushita, and R. Kaneko Hitach~ Ltd.(JAPAN) Magnetic Suspension for a Turbomolecular Pump . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .. . .. 65 G. Genta•, L. Mazzocchetti**, and E. Rava** *Politecnico di Torino and **Elettrorava S.pA.(ITALY) Application of Magnetic Bearings in a Multistage Boiler Feed Pump · · · · · ·....................... 73 G. McGinnis*, P. Cooper•, G. Janik .. , G. Jones**', and R. Shultz***• *Ingersoll-Rand Company, **New York State Electric and Gas, ***Gas-Cooled Reactor Associates, and ****Magnetic Bearings, Jnc.(USA) Active Magnetic Bearing Performance Standard Specification · · · · · · · · · · · · · · ·............ . . . . . . . . . . . . 79 M. Swann ands W. Michaud Magnetic Bearings, Inc. (USA) iii Page 994 The MALVE Experimental Circulator - The First Large Nuclear Component with Active Magnetic Bearings ........................................... · .......................... · ....... · · · .. · · · 87 P. Biihrer, J. Engel, and D. Glass ABB Kraftwerke AG(GERMANY) Application and Working Characteristics of HTGR Components Test Machines with Magnetic Bearings . . . . . . . . . .. . . .. . . . . . . . . . .. .. . . . . . . . . . . . . .. . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . .. . . . . . . . . . . . . .. . . . . . 93 H. Shimomura, S. Kawaji, and Y. Ohta Japan Atomic Energy Research Institute(JAPAN) An Applicaion of Magnetic Bearings to Titanium Powder Production · · · · · · · .. · · · ... · · ·,. · · ·. · · · · 101 T. Kimura and T. Negishi Mitsubishi Metal Corp. (JAPAN) Mag-lev Semiconductor Wafer Transporter for Ultra-high-vacuum Environment ..... 109 (Application Development of Active Magnetic Bearing) M. Ota, S. Andoh, and H. Inoue Seiko Seiki Co., Ltd., (JAPAN) Development of an Actuator for Super Clean Rooms and Ultra High Vacua ................... 115 T. Higuchi•, A Horikoshi• •, and T. Komori • • *University of Tokyo and **Nippon Seiko K.K.(JAPAN) Robust Magnetic Bearings for Flywheel Energy Storage Systems .................................. 123 RB. Zmood* ••, D. Pang••, D.K. Anand .. , and J.A Kirk** *Royal Melbourne Institute of Technology (AUSTRALIA) and **University of Maryland(USA) Design and Testing of a Flexible Rotor - Magnetic Bearing System ........................ ··.,··· 131 M. Hisatani, S. Inami, T. Ohtsuka, and M. Fujita Mitsui Engineering and Shipbuilding Co., Ltd.(JAPAN) Rotor Vibration Simulation Method for Active Magnetic Control .................................. 139 0. Matsushita, T.Yoshida and N. Takahashi Hitachi, Ltd. (JAPAN) Vibration Control of Magnetically Suspended Flexible Rotor by the Use of Optimal Regulator ..................................................... , ....... · · ·. · · · · · · · · · ·,, · · ·,, · · ·, ·, · · ·, · · · ·, · · · · · · · · · · 147 S. Akishita*, T. Morimura•, and S. Hamaguchi** *Ritsumeikan University and **NTN Corp.(JAPAN) Active Vibration Control of Flexible Rotor for High Order Critical Speeds Using Magnetic Bearings ............ , , · .. , · · ·,, · · ·, · · · ·, · · · · · · · · · ·, · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·, · · · · · · · · · · 155 K. Nonami and H. Yamaguchi Chiba University(JAPA N) Vibration Control of a Large Turbogenerator by Electromagnetic Dampers,·,·· .. , ............ -161 Chan Hew Wai C. Electricite de France(FRANCE) The Control of Propeller-induced Vibrations in Ship Transmission Shafts ...................... 169 J. Darling and C.R. Burrows University of Bath(UK) Permanent ~agnet Biased Magnetic Bearings - Design, Construction and Testing .......... 175 C.K. Sortore•, P.E. Allaire••, E.H. Maslen**, R.R. Humphris**, and P.A Studer••• *Aura Systems, **University of Vzrginia, and ***Magnetic Concepts(USA) IV Page 995 Single Axis Active Magnetic Bearing System with Mechanical Dampers for High Speed Rotor··· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·. · ...... · · · ·. · ............ · · · · · · ......................... 183 M. Miki, Y. Tanaka, Y. Yamaguchi, T. Ishizawa, and A Yamamura Nippon Ferrofluidics Corp.(JAPAN) Using High-speed Electrospindles with Active Magnetic Bearings for Boring of Non- circular Shapes · · · · · · · · · · · · · · · · · · · · · · · · · · .. · · · · · · · · · · · · · · · · · · · · · · · · · · .............. · · · · · · · ..... ·. · · · · · · · · · ........ 189 B. Moller GMN Georg Muller Nilmberg AG(GERMANY) Design and Performance of a High Speed Milling Spindle in Digitally Controlled Active Magnetic Bearings · · · · · · · · · · · · · · · · · ..................................................................... 197 R. Siegwart•, R. Larsonneur•, and A Traxler•• *ETH Zurich and **Mecos Traxler AG(SWI1ZERLAND) Monitoring and Actuating Function of the Internal Grinding Spindle with Magnetic Bearing · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 205 M. Ota, S. Ando, and J. Oshima Seiko Seiki Co., Ltd.,(JAPAN) Switching Amplifier Design for Magnetic Bearings ..................................................... 211 F.J. Keith, E.H. Maslen, R.R. Humphris, and R.D. Williams University of Vuginia(USA) Problems, Solutions and Applications in the Development of a Wide Band Power Amplifier for Magnetic Bearings · · · · · · ·.,. · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·· · · · · · · · · 219 T. Bardas*, T. Harris*, C. Oleksuk*, G. Eisenhart**, and J. Geerligs**, *Nova Corporation of Alberta and **Nova Husky Research Corporation(CANADA) Cost-effective Implementation of Active Magnetic Bearings · · ·. · ..................................... 229 D. Zlatnik and A Traxler ETH Zarich(SWI1ZERLAND) Iron Losses and Windy Losses of High Rotational Speed Rotor Suspended by Magnetic Bearings ............................................................................................... 237 H. Ueyama and Y. Fujimoto Koyo Seiko Co., Ltd. (JAPAN) Extreme Precision Magnetic Bearings for Linear and Rotary Applications ...................... 243 D.B. Eisenhaure•, J.R. Downer•, R.L. Hockney•, E.G. Johnson•, V.Gondhalekar*, M. Gerver*, K. Misovec•, M. Gaffney•, and A Slocum** *SatCon Technology Corporation and **Massachusetts Institute of Technology(USA) Performance of the Active Magnetic Bearings ............................................................ 251 Z. Cai*, Z. Zhang**, and H. Zhao• *Tsinghua University and **Beijing Management Institute of Machinery Industry(CHINA) Application of Periodic Learning Control with Inverse Transfer Function Compensation in Totally Active Magnetic Bearings ..................................................... 257 T. Higuchi•, M. Otsuka*, T. Mizuno**, and T. Ide*** *University of Tokyo, **Saitama University, and ***Fuji Heavy Industries Ltd.(JAPAN) Real Time Balancing of a Flexible Rotor Supported by Magnetic Bearing ...................... 265 Y. Kanemitsu, M. Ohsawa, and K. Watanabe Ebara Researc~ Co., Ltd.(JAPAN) Modeling and Control of Magnetic Bearing Systems Achieving a Rotation Around the Axis of Inertia ........... · · · · · · · · · · · .. · · · · · · ·. · .. · · · · · · · · · · · · · · · · · · · · · ............................................. 273 F. Matsumura, M. Fujita, and K. Okawa Kanazawa University(JAPAN) V Page 996 Design of Magnetic Bearing Controllers Based on Disturbance Estimation ................ · ... 281 , T. Mizuno• and T. Higuchi*• : *Saitama University and **'University of Tokyo(JAPAN) A Decomposition of the Jeffcott Rotor .......................................................... · · · · · · · · · · · 289 D. Fermental, E. Cusson, and P. LaRocca The Charles Stark Draper Laboratory, Inc. (USA) Performance Comparison Between Centralized and Decentralized Control of the J effcott Rotor .... · ................................................................. , ............................... 295 P. LaRocca, D. Fermental, and E. Cusson The Charles Stark Draper Laboratory, Inc. (USA) A New Approach to Sensorless and Voltage Controlled AMBs Based on Network Theory Concepts .. · · · · ............................................. · ............ · · ·. · .. · .... · · · · · · .... · ... · · · · · · · · 301 D. Vischer and H. Bleuler ETH Ziirich(SWITZERI.AND) A Design Method of a Dynamic Compensator of Conical Modes for Magnetic Bearings of a Rigid Spinning Rotor ................................................................ ·. · ·. · .. 307 C. Murakami Tokyo Metropolitan Institute of Technology(JAPAN) Linear Compensation for Magnetic Bearings .................................................. · · · · · · · ·. · 311 S. Ishida Yaskawa Electric Laboratory(JAPAN) Flexible Shell Structured Rotor Controlled by Digital Magnetic Bearings (Transputer Control), ........... : ................................................................................................ 319 H. Zhang•, T. Nagata••, Y. Okada••, and J. Tani* *Toholal. University and **Ibaraki University(JAPAN) Stability Analysis for Rotors Supported by Active Magnetic Bearings ............................ 325 H.M. Chen, D. Wilson, P. Lewis, and J. Hurley Mechanical Technology Incorporated(USA) A Self-excited Vibration of Magnetic Bearing System with Flexible Structure , ................. 329 I. Satoh•, C. Murakami .. , A Nakajima***, and Y. Kanemitsu• *Ebara Research Co. Ltd., **Tokyo Metropolitan Institute of Technology, and ***National Aerospace Laboratory(JAPA N) On the Static Stability Problem of Magnetic Levitation from Rigid Body to Flexible Plate ................................................................................................................. 337 S. Morii, N. Kawada, K Katayama, and Y. Takahashi Mitsubishi Heavy Industries Ltd. (JAPAN) Stiff AMB Control Using an H'" Approach ....... , ........................................................ 343 R. Herzog and H. Bleuler ETH Ziirich(SWITZERLAND) H'" Robust Control Design for a Magnetic Suspension System ............................... , ... , . 349 M. Fujita, F. Matsumura, and M. Shimizu Ka.nazawa University(JAPAN) Application and Testing of Magnetic Bearings and Dry Gas Sealing in Axial Inlet Process Compressors ............................... ·. · · ... · ..... · ........... · .................................. 357 C.W. Pearson, H.J. Aarnink, J. Magee, and J.G.H. Derkink · Delaval-Stork(THE NETHERLANDS) vi Page 997 2nd International Symposium on Magnetic Beaino July 12-14, 1990, Tokyo, Japan " ROBUST MAGNETIC BEARINGS FOR FLYWHEEL ENERGY STORAGE SYSTEMS R.B. Zmood (l)(z), D. Pang (2) D.K. Anand (2), J.A. Kirk (2) (1) Department of Communication and Electrical Engineering, Royal Melbourne Institute of Technology, Melbourne, Victoria 3000, AUSTRALIA. (2) Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA. Abstract Magnetic bearings a.re an essential component of flywheel energy storage (FES) systems because of their very low frictional losses, and their extremely long expected operating lifetimes. In this paper recent work on the development of magnetic bearings for a 500 Wh FES system, which is to be used for low earth orbit space applications and is being constructed at the University of Maryland, is described. In this paper two aspects of magnetic bearings are discussed. The first is the design of bearing control systems which prevent large scale self-sustaining non linear oscillations from being established, while the second is the development of an improved inductive displacement transducer which differentiates between rotor growth and rotor displacement. be used for low earth orbit satellite applications is 1. Introduction described. Attention will be focussed upon the two aspects of bearing controller design and position transducer The use of magnetic bearings for flywheel configuration, both of which have a significant impact suspension in space-borne flywheel energy storage (FES) upon the robustness of bearing operation. applications has been studied by Kirk and Studer [1,21 where they have shown that they are essential for such systems to operate efficiently, because of their very low 2. Flywheel Design frictional losses, and their extremely long expected lifetimes. The 500 Wh energy storage system is based upon a 11 pancake 11 magnetic bearing stack as shown in Fig. 1. In At the University of Maryland design studies of 300 this arrangement two magnetic bearings are shown with and 500 Wh FES systems for spacecraft applications have one positioned at the top of the stack and the other at the shown it is important to ma,ximize the flywheel spec!fic bottom. Mounted between these two bearings is the energy density (SED), and a bench mark system design motor/generator which is used for converting mechanical goal of 20 Wh/kg has been set as it exceeds, by ~n into electrical energy and vice versa. It is a three phase acceptable margin, the 14 Wh/kg of electrochemical brushless D.C. machine having permanent magnets systems [3,4,5]. Because of the required SED advanced fibre-composite flywheels are needed, and it has been shown that these need to operate at high rotational speeds, in the range 33 oog to 66 000 rpm, s~ as to make effec.tive use of these matenals. These operatmg speeds necessitate placing the flywheel in a vacuum to minimize aero- The remaining possible arrangements can measure X the displacrnents in the bearing planes of symmetry provided it is assumed that the bearing actuators and the R R LOW PASS motor/generator a.re rigid bodies. For example, let us FILTER consider the alternatives shown in Figs. 6(b) and (c ) where fc = 20 kHz the inductive sense coils a.re shown by the arrowed bars in each case. From simple geometry the displacements .t1 and INDUCTIVE BRIDGE 1·~ can be calculated from measurements x1' and x2 ' and 1 for the case shown in Fig. 6(b) are given by Fig.7. Simplified schema.tic of inductive bridge trans cl ucers. and Heeding the observations made above about the use of stainless steel in the bodies of commercial inductive transducers, care was ta.ken to only use non-ferrous materials, such as aluminium, in the construction of the experimental sensors. Aluminium was also used for the When the sensors a.re inboard of the bearings the errors in transducer target. Experiments showed that using this the computation of xi and x2 due to uncertainties in 6.£ construction made the transducers insensitive to changes will be larger than for the corresponding outboard case. in external magnetic fields. However as long as 6.f/ ei s small the error in either case can be neglected and the computed values of .t1 and x2 can be used in place of their exact values in the respective 6. Concluding Remarks bearing controllers. Two aspects of magnetic bearings for flywheel . If the motor cannot be considered to be rigid then the energy systems which contribute to their robust operat10n arrangement shown in Fig. 6( d) needs to be used. Here have been considered. the sense coils A1, A2, coils A3, A4, coils B1, B2 and coils Ba, B4 are separately connected in series. Since these coils Firstly it ha.s been shown that bearing control are symmetrically displaced about the bearing planes of systems experience limit cycle oscillations if the actuator symmetry the transducer outputs will be x1 and x2, where coil inductances are too large. The analysis above shows that for the control system to be stable the control gain_ , + ratio Cx/ Ci must lie within upper _an_d lower boun~s which xa (4) xa2 X. -- 1 are determined from the charactenst1cs of the beanng 2 actuator. These bounds are particularly sensitive to . · ,. j and actuator coil inductance. These considerations profoundly influence the design methodology of the actuators. In the + new approach the coil ampere-turns for the actuator are ,·, (5) ~ = 21>1 21>2 determined as before from static force considerations. Now 2 however the coil inductance is determined from Eq. (1) so ., as to ensure adequate control system robustness, and from , The Inductive Sensor this the number of turns for the control winding can be . calculated. From the above information the peak actuator In Fig. 7 is shown a simplified schematic of the drive current is calculated and the sizing of the control i experimental inductive bridge transducer, which tan be winding amplifiers determined. This approach should be used in any of the mechanical arrangements shown in contrasted with the one previously followed, where the Fig. 6. The sensor inductors are connected in a Maxwell winding specifications and the amplifier si~es were largely impedance bridge whose ouput is fed to a synchronous determined from static considerations. Usmg the above demodulator. The output of the demodulator passes approach we have found that bearings operates quite through a low pass filter which filters the residual high robustly, can withstand large transient disturbances, and frequency modulation products as well as any extraneous are easily able to self-suspend. noise induced into the circuitry. The filter output i~ an analog signal whose malgnitude is proportional to the Secondly it has been shown that the use of displacment .t. To ensure good balance of the bridge differential position transducers enables the rotor . circuit special care needs to be taken to retain symmetry displacement to be differe1:,tiated from rotor radial &rowt? in all parts of the circuit; especially in the wiring of the As a consequence the bearmg control system operation wi 11 inductors. -128- Page 1003 be markedly less sensitive to disturbances due to rotor growth than when single-sensor displacement transducers 11. Zmood, R.B., et.al., "Non Linear Relaxation are used. Although inductive transducers can be sensitive Oscillati?ns in Magnetic Bearings". Under to external magnetic field, in most other regards they are preparat10n. much less sensitive to extraneous effects than capacitive and optical transducers. Experience has shown that if care 12. Plant, D.P., "Prototype of a Flywheel Energy is taken to avoid using ferro-magnetic materials (including Storage System", M.S. Thesis, University o( stainless steel) in their construction then magnetic effects Maryland, College Park, Maryland, 1988. can be minimized. These types of transducers are currently being included in the design of the 500 Wh 13. Plant, D.P., Kirk, J.A. and Anand, D.K. flywheel energy storage system. "P rototype of a Magnetically Suspended 'F lywheel Energy Storage System", Proc. 24th Intersoc. Energy Conversion Engrg. Conf., Washington, References D.C., August 6-11, 1989. · 1. Kirk, J.A., "Flywheel Energy Storage - Part I, Basic Concepts", Int. J . Mech. Sci., Vol. 19 (1977), pp. 223-231. 2. Kirk, J.A., and Studer, P.A., "Flywheel Energy Storage - Part II Magnetically Suspended Super-Flywheel", Int. J. Mech. Sci., Vol. 19 (1977), pp. 233-245. 3. Anand, D.K., Kirk, J.A., Frommer, D.A., "Design Considerations for a Magnetically Suspended Flywheel Systems", Proc. 20th Intersoc. Energy Conv. Engrg. Conf., Miami Beach, Florida, Aug. 18-23, 1985, pp. 2.449-2.453. 4. Anand, DJ(., Kirk, J.A. , Zmood, R.B., et.al., "System Considerations for a Magnetically Suspended Flywheel", Proc. 21st Intersoc. Energy Conv. Engrg. Conf., San Diego, Calif., Aug 25-29, 1986, pp. 1829-1833. 5. Kirk, J.A., Anand, D.I<., "Satellite Power Using a Magnetically Suspended Flywheel Stack", J. Power Sources, VoL 22 t}988), pp. 301-311. 6. Neimeyer, W.L., Design of a High Efficiency Motor for Flvwheel Energy Storage, M.S. Thesis, University of Maryland, College Park, Maryland, 1988. 7. Nei_n~eyer, W.L. , Zmood, R.B ., et.al., "A High Efficiency Motor/Generator for a Magnetically Suspended Flywheel Energy Storage System", Proc. 24th Intersoc. Energy Conv. Engrg. Conf., Washington, D.C., Aug. 6-11, 1989. 8. Zmood, R.B., et. al., "The Effect of Structural Vibrations on lVIagnetic Bearing Operation", Proc. 24th Intersoc. Energy Conv. Engrg. Conf., Washington, D.C., Aug. 6-11, 1989. 9. Lashley, C.M., et.al. , "Dynamic Considerations for a Magnetically Suspended Flywheel", Proc. 24th Intersoc. Energy Conv. Engrg. Conf., Washington, D.C., Aug. 6-11, 1989. 10. Zmood, R.B. , et .al., "The111Behavionr of Magnetic Bearings Subjected to Large Disturbances". Submitted for publication. -129- Page 1004 1 Adv. Manuf. Eng. Vol 2 October 1990 179 Characterization of errors for on-line correction with a magnetic bearing spindle M. ANJANAPPA, D. K. ANAND and J. A. KIRK This paper is concerned with the quality assurance, via characterization and on-line correction of tool path errors, in a CNC milling machine fitted with a magnetic bearing spindle. Two classes of tool path errors, viz, geometric position errors and thermal deformation errors are characterized and investigated. Characteristics of geometric position errors revealed that, generally, the magnitude of errors increased with feed rate. The ensuing results were used in a methodology by which on-line correction of errors, both static and dynamic, could be achieved. CNC machines fitted with magnetic bearing spindles proved to be ideal for on-line error correction by providing an additional level of control that has high resolution and wide bandwidth. Experimental results indicate that errors could be reduced by a factor of three to ten in normal machining conditions. Keywords: error characterization, on-line correction, magnetic bearing spindles, tool path errors The dimensional accuracy and surface finish of a enhancing tool path accuracy on a commercial CNC machined part is a function of tool path error. The tool machining centre. path error in NC machining is defined as the vector In general, the strategy of CFI error correction by difference between the required/programmed and pre-compensation methods discussed so far is based actual tool path 1 • The magnitude of the error is both on nullifying the effect of the error itself by algebraic deterministic and stochastic in nature since it depends summation of the programmed position input with the on both repeatable (static and dynamic) and random output of the error process model based on off-line (dynamic) parameters. measurements. The table movements of the machining Previous research 2•3 suggests separating errors as centre are used to correct the error. The post proc- either cutting force independent (CFI) or cutting force essed 'Miscellaneous' and 'Go' (Mand G) machine dependent (CFD). CFI errors are those errors that occur tool motion codes are intercepted before being down- in the absence of metal cutting (i.e., dry run) and are loaded to the machine controller, and processed repeatable. CFD errors, not considered in this work, through an error compensation algorithm based on a are directly linked to the metal cutting process. It is previously generated error map. The error compens- possible to compensate for the CFI errors, either by ated codes are then downloaded to the machining pre-compensation or by on-line error correction, if centre controller, which cuts the part more accurately. they can be characterized. This method assumes that the machining operation is Pre-compensation of tool path errors consists of single point cutting and only the point-to-point error is quantifying the errors committed by the tool and corrected. implementing compensation schemes before machin- In all this work, the effect of feed rate is removed ing begins. For example, Tlusty4 uses a semi-auto- by measuring the errors at low feed rates only in order matic master part (trace test) to measure errors. Dufour to remove the dynamic effects. Hence, these tech- et al. 5 use an error matrix of coordinate corrections to niques are not suitable for high feed rate machining, improve the accuracy of large NC machine tools. which is becoming the norm as new high speed Donmez6 refined this approach by implementing stat- spindles are introduced into the market. In addition, istical principles to determine the characteristics of not all CFI errors can be compensated for using the geometric positioning errors. This same methodology pre-compensation technique. For example, errors due has been applied by Zhang et al.7 to improve the to temperature changes cannot be compensated for accuracy of coordinate measuring machines at the unless there is a mechanism to sense the temperature National Institute of Standards and Technology. Anja- and then use an appropriate correction factor to nappa et al. 8 used the error matrix approach for compensate for the axis movements on-line. One such mechanism is the on-line controller for axis move- ments. M.A. is in the Department of Mechanical Engineering, University of Several investigators (for example References 2, Maryland-UMBC, Baltimore, MD 21228, USA. D.K.A. and J.A.K. are in the Department of Mechanical Engineering, University of Mary- 9-12) have developed on-line correction techniques land-UMCP, College Park, MD 20742, USA and found them effective for reducing machine tool 0951-5232/90/040179-10 © 1990 Butterworth-Heinemann Ltd Page 1005 180 M. Anjanappa et al - Characterization of errors for on-line correction errors. It must be noted that these methodologies are ID eterministic error classification developed to compensate on-line for both CFI and CFO errors combined without distinguishing the two. Among them, the methodologies developed in Refer- ' Cutting force Cutting •for ce ences 11 and 12 can be used for on-line correction of independent error I I dependent error CFI errors. However, these techniques have limited application in a commercial CNC machining centre since they either require attachment of delicate ¼ ' i Thermal loading Static loading Dynamic loading instrumentation or access to servo controllers of ma- ( temperature ( position and ( acceleration chines. In addition, the resolution and dynamics re- dependence) weight) dependence l quirement of such an on-line controller is beyond the dependence) hardware and software capability of commercial con- trollers. These reasons make this approach difficult, expensive, and hence, impractical for many applica- Thermal Static/ Overshoot and Transient and tions. deformation geometric undershoot steady state To overcome these limitations, a test facility has errors errors errors trajectory errors been set up, at the University of Maryland, by retrofit- ting a Matsuura MCSOOV vertical machining centre with an S2M B25/500 magnetic bearing spindle and is ' discussed in detail in Reference 13. Some unique IG eo11;e_tric I pos1t1on I features of the magnetic bearing spindle are: errors D Ability to translate the spindle shaft within air gap restriction (± 0.127 mm). Figure 1 Error classification D Ability to tilt the spindle shaft within air gap restriction (± 0.5°). D Built-in three-dimensional force and position sen- Geometric position error characterization sors. Error terms Use of the magnetically suspended spindle pro- For the purpose of defining the error terms a linear vides an additional level of control for error minimiza- carriage is chosen, as shown in Figure 2. It is assumed tion. The high resolution, along with wide bandwidth, that the carriage is a rigid body, moving along the of incremental translation and tilt of spindle shaft is x-axis, and has a measuring device for the x-position. ideal for on-line error compensation. An ideal linear carriage would translate only This paper, for the first time, presents a methodo- along the x-axis. However, being a rigid body the logy by which the CFI errors (including thermal errors) carriage has six degrees of freedom. Hence, in reality, can be characterized and corrected on-line for high it must have three translational and three rotational feed rate machining. It also presents the results of motions, however small they may be. This type of experimental validation of the approach using the motion where the carriage's actual position is different magnetic bearing spindle test facility at the University from the ideal position results in geometric position of Maryland. error. These errors must be defined with respect to a reference coordinate system. For measurement conve- nience, these errors will be discussed under the cate- gories of angular errors, linear errors and orthogonality Error classification errors. CFI errors, for the purposes of this research, are The angular errors are defined as rotations about classified as shown in Figure 1. CFO errors and non- mutually perpendicular axes, and are functions of the deterministic errors are not considered here. carriage position. Ex(x), .sx(y), and Ex(z) represent Static loading produces CFI errors resulting in rotation about the x, y and z axes, respectively. static/geometric errors which show up as positional inaccuracies due to errors in production and assembly of the elements used in the machine construction. Dynamic loading results in CF! errors dependent on the acceleration and deceleration of machine compon- ents. It produces transient and steady state trajectory errors as well as feed-rate dependent overshoot and undershoot errors. Trajectory errors are not considered. in this work. By including the effect of feed rate on positioning errors, it is possible to combine static geometric errors and overslmot/undershoot errors into one error class called geometric position error. Thermal loading produces thermal deformation 0 Actual position O' Required position error, which is a function of temperature. The tem- perature change can be due to any number of sources such as servo motors, ambient temperature change, spindle motors and friction. This error is both static and dynamic in nature. Figure 2 Linear carriage with six error terms Page 1006 Adv. Manuf. Eng. Vol 2 October 79 90 181 Rotations about the x, y and z axes are also known as y 4 y' 'roll', 'pitch' and 'yaw', respectively. I The linear errors are categorized as a 'scale error' 1r '- y - Theoretical Y axis az (also called 'positioning error') and two 'straightness of y'- Motion axis I x - Reference axis motion' terms. The scale error is the difference be- I tween the actual carriage position and the scale read- ing in the x-direction represented by Dx(x). Carriage straightness errors, Dy(x) and Oz(x), are the non-linear Figure 3 Orthogonality error movement that an indicator senses when it is station- ary and reading against a perfect straight edge sup- tion only and there is a measuring device to ported on the carriage moving along the x-axis. measure its position Orthogonality errors account for the angular D Only CFI errors are considered. orientation of two or more axes with respect to each other. The definition of orthogonality is dependent Since part accuracy (tool path error) is determined upon the way the motion axis itself is defined. One by the relative position between the tool and the method is to measure the straightness in two dimen- workpiece, the vector describing this is sought. The sions and define the motion axis such that the straight- machine tool-workpiece system is considered as a nesses with respect to this are a minimum. For the chain of linkages and this relationship can be de- carriage, the motion axis will be a line such that (see scribed using homogeneous coordinate transformation Figure 2) matrices. The correlation of the error terms require the N measurement of the error terms to be made with s = ~(ot;(x) + o~i(x)) (1) respect to the same reference system. i=l The nominal tool (spindle) position is selected as is a minimum. For the carriage, choosing the x-axis as the reference point. Four right-handed orthogonal the reference motion axis, the deviation from ortho- coordinate systems are selected for the purpose of gonality of the y-motion axis with respect to the defining the error terms, one assigned to the reference x-axis is represented by £Yz, where the x and y axes point ( 0,) which is fixed in space and the other three form a plane. Figure 3 shows the orthogonality error ( Ox, Oy, Oz) are assigned to table, cross, and spindle for the I inear carriage. slides respectively, as shown in Figure 4. The transfor- mation matrices representing the relative motion be- Analytical model tween these slides are represented as i 0 where i and j can be any one of O" Ox, Oy and Oz representing the Tool path errors due to static .and dynamic determin- coordinate systems. The schematic chain of linkages is istic deformation can be represented in terms of the shown in Figure 5. geometry of the links and joints. Hence the modelling The transformation matrix describing the relative of a three-axis, flat-bed, vertical CNC machining cen- motion between the 0, and Ox coordinate systems, tre can be considered as an extension of linear car- when X is moving, can be written as, riage motion. The machine consists of three linear carriages, viz, a table slide (with motion along the RTx = RTy· yTx (2) x-axis) connected to the cross-slide through a pris- Similarly, the transformation matrix of the Z coor- matic joint, a cross-slide (with motion along the y- dinate system relative to the 0, system is given by axis) connected to the bed by a prismatic joint, and a spindle slide (with motion along the z-axis) connected RTz = RTy· yTx· xTz (3) to the column by a prismatic joint. By extension of the Finally, the transformation matrix describing the linear carriage discus(ion, this machine therefore has relative motion between the cutting tool (i.e., Oz 18 degrees of freedom. Table 1 lists all the error terms coordinate system) and the workpiece (i.e., Ox coor- that must be considered. Several assumptions are dinate system) is given by made: D xTz = (yTx)- 1(RTy)- 1 • RTz (4) The workpiece is assumed to be rigidly connected to the table slide Equation (4) reveals that we need to find three D The cutting tool is assumed to be a point in space homogeneous transformation matrices in order to de- and rigidly attached to the spindle slide termine relative motion between the cutting tool and D Each carriage is for linear motion along one direc- the workpiece. The transformation matrix for the Ox Table 1 Error terms Dx(x) = X-axis scale deviation* Ex(x) = Roll of table Dy(y) = Y-axis scale deviatton* Sy(y) = Roll of cross slide Dz(z) = Z-axis scale deviation Sy(X) = Pitch of table Dy(x) = Y straightness of X-axis* Ex(Y) = Pitch of cross slide oz(x) = Z straightness of X-axis ez(X) = Yaw of table* Dx(y) = X straightness of Y-axis* ez(y) = Yaw of cross slide* oz(y) = Z straightness of Y-axis lYx = Squareness of Z on YZ plane* Dx(z) = X straightness of Z-axis CYy = Squareness of Z on ZX plane Dy(z) = Y straightness of Z-axis ct'z = Squareness of Y on XY plane Page 1007 182 M. Anjanappa et al - Characterization of errors for on-line correction When the Oy coordinate system moves a distance Y along the y-axis the transformation matrix with respect to the reference system is given as Dy~(yx)( X- ) y ~ R T y -- l -EEzy~(Yy) ) Dz(y) 0 1 (6) where ~x(y) = Dx(Y) + iYz Y (7) Similarly, the transformation matrix when the Oz coordinate system moves a distance Z along the z-axis, with respect to the Or coordinate system, is given by -l -Ez(Z) -Ey(Z) 1 -Ex(Z) ~Ay,l(zz)) J R Tz - -EEzy~(ZZ) ) -Ex(z) 1 Dz(Z\ + Z 0 0 0 (8) where ~x(z) = Dx(z) + iYyZ (9) ~y(Z) = Dy(Z) + iYxZ (10) Figure 4 Coordinate systems for a three-axis CNC machine The ~ terms in the above equations arise due to the squareness error. By substituting equations (5) to (10) into equation (4) we get xTz = E,(x,y)-E,(Z) -E y(X, y)+ E y(Z) 1 Ex(x,y)+Ex(Z) -Ex(x,y)+Ex(Z) 1 0 0 (11) where -l E= X-c5x(x)-c5x(y)+<\(z)+a, Y+a yZ+ YE,(x,y)- Z(Ex(y)+Ey(X)J Y-c5x(X)-c5y(y)+c5y(z)+axZ + Z(Ex(x)+ Ex(y))- XE ,(x) [ Z-c5,(x)-c5,(y)+c5,(z)- YEx(x,y)+ XEy(x) 1 (12) where the term i(f k) = i(j) + i(k). Equation (1 2) represents the actual position of the tool tip with respect to the table coordinate system after motions in the x, y and z axes by the respective slides. The tool path error is found by taking the Figure 5 Chain of linkages vector difference between the commanded positions and the ac~al position arrived at. Hence, the tool path error f is given by coordinate system which moves a distance X along E= the x-axis with respect to th12 nominal position of the Oy coordinate system, is given by14 -c5x(x)-c5x(y)+c5x(z)+a, Y+ayZ+ YE,(x,y)-Z[Ex(y)+Ey(x)]J -l -c5y(x)-c5y(y)+c5y(z)+axZ+ Z[Ex(x)+Ex(y)]- XE,(x) [Ey(X) -c5,(x)-c5,(y)+c5z(z)- YEx(x,y)+ XEy(x) -Ex(X) T Ez~X) (13) y X - -Ey(X) 1 0 0 Inspection of the above equation shows that there are 18 error terms (see Table 1) required to describe (5) the errors of a three-axis milling machine. Reference Page 1008 Adv. Manuf. Eng. Vol 2 October 1990 183 14 provides detailed mathematical development. ¢ 2.54 m min-1 +1.27 m min-1 o0.762 m min-1 However, the focus of the research at the University of A 0.254 m min-1 I),. Rapid Maryland is primarily contour machining (i.e., end milling) where the z slide remains stationary during 15 the machining operation. Hence, only the xy plane of 10 E the machine tool is considered for further investiga- :::,. 5 tion. This leaves seven error terms associated with the ... 0 0 xy planar motion which are identified by an asterisk t -5 w in Table 1. Equation (13) therefore simplifies to -10 -15 E = c-Dx(x) - Dx(y) + ctz y + YEz(x) + YEz(y) J -20 -Dy(X) - Dy(y) - XE1(X) -25 (14) -30 -0.55 0 Equation (14) applies to all points inside the Slide position (m) working volume of the machine (i.e., xy plane for this case). The entire plane is divided into 0.0254 m Figure 6 Scale error along x-axis squares to keep the measurements required at its minimum. Since the overall goal of the proposed approach requires these measurements at regular in- errors show a strong dependence on position and feed tervals during a machine's lifetime, it is economical to rate. The standard deviations of the errors at each reduce the total time required for measurements. The position are approximately an order of magnitude less data measured at the nodes (centre of square) can then than the errors themselves. It is clear from this result be interpolated to obtain the errors at intermediate that if one was to measure the errors at only one feed points. Hence the tool path error at each node re- rate, the resulting information would not be valid at quires seven error terms to be measured experiment- other feed rates. Interestingly, this procedure is very ally. In addition, to include the overshoot and under- repeatable with respect to table position and feed rate, shoot dynamic errors, the data must be collected at as shown by the smal I standard deviation of the errors. various feed rates and also in both positive and A strong dependence on the direction of table motion negative directions to account for direction depen- was observed. The plot for the negative direction is dency. not shown for brevity. This direction dependence is due to backlash errors in the geared drive-trains and Experimental work different geometric errors on each face of the lead The net tool position displacement relative to the screw threads. Since the data points are well behaved, machine table for each axis is determined from seven linear interpolation between the data points is an error terms, listed in the previous section, which are acceptable method of calculating the position errors at measured under static conditions using an HP 5528A- positions between the data points. based laser measurement system 15 . The water coolant Similarly, the axial scale errors along the y-axis, system of the magnetic spindle remained off in order Dy(y), were measured and evaluated in the same to minimize thermal effects. However, the bulk manner as above. Like the x-axis, the y-axis errors spindle temperature (from thermocouples located at show a strong dependence on position and direction, strategic locations of spindle head) and machine ambi- as shown in Figure 7. As for feed-rate dependence, the ent temperatures (from thermocouples located at error appears to become smaller as the table velocity strategic locations on machine slides) thermocouple increased for negative motion. In the positive direc- voltage outputs are monitored so that thermal effects tion, however, the errors appear to be less dependent due to the servo motors and ambient conditions can on feed rate. be removed from the geometric position error data. The Y-straightness error of the x-axis, Dy(x) was Four types of measurement were conducted, viz, measured at the same five feed rates in both directions axial position, straightness, angular and squareness to obtain all the seven error terms. Each error term was ¢ 2.54 m min-1 +1 .27 m min- 1 o0.762 m min- 1 measured at 0.0254 m increments of table motion at A0.254 m min-1 !),.Rapid five commonly used feed rates (0.254, 0.762, 1.27, 2.54 m min- 1 and rapid (5.08 m min-1 )) in positive and negative directions. Six sets of data are recorded 0 at each feed rate and the standard deviations are E computed to ensure that the averages of the errors :::,. represent a repeatable error. Since the error terms are .... -1 ~ measured at several feed rates in both directions, w repeatable errors due to tbe machine's servo drive controller will also be accounted for in the final -2 geometric position error map. Results -3'-------------------~ The average axial scale error along the x-axis, c'5x(x), is -0.24 0 shown in Figure 6 for the traversing of the machine's Slide position (m) table at five feed rates in the negative direction. The Figure 7 Scale error along y-axis Page 1009 184 M. Anjanappa et al - Characterization of errors for on-line correction (see Figure 8 for the negative direction). The errors are 0 2.54 m min-1 +1.27 m min-1 o 0.762 m min-1 small (less than 2.5 ,um) compared to the axial posi- A 0.254mmin-1.t..Rapid tion errors. They showed I ittle dependence on feed rate or direction but did vary with position. The X-straightness error of the y-axis, Dx(y), on the other u hand, are slightly larger and show a larger depend- Cl> ence on feed rate and direction, as shown in Figure 9. "I' ~ Standard deviations of the straightness errors at each _g position along both axes are of the same magnitude as ,._ ~ those for the axial position errors. Due to the relative w -40 magnitude of the straightness errors compared with other errors measured, they will be neglected and assumed equal to zero in the final error map matrices. -80 Figure 10 shows the angular error of the x-axis about the z-axis (ie., yaw of table slide), ez(x). The -120 '------'--'---'----'-----'---"--__J'------'--'---' angular errors are quite small (less than 1 arc-sec) for -0.5 0 all feed rates except for 0.254 m min-1 • Examining the Slide position (m) raw data revealed that large changes in the bulk Figure 10 Angular error of x-axis about z-axis spindle and machine ambient temperatures occurred during the test. This is substantiated by the large standard deviations associated with the average errors. feed rates and the large standard deviation of the The main purpose of the measurement of angular average errors at each position. errors is to correct the straightness and axial position Figure 11 shows the angular errors of the y-axis measurements for angular rotation of the optics. There- about the z-axis (ie., yaw of cross slide), ez(y). The fore, the angular errors should be of the same mag- angular errors for positive motion are of the same nitude as the straightness errors. Therefore, the magnitude as those encountered along the x-axis. 0.254 m min-1 angular error measurements are dis- There appears to be no reason to discount the angular counted on the basis of the data recorded at the other errors measured along the y-axis during the negative translation of the table. Therefore, their sine and 1 cosine contributions to the y-axis straightness and O 2.54 m min- +1.27 m min-1 D0.762 m min-1 1 axial position error terms will be calculated and A 0.254 m min- .t..Rapid 1.2 included in the final geometric position error map. The largest contribution by the angular errors to the 0.9 straightness error measurements is -3 arc-sec. This E :,. error is equivalent to a perpendicular displacement of the table of + 2.59 ,um over the 0.178 m measurement range. The contribution to the axial position errors would be a negligible 25.4 x 10-9 Ot-;;;,L--\'\\\---------;M~~--, ,um. The squareness error between the xy axis, Cl' z, is -0.3 determined by performing two straightness measure- ments using an optical square. The squareness error -0.6 angle (clockwise positive) is calculated to be -0.9'--------'-------------~ -1 .719 x 10-3 deg using the x-axis as a reference. -0.5 0 This error results in a contribution to the y-axis Slide position (ni) straightness error and will be included in the final Figure 8 Y-straightness error of x-axis motion error map. O 2.54m min-1+1.27 m min-1 D0.762 m min-1 O 2.54 m min-1 + 1.27 m min-1 o 0.762 m min-1 A 0.254 m min-1 .t..Rapid A 0.254 m min-1 .6. Rapid 15 u Cl> 75 E "I' :::L ~ Ol-----1---A(,l!ll---------~----I ,._ 0 g ,._ -7.5 0 w ,,..__ w -15 -2.0L---------------------' -Q24 -Q06 0 Slide position (m) Slide position (m) Figure 9 X-straightness error of y-axis motion Figure 11 Angular error of y-axis about z-axis Page 1010 Adv. Manuf. Eng. Vol 2 October 1990 185 The recorded error terms are then analysed and Several 'recovery from cool down' tests were reduced. The measured angular errors were used to conducted for the y-axis, and Figure 12 shows a remove the axial and perpendicular motion of the typical error plot obtained. In these tests the deforma- table due to rotation about the tool from the straight- tion of the spindle varied linearly with respect to ness and axial position measurements. Further, the temperature. Results from having only the servos on squareness error between the x and y axes was 'warm up' are presented in Figure 13. Interestingly, the resolved into sine and cosine components and added bulk spindle temperature does not change; this is to the axial position and straightness error terms. understandable, since the spindle is well removed The resulting geometric position errors associated from the servo motor heat sources. with the motion of the table and cross-slide are represented in the form of an error matrix. This matrix Modelling consists of scale and straightness errors for each axis Using the data from these tests it is possible to for each node for five feed rates and for positive and construct a linear model of the thermal deformation negative approaches. Since error data at several feed error along the y-axis based on the change in the bulk rates is present, errors due to the servo drive and spindle temperature and the change in the ambient electronic control system are included in the map. The machine temperature. By modelling the spindle as a error matrices specifically consist of four matrices (two fixed beam, a matrix equation can be developed to for each axis): describe the thermal deformation in the y axis as 17 [Dx(x)] = (error, machine position, ± feed rate) [Dx(y)] = Dy= [T][c] (15) (error, machine position, ± feed rate) [Dy(x)] = (error, machine position, ± feed rate) where [Dy(y)] = (error, machine position, ± feed rate) [T] = [Ll Ta Ll h] (16) In summary, the geometric position errors possess [c]T = [c1 c2J (17) a position, directiQn, and feed rate dependence. All errors associated with a particular axis had a small where Ll Ta is the change in the ambient machine standard deviation but no apparent trend of the de- temperature, Ll h is the change in bulk spindle tem- pendence on the above parameters. Therefore, com- perature and c 1 , c2 are constants. pensation can be performed by using the above error matrices. More detailed information on experimental data can be obtained from Reference 16. -10 Thermal deformation error characteristics The thermal deformation of the machine tool structure §. -20 results in a net displacement of the tool relative to the C: workpiece. Thermal deformation, with the magnetic 1 -30 0 spindle, is complicated since it has air cooling and ,E_ extensive cooling water circuits around the magnetic 't -40 coils. Changes in temperature at different locations on 0 the spindle and machine frame can be measured using -50 0 Bulk spindle temperature thermocouples and linked to the thermal deformation o Ambient machine temperature error by either a functional relationship or a 'look up' 21 22 23 24 25 26 27 28 table. Temperature (°C) In this study the geometric position error and thermal deformation error are investigated. The Figure 12 Thermal deformation due to recovery from measurement and analysis of these errors are pre- cool down sented in the following sections. Experimental work 0 Bulk spindle temperature 1::,. Ambient machine temperature Tests were performed to determine the thermal defor- 4 mation errors along the x and y axes. The deforma- tions experienced by the spindle head due to the E :l. thermal shock created by the cooling water flowing 3 C: through the magnetic spindle proved to be significant. 0 :;: 0 Although a model for thermal shock was derived, it is E,_ 2 not reported here since this problem was eliminated 0 Q) by redesign of the spindle cooling system. Only the -0 errors due to changes in ambient conditions and servo motor heat sources are discussed further. Since the spindle bore/tool is centred about the x-axis of the 0'---vements (high resolution motion (of the spindle) is independent of machine and wide bandwidth incremental movements) upon slide motion, thereby allowing higher resolution nominal machine table movements. The post proc- and bandwidth of error correction. essed M and G codes are directly fed to the machine controller, which sends out motion commands for the Validation X, Y and Z movements. These movements are con- tinuously sensed by position sensors and displayed on An error correction experiment was performed to the machine controller in real time. This real time X, demonstrate and evaluate the error characterization Page 1012 Adv. Manuf. Eng. Vol 2 October 79 90 187 and on-line correction of milling errors. Experiments 0 Uncompensated, mean=22.6, std=7.11 were performed on the Matsuura MC500V vertical 1;,. Compensated, mean=1.78, std=1.27 CNC machine retrofitted with the S2M magnetic Improvement factor=12.6 spindle system and error minimization controller. This 40 experiment used the terminal point error matrix deve- loped earlier, as codified in the file LASER.MAP. The E 30 HP 5528A laser metrology system was used to ::i measure milling machine table position. The laser ,._ optics were affixed to the spindle tool holder, provid- t 20 w ing a direct measurement of relative axial table posi- tion. From machine home, the axial table position 10 command was stepped, in 0.0254 m increments, across the positioning range. 0 Figure 15 presents the measured X-axis errors -0.55 -0.4 -0.25 -0.1 (i.e., table slide scale error Dx(x)) with and without Table slide position (ml on-line error correction at a nominal feed rate18 of 2.54 m min-1. These results indicate direction-depend- Figure 76 Short-term terminal point error correction ent terminal point accuracy improvement factors of plot five and three, respectively. Although Woytowitz 16 reported the standard deviation of the terminal point D Identification of the error phenomenon independ- errors to be approximately one tenth the magnitude of ent parameters the error, the corrected error retains larger systematic D Statistical properties of the error phenomenon. errors. Since the calibrated three-sigma positional un- certainty of the spindle position is approximately Recent metrological experience indicates that up 2.54 µ,m, these systematic compensation errors were to an order of magnitude improvement in CFI position- assumed to be caused by long-term drift in the error ing accuracy is achievable using pre-calibrated error phenomena. To evaluate the short-term terminal point compensation. Improved error characterization, as error compensation capability, the laser metrology well as compensation actuation, is required to obtain procedure was repeated at a single, 2.54 m min-1 feed this goal under realistic machining conditions. The rate. With a one-day turn around, between metrology on-line, terminal point CFI error correction experiment and correction, the results in Figure 16 were ob- graphically i 11 ustrates th is point. Correction i mplemen- tained18. This experiment achieved more than an tation limitations may be characterized in terms of order of magnitude improvement, between with and bandwidth and accuracy. Relative to tool path trajec- without on-line correction, of terminal point errors. tory dynamics(< 10 Hz18), the 125 Hz bandwidth of Continuing metrological investigations by other re- the existing S2M B25/500 is sufficient for effective searchers are currently in progress to refine the error error correction. characterization. Quality assurance performance future work The performance of quality assurance by characteriza- In the immediate future, work on inclusion of dynamic tion and on-line correction of errors as reported in this errors due to transient and steady state trajectory errors paper is limited by the quality of error characterization into the correction scheme will be explored. Following and by the ability to effect the proper correction. this, the CFD errors will be characterized by following 18 Using a pre-characterized error model, the quality of the methodology developed by Zivi et al . In this on-line error representation is dependent on two prim- category, specifically the ramp errors due to deflection ary factors: of thin-ribbed components or due to the deflection of the tool while machining thick-ribbed components will be investigated. 0 Uncompensated, mean=6.60, std=5.59 1;,. Compensated, mean=1.27, std=1.78 Conclusion Improvement factor= 5.19 20 This study suggests that it is possible to assure the quality of machined parts by taking the approach of E ::i 15 careful characterization and on-line correction of mill- ,._ ing errors. CNC machines fitted with magnetic bearing 2,._ 10 spindles proved to be ideal for such on-line error w 5 correction implementation. The characterization of CFI errors revealed that the feed rate has a profound effect 0 on the positioning accuracy of machines, which can be corrected by including the feed rate as a variable in -5 the error matrix. The thermal deformation errors -10 proved to be deterministic in nature and hence can be -0.55 -0.4 -0.25 -0.1 compensated for. The experimental data showed that Table slide position (ml improvements in accuracy of up to an order of mag- Figure 75 Terminal point error correction plot nitude can be achieved using this methodology. Page 1013 188 M. Anjanappa et al - Characterization of errors for on-line correction Acknowledgements machines Ann. C/RP 34 (1985) 8 Anjanappa, M., Anand, D. K., Kirk, J. A. and Shyam, S. The authors would like to acknowledge the contribu- Error correction methodologies and control strategies for tion to this work by Mr S. Shyam, Mr M. Woytowitz numerical controlled machining. 'Control methods for and Dr E. Zivi. This work has been supported by the manufacturing processes' DSC-Vol 7 (1988) 41-49 National Science Foundation through grant NSF 9 DeVor, R. E., Sutherland, J. W. and Kline, W. A. Control 8516218 and the Engineering Research Center at the of error in end milling. 11th NAMRC (1983) 356-362 University of Maryland and ONR Program Element 10 Milner, D. A. Controller system design for feedrate 61152N through the David Taylor Research Center. control by deflection sensing of a machining process Int. }. MTDR 15 (1975) 19-30 11 Rao, S. B. and Wu, S. M. Compensatory control of roundness error in cylindrical chuck grinding}. Engng. References Ind. 104 (1982) 23-28 12 Zanbin, H. and Devries, M. f. Microprocessor-based 1 Anand, D. K., Kirk, J. A. and Anjanappa, M. Magnetic compensation of leadscrew drive kinematic errors by a bearing spindles for enhancing tool path accuracy. Adv. forecasting technique. Proc. 25th Int. MTDR Conf., Man- Manuf. Processes 1 (1986) 121-134 chester, UK (1984) 347-354 2 Anjanappa, M., Kirk, J. A. and Anand, D. K. Tool path 13 Anjanappa, M., Anand, D. K., Kirk, J. A., Zivi, E. and error control in thin rib machining. Proc. 15th NAMRC, Woytowitz, M.A. Retrofitting a CNC machining center Bethlehem PA (1987) 485-492 with a magnetic spindle for tool path error control. Proc. 3 Anand, D. K., Kirk, J. A., Anjanappa, M. Zivi, E and INCOM'89, Madrid, Spain (1989) 639-643 Woytowitz, M. A. Magnetic bearing spindle control. 14 Shyam, S. Error compensation of accuracy enhancement Proc. 15th Conf. Prod. Res. and Technol. Berkeley CA in precision machining. M.S. Thesis, The Univeristy of (1989) 31-35 Maryland (1987) 4 Tlusty, J. Techniques for testing accuracy of NC machine 15 '5528 Laser Measurement System' User's Guide, Hew- tools. Proc. 12th Int. MTDR Conf., Manchester, UK lett-Packard Literature (1971 ), 333-345 16 Woytowitz, M. A. Tool path error classification and 5 Dufour, P. and Groppetti, R. Computer aided accuracy identification for high precision milling with a magnetic improvements in large NC machine tools Proc. 21st Int. bearing spindle. M.S. Thesis, The University of Maryland MTDR Conf., Manchester, UK (1980) 611-618 (1989) 6 Donmez, A., Liu C. R., Barash, M. and Mir, M. Statistical 17 lncropera, f. P. and DeWitt, D. P. 'Fundamentals of heat analysis of positioning errors of a CNC milling machine and mass transfer'. 2nd edition, John Wiley, NY (1985) }. Manuf. Syst. 1 (1982) 33-41 18 Zivi, E. Robust control of magnetic spindle for error 7 Zhang, G., Veale, R., Charlton, T., Borchardt, B. and compensation. Ph.D. Thesis, The University of Maryland Hocken, R. Error compensation of coordinate measuring (1989) Page 1014 M. Anjanappa et al - Characterization oi errors tor on-line correction Characterization of errors for on-line correction with a magnetic bearing spindle M. ANJANAPPA, D. K. ANAND and J. A. KIRK This paper is concerned with the quality assurance, via characterization and on-line correction of tool path errors, in a CNC milling machine fitted with a magnetic bearing spindle. Two classes of tool path errors, viz, geometric position errors and thermal deformation errors are characterized and investigated. Characteristics of geometric position errors reveaied that, generally, the magnitude of errors increased with feed rate. The ensuing results were used in a methodology by which on-line correction of errors, both static and dynamic, could be achieved. CNC machines fitted with magnetic bearing spindles proved to be ideal tor on-line error correction by providing an additional level of control that has high resolution and wide bandwidth. Experimental results indicate that errors could be reduced by a factor of three to ten in normal machining conditions. Keywords: error characterization, on-line correction, magnetic bearing spindles, tool path errors The dimensional accuracy and surface finish of a output of the error process model based on off-line machined part is a function of tool path error. The tool measurements. The table movements of the machining path error in NC machining is defined as the vector centre are used to correct the error. The post proc- difference between the required/programmed and essed Mand G machine tool motion codes are actual tool path 1 • The magnitude of the error is both intercepted before being downloaded to the machine deterministic and stochastic in nature since it depends controller, and processed through an error compensa· on both repeatable (static and dynamic) and random tion algorithm based on a previously generated error (dynamic) parameters. map. The error compensated codes are then down- Previous research 2·3 suggests separating errors as loaded to the machining centre controller, which cuts either cutting force independent (CFll or cutting force the part more accurately. This method assumes that dependent (CFDl. CFI errors are those errors that occur the machining operation is single point cutting and in the absence of metal cutting (i.e., dry run) and are only the point-to-point error is corrected. repeatable. CFO errors, not considered in this work, In all this work, the effect of feed rate is removed are directly linked to the metal cutting process. It is by measuring the errors at low feed rates only in order possible to compensate for the CFI errors, either by to remove the dynamic effects. Hence, these tech- pre-compensation or by on-line error correction, if niques are not suitable for high feed rate machining, they can be characterized. which is becoming the norm as new high speed Pre-compensation oi tool path errors consists of spindles are introduced into the market. In addition, quantifying the errors committed by the tool and nor all CFI errors can be compensated for using the implementing compensation schemes before machin- pre-compensation technique. For example, errors due ing begins. For example, Tlusty4 uses a semi-auto- to temperature changes cannot be compensated for matic master part (trace test) to measure errors. Suforer unless there is a mechanism to sense the temperature et al.' use an error matrix of coordinate corrections to and then use an appropriate correction factor to improve the accuracy of large NC machine tools. compensate for the axis movements on-line. One such Donmez" refined this approach by implementing stat- mechanism is the on-line controller for axis move- istical principles to determine the characteristics of ments. geometric positioning errors. This same methodology Several investigators (for example References 2, has been applied by Zhang et al. 7 to improve the 9-12) have developed on-line correction techniques accuracy of coordinate measuring machines at the and found them effective for reducing machine tool National Institute of Standards and Technology. Anja- errors. It must be noted that these methodologies are nappa et al. 8 used the error matrix approach for developed to compensate on-line for both CFI and enhancing tool path accuracy on a commercial CNC CFO errors combined without distinguishing the two. machining centre. Among them, the methodologies developed in Refer- In general. the strategy of CFI error correction by ences 11 and 12 can be used for on-line correction of pre-compensation methods discussed so far is based CF! errors. However, these techniques have limited on nullifying the effect of the error itself by algebraic application in a commercial CNC machining centre summation of the programmed position input with the since they either require attachment of delicate instrumentation or access to servo controllers of ma- chines. In addition, the resolution and dynamics re- M.A. is in rhe Department oi Mechanical Engineering, University oi quirement of such an on-line controller is beyond the Maryland-UM BC. Baltimore. ,'vlQ 21 228. USA. Q.K.A. and /.A.K. Jre hardware and software capability of commercial con- in the Qep,1rrment al MechJnicJI Engineering, Universit_y of Mary- trollers. These reasons make this approach difficult. 1,md-UMCP. Colle!:ie P.1rk. ,1,1Q .:07-42. USA 0951-5232/90/010011-04 © 1990 Butter.vonh-He,nemJnn Ltd Page 1015 Adv. ,\,1anur: Eng. Vol 2 October 1990 expensive, and hence, impractical for many applica- in this work. By including the effect of feed rate on tions. positioning errors, it is possible to combine static To overcome these limitations, a test facility has geometric errors and overshoot/undershoot errors into been set up, at the University of Maryland, by retrofit- one error class called geometric position error. ting a Matsuura MC500V vertical machining centre Thermal loading produces thermal deformatio'n with an 52M 625/500 magnetic bearing spindle and is error, which is a function of temperature. The tem- discussed in detail in Reference 13. Some unique perature change can be due to any number of sources features of the magnetic bearing spindle are: such as servo motors, ambient temperature change, O Ability to translate the spindle shaft within air gap spindle motors and friction. This error is both static restriction (± 0.127 mm). and dynamic in nature. O Ability to tilt the spindle shaft within air gap restriction (± 0.5°). Geometric position error characterization O Built-in three-dimensional force and position sen- Error terms sors. Use of the magnetically suspended spindle pro- For the purpose of defining the error terms a linear vides an additional level of control for error minimiza- carriage is chosen, as shown in Figure 2. It is assumed tion. The high resolution, along with wide bandwidth, that the carriage is a rigid body, moving along the of incremental translation and tilt of spindle shaft is x-axis, and has a measuring device for the x-position. ideal for on-line error compensation. An ideal linear carriage would translate only This paper, for the first time, presents a methodo- along the x-axis. However, being a rigid body the logy by which the CFI errors (including thermal errors) carriage has six degrees of freedom. Hence, in reality, can be characterized and corrected on-line for high it must have three translational and three rotational feed rate machining. It also presents the results of motions, however small they may be. This type of experimental validation of the approach using the motion where the carriage's actual position is different magnetic bearing spindle test facility at the University from the ideal position results in geometric position error. These errors must be defined with respect to a of Maryland. reference coordinate system. For measurement conve- nience, these errors will be discussed under the cate- Error classification gories of angular errors, linear errors and orthogonality errors. CFI errors, for the purposes of this research, are The angular errors are defined as rotations about classified as shown in Figure 1. CFO errors and non- mutually perpendicular axes, and are functions of the deterministic errors are not considered here. carriage position. 1: ,(x), 1: ,( y), and 1: ,(z) represent Static loading produces CFI errors resulting in rotation about the x, y and z axes, respectively. static/geometric errors which show up as positional Rotations about the x, y and z axes are also known as inaccuracies due to errors in production and assembly 'roll', 'pitch' and 'yaw', respectively. of the elements used in the machine construction. The linear errors are categorized as a 'scale error' Dynamic loading results in CFI errors dependent on (also called 'positioning error') and two 'straightness of the acceleration and deceleration of machine compon- motion' terms. The scale error is the difference be- ents. It produces transient and steady state trajectory tween the actual carriage position and the scale read- errors as well as feed-rate dependent overshoot and ing in the x-direction represented by b,(x). Carriage undershoot errors. Trajectory errors are not considered straightness errors, Dy(x) and b.,(x), are the non-linear movement that an indicator senses when it is station- Deterministic error classification ary and reading against a perfect straight edge sup- ported on the carriage moving along the x-axis. Orthogonality errors account for the angular orientation of two or more axes with respect to each Cutting force Cutting force independent error dependent error other. The definition of orthogonality is dependent Thermal loading Static loading Dynamic loading (temperature ( position and ( acceleration dependence) weight) dependence l de endence) Thermal Static/ Overshoot and Transient and deformation geometric undershoot steady state errors errors errors trajectory errors 0 Actual position O' Required position Geometric position ~--- errors Figure I Error c/assitlcacion Figure 2 Linear carriage with six error terms Page 1016 upon the way the motion axis itself is defined. One workpiece, the vector describing this is sought. The method is to measure the straightness in two dimen- machine tool-workpiece system is considered as a sions and define the motion axis such that the straight- chain of linkages and this relationship can be de- nesses with respect to this are a minimum. For the scribed using homogeneous coordinate transformation carriage, the motion axis will be a line such that (see matrices. The correlation of the error terms require the Figure 2) measurement of the error terms to be made with · ,'/ L respect to the same reference system. S = (c5;,(x) + c5;,(x)) (1) The nominal tool (spindle) position is selected as i-1 the reference point. Four right-handed orthogonal is a minimum. For the carriage, choosing the x-axis as coordinate systems are selected for the purpose of the reference motion axis, the deviation from ortho- defining the error terms, one assigned to the reference gonality of the y-motion axis with respect to the point ( 0,) which is fixed in space and the other three x-axis is represented by a,, where the x and y axes (0,, Oy, 0,) are assigned to table, cross, and spindle form a plane. Figure 3 shows the orthogonality error slides respectively, as shown in Figure 4. The transfor- for the linear carriage. mation matrices representing the relative motion be- tween these slides are represented as ; Ti where i and j Analytical model can be any one of 0,, 0., Oy and 0, representing the Tool path errors due to static and dynamic determin- coordinate systems. The schematic chain of linkages is istic deformation can be represented in terms of the shown in Figure 5. geometry of the links and joints. Hence the modelling The transformation matrix describing the relative of a three-axis, tlat-bed, vertical CNC machining cen- motion between the 0, and 0, coordinate systems, tre can be considered as an extension of linear car- when X is moving, can be written as, riage motion. The machine consists of three linear (2) carriages, viz, a table slide (with motion along the x-axis) connected to the cross-slide through a pris- matic joint, a cross-slide (with motion along the y- axis) connected to the bed by a prismatic joint, and a spindle slide (with motion along the z-axisl connected to the column by a prismatic joint. By extension of the linear carriage discussion, this machine therefore has 18 degrees of freedom. Table 1 lists all the error terms that must be considered. Several assumptions are made: D The workpiece is assumed to be rigidly connected to the table slide D The cutting tool is assumed to be a point in space and rigidly attached to the spindle slide D Each carriage is for linear motion along one direc- tion only and there is a measuring device to measure its position D Only CFI errors are considered. Since part accuracy (tool path error) is determined by the relative position between the tool and the y J y' I II -- y - Theoretical Y axis ar y'-Motion axis I x - Reference axis I Figure 4 Coordinate systems for a three-axis CNC Figure 3 Orthogonality error machine Table 1 Error terms ti,(x) = X-axis scale deviation• e,(x) = Roll oi table 6v(Y) = Y-axis scale deviation• ev(y) = Roll oi cross slide ti,(zl = Z-axis scale deviation e v(X) = Pitch of table Dv(x) = Y straightness oi X-axis" e,(y) = Pitch oi cross slide 6 ,(xl = Z straightness of.,¥-axis e,(x) = Yaw of table• b,(y) = X straightness oi Y-axis" s,(y) = Yaw oi cross slide" 6,(yl = Z straightness oi Y-axis a, = Squareness oi Z on YZ plane• 6,(Zl = X straightness oi Z-axis a y = Squareness of Z on ZX plane u"(Zl = Y straightness oi Z-axis er, = Squareness oi Y on XY plane Page 1017 -Ey(Z) -1:,(z) 1 0 (8) where llx(Z) = Dx(Z) + rxyZ (9) Lly(Z) = Dy(Z) + rxxZ (10) The 6.. terms in the above equations arise due to the squareness error. By substituting equations (5) to (10) into equation (4) we get xTz = E,(x,y)-e,(z) -E,(X,y)+E,(Z) -e,(x))+e,(z) 1 E,(,l,y)+E,(Z) E,(x,y)-E,(Z) [ -e,(x,y)+e,(z) 1 0 0 0 '] (11) where Figure 5 Chain of linkages E= Similarly, the transformation matrix of the Z coor- X-<>,(x)-6,(y)+<>,(z)+a, Y+a.Z+ Ye,(x,y)- Z(e,(y)+e,(x)J dinate system relative to the 0, system is given by Y-6,(x)-<>,(y)+<>,(zl+a ,z + Z(E ,(xl+ E ,(y))-X E,(x) [ Z-6,(xl-6,(y)+c>,(z)-YE,(x,y)+Xe,(xl RTz=RTr·YTl·xTz (3) 1 Finally, the transformation matrix describing the (12) relative motion between the cutting tool (i.e., Oz coordinate system) and the workpiece (i.e., Ox coor- where the term i(j, k) = i(J) + i(k). dinate system) is given by Equation (12) represents the actual position of the tool tip with respect to the table coordinate system xTz = (yTx)- 1(RTy)- 1 • RTz (4) after motions in the x, y and z axes by the respective slides. The tool path error is found by taking the Equation (4) reveals that we need to find three vector difference between the commanded positions homogeneous transformation matrices in order to de- and the act!1al position arrived at. Hence, the tool termine relative motion between the cutting tool and path error E is given by the workpiece. The transformation matrix for the 0, coordinate system which moves a distance X along E= the x-axis with respect to the nominal position of the Or coordinate system, is given by 14 -6,(x)-. 6,(y)+c>,(zl_+a, Y+a,Z+ Ye,(x.y)- Z[e,(y)+e.(x)l] X] -<),(x)-6,(y)+<),(z)+a,Z + Z[e,(x)+,,(yJI-Xe (x) [1 -1:z(x) Ey(X) o,(x) - -6,(xl-<>,(y)+<>,(z)-Ye,(x.yJ+XE,(x) ' T _ Ez(X) 1 -e,(x) Dy(X) (13) y X - [ -Et'<) e,(x) 1 Dz(X) 0 0 1 Inspection of the above equation shows that there are 18 error terms (see Table 1) required to describe (5) the errors of a three-axis milling machine. Reference When the Ov coordinate system moves a distance 14 provides detailed mathematical development. Y along the y-axis the transformation matrix with However, the focus of the research at the University of respect to the reierence system is given as Maryland is primarily contour machining (i.e., end milling) where the z slide remains stationary during -e,(y) -Ey(y) (6..,(x) J the machining operation. Hence, only the xy plane of T -[ 1 -e,(y) Dr(Yl - y the machine tool is considered for further investiga-E,~y) R y - -Ev(Y) -1;,(y) 1 oz(y) tion. This leaves seven error terms associated with the 6 0 0 1 xy planar motion which are identified by an asterisk in Table 1. Equation (13) therefore simplifies to (6) where E = c-c5,(x) - O~(y) + rx_, y + Ye,(X) + Ye,(y) J -Dy(x) - Dy(y) - Xe,(x) A,(yl = o,(yl + <¥, Y (7) (14) Similarly, the transformation matrix when the 0, coordinate system moves a distance Z along the Equation (14) applies to all points inside the z-axis, with respect to the 0, coordinate system, is working volume of the machine (i.e., xy plane for this given by case). The entire plane is divided into 0.0254 m Page 1018 squares to keep the measurements required at its O 2.54 m min-1 +1.27 m min-1 CJ0.762 m min-1 minimum. Since the overall goal of the proposed ..i.. 0.254 m min-1 A Rapid approach requires the~e ~e~su:eme~t~ at regula~ in- tervals during a machines lifetime, 1t 1s economical to reduce the total time required for measurements. The data measured at the nodes (centre of square) can then e :::,. be interpolated to obtain the errors at intermediate ,._ 0 points. Hence the tool path error at each node_ re- ,._ quires seven error terms to be measured experiment- w ally. In addition, to include the. overshoot and under- shoot dynamic errors, the data must be collected at various ieed-rates and also in both positive and negat- ive directions to account for direction dependency. . Slide position (ml Experimental work Figure 6 Scale error along x-axis The net tool position displacement relative to the machine table for each axis is determined from seven linear interpolation between the data points is an error terms, listed in the previous section, which are acceptable method of calculating the position errors at measured under static conditions using an HP 5528A- positions between the data points. . based laser measurement system ts. The water coolant Similarly, the axial scale errors along the y-axis, system of the magnetic spindle remained off in order c:>y(y), were measured and evaluated in the same to minimize thermal effects. However, the bulk manner as above. Like the x-axis, the y-axis errors spindle temperature (from thermocouples located at . show a strong dependence on position and direction, strategic locations of spindle head) and machine ambi- as shown in Figure 7. As for feed-rate dependence, the ent temperatures (from thermocouples located at error appears to become smaller as the table velocity strategic locations on machine slides) thermocouple increased for negative motion. In the positive direc- voltage outputs are monitored so that thermal eftects tion, however, the errors appear to be less dependent due to the servo motors and ambient conditions can on feed rate. be removed from the geometric position error data. The Y-straightness error of the x-axis, by(x) was Four types of measurement were conducted, viz, measured at the same five feed rates in both directions axial position, straightness, angular and squareness to (see Figure 8 for the negative direction). The errors are obtain all the seven error terms. Each error term was small (less than 2.5 µm) compared to the axial posi- measured at 0.0254 m increments of table motion at tion errors. They showed little dependence on feed five commonly used feed rates (0.254, 0.762, 1.27, rate or direction but did vary with position. The 2.54 mmin- 1 and rapid (5.08 mmin- 1)) in positive X-straightness error of the y-axis, o,( yl. on the other and negative directions. Six sets oi data are recorded hand, are slightly larger and show a larger depend- at each feed rate and the standard deviations are ence on feed rate and direction, as shown in Figure 9. computed to ensure that the averages of the errors Standard deviations of the straightness errors at each represent a repeatable error. Since the error terms are position along both axes are of the same magnitu~e as measured at several feed rates in both directions, those for the axial position errors. Due to the relative repeatable errors due to the mach(ne'_s servo_ drive magnitude of the straightness errors compared with controller will also be accounted tor in the tmal other errors measured, they will be neglected and geometric position error map. assumed equal to zero in the final error ,:nap matri_ces. Figure 1O shows the angular error ot the x-axis about the z-axis (ie., yaw of table slide), e~(x). The Results The average axial scale error along the x-axis, Ox(x), is shown in Figure 6 for the traversing oi the machine's O 2.54mmin-1+1.27mmin- 1CJ0.762 mmin- 1 table at five feed rates in the negative direction. The .i,.Q.254 mmin-1 A Rapid errors show a strong dependence on position and feed rate. The standard deviations of the errors at each position are approximately an order of magnitude less 0 than the errors themselves. It is clear from this result e that if one was to measure the errors at only one feed :. rate, the resulting information would not be valid at ~ -1 other feed rates. Interestingly, this procedure is very ... w repeatable with respect to table position and feed rate, as shown by the small standard deviation of the errors. A strong dependence on the direction of table motion was observed. The plot'for the negative direction is not shown for brevity. This direction dependence is due to backlash errors in the geared drive-trains and different geometric errors on each face of the lead Slide position (ml screw threads. Since the data points are well behaved, Figure 1 Scale error along y-axis Page 1019 O 2.54 m min-1 +1.27 m min-• C0.762 m min-1 angular errors are quite small (less than 1 arc-sec) for 1 A0.254 m min-1 .::.Rapid all feed rates except for 0.254 m min- • Examining the 1.2 raw data revealed that large changes in the bulk spindle and machine ambient temperatures occurred 0.9 E during the test. This is substantiated by the large . ::,. standard deviations associated with the average errors. e The main purpose of the measurement of angular ui 0.3 errors is to correct the straightness and axial position 0 measurements for angular rotation of the optics. There- fore, the angular errors should be of the same mag- nitude as the straightness errors. Therefore, the 0.254 m min- 1 angular error measurements are dis- -0.6 counted on the basis of the data recorded at the other -0_9.....__ ________________ _. feed rates and the large standard deviation of the -0.5 0 average errors at each position. Slide position (ml Figure 11 shows the angular errors of the y-axis Figure 8 Y-straightness error of x-axis motion about the z:-axis (ie., yaw of cross slide), E~(y). The angular errors for positive motion are of the same magnitude as those encountered along the x-axis. There appears to be no reason to discount the angular errors measured along the y-axis during the negative translation of the table. Therefore, their sine and cosine contributions to the y-axis straightness and O 2.54 m min-1 +1.27 m min-1 C0.762 m min-1 axial position error terms will be calculated and A 0.254 m min-1 .::.Rapid included in the final geometric position error map. The largest contribution by the angular errors to the straightness error measurements is - 3 arc-sec. This error is equivalent to a perpendicular displacement of the table of + 2.59 f.Lm over the 0.178 m measurement range. The contribution to the axial position errors would be a negligible 25.4 x 10-9 f.Lm. The squareness error between the xy axis, a,, is determined by performing two straightness measure- ments using an optical square. The squareness error angle (clockwise positive) is calculated to be -1.719 x 10-1 deg using the x-axis as a reference. This error results in a contribution to the y-axis straightness error and will be included in the final -2.0'--------------------' -0.24 -0.06 error map. Slide position (ml The recorded error terms are then analyzed and Figure 9 X-straightness error of y-axis motion reduced. The measured angular errors were used to remove the axial and perpendicular motion of the table due to rotation about the tool from the straight- ness and axial position measurements. Further, the squareness error between the x and y axes was resolved into sine and cosine components and added O 2.54 m min-1 +1.27 mmin-1 c0.762 m min-1 O 2.54 m min- 1 + 1.27 m min-1 a 0.762 m min-1 A 0.254 m min-1 ARapid A 0.254 m min-1 A Rapid u.. "I ' .. ~ 2... ::! 0 ui ..-40 .. . UJ -80 -120 ,...___. _ __.. _ _.____.....__....__...___.____._ __._ __, -0.5 0 0 Slide position (ml Slide position (ml Figure 10 Angular error of x-a.'(iS about z-axis Figure 11 Angular error of y-axis about z-axis Page 1020 to the axial position and straightness error terms. The resulting geometric position errors associated with the motion of the table and cross-slide are -10 represented in the form of an error matrix. This matrix consists of scale and straightness errors for each axis e -20 ::I. for each node for five feed rates and for positive and C negative approaches. Since error data at several feed ·2 -30 rates is present, errors due to the servo drive and C E electronic control system are included in the map. The ... error matrices specifically consist of four matrices (two -; -40 C for each axis): -50 0 Bulk spindle temperature [O,(x)I = (error, machine position, ± feed rate) Ambient machine temperature [<5,(y)I = (error, machine position, ± feed rate) fO 23 24 r(x)I = (error, machine position, ± feed rate) 21 22 25 26 27 28 [Dy(y)I = (error, machine position, ± feed rate) Temperature (°C) In summary, the geometric position errors possess Figure 12 Thermal deformation due to recovery from a position, direction, and feed rate dependence. All cool down errors associated with a particular axis had a small standard deviation but no apparent trend of the de- pendence on the above parameters. Therefore, com- 0 Bulk spindle temperature pensation can be performed by using the above error ~ Ambient machine temperature matrices. More detailed information on experimental 4 data can be obtained from Reference 16. e :I. 3 C .2 Thermal deformation error characteristics 0 E 2 The thermal deformation of the machine tool structure 0 results in a net displacement of the tool relative to the .. C workpiece. Thermal deformation, with the magnetic spindle, is complicated since it has air cooling and extensive cooling water circuits around the magnetic coils. Changes in temperature at different locations on 26.0 26.4 26.8 27.2 27.6 the spindle and machine frame can be measured using Temperature (°C) thermocouples and linked to the thermal deformation error by either a functional relationship or a 'look up' Figure 13 Thermal deformation due to warm up table. In this study the geometric position error and understandable, since the spindle is well removed thermal deformation error are investigated. The from the servo motor heat sources. measurement and analysis of these errors are pre- sented in the following sections. Modelling Experimental work Using the data from these tests it is possible to construct a linear model of the thermal deformation Tests were performed to determine the thermal defor- x error along the y-axis based on the change in the bulk mation errors along the and y axes. The deforma- spindle temperature and the change in the ambient tions experienced by the spindle head due to the machine temperature. By modelling the spindle as a thermal shock created by the cooling water flowing fixed beam, a matrix equation can be developed to through the magnetic spindle proved to be significant. describe the thermal deformation in the y axis as 17 Although a model for thermal shock was derived, it is not reported here since this problem was eliminated or= [n[cl (15) by redesign of the spindle cooling system. Only the where errors due to changes in ambient conditions and servo motor heat sources are discussed further. Since the [n = [l'.lT,t.Tb) (16) spindle bore/tool is centred about the x-axis of the [Cl T = [C1 C2] (17) spindle housing, the deformation errors along the ,'<-axis are symmetric, with no effect on tool position. where l'.l T. is the change in the ambient machine Hence, the following model was developed only for temperature, a. Tb is the change in bulk spindle tem- the y-axis thermal deformation errors. perature and C1, c2 are constants. Several 'recovery from cool down' tests were A least squares fit can be performed to solve for C1 conducted for the y-axis, and Figure 1 2 shows a and Ci typical error plot obtained. In these tests the deforma- tion of the spindle varied inearly with respect to [nT6y = [nf[n(C) (18) temperature. Results from having only the servos on [cl = ([TJ)f[T))- 1 [nr o, (19) 'warm up' are presented in Figure 13. Interestingly, the bulk spindle temperature does not change; this is The unbiased variance is given by: Page 1021 ai = J(c)/(N - n) (20) CAD where N is the number of data sets and n is the number of parameters (constants). Now N Post processor J(c) = L e7 (21) where e; is the error of the least squares fit and is M/G codes given by e = c5y - [n[cl (22) X, Y, Z position Two hundred and eighty-three data sets were Machine \ Error used to evaluate the C vector. The manipulation of rn controller controller and Dy was accomplished using the MATLAB software package. The following results were calculated [cl= (5.7456 - 10.2997JT ,umdeg- 1C (23) Slide movement Magnetic bearing a = 2.8245 ,um (unbiased standard deviation) (24) controller Therefore, the thermal deformation error of the Matsuura/S2M milling machine along the y-axis is Nominal given by: motion Magnetic spindle Dy = [t. r.t. Tb][5.7456 - 10.2997JT ,um (25) movement The bulk spindle temperature, as used here, in- cludes the thermal effects due to the heating of Incremental bearings on the spindle head. movement Results Quasi-static thermal deformation errors (gradual tem- Accuracy enhanced perature changes in the machine components) be- part haved linearly with respect to temperature changes, and thermal deformation errors along the x-axis Figure 14 Schematic diagram of hierarchical error cor- proved negligible compared to those along the y-axis. rection A magnetic bearing spindle error compensation controller, under development, can use the thermal deformation model of linear deformation to correct for with the machine program code remaining un- the errors produced by quasi-static temperature changed. In operations like end milling, orientation of changes. By monitoring the above two temperatures the tool is important and can be changed easily with a thermal error can be compensated for by moving the magnetic spindle. This methodology appears to be a tool inside the air gap of the magnetic spindle. practical way to comprehensive error compensation. This approach differs from pre-compensation methods discussed in earlier sections in the following way Error correction methodology D The M and G code input to the machine controller Figure 13 shows a schematic diagram of the hierar- need not be changed; hence the source code is chical error correction methodology that has been kept intact developed and implemented at the University of Mary- D The error correction is achieved in real time, with land. The details of this methodology and its valida- tion have been reported elsewhere 18 on-line control of the spindle shaft translation and • In this approach, tilt the error correction is achieved by superimposing 0 The resolution and bandwidth of the incremental magnetic bearing spindle movements (high resolution motion (of the spindle) is independent of machine and wide bandwidth incremental movements) upon slide motion, thereby allowing higher resolution nominal machine table movements. The post proc- and bandwidth of error correction essed M and G codes are directly fed to the machine controller, which sends out motion commands for the X, Y and Z movements. These movements are con- Validation tinuously sensed by position sensors and displayed on the machine controller in real time. This real time X, An error correction experiment was performed to Y and Z position information is fed to a control demonstrate and evaluate the error characterization system to generate incremental motion signals for a and on-line correction of milling errors. Experiments magnetic spindle controlter. These signals are propor- were performed on the Matsuura MC500V vertical tional to the position vector and the three orientation CNC machine retrofitted with the 52M magnetic vector terms of the error matrix. The displacement-bias spindle system and error minimization controller. This thus induced is used to translate and tilt the spindle- experiment used the terminal point error matrix deve- tool system within its air gap. Accuracy is thus loped earlier, as codified in the file LASER.MAP. The achieved by incremental motion of the spindle itself HP 5528A laser metrology system was used to Page 1022 measure milling machine table position. The laser searchers_ are_ currently in progress to refine the error optics were affixed to the spindle tool holder, provid- characterization. ing a direct measurement of relative axial table posi- tion. From machine home, the axial table position Quality assurance performance command was stepped, in 0.0254 m increments, across the positioning range. ~he performa_nce of quality assurance by characteriza- Figure 15 presents the measured X-axis errors tion a~d ~n~hne correction ?f errors as reported in this (i.e., table slide scale error o,(x)) with and without paper 1s limited by the quality of error characterization on-line error correction at a nominal feed rate 18 of and by the ability to effect the proper correction. 2.54 m min - 1. These results indicate direction-depend- Using a pre-characterized error model, the quality of ent terminal point accuracy improvement factors of on-line error representation is dependent on two prim- five and three, respectively. Although Woytowitz 16 ary factors: reported the standard deviation of the terminal point 0 Identification of the error phenomenon independ- errors to be approximately one tenth the magnitude of ent parameters the error, the corrected error retains larger systematic 0 Statistical properties of the error phenomenon. errors. Since the calibrated three-sigma positional un- certainty of the spindle position is approximately Recent metrological experience indicates that up 2.54 µ.m, these systematic compensation errors were to an order of magnitude improvement in CFI position- assumed to be caused by long-term drift in the error ing accuracy is achievable using pre-calibrated error phenomena. To evaluate the short-term terminal point compensation. Improved error characterization, as error compensation capability, the laser metrology well as compensation actuation, is required to obtain procedure was repeated at a single, 2.54 m min-1 feed this goal under realistic machining conditions. The rate. With a one-day turn around, between metrology on-lin~, terr:1inal point CFI error correction experiment and correction, the results in Figure 16 were ob- gr~ph1c_ally il_lustrates this point. Correction implemen- tained18. This experiment achieved more than an tation hm1tat1ons may be characterized in terms of order of magnitude improvement, between with and bandwidth and accuracy. Relative to tool path trajec-18 without on-line correction, of terminal point errors. tory dynamics (> 10 Hz ), the 125 Hz bandwidth of Continuing metrological investigations by other re- the existing 52M 825/500 is sufficient for effective error correction. O Uncompensoted, meon=6.60, std=5.59 A Compensated, meon=l.27, std=l.78 Future work Improvement factor= 5.19 In the immediate future, work on inclusion of dynamic 20 errors due to transient and steady state trajectory errors E into correction scheme will be explored. Following :,. 15 this, the CFD errors will be characterized by following 2- 10 the methodology developed by Zivi et al 18 . In this w category, specifically the ramp error due to deflection 5 of thin-ribbed components or due to the deflection of the tool while machining thick-ribbed components 0 will be investigated. -5 -10 Conclusion -0.55 -0.4 -0.25 -0.1 Tobie slide position (ml This study suggests that it is possible to assure the Figure 15 Terminal point error correction plot quality of machined parts by taking the approach of careful characterization and on-line correction of mill- ing errors. CNC machines fitted with magnetic bearing spindles proved to be ideal for such on-line error <> Uncompensated, meon=22.6, std=7.11 correction implementation. The characterization of CFI A Compensated, meon=l.78, std=1.27 errors revealed that the feed rate has a profound effect Improvement foctor=12.6 on the positioning accuracy of machines, which can 40 be corrected by including the feed rate as a variable in the error matrix. The thermal deformation errors 'E proved to be deterministic in nature and hence can be ::,. 30 compensated for. The experimental data showed that improvements in accuracy of up to an order of mag- ~ 20 w nitude can be achieved using this methodology. 10 Acknowledgements 0 The authors would like to acknowledge the contribu- -0.55 -0.4 -0.25 -0.1 tion to this work by Mr S. Shyam, Mr M. Woytowitz Tobie slide position (ml and Dr E. Zivi. This work has been supported by the Figure 16 Short-term terminal point error correction National Science Foundation through grant NSF plot 851 6218 and the Engineering Research Center at the Page 1023 University of Maryland and ONR Program Element manufacturing processes' DSC-Vol 7 (1 988) 41-49 61152N through the David Taylor Research Center. 9 DeVor, R. E., Sutherland, J. W. and Kline, W. A. Control oi error in end milling. 11th NAM RC (1 983) 10 Milner, D. A. Controller system design for feedrate References control by deilection sensing of a machining proces~ Int. J. MTDR 15 19-30. 1 Anand, D. K., Kirk, J. A. and Anjanappa, M. Magnetic 11 Rao, S. B. and Wu, S. M. Compensatory control of bearing spindles for enhancing tool path accuracy. Adv. roundness error in cylindrical chuck grinding J. Eng. Ind. Manuf. Processes 1 (1986) 121-1 34 104 (1982) 23-28 2 Anjanappa, M., Kirk, J. A. and Anand, D. K. Tool path 12 Zanbin, H. and DeVries, M. F. Microprocessor-based error control in thin rib machining. Proc. 15th NAMRC, compensation of leadscrew drive kinematic errors by a Bethlehem PA (1987) 485-492 forecasting technique. Int. J. MTDR (1984) 347-354 3 Anand, D. K., Kirk, J. A., Anjanappa, M. Zivi, E and 13 Anjanappa, M., Anand, D. K., Kirk, J. A., Zivi, E. and Woytowitz, M. A. Magnetic bearing spinal control. Proc. Woytowitz, M. A. Retrofitting a CNC machining center 15th Cont. Prod. Res. and Technol. Berkeley CA (1 989) with a magnetic spindle for tool path error control. Proc. 31-35 INCOM'89, Madrid Spain (1989) 4 Tlusty, ), Techniques for testing accuracy of NC machine 14 Shyam, S. Error compensation of accuracy enhancement tools. Int. J. lvlTDR 12 (1971) in precision machining. M.S. Thesis, The Univeristy of 5 Dufour, P. and Groppetti, R. Computer aided accuracy Maryland (1987) improvements in large NC machine tools Int. J. MTDR 15 '5528 Laser Measurement System' User's Guide, Hew- 21 (1980) lett-Packard Literature 6 Donmez, A., Liu C. R., Barash, M. and Mir, M. Statistical 16 Woytowitz, M. A. Tool path error classification and analysis of positioning errors of a CNC milling machine identification for high precision milling with a magnetic J. Manuf. Syst. 1 (1 982) bearing spindle. M.S. Thesis, The University of Maryland 7 Zhang, G., Veale, R., Charlton, T., Borchardt, B. and (1989) Hocken, R. Error compensation of coordinate measuring 17 lncropera, F. P. and DeWitt, D. P. 'Fundamentals of heat machines Ann. CJRP 34 (1985) and mass transier'. 2nd edition, John Wiley, NY (1985) 8 Anjanappa, M., Anand, D. K., Kirk, J. A. and Shyam, S. 18 Zivi, E. Robust control of magnetic spindle for error Error correction methodologies and control strategies for compensation. Ph.D. Thesis, The University oi Maryland numerical controlled machining. 'Control methods for (1989) Page 1024 MAGNEl1C BEARING SPINDLE CONTROL FOR ACCURACY ENHANCEMENT IN MACF:IINING E.L Zivi1 D.I(. Anand M. Anjanappa2 J.A Kirk Department of Mechanical Engineering and Systems Research Center University of Maryland-UMCP, College Park, MD 20742 1 Senior Iroje~t E1:gineer, David Taylor Research Center, Annapolis, MD Umvers1ty of Maryland-UMBC, Baltimore, MD 21228 ABSTRACT Utilization of a magnetic bearing spindle can not only provide benefits of high speed machining, but can also enhance part accuracy. Error compensation, exploiting the ability of a magnetically suspended spindle to translate and tilt, within air gap limitations, provides perturbational corrective motions. This hierarchical error compensation structure was implemented using a microprocessor based error minimization controller providing real-time error compensation based on a pre-calibrated error characterization driven by on-line process monitoring. Ongoing error metrology, along with levitation system identification and modelling. provided the basis for the control system synthesis. An error compensation methodology was derived which provides the ability to correct a general class of cutting force independent, as well as, cutting force dependent, dimt:nsional errors. The cutting process is viewed as an ordered sequence of tool path trajectorit:s. Sharing of numerical control part program codes, augmented by handshaking functions, enables coordination of computer numerical control and error compensation functions along the tool path tmjectory. Using feed forward compensation, active magnetic bearing spindle error compensation of several sample t:rror sources was expc:rimentally evaluated. INTRODUCTION The purpose of this research was to enhance the accuracy of the metal removal process through introduction of hierarchical and incremental error compensation. This incremental compensation has been provided via translation of a magnetically suspended spindle, within the active magnetic bearing (AMB) air gap. Much of the classification and identification of tool path errors, used in the error compensation process, was derived from the related metrological investigation of Woytowitz (1989). Accuracy can be ddined as the dimensional conformance of the finished part to the dimensional and geometric specifications (Hacken, 1980). During the metal removal process, finished part dimensional errors are generated by the interaction of various physic:il phenomenon. Machining errors may be divided into two primary classes: cuui11g force To be presented at the 1990 ASME Winter Annual Meeting, November 1990 Page 1025 independem (CFI) and cwLing force dependem (CFO) (Anjanappa et al., 1987). Sources of cutting force independent errors (Woytowicz, 1989) include: • Kinematic errors in the slides and leadscrew, • Dynamic positioning and contouring errors, • Fixturing errors, • Thermal transients. Cutting force dependent error sources, which are directly related to the metal removal process, include: • Tool and workpiece compliance, • Tool degradation, • Contouring errors generated by differing axial components of cutting forces, • Thermal variations resulting from the cutting process. Various error sources contain both deterministic and stochastic components. These errors can be represented as a vector difference between the required and actual tool paths. Two primary strategies have been employed to minimize machining errors, viz, error avoidance and error compensation. Error avoidance strategies involves improvements in the fundamental machine accurac..-y. Model-based error compensation, as adopted in this research, assumes that the deterministic error is repeatable and can be determined a priori (Woytowitz, 1989). One unique aspect of this research is the utilization of magnetic bearing technology to provide the tool path error compensation mechanism. As shown in Fig. 1 (SKF, 1981), magnetic bearings can be used to replace conventional mechanical spindle bearings. In this . application, magnetic bearings provide support in four radial and one axial degrees-of-freedom. Since the magnetic bearings are typically open loop unstable, position sensors provide feedback to a stabilizing levitation controller. An integral spindle motor controls the sixth (spin) degree- of-freedom. Mechanical touch down bearings also serve as backup bearings. Figure l Magnetic Spindle Structure The present investigation approaches the machining process accuracy enhancement problem from a control sy:stems viewpoint. This involves the application of system identification, analysis, modelling, control system synthesis, and implementation methodologies to achieve magnetic bearing spindle based error compensation. The mathematical development of these methodologies has bc::,::n reported separately. Page 1026 ACCURACY ENHANCEMENT Accuracy enhancement methods attempt to compensate for cutting process dimensional errors based on direct observation, estimation, or model-based prediction (Blaedel, 1980). Optical error observation methods, for machine translation and rotation errors, have been established by Lt:ete (Leete, 1961). More recently, Ni and Wu (Ni and Wu, 1987), have developed a five degree-of-freedom on-line laser metrology system. Gayman (Gayman, 1987) has discussed various error sources and compensation methods. Highly accurate linear displacement transducers including optical or electromagnetic sensors on glass scales and fine tooth rack and pinion feedback drives can be used to directly measure table position. Cutting force estimates, based on sensed bending have been used by Watanabe and Iwai (Watanabe and lwai, 1983) to estimate cutter detlection. Model-based error compensation assumes that the error is repeatable and can be determined a priori (Woytawitz, 1989). T!usty (1971) has developed a master part method for measurement of the CFI positioning errors of a vertical milling machine. More recently, Pautler (1983) has reported the development of an optical spaceframe for three dimensional measurements with a l micro11 resolution and a 10 micron long term repeatability. Dufour and Groppetti (1980) introduced the formulation of an error matrix representation of off-line positioning error measurements. Donmez et al., (1982) refined this approach using statistical techniques. Position dependent milling machine errors were compensated using modified part programs resulting in a 40% improvement in part accuracy. Subsequently, Donmez (1985) developed an interface to a turning center controller for direct compensation using laser metrology error maps. Similarly, Sudhakar (1987) has employed laser metrology based error mapping to modify part programs for error compensation of a vertical milling center. Ferreira and Liu (1986) have constructed a rigid body kinematic error model, composed of linear links and joints, for a three axis machining center. This model requires a small set of measured error vectors, augmented by a heuristic model building procedure, which includes thermal effects. Several researchers have investigated the application of incremental displacement actuators for error compensation. Chaudhuri et al., (1977) has proposed and analyzed the use of hydrostatic bearings with negative stiffness to compensate for machine/tool static det1ections. In this analysis, it is shown that over compensation leads to instability. Kanai and Miyashita (1983) have also discussed the application of hydrostatic, aerostatic, and piezoelectric actuators for correction of kinematic and dynamic motion errors. Kouno (1984) has implemt:nted a microprocessor controlled piezoelectric incremental error compensation using L VDT measured position feedback. Starosolsky and Stetson (1987) have discussed the potential of two-stage actuation to provide the range of a coarse actuator stage, coupled with the higher bandwidth of a fine actuator stage. MAGNETIC BEARING SPINDLE FACILITY In order to experimentally evaluate potential active magnetic bearing (AMB) error compensation schemes, considerable effort was invested in the establishment of the magnetic spindle laboratary. This facility is composed of the following principal elements (see Fig. 2); • Matsuura CNC vertical milling machine, • S2M magnetic spindle system ( model 825/500), • Metrological apparatus including laser interferometer, • Instrumentation and data logging, • Error minimization controller. Hardware interfacing details have recently been reported by Woytowitz (Woytowitz, 1989) and will not be repeated herein. Implementation of the active magnetic bearing (AMB) error correction methodology involves the interaction and coordination of four independent controllers, viz, existing CNC controller, active magnetic bearing controller, variable speed spindle drive, and on-line error minimization controller. The functional requirements can be summarized as, providing the operational control necessary to operate the CNC mill with the magnetic bearing spindle, impl<=m ... :f } '" ' • 11 • t 3 ! / -c .... _':::-:. ____ ---l. ~·j l s O! I i -l f solid~ x - Simu~ation & experimene (eopl j -• dasned & a - Simulation & experiment {boc., I -6 -l 0 1 s ,; 7 8 3 Time, m.s , ,Sensed, Mer 5~ariog faeces ,;ooo J oL• ,// ;~:,.. \~ l. 200 ~ of,----~~J ~ j ~ 'l i'11--~ -200 \~ I -•oo -,ooL------------------------------- i -1 0 l 2 l • s .; 1 •- ---9 Fig.4 Spindle Simulation Validation - Displacement & Force " 10 a g n n· l i C u d _:~ e -10 r I d I -15 b -20 10• lO' F'requency ~ H'Z. ? n soj a s " or -so r d e r Data uarkers denoce g -100 r experimental resuLes " -150 i- s" -200 to• 10' 10' 10' Frequcency, H~ Fig.5 Spindk Simulation Validation - Frequency Response Page 1030 command applit:d both to top and bmtom bearings. This simulation also si:rves to validate the ini:rtial spim.lk model developed. lnercl~i SpLndle $tep K~sponse ' I ~ .. Top uedr1nq m~~nu•eU response ., ~ o .. 11oc.c.0111 be.trinq me.t-sured res~onse s -~ '\.~~. s:olitl .. Top s u1ulo1t.ed .casponse w/ Xt .. l. 2 ? ' l ":'~x,. dashed "" !lOt.CO-D'I s-it1u.1lat.ed ..-cS?Onse "'/ Kb - i. l n 1,.\• (lt-t.~ Kb .. tot"CC :.:.c.J.ii.ng rel. r.o P.nqr. e!:.tina.t.~!l) d l 0 t '-,~~~ e ' \~.~. -• ' . 0 • i -2 t l 0 n -3 ·• :: ~ - 01- '---~----~---5 -~s- --1 ---a- --9 -- 1,1 Fig.6 Spindle Step Response ERROR MlNIMIZATION CONTROL SYSTEM SYNTHESIS As discussed before various methods have been employed to implement two fundamental error minimization approaches, viz, Error avoidance and Error compensation. Error avoidance involves improvements in the fundamental machine accuracy. One common operational error compensation method involves a "cut, measure, adjust" cycle. Using this iterative approach, the machining process is adjusted until the finished part satisfies the accuracy requirements. This approach is generally time consuming, wastes workpiece material, and may require constant re-adjustment. Technology based error compensation methods attempt to cancel errors determined from direct observation, estimation, or model- based prediction (Baedel, 1980). Direct observation systems suffer from several limitations, such as, dedk.-ated metrology equipment requirement, require delicate instrumentation generally unsuited for a production environment, and that no method exists to directly measure tool or workpiece deflection. Although cutting force measurements have been successfully used to estimate cutter deflection, general error estimation approaches suffer due to the complexity and wide variations encountered in the metal removal process, as well as, problems associated with accurate process monitoring. Two aspects of fundamental machine accuracy merit further analysis. First, note that typical axis positioning loops, in a typical CNC machine, do not feedback the desired axis position. Instead, servo motor position feedback is employed to close the control loop since it is easier to measure and avoid controller performance problems. Introduction of table position feedback creates controller synthesis problems due to the mechanical drive train and table non-linearities including: compliance, hysteresis, stiction, and backlash. If the mechanical elements are included in the loop, stability requirements result in substantial control system bandwidth degradation. Various techniques, such as leadscrew and backlash compensation, have been implemented (Yasnak, 1980) which attempt to compensate for open loop mechanical axis positioning errors. The second limitation involves the cross coupling of multi-axis motion Page 1031 control. Although axis cross coupling compensation schemes, such as scan decrease multi-axis contouring errors, the effectiveness of these methods is limited. This limitation occurs since the error dynamics and corrective actions are derived from the same axis positioning loops. For the typical case of dynamically matched axes, the time constants of the compensation dynamics are similar to those of the error dynamics. Recently, robotic applications have employed hierarchical control structures to resolve compliant element robotic positioning problems. The hierarchical positioning strategy provides one set of actuators for gross motion and a second, higher bandwidth, actuator set for fine motion compensation. In this research, the ability of the magnetic spindle to translate, wi,hin air gap limitations, is employed to implement the fine motion control providing hierarchical based error compensation. Previously reported applications of hydrostatic, aerostatic, and piezoelectric incremental displacement actuators for correction of compliance, kim:matic, and dynamic motion errors (Chaudhuri et al., 1977, Kanai and Miyashita, 1983, Kouno, 1984), have tendt:d to lack a general error compensation approach. Staroselsky and Stelson (1987) have presented a more systematic analysis of tht: benefits of two stage actuators for milling applications. This approach is limited due to the reliance on ball screw drives for both coarse and fine motion control. Magnt:tic spindle based hierarchical compensation includt:s the intrinsic high spt:t:d machining capabilities, as well as, internal spindle position and bearing force monitoring facilities. Establishmt:nt of an error minimization mt:thodology requires resolution of several issues: • On-line det..':rmination of (apparent) errors, • Calculation of corrective action, • Actuation of corrective action, • Coordination of machining and compensation. Error determination is bast:d on pre-calibrated representations codified in an error map formulation. On-line monitoring of the machining process, using interfaces described in earlier section, provides the independent parameters, used to extract real-time error estimates, from the error map representation. These perturbational corrective actions are implemented by displacing the spindle within the magnetic bearing air gap. Since the machining process is reviewed as a sequence of tool path trajectories, coordination is provided by downloading a representation of the part program to the error minimization controller. Inclusion of handshaking functions, allows the CNC and error minimization controllers to operate in a coordinated fashion. Since the error minimization controller has a complete representation, of the desired tool path, future errors can be anticipated and thus more effectively compensated. The conceptual error compensation structure is diagrammed in Fig. 7. Cutting process parameters, such as magnetic bearing forces and spindle displacements are a,;ailable to derive cutting force dependent (CFD) error formulations. In the current investigation, compensation has been limited to cutting force independent (CFI) facrors driven by the programmed tool path trajectory. After summing the online CFI and (potential) CFD error estimates, the incremental corrective motion commands are transformed into the magnetic spindle coordinate system and applied to the levitation controller ( see Fig. 8 for the physical structure of the accuracy enhanced system). The portion of the figure, above the dotted line, represents the conventional CNC milling machine. The accuracy enhancement, shown below the dotted line, includes the error minimization controller the magnetic spindle system, and the required integration and coordination logic. ERROR COMPENSATION CONTROLLER IMPLEMENTATION The error minimization controller has been implemented using an Intel Multibus I real-time computer system. This system is bused on an Intel SBC386/24 processor board containing a 16 MHz 80386 CPU and 80387 floating point processor. Real-time I/0 is provided by Multibus-based ND, DIA and digital I/0 boards. The analog-to-digital (ND) processing is performed using a Date! ST701 intelligent ND board. In order to provide sufficient performance, the ST701 was modified to incorporate onboard hardware scan clocking (Zivi et al., 1989). Initiation of ND channel scans (strobes) is switch selectable at a software Page 1032 from SPiodle 6 v1, ~2• 4w1• °'•,12 -... CFD Fv1• ?v2~ Fwi• ~w2 '--9 Coapensa1:.ion Spindla S{Ml-4, w .-., CFl C0•ia•n:1a.c.1.on: I i -T•rainal .error Map PtPil XiHiDaS CNC '"· -Trajec1:.0ry Error Map X, Y~ Z Oeair&d Poaic.ion ~ I CooNin&co I --ft..11.•P error K.Ap i. 'f. i Voloc.iey cc-a.ands 0 Tra-natOr'II -Oynaa.i,.c &rror Map - CO•J)49RA4C.ion Han4.sfi4kinq ,, ' '~ Coapansac.ioa: "xi rroa er:-fnaded CHC Codes 4-x ca ...l.: '<0,:Y "Yl 4q!.£C.tlClil Fig.7 Conceptual Error Compensation Structure NOTE, X. k Y-~ loops omitted for bl'evity Z.AXIS DC I I z..,XIS Ol'TICAL • • • SE!lVO/Dll[VE I MOVEMENT ENCODER x. f Y. j z. Commimd,~d- Pon.,Um t key, which initiates the standard application shutdown procedure. Due to the installation of hardware interrupt service routines, real-time processing should never be aborted by other means (such as pressing "'C). In the case of an improper shutdown (no FORTRAN STOP message), the computer should be immediately rebooted to avoid corruption of tht: system. The basic accuracy enhancement software structure is presented below; 1. Initialize l/0 hardware 2. Read analog UO configuration file 3. Load error maps 4. Load part program representation 5. Initiate real-time processing: (a) Initialize combined ND & position interrupt handler (b) Initialize M-CODE interface interrupt handler (c) Initialize & start intelligent ND processor (d) Spawn control task ( e) Wait for termination event (f) Shutdown real-time processing 6. Optionally write results file 7. Shutdown application. Step 1 initializes and performs a simple sanity check for the binary posmon interface. In addition, the intelligent ND processor is reset and the five degree-ot'..freedom DIA spindle position command interface is initialized to the home position (center of the air gap). This latter operation is essential since the D/A hardware powers up in a minus full scale (-10 V) condition which exceeds air gap levitation limits. Step 2 reads and processes the user specified .CFG ASCII coded configuration file which describes the mapping from physical analog I/0 channels to logical software sensor and actuator variables. Physical channel numbers O through 31 refer the 32 available ND inputs while channel numbers 32 through 39 refer to the eight available DIA channels. The configuration file also contains the sensor and actuator scale factors, offsets, and additional descriptive information (Zivi et al., 1989). Step 3 loads the user specified ASCII coded .MAP error map file which contains the representation of the machine errors to be compensated. The currently defined error representations are: Termi11al poim error = f(positio11, 11omi11al feedrate) Trajectory error = f(posi1io11, feedrate) Ramp error = [(position, feedrate) Dynamic error = f(positio11 relarive to activation) In the current implementation, the first three error representations are mutually exclusive while the fourth provides an additive Y-axis correction. The first three error representations are implemented as two dimensional error maps defining a axial or ramp error in the terms of the position and velocity along the axis. Ramp errors occur due to the cutting force dependent defection of thin ribs. Since the S2M B25/500 magnetic spindlt: tilt is limited to ± 0.04 degrees, by air gap limitations, this investigation does not include ramp error compensation. To support the trapezoidal compensation experiment, a minor variant of the, generic CTRL program, CTRLxy, was created which interprets axial trajectory errors in terms of the Page 1034 orthogonal axis position and nominal vt:locity. Stt:p 4 !oar.ls tht: user spt:citied .CNC ASCII codt:d file which provides a reprt:sentation of the CNC part program as requirt:d to support cooperation between the CNC and error minimization controllers. The structure of the .MAP and .CNC files is defined in derail in (Zivi 1990). Upon successful completion of the preliminary processing, step 5 initiates real-time processing via a FORTRAN main program call to a PLJM subroutine, STARTUP. After initializing the proper PLJM execution environment, step (a) spawns an RMX interrupt task which establishes the combined binary position and analog input interrupt handler and then terminates. Step (b) spawns a second RMX interrupt task which establishes the M-CODE handshaking interface interrupt handler and then also terminates. Step (c) spawns an RMX task which stans the Datel ST701 intelligent ND processor and then terminates. Step (d) spawns an RMX (control) task which performs the error compensation functions. After spawning the synchronous tasks, STARTUP suspends itself (step (e)) and waits for a shutdown signal implemented using an RMX semaphore. The shutdown signal may be generated by successful completion of the c:rror compensation process, detection of a software error, or entry of the key, by the: operator. Regardless of the source, or current state of the real-time processing, the shutdown signal initiates step (f) which systematically terminates all real-time: tasks and interrupt handlers. Once the real-time PLJM software has been shutdown, control is returned to the FORTRAN main program. Step 6 provides the option of creating a results file log containing the binary position data, analog input signals, and other selected variables in MATLAB compatible time series formaL This important capability allows post test analysis and debug of the error compensation process. Step 7 finalizes shutdown of the error compensation process, returning the operator to the RMX II operating system. As outlined below the control task performs the actual real-time error compensation functions; 1. Lookup ND & DIA l/0 mapping 2. Initialize error compensation 3. Establish error compensation origin 4. DO FOREVER (a) Wait for signal from interrupt handler (b) IF new M-CODE received from CNC controller THEN Change operational mode (c) Lookup error from error maps ( d) Transform & rate limit compensation ( e) Output compensation to levitation controller (t) Optionally log current control parameters 5. END OF DO FOREVER LOOP The control task has been developed as a distinct, self contained module to facilitate future enhancements and extensions. CONTROL SYSTEM VALIDATION Several error compensation experiments were performed to demonstrate and evaluate the magnetic spindle error compt:nsation methodology. Experiments were performed on the Matsuura MC500V vertical milling machine retrofitted with the S2M magnetic spindle system and error minimization controller. Cutting Force Independent Error Compensation Non-cutting terminal point error compensation was performed first. This experiment used the terminal point error metrology of Woytowitz (1989) as codified in the error map file LASER.MAP. During both the metrolob'Y and compensation phases, an HP 5528A laser metrology system was used to measure milling machine table position. The laser optics were affixed to the spindle tool holder, providing a direct measurement of relative axial table position. From machine home, the axial table position command was stepped, in one inch increments, across the positioning range. Figure 9 presents the measurer.I X-axis errors before: Page 1035 and am:, ,-,mpc;:nsation at a 11uu1inal fc;:c;:drates of 100 ipm. /4 ·--· ,---,Xe.JA.,---,---, ,: l•provern•ut factor• 5.09 r 0.5 1' 0 r 0 "i -o.s Solid • ~ncomp., iue4n - 0.26, sLU - 0.22 L s Dashed • co~p., mean• 0.05, sea• 0.07 - l __ ___.._._ ___ ,,____,, ____ ,,_ __ _. ____~ ---------·----' -20 -1a -lti -14 ·12 -10 -a -6 -, ·l a x-a>!. Comma.ad VOLKMAN ,.._,_ S?M SPINDLE ...,.._,.. EXCITATION CO IfT ROLLER COIITROLLER Levitation p..,,. and r...ibadt Fig.2 Magnetic Bearing Facility Configuration interlock measures, interfacing necessary for communication to real-time process moniloring and control data, and coordination necessary to implement the error correction scheme. Central to this research is the implementation of the error minimization controller. The basic elements of the accuracy enhancement will be discussed in detail in a later section of this paper. Various on-line process parameters are provided to the error minimization controller as inputs lo the control algorithm. Based on these inputs, the error minimization control uses e predetermined error characterization to generate perturbational control signals to translate the AMB spindle to correct for dimensional errors. Available input parameters include: • X, Y, Z axis position commands, • X, Y, Z axis velocity commands, • Spindle displacement and bearing forces, • CNC part program commands, • Thermal conditions. Extraction of real-time X, Y, and Z axis position and velocity command data from the Ynsnac 3000G CNC controller was achieved by various hardware and software debugging methods applied to locate internal position data which could be extncted and provided to the error minimization controller. Several surgical ROM modifications were implemented to provide position dafa at a predictable (8 ms) update rate. Due to the high levels of electromagnetic interference (EMI) and potential for ground loops, all digital signals were opto- isolated and analog signals were differentially buffered. Since the B25/500 spindle imbalance induced runout exceeds the calibrated zero disturbance positional uncertainty by an order of magnitude, an effort was made to dynamically balance the spindle. Using the S2M provided spindle position data, and a Tektronix 2430A digital oscilloscope, two plane balancing, as recommended by Rao (1986), was performed. Spindle balance testing, performed during the calibration phase, of this research, detected no significant difference between runout with standard commercial quality single set screw tool holders and with dynamically balanced collet type holders. SYSTEM MODELLING Derivation of an analytic model of the S2M magnetic levitation system was required to analyze the magnetic spindle capabilities and to support control system synthesis. This process combined engineering analysis with experimental data to generate a validated model which closely replicates the actual system structure and behavior. As shown in Fig. 3, the magnetic levitation system is comprised of four major components: • PID controller including sensor signal conditioning, • Power amplifier end bearing stator windings, • Magnetic levitation forces, 286 Page 1049 Spindle rotor rigid body dynamic.~. cro•• coupllnq rore•• Controll•r co-•nd. ~---~ Splndl• Poaltion #Jtp/Coll Kaq k«c-lnq Ke<:hanleal Oyna•lca -~- Pol• P•lr Pol• Petr fluJC Coa11 Posltton S•n••d Pttyalcal Po•ltlon reeidback h•it1on r•.ctJ,«ck Concro\ler ....,plitier &oarlng/Splndl• Kodol Fig.3 S2M Magnetic Levitation System Structure The magnetic spindle dynamic model was implemented using the ACSL simulation language. This simulation model (Zivi, 1990) has a one-to-one correspondence with the actual structure of the S2M B25/500 magnetic spindle system. The simulation includes control signal and coil current limits; coil current rate limits; magnetic saturation, nonlinearities, and losses; air gap reluctance variations; and constant flux compensation. The S2M controller includes spindle position sensor signal demodulation, filtering, and the PIO control algorithm. The sensors and demodulation process is modelled as zero order system. After summing the Pl and O components, a final single pole of 10 KHz low pass filtering is applied to the control signal. S2M circuit board analysis, augmented by time and frequency domain experimentation, produced the analytical model. The modelling or amplifier dynamics was based on time and frequency domain experimental data and builds on the steady state parameter Identification. Equations for spindle rotor was derived from a simple inertial model, subjected to small angle gyroscopic effects. Simulation model validation was performed using experimental large signal step response and small signal frequency response data. As shown in Figs. 4 and 5, the simulation closely tracks the experimentally observed large signal step response. Figure 4 presents the spindle rotor displacement along with sensed bearing forces. The sensed bearing force data represents S2M bearing monitoring data which corresponds to the magnetic bearing pole pair differential coil current multiplied by the linear force coefficient. Sensed differential magnetic bearing force differs from the actual net bearing force due to the effect of variable air gap reluctance, magnetic saturation, and nonlinearities. The small signal simulation validation results of Fig. 5 compare experimental and simulation closed loop Bode frequency response. To obtain the experimental frequency response characterization, an HP 3582A spectrum analyzer was used to inject small signal (25 mV mts) sinusoidal excitation, into the S2M PIO controller feedback loop through the customary user spindle position command interface. Spindle displacement response was measured using the S2M sensed spindle position instrumentation interface. Simulation based frequency response was obtained from a linear state space model extracted from the nonlinear simulation using the ACSL numerical Jacobian solver. Prior to computation of the Jacobian, the ACSL equilibrium finder was used to ensure that the simulation was properly trimmed to steady state conditions with a null input command. The resulting state space linear model was imported into the MATLAB linear analysis environment to compute the Bode response. The gain increase in the 125 Hz range results from the derivative feedback and the rigid body spindle modes. A~ noted on the Fig. 5 graph, the spindle rotor first bending mode is also present in the experimental results. Figure 6 compares experimental and simulated step response for the case where a step 287 Page 1050 M l l • 0 , ., ' solld • x • Slmulatlon • experlfflent (topl -• dashed & o - Slmulatlon • experl11ent (bot.I .,'------''------'--___.,_ _ _._ __ ...._ __ _.__~.___ _ _._ _ ......, __ ~ -1 0 l l ) 5 1 8 Time, 11s l b f ' -400 ' ', .... .....' _ .. :, ... ' ,.,, -too'----'---'----'----'----'---'---'----'---~-~ -1 0 l l l 5 7 8 Fig.4 Spindle Simulation Validation - Displacement & Force II 10 ps~oiLS.11 J,nd 1.,;..Jtp. 11 pJ,.l'.jlMT R e.s 1>11.q.s IL, a g . ~. . Flrst D ' bending l t 0 mode . u _, 'I. d 'I e ·."'' " . -10 ' .... d b -15 -10 10• 10 1 10 1 10 1 Frequency, p "" h 50 a e• 0 .. -50 d e -100 Data marl key, which initiates the standard application shutdown procedure. Due to the installation of hardware interrupt service routines, real-time processing should never be aborted by other means (such as pressing "C). In the case of an improper shutdown (no FORTRAN STOP message), the computer should be immediately rebooted to avoid corruption of the system. The basic accuracy enhancement software structure is presented below; 1. Initialize 1/0 hardware · 2. Read analog 1/0 configuration file 3. Load error maps 4. Load part program representation 5. Initiate real-time processing: (a) Initialize combined AID & position interrupt handler (b) Initialize M-CODE interface interrupt handler (c) Initialize & start intelligent AID processor (d) Spawn control task (e) Wait for termination event (f) Shutdown real-time processing 6. Optionally write results file 7. Shutdown application. Step 1 initializes and performs a simple sanity check for the binary position interface. In addition, the intelligent AID processor is reset and the five degree-of-freedom D/A spindle position command interface is initialized to the home position (center of the air gap). This latter operation is essential since the D/A hardware powers up in a minus full scale (-10 V) condition which exceeds air gap levitation limits. Step 2 reads and processes the user specified .CFG ASCII coded configuration file which describes the mapping from physical analog 1/0 channels to logical software sensor and actuator variables. Physical channel numbers O through 31 refer the 32 available AID inputs while channel numbers 32 through 39 refer to the eight available D/A channels. The configuration file also contains the sensor and actuator scale factors, offsets, and additional descriptive information (Zivi et al., 1989). Step 3 loads the user specified ASCII coded .MAP error map file which contains the representation of the machine errors to be compensated. The currently defined error representations are: Tenni11al point error = [(position, 11omi1tal feedrate) Trajectory error = f(positio11, feedrate) Ramp error= [(position, feedrate) Dy11amic e1ror = f(positio11 relative to activatio11) In the current implementation, the first three error representations are mutually exclusive while the fourth provides an additive Y-axis correction. The first three error representations are implemented as two dimensional error maps defining a axial or ramp error in the terms of the position and velocity along the axis. Ramp errors occur due to the cutting force dependent defection of thin ribs. Since the S2M B25/500 magnetic spindle tilt is limited lo ± 0.04 degrees, by air gap limitations, this investigation does not include ramp error compensation. To support the trapezoidal compensation experiment, a minor variant of the generic CTRL program, CTRI..xy, was created which interprets axial trajectory errors in terms of the 292 Page 1055 orthogonnl axis.position and nominal velocity. Step 4 loads the user specified .CNC ASCII coded file which provides a representation or the CNC part program as required to ~upport cooperation between the CNC and error minimization controllers. The structure of the .MAP and .CNC files is defined in detail in (Zivi 1990). Upon successful completion of the preliminary processing, step 5 initiates real-time processing via a FORTRAN main program call to a PL)M subroutine, STARTUP. After initializing the proper PL)M execution environment, step (a) spawns an RMX interrupt task which establishes the combined binary position and analog input interrupt handler and then terminates. Step (b) spawns a second RMX interrupt task which establishes the M-CODE hnndshnking Interface interrupt handler and then also terminates. Step (c) spawns m1 RMX task which starts the Daiei ST701 intelligent AID processor and then terminates. Step (d) spawns an RMX (control) task which perrorms the error compensation £unctions. After spawning the synchronous tasks, STARTUP suspends itself (step (e)) and waits for a shutdown signal implemented using an RMX semaphore. The shutdown signal may be generated by successful completion of the error compensation process, detection of a software error, or entry of the key, by the operator. Regardless of the source, or current state of the real-time processing, the shutdown signal initiates step ({) which systematically terminates all real-time tasks and interrupt handlers. Once the real-time PL)M software hns been shutdown, control is returned to the FORTRAN main program. Step 6 provides the option of creating a results rile log containing the binary position data, analog input signals, and other selected variables in MATLAB compatible time series format. This important capability allows post test analysis and debug of the error compensation process. Step 7 finalizes shutdown of the error compensation process, returning the operator to the RMX II operating system. As outlined below the control task performs the actual real-time error compensation functions; 1. Lookup AID & DIA 1/0 mapping 2. Initialize error compensation 3. Establish error compensation origin ' 4. DO FOREVER (a) Wait for signal from interrupt handler (b) IF new M-CODE received from CNC controller THEN Change operational mode (c) Lookup error from error maps (d) Transform & rate limit compensation (e) Output compensation to levitation controller (f) Optionally log current control parameters 5. END OF DO FOREVER LOOP The control task has been developed as a distinct, self contained module to facilitate future enhancements and extensions. CONTROL SYSTEM VALIDATION Several error compensation experiments were performed to demonstrate and evaluate the magnetic spindle error compensation methodology. Experiments were performed on the Matsuura MCSOOV vertical milling machine retrofitted with the S2M magnetic spindle system and error minimization controller. · Cutting Force Independent Error Compensatiqn Non-cutting terminal point error compensation was performed first. This experiment used the terminal point error metrology of Woytowitz (1989) as codified in the error map file LASER.MAP. During both the metrology and compensation phases, an HP 5528A laser metrology system was used to measure milling machine table position. The laser optics were affixed to the spindle tool holder, providing a direct measurement of relative axial table position. From machine home, the axial table position command was stepped, in one i11clt increments, across the positioning range. Figure 9 presents the measured X-axis errors before 293 Page 1056 and after cnmpen~ation at a nominal feedrntes of too ipm. J( ~--1 Tei:mlnp Le.alp LJ:01111 enaau,on .__::1,1)0_1 P"',---~----, Improvement 'factor - 5.09 E r r 0.5 0 r ;. ,.. ~__ ... __ .,.. ... _..._ --:.I. ..- _,.__ +- __ ,_ - .... -- -+--.,--..._- ... ,..-- .... - .... ..+- - ~- _ .. - .. l -0.5 Sol,ld - ~ncomp,; mean. - 0.26, std - 0. 22 .l. Dashed - comp., 111ean - 0.05, std - 0.07 _ ____,L_ ___- ..1_-.1..... ____ i _____ . ___ -l -20 -18 -16 -14 -1] -10 -8 -6 -4 -2 0 x-a•ls Po11ltlon, inches X l _,'l'.e.1:.lllllfL,e.Qlrt....J:nmvensat 1100. t 1,0.IL.lP,-.---~-~ Sol~d • ~ncomp:, mean - -0.26, std - 0. l4 E r o. 5 • oas~ed - comp,, aea~ - -o.pe, std - o.os r 1 0 r 0 .. l -0.5 l Improve_m_en_t ,actor8 _. _.__ ____ ,-__3. 14 ..__ _, -1 -- -20 -18 -16 -14 -12 -10 -8 -6 -( -a 0 x-ails Position, Inches Fig.9 X-axis, 100 ipm Terminal Point Error Compensation Short Term Terminal Polnt Compensation, -100 1pm I . 6 -----r------.-·----.----,---,,---~---·,---r---..--- ~olld, • uncomp., .•e an - 0.89~ std~ O.l X rashed - c~mp., ;ean - 0.07i std - 0.05 ~aprov~ment factor~ ll.61 II II ' l '' 8 l l E r r 0.8 • I 0 r .. 0,6 I l B 0.4 ' ! ' 0,2 -, ...,.__..,. __ _. ................... ....__ ·-- .... --•-- ...... r'· ...... 0 -lo -18 -16 -H -12 -10 -8 -6 -4 -1 0 x-aats Position, inches Fig. 10 Short Term X-axis, 100 imp Terminal Point Error Compensation 294 Page 1057 These resu!ls indicate direction dependent terminal point accuracy improvement factors of five and three. Although Woytowitz reported the standard deviation of the terminal point errors to he approximately one tenth the magnitude o( the error, the positional behavior, shown in Fig. 9, retains larger systematic errors. Since the calibrated 3 sigma positional uncertainty of the spindle position is approximately 0.1 mil, these systematic compensation errors were assumed to he caused by long term drift in the error· phenomena. To evaluate the short term terminal point error compensation capability, the laser meJrology procedure of Woytowitz was repeated at a single, 100 ipm feedrate. With a one day turn around, between metrology and compensation, the results of Fig. 10 were obtained. This experiment achieved more than an order of magnitude improvement between uncompensated and compensated terminal point errors as expected by the uncompensated error statistics (Woytowitz, 1989). Continuing metrological investigations, by other researchers, are currently in progress to refine the error characterization. Cunine Force Dependent Error Compensation One of the CFO error compensation demonstration involved correction of a linear distortion of a prismatic part. As shown in Fig.11, the nominal test part geometry is rectangular, 1 illclt in width, and 5 illc/1es long. Using perturbation of the part program, the programmed shape was distorted into a trapezoidal form. The resulting trapezoidal part program specifies a linear variation in width from 1.008 incli ( +4 mils per side) to 0.992 inclt (-4 milr per side). The error map, required to remove the distortion, specifies a simple linear Y-axis error as a function of X-axis position and direction of feed. Figure 12 presents the error compensation results. This work has reported initial error compensation experiments and demonstrated the implementation or a general accuracy enhancement methodology. Future qualitative improvements resulting from melrological refinements and enhanced magnetic spindle performance are anticipated. CNC Programmed Compensated Table Trajectory Spindle Trajectory LI [~~- -~~ ::-- -~:icW ...__I.- [ 5 in .1]1 1.008 in 0.992 in 1 in Fig.11 Trapezoidal Test Part ·,.· ..-. ·~ ERROR ,. ... ------ (inchei) , .... ' - ----- -"'-- - 11 &ISlllllE ......... -- 0 CONPl!IISATED .......... ----- ..... ----- -111 POSITION ALOIIG TEST PART (inches) Fig.12 Trapezoidal Error Compensation 295 Page 1058 f<;rror Enhnncement Performance Compensation based accuracy enhancements are limited by the quality of the error representation and by the ability to effect the proper compensation. Using a pre-calibrated error mocfel, the quality of the error representation is dependent on two primary factors, viz; identification of the error phenomenon independent parameters, and statistical properties of the error phenomenon. Recent metrological experience indicates that the CFI error repeatability may approach values of an order of magnitude better than the CFI accuracy. This implies that up to an order of 1m1gnitude improvement in CFI positioning accuracy is achievable using pre-calibrated error compensation. Improved error characterization, as well as compensation actuation, is required to qbtain this goal under realistic machining conditions. The terminal point CF[ compensation experiment, previously presented in this chapter, grnphically illuslrntes this point. Short term error improvements of an order or magnitude were achieved, while long term improvements of three to five were observed. Compensation implementation limitations may be characterized in terms of bandwidth and accurncy. Relative lo tool path trajectory dynamics ( < 10 Hz), the 125 Hz bandwidth of the existing S2M 1325/500 is sufficient for effective error compensation. Although the CFI positional accurncy or the magnetic spindle is app;oximately 0.1 mil, cutting forces and inertial imbalance have been shown to produce significantly larger positioning errors. Movement toward more direct observation or online cutting accuracy, coupled with effective hierarchical compensation can significantly enhance part accuracy. In order to improve the error compensation c11pability, or mngnetic spindles, the effective stiffness must be improved. Stiffness improvements or five to ten times existing values are desirable. CONCLUSIONS This research has, for the first time, established the ability of a magnetic bearing spindle to provide accuracy enhancement through incremental error compensation. Key conclusions arc listed below: • magneti<: bearing spindles can provide simultaneous high speed, error compensation, and process monitoring capabilities, • a general and flexible accuracy enhancement methodology has been formulated implemented and demonstrated, • the. hierarchical control structure, using an AMB spindle, is an effective method for error compensation, • although, the current spindle bandwidth of 125 Hz is adequate to. compensate CFI tool path errors, spindle performance improvements are required for effective CFD error compensation. ACKNOWLEDGEMENTS This project was supported by the National Science Foundation through grant NSF 8516218 and the Engineering Research Center at the University of Maryland. In addition, this project was supported, in part, by the David Taylor Research Center Independent Research Program, sponsored by the Office of the Chief of Naval Research under task area ZR·000-01-01.. REFERENCES Anjanappa, M., Kirk, J. A, Anand, D. K., 1987, ''Tool Path Error Control in Thin Rib Machining", Fifteenth NAMRC, pp. 485.492. Dlaedel, K. L, 1980, "Error Reduction", Technology or Machine Tools, M7TF, Vol 5. Chaudhuri, P. S., Bollinger, J. G., Beachley, N.H., 1977, "Self Compensation of Machine Tool Deflections with Negative Stiffness Structural Elements", Proc. 5th NAMRC Conf.. Donmez, M. A., 1985, ''A General Methodology for Machine Tool Accuracy Enhancement Theory, Application and Implementation'\ Plt.D. Dissertation, Purdue University. 296 Page 1059 Dufour, P., Groppetti, R., 1980, "Computer Aided Accuracy Improvements in L·uge NC Machine Tools", Imema1ior1al Joumal of MTDR, Vol. 21. Ferreira, P. M., Liu, C.R., 1986, "A Contribution to the Analysis and Compensation of the Geometric Error of a Machining Center", CIRP A1111als, Vol. 35, pp 259-262. Gayman, D. J., 1986, "Calibration, Compensation, and CC', Ma11ufacturi11g E11gi11ccri11g, pp 34-39. 1-Iocken, R. J., 1980, "Ouasistatic Machine Tool Errors", Tecl1110/ogy of Macltine Tools, MTTF, Vol 5. Kanai, A., Miyashita, M., 1983, "Nanometer Positioning Characteristics of Closed Looped Differential Hydro-or Aerostatic Actuator", CIRP A1111als, Vol. 32, pp 287-289. Kouno, E., 1984, "A Fast Response Piezoelectric Actuator for Servo Correction of Systematic Errors in Precision Machining", CIRP Annals, Vol. 33, pp 369-372. Leete, D. L, 1961, "Automatic Compensation of Alignment Errors in Machine Tools", Jmemntional Joumal of MTDR, Vol. 1. Ni, J., Wu, S. M., 1987, "A New On-line Measurement System for Machine Tool Geometric Errors", 151/r NAMRC. Poulter, K. F., 1983, "The NPL Optical Spaceframe", CIRP A1111als, Vol. 32, pp 469-473. Rao, S., 1986, Meclianical Vibrati01u, Addison Wesley, Reading, MA, pp 421-426. "Active Magnetic Bearing Spindle Systems for Machine Tools", SKF /11dustries, /11c., King of Prussia, PA, 1981. Staroselsky S., Stetson, K., A., 1987, ''Two-stage Actuation for Improved Accuracy of Contouring", Proceedings of the 1987 America/I Control Co11fcrc11ce, June 15-17. Shyam, S., 1987, "Error Compensation for Accuracy Enhancement in Precision Machining", Masters 711esis, University of Maryland. Tlusty, J., 1971, ''Techniques for Testing Accuracy of NC Machine Tools", /11tcmatio1wl Joumal of MTDR, Vol. 12. Watanabe, T., Iwai, S., -1983, "A Control System to Improve the Accuracy of Finished Surfaces in Milling", Joumal of E11gi11~eri11g for Jndustry, Transactions of ASME, Vol. 105, pp 192-199. Woytowitz, M. A, 1989, ''Tool Path Error Classification and Identification for High Precision Milling with a Magnetic Bearing Spindle", Master 171esj,f, University of Maryland. Ya.mac 3000G Operator's Manual, Yaskawa Electric Mfg. Co. Ltd., Japan, 1980. Zivi, E., Romero, R., Harrell, D., Bankert, J., 1989, Mag11ctic Bearing Spindle Laboratory Refere11ce Ma11ual, University of Maryland. Zivi, E., 1990, "Robust Control of Magnetic Bearing Spindle for Milling Tool Path Error Minimization", PILD. Dissertation, University of Maryland. 297 Page 1060 ·PROCEEDINGS OF THE SEVENTH · INTERNATIONAL CONFERENCE OF MECHANICAL POWER ENGINEERING VOLUME I II COMBUSTION IV ENERGY Cairo University Faculty of Engineering December 17-20, 1990 Page 1061 MAGNETIC BEARING APPLICATIONS D.K. Anand, Professor M. Anjanappa. A'isistant Professor Advanced Design and Manufacturing Laboratory Department of Mechanical Engineering The University of Maryland College Park, MD 20742 U.S.A. ABSTRACT The work pre~tnted in this paper discusses magnetic bearing applications in two areas, viz. energy storage dnd machining. For energy storage applications, a design model fur magnetic force compatation is developed and results of applying the model are presented. The bearing control~.\ stem is analyzed by simulating its response to perturbations. A linear model of the plant ·,, used for the simulation, and to establish bounds on stability. Real time simulation is u~cd to analyze the effect of changes in the control system feedback loop on bearing impulse ..;sponse. The results of the analysis determine the parametric design of the energy storag.: flywheel system. For machining, a magnetic bearing spindle and controller, with its unique features, retrofitted to existi11g machine tools. has been shown to minimize tool path error while maintaining high ~nctal removal rate. A general and flexible accuracy enhancement methodology has be=n formulated, implemented and demonstrated. It was shown that the hierarchical control -tructure, using active magnetic bearing spindle, is an effective method for compensation oi tool path errors. 1. INTRODUCTiON The potential of magnetic bearings is enormous, and the advantages over conventional ball bearings nur.i';'J 'ms. Magnetic bearings require no lubricants, which completely eliminates outgassi::-15 problems for space applications. Furthermore, magnetic bearings effectively eliminate internally and externally induced vibrations since they can be made mechanica11y soft. That is, the orthogonal control directions b€have as though they are separated by a soft spring. This helps to damp vibrations in one part of the system and prevent vibrations r:om being transmitted into other parts of the system. Magnetic suspension is particL i:1rly attractive in conjunction with the use of high-strength composites for the flywheel c": :sign. Composites allow the attainment of very high speeds and consequently high .::ncrgy to weight ratios. A magnetically mpported bearing could theoretically have a reliable lifetime on the IV /3-1 Page 1062 order of 20 years. This extraordinary lifespan is attributed to the total elimination of bearing friction. The life-time, in fact, should be governed only by the life of the control and motor electronics. Magnetic bearings have been considered for a wide variety o f applications. Notably, the support of high speed ground vehicles such as trains and rocket sleds, and more frequently in applications for the support of reaction wheels for spacecraft attitude control, control moment wheels, gyroscopic wheels, and energy storage wheels. More recently, magnetic bearings have been considered for applications in supporting space telescopes, vibration damping, and machine tools. This paper is concerned with two specific applications currently under research at the Advanced Design and Manufacturing Laboratory of the University of Maryland. The two applications include energy storage using magnetic bearings and machining using magnetic spindles. Detailed computations and design algorithms are presented in references. 2. ENERGY STORAGE USING :MAGNETIC BEARINGS A prototype active pancake magnetic bearing successfully devel( ped at The University of Maryla.:.d is shown in Figs. 1 and 2. "Pancake" refers to the sand.viching of permanent magnets between fe'Tomagnetic plates. A cross section of the bearing is shown in Fig. 3. The flux distribution from the permanent magnets, which support he bulk of the rotor weight is shown in path A Four electromagnetic coils are located near the permanent magnet'.s to control the rotor about its unstable equilibrium point, i.e., the point at which the air gap is consta~1t around the stator. When the rotor displaces radially, the motion is se_nsed by a pos1tior1 transducer at the periphery of the rotor. The control system responds by sending a control current through the coils which results in an additional corrective flux distribution (path B). This flux adds to the permanent magnet flux o 1 the large gap side and subtracts from the PM flux on the small gap side. The net result is a corrective force which moves the rotor back to the center (nominal) position. An identical radial control system exits for the other orthogonal direction. The control in the axial direction is passive. The design specificztions of the bearing and control system are obtained via simulation results. The requireme:its for a typical energy storage system are given in Table 1 along with the simulation results. Geometrically, an ideal system should be as compact as possible. thus the proposed m w system is a stack arrangement of two magnetic bearings as shown in Fig. 4. It is assumed that, in general, the stack 2rrangement can be designed as two separate bearings. This arr,ingement allows for the control of rocking motion by independently controlling the two radial control systems. The control system for stabilizing the m: gnetic bearing is shown in Fig. 5. Basically, an eddy current transducer provides the rad: J position of the flywheel. The transducer signal produces an ~rror signal that drives a current through four electromagnets. Th' IV/3-2 Page 1063 magnetic flux of the electromagnets adds on one side and subtracts the permanent magnet flux on the other side, producing corrective differential force. The system shown in Fig. 5 was fabricated, tested and used to stabilize the magnetic bearing. Results from the system parametric design, and the control system analysis, show that energy storage flywheel can be built by incorporating characteristics of a previously built magnetic bearing into a stack arrangement. The major conclusions of this study are: • The system consisting of a stack arrangement of two bearings similar to the earlier prototype is a viable approach. • Some method of reducing permanent magnet unbalance must be incorporated. Flux reduction and flux shunting of the permanent magnet are appropriate methods. • A control system identical to the prototype system provides sufficient response to external disturbances if the feedback gain is tuned. The effects of nonlinearities, particularly those leading to limit cycles need further evaluations. • Capacitive, saturation, and hysteresis effects of the iron should be included in the model but avoided in the operating range of the bearing. Back up bearings are conveniently included in the stack arrangement c:nd ·are required to maintain flywheel excursions in the operating range of magnetic bearing control systems. 3. MACHINING USING :MAGNETIC BEARING SPINDLE A Magnetic bearing spindle, with its unique features, retrofitted to existing machine tools, provides a solution to minimize the tool path error while maintaining high metal removal rate in thin rib machining. The work reported in this paper shows that by using error maps and spindle control fo f a Matsuura-S2M system] that tool path error minimization is both practical and achievable. In order to develop an error minimization controller, first of all, a CNC machine fitted '1ith a magnetic spindle is needed. In addition, such a system must provide an user interface 'fihere the user can tap into the current status of the machine and be able to command the translation and tilt of the spindle rotor on-llhe and in real time. Since, no such system is available, the University of Maryland has retrofitted an S2M-B25/500 magnetic spindle to an existing Matsuura MC500 CNC machining center. Mechanical retrofitting work required several modifications to the original machining tenter. It required disassembling the conventional spindle head from the machining center, tut off the existing spindle casting to leaving only the guide ways intact and then mount the te,,,,, magnetic spindle in its place. Electrical interj1cing required for the active magnetic bearing (AMB) error correction IV/3-3 Page 1064 methodology involves the interaction and coordination of four independent controllers: • Existing CNC controller, • Active magnetic bearing controller, • Variable speed spindle drive, • Online error minimization controller. While the existing Matsuura MC500 Yasnac CNC 3000G controller was retained, the latter three controllers were insta11ed as part of the active magnetic bearing retrofit. Previous research suggests separating errors as either cutting force independent (CFJ) or cutting force dependent (CFD). CFI errors are those errors that occur in the absence of metal cutting (i.e., dry run) while CFD errors can be directly linked to the metal cutting. Deterministic tool path errors, for the purposes of this research, are classified as shown in Fig. 6. The non-deterministic errors (such as errors due to chatter) are not considered here. The CFI error classification has been reported before and it is very much similar. The CFD error classification, however, is chosen based on the most frequent errors in the machined part. Figure 7 shows a typical plot obtained for the average Axial Position en-ors along the X-axis for the traversing of the machine's table at five feed rates in the negative direction. The errors show a strong dependence on position and feed rate. The standard deviations of the errors at each position are approximately an order of magnitude less than the errors themselves. If one was to measure the errors at only one feedrate, the resulting information would not necessarily be valid at other feedrates thereby corroborating the fact that dynamic error map is essential. The thermal deformation of the machine tool structure results in a net displacement of the tool relative to the workpiece. The deformations experienced by spindle head due to thermal shock primarily due to cooling water and air circuits proved to be very large. However, the thermal study is not reported here since this problem, was eliminated by redesign of the spindle cooling system. The remaining thermal error is the gradual ( quasistatic) thermal deformation of the machine tool. Several "recovery from cool down" tests were conducted for the Y-axis and Fig. 8 shows a typical error plot obtained. In these tests the deformation of the headstock varied linearly with respect to temperature. A magnetic bearing spindle error min mization controller can use the thermal deformation model of linear deformation to cc rrect for the errors produced by quasistatic temperature change. One determini~tic CFD error encountere(. in thin rib machining is ramp error. Ram_P error is the result cf the deflection of a compliant work piece by cutting forces and IS defined as the difference between the thickness at the top and the thickness at the bottom of a thin rib, which is often encountered in the manufacture of microwave guides. Since the geometry of the work piece is known, it is possible to relate the ramp error to the forces imparted by the cutter. Page 1065 As a first iteration of ramp error identification, several thin rib test parts were produced on the Matsuura/S2M machine and on a conventional spindle Matsuura MC-510V milling machine. Figure 9 presents the results of the part metrology. The, errors produced by the magnetic bearing spindle have a larger scatter than those produced by the conventional bearing spindle. This large scatter can be linked to the stiffness of the magnetic bearings. Improving bearing stiffness is one way to improve the performance. Control Methodology and Implementation The robust controller uses cutting force (from built-in sensors on the magnetic bearing spindle) and the error map as input, and generates a displacement bias for the magnetic bearing spindle as output. The bias, which is proportional to the tool path error at any given tool position, is used to translate and tilt the spindle to minimize the tool path error. Central to this research, is the implementation of the error minimization controller. The basic elements of the accuracy enhancement retrofit are depicted below the dotted line of the simplified control system block diagram given in Fig. 10. The theoretical development necessary to support the derivahon of the robust, multivariable controller has been previously reported. Implementation of the error compensation methodology also requires mechanisms to coordinate and sequence CNC and error minimization controller operations. The present approach involves the down loading of the part program, in M & G codes, to both the CNC and error minimizat:on controllers. In this scenario, the CNC and error minimization controller execute the same part program simultaneously. This allows the error minimization controller to cooperate with the existing CNC controller and completely defines the desired tool trajectory. The error minimization controller implementation is performed using an IEEE 796 (Multibus) based computer system. This system utilizes an Intel 386/387 processor pair and executes the Intel RMX II operating system. Evaluation of the error minimization capabilities of the magnetic spindle retrofitted Matsuura MCSOO has been performed by comparing the dimensional accuracy of a sequence of sample parts. This sequence uses the MC500, with no error correction, as the baseline with which to evaluate various error map formulations and control system implementations. From the experimental results, the following conclusions could be d:-awn; • Magnetic bearing spindles can provide simultaneous high speed, error compensation, and process monitoring capabilities. • A general and flexible accuracy enhancement methodology has been formulated, implemented and demonstrated. • '~~he hierarchical control structure, using a AMB spindle, is an effective IV/3-5 Page 1066 method for compensation of machining dimensional errors. • The current spindle bandwidth of 125 Hz is adequate to compensate dynamic tool path errors. • At conventional cutting speeds, the low dynamic stiffness, of the S2M AMB spindle significantly limits accuracy and stability. • Based on the facility and control structure established herein, considerable future qualitative improvements should be possible with metrology and AMB spindle enhancements. • A second generation spindle design, which includes advanced control concepts could provide significant stability and performance improvements. 4. ACKNOWLEDGEMENT Part of the research work reported in this paper represents a cooperative activity of the personnel from the University of Maryland, the National Institute of Standards and Technology [formerly the National Bureau of StandardsJ, the Westinghouse Corporation, the David Taylor Naval Research Center and the Magnetic Bearing, Inc. This work has been supported by the National Science Foundation through grant NSF 8516218, Engineering Research Center at the University of Maryland, ONR Program Element 61152N through the David Taylor Research Center, Goddard Space Flight Center Grant NAG5-396, and TPI, Inc.. We deeply appreciate Professor A Gupta who has agreed to read this paper. REFERENCES 1. Anand, D.K., YJrk., J.A and Frommer, D.A "Design Considerations for a Magnetically Suspended Flywheel System", Proceedings of 20th IECEC Conference, August 18-23, 1985, pp: 2.449-2.453, Miami, Florida, USA. 2. Kirk, J.A., Anand, D.K., and Khan, A.A, "Rotor Stresses in a Magnetically Suspended Flywheel System", Proceedings of 20th IECEC Conference, August 18-23, 1985, pp: 2.454-2.462, Miami, Florida, USA. 3. Bangham, M.L., "Simulation and Design of a Flywheel Magnetic Bearing", A1.S. Thesis, University of Maryland, College Park, 1985. 4. Anand, D.K., Kirk, J.A., Anjanappa, M., Zivi, E.1 and Woytowitz, M., "Magnetic Bearing Spindle Control", Proceedings of 15th Conference on Production Research and Technology, pp.31-35. 5. Anand, D.K., Kirk, J.A., Anjanappa, M., "Tool Path Error Control for End Milling of Microwave Guides", Proceedings of 7th World Congress on the Theory of Machines and Mechanisms, Sevilla, Spain, 1987, Vol.3, pp.1499-1502. 6. Anand, D.K., Kirk, J.A., and Anjanappa, M., "Magnetic Bearing Spindles for Enhancing Tool Path Accuracy. . ,Advanced Manufacturing Processes, Vol. 1, No. 1, PP· 121-134, 1986. 7. Zivi, E., 11 Robust Control of Magnetic Spindle for Error Compensation", Ph.D., 1nesis, IV /3-6 The University of Maryland, 1989. TABLE 1. REQUIREMENTS FOR·3oo WHR (108 KJ) ENERGY STORAGE SYSTEM SOUJllC.E qeO\hRIEMENT )0.,0. ...-.N. .•_n,,-.,K. o,.,, :S"OJILt.0£ , . .:>E StG• P•AA. .. E. TE• ,:: 1· l 10 ... ,l. ~OWEII ;;:ONSVldPTION TOT "'L ~NIERG• ::Ol>fAVMl91'10h F(.YWMEE>... oEs-•G" I •tov,AEYEtH 3-TA.TOR SIZ.£ A.,.•Gf ),,.. ~o 5-,fl ,o ~,._-. wi,t£f.L 0lM1:;NS10N •EOVfAE»ENT • ,.., TO , 2~ g. mlt'I/ '5iAB1..C S,'l'S'ri_v uNQEFI "Z--., AAOi;i,.t_ ;_QA·(" Y.AGKE'T 4AE"- toe"-G.NE T _£ N--,;j;TM P01..~ "4CE tt\11c,u,. .1 e, ss LYWHEEL FIGURE 1. PANCAKE MAGNETIC BEARING IV /3-7 Page 1068 MAGNET PLATES FIGURE 2. EXPWDED VIEW OF STATOR FOR PANCAKE BLARING Set.TOR ROTOR FIGlJRE 3. CROSS SECTIO:t< OF P Ai~CAKE BEARING IV /3-8 Page 1069 FIGURE 4. STACK J\RRANGEMENT FOR PROPOSED BEARING i J( ~iLTE~ '-----I FEEDBACK GAIN CDMFENSATlON EDDY CUlsRENT ~ET WORK ~'iAN'.:OUCER FIGURE 5. CONTROL SYSTEM BLOCK DIAGRAM I Deterain.1.sLic: £rror Cla•aitication I !cvttl.1>9 Porctt 1nd-nd•nt 1 jcuttinq force Dep,ondentl I ~ .....,.; l..oo4u,q Static l.o6dinq t,yruaaic 1.o&dinq S~tie •aperoture cb•ni;,• (poai~1.on ' v•i.9ht: (accoleration & t,yn.aa1c ' l..oo4inq I dt:pendencel depe.ndenc•J retardation (cutt..inq proe•:s• I dependence) d•pendenc•) I ! I CONTROLLEll TRJJ.abi•nt ""'chin• 't_, {fl ,, 'retllperat.ure (C) FIGURE 8. THERMAL DEFORMATION ALONG Y-AXIS IV/3-10 Page 1071 ••• i ..... 0 0 ......... Cj , 0 0 ·..·..- D B . D B -~·~ ....,.,"' grror (1achee} O.....,.c•a9-rlftt ·..-..-. I 0 I II C 0 II ··- II II I ....1 111 II • ,. .. .. .. ,. .. .. • .. ... Pee4.rat.• j!p,a.l FIGURE 9. THIN RIB RA~iP ERROR (DOWN MILLING) :--;on: X- ~ Y-AXIS LOOPS O\IlTTED FOR BRE\"JTY Z-AXIS DC Z-AXIS OPTICAL 1,---o, ~ • • • SERVO/DRIVE MO\'Elv!ENT ENCODER X, }" i. VELOCITY COMMAND NUMERICAL COMPCTEH POSITlON FEEDBACK CONTROL :-UMERJCAL CODES co.:,,;TROL EXISTING MACHINE -- -----''\- - ---------------------- ACCURACY HAND ENHANCEMEN T SHAKE , , CNC POSITION/VELOCITY y ,7 ~CFFTOT I RC NG ES ERROR MAGNETIC .___ j.....-.,.... I ::: \1AGNETJC MINIMIZAT10K r---,..,' BEARING SPIXDLE CONTROLLER CONTROLLER ,I'\ ' ::. j ) ERROR \!AGNETIC THERMA L ' CORRECTIO!-<" SUSPENSIO!\ DATA FORCE l.: DlSPLACEMENT Cl'TTI:" Press to continue with no changes. Figure 5. The control system block diagram for the active magnetic bearing with a flywheel attached to the suspension ring is shown at top. All 18 parameters entered during the control system design procedure are displayed in the bottom half of the diagram. cation to the circuit. parameters, namely, the reference signer's intuition about variations Some additional input parameters voltage, Ka, and the natural frequen- based on electromagnetic design related to the physical dimensions of cy of the bearing-flywheel system. theory. the flywheel must now be provided When all the input activities and In summary, the CADAMB system by the designer. These include the computations are finished , the con- proves to be a helpful tool in estab- weight of the flywheel and the dis- trol system is ready to be analyzed lishing the feasibility and limitations placement of the flywheel from its using the CC software package devel- of an energy storage system. In addi- central position at steady stl}.te. De- oped at the University of Maryland. tion to being very user-friendly and fault values for these parameters are Use of CC for analysis and plot- interactive in nature, the system in- provided by CADAMB in parentheses generating purposes necessitated the cludes features such as a library of along with each prompt. This is fol- development of an interface between several permanent magnets, auto- lowed by prompts to input Kx and K;. CADAMB and CC. T his interface matic saving of design parameters at The default values for Kx and K; are takes the transfer functions of each the end of execution in a file for fu- also either hard-wired values, those of the blocks of the control system ture use, rigid error-trapping rou- computed during magnetic bearing from CADAMB and translates them tines for input handling, and auto- design and passed into the control into a format suitable for CC. CC matic transfer of necessary system design session, or values used generates the root locus plots , time parameters from bearing design mod- in a previous iteration. response, and Bode plots for the con- ule to control system design This concludes the parameter in- trol system designed in CADAMB . module. • put phase of control system design. Next, all 18 parameters that have Typical Results For Further Reading been entered so far are summarized The CADAMB system has been I. Anand, D.K. , Kirk, J.A., and Frommer, and ·displayed as shown in Figure 5. used to simulate several active mag- D.A., "Design Considerations for Magnetical- Computation of the control system netic bearing designs for flywheel ap- ly Suspended Flywheel Systems." Proceed-ings ofIECE, Miami Beach, Fla., Aug. 18- 23, design parameters, which are dis- plications. It has computed the per- 1985. cussed in the system methodology meances in all the flux paths , useful 2. Eisenberg, B. , "The Attraction to Mag- section earlier, begins. This results flux available across the air gap, Kx, netic FEA," Mechanical Engineering, Dec. in the evaluation of the gains of indi- K;, and Ka. The software generates 1988. 3. Kirk, J .A. "Flywheel Energy Storage: vidual blocks of the system. The de- the typical control system analysis Part I-Basic Concepts," International Jour- signer is prompted to c ose a value plots, such as Bode and root locus nal of Mechanical Science, Vol. 19, No. 4, pp. for the variable resistance that lies plots. The results obtained by vary- 223-231, 1972. inside the limits. ing some critical parameters and 4. Robinson , A.A., "A Lightweight, Low- studying the variation results using Cost, Magnetic Reaction Wheel for Satellite CADAMB now calculates three im- Attitude-Control Applications," ESA Journal, portant control system characteristic the CADAMB system satisfied the de- Vol. 6, pp. 39-46, 1982. 30 I DECEMBER 1990 / MECHANICAL ENGINEERING Page 1077 M. Anjanappa Assistant Professor. Mechanical Engineering, The University of Maryland-UM BC, Baltimore, MD 21228 Manufacturability Analysis r M. J. Courtright Flexible Manufacturing Cell Senior Design Engineer. Westinghouse Electric Corporation, The conventional product development cycle time in producing a part can be reduced Baltimore, MD 21203 by eliminating design errors and difficult to machine features before manufacturing process begins. This paper discusses the identification, development, and operation of an approach which uses a global data base of flexible manufacturing cell capa- D. IC Anand bilities in order to analyze a design for manufacturability. Designs which the cell is Professor. unable to produce are rejected, and ways in which a design may be made more producible are suggested to the user. This paper addresses issues, such as availability of material, fixture, and tool and the achievability of tolerance. The approach is J. A. Kirk implemented on a cell containing a machining center and material handling equip- Professor. ment operating under a rapid prototyping protocol. An important contribution of this work is the wide variety of manufacturability constraints covered and the con- Department of Mechanical Engineering venience of including it in the overall process of product development. and The Systems Research Center, The University of Maryland-UMCP, College Park, MD 20742 Introduction The initial stages of the product development cycle are the royd [9], "although designers will generally assert that they most critical [l]. The design decisions made initially commit take account of manufacturing problems whenever possible, major resources in the remainder of the cycle. These initial the fact is that, as a subject, design for manufacture hardly design decisions can be changed if found necessary, with access exists." Hence one of the general research areas addressed in to suitable manufacturability analyzer, with least effort before this paper is the identification of comprehensive manufactur- finalizing the design resulting in a significantly reduced cycle ability constraints. time and hence reducing the product cost. Atkinson [2] reports The approach to manufacturability analysis depends on that reductions of up to 40 percent can be realized in the whether the product under consideration is a part or a complete "product development time," when design for manufactur- system. The latter can introduce a level of complexity that is ability is practiced. several order of magnitude larger than that of a part. Even Although, various investigators [3-5] have discussed general for a part it is appropriate to initially speak about a class of design criteria and rules of thumb that should be used when components aggregated by the group technology approach. In designing for manufacturability, there is little published ma- this paper, we are interested in limiting our consideration to terial available on the subject of analyzing a design for man- prismatic parts that can be manufactured within a flexible ufacturability per se. Barash [6] reports that by grouping parts manufacturing cell. into families, efficiency, quality, and therefore low cost can The objective of this paper is to identify parameters deter- be achieved. He uses a subset of group technology whose mining whether a part is manufacturable and to develop an objective is to design a part that readily fits into an existing analyzer compatible with the University of Maryland's Flexible group, thereby improving manufacturability. Hoffman [7], has Manufacturing Cell (FMC). With access to FM C's global data studied the aspect of dimension tolerances and their constraints base of available cutting tools, material, and fixtures, the man- on machining, reducing tolerances, and process inaccuracies ufacturability analyzer can dissect the design, feature by fea- to a system of linear inequalities. He concludes that the ap- ture, interface with the user areas of concern or difficulties proach is difficult and needs further development. Parkinson and offer information on correction. The manufacturability [8] views tolerances and basic dimensions as parameters that analyzer could veto any design, the system hardware is unable affect overall cost of machining and assembly. He does not to handle, before the process planning begins. Although, not address the parts dimensions' and tolerances required for its considered in this work due to a single cell setup, the alternate function, only those needed for assembly. According to Booth- methods such as subcontracting must be considered. The sug- gested methodology can be readily extended to include this. Contributed by the Design Automation Committee for publication in the Work reported in this paper begins with a brief introduction JOURNAL OF MECHANICAL DESIGN. Manuscript received January 1990. to the cell and protocol at the University of Maryland followed 372/Vol.113, DECEMBER 1991 Transactions of the ASM E Page 1078 USER Table 1 Manufacturability parameters lor a general FMC Ad esign is machinable bj Information needed to check manufacturing constraints COMMERCIAL CAD FEATURE BASED an FMC with one CNC Dim tol. Contours, Tool inte Weight. [SOLID MODELER] [AO machine and one robot Thin wall Shapes. fBrences Outer Material if it can be made- Radii S1Z8 drawing file (D ~~~fln IGES f i I e 11 within the specified drawing limits Can design use cell's, stock sizes? * * GLOBAL DAT A BASE USER cutting tools? * * * * [TOL MATL. l fixtures? * f i e software? * * * ' I * CNC machines? * * * * * robot? INTELLIGENT AGV? * PROCESS PLANNER * 21 with in a maximum lead time NIA NIA NIA NIA NIA [HUMAN FIXTURING COMPUTER ASSISTED I_ DECISION FIXTURING 31 with in a minimum frequency. What is the: ra, mat supplf * cycle time? ' * * * * tool wear? * * cell availability? ' ' yield? * * handling time? ' * 41 within a maximum cost. Cost of, raw mat,? * Fig. 1 Rapid prototyping protocol cycle time? * * * * * tool wear? ' * * yield rate? * handling? ' * by the approach to manufacturability analysis, and the de- * pallet storage? velopment and implementation of the manufacturability ana- ' human supervision? lyzer with an example. overhead? Flexible Manufacturing Cell and Protocol FMC's have become more widespread since they allow high Table 2 Manufacturability parameters related to cycle lime degree of flexibility for batch size part production. One such Ad esign is nochinoble by Infornot ion needed to check nonufoctur in g constraint, FMC has been set up at the University of Maryland consisting on FM[ with one [N[ Din. tol. Contours, Tool inte Weight, of a Matsuura 510 machining center, a robot, and a simulated noch in e ond one robot Thin wol I Shapes, ferences Outer Material AGV. This FMC has the following capabilities [10]: if it con be node- bending, Rodi i size surf. fin • handles prismatic raw stock " uses the Rapid Prototyping Protocol (RPP) Cycle tine: ., is limited to the tools in the cell Nunber of cutter changes * ' ' * " has no fixture intercepts Speed of noter io I renovo I * * * • can handle one part at a time. Anount of noteriol renovol * * ' Nunber of port orientation The Rapid Prototyping Protocol (RPP), shown in Fig. 1, ' * * * Nunber of fixtures ' * * ' outlines how the different components interact and how the ' ' system incorporates a wide variety of capabilities including feature based Computer Aided Design (CAD), a feature ex- tractor for converting wire frame designs to a feature based of energy consumed to cut metal, or by how long a cutting design, a manufacturability analyzer (which is discussed in this tool lasts [12]. Although that definition may be useful in com- paper), Computer Aided Process Planning, knowledge based paring metals, it does not apply to designs. Another definition process planning and a cell. relates manufacturability to various parameters such as, tool In this environment, the user sketches his design (at the top life, limiting rate of metal removal, cutting forces, surface of the flow chart) and then has it manufactured (at the bottom finish, and chip shape. The above definitions are more specific of the flow chart). If a commercial CAD is used, the IGES about the material removal process but vague about the design format file of the design is processed through a feature ex- specifics. Also, it is important to note that usually manufac- tractor, which extracts machinable features. The output, a turability and machinability do not mean the same thing since, feature file, becomes the input to the proposed manufactur- manufacturability encompasses machinability and much more. ability analyzer. If it is found manufacturable, the process Nevertheless, since the RPP and FMC at the University of planning and machining of part takes place automatically. For Maryland concerns only machining, the two words are used more details on RPP the reader is referred to [11]. here synonymously. A generic definition of manufacturability must consider pa- rameters that affect all aspects of manufacturing that makes Manufacturability a product competitive in the market. It is beyond the scope of A literature search on the subject of manufacturability yields this paper even to attempt to list all the specific parameters a variety of definitions, often defined only for a specific case. that affect the manufacturability. This paper focusses on only One such example is the measure of manufacturability in terms one aspect, the design for manufacturability. In other words, Journal of Mechanical Design DECEMBER 1991, Vol. 113 / 373 Page 1079 a design is considered to be manufacturable in a typical batch Design for Manufacturability. So far we discussed the nec- manufacturing environment if it can be made; essary parameters that must be considered for analyzing a design for manufacturability for an FMC. The following sec- (]) Within the specified drawing limits. tion discusses how the analysis is done. Cook [13] summarizes Specifically, answer questions like are there suitable the objective of any manufacturability analysis as "producing stock sizes, cutting tools, fixtures, software, machines, satisfactory parts at the lowest possible cost can be called as material handling equipment, and storage pallets avail- the first law of production." able? The analysis must consider all the parameters listed in Table (2) Within a maximum lead time. 1 while minimizing the cost of a part. The goal of the analysis Is it possible to acquire the above items, applying them, is to let the designer know, immediately, whether his design and get one good part through the machining cycle is manufacturable within the given FMC, and suggest ways in within the required lead time? which the part may be made more producible. The cost of (3) Within a minimum frequency. manufacturing a part is discussed widely in literature [13, 14]. In other words, is there adequate raw material and Specifically, for an FMC with a vertical milling machine it can pallet supply? be written as, What is the cycle time, tool wear and breakage, ma- chine availability, yield, and material handling time. (1) (4) Within a maximum cost. where, CMc is the machining cost, CMAT is the material cost, Specifically, what is the cost ofr aw material, cycle time, and CT is the tool cost incurred per unit part. tool wear and breakage, machine changes, yield rate, The machining cost is further expanded as, material handling, pallet storage, human supervision, and overhead? CMc= C1Uc+ lnc) (2) where C1 is a constant which depends on machine cost, labor The four requirements of manufacturability and the related cost, and overheads, tc is the actual cutting time, and tnc is the parameters listed above are applicable to prismatic part designs noncutting time such as tool setup, in-process inspection, etc. which is to be manufactured in a typical batch manufacturing The cutting time in minutes, for a milling operation is given facility. However, not all of them are applicable to an FMC by, containing one CNC machine. Requirement No. 1 places the burden on the shop to meet the drawing. When addressing the L (3) FMC of interest, the parameters are similar, but the burden tc= fNz is placed on the designer. Requirement No. 2 asks if the time where/is the feed per revolution per tooth (m/rev/tooth), it takes to collect all the items mentioned in No. 1 plus cycle N is the rotational speed (rev per minute), z is the number of time is less than the required time. In a machine shop, this can teeth in the tool, and L is the length of cut (m). be a long process. Frequently, the machine shop spends a great The tool cost is written as, amount of time preparing fixtures and altering machines, and the lead time limit is not met. When addressing the FMC, this (4) process is different. Either the design can be machined by the CT= C1aai(~) equipment in the cell, or it cannot. Time is not a factor. For where Ctoal is the cost of the milling cutter tool, and T is all practical purposes, if No. 1 can be met, then No. 2 is also the tool life in minutes. T can be obtained using the Taylor's met. Therefore, No. 2 can be deleted from the definition of tool life equation, manufacturability requirements for the FMC. In Requirement No. 3 the capacity of the shop is checked for. When addressing (5) the FMC, the parameters remain the same with the exception where Vis the cutting speed in m/min and n is a constant. of the parameter that deals with using multiple machines. This Substituting in the original equation, the total cost becomes, parameter does not apply since the FMC has only one CNC 11 machine. Requirement No. 4 remains the same when applied CmT= C1 ( fN L z + tnc ) + Ctool ( fNLzVCl/" n) + CMAT (6) to FMC. Parameters. Table 1 shows the definition of manufactura- The above equation is used to calculate the cost of machining bility of a general FMC, and the related parameters. The col- a part in FMC. In addition, it is useful to minimize the cost umns of the matrix show the characteristics of the machined with respect to any of the parameters such as material cost, part, namely the drawing limits. The asterisks show how the cutting speed, and tool life. Implicit in the above equation is manufacturability parameters depend on the machined part. the effect of tolerance on the cost of production which must For example, as per requirement No. 1, the available stock be chosen by the designer. Tolerances should be applied to sizes must meet the drawing. It is necessary to know the part's permit the greatest speed and economy of manufacturing of outer dimensions and material so there are asterisks in the a part, consistent with functional requirements. The cost of "weight/outer size" and "material" columns. When deter- manufacturing a part (considering only the tolerance) can be mining whether a design is machinable, some parameters may written as, be considered immediately, while others may not be considered n k· until after the process plan is completed. For example, the C=E-½ (7) i-1 t; parameters of requirement No. 1 (drawing limits) does not depend on machining process, where as the parameters of where, t; is the tolerance of a critical dimension, n is the requirement No. 3 and No. 4 (cost and frequency) depend on number of critical dimensions, and k; is the constant corre- the process plan heavily. sponding to the generation of the ith dimension which depends The parameter of cycle time is important since it is referred on the man/machine used. The cost increases parabolically to in requirements No. 2, ~o. 3, and No. 4. Like the four with the decrease in tolerance. The analysis used here, therefore manufacturability requirements, it has its own parameters. alerts the designer if the tolerances are too tight and cannot Table 2 lists the parameters related to cycle time. The RPP be made in normal operating conditions but requires a slower developed at the University of Maryland is arranged so that and controlled machining thus increasing the cost of machin- frequency is not directly calculated but is determined by the ing. When checking for manufacturability, it is therefore nec- process planner. essary to recognize the distinction between the standards of 374 / Vol. 113, DECEMBER 1991 Transactions of the ASME Page 1080 accuracy which it is possible to obtain and the standards of ENTER accuracy which it is economically acceptable to maintain. Hence, in this analysis, for milling operations in an FMC environment a nominal accuracy for normal machining is cho- ASSIGN DEFAULT READ IN USER sen to be different from the nominal accuracy for controlled TOLERANCES SELECTED FEATURE machining. If the tool is a "drill," the hole may have a surface finish anywhere from 1.6 to 6.35 µm (63 to 250 µin) [15] depending DISPLAY DESIGN DISPLAY FEA TLJRE INFORMATION on the condition of the drill's cutting edges. Whereas a ma- chinist will look over the drills, and choose one that is in good shape and can generate a good finish, an automated system OFFER MENU READ IN NEW will not. It will use whatever drill is in the CNC magazine TOLERANCE VALUE without knowing its condition. Therefore, the analyzer chooses ALTER 6.35 µm (250 µin) as the achievable surface finish. TOLERANCE Drills in addition, create oversized holes. A small diameter CHANGE TOLERANCE, REDISPLAY FEATURE drill will oversize by 0.0762 mm (0.003 in), but a larger drill VIEW ALL I NFDRMA TI ON may oversize up to 0.2032 mm (0.008 in). The oversize directly TOLERANCES affects the profile tolerance hence the expected achievable pro- file varies from 0.0762 to 0.2032 mm (0.003 to 0.008 in). Circularity is also affected but in a more complex manner. EXIT PROGRAM Circularity is a description of shape, not size; so, a hole that DISPLAY INFOR- is oversized 0.2032 mm (0.008 in) all around the diameter is MATION OF ALL perfectly circular. Similarly, a hole that is not oversized at all CREATE FILE FOR FEATURES is also perfectly circular. Neither case should be expected to TOLERANCE DATA BASE occur, however, since a hole is often oversized in only one direction, creating an oblong shape. Judgment was used to determine that the expected achievable circularity of a hole is EXIT equal to one half the expected achievable profile. Fig. 2 Control !low chart ol tolerance inpul program If a better profile or circularity is required, a "reamer" should be considered. A reamer can easily create a surface finish of 1.6 µm (63 µin), and judgment was used to determine that the expected achievable profile and circularity of a reamed from deflection can range from 0.1016 to 0.508 mm (0.004 to hole is three times better than with a drilled hole [15]. 0.020 in), but he also shows data where deflections range from In case of "end mills" it is difficult at best to generalize the 0.0254 to 0.3048 mm (0.001 to 0.012 in). The program assumes achievable tolerances and surface finish. There has been much a deflection of 0.254 mm (0.010 in) under general machining research in the area of end mill mechanics, and the subject is conditions and a deflection of 0.0508 (0.002 in) under con- very complex since the achievable accuracy depends on nu- trolled conditions. merous factors both deterministic and stochastic. Some of the The suggested processes for the controlled machining were parameters are deformation of the end mill, tool vibration, obtained from Tlusty's work [18]. He shows that close tol- the cutting speed and feed, tool geometry and the workpiece erances are held with axial and radial cutting depths equal to material and geometry [16-18]. Furthermore, the amount of one fourth of the tool diameter. The suggested speed and feeds deformation depends on spindle and machine tool structure were adapted from [15]. which is machine tool dependent. Data in [18] was used as a The above information is used to analyze a design for man- basis for most end mill tolerances, but judgment was used to ufacture in an FMC. Following is a detailed discussion of the determine specific values. Since, the end milling is the most manufacturing analyzer development and implementation. common operation in the manufacture of prismatic parts, we will consider both normal and controlled machining condi- The Manufacturability Analyzer tions. Among its many other functions RPP calls two functions, The surface finish obtainable by end milling can range from viz., tolerance input and manufacturability analyzer, which 0.4572 to 25.4 µm (18 to 1000 µin) although a range of 0.8128 address manufacturability [20]. to 6.35 µm (32 to 250 µin) is more common [19]. The analyzer chooses the expected surface finish to be 6.35 µm (250 µin) Tolerance Input Algorithm. Although, in conventional de- during normal machining practice and 1.6 µm (63 µin) during sign environment the tolerance and material information are controlled conditions. entered at the drafting stage, for automated manufacturing There are two components that must be added to determine (such as RPP) the designer waits until the tolerance input the expected profile, flatness, and circularity. One component program processes the feature file. This is necessary because is the machine tool spindle positioning inaccuracy, and the this information entered during the design stage will be lost other is the deformation of the tool and spindle mentioned when processed through the IGES translator to create a design above. First, the positioning inaccuracy describes how far the file in the standard neutral format. The tolerance input pro- spindle might be from where the software commands it to be. gram accepts the "feature file" and performs interactive input In the case of the Matsuura machine tool, the spindle may be and output of tolerances and material information. Figure 2 off 0.00762 mm (0.0003 in) in any direction. Therefore, even shows the control flow chart of tolerance input program. For before tool deflections are taken into account, the expected each feature in the design data base, the program assigns de- profile cannot be better than 0.01524 mm (0.0006 in); circu- fault tolerance values. For tolerancing, the ANSI Yl4.5-1982 larity cannot be better than 0.01524 mm (0.0006 in); and the standard is used. Following the criterion of minimizing the expected flatness cannot better than 0.00762 mm (0.0003 overall cost of the part production, as discussed in the previous in). These numbers, it must be noted, are specific to the FMC section, it assigns 0. 762 mm (0.030 in) for profile, for surface used and must be reevaluated as the machines get older. finish it assigns 7 .62 µm (300 µin), and for flatness it assigns The other component that must be added to that is deflection 0.254 mm (0.010 in). If the feature is circular, then flatness caused by tool spindle deformation. Tlusty [18] suggests errors does not apply and a circularity of 0.381 mm (0.015 in) is Journal of Mechanical DECEMBER 1991, Vol. 1131375 Page 1081 Table 3 Output file of tolerance input program ENTER Output from the tolerance input program Design name: mdemo DISPLAY DESIGN FEATURE# PROFILE SURFACE FLATNESS/ DETERMINE IF (mm) FINISH (µm) CIRCULARITY (mm) COMPARE DESIGN FEATURES [AN BE 0 0.381 7.62 0.152 WITH AVAILABLE MACHINED WITH TOOLS STOCK MATERIAL ON THE [N[ 1 0.762 7.62 0.381 MAGAZINE 2 0.229 7.62 0.025 DISPLAY RESULTS 3 0.038 7.62 0.152 DISPLAY RESULTS 4 0.381 1.65 0.152 COMPARE DES I GN 5 0.203 7.62 0.381 TO [ELL FIXTURES DETERMINE IF 6 0.762 7.62 0.381 FEATURE TOLERANCES 7 0.762 1.52 0.013 DISPLAY RESULTS CAN BE MET US I NG THE [ELL [N[ AND 8 0.762 2.54 0.381 CUTTING TOD~S COMPARE DESIGN TD [NC TRAVEL to generate each feature without considering the tolerance re- LIMITS ANO STOCK DISPLAY RESULTS SIZE LIMITS quirements. The control flow chart is shown in Fig. 3. The analysis considers form, profile, orientation, location, and DISPLAY WHETHER THE DESIGN IS runout as given in ANSI Y14.5. DISPLAY RESULTS MANUFACTURABLE To begin with, using the global data base, the design is checked to see if it can use any of the stock material. If no material of the correct type and size is found, the design is CREATE FILE OF ANALYSIS RESULTS determined to be not manufacturable. If material is found that is unnecessarily thick, the user is warned that excessive ma- chining is required and that improvements could be made. The EXIT analyzer then searches the global data base for available fix- Fig. 3 Control flow chart ol manufacturability analyzer tures and machining centers which can handle the dimensions of the raw material and allow the spindle travel necessary for FEATURE FEATURE machining. If no fixture is adequate or if no machine is ad- #3, HOLE #4, HOLE equate, the design is not manufacturable. Since, there may be FEATURE #I, GROOVE other FMC's or better tools that can manufacture the part, FEATURE the global data base includes other machines and fixtures for #7. SIDE CUT program simulation purposes. At this point the design is analyzed to determine if the avail- able cutting tools are capable of machining the part with con- siderations given to dimensions, radii sizes, and whether the feature bottom is round, conical, flat, or whether the feature goes all the way through the part. Recommendations are made to change the corner radii if it differs from the tool radius that has been selected. For each feature a list of useable cutting tools is made. Tool parameters important in the process include FEATURE tool type (drill, reamer, flat end mill, ball end mill), tool di- #6, POCKET ameter, flute length, length of tool from collet, and finally the FEATURE collet shape. Cutting tools are removed from the list if, while #5, POCKET machining one feature, the collet will strike the side of another FEATURE FEATURE feature. If there is one, or more, tools available for machining #0, HOLE #8, POCKET each feature, the design is manufacturable. If not, suggestions Fig. 4 Example part are made on how to remedy the problems. At the end the analyzer generates a file assigning a list of useable tools to each feature. The last part of the analysis covers the tolerances assigned instead. These numbers, it must be noted, are specific to the FMC used and must be reevaluated as the machines get and is discussed next. older. Using menu driven program the user can either exit the The program handles four types of tolerances: profile, sur- program at this point (if the default tolerances are satisfactory) face finish, flatness, and circularity which constrains feature or choose to change the tolerances. Before returning to RPP, size and shape only. The analysis of surface finish applies only a new file "feature plus tolerance file" is created. to feature sides and not to feature bottoms. The analyzer, with access to the file generated above, looks at each feature and Manufacturability Analyzer. The manufacturability ana- the tools assigned to each feature, and searches for one capable lyzer can now be called by RPP which reads the "feature plus of holding the requested tolerances. Both normal and con- tolerance file." Then, the analyzer, with access to the FMC's trolled machining conditions are considered to determine the global data base describing all the machining capabilities and manufacturability. If no tool in the list is capable of holding limitations performs the analysis of part in two stages with the the tolerances, the feature cannot be machined correctly, and following two objectives; the design is considered unmanufacturable. (I) Selection of multiple tools-machine-fixture for each At the end of the Manufacturability tests, an ASCII file is feature. ··· generated listing the selected stock, machine tool, fixture, and (2) Determination of an optimum tool-machine-fixture a list of all features and the cutting tools capable of machining for each feature. them. Finally, a separate list of the feature with tight tolerances In the first stage it checks the manufacturability of part and requiring specific tools and their recommended cutting speeds, generates a list of possible machines and tools that can be used feeds, and depths is generated. If the design is not manufac- 376 / Vol. 113, DECEMBER 1991 Transactions of the ASME Page 1082 Table 4 Output file of manufacturability analyzer Output from the design for manufacturability analyzer Design name: mdemo ANALYS!i RESULl SELECT- REMARKS ION Typonunborhoreto highllg'1tfoatuco but it requires facing off 38.1 mm (1.50 in) STOCK stock which is excessive machining. A better successfu ANALYSI! #1 stock size could be selected if the total design height was less than (35.56 mm (1.40 in) FIXTURE successfu fixture ANALYSIS #1 MACHINE machine successfu ANALYS!i #'s 1,2 TOOL unsucces- ANALYS!i sful <0(502,507,508)} > < 1(516} > <2{502,507,508) > <3(502,507,508)> <4{see note}> <5{see note}> < 6{see note}> < 7{504,505,506,513,515} > <8{513} > [NOTE: #4(hole): no tools with correct diameter or length. #5(pocket): no tools to make sharp corners. Fig. 5 Screen display of manufacturability analyzer #6(pocket): tools found, but interfere with feature #7. TOLERA- unsucces- tions are included. When the analysis is done the user is returned <2{controlled, drill& to RPP. reamer,508&518, 1.27 &1.524,0.00018&0.00028} > <3{ controlled,drill&reamer,508&518, 1.27& 1.524, Implementation. The analyzer program, written in C, runs 0.00018&0.00028} > <4{no tolerance analysis)> on the Sun computer system which is also the host of RPP. <5{no tolerance analysis}> <6{no tolerance analysis}> < 7 { none: surface finish and flatness The analysis in this environment must be able to read and cannot be met}> < 8( controlled,flat end create standardized files which the other parts of RPP can mill,513,3.556, 0.00018,1.27,1.27} > interact with. The files to be read by the manufacturability analyzer are "feature file" and "global data base file." The stock. The user can either decide to change the design or opt standardized file it creates is already discussed in the previous to continue with the existing design. section. When the user is ready, the program selects the CNC machine The "feature file" which is generated by the feature extractor tool and fixture and displays both. If it had been unable to is an ASCII file listing of each feature and relevant dimensions select either, it would have declared the design unmanufac- using the format developed at the National Institute of Stand- turable. The user would be able to continue the analysis, but ards and Technology (formerly, National Bureau of Stand- a design change would be needed before the process planner ards). The features may be holes, pockets, grooves, or side could begin. However, the part is not yet found unmanufac- cuts, and the features may have flat, conical, or round bottoms, turable, and the process continues. or may extend all the way through the part. More details on Now, the program analyzes the data bases to determine if feature extractor are available in reference [21]. each feature can be machined with the cutting tools available. The other ASCII file to be read is the global data base file If there had been no problems, the program would have stated which describes the hardware capabilities and limitations of so. However, the design is found to have three features which FMC. It lists the available stock materials, fixtures, and ma- cannot be machined. Each of the features (No. 4, No. 5, No. chines and also the cutting tools on the tool magazine. In each 6) is described, and the problems listed. Feature No. 4 is a case, it includes relevant data, such as stock and fixture di- drilled hole, but no drill of the correct diameter was located. mensions, machine tool travel, and spindle positioning accu- Feature No. 5 is a milled pocket with sharp corners (very small racies, and cutting tool dimensions. radii) too small for any of the available end mills. Feature No. 6 is a pocket for which a tool was found, but the tool collet An Example will strike feature No. 7 which is a side cut. Consider a user who is operating the FMC through RPP Even though the design has been found unmanufacturable, and has designed a part, as shown in Fig. 4, using a commercial the user chooses to continue to see what other problems may CAD system (CADKEY) and then process through IGES trans- exist. The tolerance analysis is performed, and the user is lator and feature extractor to obtain the feature file. The user informed that feature No. 7 cannot be held to either the re- then calls the tolerance input program, which assigns default quested surface finish or the flatness tolerance. Since no tools tolerances. Using the terminal mouse and the menu, the user had been found for features No. 4, No. 5, or No. 6, they are requests Change Tolerances to assign the design tolerance for ignored. Features No. 0 through No. 3, and feature No. 8 are each feature, as listed in Table 3, and returns to RPP. found to have achievable tolerances. Features No. 2 and No. The user now requests the manufacturability analyzer, and 3, both drilled holes, will require special care during machining; the screen changes to show an oblique view of the design, a so, the tool numbers, reamers, speeds, and feeds are entered new menu, and a text panel as shown in Fig. 5. The user selects into the output file for the process planner to use. Feature No. Continue and the analysis begins. After the stock size analysis 8, a milled pocket, will also require special care; so, its tool is complete, it displays that the part can be made from an number, speed, feed, and depths of cut are also entered into available stock and that a block of aluminum 152.4 the file. The analysis is now complete, and the analyzer creates x 76.2 x 76.2 mm3 (6 x 3 x 3 fn3) is selected. However, 38.1 mm an ASCII file which is listed in Table 4. The user now exits (1.5 in) of material will have to be removed from the top which back to the main protocol program. is considered to be excessive machining. The user is advised that a 35.56 mm (1.4 in) thick design would facilitate a better Conclusions stock selection since a 38.1 mm (1.5 in) thick material is in The development of the tolerance input program and the Journal of Mechanical Design DECEMBER 1991, Vol. 113 / 377 Page 1083 manufacturability analyzer has provided a useful tool to the 2 Atkinson, A. 0., "Design for Manufacturability: Computer Integrated designer in the FMC environment for the purposes of checking Design and Manufacturing for Product Development," SAE Technical Paper Series, 851587, September 1985, pp. 3-4. his design for manufacturability. The Analyzer is successful 3 Ranta, M., Unui, M., Kimura, F., "Process Planner with Produceability since it provides a wide variety of analysis and presents the Feedback," Research Center for Advanced Science and Technology, The Uni- results to the user in a cohesive way without human interven- versity of Tokyo, 1988. tion. As shown in the example, the program draws upon the 4 Boothroyd, G., Fundamentals of Metal Machining and Machine Tools, Scripta Book Co., Washington, 1975, p. 75. broad definition of manufacturability to show the user the 5 Steven, L. C., and Dixon, J. R., "Creating and Using a Features Data wide spectrum of possible problems in a design. Furthermore, Base," Computers in Mechanical Engineering, Vol. 5, No. 3, 1986, pp. 25-33. since it will be rejecting designs for problems ranging from 6 Barash, M. M., "Group Technology Considerations in Planning Manu- stock selection to surface finish, the designer will be encouraged facturing Systems," Transactions of SME CAD/CAM IV Conference, Novem- ber 1976, pp. 157-166. to consider those issues from the very beginning of product 7 Hoffman, P., '' Analysis of Tolerances and Process Inaccuracies in Discrete development cycle. Nevertheless, the analyzer is far from com- Part Machining," Computer Aided Design, Vol. 14, No. 12, March 1982, pp. plete and requires further work. 83-88. 8 Parkinson, D. B., "Assessment and Optimization of Dimensional Tol- erances," Computer Aided Design, Vol. 17, No. 4, May 1982, pp. 191-199. Future Activities 9 Boothroyd, G., and Poli, C., "Designing for Economic Manufacture," Annals of College International Pour L 'Elude Scientifique Des Techniques de One immediate area of investigation is to consider alternate Production Mechanique, Vol. 28, No. I, 1979, pp. 345-350. options of manufacturing when a part fails manufacturability 10 Anand, D. K., Kirk, J. A., Anjanappa, M., and Chen, S., "Cell Control test. Several alternatives such as special tools, fixtures, and Structure of FMP for Rapid Prototyping," ASME Publication PED Vol. 31, machines will be considered. If all fails, the option of sub- Advances in Manufacturing Systems Engineering, 1988, pp. 89-99. 11 Anand, D. K., Kirk, J. A., Anjanappa, M., Magrab, E., and Nau, D.S., contracting and the associated costs will be considered. "Protocol for Flexible Manufacturing Automation with Heuristics and Intel- Another area of future work is to explicitly include the effect ligence," Proceedings of the MI-88, pp. 209-217, ASME, May 1988, Atlanta, of position tolerance of features including the effect of tol- GA. erance stacking. The method reported in Hoffman [7] will be 12 "Increased Production Reduced Costs," Machinabi/ity Research Pro- gram, US Air Force, Curtiss-Wright Corp., 1951, pp. 14-16. used to construct a system of inequalities which the working 13 Cook, N., Manufacturing Analysis, Addison-Wesley Publishing Co., 1966. dimensions and inaccuracies of machining operation must sat- 14 Dieter, G. E., Engineering Design: A Materials and Processing Approach, isfy if a given tolerance specification must be met. The meth- McGraw Hill, 1983. odology developed in reference 8 will be used to evaluate the 15 Machining Data Handbook, 2nd edition, Machinability Data Center, Dept. of Defense Information Analysis Center, Metcut Research Associates, Inc., 1987, effect of tolerance on assemblability. It will be an interesting pp. 180-345, 855. problem to investigate the effect of tolerance stackup on the I 6 Tlusty, J., and Machneil, P., "Dynamics of Cutting Forces in End Milling," cost minimization approach taken in the present work. Annals of CIRP, Vol. 24, 1975. 17 Merchant, M. E., "Metal Cutting Research-Theory and Application," Machining Theory and Practice, American Society of Metals Publication, Cleve- Acknowledgment land, 1950, p. 36. The work reported in this paper was partially supported by 18 Tlusty, J., "Machine Dynamics," Handbook of High Speed Machining Technology, Chapman and Hall, New York, 1985, p. 155. the Engineering Research Center at the University of Mary- 19 Olivo, C. T., Advanced Machine Technology, Breton Publisher, North land. Scituate, MA, 1982, p. 114. 20 Courtright, M. J., "Manufacturability Analysis for a Flexible Manufac- References turing Cell," M.S. Thesis, 1988, The University of Maryland, College Park, MD. I Gossard, D. C., Zuffante, R. P., and Sakurai, H., "Representing Di- 21 Kumar, B. J., Anand, D. K., and Kirk, J. A., "Knowledge Representation mensions, Tolerances, and Features in MCAE System,'' IEEE Computer Graph- Scheme for an Intelligent Feature Extractor," ASME Computers in Engineering ics & Applications, Vol. 8, No. 2, 1988, pp. 51-59. Conference, August 1988, CA. 378 / Vol. 113, DECEMBER 1991 Transactions of the ASM E Page 1084 AUTOMATED INSPECTION DATA ANALYZER FOR CLOSED LOOP MANUFACTURING by M. Anjanappa Department of Mechanical Engineering University of Maryland - UMBC Baltimore, Maryland 21228 J.J. Dickstein Westinghouse Electric Corporation (D&ESC) Baltimore, Maryland 21203 D.K.Anand J.A. Kirk Department of Mechanical Engineering University of Maryland - UMCP College Park, Maryland 20742 Page 1085 ABSTRACT in an intelligent manner for corrective action purposes [1 ] . Usually,• dimensional inspection and verification of the finished piece parts · Dimensional inaccuracies in the workpiece can be qualified occur as the last step in the manufacturing. It is only then whether and quantified by analyzing the specific processes that a part we know if the parts were made correctly and will perform the undergoes in the manufacturing cycle. A general list of error required function. In most cases, at this point in time, it is too late sources in milling was shown to produce various dimensional to correct for any errors that may have occurred midstream in the conditions which could lead to an out of tolerance condition on the manufacturing cycle. If the finished part does contain any errors, machined _eart boundary and internal features. An Inspection Data a studr is usually undertaken to determine if these parts can be used Analyzer (IDA), is developed which uses information solely from "as is.' The amount of time spent on this analysis usually depends the inspection report to determine specific tool, machine and on the cost and amount of time required to manufacture that batch fixture errors that might have existed in the manufacturing process. of finished parts. This process can be very costly and time consum- To determine logic for the routine, a simple part was manufactured ing, and in most cases the parts will be scrapped anyway. at the University of Maryland using their existing FMP, which Today's philosophy about quality assurance emphasizes includes process planning and automatic NC code generating preventing defects not just detecting them. An ideal closed loop capability. A modern CMM was used to physically inspect the part manufacturing system would rely on timely inspection data, such for dimensional values. Results of the report indicated that some as first part inspection, to control errors in the manufacturing dimensions were in error. These dimensional values were studied process. with the aid of a senior manufacturing expert to develop initial logic A typical first part inspection would involve; for the IDA. Four analysis programs were shown to be needed to • part measurement fully determine the scope of the problem. To sort out confusing • determine the errors by comparing to design tolerance :and multiple error sources two other analysis routines were • determine the most probable cause of such error developed. It was shown that these routines consisted of a tool • recommend corrective action parameter and machine fixture analysis sections. Tasks 1 and 2 can easily be automated with advanced Coor- dinate Measuring Machines (CMM) and standard language for- INTRODUCTION mats IGES and DMIS. However, tasks 3 and 4 are complex and require an expert to analyze the data which can be time consuming With the introduction of computer assisted design, process and expensive. Often, for the above reasons, first article inspection planning, NC code generation, fixturing, and manufacturmg, the is not exercised, risking the possibility of scrapping an entire batch. batch manufacturing of precision machined parts can be ac- Hence it is proposed that by automating tasks 3 and 4 with an complished without the use of enormous amounts of paper work Inspection Data Analyzer (IDA), the ideal closed loop manufac- and formal documentation. In recent years specifications for tunng system can be achieved. . neutral language formats, such as Initial Graphics Exchange This paper deals with developing and validating such an IDA Specification (IGES) and Dimensional Measuring Interface using a combined algorithmic and heuristic approach for parts that Specification (DMIS), has emerged making the once dreamed are manufacturable within the existing Flexible Manufacturing .a bout "paperless" factory of the future slowly becoming a reality. Protocol (FMP) at the University of Maryland . However, if an error exists in any one of the above databases, it would most likely be carried on through the other manufacturing ERRORS IN FINISHED FEATURES processes, makin~ detection difficult. Because of this, final part and database inspect10ns are critical to ensure correct manufacturing In the design and manufacture of a part, dimensions and operations. tolerances are needed to accurately outline end requirements. Toe· The manufacture of precision parts usually involves a series of standard for specifying tolerances is given by the American Nation- complicated manufactunng processes with a good probability that al Standards Institute (ANSI Y14.5), and is used in this work. · some sort of errors will occur. An impertant capability in manufac- turing is the ability to be able to extract information from a process 'regarding it's quality and consistency, and to use that information Page 1086 - As mentioned before, the scope of IDA reported in this paper ERROR SOURCES is limited to the existing capability of FMP at the University of Maryland. Currently, five features are allowed to exist in this FMP Grttinf Tool Errors of which three features can be analyzed by IDA which is compatible 0 the many variables affecting any machining operation, the with the existing manufacturability module as described by [2). cutting tool - while small and relatively inexpensive - is one of the These include slots, pockets, and holes as defined in [3). Errors most critical [4]. Errors in the cutting tool can occur before and that occur in these features are a direct result of the inc onsistences during the machining process. The errors considered here include: or inherent errors in the manufacturing process. (See Fig. 1.) incorrect tool size and type, tool wear, tool runout, and tool deflec- tion. SI.QI An improper tool size can obviously affect finished feature size A slot is defined as a feature whose boundin~ edges lie on to a varying de~ree. In the case of a drilled hole, it can be easily multiple adjacent faces of the workpiece. This defmition accom- determined by inspecting the finished size. This holds true to the modates many different feature configurations. Slots can contain same degree when talking about a slot or pocket, except validation edges that are defined by a purely X locating dimensions ie. the is a little more difficult. In order to determine proper tool size, the edges are perpendicular to the X axis. On the other hand, they can center line of the x and 'I. cutting path must be exactly known. The contain edges that may be defined by purely Y locating dimensions, defined cutting edge will be determined by this x and y position ie. edges are perpendicular to the Y axis. Additionally, slot edges plus one half of the cutting tool diameter. In contour cuttin~, the can contain many sides and be defined by a combination of the number of passes may be large depending on the required fimshed above, purely X and Y locating dimensions, and edges defined by tolerance. Rough and finish cutting operations use different styles bothXand Y. of cutters and NC programs must be analyzed to determine where in the program the final cut took place and what location. POCKET Typically tool wear, runout and deflection errors occur during The pocket is defined as a feature whose bounding edges lie the machining cycle. One of the most common problems with on a single face of the workpiece. Hence, by definition, pocket cutting tools is that after a period of time, they will begin to wear. edges cannot break out anywhere in the overall workpiece bound- Using a tool that is worn creates dimensional inaccuracies and ary. This means that the feature cannot be described by purely X surfaces with poor finish. There are many methods that can be used or Y dimensions as in the slot above. Pocket boundary edges have to determine tool wear either directly or indirectly. Indirect to enclose themselves, hence edges must either be at right angles methods, in general are easier to carry out, and usually involve to one another and be described by X and Y, or at an~les to one comparisons between the tool in question and one that is new. another and be described by a combination of X and Y dimensions. These methods include measuring the changes in amount of power consumed, workpiece geometry, tool forces and tool junction temperatures. Tool runout and deflection is caused by the shank deforming due to high cutting forces or improper tool material. Any cutter runout or deflection can cause feature sizes to change EDGE DEF !NED BY by redefining the desired cutting position. Small diameter cutters )J2?1::E A rnHBINATIOt~ OF are the most susceptible to this o/I)e of problem. Stiffer cutters can X & Y otHENSlDNS Y! IFHfllEtif be obtained by minimizing the distance the tool protrudes from the ~'"" chuck. Carbide cutters are generally three times stiffer than high speed steel cutters of the same size and configuration [5]. IURY XC EFl~O Plff!J Yl EF!IBJ Dil[W.Tlrn [f X. 00 Y[ IF[tfO EDGES DEFINED BY PURELY EOCH.[EfH{OBYA C!Kl!W.T!{tl[FYIID Machine Errors X AMJ Y OIHENSIONS X 00 YD ll'ENS!OO Machine errors typically small for a new and calibrated machine. However as the machine gets older wear of parts can become large. These errors can be classified as position errors, SDUNDARYMLJSTBE EDGE USED TO LOCATE EDGE USED TO LOCATE X DEFINED FEATURES Y DEFINED FEATURES thermal deformation errors and stochastic errors. Some of the \~~~\~UDNHOARYITERTIARY ( SECONOARYITERTIAR ~·~"" ) DATUM) contributing factors that contribute to position errors are the servo lab, scale errors, out of calibration and spindle tram (non perpen- dicularity of spindle axis to table plane). The thermal error nor- mally occurs over a period of time and if a rart is machined over a T~RU H(U PART THICKNESS long period of time, can induce therma errors. An improper relationship between the part feed and cutter speed can on the 1l( y other hand contribute to chatter and hence stochastic in nature. Accurate location of the table is only important when the part X is being moved relative to the cutter, as in the smaller class of machines. Calibrating the X-Y positioning refers to the amount of actual movement of the machine versus the commanded move- Fig. 1 Standard Features ment. This is commonly referred to as tool path error. This can HOLE. cause, features to be dimensionally incorrect. Many methods exist J:,.. hole is defined as a feature whose bounding edges lie on for compensatin~ for this type of error [6]. Machine errors will multiple non-adjacent faces of the workpiece. As an additional however be identified as a single error in this work since it is beyond constraint, for this thesis, the bounding edges must be purely the scope of this work to be more specific. circular in nature. Location is specified by X and Y locating dimen- sions on one surface of the workpiece. Misce)laneous Errors BOUNDARY FEATURE Fixture Errors, A fixture is generally defined as a means or system for accurately securing and locating a part in position while The boundary must be described by feature edges, which in a manufacturing related operation is carried out. In machining, the total classify the part as a prismatic part. The part must contain a fixture will establish and contain a predetermined tolerance be- definite length, width and thickness that can be described by a tween the workpiece and the cutting tool. To avoid chatter, fixtures. combination of one, two or three points. should be structurally stron~ and the workpiece should be located. The definition of above features are based strictly on their as close to the table as possible [7]. Three possible problem areas· boundary attributes in relation to workpiece and for more details common to fixturing are locating and posit10n, clamping, and chip see reference [3]. control. Page 1087 'Location and Position' refers to the known and desired relationship between the workpiece and fixture. Fixtures are nor- mally mounted on the machine in relation to the cutting tool. m~nce the relationship between the workpiece and the tool is directly known and can be established within an acceptable range of tolerance. Therefore, overall feature and part size accuracy is thus dependant primarily on the accuracy of position between the workpiece and fixture [7]. Mounting errors, may in a number of cases amount to twenty to sixty percent of the total machining error ____ t, __ _ [8]. Some common ways of locating a part include the use of: 1~1.t.ldtd I locating pins, locating edges and V-blocks. I Cl,f,!PftllM I I Paf\Gtll I 'Clamping' refers to the means by which a workpiece is held ---,--- Ml"111C.U1~ in position on the fixture or work table. The type of clamp general- 1 ly depends on the following: manufacturing operation, workpiece I ----i ;, 1---, size and shape, freguency of use, clamping area and location, must I OldlAdPmONI I not to interfere with the cutting tool, and minimization of part I I vibration. Additionally, the clamps should exert a constant pres- I I sure and be located over a solid area to avoid part distortion or I I deflection while machining. Clamps must also be designed to be I Ii ._,~ Il -1> vibration free themselves and easy to use. I 'Chip Control' is a matter of prime importance on any machine r- .3_ - -:_[)_al ai° :. _. _ ,: tool involving chips [7]. Three basic chip problem areas in a fixture are: corner relief, area relief and chip removal. Care must be l~!li exercised in preventing the chips from getting in the immediate ,--_I ,-,.,--.~ I I I tool-workpiece area since it can lead to the production of parts with - •:=~•mo ! : poor surface finish. - - - - OESIGH ENGINEER ~ I OTHER INFORMATION I Incorrect Stock Size Incorrect stock size can lead to incorrect boundary feature sizes. Specifically, the length, width, and the ~ - - - - - - - - - - - - - - _I thickness of the workpiece will be directly affected. Most parts manufactured today have at least one or more of their outside edges machined. If excess material is to be removed, and the stock Fig. 2 Flexible Manufacturing Protocol size is incorrect, machining parameters can be adjusted to compen- sate .. and bosses as described by [3], and 2) they only can be created by Workpiece Deflection This is the same as a tool deflection machining access to the top face of the part. error except that the compliant workpiece deflects and the tool is Next, the feature file is input to the manufacturability module. assumed to be rigid. This program allows the user to input any specific feature size or Boundary Sjze Errors This error (f inished part boundary size) locat10n tolerance and surface finish requirements. If none are will not only cause the overall size dimensions to be incorrect, but specified, easily achievable default tolerance values are assigned. will cause pocket, slot and hole locations to be incorrect as well. . Based on the part's size, features and tolerances, the program determines if any or all of the requirements can be met, given the ERROR FILE GENERATION cell's capabilities. Additional requirements for special fixtures, tools, machine feeds and speeds will be displayed if so required to To help experimentally develop the analysis routine, it was meet end tolerances. Once the part is determined to be proposed to design, machine and inspect a simple test part. All machinable in the existing FMC, a process plan file is generated. phases of the design and manufacture would be accomplished A full description of this file can be found in [9]. through the aid of FMP at the University of Maryland and the A file containing the appropriate M and G codes per EIA RS CMM facility at the Westinghouse CorP.oration. It is therefore, 274D is created next. This file is then processed into specific relevant to briefly describe these two facilities. machine readable code that can directly control the NC machine. There are two FMC's at the University of Maryland, viz a Information is then down loaded to the machine through it's RS vertical machining center-based FMC and a turning center-based 232 serial port, and machinini can commence. All of the FMP is FMC. The cell hierarchy is regulated through the use of a Flexible operational except for the fixturing planner which is currently Manufacturing Protocol (FMP) as shown in Fig. 2. This protocol under development. was designed to ensure database standardization with utmost In it's current confi~ration, the FMP does not have capability flexibility. The protocol can be characterized by two specific tyi;ies for piece part inspect10n. It would therefore be desirable to of activities known as FMP/D and FMP/M. FMP/D is the portion develop a closed loop inspection protocol for final part acceptance of the protocol that contains all information related to the com- and verification before the entire batch is manufactured. This ponent design, whereas FMP/M contains information related to its method involves linking FMP/ D and FMP/M tasks with the CMM, manufacture. Additional information about the FMP can be found by using the IGES database. The protocol pertaining to closed loop in [9]. manufacturing with first piece part inspection is shown by dotted . Initially, the user can design a part by using either commercial- lines in Fi[ure 2. VWS2 feature based CAD cannot be used unless ly available CAD packages or by a feature based CAD system an IGES file for the part exists. From the IGES database, a DMIS · known as VWS2 (originally developed at the National Institute of generating program residing on commercial CAD packages (such Standards and Technology). Usually, commercial CAD packages as CIM CMM or BRAV 03 CMM) can directly create CMM are run on the IBM AT and VWS2 runs on the SUN work station. inspection paths. Hence, inspection path generation can occur in If a commercial CAD package is used the design data file must be parallel with NC machining path generation. The inspection paths converted to the IGES format. The IGES file is used as input to are nothing more than X-Y-Z movements and defined touches of an intelligent feature extractor which resides on the SUN and the measurement probe which determine actual part size, feature determines the type, size and location of all feature boundaries. size and position. All this information is described and stored in Output from the feature extractor is a file known as a feature file, the neutral file format called DMIS. Each specific CMM is re- having the same format as what would have been obtained if the quired to have a translator, which would take the neutral DMIS VWS2 program was used. Features must conform to the following database and convert it into specific machine instructions. Cur- 1 1 limitations: 1) they can only consist of holes, slots, pockets, bridges Page 1088 rently, the BROWN & SHARPE CMM supports the DMIS language, to automatically inspect the part for compliance with database format. Depending on part geometry and tolerances, stated drawing tolerances. A DMIS language translator is not yet special inspection fixtures may be required, but are not being available for SHEFFIELD inspection equipment, hence the considered in this problem. machine was manually programmed off line. The output of the Actual finished part dimensions would be determined by the inspection routine was a file which contained the actual part CMM and stored in a neutral data file. This data is then compared dimensions and values for deviations from nominal. The results of line by line with the feature design file, which is output from the the inspection report revealed that certain dimensions were incor- manufacturability routine as described by [2]. This file contains the rect. A detailed review of the report, line by line, to try and allowable upper and lower part and feature dimensional limits. determine the cause of error was conducted. By analyzing all Additionally, surface finish and flatness are included. An off-line dimensional values with manufacturing experts, the initial logic for program written in TURBO C would determine the magnitude of the IDA was formed. all errors and check with the feature design file to see if any exceed the allowable desi~n limits. The resulting information would be INSPECTION DATA ANALYZER (IDA) stored in a file which is known as the error file. This file would serve as input to IDA which will be discussed in the following Little research has been done in the area of identifying and section. analyzing process errors that occur in manufacturing. Most of the work in this area involves the determination, measurement and correction of specific error sources strictly in terms of variables that can be applied to mathematical functions. Error sources are inves- tigated and discussed on a individual basis. Only one specific reference was located which addresses the genenc problem of error source identification, given multiple possibilities. Some basic ·g uidelines and rules about how to go about HOLE #2 troubleshooting manufacturing processes was found in [4 j. It states. that troubleshootin~ is a very difficult task in which few individuals receive formal traimng, hence knowledge is limited. Tables that list general problems, possible causes and solutions in various manufacturing processes including milling are contained. These tables are general in nature and at best can only be used as starting point. Koval and Igonin [10], [11], have analyzed in detail the specific error elements that exist when manufacturing parts on an NC milling machine. These elements include the NC program, machine, milling fixture, cutting tool and the workpiece. Several specific error source possibilities are given for each error element. Diagrams of error components for point to point and contour Fig. 3 Sample Part machining are provided along with some specific values. In another paper Koval [12] describes a method for calculating the The part would be made of aluminum alloy (6061-T6), and overall contouring accuracy of a NC milling machine based on a contain three typical features that are allowed by the feature based detailed mathematical description of the processes that occur in CAD program VWS2. The part was designed and drawn using elements of the NC and MFTW (machine - fixture - tool - CADK EY V3.12 running on a IBM. Dimensioning and tolerancing workpiece) systems during the course of machining. Enou*h detail were performed in accordance with the most recent version of the is presented so that given all mathematical values, the process Y14.5 specification. Details of the sample part, showing overall tolerance" could be accurately determined. size and features can be seen in Fig. 3. The part geometry data was Much has been written about statistical process control, which then translated to IGES format and down loaded to FMP residing is a commonly used technique to detect process trends. This on SUN 3/160 host system. The intelligent feature extractor ex- methodology works well for determinini when in time a l?rocess is tracts features, and creates a feature file in VWS2 part model getting out of control. It cannot determme how and why it's out of format. Details of feature. extractor can be obtained in reference control, but can only be used as a general guide in determining [3]. The VWS2 generates the process plan and the appropriate NC process capabilities and limitations. codes. Several different process plan files were generated for the Dimensional inaccuracies in the workpiece can be qualified sample part. Of main interest to us, is the selected feeds, speeds and quantified by analyzing the specific processes that a part and tool sizes that were chosen to machine the part. The feeds and undergoes in the manufacturing cycle. Every step of each in- speeds that were generated, represented typical values that are dividual process can be analyzed to determine the specific most commonly used in similar manufacturing operations today. The probable cause of error. The possible source (s) of error can be design part tolerances were not a factor in determining machining anything from inconsistences in the design stage up to and includ- parameters. All that was required for our test were tolerances that ing final part inspection. This paper will only deal with a specific could be easily obtained using the modern machine tools and period in the manufacturing cycle which includes the loading of methods of today. A Matsuura 510 CNC milling center was used raw material into the fixture, up until the final machining step. to machine the part to the desired configuration. The NC code was The logic is patterned after steps that would be taken by a directly down loaded by the VWS2 program to the machine manufacturing engineer, when trying to determine why a part has throu~h it's RS 232 serial port. Rigid table clamps were used to been machined incorrectly. After a part has been machined for the restram the part in place while the machining operation was carried first time, it is thoroughly checked to assure that all manufacturing out. The process plan, NC code, and machimng operations were processes are correct. This procedure is commonly known as first not individually verified to be correct. Initially one part was article inspection, in which the machine, NC tapes and tools are machined using these exact steps. approved for additional quantity part production. It is at this point The next ster was to inspect the part to determine what the in the manufacturing cycle that most errors occur. The results of, actual part and mdividual feature dimensions were. This was any inspection report will show that most dimensions will not be : accomplished by using a SHEFFIELD RS 150 CMM, linked to a exact [13]. These errors are due to the inherent accuracy of the HP model 310 computer. The CMM was located in the inspection machine and overall process. Based on the size, type and general department at Westinghouse Electric Corporation. The stated trend of errors, it is to be determined if the values are normal for machine accuracy was in the range of .0003, which was acceptable that specific type of machinin~ operation. If any dimension ex- for our needs. The CMM was programmed, using HP BASIC ceeds the process error, a possible problem most likely exists. Page 1089 · In the inspection report, one of the first things that gets atten- Table 1. Error sources for each feature tion is the feature or dimension that is in error. The next step would be to determine exactly what operation generated that error. In detail, when, how and by what means were these features TOOL ERRORS MACHINE ERRORS MISC. ERRORS generated. Included in this study is the analysis of all tool - l!: wz Q; osition. Hence, this is the reason the error is first checked to see 1f it grew. If the error amount did not grow, it is The program will not be executed unless an out of tolerance concluded that the cause of error is in the fixture setup or in the condition is found. Assuming more than one hole exists of the same initial position definition. The _possibility still exists that the error size, other hole sizes are checked to see if correct. If some of them could be in the machine. This 1s later verified in another routine are correct in size and some aren't, it is assumed that something in by checking to see if a setup error was found to exist in any of the the process changed between the correct and incorrect holes. If all other error determination routines. If a setup error was not dis- or any of the holes were the same size, then by definition the same covered in any other routine, it is assumed that most of the error tool should have been used. At this point the routine, branches to was due to the machine. If a setup error was responsible for any determine the general cause of error. Hence, the first area to other errors anywhere on the part, it should show up in multiple investigate is whether the same sized tool was used for all similar places as other dimensions would be affected. This assumes that holes. This may be difficult to detennine, but two areas can be only one setup was used to machine the entire part, and that easily checked: 1) The NC program can be analyzed to see if the machine error was not responsible for any other feature errors. correct tool was called out in the listing to the machinist and, 2) Further discussion about this logic and assumptions takes place in The tool holders would have to be manually checked to see if they the sections ahead. contained the proper tool. If the same and correct sized tool was Page 1092 used for all similar holes, it is assumed that machine chatter, tool possible sources of error that each program could determine, it can runout or wear occurred midstream in the process of drilling the be concluded that both programs would not be used by all routines. holes. Going back in the routine to the point where it branched, if The tool error analysis program would take inputs from the stock all hole sizes were incorrect, all the tool parameters would have to size and slot & pocket edge analysis routines. The machine - fixture be checked. Logic, as executed in previously routines would first analysis program would accept inputs from the slot and pocket, check to see if the tool size was correct. This would be ac- edge, stock size and X & Y hole location analysis routines. The complished as stated above. Additional sources of error could be hole diameter analysis routine would have to stand by itself, since the existence of tool runout or wear. In general, tool runout is more the tool used for drilling or reaming a hole is much different than likely to occur than tool wear, hence that condition is checked first. for contour cutting a defined edge. If the hole is oversized, it is concluded that tool runout existed. This is due to the fact that most small sized drills or reamers can Combined too) error analysis routine. The combined tool bend very easily if not given the correct feed-rates. If the hole is error analysis routine shown in Fig. 8, determines errors that may undersized, it is concluded that tool wear was present. Tool wear exist when contour cutting a feature edge. This operation is used is a less likely source of error because the drill or reamer will in the creation of slots, pockets and part boundaries. One way that noticeabl;y and not affectively cut into the material. Usually, tool tool parameters can be checked is to compare the specific error runout will eroduce holes that are oversized, whereas a tool wear t~es and amounts generated from each error analysis routine. In condition will most likely produce holes that are undersized. this program it is determined first if the same tool was used for more than one edge creation. If a different tool was used for each feature, then no tool error logic may be applied since each tool would have to be examined separately. The first error type that is analyzed are tool size errors. If the same size tool was used in more than one place, each routine is checked to see if for that tool, any i ~{AD 111 l\JUll l_!-RfWfr< [J-AlA J size errors exist. Any of the same two errors flagged will be a good indication that the error is real. From this point, it is determined if the amount of error from Al( BOUNDARY and fixture setup errors can be difficult to distinguish when tool or CREATION ? other w,es of errors exist. Fixture setup and machine errors will be verified by determining which exists rn the two feature analysis routines and comparin~ the results with data from the stock analysis routine. A detailed flow chart showing our logic can be seen in Fig 9. Error types from the other two routines are read in and stored. By default, a set up error will exist in each routine because this last error message generated before exiting each of the programs. Next in each routine, it is checked to see if a boundary edge error exists. Ifn one exists the analysis is terminated. IS Common knowledge says that if a setup or tool error exists in the MORE THAN ON[ YES stock size analysis routine, then the boundary will be incorrect. This TOOL RUNOUT ERROR FLAG assumes that at least one outer edge of the part has been machined. SET? Normally this machined edge is taken as the datum surface. NO Assumin& a boundary edge error exists, tool errors are checked for existence m the stock size analysis routine. If a tool error exists, , this could be misleading us to believe that a setup error is the cause. Fig. 8 Combined tool error analysis As part of this analysis it is checked to see if both boundary edges are machined. If they are this means that the tool touched both Combining Error Analysis Logic The above error analysis parallel edges of the boundary in question. This also assumes that routines determined the most likely source of error which was the same tool whether right or wrong was used to machine this based on solely dimensional and data base analysis. Questions outer boundary. Next check to see if the distance from any one of arise when you consider that there may be multiple error sources the two boundary edges in question to the feature edge is correct. present or that the initial error determination may be incorrect If the distance is not correct it can be safely said that the feature when reviewing all data from the other routines. In this section of location was incorrect solely due to the part boundary being incor- our logic, all data is sorted through in an attempt to make some rectly machined due to the tool error. If the distance from one more informed judgments in determining the most probable sour- boundary edge to the feature location is correct it can be deter- ces of error. mined that a setup error existed and most likely the setup error In,reviewing the overall logic, it was apparent that our com- offset the tool error for that specific edge in question. This is bined error analysis routines should be broken up into two parts. assumed because if the tool is incorrect and both parallel boundary One of the parts consists of the tool parameters analysis, and the edges are machined, then the feature location shouldn't be correct other consists of the machine - fixture analysis. By reviewing the relative to any one edge. Going back , if one boundary edge is Page 1093 ACKNOWLEDGEMENT READ IN ERROR This work has been partially supported by the Engineering TVPESFROM OTHER PROGRAMS Research Center at the University of Maryland and Westin~house Electric Corporation is acknowledged for allowing to use mspec- tion equipment and associated personnel with special thanks to CONTINUE Michael Nussbaum. REFERENCES 1.Dooley, K. & Kapoor, S.G. "An Enhanced Quality Evalua- tion System for Continuous Manufacturing Processes - Part 2: Application", In Manufacturing Metrology: Proceedings of the Winter Annual Meeting of the ASME, Chicago Illinois, Nov 27 - Dec 2 1988, edited by Sathyanarayanan G., Radhakrishnan V, & Raja, J., pp 21. 2.Courtright, M.J., "Manufacturability Analysis for a Flexible NO Manufacturing Cell", Master Thesis, University of Maryland, Col- lege Park, December 1988. 3 .Kumar, B.J. , "Integration and Testing of a Intelligent Feature Extractor within a Flexible Manufacturing Protocol", Proceedings of the 16th NAMRC, May 1988, Urbanan, IL, (with D.K. Anand and J.A. Kirk). 4."Troubleshooting Manufacturing Processes", Society of Manufacturing Engineers, edited by Gillespie, L.K., S.M.E., Dear- born Michigan, 1988, pp 2-1. 5."Fundamentals of Precision in High Speed Machining", Bos- ves ton Digital Corporation, Milford, MA. 1987, pp. 2-8. 6.Anand,D.K., Kirk, J.A., Anjanappa, M., 'Tool Path Error SETUP CAN'T DETERMINE Control of End Milling of Microwave Guides", Proceedings of 7th ERROR ERROR SOURCE World Congress on the Theory of Machines and Mechanisms, SET UP AND TOOL September 1987, Universidad de Sevilla, Sevilla Spain. ERRORS ARE OFFSETING EACH OTHER 7.'Tool Engineers Handbook", American Society of Tool and Manufacturing Engineers, 1st ed., McGraw Hill, New York, 1949, pp 499, 1544, 1550, 1562. 8.Bazrov, B.M. & Sorokin, A.I., 'The Effect of Clamping Se- Fig. 9 Combined machine fixture analysis quence on Workpiece Mounting Accuracy", Soviet Engmeering Research, Volume 2, No. 10, 1982, pp 92. ·m achined, and assuming the machined edge is the datum edge a 9.Chen, S., "Structure of a Flexible Manufacturin¥, Protocol setup error could still exist. This is due to the fact that from the for Design and Control of a Vertical Machining Cell', Masters datum edge, the feature location would be correct, but again the Thesis, University of Maryland, College Park, December 1987. boundary size will be incorrect. From here check to see if a setup 10.Koval, M.l. & Igonin, G.A., "Contour Milling in NC Milling error existed in all three of the routines. If it didn't the error source Machines: Calculation of Error Components", Soviet Engineering cannot be determined because the data is truly misleading. If it Research, Volume 56, No 6, 1985, pp 44. :does then it can be concluded that without a doubt a setup error 11.Koval, M.I. & Igonin, G.A., "Comparative Analysis of . does exist. Again setup errors will exist as a default from the other Machining Error Components for a Heavy NC Machine Tool" two routines, but also in stock size routine. Trying to weed this out Soviet Engineering Research, Volume 50, No. 9, 1979, pp 9-13. ' involves checking for tool errors and then making the determina- 12.Koval, M.I., "Calculating the Machine Error of an NC tion that a tool error exists only and not a setup or calibration error. Machine Tool", Soviet Engineering Research, Volume 1, No. 7, That is why, if no tool errors existed in the stock size analysis 1981, pp. 67-73. routine, the other logic as previously described was not executed. 13.Bjorke, O.Y., "Computer Aided Tolerancing", Tapiar, Fin- land, 1979. EXPERIMENTAL VALIDATION , The experimental validation of the concept has been success- fully shown for one sample part. The sample part discussed before, was cut with a known tool runout and then the part was processed through IDA which flag~ed this error. An exhaustive experimen- tation to cover all combmation of error sources is under progress and will be reported at a later time. It is proposed to dehberately introduce a known combination of error sources while machining .parts and then check if IDA can flag them as error sources. CONCLUSION An automated inspection data analyzer has been developed which is integrated in the existing Flexible Manufacturing Protocol .at the University of Maryland. The IDA has been developed by using both algorithmic and heuristic techniques. The algorithmic and heuristic rules are incorporated in the form of a PC based , computer program which has been successfully tested for a typical :p rismatic sample part. Page 1094 INTEGRATED COMPUTER AIDED MANUFACTURING FOR PROTOTYPE MACHINING By Daniel C. Hudson Research Assistant Da-Chen Pang Research Assistant James A Kirk Professor Davinder K. Anand Professor and M. Anjanappa Assistant Professor UNIVERSITY OF MARYlAND Systems Research Center and Mechanical Engineering Department College Park, MD 20742 Tel: (301) 454-8864 Page 1095 Abstract parts need to be made to offset these costs and still make a profit. This paper discusses the requirements for systematic computer aided production of prismatic and axi-symmetric When an item's production level dips below that parts using computer numerical controlled machine tools. where a Flexible Manufacturing Cell is still profitable, it is The research work addresses the problem of rapid made in an individual or "small batch" fashion on general prototyping in small lot size batch production environment. machinery in a machine shop. Although NC equipment is The assumed input to the environment (i.e. job shop] is a beginning to appear in these shops, the techniques used are required part and the output is the physical prototype. little different than those used in the 1950's and 60's. The total job shop needs for rapid prototyping is fully To bring the machine shop up to the current level of discussed in the paper and a technique for the group technology, a new strategy is proposed. It encourages a technology coding of parts is presented. The complete task migration of the automat10n techniques used in the Flexible is shown to be solvable in five parts and the input and Manufacturin$ Cell and the Transfer Line to that of small output requirements of design retrieval, part evaluation, batch product10n.[2] It is called the Rapid Prototyping part cost estimation, numerical code generation, and tooling Center (RPC). database organization is presented. An example part is presented which demonstrate the effectiveness and The goal of the Rapid Prototyping Center is to make feasibility of the system. use of programmable machines, robots and other modern devices, normally found on the shop floor of a large factory, Introduction as common in the average machine shop.[3] As stated earlier, one of the main, obstacles toward this ~oal is the The automated techniques which are employed to expensive changeover of both software (machme and robot make a part are directly related to the volume of programming) and hardware ( tools and fixtures) needed production.[1] (figure 1) If millions of a particular item are each time a new part is made. To lower these costs, it has to be produced, a transfer line or special system is created been proposed that the changeover process should also be to manufacture and assemble the pieces. These techniques automated. One example of Tota/Automation is the involve the formation of a set of machines and men devoted Flexible Manufacturing Protocol (FMP) currently under solely toward making that one item. The initial investment developed at the University ofMaryland.[4,5) on a transfer line or special system is high, but in the long Unfortunately, Tota/Automation is still in the run, these dedicated processes make both higher quality and developmental stage and found only in laboratories. less expensive products. An alternative to Total Automation is to incorporate If an item needs to be produced on a large scale, but currently available commercially supplied computer not on that of a transfer line, a Flexible Manufacturing packages into shop operations. Most of these are marketed System or Manufacturing Cell is commonly used. These under the moniker "CAM system" but a closer analysis techniques use the same type of automated equipment as reveals them to be much less. State-of-the-art commercially the transfer line (NC Machines and Robots) but do so on a available CAM systems, like Point Control's SmartCAM, much smaller scale and incorporate more flexibility. The provide the user with a powerful NC code generation major drawback to these methods is the high cost of the facility, but little else. In order to get help at the desk, a changeover needed to make each different part. This machinist would need to apply numerous different program expense is due to the level of knowledge needed to dedicated to the ap_propriate task whether it be evaluation, communicate with and reconfigure today's automated estimation or planmng.[6,7,8) equipment. To use a Flexible Manufacturing Cell, enough Page 1096 In short, to come up with a system approaching what West Germany, as best suited for integration into DPCAM. could be considered true Computer-Aided Manufacturing (figure 4) the user is required to employ a multitude of individual, incompatible, programs.[7,8] As a result, most machine The Opitz system uses a hybrid technique to create a shops lag behind the times because a complete computer- two part, nine-digit code describing both design and aided system for automated machining is not yet available manufacturing attributes.[9,10] The first five digits reflect and current alternatives do not meet expectations. the form or geometry of the part while the latter four digits give information such as stock shape and material. An With FMP and other like systems years away from unanticipated advantage within the structure of the Opitz completion and the lack of a comprehensive commercial S)'.s~e,m was f~mnd in the layout of each coding digit. J\s each CAM system, it would appear that the flexible Rapid d1g1t s value mcreases, a more complex configuration 1s Prototyping Center will have to wait. This would not be so if indicated; a characteristic with important ramifications available technology and advances already made in Total toward the development of the Part Evaluator.[11] Automation research were combined into an complete CAM system useful to the machinist now. Such is proposed The Opitz system is incorporated into DPCAM and implemented in this research under the name DPCAM. through the use of window graphical representations; each (figure 2) reflectin~ a single possible Opitz configuration. When the user begms to work with a new part, he is steered into the Objectives ofDPCAM Opitz module. The code is arrived at by choosing from among the various sets of drawings, ones that best reflect . The objective of the J?PCAM ~ystem is to provide an t~e char1;1cter of the p1;1rt.[12] Since DPCAM only uses the mtegrated set of computer aids to assist the machmist from first section of the Opitz code, the output of the module is a the design stage thru to the finished part. As a complete five digit number. system, it should help answer the basic questions seen during the machining of any part: To initiate Design Retrieval, a database of old parts needs to be created, which includes basic part information. - Have I done this before? In DPCAM, this Old-Part Database is automatically created - How difficult will the job be? and updated each time a new set of part data is entered for - How much will it cost? processing. It's entries include, part name, a short - D.o I have the necessary equipment to perform the descriptive note and the Opitz code. The Opitz code Job? provides the information on the part's configuration and - How will the NC Codes be created? manufacture needed to drive a search while the other entries include useful details on where more about the part To satisfy these requirements, the proposed system is might be found. To generate a list of parts that mi~ht divided into five major sections: provide useful information for the current application, a new item's Opitz code is compared to previous ones found - Design Retrieval in the Old-Part Database. Any matches are flagged as - Part Evaluation possible candidates for retrieval. This abbreviated list of old - Estimation parts is then made available to the user for further - Equipment Management investigation. - Code Generation Part Evaluation Each of these sections is linked together under a common graphics interface and are setup in such away to Before a machinist begins to remove metal from a facilitate an easy transfer of information from one element piece of stock, he has already formulated each step of the to an other. (figure 3) machining process in his mind. The creation of this process plan is one of the key elements in the production of a part. Elements ofDPCAM It is also one of the elements incomplete within the Flexible Manufacturing Protocol. If it is not yet possible to automate Design Retrieval the planning process, what aid can be given to the machinist now to more easily create better plans'? One way is through The major stumbling block in the path to a truly the calculation of a Machining Index. Such an index, automated manufacturing center is the need for flexibility. · ranging from O=easy to lO=hard, would reflect the Today, the cost of flexibility is a slow system; the result of complexity or "manufacturability" of a part.[13] re?rdering the cell for each different part that comes along. With this type of setup it is inevitable that similar items and In creating a process plan, a machinist is influenced procedures will be recreated; in affect "reinventing the by many factors: geometry, tolerances, materials, fixturing; wheel" again and again. This waste of time and material the list goes on. The demands required to meet these could be reduced if a mechanism was in place that would criteria dictate the route the machinist takes through the allc:iw a machi~ist access to previ~usly created plans and manufacturing process. In formulating a Machining Index, estimates applicable to a current JOb. Such a Design it is proposed to take a set of machining factors and codify Retrieval system is currently available in a new them into a global index. This index could then provide a manufacturing philosophy called Group Technology. yard stick to the machinist indicating the relative complexity of a particular undertaking. By applying this standardized ~n searching for a Group Technology coding system Machining Index, a shop would achieve more uniform for us~ m DPC;AM, two minimum requirements were process decisions and cost estimates. estabhshed. Fir~t, the system must incorporate both design and manufacturmg characteristics so it is useful as a An examination of part manufacture indicates that the primary elements of the machining index are: retrieval tool for the RPC. Also it must lend itself well to ~ntegration into an user-interactive,;1,ystem with a graphical - Geometric Shape mterface. A survey of current schemes pointed to the Opitz system, developed by H. Opitz of the University of Aachen, - Tolerances Page 1097 - Surface Finish provide enough detail for the creation of an accurate - Material estimate. The combined evaluations of these factors should Once the work element structure is complete, a reveal the complexity of a part from the manufacturing matrix of procedure times is developed to fill the slots point-of-view.[14,15] necessary for a complete estimate. Many different ways are currently used to generate estimate time values for To determine a part's Machining Ind_ex, a user w~mld individual shop activities. Among the most popular are the enter the proper value mto each of the previously descnbed use of standard handbooks and a machinist's "rule of Index sub-elements. The amount information needed is thumb".[17] reduced by gleaming ge?metry data from the _p~rt's Opit~ Code. The key to creatmg an accurate Machmm~ Index is Standard Estimating Handbooks, such as the linking the individual elements in such a way that it reflects American Machinist Cost Estimator Guide, provide tables their proper contribution to the whole.[15] Work by H.G. of standard times for a wide range of shop activities. To use Smart and D. Kochan indicates that part geometry and them all a machinist has to do is find a match for each tolerances are the driving factors for determining the !?art's activity, and plug the given value into the correspon~ing . manufacturability. i:iies_e facts asi~e, the only ':Vay to figure location of his work element structure. Problems wtth this in the proper weightmg is to compile an extensive study of method occur when the machinist attempts to find exact your or another comparably equipped shop's m~n~facturing matches to particular machining activities. The standards activities. This insures that the calculated Machmmg Index books can only cover so much material. As a result, they reflects a part's manufacturability for the shop of interest. make many broad assumptions in their time calculations. In Such a study would determine the relative importance of each of the sub-elements, based on the investigated facility's a setting like the RPC, wh_ere the new~st machinery !ind techniques are used, the times stated m the books will most equipment and operational expertise .. The initial w~ight!ng were obtained from a study of operations at the Umversity likely be a poor reflection of what actually occurs. of Maryland's Flexible Manufacturing Laboratory. The other option availabl~ is to assemble a set ~f. CostO:ime Estimation "rule of thumb" estimating data dITectly from the machm1sts in your RPC. This technique offers much improved In order to get the job, a manufacturer must produce accuracy over the "standard" method since information is the best estimate of the item's total cost. The accuracy of based on the equipment and actions typically used in the this estimate should be sufficient to insure that not too low shop of interest. The main drawback of "rule of thumb" or too high a price is given; either of which could cause information is that in order to assemble an accurate financial ruin. Thus it could be said that the success of a database a historical study must be conducted on the manufacturer rests on the accuracy of his estimates. operatio~s of the particular shop. Unfortunately, the added complexities of todays Since a "rule of thumb" technique offers the potential marketplace in combination with the rapid turnover of for greater accuracy then the use of standard time tables, technology on the shop floor, makes the calculation of this is the estimating techniques incorporated into DPCAM. accurate estimates difficult. One way to overcome these The required knowledge base is assembled through ~ historical study of shop estimates. The proper techmque for obstacles is to provide _the ~stima~or with new~r.techniques and equipment. Only m this way 1s greater efficiency and this study would involve the organization of jobs into varying awareness possible.[16] steps of difficulty. Using the RPC's work element structure as a base, the times for each level of difficulty can then be In considering the estimator for DPCAM, the entered into the individual RPC estimate categories. The accuracy of the knowledge base can be improved by decision is made to create a Computer-Aided Cost increasing the number of step divisions and the amount of Estimator. It will not be a computer Ero~ra~ that creat~s data used in the averaging process. To allow for operations an estimate by itself, but more of an 'advisor to W<;lrk with as soon as possible, an initial database is assembled through the machinist. By providing suggested values for different a short investigation of machining activities at the University areas the DPCAM output aims to provide a more of Maryland's RPC. consi~tent set of estimates then possible with manual techniques. The final element needed within the estimator is a methodology to choose among the tables of assembled The first step in developing anl es~imate is the creation of a ''work element structure . (figure 5) A work expert data for the appropriate time value. An ideal element structure serves as a framework for "hanging" on estimate "driver" would be one which describes the overall the individual values and times that make up the total difficulty of a particular part's manufacture. Such _a :'alue estimate. Subdividing the estimate into a structure has exists in the form of the DPCAM-produced Machmmg advantages, such as allowing for individual area cost reeorts Index. The Machining Index could be input into the. and the tracking of estimate accuracy as actual productmn Estimator to direct th~ program towar:d _the appropnat~ time data. Incorporatmn of the Machmmg Index value mto proceeds.[17] a searching structure gives the system the measure of a For the DPCAM Estimator, the structure needs to part's "manufacturability" needed to complete the estimate. be general so that it can accurately report the wide range of items fabricated in a RPC environment. As such, the Equipment Manager manufacturing process is divided into three major areas: When a machinist receives a job, he need to know 1. Preparation the available tools in order to make a process plan ~.nd write 2. Testing NC codes. After collecting tools, he mounts them on a tool 3. Production magazine of a NC machine and can then fabricate a part. Preparation and utilization of the tools are daily activities in In turn, each of these must be subdivided further to a machine shop. A equipment manager helps to handle the use of tools and improves the efficiency of a manufacturing Page 1098 system. The purposes for the equipment manager are: supplied by a designer's blueprint and the ma~hinist's knowledge on items such as feed rates and spmdle speeds - Building a tool library and tool magazine files to will be the only required input. The module can be broken assist the preparation and selection of the tools, into three sections: - Incorporation with the NC code generation module to use the tools in the tool magazine, - Creation of a new Part File - Providing information for tool management, such - Editing of an old Part File as the minimizing of the tool redundancy, or other - Processing a Part File to M+G code. application. Ideally the code generated by the module should The equipment manage~ collects all.the cutJing tools model typical machining operation. (figure 6) in the machine shop and stores m the tool library f!le. The tools which are mounted on the NC machine are recorded The goal of the Code Generator is to take blueprint in the tool magazine file. A new tool magazine file is part geometry and machinist process plan data as inpu~. generated by selecting tools fr~m library file and assig~in& Output of the module should be M+G codes that provide each tool an index number, which refers the tool locat10n m ideal machining operations toward the desired shape. 1:he the NC machines. The tool magazine file will be first step toward this is the creation of an intermediate file. automatically loaded into the NC code generator module to assist tool selection. An intermediate file is used as a provision to create M+G codes for different machining centers. Most CNC For each tool, the information includes the machines use M +G code, but incorporate slight deviations following: unique to their machine.[18] By creating an intermediate Part File containing all necessary machining parameters, - Tool number/index, slight formatting changes in an M +G processor will allow -Tool type, the module to make codes for different machines. - Tool diameter/width, - Tool length/cutting length, The intermediate Part File contains all the necessary - Others. information needed to machine a particular piece. (figure 7) It is entered in such a way that process plan and machine The tool number/index is a three digit number which parameter data are combined with the appropriate can help to or~anize the tool library or set up tool magazine. geometric information. This is achieved by having the user The tool type 1s classified by the usage and shape of the enter the information in ordered sets of operations or tools, such as the end mill, face mill, T slot cutter, etc. The feature types. Each of these sets is further divided into tool diameter/width describes the dimension of cutting edge. subsets of contours based on cutting order and cutting For drills and milling tools the tool diameter represents the operation. The computer prompts the user to work his way cutting capability, but for groover and cutoff tools the tool through the hierarchy to the appropriate level and then width does. The tool length describes the shape of the tools requests all needed information to machine the feature. and the cutting length represents the ability of the cutter. The saved Part File preserves this ordering so that proper The other information can be used to input the number of editing and processing can then take place. thread, manufacturer, material of cutter, cutting angle or any other data. The editing functions created for the Code Generating module take advantage of the Part File's The equipment manager also includes an editor used hierarchical structure. The user can add, delete or modify to add, delete, or change the tool information. It allows the the Part File at any level. This makes functions ranging printing of the tool data or the viewing of the information on from the addition or deletion of an entire contour set or the screen. feature to the modification of a single contour parameter, a simple operation. Code Generation M +G codes are generated by running a completed The common perception of the manufacturing Part File through the Code Generator's M +G processor. process is the physical creation of a part; the working of The processor functions as a translator, assembling the metal. Thus it comes as no surprise that most of the information supplied by the Part File into the M +G format available aids to the machinist are in the area of metal the turning center being used expects. The processor cutting and forming. The amount of research and the included in DPCAM creates code formatted to satisfy a volume of products available in this area, such as Computer Fanuc OT and a Yasnac 3000G class controllers, the type Numerically Controlled (CNC) machine tools and currently available. (figure 8) [19,20,21] The processor also programing aides for these tools, far outstrip advances includes the functions needed to download prepared M +G made on other "less glamorous" topics. codes to the machining center Control Units. In order for the RPC to achieve the desired level of DPCAM Operation flexibility and automation, CNC machines must be incorporated into the machine shop. To provide the user In its completed form, DPCAM is broken into two with assistance in this migration, DPCAM incorporates a sections; initialization and application. (figure 9) At the NC Machine Code Generation module. To keep up with initialization level, the user must input the basic information current technology, the module should provide a machinist needed by the software; a part name and an Opitz code. A an easy access to the power and flexibility of today's CNC short note can also be attached containing additional machines. This is done by removing the need for fluency in information. Once the program has received these basic the cryptic M+G language they communicate in. characteristics, it goes about its first task, Design Retrieval. The results of the search are displayed to the user as the The Code Generation Modules for axi-symmetric program moves into the applications level. and prismatic parts developed forDPCAM should allow a machinist to program a CNC machines easily. Information Page 1099 The applications level greets the user with a menu of provide the user with a tool closer to the true definition of the functions available in DPCAM. After the user makes CAM then commercially available systems. This was his choice, the appropriate module is started, which upon achieved by applying state-of-the-art techniques developed completion, returns him again to the menu. The user has for the total automation problem to the integrated system. the option to use as many applications as he desires, work A number of sample parts have been produced and on another part or quit the DPCAM system. depending on the part manufactured, a time savings of up to 50% has occurred. Future Work References DPCAM is currently implemented at the University of Maryland's Flexible Manufacturing Laboratory. This is a 1. Tien-Chien Chang, An Introduction to Automated "test" version, however, and there is room for improvement. Process Planning Systems, Prentice Hall, Inc., Englewood Cliffs, New Jersey, 1985. Improved Knowledge Base 2. B. Malakooti, "A Methodology for the Automation of The Evaluator and the Estimator both rely on a Medium or Small Manufacturing Companies," Computers knowledge base as the basis for their suggestions to the user. in lndustty, Vol. 7, No. 4 ,pp 333-341, Aug 1986. Thus, these modules can only be as accurate as the information that forms their evaluating foundations. The 3. J.A. Kirk, "The Use of IGES in Rapid and Automated knowledge currently incorporated into DPCAM was Design Prototyping," Advances in Design Automation-1988, compiled in short one-on-one discussions with machinists at ASME, New York, New York, pp 27-32, 1988. the Flexible Manufacturing Laboratory's machine shop. While this data is sufficient for a test version, it is not 4. Sujen Chen, Structure of a Flexible Manufacturing accurate enough for everyday operations. Protocol for Design and Control of a Vertical Machining Center, Master Thesis, University of Maryland, College Improving the knowledge bases requires a historical Park, Maryland, 1988. study of manufacturing operations in the shop of interest. First the manufacturability characteristics of the shop 5. Rajiv Uppal, Flexible Manufacturing Protocol Driver for should be determined; based on the available equipment a Vertical CNC Machining Center, Master's Thesis, and the employed machinist's level of experience. This University of Maryland, College Park, Maryland, 1987. manufacturability breakdown can then be subdivided into the desired number of steps and, in combination with the 6. John Herzog, ''Take Full Advantage of Computer-Aided RPC's work element structure, used as the basis for an Cost Estimating," Modem Machine Shop, Vol. 61, No. 4, pp estimate time study. Once such a study is completed, the 92-98, September 1988. new data can be inserted into the Evaluator and the Estimator. 7. Edward G. Hoffman, "Microcomputer CAD/CAM for All Shops, Part I," Modem Machine Shop, Vol. 60, No. 5, More Complete Automation pp 82-90, October 1987. Once an accurate set of knowledge bases are in place 8. Edward G. Hoffman, "Microcomputer CAD/CAM for and confidence is built up in the automatic systems included All Shops, Part II," Modern Machine Shop, Vol. 60, No. 6, in DPCAM, the human supervisory role in some modules pp 102-107, November 1987. could be phased out. This especially comes into play in the Evaluator and Estimator modules where final values could 9. H. Opitz, A Classification System to Describe be arrived at with much less intervention. Workgeces, Part 1, Pergamon Press Ltd., Headington Hill Hall, xford, 1970. Revised Code Generation/Equipment Management 10. H. Opitz, A Classification System to Describe An "easier to use" Code Generation module could be Workgieces, Part 2, Pergamon Press Ltd., Headington Hill developed that would provide a more automatic generation Hall, xford, 1970. process. This would result by removing some of the burden m the areas of process, s~eed and feed selection through the 11. C.C. Gallagher, Group Technology Production Method incorporation of a set of 'machining rules". With a these in Manufacture, Ellis Horwood Limited, Chichester, West modifications made to the system, the user would simply Sussex, 1986. need to enter blueprint information in the desired cutting order to create the necessary M +G codes. 12. Richard E. Billo, "Enhanced Grouri Technology Modeling with Database Abstractions,' Journal of A more powerful Equipment Manager, with Manufacturing Systems, Vol. 7, No. 2, pp 95-106, 1988. provisions for tool-life predictions could be integrated with the Code Generator. This would allow for automatic tool 13. Mike Courtright, Manufacturability Analysis Software selection as well as warnings when a tool is about to fail or for a Flexible Manufacturing Cell, Master's Thesis, needs to be sharpened. University of Maryland, College Park, Maryland, 1988. Conclusions 14. D. Kochan, CAM: Developments in Computer Integrated Manufacturing, Sprmger-Verlag, New York, This research has shown that a considerable gap New York, 1985. exists between the goal of Rapid Automated Prototyping and the currently available commercial CAM systems. The 15. H.G. Smart, "Least Cost Estimating with Group purpose of this work was to provide an integrated CAM Technology," Journal of Manufacturing Systems, Vol. 1, No. system while working toward total automation for small- 1, pp 99-110, 1983. scale manufacturing. This concepfbas matured into a software package called DPCAM. The system strived to 16. Phillip F. Ostwald, Cost Estimating, 2nd. Edition, Page 1100 Prentice Hall, Inc., Englewood Cliffs, New Jersey, 1984. 17. Rodney D. Stewart, Cost Estimators's Reference Manual, John Wiley & Sons, New York, New York, 1987. 18. Michael Sava, Computer Numerical Control, Reston Publishing Company, Inc., Reston, Virginia, 1983. ,----------~-- 1 I 19. Fanuc OT-Model A Operator's Manual, Fanuc Ltd., 1985. Port Blueprint 20. Yasnac 3000G Operator's Manual, Yaskawa Electric DPCAM Mfg. Co., Ltd., 1980. Method: I 21. Slant Jr. Turning Center Instruction Operation Manual, Ercor rote 1rJexible I , Nakamura-Tome Precision Industry Co., Ltd., Tsurugi tool, fir ,II 11,nufoctu-ing I Rapid rmhire shop I Protocol , Ishikawa, Japan, 1986. (llef'Otionsin I IJncori,letel : Prototyp Ing !rll!Ctnplele 1 [enter poci3 2 .;;' .; ·c - =n "' .~.. C .0, :, 5 u Special E ~ c :c 0. u 4 C .; ·5, C Mein Elore end Moch1n1ng Other Holes 7 0 ·c A/6>3 Rotctlonol of Plane Teeth and 0 ! Mcchllnlng Surfaces Forming 6 .0. . A/6<3 C 0 AiC<4 z 9 Special Figure 4: Opitz System [9] Exa,1 ..... Blueprint Machinist's Adjust Bl<'ll'iots lofornotion Koo,lec\)e Inputs Creatlooof a Fixbre 111d 11-ocessP!so Ji Selectfon loltlal lloclll,.arli llachin (set-aspect-value-dkc) Forms package making the syntax appear informal. It Enter the form-name > screw gives functions useful names, eliminates unnatural Lisp Enter the slot > material requirements, and eliminates the need to memorize Enter the aspect > = function syntax. Enter the value > steel An example of a useful function name is make-new- design-class, rather than form, or make-form, or Typical DKC functions, functionally same as the store-form. Typically a Forms function name has a -dkc original Forms functions, are listed in Appendix 1. For tacked on the end when modified for DKC. For more information on the syntax, see Reference 15. example, the Forms function call for a screw: > (set-aspect-value #!screw 'material''= steel') DKC browser becomes the following DKC function call: The DKC browser, a graphic interface for DKC, is a window-based tool for creating, viewing, and modify- > (set-aspect-value-dkc screw material= steel). ing hierarchical knowledge bases which are represented as Forms frame trees. The layout of the browser If a command name is entered with no arguments ( or consists of a four-part window viz, a graphic window, a an incomplete argument list), the DKC package will text window, a menu panel, and a command line as prompt for the rest of the information. For example, shown in Figure 2. 4----- ---e, i i Components NAME: MlO x 1 socket head \17 screw w \17 t Isa: socket hEad scrEw r~uts I WashErs I ScrEws I TYPE· MlO X 1 metric I w w w w DIAMETER: 10 mm Slotted Phillips Hex. Socket Screws Head Head Head PITCH 1 mm Screws Screws Screws LENGTH: 20 mm I 7 COST: 0. 18 MlOxl 20mm Soc.Hd.Sc, MATERIAL stainless steel i i i t C Left ) C Up ) C Right ) C Menu ) C Exit ) (Search) C Down ) C Edit ) ( Config) ( Display) i i DKC> Figure 2. DKC browser 38 Knowledge-Based Systems Page 1114 The 'graphic window' shows a section of the know- vibration isolation 16- 20 . In all cases, suspending a load ledge base as a tree graph with forms as nodes, drawn magnetically eliminates friction; the bearing type deter- as boxes with form names as labels, with the links mines if operating power is required. There are three drawn as vertical and horizontal solid lines. Any one of types of magnetic bearings, based on the type of the forms on the display may be selected, causing its magnets used viz, permanent magnet (PM), electro- representative box to become shaded. The 'text win- magnet (EM), and combination of electromagnet and dow' then will display the slot and aspect information permanent magnet (EM/PM). Magnetic bearings, associated with the selected form. The 'menu panel' along with its subclasses and the three particular will contain features such as panning buttons, search, systems under development at UMCP, will be dis- edit, system menu, configure, display, new root, and cussed in the following sections to demonstrate DKC. new tree. In the following paragraphs these items will be discussed in detail. Panning buttons (right, left, up, down) can be used Energy storage application to traverse the hierarchy displayed in the graphic The magnetic bearing at UMCP used for flywheel window. (Search) adjusts the displayed hierarchy to energy storage is a so-called pancake bearing which is a show a specified form. (Edit) initiates data input and radially active ( active EMs) and axially passive (passive or modification. (System menu) displays a popup PMs) magnetic bearing. Since there is no mechanical window with system level commands. (Configure) will friction involved between the rotor and stator, high be the user's link to a profile facility, and allows display rotational speeds can be achieved, thereby increasing parameters to be set. (Display) can be used to display the energy storage capacity. The biaxial position pre-configured system and/or user information. (New sensors are used as feedback elements for proper root) serves a dual purpose: it allows an easy means for control of EM currents providing active radial position- isolating part of a tree and it provides a way to cluster ing control. many unrelated designs. Such a selectable root feature The main configuration, shown in Figure 3, consists thus allows one data structure to contain all the of a magnet plate assembly and two outer control knowledge, without forcing any semantic relationships plates. Sandwiched between the magnet plates are four between designs. (New tree) loads in a new design symmetrically placed PMs. Further, the magnet plate hierarchy. assembly is sandwiched between the two control plates with four control coils surrounding four ferromagnetic Implementation considerations control-pins which act as structural elements. To hold the assembly together, a bolt is placed as a centre post, The DKC system must permit multi-user access be- and fastened with a nut. The rotor is a flywheel pressed cause product designs typically have multi-person on to a return ring which closes the magnetic flux path. design teams. Hence the data storage must be struc- tured to prevent data corruption as a result of simultan- eous modifications. In addition, due to the potential for Machine spindle control application the very large size of these KBs, it may be divided The magnetic bearing spindle is a high technology among several storage devices (disks) which are net- spindle used primarily by aerospace industries for very worked together. One solution is to have an access high speed machining. The magnetic bearing spindle at program coordinate communication between active UMCP has one thrust bearing and two radial EM type users through which individual browsers access the bearings. The thrust bearing provides axial support to knowledge. In situations where not all users must have the spindle, and the radial magnetic bearings provide the same level of clearances, a hierarchical access the radial support. Position sensors provide three structure must be provided. dimensional position data of the rotor which is then For portability, the DKC package can be imple- used to keep the rotor in its central position by mented in any CommonLisp environment. The graphic appropriately changing the current flowing through the interface however, is not portable because window control coils. Figure 4 shows the major components of systems often are hardware dependent. For example, the magnetic bearing spindle. the DKC system reported in this paper is being done on a Texas Instrument Explorer making it difficult to implement on other systems due to the graphics Vibration isolation application incompatibility, which is a limitation at present. The UMCP vibration isolation bearing supports a large, cantilevered, rotating load. It is an EM/PM, radially-active, axially-passive type. The main bearing IMPLEMENTATION OF A DKC FOR configuration consists of 16 Rare Earth Cobalt MAGNETIC BEARINGS (RECO) PMs fit into a central ring which is sandwiched Systems with magnetic bearings between two flux rings. An aluminium housing sandwi-ches eight EM coils (four at each end) and all other Magnetic bearings are becqming increasingly valuable pieces. Figure 5 shows the major components of the as the identification and development of appropriate UMCP vibration isolation magnetic bearing system. applications continue. The Advanced Design and Manufacturing Laboratory at the University of Mary- Magnetic bearing hierarchy land at College Park (UMCP), USA, is performing extensive research into magnetic bearings as applied to The energy storage and vibration isolation bearings are inertial energy storage, machine spindle control and instances of the design class of EM/PM magnetic Vol 4 No 1 March 1991 39 Page 1115 Rotor I ~ Stator -~--0 t I Bolt Control plate Control pin Control coi 1 magnet plate Fl~whEEl Permanent magnet Return ring Nut Figure 3. Magnetic-bearing energy storage system bearings, while the spindle control bearing is an energy storage (ES), spindle control (SC), and vibra- instance of the design class of EM magnetic bearings. tion isolation (VI). To these subclasses the specific EM, PM and EM/PM magnetic bearings are all, in bearings will be attached. (See Figure 6). turn, a subclass of magnetic bearings, which is a Because the example bearings being discussed are subclass of the general class of bearings. With the instances of a design class, they have no descendants. above logic it is clear that the root of the hierarchy is This is not a limitation of the DKC structure, but just a 'bearing'. Possible descendants of the root class of reflection of the design semantics chosen for this 'bearing' are for example 'ball bearing' and 'roller project. This leads to the question of how to represent bearing' in addition to 'magnetic bearing' ( as well as a the components within the hierarchy. Several authors plethora of others). Similarly, each of these may have suggest an :IS-Part link analogous to the :ISA link, but subclasses. For the magnetic gearing subclass, there is indicative of a component-type relationship 11, 21 , 22 . 'PM magnetic bearing' and 'EM magnetic bearing' in This method, however, leads to redundancy within the addition to 'EM/PM magnetic bearing'. With this DKC tree. For example, if one hundred different information the hierarchy can be formed. bearings used the same control-pin design, then an Although the instances of magnetic bearings can be :IS-Part link would mean having one-hundred identical attached to the appropriate subclasses (i.e. EM, PM, forms, representing the control-pin, spread throughout EM/PM) it is useful to subdivide the design classes the tree: a massive waste of space. It would be better to first: this time by application, not functionality. That is, have one control-pin form which any other form could each type of magnetic bearing will be divided into use; this is the preferred method. This capability is 40 Knowledge-Based Systems Page 1116 l Rear touchdown ball bearing Thrust bearing position sensor Thrust magnetic bearing Rear radial position sensor Rear radial magnetic bearing Front radial magnetic bearing / Front radial bearing sensor Front touchdown ball bearing Figure 4. Magnetic-bearing spindle control system implemented by creating a form representing the e Auxiliary is part of the hierarchy. control-pin. Then a bearing form would make use of • Inheritance is no problem if the properties of design the pin (in fact, all of the bearing's components) by a are independent of our decomposition of bearing slot whose value would be a procedure which refer- knowledge. ences the control-pin form. This way there is only one • There is one definite place to put auxiliary forms, control-pin form; but it may be called by any number of rather than a place for each subclass. designs. This particular mechanism highlights another • Only two new forms are needed (design, auxiliary), very important concept: 'forms may reference other rather than the many needed to properly locate forms through inheritance and through explicit pro- singular components. cedure calls'. • No effort is wasted and no extra effort is needed if a If one creates forms for each of the components (i.e. more complete hierarchy becomes necessary. coil, housing, plate, etc.), the next task is to determine where each should be located within the hierarchy. So configured, the auxiliary parts may include There are several alternatives. One method is to create standard items such as the bolt, nut and epoxy. If this one big hierarchy with 'design' as the root and have all subclass is called 'components', then the complete tree the forms fit logically within this hierarchy. This for the UMCP Magnetic Bearing can be created. provides unlimited flexibility, but at the cost of extra Figure 7 shows the overall hierarchy. effort to create. Alternatively, another subclass of 'bearing' called 'auxiliary' can be created which is not Magnetic-bearing frames really a bearing subclass, but just a convenient location to store auxiliary forms for bearings. This method, Having created a design hierarchy for the example however, makes it difficult to expand the tree beyond bearings, the knowledge implicit in the semantic bearings. A third alternatLve is a compromise of the relationships between design objects has been cap- first two, and consists of creating a general 'design'form tured. This definitive knowledge may be stored in the to be the root. This form would have the 'bearing' frames within appropriate slots: drawings, parts lists, subclass, as well as any others that might be created. sub-part specifications, etc. For each sample bearing Additionally, it would have the 'auxiliary' subclass in there would be a 'drawing' slot with an IF:NEEDED which to place the components. This decomposition aspect whose procedure references the assembly draw- strategy has several advantages: ing; a set of 'part' slots each with a :NAME aspect, a Vol 4 No 1 March 1991 41 Page 1117 1. Central ring 2. Flux ring 3. Pole piece 4. Aluminum housing 5. Draw rod 6. EM Coil 7. Socket head screw 8. Wave washer 9. Touchdown ball bearing 10. Position sensor 11. RECO PM's 12. Rotor spindle sleeve Figure 5. Magnetic bearing vibration isolation system Magnetic Bearing is a Bearing PM Mag.Erg. EM/PM Mag. Erg. IS a IS a is a Magnetic Bearing Magnetic Bearing Magnetic Bearing E .. S. Mag. Erg. V.I. Mag. Erg. E.S. Mag. Erg. S.C. Mag. Erg. V.I. Mag. Erg. is a is a IS a IS a IS a EM Mag.Erg. EM Mag.Erg. PM Mag.Erg. PM Mag.Erg. PM Mag. Erg. UMCP_Mag. Erg. UMCP_Mag. Erg. MCPMag.Erg IS a IS a is a S.C. Mag. Erg. S.S. Mag. Erg. V.I. Mag. Erg. Figure 6. Magnetic-bearing hierarchy :QUANTITY aspect, and :IF-NEEDED aspect whose Note that this, however, does not capture the know- procedure referenced tlte appropriate form; and a ledge intrinsic to the design objects themselves. In 'parts-list' slot with an :IF-NEEDED aspect whose addition, there is some redundancy between the procedure returned a list of all the parts belonging to :NAME and :IF-NEEDED aspects which is necessary that form. because inheritance requires a specific slot name, not a Figure 8 shows the 'UMCP magnetic bearing ISA pattern for a slot name (i.e. part X). energy storage magnetic bearing' as discussed above. Frames for each of the parts of the above bearing can 42 Knowledge-Based Systems Page 1118 Design is a root All;'liary IS a Design Washer Nut Magnet plate Control pin Control coil Ball bearing Rolle: bearing is a is a is a is a is a is a IS a Component Component Auxiliary Auxiliary Auxiliary Bearing Bearing EM Mag.Erg. M/PM Mag.Erg. is a IS a IS a Screw. Mag.Erg. Mag. Brg. Figure 7. Overall hierarchy UMCP Pancake Magnetic Bearing ISA EM/PM Mag. Brg. for Energy Storage .... Drawing :IF-NEEDED (get-drawing) Partl :NAME magnet-plate-assembly (include PM's) :IF-NEEDED (get magnet-plate-assembly) :QUANTITY 1 Part2 :NAME control-coil :IF-NEEDED (get control-coil) :QUANTITY 8 part3 :NAME control-pin :IF-NEEDED (get control-pin) :QUANTITY 8 Part4 :NAME control-plate :IF-NEEDED (get control-plate) :QUANTITY 2 Part5 :NAME bolt :IF-NEEDED (get bolt) :QUANTITY 1 Part6 :NAME nut :IF-NEEDED (get nut) :QUANTITY 1 Part7 :NAME flywheel :IF-NEEDED (get flywheel) :QUANTITY 1 Part8 :NAME return ring :IF-NEEDED (get return ring) :QUANTITY 1 Parts-list :IF-NEEDED (get parts-list) Figure 8. Energy-storage system frame containing definitive knowledge Vol 4 No 1 March 1991 43 Page 1119 be created similarly, but with slight differences. Con- hierarchy. All of this is definitive knowledge describing sider the 'Control pin' frame (see Figure 7). The pin is the design objects. Attention must be paid to the an individual part: not a design class nor an assembly. knowledge which explains. Therefore it will have unique characteristics, such as One of the difficulties in capturing explanatory material and manufacturing specifications. Naturally knowledge is the determination of what level of detail the pin will have a mechanical drawing, but this is to capture. Because this can be decided only at design common to all designs, so the control-pin frame can time, a DKC system must be flexible enough to accept inherit the appropriate procedure. a wide spectrum of detail. In other words, the system It is useful to note that the 'Energy storage magnetic should allow the designer to determine what knowledge bearing' and the 'UMCP magnetic bearing' frames to capture. The type of knowledge could vary from represent the class and instance categories of frames, simple statements to extensive modelling simulation respectively; see Figures 6 and 7. On the other hand, results to anything else the designer believed was the 'Control pin' and 'UMCP magnetic bearing' frames appropriate. A frame-based knowledge system pro- represent the piece-part and assembly categories of vides the capability to capture all these types of frames, respectively. Because these sets of characterist- knowledge via the slot-aspect-value structure. Even- ics are orthogonal, a matrix can be created to demons- tually, for example, slots could contain procedure calls trate the four possible characterizations of a given to simulation programs which were the basis for certain frame. design decisions. Implemented this way, the DKC To this point, design knowledge regarding the system starts to become an interactive design tool, not configuration of design objects (hierarchy and compon- just a knowledge base. The first step however, is to ent specificiations), and the geometric definitions of the implement a mechanism for capturing statements which design objects ( detail and assembly drawings) have explain design decisions. been captured. However, the characteristics of the Consider again the 'Control pin ISA auxiliary' frame. classes within the hierarchy must also be considered. As previously indicated, its frame would have a For example, all bearings have certain characteristics, 'material' slot; for this case the value of the slot would such as frictional coefficient, load-carrying capability, be 'nickel iron alloy'. However, at present there is no etc. These slots should be included in the 'bearing' way to provide an explanation of this choice within the frame, and provide appropriate default values. But any frame. Creating a new aspect called: DOC for the bearing, or class of bearings with a known value should material slot, as shown in Figure 9, solves this problem. · specify it. For example, magnetic bearings have zero Then by assigning this aspect a value of 'to permit high friction, so the 'magnetic bearing' frame will declare flux levels on the order of 1.5 Teslas without satura- the friction coefficient slot to have a value of zero. The tion', this elusive chunk of knowledge is captured and effect is that a UMCP magnetic bearing ( or any other stored systematically. magnetic bearing) will inherit this value. The :DOC aspect can be used with any slot, so every The load-carrying characteristics of the magnetic characteristic of a design object may have documenta- bearings demonstrates a common design dilemma. For tion logically associated with it. Choosing the previ- EM/PM magnetic bearings (for which the PM's support ously used example, 'UMCP magnetic bearing' frame, the load), the load-carrying characteristics can be it is evident that the documentation for part 3 explains determined functionally by analysing the bearing de- the need/use of the control-pin, and explains why there sign. However, these characteristics might actually be are eight. Similar documentation would be appropriate parameters which drive the design. Therefore a know- for other slots. Additionally, a documentation slot ledge capture decision must be made: is the load-carry- could be created to contain general information about ing capability an input or an output. In this case, as in the entire object. Figure 10 shows the example frame many design situations, there is a specification range implemented following the above discussions. ( often a minimum or a maximum), any value in which is Figures 11 and 12 show, respectively, the 'UMCP satisfactory. This lends itself to two slots: a load-carry- magnetic bearing ISA spindle control magnetic bear- ing specification, and a load-carrying actual value. ing' and 'UMCP magnetic bearing ISA vibration Continuing in this manner one would incorporate a isolation magnetic bearing' frames showing both defin- wealth of knowledge about bearings at all levels of itive and explanatory information. Auxiliary Material = nickel-iron-alloy :DOC to permit high flux levels on the order of 1.5 Teslas wihout saturation Figure 9. Control-pin frame containing both definitive and explanatory knowledge 44 Knowledge-Based Systems Page 1120 UMCP Pancake Magnetic Bearing ISA EM/PM Mag. Brg. for Energy Storage Documentation :GOAL support an energy storage flywheel Partl :NAME magnet-plate-assembly (include PM's) :QUANTITY 1 :DOC the permanent magnet sub-assembly Part2 :NAME control-coil :QUANTITY 8 :DOC to generate controlling magnetic field part3 :NAME control-pin :QUANTITY 8 :DOC conductive center structure for control pins Part4 :NAME control-plate :QUANTITY 2 :DOC top and bottom plates ( contain the electro-magnets) Part5 :NAME bolt :QUANTITY 1 :DOC stack fastener Part6 :NAME nut :QUANTITY 1 :DOC stack fastner Part7 :NAME flywheel :QUANTITY 1 :DOC energy storage spinning rotor Part8 :NAME return ring :QUANTITY 1 :DOC to provide return path to magnetic flux Figure 10. Energy-storage system frame containing both definitive and explanatory knowledge Magnetic bearing KB illustrate the methodology of implementation, a few Having developed an understanding of magnetic bear- representative parts from each of the UMCP magnetic ings, the frames which represent them, and the bearings are discussed here. hierarchy in which they fit, the KB was populated. In Consider the 'Control pin' frame. With piece-parts, certain cases, there was similarity between parts of such as the control pin, it is possible to create a slot for different bearings, and when appropriate, DKC me- each feature allowing inheritance and appropriate chanisms were used to take advantage of it. To documentation for each feature. Such documentation Vol 4 No 1 March 1991 45 Page 1121 UMCP Spindle Control Magnetic Bearing ISA EM Mag. Brg. for Spindle Control Documentation :GOAL Control of a high accuracy machining spindle Partl :NAME spindle rotor :QUANTITY 1 :DOC the spindle itself Part2 :NAME rear touchdown ball bearing :QUANTITY 1 :DOC backup bearing part3 :NAME thrust bearing position sensor :QUANTITY 1 :DOC senses vertical motion of spindle rotor Part4 :NAME thrust magnetic bearing :QUANTITY 2 :DOC determines weight and vertical air gap Part5 :NAME rear radial bearing position sensor :QUANTITY 2 :DOC senses radial motion of spindle rotor Part6 :NAME rear radial magnetic bearing :QUANTITY 1 :DOC determines radial forces and air gap Part7 :NAME front touchdown ball bearing :QUANIJTY 1 :DOC backup bearing part8 :NAME front radial bearing position sensor :QUANTITY 1 :DOC senses radial motion of spindle rotor Part9 :NAME front radial magnetic bearing :QUANTITY 1 :DOC determines radial forces and air gap PartlO :NAME spindle housing :QUANTITY 1 :DOC houses all coils and non-rotating parts Figure 11. Spindle-control system frame containing both definitive and explanatory knowledge 46 Knowledge-Based Systems Page 1122 Documentation :GOAL Isolate vibrations of a rotating load Partl :NAME central ring :QUANTITY 1 :DOC housing for permanent magnets Part2 :NAME flux ring :QUANTITY 2 :DOC housing for pole pieces part3 :NAME pole piece :QUANTITY 8 :DOC mount for EM coils Part4 :NAME aluminum housing :QUANTITY 2 :DOC assembly containment piece Part5 :NAME draw rod :QUANTITY 8 :DOC assembly alignment component Part6 :NAME EM coil :QUANTITY 8 :DOC the active bearing Part7 :NAME socket head cap screw :QUANTITY 8 :DOC main housing fastener part8 :NAME wave washer :QUANTITY 8 :DOC assembly component Part9 :NAME touchdown ball bearing :QUANTITY 2 :DOC backup bearing system PartlO :NAME position transducer sensor :QUANTITY 2 :DOC position sensor partll :NAME RECO permanent magnet :QUANTITY 16 :DOC passive magnetic bearing system Part12 :NAME rotor spindle sleeve :QUANTITY 1 :DOC spindle housing Figure 12. Vibration-isolation system frame containing both definitive and explanatory knowledge Vol 4 No 1 March 1991 47 Page 1123 might seem to do no more than verbalize information calculate the resultant constraint. The number of turns contained by the drawings. For example, a feature is constrained by flux requirements and space limita- labelled 'main-diameter' belonging to the control-pin . tions, but is not determined uniquely. Therefore, when might have a value of 20.32 mm with a tolerance of +0 a value is specified an :IF-ADDED procedure checks and -0.025 mm, with an explanation 'to mate with the for consistency and returns appropriate information. control-coil' (see Figure 13). But this does more than The coil, thus, has demonstrated a significant differ- reiterate drawing data: it shows causality. That is, upon ence regarding design constraints. perusing the drawings it might be unclear whether the Now consider the 'Touch down ball bearings' frame coil size determined the pin size or vice versa. This which is part-9 in the 'UMCP magnetic bearing' frame. documentation relieves the ambiguity, and redirects Like most magnetic bearings, the UMCP vibration attention to the appropriate form. Certainly this places isolation magnetic bearing can maintain suspension as importance on the language used in comments, but in long as displacements are small ( due to non-linearities). many cases the difficulty using appropriate wording is Therefore ball-bearings are incorporated into the de- drastically less than that of determining the motivation sign to act as backup system. Before the rotor displaces behind an unexplained design feature. too far, it will engage the touch down ball bearings and As a second example, consider the magnet plate allow the magnetic circuitry to re-effect suspension. which is a part of 'magnet-plate-assembly' frame which The design consists of determining the radius and the is in turn part-1 in the 'UMCP magnetic bearing ISA bearing design itself, which is associated with the energy storage magnetic bearing' frame. The principal ball-bearing sub-class of the general bearing hierarchy. features are diameter, thickness, pole face angle, pole Determining the radius requires calculating the range face thickness, and material saturation level 16 • These of static controllability, which in turn requires knowing five features are independent, and different combina- the maximum bearing force and the static stiffness. tions will yield different bearing characteristics. The Then, as a rule-of-thumb, the backup bearing is given a selection of these values is based upon experience, radius 90% of the range of static controllability. intuition, and iterative testing. However, certain heur- Because this method determines exactly the backup istic knowledge exists: bearing radius, it is implemented with an :IF- NEEDED. However, the procedure assumes it will be • pole face thickness < = 1/16 * diameter able to find ( or compute) the force and stiffness. If this e plate thickness>= 1.75 * pole face thickness data had not been established previously, the :IF- NEEDED would not have succeeded. Additionally, This knowledge is incorporated as a recommended once the radius is kown, the actual ball bearing design range which a designer may accept or override. is implemented with an :IF-NEEDED; but because the Figure 14 shows the resulting .frame for the magnet- ball-bearing hierarchy has not been implemented, this plate-assembly. procedure is inoperative. The third example is the 'control coil' frame which is To illustrate the inheritance nature of the DKC part-2 in the 'UMCP magnetic bearing' frame, which system, consider the example of the design of 'Control has much less independence than the magnet plate coil' for vibration isolation system. Since it is similar to assembly. The fundamental parameters are diameter, the control coils of the energy storage system discussed wire diameter and number of turns. The diameter is before, rather than duplicating that information, a determined uniquely by the control-pin diameter. single control coil frame describing the general metho- Therefore the coil frame has a slot labelled 'diameter' dology is developed, and each bearing accesses that with an :IF-NEEDED aspect that fetches the pin frame. Further it is appropriate to locate every such diameter. The wire diameter is constrained by several occurrence and replace them with pointers to this other parameters, so its slot has a procedure to frame. Fortunately the DKC search functions and Control-Pin ISA Auxiliary Material = nickel-iron-alloy :DOC to permit high flux levels on the order of 1.5 Teslas wihout saturation Featurel :NAME main-diameter = 20.320::8.025 mm. :DOC to mate with the control-coil. Figure 13. Control-pin frame after knowledge-base aevelopment 48 Knowledge-Based Systems Page 1124 Magnet-plate ISA Auxiliary Material = nickel-iron-alloy :DOC to permit high flux levels up to 1.5 teslas without saturation Feature 1 :NAME diameter = < > :DOC a fundamental parameter which we'll not give a default value Feature 2 :NAME thickness :IF-ADDED (compare with 1.75 times the pole face thickness) :DOC should be > 1.75 *pole-face-thickness to avoid saturartion Feature 3 :NAME pole-face angle = < > :DOC another fundamental parameter to which no defult value is assigned Feature 4 :NAME pole -face-thickness :IF-ADDED (compare with 1/16 * diameter) :DOC Feature 5 :NAME material-saturation-level :IF-ADDED (get material-saturation-level from table) :DOC the value is determined by the selected material ... _,, Figure 14. Magnetic-plate frame after knowledge-base development frame manipulation functions simplify this process into FUTURE WORK a few basic commands. The DKC system has been implemented for the three The proposed DKC system is far from being complete magnetic-bearing-based systems. As part of the on-go- and robust. There are several significiant obstacles ing research projects, several magnetic-bearing-based which must be overcome for the DKC system to be inertial energy storage systems were designed. It was genuinely valuable to the design community. The particularly useful to be able to have access to the effects (if any) of choosing a particular design process explanatory design knowledge, in addition to tradi- must be understood; the applicability of the system to tional definitive design do<:;umentation, while sizing the design with arbitrary knowledge decomposition magnetic bearing components for different energy schemes must be demonstrated; the utility of the storage capacities. Another important advantage proposed user friendly interface must be verified; and gained from this system was that it allowed new design the robustness of the system to large varied designs members to get insight into the original designer's must be validated. These requirements are in addition intent, on-line, without hunting for lost scratch papers to the implementation problems, which although dif- saving precious lead time. ficult, are understood. As a whole this may seem an Vol 4 No 1 March 1991 49 Page 1125 enormous task (it is). But the initial DKC scheme, 12 Brown, F M 'The Frame Problem in Artificial implemented here for three magnetic-bearing-based Intelligence' Proceedings of the 1987 Workshop of systems, has shown that it can be a valuable and very the American Association for Artificial Intelligence worthwhile engineering tool for product designs. Morgan Kaugman Publishers, USA (1987) 13 Charniak, E, Riesbeck, C K, McDermott, D V and CONCLUSIONS Meehan, J R Artificial Intelligence Programming 2nd ed. Hillsdale Lawrence Erlbaum Associates The structure for a knowledge-based DKC system, (1987) capable of retaining both the traditional definitive 14 Hendler, J, Ostertag, E 'An AI-based reuse system' knowledge and the elusive explanatory knowledge, has Technical report No CS-TR-2197 University of been developed. The DKC package is built on top of Maryland, USA (1989) the Forms package which is a set of CommonLisp 15 Herndon, J A 'A Frame-based implementation of a functions which implements a frame system. It provides design knowledge capture scheme' Master's Thesis many capabilities including the fundamental functions University of Maryland, USA (1989) to create frames, modify frames, view frames, and 16 Jeyaseelan, M A 'CAD Approach to Magnetic delete frames. It serves dual purposes by improving the Bearing Design' Master's Thesis University of syntax of the Forms commands by relieving the user Maryland, USA (1988) from the need to memorize syntax or Lisp notation and 17 Plant, D P Prototype of a Flywheel Energy Storage more importantly, it describes the feel that is appropri- System Master's Thesis University of Maryland, ate for an engineering KB system. Preliminary results USA (1988) indicate that DKC package is a valuable engineering 18 Anand, D K, Kirk, J A, and Anjanappa, M tool for complex and long life product design. 'Magnetic bearing spindles for enhancing tool path accuracy' Advanced Manufacturing Processes Vol 1 No 1 (1986) pp 121-134 ACKNOWLEDGEMENTS 19 Zmood, R, Anand, D K and Kirk, J A 'The design of a magnetic bearing for high speed shaft driven The work reported in this paper was supported by the application' Proceeding of 22nd Intersociety Energy National Air and Space Administration, USA, through Conversion Conference Philadelphia, USA, August grant NASA NAG5-0-955. 10-14 (1987) 20 Anjanappa,M, Anand, D K, Kirk, J A, Zivi, E and REFERENCES Woytowitz, M 'Retrofitting a CNC machining center with a magnetic spindle for tool path error 1 Ullman, D G and Dietterich, T A 'Mechanical design control' Proceedings of INCOM'89 Madrid, Spain, methodology: Implications on future development September 22-26 (1989) pp 639-644 of computer aided design and knowledge based 21 Tsai, J P 'A kowledge-based system for software systems' Engineering with Computers Vol 2 (1987) design' IEEE Journal on Selected Areas in Commu- pp21-29 nications Vol 6 (1988) pp 828-841 2 Asimow, M Introduction to Design Prentice Hall, 22 Rich, E Artificial Intelligence McGraw-Hill, USA Englewood Cliffs, USA (1962) (1983) 3 Dieter, G E Engineering Design: A Materials and Processing Approach McGraw-Hill, USA (1983) 4 Ostrofsky, B Design, Planning and Development Methodology Prentice Hall, Englewood Cliffs, APPENDIX USA (1977) Typical DKC functions: 5 Hubka, V Principles of Engineering Design Butter- worth, UK (1982) • make-new-design-class creates a new form represent- 6 Wechsler, DB and Crouse, KR 'An Approach to ing a class of objects. Will prompt for name, parent, Design Knowledge Capture for the Space Station' and characteristics if not supplied. NASA Space Station Technical Report TR- • make-new-design as above, but representing a spe- N87-12597 USA (1985) cific instance rather than a class. 7 'Computer Aided Design Report' Computer Aided • run-dkc the function to enter DKC mode. Design Vol 5 No 12 (1982) • end-dkc the function to exit DKC mode. 8 Jarke, M, Jeusfeld, M and Rose, T 'Modelling software processes in a knowledge base: the case of Input functions information system' Knowledge-Based Systems • set-aspect-value-dkc sets the value of a given aspect Vol 1 No 4 (1988) pp 197-210 of a given slot of a given form. 9 Cullen, J and Bryman, A 'The knowledge acquisi- • set-slot-value-dkc sets the value of the = aspect of a tion bottleneck: Time for reassessment' Expert given slot of a given form. A subset of set-aspect- Systems Vol 5 No 3 (19&8) pp 216-225 value. 10 Garg-Janardan, C and Salvendy, G 'A conceptual • set-slot-always-dkc sets the value of the :always: frame work for knowledge elicitation' Int. J. Man- aspect of a given slot of a given form. Not a subset of Machine Studies Vol 26 No 4(1987) pp 521-531 set-aspect-value ( see Charniak et al 13 ). 11 Brachman, R J 'The Basics of Knowledge Repre- • add-if-added-dkc adds a given procedure to an sentation and Reasoning' AT&T Technical Journal additional :IF-ADDED aspect of a given slot of a Vol 67 No 1 (1987) pp 7-24 given form. 50 Knowledge-Based Systems Page 1126 Read functions from a given form. • aspect-value-dkc gets the value of a given aspect of a • delete-slot-aspect removes all the aspects of a given given slot of a given form. slot of a given form. • slot-value-dkc gets the value of the = aspect of a • delete-slot-value removes the = aspect of a given slot given slot of a given form. Subset of aspect-value. from a given form. Subset of delete-aspect. • slot-always-dkc gets the value of the :always: aspect • delete-all-forms removes all forms from working of a given slot of a given form. Subset of aspect- memory. Requires extreme care. value. • show-form-dkc display known information of a given Hierarchy functions form. • disconnect-from-parent disconnects a given form and all its descendants from its current hierarchy; effect- Deleting functions ively, replaces the parent of a given form with nil. • delete-form removes a form and all of its depend- • change-from-parent moves a given form to a differ- ents. Requires care. ent location in the hierarchy; changes the parent of a • delete-aspect removes a given with a given aspect given form to a given parent. Vol 4 No 1 March 1991 51 Page 1127 Application of stochastic optimal control to thin rib machining Prof. M. Anjanappa Prof. D.K. Anand Prof. J.A. Kirk Indexing terms: CNC machines, Controllers, Optimal control surface finish. Thin rib components, such as microwave Abstract: The optimal control of stochastic array plates, are machined from a solid block of material. systems, such as a thin rib machining process, can Fig. 1 shows a microwave array plate used in mobile lead to improved productivity and enhanced accu- racy. This paper addresses the problem of identifi- cation and optimal control of stochastic tool path error in a thin rib machining process, both ana- lytically and experimentally. Tool path error, in numerically controlled machines, consists of both deterministic and stochastic components and is defined as the vector difference between the pro- grammed path and the actual path taken by the tool relative to the workpiece. A methodology is developed to identify the cutting process param- eters based on experimental data from the thin rib machining of microwave guides. An LQG optimal A=23.876mm r,=::-As --, f-D C controller was designed to minimise the stochastic B= 22.860mm ~m11<1111111111Jl,_* tool path error. The results of optimal controller C= 3.810mm section X-X D D= 0.508mm simulation are discussed. The microprocessor- based online optimal controller was validated, on Fig. 1 Microwave array plate (courtesy Westinghouse Corp.) a small computer numerically controlled (CNC) milling machine, to demonstrate improved per- radar equipment. Typically, complex waveguides and formance in the thin rib machining of microwave array plates have many free-standing thin ribs, require guides. tight tolerance, have odd contours, need almost 95% of material removal from bar stock, and must be burr free to avoid microwave attenuation. 1 Introduction In the earlier experimental work by the authors [1] it was shown that in machining radar components, such as In the metal cutting industry, it is well known that microwave guides, the uncontrollable stochastic inputs to cutting time can be reduced by increasing the feedrate. the cutting process are significant. Some examples of However, increasing the feedrate beyond a critical value uncontrollable inputs are the dynamics of the cutting will result in unacceptable tool path error and lead to process, especially due to low stiffness of workpiece, and chatter. Tool path error and chatter will show up as metallurgical variations in the workpiece material. Since dimensional inaccuracy and poor surface finish in the there is no generally acceptable practical method avail- machined surface. Therefore, for a required quality of able to quantify these errors, the current practice is to surface finish and dimensional tolerance, there exists a minimise this error by decreasing the feedrate and maximum limit on feedrate that can only be raised by increasing the number of passes, resulting in lower developing an improved control scheme for feedrate material removal rate (MRR); this method is expensive. modulation. This paper presents a methodology where the stochastic End milling, to produce thin ribbed components, is components are included in modelling the cutting one of the major operations in the electronic and aircraft process, thereby attaining a more explicit relationship industries. Traditionally stock removal is achieved by between machining parameters and the output of the taking several rough cuts and one or more finish cuts process. The resulting methodology is used to develop an from a solid block of material. The number of passes and optimal controller to minimise the tool path error, while machining time is a function of dimensional accuracy and maintaining high MRR, which can lead to considerable technical and economical benefits. Paper 7702D (C9), first received 8th August 1989 and in revised form 21st August 1990 Prof. M. Anjanappa is with the Department of Mechnical Engineering, 2 Process modelling University of Maryland Baltimore County, Baltimore, MD 21228, USA Profs. D.K. Anand and J.A. Kirk are with the Department of Mechani- The modelling of a thin rib machining process, such as cal Engineering, University of Maryland at College Park, College Park, the end milling of microwave guides, involves an under- MD 20742, USA standing of the complex interaction between the machine 228 IEE PROCEEDINGS-D, Vol. 138, No. 3, MAY 1991 Page 1128 tool structure, the cutting process dynamics and the equation of the process is written as workpiece characteristics. The process modelling of end milling, for subsequent use in online control of process x(n + 1) = Ax(n) + Bu(n) + l(n) (1) outputs, has been reported by several investigators. Srini- y(n) = Kx(n) for n c (0, L) (2) vasan [2] reported that, in multiaxis machine tools, the use of coupled controllers can lead to improved contour- r- - - - - - - - - --- - - - - - - - - - - - , 1 plant : ing and tracking control. Tlusty and Smith [3] quantified i(n) x(n+ 1) I the effect of forced vibrations on the stability of the - I I process of end milling and validated the theory via simu- u(n) I lation. Villa et al. [ 4] discusses the building of a model I I relating surface texture to machining parameters, and a I I method to use such a model for process control is given. -------------------I Milner [5] developed an adaptive control system for end Fig. 2 Block diagram of the thin rib machining process milling, to maintain the deflection of the tool within certain limits. The deflection of the spindle nose was fed where back and compared with a predetermined reference (allowable), and the error signal was used to modulate x(n) = state vector (2 x 1, cutting force variation in the control input, i.e. the feedrate. Watanabe and Iwai newtons) [6] have reported the successful application of adaptive u(n) = scalar input (feedrate variation in mm/min) control to increase the accuracy of the finished surface in l(n) = white noise vector (2 x 1) conventional end milling. The deflection of the spindle y(n) = scalar output (surface profile height m nose is used to compute the tool deflection at the tool- micrometres) workpiece interface, which is used to shift the tool to L = length of the workpiece or duration of cutting compensate for the tool deflection. A, B, K = system parameter matrices of appropriate Following a different approach, at General Dynamics dimension and units. Convair Division [7] a technique called 'Net machining' Eqns. 1 and 2 are essentially perturbation equations since is used to minimise the 'ramp error' in thin rib machin- the state, control and output parameters can be con- ing. Using this technique, multiple cutting passes are sidered as perturbations over the nominal values. The made on each side of a free-standing rib, the passes being white noise is assumed to have zero mean and to be made on alternate sides of the rib from which suc- uncorrelated. Also we assume that the cutting force cessively deeper amounts of material are removed. This variation from the nominal value is zero mean. The technique is reported to have successfully reduced the assumption of zero mean for the state vector is not a ramp error due to deflection of thin ribs, but with the limitation for the proposed procedure. penalty of greatly increased part machining time and Tool path error and chatter are the two major limiting hence cost. For a more detailed review of research efforts factors in achieving high MRR while maintaining dimen- in the area of adaptive control of end milling for tool sional accuracy and good surface finish. In this research, path error control, the reader is referred to [8]. chatter will be removed as a limitation by choosing a In all of the above reported work, the effects of cutting regime in which the MRR is large (but inside the machine dynamics, cutting process dynamics and work- known chatter level) and tool path errors dominate piece compliance are neglected, thereby removing sto- machine performance, such as in thin rib machining. chastic components from the modelling of the process. Also, the deterministic tool path errors will be removed This is primarily due to the nature of the problem, which by means of appropriate calibration, compensation, and requires extensive methodology even for a moderate gain workpiece preparation. The remaining tool path error is in accuracy. However, this is not true for the end milling stochastic in nature, and is the focus of this paper. of thin ribbed parts, such as microwave guides, where the cutting force fluctuation above the deterministic profile due to uncontrollable inputs is relatively large and sto- 3 Identification chastic in nature [1]. Process identification is a wide-ranging subject, and In this work, the thin rib machining process (end various approaches have been proposed by different milling) is modelled as a discrete stochastic system by researchers over the years [9]. In this research, the including the uncertainties due to process dynamics as approach taken is to apply correlation techniques on uncontrollable inputs. The selection of proper control experimentally obtained data [10] to determine the inputs, state variables and controlled outputs depends on system parameter matrices A, B and K. the particular problem at hand and the facility con- Noting that the white noise is not correlated with straints. For the case of controlling the tool path error in either x(n) or u(n) and that u(n) is deterministic, the state the end milling of parts such as microwave guides, the equation can be expressed as output was chosen as the machined surface profile height. This output must be controlled to lie within a specified X = AXA' + BUB' + A (3) error band (i.e. the allowable tolerance). The control where X, U and A represent the covariance matrices of input was chosen to be the feedrate. The state variables x(n), u(n) and l(n). Similarly, the post multiplication of were chosen to be the biaxial cutting force, which can be eqn. 1 with its transpose yields measured using a high-freqtiency force dynamometer. The uncontrollable inputs are represented as white noise X(p) = AX(p + 1) for p = 0, 1, ... , P (4) input to the system. For the purpose of this work, the where X(p) is the autocorrelation of x(n) and P is the process is assumed to be a linear, stationary and ergodic number of discrete steps required before the correlation stochastic process. This assumption will be verified later function goes to zero. By defining in the paper. Fig. 2 shows the block diagram of the thin rib machining process. The stochastic linear difference X(p) - AX(p + 1)2 = E 2 (5) IEE PROCEEDINGS-D, Vol. 138, No. 3, MAY 1991 229 Page 1129 the coefficients of A can be obtained by least-squares with the machine. A specially designed and built high- fitting. frequency force dynamometer was used to obtain the With this, there are four unknowns in eqn. 3 which is three orthogonal force components. more than the number of unique equations. The approach taken was to select the magnitude of the white Table 1 : Thin rib machining parameters noise intensity matrix. Since there is no generally accept- Axial depth of cut 3.81 mm able procedure available, the judicious choice depends on Radial depth of cut 0.508 mm the designer's past experience and understanding of the Diameter of cutter 4.7625 mm physical problem at hand. Two of the factors that need to Tool material high-speed steel be considered in such a selection are the bandwidth of Number of flutes in tool 2 the noise, and the modelling error due to the assumption Helix angle of tool 30 degrees Spindle speed 5600 rev/min of linearity of the process. As a first approximation, the Nominal feedrate 25.4 mm/min magnitude of the variance of l(n) is chosen to be equal. Feed per tooth 0.0023 mm The actual magnitude, however, will be calculated using Workpiece material aluminium 6061 T6 the experimental data. With the above assumption, there Type of machining down milling Coolant status dry cutting are three unknowns whose values can now be obtained. Following a similar procedure, consider the output eqn. 2, which when post multiplied by x'(n) and taking The x and y axis cutting force signals were recorded the estimate of product variables yields on a magnetic tape recorder. Further, the x and y axis cutting force signals were fed through a lowpass filter fol- E{yx'} = KX (6) lowed by a highpass filter into the digitiser. The digitiser where X is the covariance matrix of x(n). Eqn. 6 decom- was a CDC Cambridge data acquisition system fitted poses to two scalar equations. Knowing the experimental with a Cipher magnetic digital tape recorder and a 16- data of x(n) and y(n), the parameter K can be obtained. channel 12-bit analogue to digital convertor. A digitisation rate of 10 000 samples per second was 3.1 Experimental data generation chosen since the frequency of interest was below 5000 Hz. Since the research interest lies in the stochastic com- To aid in the synchronisation of the cutting force signals ponents of both parameters due to process dynamics, the with the surface profile signals, the final 20 seconds of deterministic components of experimental data are either data were digitised. The falling edge of the cutting force removed or compensated. To attain this goal, care was signals and of the surface profile signals were used as the taken to ensure either the absence of or compensation for reference points for synchronisation purposes. The mag- deterministic tool path errors in all the ensuing experi- netic tape containing the digital data of cutting force in ments. All thin rib machining experiments were con- blocked format was then mounted on a UNIVA C 1190 ducted on a low-horsepower Dyna DNC vertical milling for use with the system identification program, which will machine by finish milling the thin rib of the specimen to be discussed later in this paper. its final thickness. The process output, the surface profile height signal, Fig. 3 shows the schematic diagram of the experimen- was then obtained using a Taylor-Hobson Talysurf 4 tal setup used for cuttinmg force datal ge neration and profilometer. Fig. 4 shows the schematic diagram of the -~ A=1.016mm magnetic 1 I I surface profile tape recorder 1 gB=: 3i.i8.1~ ~m~~mm height signal O I 1 E= 40.64 mm l I --1 1 * r,----=r~ ( filter 1 I 1 B~_l I 1----- ------1 !~- spec~~-~J ! A/0 convertor I I '------____J I I ____,__ I digital 1 tilter I tape recorder 1 I_ ______ II Fig. 4 Experimental setup for surface profile measurement ,-- - ----- - --"-'~~-I I I experimental setup used for surface profile recording. The digital tape rec. AID conv specimen was positioned such that the traverse length I I included the falling edge at the end of the machined IC ambridge digital I surface. The falling edge would later be used as the refer- ,data <3~uisiti (2FR3/3MX)l/2 (31) dF/dt > Mw3X (32) The number of turns for the EM coils presented as the function of the force slew rate becomes N 8{2BuVcc (33) < dF 1tµo dt Page 1143 The maximum supply current for the EM coils can be calculated using equation (12), lmax = 4BEMgo/,uoN (34) The power amplifier of the control system can be chosen based on the its voltage and current reqmrements. . PM/EM MAGNETIC BEARING DESIGN The flowchart for the design methodology of the PM/EM bearin~ is shown in Figure 8. The design procedures start with design requirements for the magnetic bearmg including the mass of the flywheel, the axial force, the radial force and the linear operating range. There are some initial inputs such as the saturation flux density of the magnetic material, the recoil permeability of the PM material, the operating point of the permanent magnet, the useful flux ratio, and power amplifier voltage. These values can be update or changed with the choice of the specific materials and designs. The bearing design is an iterative processes so the number of steps just shows a possible sequence. These procedures are used for the magnetic bearing flywheel energy storage system and designer can revise the procedures for other applications. (1) Flux density consideration The flux densities in any section of the magnetic bearing are limited by the saturation value of the magnetic material so the combined flux densities from the PM and EM are less than the saturation value. If there are equal flux densities from the PM and EM, the bearing can generate a maximum force. In most applications the flux density from the PM is greater than that from the EM. (2) Geometric relationship consideration Our PM/EM bearing IS a small gap suspension design so the linear range is less than 15% of the air gap. To avoid large leakage flux and cross-talk between the pole faces of the magnet plates and return ring, the pole face thickness is at least 3 times of the air gap. Also, there is a minimum thickness for the PM to prevent too much leakage between.the two magnet plates. (3) Axial drop, axial load, and radial force consideration The magnetic bearing is designed to satisfy the force requirements by choosing the flux densiti~s a.nd the g~om~tric .di~ensions. Because of ?ur r.adia! active bearing ~esi$n the load capabihty m the axial directmn 1s weaker than the radial directmn. If the bearmg IS used to handle the same force in both directions, the axial force requirement becomes dominate. To avoid the possibility that a larger axial drop may worsen the magnetic properties of the bearing the ratio of the axial drop and the pole face thickness is limited to 20%. ' ( 4) Selection of a feasible design After satisfying the performance requirement and physical constraints a feasible design is chosen including the flux densities from the PM and EM, the mean radius, the air gap, the pole face thickness, and other dimensions. (5) Permanent magnet design Using the information from the previous step the parameters of the permanent magnet design such as the magnet strength, thickness and cross section area can be decided by applying the equation (23), (24) and (25). (6) Electromagnetic coil design Based on the stability and force slew rate considerations the number of turns for the EM coils as well as the voltag~ and current for the power amplifier can be decided. Page 1144 (7) Characteristics of the PM/EM bearing The performance parameters such as Xstb, Xlin, Ka, C, K.7., Kx and Ki for the bearing can be calculated using the equation (15), (16), (17), (18), (19), (20) and (21). (8) Optimization design · A optimization method for the PM/EM bearing design has been developed at the University of Maryland [8]. The designer can define an objective function with all equality and inequality constraints to find an optimum design. After finishing the preliminary design the bearing needs a detailed study such as a finite element model for magnetic circuit agreement and dynamic simulation. Also, the control system and overall bearing flywheel system need further investigation but these are beyond the scope of this paper. EXAMPLE An example for the pancake magnetic bearing design is presented to demonstrate the proposed design methodology. Assume a pancake magnetic beanng for the energy storage system having a flywheel weight of 8 lbs. The bearing is designed to handle at least 16 lbs force at both axial and radial direction with an axial drop of no more than 20% of its pole face thickness. The magnetic bearing should allow at least 0.006 inch for the radial displacement before limited by the mechanical touchdown bearing. The magnetic material for the bearing is nickel iron which has a saturation flux density of 1 Tesla. The maximum radius for the bearing is limited to 2 inch and the minimum height of the permanent magnet is 0.3 inch. The power amplifier of the control system has a voltage 24 volts and a maximum supply current 1.5 Ampere. The useful flux ratio is assumed to be 40% for this design. (1) Design Requirements & Physical Constraints The performance requirement and physical constraints of the magnetic bearing are rewritten as the following: M = 8lbs FA> 16 lbs FR> 16 lbs Bsat = 1 Tesla Rmean < 2 in Xtd = 0.006 inch dp/tpf < 0.2 Lm > 0.3 inch Vee -;;-24 V lmax < 1.5 Amp RT/Rg = 0.4 (2) Flux Density Consideration The flux density generated by the permanent magnet across the air gap is assumed to be 50% of the saturation value of magnetic material. The flux density from the EM coils is 40% of the saturation value. Bu = 0.5 Bsat = 0.5 Tesla BEM = 0.4 Bsat = 0.4 Tesla (3) Geometric Relationship The touchdown gap is designed to be 15% of the air gap and the pole face thickness is three time of the air gap. go= Xtd/0.15 = 0.04 in Page 1145 tpf= 3go = 0.12in ( 4) Axial Drop, Axial Load and Radial Force Requirement The axial stiffness equation is used to find the mean radius for the magnetic bearing. dp = WA/Kz = 0.2 tpf = 0.024 in Rmean = 2.89 in > 2 in (Failure!) Because the calculated radius is larger than the alJowable size the above design must be changed. One way is to choose the bearing radius as the maximum allowable value and to find the required flux density at the air gap which can satisfy the requirement. Rmean = 2 in Bu = 0.6 Tesla BEM = 0.3 Tesla FA= 20.9 lbs > 16 lbs (OK!) FR= 25.1 lb> 16 lbs (bK!) (5) Permanent Magnet Design The permanent magnet is chosen to use the rare earth Recoma 20 material which has a remanence of 0.85 Tesla and a recoil permeability of 1.05. The length of the permanent magnet is assumed to be 0.3 in. The cross section area for the air gap is calculated to he 0.377 in2. The radius and the operating flux density of the magnet can be calculated as the below Am = 0.829 in2 Rm= 0.94 in Bm = 0.68 Tesla (6) Electromagnetic Coil Design The radial passive stiffness of the bearing is calculated to be 1567 lb/in. If the relative stability ratio is assumed to be 2, the number of turns for the EM coil can be calculated using the stability criteria N < 1790 turns If the bearing is assumed to handle a step input force of 16 lbs at the touchdown gap. The force slew rate and the number of turns for the coil are: dF/dt = 31254 N/s N < 1320 turns Finally the number of turns for the EM coil is chosen to be 1000 turns so the maximum supply current is 0.97 ampere which satisfies the constraint of the power amplifier. (7) Characteristics of Pancake Magnetic Bearing The performance parameters for the bearing are listed as the following: Kx = 1567 lb/in Ki= 29.1 lb/Amp Ka = 2667 lb/in Kz = 332 lb/in C = 146 Amp/in Xstb = 0.018 in Xlin = 0.0066 in DISCUSSION AND CONCLUSION In light of the demands of modern technology for more efficient and economic energy conversion, magnetic bearings certainly fit the requirements. The various magnetic bearings differ in function and form but a major commonality between them should be the theory that governs all physical and magnetic behavior. Although the specific numbers of these mathematical models for a flywheel Page 1146 magnetic bearing are unique, the design methodology and magnetic developments encompass all such devices. As always, one must be careful to study the physical constraints and boundary conditions placed on the problem. University of Maryland has been successful in developing two different sizes of bearings and an operational combination of two bearings in a stack configuration. The success has come from proposmg, modifying, and verifying the mathematical models presented here. A few grey areas remain, such as the crosstalk between magnetic flux paths and harmonic disturbances, which were beyond the scope of this paper. Future methodology will include dynamic effects, digital rather than analog control, and finite element analysis of the magnetic circuitry. As the system becomes more complex, so do the questions that are raised about its optimization. SYMBOLS AND ABBR EVIA TIO NS Ag: Cross Section Area of Air Gap; for PM/EM Bearing = 1tRmeantpf/2 Am: Cross Section Area of Permanent Magnet = 1tDm2/4 BEM: Flux Density by Electromagnet at Pole Face Bm: Operating Flux Density of Pennanent Magnet Br: Remeance of Permanent Magnet Bsat: Saturation Value of Magnetic Material Bu: Useful Flux Density by Permanent Magnet at Pole Face Bg: Flux Density Across Air Gap C: Current/Displacement Ratio of Control System Cx: Displacement Feedback Gain in Control System Ci: Current Feedback Gain in Control System Dm: Diameter of Permanent Magnet dp: Axial Drop of Flywheel FA: Maximum Axial Force FR: Maximum Radial Force at X = Xtd Frad: Restoring Radial Force= Kil -KxX go: Air Gap He: Coercive Force of Permanent Magnet Hm: Magnetizing Force of Permanent Magnet lmax: Maximum Control Current to Electromagnetic Coils Ka: Active Stiffness of Magnetic Bearing= CKi - Kx Ki: Force/Current Sensitivity of Electromagnetic Coils Kx: Passive Radial Stiffness of Magnetic Bearing Kz: Passive Axial Stiffness of Magnetic Bearing Lind: Inductance of Electromagnetic Coils Lm: Length of Permanent Magnet 1\1: Mass of Flywheel . N: Number of Turns of One Electromagnetic Coils Rg: Reluctance of Air Gap at Pole Face RL: Reluctance of Leakage Flux Rm: Reluctance of Pem1anent Magnet RT: Total Reluctance= RgRL/(Rg+RL) Rmcan: Mean Radius of Middle Point of Air Gap tpf: Pole Face Thickness Xlin: Linear Range of Magnetic Bearing Xstb: Stable Range of Magnetic Bearing= Xlin (1 +Ka/Kx) Xtd: Touchdown Gap Vee: Amplifier Supply Voltage µo: Permeability of Free Space= 41tx10-7 H/m µr: Recoil Pem,eability of Pem1anent Magnet Page 1147 cdFlt Force Slew Rate 6Bm: Varying Flux Density of Pennanent Magnet REFERENCE 1. Iwaskiw, A. P., "Design of a 500WH Magnetically Suspended Flywheel Energy Storage System", Master Thesis, University of Maryland, College Park, 1987. 2. McCaig, M., Clegg A.G., "Permanent Magnets in Theory and Practice", John Wiley & Sons, Inc., New York, 1987. · 3. Parker, R. J., "Advances in Permanent Magnetism", John Wiley & Sons, Inc., New York, 1990. 4. Sabnis, A. V., "Analytical Techniques for Magnetic Bearings" PhD Dissertation, Univ. of California, Berkeley, 1974. 5. Strnat, K. J:, "Modern Permanent Magnets for Applications in Electro-Tecirno_logy", ~roceedings of International Workshops on Rare-Earth Permanent Magnets and Apphcat10ns, Pittsburgh, Penn., 1990. 6. Zmood, R. B., Pang D., Anand D. K., Kirk, J. A., "Improved Operation of Magnetic Bearings for Flywheel Energy Storage System", Proceedings of 25th Intersociety Energy Conversion Engineering Conference, Reno, Nevada, 1990. · 7. Maslen, E., Hermann, P., Scott, M., Humphris, R.R., "Practical Limits to the Performance of Magnetic Bearings: Peak Force, Slew Rate, and Displacement Sensitivity", Proceedings of NASA Workshop on Magnetic Bearings, Langley, Virginia, 1988. 8. Pang, D., Kirk, J. A., Anand, D. K., Huang, C., "Design Optimization for Magnetic Bearing", Proceedings of 26th Intersociety Energy Conversion Engineering Conference, Boston, Mass., 1991. B(T) Q H (Am-1 ) Fig. 1 PM/EM ¥agnetic Bearing Fig. 2 P.M Hyseteresis Loop Page 1148 B Br Bm _ IL\Bm H Fig. 3 Ideal PM B-H Curve -, - =-Bm-Am - -1 ' ' + g I PM I Rm I I I Rg I RT BrAliRm Ni L - - - _, Ni Fig. 4 PM/EM Magnetic Circuit Page 1149 {kAlm] Radial Foroes 800 600 400 200 Uneu Region S1tuntion Re1ion 1.4 o,4 Corre +a:i +oo [Nikias and Petropulu, 1993]. Functions of singular values of {9) are subsequently used in c.cm.,m2,···,m._1) = I I ... I c.(ri,i2,····r·-1)· cutting state identification. (5) The constrained third order mean, CTOM, [Raghuveer and Nikias, 1986], provides an alternative set oflinear algebraic equations for the determination of the AR coefficients, a(i). Define A plh order AR, auto regressive, process is described by ; are mutually independent and uniformly distributed over (0, 21t]. A study of the singular values and R, Q and r2-ralios of the R, Q and r2 matrices associated with (O,s) (-1,s-l) (-s,O) (14) (17, 18) and related functions is given in [Berger, Minis, et al., 1997) and [Berger, Belai and r= Anand, 2001). Results for the TOR algorithm's analysis of(l7, 18) are repeated here for (1,o) (0,1) (-st 1,-s) completeness. The function f1(t), (17), Fig. l(a) is self-phase coupled at a frequency of 100 Hz. The {s,s) (s- l,s-1) (0,0) means of the dominant pairs of singular values ofR are seen to be linear functions of max lag in Fig. I (b ). The sampling frequency is I 024 Hz. The corresponding R-ratio, Fig. I (c ) , converges a= [l,a(l), ... ,a(p}f, b = [p,0, ... ,0f, {ij) = c/(ij) and r is (p+l)2 X (p+I) withs= p. A least to a value of2.0 for maxlag > 60. Similar behavior is exhibited by the singular values of Q, ( 11 ). squares Solution of(l4) is a= (rTr)"1 c1b Which implies that It is evident that the number of pairs of singular values equals the number of different frequency components in f1(1). (15) Function f2(t), ( 18), Fig. 2(a), exhibits phase coupling of 90 and 100 Hz components. The " sampling frequency is I 024 Hz. The coupling of side bands to the central I 00 Hz frequency component has been observed in experimentally derived time series associated with light and STATE (JHARACTER1ZATI0N medium orthogonal cutting. Singular values of the R, Fig. 2(b), and Q matrices and the Rand Q- ratios as functions ofmaxlag are identical. For maxlag = 102 the R-ratio, Fig. 2(c), R ~ 1.0 an 102. It is seen from Figs. 1 and 2 that the R-ratio that and singular value plots serve lo identify f1(t) and f2(t). In these cases the R-ratio, evaluated al a single point, max lag= l 00, serves to differentiate between f1 and f2• (16) CUTTING STATE CHARACTERIZATION where q = min (m,n), o1 ~ o2 ~ ... o ~ 0 are the singular values and Rm,n denotes a real mxn 1 matrix. If o ~ ... ~ o, ~ o,+1 = ... = oq = 0 then rank (A)= r [Golub and Van Loan, 1993]. The experimental apparatus employed in the collection of cutting tool acceleration data 1 consists of a Hardinge CNC lathe, a force dynamometer utilizing three Kistler force transducers The singular values of A may be ordered as described in ( 16). Denote the ratio and its associated electronics and a Hewlett Packard 3566A digital spectrum analyzer for data (o +oJ/(o +o for a matrix A as the A-ratio. The R, Q, and r matrices (9,11,15), are shown to acquisition and real time analysis. All experiments involved only right-handed orthogonal 1 3 4) 2 discriminate between test functions and between experimentally measured cutting states. cutting. Cylindrical work pieces of 1020 steel were machined under a wide range of cutting conditions. Since all work pieces were short, work piece modal characteristics did not affect the The following quadratically phase coupled functions, f;(t), where turning dynamics. The sampling rate was 4096 Hz and the cut-off frequency was 1I 00 Hz. Record lengths were from 20s to 60s except for chatter records which had a shorter duration. Sequences of cutting experiments were performed in which either the depth of cut or the (l 7) turning frequency was varied with all other cutting parameters held constant. In the following, + +; two sets of experimental data are analyzed. From the March 5 set, for which the depth of cut = 02 cos(2,r · 200! 1 + /2) 2.8 mm, feed rate= 0,007 in/rev, surface speed= 90 m/min, experiments 6 and I were selected. For these the spindle speeds were 380 rpm and 371 rpm, respectively. Experiments I and 6 exemplify the chatter and non-chatter cutting states respectively. For the March 5 experiment 6 fi(t) = 0.9 cos(211' · 90t + ;1) + cos(211' · lOOt + ;2 ) data set singular values of R, Q and r2 and the R, Q and Ti-ratios vs maxlag are shown in Fig. 3 (18) for TOR, CTOM and OARM, respectively. Except for the scale, the singular value plots for TOR and CTOM are nearly identical. The R and Q-ratios are nearly identical as well. For + 0.2 cos(~II' · l 90t + ;, + ;2 ) max lag = 150, R ~ Q = 1.25 and r2 = I. 77. It is seen that for I0 0 < maxlag < 150 the values of the Rand Qare< 1.65. For 130 < maxlag <150 the values ofr1 < 2.0 6 BERGER, BELAI, ANAND, TIME SERIES ANALYSIS WITH SVO ALGORITHMS BERGER, BELAI, ANAND, TIME SERIES ANALYSIS WITH SVD ALGORITHMS 7 • For the March 5 experiment I data set singular values of R, Q and r2 and the R, Q and r2 - ratios vs. maxlag are shown in Fig. 4 for TOR, CTOM and OARM, respectively. As in the maxlag" 40 corresponds to the crossing ofMSV(J,l,40) and MSV(5,l,40) in Figs. 5(a) and 5(c). previous case the singular value plots for Rand Q differ by a scaling factor and the Rand Q- In the chatter case, Figs. 6(a) and 6(c) the crossing ofMSV(3,l,150) and MSV(5,l,I50) occurs at ratios are nearly identical. For 20 < maxlag < 150 the R, Q and r -ratios are >2.0. It is apparent maxlag " 150. As before, the intersection point provides a necessary condition for chatter. 2 that the R, Q and r2-ratios differentiate between the chatter state of experiment I and the medium cutting state of experiment 6. CONCLUSIONS The algorithms OARM and CTOM were shown to resolve the peaks in the bispectrum of Denote a singular value, over an interval a ~ maxlag !> b, by SY (i,a,b) = o; and a mean a set of phase coupled test functions more accurately than the TOR algorithm, [Nikias and · singular value over an interval by MSV(i,a,b) = (o; + 0;+1)/2. Let a singular value trajectory be = Petropulu, 1993; Raghuveer and Nikias, 1986]. The present study demonstrates that for a set of denoted by SVT(n,a,b) where n a positive integer identifying a singular value trajectory and a experimentally measured cutting tool accelerations ratios of singular values associated with and bare defined above. Denote a mean singular value trajectory by MSVT(n,a,b) where TOR, CTOM and OARM identify the cutting states. However, the relative computational MSVT(m,a,b) = (SVT(q,a,b) + SVT(r,a,b))/2 where SVT(q,a,b) and SVT(r,a,b) intertwine and m simplicity and speed ofTOR indicates greater effectiveness than CTOM and OARM in the identifies the MSVT( m,a,b ). online control of cutting states. The location or the intersections or the mean singular value trajectories, MSVT, provides a necessary condition for chatter. . .1~ Fig. ~· MSV(l,1,150) = (o1 + 0 2)/2 and MSV(J,1,150) = (o3 + 0 4)/2. Denoting the mtertwtnmg pairs 0 1, 0 2 and o3, o4 by n=l,2, respectively then the upper MSVT(l,1,150) = MSV ACKNOWLEDGMENTS (1,1,150) and the lower MSVT(2,l,150) = MSV(J,l,150). In Fig 2, MSV(l,1,102) = (o The authors acknowledge the support ofN.S.F. through GER-9354956. The 1+oi)/2, MSV(J,1,150) = (o1+o4)/2, MSV(S,l,IOO) = (os+o,)/2, MSV(l,102,150) = (o1+o2)/2, and etc. Then MSVT(l,l,!02) = MSV(l,1,102), encouragement of P. Grootenhuis and D. J. Ewins, Imperial College of Science and Technology. MSVT(l,102,150)= MSV(5,l02,150), MSVT(2,l,l02) = MSV(J,1,102), MSVT(2,102,150) = London, and H. Russell, University of Maryland, College Park, is greatly appreciated. The MSV(3,I02,l50), MSVT(3,l,102) = MSV(5,l,102), MSV1(3,102,150) = MSV(l,102,150). assistance ofT. Miller in the preparation of the manuscript is gratefully acknowledged. In Figs. 3(b) and 3(d), the non-chatter case, the peak occurring in the Rand Q-ratios at REFERENCES u maxlag • 60 corresponds to the crossing ofMSV(J,1,60) and MSV(5,l,60) in Figs. 3(a) and 3(c). In the chatter case, Figs. 4(a) and 4(c) the crossing ofMSV(3,l,150) and MSV(S,1,150) occurs at I. G. K. An, S. B. Kim and E. J. Powers, "Optimized Parametric Bispectrum Estimation," maxlag = 150. The location of this crossing point provides a necessary condition for chatter. Proceedings ofICASSP, New York, 1988, 2392-2395. From the January 28 set for which the feed rate= 0.007in.rev, spindle speed= 297 rpm, 2. B. Berger, I. Minis, M. Rokni, M. Papadopoulos, K. Deng and A. Chavalli, "Cutting State surface speed= 90 min, experiments Sb and 7b were selected. For these the depths of cut were Identification," Journal of Sound and Vibration, 200, I, 1997, 15-29. 2. 7 mn and 2. 725 mh. Experiments 7b and 8b exemplify the chatter and non-chatter cutting states, respectively.' l B. Berger, J. A. Manzari, D. K. Anand and C. Belai, "Auto-Regressive SYD Algorithms and Cutting State Identification," Journal of Sound and Vibration, to appear. For the January 28 experiment Sb data set singular values of R, Q and r2 ratios vs maxlag are shown in Fig. 5 for TOR, CTOM and OARM. Except for the scale, the singular value plots 4. G. H. Golub and C. F. Van Loan, Matrix Computations, The Johns Hopkins University for TOR and CTOM are nearly identical. For 100 < maxlag < 150, R Q = 1.3. For 112 Press, Baltimore MD, 1993. ~ < maxlag < 150, r2 < 2.0. 5. C. L. Nikias and A. P. Petropulu, Higher-order Spectra Analysis, Prentice Hall, Englewood Cliffs, N.J., 1993. • The January 28 experiment 7b data set singular values of R, Q and r 2 and the R, Q and r2- ratios vs. maxlag are shown in Fig. 6 for TOR, CTOM and OARM, respectively. As before the 6. C. L. Nikias and A. P. Mendel, "Signal Processing With Higher-Order Spectra," IEEE ~ingu_Jar value plots for R and Q differ by a scaling factor and the R and Q-ratios are nearly Signal Processing Magazine, July, 1993, 10-37. identical. For 20 < maxlag < 150 the R, Q and r2-ratios are> 2.0. As before the R, Q and r2- ratios differentiate between the chatter state of experiment 7b and the medium cutting state of 7. M. R. Raghuveer and C. L. Nikias, "Bispectrum Estimation Via AR Modeling," Signal experiment Sb. Processing, IO, 1986, 35-48. In Figs. 5(b) and 5( d), the non-chatter case, the peak occurring in the R and Q-ratios al Page 1158 8 BERGER, BELAI, ANAND, TIME SERIES ANALYSIS WITH SVD ALGORITHMS BERGER, BELAI, ANAND, TIME SERIES ANALYSIS WITH SVD ALGORITHMS 9 3~--.---.---,----,---..,---.----r---.---.---, .. -~ U) Ql ~ ·;;; 1 Ql (/) Ql E i= -1 -1 -1.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 time (s) 0.4 0.5 0.6 0.7 0.8 0.9 (a) time(s) (a) 12 8 10 7 6 ~ 8 U) :::, Ql ~ .:1 5 19 6 >"' :::, ni 4 I :5 4 g>3 i:i5 2 2 50 100 150 Max Lag Max Lag (b) (b) .3 3 2.5 2.5 0 ~ 0 ' 2 a: 2 a~: 1.5 1.5 10 50 100 150 1 0 50 Max Lag 100 150 (c) Max Lag (c) Figure 1: Fl TOR: (a) Time series (b) TOR Singular Values (c) R-rnt.io Figure 2: F2 TOR: (a) Time series (b) TOR Singular Values (c) H-rntio ft Page 1159 10 BERGER, BEi.Ai, ANAND, TIME SERIES ANALYSIS WITH SVD ALGORITHMS BERGER, BEi.Ai, ANAND, TIME SERIES ANALYSIS WITH SVD ALGORITHMS 11 8 X 10 12.-----~-------- 4 11 X 10 14 4 u 3.5 12 3.5 ., 10 3 Q) 3 :, 0 iii ia > a ~ 2.5 ti; ~25 1 a: i 6 a: C: iii 2 2 4 2 1.5 1.5 1 0 50 100 150 1 0 50 100 150 Max Lag (b) Max Lag X 1QH (b) 14 4 11 X 10 10 4 12 3.5 ., 10 3.5 Q) 3 8 :, iii 8 0 > xi ti; -~ 2.5 3 .ii 8 :5 6 0 "' i O> -----------> C: 2.5 iii 2 .lil 1 :, Cl> 4 0 1.5 .I: en 2 1 2 1!111 0 50 100 150 1.5 Max Lag (d) 0 1 )( 1025 0 100 0 50 100 150 7 4 Max Lag Max Lag 6 (c) (d) 3.5 X 1019 ., 5 2.5 4 ., 3 :, .0 ~4 ,, 3.5 ti; ~ 2.5 2 i3 -"' C 2 XI 3 iii 2 i 1.5 0 > 1.5 fa .lil :, !}·5 Cl> 1 1 C: 0 50 100 150 iii 2 Max Lag (I) Max Lag (e) 0.5 1.5 Figurr -t: Rl'\I \lard1 fi rxperiment 1: (a) Tor Singular Vahws {I,) TOfl 1 50 100 0 50 100 150 fl-ratio (r) ('TO\! Singular Values (d) CTOM Q-ratio (e} ORA~! Singular Max Lag Max Lag \"ah1<•s (I") Oil.\\! rrratio (e) (f) Figure 3: RPM March 5 experiment 6: (a) TOR Singular Values (h) TOR R -ratio (c) CTOM Singular Values (d) CTOM Q-ratio (e) ORAM Singular Values (f) OHA~l rrratio Page 1160 12 BERGER, BELAI, ANAND, TIME1SERIES ANALYSIS WITH SVD ALGORITHMS BERGER, BELAI, ANAND, TIME SERIES ANALYSIS WITH SVO ALGORITHMS 13 35 4 700 4 30 3.5 600 ,3.5 "'25 ~ 3 "'500 a, 3 ::, ~ 20 .Q 1ii g 400 .Q :a 'i 2.5 i o/ 2.5 15 a: C: i'"3 00 a: 2 C: Q) 10 2 Vi 200 5 1.5 100 1.5 1 50 100 150 0 50 100 150 1 0 50 100 150 Max Lag Max Lag Max Lag Max Lag (a) (b) (a) (b) X 10' 5 3 4 X 106 4 2.5 3.5 5 3.5 :"a,,' 2 3 fil4 3 ::, ~ .Q ~ 2.5 ------~- :i 0 :'" l? i 3 0 in 1 2 "' ~2 2 1.5 1.5 1 0 50 100 150 I 0 50 100 150 Max Lag Max Lag Max Lag Max Lag (c) (d) (c) (d) X 10• 6 2 4 X 1012 4 J 3.5 10 3.5 ., 1.5 a, 3 :, "a, V 3 ::', 8 "iu > .Q tij 0 ~ o/ > 2.5 6 ~ 2.5 ::, Cl ~"' :O'" I i ~"' C: l en 2 C: in 4 2 0.5 1.5 2 1.5 1 1 50 100 150 0 50 100 150 0 0 50 0 50 100 150 Max Lag Max Lag Max Lag Max lag (e) (I) (e) (f) Figure 3: Depth uf Cut .January 28 experiment Su: (a) TOR Singular Valurs Figure 6: Depth of Cut fanuary 28 experiment 7b: (a) TOR Singular Val11£i1 (b) TOR R-rntio (c) CTml Singular Values ( >AND< < predicate-2 > > < < > > for the parent rule and the parent fact. When a particular AND ... predicate-n task is executed, the rules from its rule group are repeat- THEN< < action-11 > >AND< < action-12 > > < < edly applied until its termination condition is satisfied. AND ... action-1 m > > Some rules may apply (fire) successfully. Every time a ELSE< < action-21 > >AND< < action- rule fires, some new facts are generated and added to the 22 > > fact base The generated or inferred facts contain valid AND ... < < action-2k > >) pointers in their parent fact and parent rule slots. The predicates are constructed in a form similar to the Eventually, the last task is executed. If features have well-formed formulae of predicate calculus. When a rule been found, the last few facts contain the value 'is a is first specified, the inference engine examines each term feature' in their fact attribute field, indicating that this appearing within each well-formed formulae. Depending fact denotes the existence of a particular feature. The on what the term is, it processes the subsequent terms in name of the data structure that contains the parameter a particular fashion. Eventually, the inference engine for this feature would appear within the fact-parameters Page 1166 224 M. AnJanappa et al. TASK 70 Objective: To extract the outermost faces for the drawing part Task Prerequisite: Task-60. PDCKE~ SLD' Initial conditions: set the variable 'extracted-faces' to nil. Termination condition: The variable 'extracted-faces' : []HOLE: becomes true. I I I I I I Rule-1 I HOLE I I I I IF the variable 'extracted-faces' is nil AND the stock-shape is rectangular THEN create data structures for six faces corresponding to the boundary planes AND arrange the planar contours on each face according to their levels of nesting AND create a linked data structure for the six faces AND set the variable 'extracted-faces to true. Rule-2 IF the variable 'extracted-faces' is nil AND the stock-shape is cylindrical THEN create data structures for a cylindrical face Figure 4. Conceptual feature extraction of an example part. corresponding to one boundary plane AND create data structures for two faces corresponding to remaining boundary planes AND arrange the planar contours on each face according to their levels of nesting AND create a linked data with alternating signs. However, the resulting shapes are structure for the three faces AND set the variable 'extracted- not necessarily related to manufacturing processes and, faces to true. at times, can become quite difficult from that consider- ation. Hirschtik and Gossard (1986) described an extru- sion advisor system which defmed generic features as Figure 3. Production rules corresponding to Task-70. terms of a char.icteristic pattern set. Currently the system is limited to 2-dimensional parts made up of straight lines field of the particular fact. Consequently, one ends up and circular arcs and containing straight walls. with a network of facts with end facts denoting the dis- None of the literature methods make use of ICES rep- covery of features. More details can be obtained from resentation of a part. Instead they all work with specific reference (Kumar et al. 88). solid modellers only. Hence the IFEM presented here is unique in that it extracts machinable features from any 5. 5. Discussions with an example ICES input file and is therefore CAD system indepen- dent. Although, solid modellers are finding wide usage Since there are other feature extractors reported in the there still exists a large group of users without access to literature it is instructive to compare them with the solid modellers and also users who have to deal with old IFEM. Grayer (1976) obtained NC tool paths from a drawing files for which ICES is the most desirable stored part representation for 2½ dimensional CAD data option. for pockets and holes. This program is specific to As an example ofIFEM, a prismatic part was designed BUILD, a solid modeller, and limited to pockets with with CADKEY and then processed through the ICES vertical walls and the specific feature type is not called translator. On the SUN workstation, the feature out. Kyprianou (1980) applied a 3-dimensional syntact extractor ( written in Lisp) was invoked from within the pattern-recognition scheme for the automatic classifi- Franz Lisp environment. The nine tasks were executed cation of generic depressions and protrusions within a automatically and the result was displayed on the screen. part. This program is also specific to BUILD. Armstrong Figure 4 shows the conceptual feature extraction for an et al. ( 1984) developed a system to generate NC tool example prismatic part containing six morphological fea- paths for a part created by the PADL-1 solid modeller tures, namely a rectangular slot, a rectangular pocket, and stored in BREP data format. Specific features are and four cylindrical holes. The features extracted are fea- not identified as such but tool paths are generated. tures that needs to be removed by machining to obtain Henderson (1984) used the production rule approach to the desired part. identify swept features from the solid modeller, ROMULUS, BREP database. Later Henderson (1986) used a bottom-up algorithm, constructing macro-features 6. Manufacturability analyser from small elements. Woo (1977) used a convex hull technique to represent the part geometry as a series The initial stages of the rapid prototyping cycle are the expansion of the object in terms of convex components most critical for cycle time reduction. The design Page 1167 Automated rapid prototyping: I-configuration 225 decisions made at this stage commits major resources for manufacturability analyser can reject any design which the remainder of the cycle. These initial design decisions cannot be manufactured with existing system hardware can be changed (if found necessary), with access to a suit- before the process planning begins. able manufacturability analyser, with least effort before In the following sections a brief description of the finalizing the design thereby resulting in a significantly manufacturability analyser is presented. Additional reduced cycle time and reduced product cost. It is details of the analyser can be found in Courtright ( 1989). reported in (Atkinson 1985) that reductions of up to 40 per cent can be realized in the product development time, when design for manufacturability is practised. 6.1. Manufacturability The purpose of the manufacturability analyser is to identify manufacturing and costs parameters and then to A general definition of manufacturability must con- develop a module which is compatible with the database sider parameters that affect all aspects of manufacturing structure of the FMC at the University of Maryland. which make a product competitive in the market place. With access to FMC' s global database of available To make the problem manageable the manufacturability cutting tools, material, and fixtures, the manufactur- analyser developed for the RPP focuses on one aspect of ability analyser can decompose the design, feature by manufacturing, namely design for manufacturability. feature, interface with the user areas of concern or Table 1 shows a manufacturability parameter matrix difficulties and offer information on correction. The for a general FMC. The columns of the matrix show the Table 1. Manufacturability Parameters for a general FMC. Information needed to check manufacturing constraints A design is manufacturable in Dim. tolerances an FMC with one CNC Thin wall Contours machine and one robot if it can bending Shapes Tool Weight be made: Finish Radii interference Outer size Material ( 1) within the specified drawing limits: Can the design use FMC's stock sizes? cutting tools? fixtures? software? CNC machine? robot? AGV? (2) within the lead time (3) within a minimum frequency What is the raw material supply? cycle time? tool wear? cell availability? yield? handling time? (4) within a maximum cost. Cost of raw material? cycle time? tool wear? yield rate? handling? pallet storage? human supervision? overhead? Page 1168 226 M. Anjanappa et al. characteristics of the machined part and the asterisks 6. 3. The analysis package show how the manufacturability parameters depend on the machined part. For example, as per requirement # 1, Among its many other functions RPP calls on two the available stock sizes must meet the drawing for the functions, viz., tolerance input and manufacturability part to be manufacturable in an FMC. It is necessary to analyser, to address manufacturability. know the part's outer dimensions and material so there In the conventional design environment the tolerance are asterisks in the weight/ outer size and material col- and material information are entered at the drafting umns. When determining whether a design 1s stage. For automated manufacturing in the RPP the machinable, some parameters may be considered imme- designer waits until the tolerance input program begins diately, while others need not be considered until after to process the feature file and then provides tolerance process plan is completed. For example, the parameters input. This logic is necessary because the tolerance infor- of requirement # 1 ( drawing limits) do not depend on the mation entered during the design stage is lost when the machining process, whereas the parameters of require- CAD database is processed through the IGES translator ment # 3 and # 4 ( cost and frequency) depend on the to create a design file in the standard neutral format. The process plan. tolerance input program which has been developed can accept the feature file and perform interactive input and output of tolerances and material information. Following 6. 2. Design for manufacturability the criterion of minimizing the overall cost of the part production, as discussed in the previous section, the program assigns default tolerance values in ANSI In Cook (1966) it is stated that 'producing satisfactory Y14.5-1982 format. These numbers, it must be noted, parts at the lowest possible cost can be called as the first are specific to the FMC used and must be re-evaluated law of production'. A manufacturability analysis must as the machines get older. Using a menu driven program consider all the parameters listed in Table 1 to minimize the user can either exit the program at this point (if the the cost of a part. The goal of the manufacturability default tolerances are satisfactory) or choose to change module is to let the designer know, immediately, whether the tolerances. A new file, feature plus tolerance file, is his design is manufacturable within the given FMC. The created as a result of using this module. module will also suggest ways in which the part may be The manufacturability analyser is nw entered and this made more producible in the given FMC. The cost of module reads the feature plus tolerance file previously manufacturing a part is discussed widely in the literature created. Then the analyser accesses the FMC's global (Dieter 1983, Gasson 1973, Boothroyd 1979). For database ( describing all the machining capabilities and example, the cost of manufacturing a part ( considering limitations of the FMC) and performs the manufactur- only the tolerance) can be written as, ability analysis using the following two objectives: :t ( 1) Selection of multiple tools-machine-fixture for each C= k; (1) i-1 tf feature. (2) Determination of an optimum tool-machine- where, t; is the tolerance of a critical dimension, n is the fixture for each feature. number of critical dimensions, and k; is the constant cor- The analyser achieves its objective using a two-stage responding to the generation of the ith dimension which logic approach. In the first stage it checks the manufac- depends on the man/machine used. The cost increases turability of the part and generates a list of possible parabolically with the decrease in tolerance. The module machines and tools that can be used to generate each used with RPP therefore, alerts the designer if the toler- feature, without considering the tolerance requirements. ances are too tight and cannot be made in normal The control flow chart is shown in Fig. 5. This stage con- operating conditions but require a slower and more con- siders form, profile, orientation, location and runout as trolled machining, thus increasing the cost of machining. given in ANSI Y14.5. The following issues, that are rel- When checking for manufacturability it is necessary to evant to manufacturing in the FMC environment, are recognize the distinction between the standards of considered: accuracy which it is possible to obtain and the standards of accuracy which it is economically acceptable to main- • stock size: availability, excessive machining tain. Hence, in this module, for milling operations in an ,. machines: limits of movements, accuracy FMC environment a nominal accuracy for normal " cutting tools: shape, size and geometry machining is chosen to be different from the nominal " tolerance: achievability, normal versus controlled accuracy for controlled machining. machining Page 1169 Automated rapid prototyping: I-configuration 227 ENTER Output from the tolerance input program Design name: mdemol FEATURE# PROFILE SURFACE FLATNESS/ DISPLAY DESIGN (mm) FINISH (µm) CIRCULARITY (mm) DETERMINE IF 1 0.762 1.52 0.013 COMPARE DESIGN FEATURES CAN BE WITH AVAILABLE MACHINED WITH TOOLS 2 0.762 2.54 0.381 STOCK MATERIAL ON THE CNC 3,4,5,6 0.D38 7.62 0.152 MAGAZINE 7 O.D38 7.62 0.152 DISPLAY RESULTS Output from the design for manufacturability analyzer DISPLAY RESULTS Design name: mdemol COMPARE DESIGN ANALYSIS RESULT SELECT-ION REMARKS TO CELL FIXTURES DETERMINE IF FEATURE TOLERANCES STOCK stock successful DISPLAY RESULTS CAN BE MET USING ANALYSIS #1 THE CELL CNC AND FIXTURE fixture lbut it requires part to be held along CUTTING TOOLS successful ANALYSIS #1 !broad side. COMPARE DESIGN MACHINE machine TO CNC TRAVEL successful ANALYSIS #'s 1,2 LIMITS AND STOCK DISPLAY RESULTS SIZE LIMITS TOOL unsucces- ANALYSIS sful <1{504,505,506,513,515}> <2{513}> DISPLAY WHETHER <0{502,507,508)}> <1{516}> <2{502,507,508}> DISPLAY RESULTS THE DESIGN IS <3,4,5,6{502,507,508}> <7{see note}> MANUFACTURABLE !'!QIE; #7(slot): no tools to make sharp corners-Increase orner radii. CREATE FILE OF ANALYSIS RESULTS TOLERA- unsucces~ <2{controlled,flat end mill,513,3.556, Kl.00018,1.27,1.27} > <3,4,5,6{controlled, Figure 5. Control flow chart of manufacturability analysis. klrill&reamer,508&518,1.27&1.524,0.00018&0.00028} > <7{no tolerance analysis}> At the end of the manufacturability tests, an ASCII file Figure 7. Summary of results. is generated listing the selected stock, machine tool, fix- ture, and a list of all features and the cutting tools where the user has designed a part, as shown in Fig. 6, capable of machining them. In addition, a separate list of using a commercial CAD system (CADKEY). The CAD the features with tight tolerances requiring specific tools database is then processed through the IG ES translator and their recommended cutting speeds, feeds and depths and then through IFEM. The result is the feature file. is generated. If the design is not manufacturable, infor- The user then calls the tolerance input program, and mation concerning the cause and possible solutions are then enters the manufacturability analyser. Figure 7 included. shows the summary of results obtained for the example part when the analysis was used to check manufacturabi- 6.4. An example lity with the specific FMC of the University of Maryland. The analyser program, written m C, runs on a Sun computer system. As an example, consider the case 7. Intelligent process planning FEATURE #1 SIDECLJT FEATURE AI techniques can be used to automate ( at least par- #2 CIR CUL AR POCKET tially) several of the reasoning activities involved with process planning. One example of this is the semi- FEATURE intelligent process selector (SIPS), which uses AI tech- #4 HOLE niques for generative selection of machining operations for the creation of metal parts (Ide J ,;s 7, N i r;g7, and Nau et al. 1986). SIPS (written in LISP) considers a part to be a collection of machinable features and for each feature it generates a sequence of machining steps to use in creating that feature. It does this by reasoning about the intrinsic capabilities of each manufacturing oper- FEATURE ation. Process selection by SIPS duplicates both the #7 SLOT high-level process selections done by a human process Figure 6. Example part for nfanufacturability analysis. planner (e.g. mill this face) and the lower-level process Page 1170 228 M. Anjanappa et al. selection done by the human NC programmer (e.g. each feature, the first plan SIPS fmds for creating that rough-end-mill this face). feature is guaranteed to be the least costly one. SIPS uses a new approach to knowledge represen- To do tool selection SIPS considers a sequence of three tation, hierarchical knowledge clustering, in which the specific tasks, viz., determining what type or family problem-solving knowledge is organized in a taxonomic cutting tools can successfully manufacture the part, hierarchy. Each node in the hierarchy is represented by determining a proper tool size to fit the constraints of the a frame. SIPS contains three such hierarchies: one for feature, and determining the tool material that can best machinable features, one for machining processes, and produce the required finish. one for cutting tools. For example, Fig. 8 shows the Given a specific machining process, the scope of tool names of some of the frames in SIP' s hierarchy of selection is limited to identifying the best tool material to machining processes, as printed out by SIPS graphic use for the process. The approach does not satisfy all interface. Stored in each frame is detailed information aspects of tool selection but it does provide an initial about the machining process it represents, including approach to the problem, and this will lead to more effec- information on what kinds of machinable features the tive use and selection of cutting tool materials with future process can create, what the best machining tolerances work. are that it can satisfy, what kinds of machinable features The knowledge representation scheme in SIPS pro- must already be present in order to perform this process, vides a natural way to represent, organize, and manipu- what the process costs, etc. late knowledge about machinable features, machining In SIPS, a component part is represented as a collec- processes, and cutting tools. In a general sense, it is tion of machinable features, each of which is an instanti- similar to the reasoning process that a human process ation of one of the frames in the feature hierarchy. SIPS planner goes through every time a part is considered for creates plans for each of these features independently. planning. One significant problem with this approach is feature SIPS currently runs on symbolic lisp machines, Texas interaction. For example, it may be easy to create a hole Instruments Explorers in Zeta Lisp, and on Sun work- in a flat surface if the surface is unobstructed, but the stations and Silicon Graphics Iris workstations in Franz same task may be impossible if some other part of the Lisp. At present SIPS knowledge base consists of more workpiece interferes with the tool trajectory. To handle than 990 frames describing machinable features, problems such as this, an interface has been created machining processes, and cutting tools. The knowledge between SIPS and the PADL solid modeller. Before base is set up primarily to work on prismatic parts having attempting to create a plan for a feature, SIPS queries machinable features such as holes, pockets, and slots: but PADL to see if various global geometric constraints are is being extended to deal with lathe-turned parts as well. satisfied. If these constraints are satisfied, SIPS proceeds Most approaches to the integration of solid modelling to create a plan for the feature. with automated process planning have essentially SIPS considers each feature as a goal to be achieved, involved using the modeller as a front end to the process and decides how to achieve this goal by surveying back- system, by taking machinable features from the modeller wards to develop a sequence of machining operations and sending them to the planning system, which then capable of achieving the goal. The search is done by reasons about these features without further interactions using a 'best-first branch and bound' procedure. For with the solid modeller. In order to generate correct process plans for complex objects, this approach is not sufficient. For producing correct process plans for complex objects, it is necessary for the process planning COUNTERBDRING system to interact extensively with the solid modeller HOLE-FEATURE-PROCESS while the process planning is going on. For this reason, COUNTERSINKING additional work is underway on making SIPS efficient to PROCESS answer queries and make incremental changes between the modeller and process planner. To satisfy this, a new feature extraction scheme is also under development. HOLE- IMPROVE-PROCESS 8. Accuracy enhancement To achieve the benefits of automation for rapid proto- Figure 8. Example frames used m SIP's hierarchy of typing it is necessary to ensure that part tolerances and machining process. surface finish are produced within acceptable limits. This Page 1171 Automated rapid prototyping: I-configuration 229 requires that the machine tool be properly maintained Cy (y) = Roll of cross slide and compensated for wear. Wear compensation can be Cy ( x) = Pitch of table achieved by controlling the tool path either by pre- ex(Y) = Pitch of cross slide calibrated compensation of the machine tool or by active ez(x) = Yaw of table on-line correction of the machine tool during the cutting Cz(Y) = Yaw of cross slide process. C\'.x = Squareness of Z E YZ plane Tool path error can be defined as the position vector C\'.y = Squareness of Z E ZX plane difference between the programmed path and the actual C\'.z = Squareness of Y E XY plane path of the tool relative to the workpiece. It is given by: Equation 3 assumes that the CNC machine tool table C('X, Y, Z) = (xA - X)z+ (yA - Y)/+ (zA - Z)k (2) translates along x-axis, the cross-slide translates along y-axis, and the spindle head translates along the z-axis. where, (xA,YA, ZA) are Cartesian coordinates of the actual A careful inspection of equation (3) reveals that there are tool tip and ( X, Y, Z) are the coordinates of the pro- 18 individual error terms that must be specified to obtain grammed tool tip relative to the workpiece. Tool path the tool path error at any point in space (X, Y, Z) inside errors are classified as cutting force independent errors the working volume. A methodology by which these and cutting force dependent errors. Although both these errors can be measured and mapped to generate a soft- errors are equally important, only the cutting force inde- ware 'error map' ( over the entire working volume) has pendent errors are currently corrected in the FMC. The been reported before (Anjanappa et al. 1988). Once this work being conducted at the University of Maryland rep- error -map is created, the actual position vector of tool resents a comprehensive tool path error correction tip P( XA ,YA ,zA), can be found using the following scheme for a vertical machining centre. The reader is equation: referred to Anjanappa (1986) for detailed information on tool path errors. P(xA,YA,ZA) = P(X, Y,Z) + f(X, Y,Z) (4) The cutting force independent errors occur in conven- where, P-(X, Y,Z) is the position vector of programmed tional machines due to environmental conditions and tool tip and f(X, Y,Z) is the tool path error at (X, Y,Z) normal usage. These errors include errors due to weight location which is obtained a priori and stored in the form deformation, thermal deformation and positional inac- of an error map. It should be noted that the error map curacies. These errors are static and dynamic determin- defining e must be regenerated whenever a significant istic in nature and are repeatable. For a three axis, change in environment or machine tool wear occurs. flat-bed, CNC vertical machining centre, deterministic The accuracy enhancement package (written in Basic) tool path error e can be represented in terms of geometry shown in Fig. 9 automatically corrects the tool path of links and joints. Following the methodology of error. The NC codes before being downloaded to the Anjanappa et al. (1988), the equation (2) can be CNC machine controller are intercepted and processed expanded as: through this package. The package, using a stored error map of the machine tool, compensates the NC position - Ox(x)- Ox(y) + Ox(z) + C\'.zY + C\'.yZ codes to include tool path errors and then it transmits the x Y[ez(x) + ez(y)] - Z[ex(y) + ey(x)] - Oy(x)- Oy(y) + Oy(z) + C\'.xZ + Z[ex(x) f(X, Y, Z) = + ex(y)] -Xez(x) NC CODES - Oz(x)- Oz(Y) + Oz(z) ( M&G l - Y[ex(x) + ex(y)] + Xey(x) (3) ACCURACY ENHANCEMENT~ PATH '----..... where, I ACCURACY ERROR :/coNVENTIDNAL Ox( x) = X-axis scale deviation MAP ENHANCEMENT PATH PACKAGE Oy (y) = Y-axis scale deviation Oz(z) = Z-axis scale deviation Oy ( x) = Y straightness of X-axis Oz( x) = Z straightness of X-axis [NC Ox(Y) = X straightness of Y-axis CONTROLLER Oz (y) = Z straightness of Y-axis ACCURACY Ox(z) = X straightness of Z-axis ENHANCED Oy(z) = Y straightness PART ex( x) = Roll of table Figure 9. Schematics of accuracy enhancement package. Page 1172 230 M. Anjanappa et al. compensated codes to the CNC controller. The machine interferometry system can be distributed if it is used on now accepts the compensated NC code and executes the more than one machining centre and the recurring cost slide motions resulting in enhanced accuracy of the of generating error map can be minimized by automating machined component. The compensation of NC codes is the process (e.g. using a PC-based control computer). transparent to the user. There are several other techniques used by various investigators to minimize the tool path error. For 9. Conclusions example, Tlusty ( 1971) uses a semi-automatic master part to measure errors. Dufour and Groppetti ( 1980) use A rapid prototyping protocol (RPP) has been devel- an error matrix coordinate corrections to improve the oped for automated rapid prototyping of a designer's accuracy of large NC machine tools. Zhang et al. (1985) component in the machining cell at the University of used a similar approach to improve accuracy of coor- Maryland. The protocol creates an environment where dinate measurement machines at the National Institute the design engineer becomes involved in the manufac- of Standards and Technology. In all of the above work, turing process of the component being developed. The the effect of feedrate was removed by measuring errors at designer is aided by several software tools with emphasis low feedrates in order to remove the dynamic effects. The on heuristic and intelligence. The feature-based design error map for RPP, however, does include the effect of system, intelligent feature extractor, manufacturability feedrate an effect which was observed to be significant. analyser, accuracy enhancement package, and intelligent The effect of feedrate is especially important in future process planning are some of the aids that were devel- machining as high feedrate machines are being devel- oped and tested successfully in the RPP. The integration oped to improve material removal rates. of these aids into the RPP, and the implementation of the To validate the compensation algorithm, a sample part RPP, is detailed in Part two of this paper. was designed with a geometry that required cutting using Although the RPP has been developed in a machining linear, linear interpolated, and circular interpolated application, the overall concept and module integration motions. To begin with, the sample part was machined is equally applicable to other areas such as flexible auto- by downloading the M and G codes directly into a mation for printed circuit board assembly or flexible Matsuura CNC machining centre. Later, the same part automatic mechanical assembly. was machined by processing the M and G codes through the accuracy enhancement package and downloading the compensated M and G codes to the same machining Acknowledgement centre. The two parts were then inspected on a Mitutoyo coordinate measurement machine. The results showed The authors would like to acknowledge the contri- an improvement of 6-fold on the arc dimensions and bution to this work by Dr B. J. Kumar, S. Chen, and 3-fold on the linear dimensions for the compensated part. M. J. Courtright. This work was supported, in part, by In other words, the part cut with compensated M and G the Engineering Research Center, The Systems Research codes showed less deviation from the nominal dimensions Center, The National Science Foundation and The compared to the part cut from uncompensated codes. National Institute of Standards and Technology. The improvement was more pronounced for dimensions generated by circular interpolation. Accuracy enhancement method is a cost-effective References method in maintaining the machining process under a tight tolerance band thereby assuring the quality of parts ANAND, D. K., KIRK, j. A., ANJANAPPA, M., and PECHT, being machined. However, there are two additional costs M. G., 1984, Supercomputers and hierarchical control: a incurred via this method of accuracy enhancement. The view point. Proceedings of the NSF Study on Supercomputers in capital cost of a laser interferometry system which is Mechanical System Research, Lawrence Livermore Laboratory, required to calibrate the errors of the machine tool and September, Livermore, CA. ANA:sJD, D. K., 1986, Research in flexible manufacturing. periodic recurring cost of generating the error map and Second Annual SRC Conference, September, College Park. maintaining the accuracy enhancement package. Given A:sJA:sJD, D. K., KIRK, J. A., ANJANAPPA, M., 1987, Tool these costs this method can still be cost-effective com- path error control of end milling of microwave guides. Pro- pared to purchasing a more expensive accurate ceedings of 7th World Congress on the Theory of Machines and machining centre to begin with. The added advantage of Mechanisms, 3, pp. 1499-1502, September, Sevilla, Spain. ANAND, D. K., KIRK, j. A., ANJANAPPA, M., MAGRAB, E. the accuracy enhancement method is that it allows an and NAU, D. S., 1988, Protocol for flexible manufacturing older machine with spare capacity to be used instead of automation with heuristics and intelligence. Proceedings of the buying a new machine. Further, the cost of the laser MI-88, pp. 209-217, ASME, May, Atlanta, GA. Page 1173 Automated rapid prototyping: I-configuration 231 ANJANAPPA, M., 1986, Error minimization in machining. tocol. Proceedings of the 2nd IASTED International Conference, Ph.D. Dissertation, University of Maryland. pp. 71- 75, December, Los Angeles, CA. ANJANAPPA, M., KIRK, J. A., ANAND, D. K., and SHYAM, KRAMER, T. R., and JUN, J., 1986, Software for an auto- S., 1988, Error correction methodologies and control strate- mated machining workstation. Proceedings of the 3rd Biennial gies for numerical controlled machining. Control Methods for International Machine Tool Technical Conference, September. 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Thesis, University of Manufacturing, ASME DED 21, 101-116. Maryland, College Park. NAU, D. S., 1987, Hierarchical abstraction for process plan- DIETER, G. E., 1983, Engineering Design: A Materials and ning. Proceedings of Second International Conference Applz'calions of Processing Approach (McGraw-Hill, New York). Artificial Intell(gence in Engineering, June. DIXON, J. R., 1986, Artificial intelligence and design: a mech- NAU, D. S., GRAY, M., 1986, SIPS: an application of hin- anical engineering view. Proceedings of the 8th North American archical knowledge clustering to process planning. Proceed- Association for Artificial Intelligence Conference, Boston, ings, Symposium on Integrated and Intelligent Manufacturing, Massachusetts, pp. 872-877, August. ASME Winter Annual Meeting, Anaheim, CA. DUFOUR, P., and GROPPETTI, R., 1980, Computer aided pp. 219-225. accuracy improvements in large NC machine tools. Proceed- RICKERT, Jr., W. K., 1987, The use of IGES in automated ings of 21st MTDR Conference, Manchester, UK, pp. 611-618. CNC machining. M.S. Thesis, Mechanical Engineering. FRANCIS, P. H., 1986, Toward a science of manufacturing. College Park, University of Maryland, February. Mechanical Engineering, 108 (5), 32-37. SMITH, B., and WELLINGTON, J., 1986, Initial Graphics GASSON, P., 1973, Theory of Design (Harper & Row publishers, Exchange Specifications (IGES), Version 3.0, Report No. Inc.). NBSIR 86-3329, National Bureau of Standards, GERSHWIN, S. B., 1984, A central perspective on recent trends Gaithersberg, Maryland. in manufacturing systems. Conference on Decision and Control, TLUSTY, J., 1971, Techniques for testing accuracy of NC December, Las Vegas, Nevada. machine tools. Proceedings of 12th-t1vfTDR C011/ire11((', GRAYER, A. R., 1976, The automatic production of machined Manchester, UK, pp. 333-345. components starting from a stored geometric description. UNGER, and RAY, S., 1988, Feature based process planning at Programming Languages for Machine Tools 1976 Proceedings, the AMRF. ASME Computers in Engineering Conference, San North Holland. Francisco, California, August. HENDERSON, M. R., 1984 Extraction of feature information VAGHUL, M., DIXON, J. R., and SINS\lEISTER, G. E., 1985, from three dimensional CAD data. Ph.D. Theses, Purdue Expert system in a CAD environment: injection molding part University. design as an example. Proceedings ofASME Computers in Engin- HENDERSON, M. R., 1986, Automated group technology part eering Conference, Boston, Massachusetts, August. coding from a three dimensional CAD database. ASME UPPAL, R., 1987, Flexible manufacturing protocol driver for Winier Annual Meeting, Anaheim, California, pp. 1221- 232. vertical machining center. M.S. Thesis, Universitv of HIRSCHTICK, J. K. and GOSSARD, D. C., 1986, Geometric Maryland, August. · reasoning for design advisory systems. ASME Computers in Woo, T. C. 1977, Feature extraction by volume decompo- Engineering Conference, Chicago, pp. 263-270. sition. Proceedings of the Conference on CAD/ CAM in Mechanical IDE, N. C., 1987, Integration of process planning and solid Engineering, MIT, Cambridge, Massachusetts, March 26. modeling through design by features. Masters Thesis, Com- ZHANG, G., VEALE, R., CHARLTON, T., BORCHARDT, B., puter Science Department, University of Maryland. and HOCK EN, R., 1985, Error compensation of coordinate KIRK, J. A., ANAND, D. K., ANJANAPPA, M., and UPl'AL, measuring machines. Annals of CIRP, 34. R., 1986, Implementation of a flexible manufacturing pro- Page 1174 l'.\T J. CO:V!PL;TER 1/\TEGRATED MANUFACTURING, 1991, VOL. 4, NO. 4, 232-240 Automated rapid prototyping with heuristics and intelligence: Part II-implementation J, A. KIRK, D. K. ANAND and M. ANJANAPPA t Abstract. This paper deals with the integration of several USER design and manufacturing software modules implemented as the rapid prototyping protocol (RPP) for automated rapid pro- totyping of prismatic parts. A machining cell is defined and the COMMERCIAL CAD FEATURE BASED [SOLID MODELER l CAO cell control structure for rapid prototyping of quick design changes is developed. The software module input/output drawing file (D formats and their interfacing issues are discussed. An example of how the RPP works with a machining cell is included. The successful demonstration of the protocol documents the smooth information flow through the control structure. It also demon- USER strates that, with suitable heuristic and intelligence tools, the [TOL MATL.l user can design and manufacture a component in one inte- file grated session. ORDERED PROCESS INTELLIGENT PLANNER PROCESS PLANNER 1. Introduction HUMAN FIXTURING COMPUTER ASSISTED DECISION FIXTURING Frequently, it is imperative to 'shorten' the time needed from 'concept to product' (i.e. cycle time) to make the product a success. A major portion of this cycle time is consumed by the iterative process of design-pro- totype-redesign with incremental modification for each iteration. Customarily the iteration stops when the proto- type satisfies the design goals. Hence, one of the major goals of' today's manufacturing systems is to obtain automated rapid prototype production of a designer's component. Figure I. Rapid prototyping protocol (RPP). A rapid prototyping protocol (RPP), as shown in Fig. 1, is configured for automated rapid prototyping of a designer's component in a machining cell at the Uni- based design system, intelligent feature extractor, versity of Maryland (see Part I of this paper). The manufacturability analyser, intelligent process planning, purpose of developing RPP is to provide a shell in which and accuracy enhancement package are some of the aids an engineer designs a component ( at the top of the flow that are developed and used in the RPP. chart) and then has the component manufactured (at the The class of components under consideration are bottom of the flow chart). He is aided by several tools prismatic parts in which the raw material starts out as with emphasis on heuristic and intelligence. Feature- solid rectangular raw stock and the designer's component is produced by machining operations which subtract fea- Authors: J. A. Kirk, D. K. Anand and M. Anjanappa. Department of tures from the raw stock, thereby producing the desired Mechanical Engineering and The Systems Research Center, University component. This paper, Part II of two parts, deals with of Maryland-UMCP, College Park, MD 20742; tDepartment of Mechanical Engineering, University of Maryland-UMBC, the integration issues of the RPP, particularly its cell Baltimore. MD 21228. control structure and the implementation. O!l'., I· I 1l2X/ 1l I $'.l.110 (i) I 1111I T;iylor & Francis l.td. Page 1175 Automated rapid prototyping: II-implementation 233 2. The rapid prototyping protocol the manufacturing processes include transportation of the raw material into the cell with an AGV, transferring Although the focus of this paper is the integration and the material from AGV to the machining centre, implementation of RPP it is worthwhile to give a brief unloading the finished part from the machining centre to overview as to its operation. the AGV, and transferring the finished part out of the At the top of the flow chart (see Fig. 1), the user can cell using the AGV. design components by two different approaches. In the first approach a commercial CAD system, such as CADKEY and ANVIL, is used to create the design and 2. 1 . Standardization and flexibility store the design in an initial graphics exchange specifica- tion (IGES) format (file 2 in Fig. 1). This file (Smith et The RPP can operate efficiently if a high degree of al. 1986) is then processed through the feature extractor standardization exists throughout the system. Notice in which decomposes the IGES file into a collection of fea- Fig. 1 that seven different types of files exist at different tures such as pockets, slots, holes, etc. As output the stages. One of the important aspects of the RPP is that feature extractor creates the feature file (file 3 in Fig. 1 ). standardization of data files is introduced in four of these In the second (alternative) approach the component is seven file types. They are #2-IGES file, #3-feature designed by using a special feature based design system, file, #5-process plan file, and #6-M & G code file, VWS (Kramer et al. 1986). In this path the feature file and are described below. ( file 3 in Fig. 1) is created directly. The IGES file of the RPP is consistent with IGES The feature file is then fed to the manufacturability Version 3.0 which specifies ftle structure format, a analyser (Courtright 1989). Prior to manufacturability language format, the representation of geometric, topo- analysis, the software assigns default tolerance values for logical, and non-geometric product defmition data. each feature, and the user then has the option to edit the Although IGES has addressed the need for data tolerance if necessary. Then, the analysis is done with exchange, it cannot handle tolerances, materials and access to a global database describing all the machining surface finish information. The part model format capabilities and limitations of the machining cell. Each (PMF), used by the National Institute of Standards and portion of the analysis corresponds to one of the par- Technology (NIST) to transfer part information in their ameters affecting manufacturability (i.e. form, profile, vertical workstation, was chosen as the standard for the orientation, location and runout as given in ANSI feature file in the RPP. It deals only with machinable Y 14. 5). For each of these portions, the program displays parts, and it supports only a boundary representation warnings and suggested improvements in the design solid modeller. before continuing. Part I gives the details of the analysis The process plan file describes the manufacturing methodology. At the end the manufacturability analyser activities to be carried out at the system level and cell creates an ASCII output file and a 'feature plus toler- level to accomplish the manufacturing tasks. Although ance' file (file 4 in Fig. 1) . there is no standard in the process plan file format, the There are two parallel paths that can be followed in process plan format, used by NIST, is selected to be the producing the process plan. On the left side is the process plan file format for this work. The process plan ordered process plan which uses a well established file format will be discussed in depth in later sections. approach of user interaction. The intelligent process M & G Codes, as specified in EIA RS-274D, are the planner, on the other hand takes the feature file as the standard for cutting codes for all CNC machines and this input and outlines the required machining processes standard was chosen for the RPP. automatically. This is discussed in more depth in Nau et al. (1986). Following either path, a CAM database is generated for CNC machining. The CAM database is 3. Control structure complete once the fixturing information is included. As of now the computer-assisted fixturing is unavailable. The RPP for rapid prototyping can be represented by Human intervention is required to take fixturing two different blocks as shown in Fig. 2. The top block decisions. This CAM database is then processed through represents the rapid prototyping protocol for design a pre-processor to generate EIA RS 244 standard M & (RPP/D) where all the required manufacturing related G codes. A post-processor then translates this into the data, such as feature file, process plan file, and NC code machine specific codes. file for a particular part are prepared. The lower block is Based on the process plan generated by the process the rapid prototyping protocol for manufacturing planner, the cell host will coordinate the activities on the (RPP/M) where the manufacturing processes take place, shop floor to machine the 'part. Tasks involved during such as transportation, loading/unloading, and Page 1176 234 j. A. Kirk et al. USER Ce I I Boundary RPP/0 ( PART DESIGN) CAD FEA TLJRE EXTRACTION MANUFACTLJRABIL JTY MACHINING CENTER PROCESS PLANNING NC CODE GENERATION ACCURACY ENHANCEMENT RPP/M Row Mater, o I In (MANUFACTURING) • CELL CONTROL USER PART Figure 4. Schematic diagram of the cell. Figure 2. Functional block diagram of RPP. cell facility either by the direct link or by usmg the machining of the part. Both blocks, taken together, form RPP/D and RPP/M for rapid prototyping. At the top level of the RPP hierarchy ( see Fig. 3) is a the RPP. system manager that manages the cell level components The philosophy and operation of the RPP/D has been for multiple cells and distributes and schedules the pro- reported in Part I of this paper. The link between the duction tasks. The cell hosts reside at the second level of RPP/D and RPP/M, as well as the structure of the the hierarchy and an equipment controller is placed RPP/M remains unexplored and is addressed in this paper. Specifically the cell attributes, the cell configur- between each cell host and the shop floor components. Notice that the AGV control module is at the same level ation and system hierarchy, the cell capability and user as cell host in order to serve as a material transportation environment will be discussed. cell delivering parts between several cells. The relation- For high flexibility the cell and its components must be ship between modules is a master-slave relationship. No modular and fit into a structured hierarchy. Based on the direct handshaking is allowed between any two modules concept of modularity and hierarchical control (Cutkosky at the same level of hierarchy. The information path et al. 1983, Hammer 1987, Ono 1987, Weck et al. 1987, between modules at the same level is controlled and and McLean 1986) for rapid prototyping, the system configuration of the RPP/M is defined as shown in handled by a module at a higher level, as shown in Fig. 3. Fig. 3. The machining cell at the University of The machining cell is designed for automated Maryland, is configured around a robot; an AGV and a machining centre are available as shown in Fig. 4. Other machining subject to the following limitations: cell components include a gripper and vice that work e The cell will handle prismatic blanks. together with the robot arm and machining centre, • Tools are limited to those loaded in the tool maga- respectively. The dashed line in Fig. 4 represents a cell boundary, with the AGV travelling through the cell zine. e The cell will machine without fixture intercepts. boundary and delivering the part. The user accesses the e Equipment status is always known. 9 There is one part for each AGV run. The RPP for rapid prototyping is designed to be a multi- user system, and can be accessed from either the system CELL #2 AGV workstation or a remote PC as a terminal. For each level CELL HOST of cell hierarchy, there is a manual mode, auto mode, and help mode. With the manual mode, the user is able to access the status of components in the next lower level of hierarchy as well as control these components. When in auto mode, control is returned to the uppermost hierarchy. These modes will help the user in setting up GRIPPER VMC VISE ROBOT the cell, controlling individual components, diagnosing Figure 3. System configuration. the cell, and recovery from failures. Page 1177 Automated rapid prototyping: II-implementation 235 Since the intelligent vice, gripper, and AGV were not us available at the current stage of development of the Uni- versity of Maryland cell, these components are simulated -U-TI-L-IT-IE-S- - FMP/0 11 11 thereby providing a complete experimental platform to , , CAO , , validate the RPP behaviour. In operation the computer :,:· FIXTURING :,:, takes in command from the parent module of the compo- : :- MANUFACT- : : nent and shows it on a CRT screen. A human reads the : : . URABILITY : : command from the screen, executes it, and responds to : : PROCESS : : I I PLANNING I I ~------- _______ JL _______ 1~----- the PC with the current status of the component or the status of execution. The PC then converts the status into a specific format and returns the information to the com- Figure 6. User interface shell (UIS). manding module as a handshaking signal. controls, and monitors all of the cells and its logical oper- ation flow chart is shown in Fig. 7. SCP will accept 3. 1 . Software structure system level process plans as input in the automatic mode. It will also accept system level work elements (e.g. The software structures of the RPP are defined in command AGV to go to a target location) in manual Fig. 5. Functions performed by each module are mode. Only one SCP can run at a time. The cell control described in the following paragraphs. program (CCP) module will accept and execute the cell The user interface shell (UIS) module is the program through which multiple users can access the utilities of the system. UIS, shown in Fig. 6, provides optional entries in the RPP/D for the user to select from. It is also the program through which the user can enter the system control program (SCP) of RPP/M in order to carry out the manufacturing tasks. The system control program (SCP) module manages, ENGAGE WITH REQUIRED COMPONENTS T UIS User Interface System Shell computer I SCP System Control Program I D CCP Cell 12 Cell Cell II AGV Control host controller PAUSE FOR Program simulation WARNING ANO CHECKING l ECP Equipment Equipment Control controller Program ! j t I t I I Gripper Vise Robot VMC controller controller controller controller simulation simulation simulation simulatior I I 1 I ( Human D VMC I Figure 5. Software structure. Figure 7. System control program (SCP). Page 1178 236 J. A. Kirk et al. USER C User ) -------------T------------sU N UIS User Interface System Shell computer I SCP System Control Program f • C CCP AGV Cell #2 Cell Cell #I controller Control host simulation Program L 1---·-r---~ I ECP I IP .JI(! SYS/Pl I Equipment I Equipment I Control 1co ntroller I Program I I I Figure 8. Cell control program (CCP). Figure 10. Hardware map. level process plan. CCP, shown in Fig. 8, first decom- poses the process plan into a collection of cell level com- mands, relays these commands one at a time to the equipment controller and assures that the status of the command is in the proper sequence. CCP also accepts cell level command in the manual mode. The major responsibility of the equipment control program (ECP) module is to accept cell level commands issued from cell host and execute those commands on the appropriate piece of equipment (see Fig. 9). All the software modules inside the cell boundary have been developed and implemented (Anand et al. 1988). Interfaces for each module are discussed in later sections. The hardware available for this work is mapped on to software as shown in Fig. 10. 3.2. RPP/D-RPP/M interface issues RECEIVE RELAY STATUS The SCP needs a driver which defines the sequence and procedures to be carried out to accomplish the manufacturing task. This includes the control of system RESPONSE TO CCP level components, such as control of AGV to travel through cell boundary and control of cell components, Figure 9. Equipment control program (ECP). such as the vice, gripper, robot, and machining centre, Page 1179 Automated rapid prototyping: II-implementation 237 which cannot be seen by SCP. The SCP also needs the NC codes for the specific machining tool to cut the part. The process plan file in RPP should provide the former information while the post-processor provides the NC code file. The information required for the SCP is thus defined as the process plan files and the NC code file. There are two types of process plan files: the system Cell #2 CCP ACY level process plan files (PP-SCP), which are used to drive the SCP, and the cell level process plan files (PP-CCP), -1l which are used to drive the cell host (CCP). Each manu- ~ Ii' ~ ,~,, facturing task of a particular design consists of a SCP NC code data process plan file and one or more CCP process plan files generated by the processor planner in RPP/D. The ECP relationship between PP-SCP and PP-CCP 1s a master- slave relationship. The general structure of a process plan file consists of four different sections: the header section, the parameters Gripper section, the requirements section, and the procedure sec- controller tion. The header section defines the general information about the file such as the plan ID, plan version, plan type, and plan name. The parameters section declares Human parameters which are defined at run time. The require- ment section declares required process plan files and Figure 11. Software 1/0 types. hardware components. The procedure section describes the procedure for accomplishing the given task. The data type of information. Each data type has its own PP-CCP procedure section consists of cell level work natural format that cannot be changed. elements which will be decomposed into cell level com- The fundamental I/0 format consists of 64 characters, mands by the cell host. The work element is defmed as as shown in Fig. 12. Based on this fundamental format, the lowest level of manufacturing commands that are rec- we first define the cell level command format. Every work ognized by the process planner. element in PP-CCP is a task to be completed by one or more cell components. This implies that the large field can be filled in with one of the four components-vice, 3. 3. Software If O types gripper, robot, and vertical machining centre (VMC). The parameter field is divided into 3 sub-fields with 15 The software input/output (I/0) types between digits for each sub-field. The parameter can be the con- various software modules is shown in Fig. 11. I/0 of tents of the command, numerical values that shows the each software module in RPP/M is classified according to target point to be reached, or just blanks. three major types of information: request type, status Another type of information that needs to be formatted type, and NC code data type. The request type of infor- in the lowest level of hierarchy is the status type. Simi- mation encompasses all the requests that need hardware larly, the format described previously for cell level com- service. Status type of information covers all the status mands can be applied to the status type of information. reports as the result of status requests. NC code data type For the link between CCP and ECP, the format for includes all the files that are to be used in the manufac- request type and status type are exactly the same as those turing processes such as PP-SCP, PP-CCP, and NC code at the lowest level, respectively, except there is one more file. target (ECP) for both. The format for the link between The communication between CCP and SCP is done SCP and CCP is also similar to that discussed previously. through the use of a mailbox. This increases the flexibility of the cell so that in case the SCP is idle or down, the cell 0 23 4 1112 1718 utility is still available for some other system. All soft- I 11 ware modules are activated by request type of infor- Il l Lf orget fie Id LS tatus fie Id J • mation. Because this is a closed loop system, every Space Paraneters fie Id lnfornat ia n type request type of I/0 will be associated with a status type End af nessage I EDM I character of I/0. To simplify the complexity and increase the flex- ibility of the system, the I/0 format is unified except for Figure 12. Fundamental I/0 format. Page 1180 238 ]. A. Kirk et al. 4. Implementation (steplist samplel (features (features 4.1. Design (5 feature_ type pocket_center center_X 76.2mm In our environment, the user creates his design using center_Y 15.87499746 mm either a commercial CAD tool (ANVIL or CADKEY) or length 38.1 mm a feature based design system (VWS). For the example width 19.05 mm depth 6.35 mm part, shown in Fig. 13, CADKEY was used to sketch the corner_ radius 5.08 mm) design and then generate an IGES file. Commercial header (header CAD systems typically use wireframe representations of design_ID samplel part geometry and have IGES translators. material aluminum 6065 The IGES block_size file is then stripped of extraneous data and (block_ size length 152.4 mm is reduced to a form which has the minimum data width 76.2 mm necessary to defme the part. This file represents a height 25.4 mm) description sample!))) compact listing of all the features which are required to produce the part (Rickert 1987). Figure 14. Excerpts from feature file. FEATURE #2 necessary modules become available to generate the (HOLE) FEATURE #5 ( POCKET l appropriate process plans and the NC codes. FEATURE # 1 FEATURE #5 ( HOLE l ( SLOT l FEATURE #3 (HOLE) 4.3. Manufacturability At first the feature file was processed through the toler- ance input program which assigned the default tolerance for each feature ar;id prompted the user to edit the toler- ance if necessary. A new file feature plus tolerance file was created at the end of this session. The manufactur- ability analyser is entered now to check for manufactur- FEATURE #4 ( HOLE l ability of the example part with access to the global data base file of the existing machining cell. The manufactur- Figure 13. Example part. ability analyser found the part was manufacturable but suggested that one dimension of the pocket need to be 4. 2. Feature extraction Output from the tolerance input program The compact IGES file is then processed through the Design name: samplel feature extractor which decomposes the data into a col- FEATURE# PROFILE SURFACE FLATNESS/ (mm) FINISH (µm) CIRCULARITY (mm) lection of machinable features such as pockets, slots, ... ... ... .. . holes, etc. The feature extractor software is executed in 5 0.762 2.54 0.381 the Franz Lisp environment on a SUN microcomputer. Output from the design for manufacturability analyzer After the individual features are identified by the feature Design name: sample! extractor a feature file is created. Two types of files are ANALYSIS RESULT SELECT-ION REMARKS typically generated, viz, .pd format files and .pmf format i:OCK stock successful ALYSIS #1 files. The .pd file is generated for a single face at a time FIXTURE fixture lbut it requires part to be held along and contains the feature parameters for that face. In successful ANALYSIS #1 [broad side. order to create this file, the feature extractor first groups MACHINE machine successful ANALYSIS #'s 1,2 the individual features according to the faces that they lie TOOL successful on. The .pmf file represents the features in three dimen- ANALYSIS < ... > <5{513}> sions and only one such file is generated for the complete TOLERA- successful feature of .pmf feature file. < ... > <5{controlled,flat end mill,513,3.556,0.00018, 1.27,1.27}> The feature extractor is also able to recognize more complicated 3-D shapes which may be machined after the Figure 15. Excerpts from manufacturability output file. Page 1181 Automated rapid prototyping: II-implementation 239 machined under controlled machining condition to main- The SCP executes the instructions contained within this tain the design tolerance. The output of the tolerance file. Essentially, that would include asking the AGV to program and the manufacturability analyser is shown in deliver a blank into a specific cell, and, upon delivery, Fig. 15. For brevity, only the output pertaining to the issue a process plan file to the cell host. The process plan pocket feature is shown. incorporates information regarding the name of the NC code file. The cell host decomposes the work elements contained within this file into cell level commands. These 4. 4. Process planning are communicated to the ECP (using a specific type of handshaking arrangement). Individual actions like In the current version of the machining cell, the downloading the NC code, unloading the part would process planner and the NC code generator modules are result from the execution of such cell level commands. present within one computer program called VWS which resides on the SUN microcomputer. The VWS program (an acronym for vertical work station) is a modified 4. 7. Machining with accuracy enhancement version of a similar named program developed at the National Institute of Standards and Technology Before the NC codes are downloaded to the CNC (McLean 1986). Because this model is interactive in machine controller they are processed through the nature, it is possible to enter its environment and execute accuracy enhancement package (see Part I of this paper). the individual components separately. In order to process This package modifies the NC codes using a software a features file created by the feature extractor, the user error map of the machine in order to compensate for first executes the process planner module. known deterministic errors present in the machine. Fol- lowing the above steps the sample part was successfully machined. 4. 5. CAM database During the manufacturing process, the computers interact with each other based on the control hierarchy. The next step is to process the CAM database into The whole process took about twenty minutes after the standard cutting codes capable of driving the machining part was designed on CAD KEY. This demonstration centre. These codes are called M and G codes and are was helpful in validating the manufacturing information specified as EIA RS-274 standards. These M and G flow through the control structure for rapid prototyping. codes are standard and can be found in all CNC machines which accept M and G codes, thus insuring that the M and G codes generated by the RPP are machine independent. 5. Conclusions In its present implementation, after the M and G code database has been generated the prismatic raw stock is The rapid prototyping protocol presented in this paper manually fixtured on the machine tool table at a prede- proposes a systematic way to make efficient use of infor- termined reference location. At the end of all cutting the mation resources for computer-integrated production finished part is currently manually unloaded. method. Software structure for cell control is defmed and functions to be achieved by each software module are dis- cussed. The demonstration of successful automated and 4. 6. Cell control rapid manufacturing of the sample part shows that enough information flows smoothly through the protocol The control of the cell takes place at the following pro- structure. gressively lower levels of hierarchy namely, the system level, the cell level, and at the equipment level. Accord- ingly, there are different software modules to control and coordinate the activities at the above levels. These Acknowledgements modules, UIS, SCP, CCP, and ECP, (discussed in the previous section) links the user to RPP/M. A data The authors would like to acknowledge the contribu- transfer protocol has been specified to standardise the tion to this work by Dr B. J. Kumar, S. Chen, and interaction between individual equipment and the ECP. M. J. Courtright. This work is supported in part by the The user sits at the top of the control hierarchy. After an Engineering Research Center, Systems Research Center, NC code (M and G) file is generated, the user supplies National Science Foundation and The National Institute the name of a system level process plan file to the SCP. of Standards and Technology. Page 1182 240 Automated rapid prototyping: II-implementation References AGV Automated Guided Vehicle AI Artificial Intelligence ANAND, D. K., KIRK, j. A., ANJANAPPA, M., and CHEN, S., ANSI American National Standards Institute 1988, Cell control structure of FMP for rapid prototyping. CAD Computer Aided Design CAM Advances in Manufacturing Engineering, PED 31, 89-95. Computer Aided Manufacturing CUTKOSKY, M. R., FUSSELL, P. S., and MILLIGAN,jr., R., CCFILE Cell Control File 1983, Precision flexible manufacturing cells within a manu- CCP Cell Control Program facturing system. Technical Report, Carnegie-Mellon CNC Computer Numerically Controlled University, Pittsburgh, PA. ECP Equipment Control Program HAMMER, H., 1987, Flexible manufacturing cells and systems EIA Electrical Industrial Association with computer intelligence, Robotics and Computer-Integrated FED Feature Based Design Manufacturing. 3 (1), 39-54. FMC Flexible Manufacturing Cell KRAMER, T. R., andjUN,j., 1986, Software for an automated IFEM Intelligent Feature Extraction Methodology machining workstation. Proceedings of the 3rd Biennial Inter- IGES Initial Graphics Exchange Specification September. M&G Miscellaneous and Go codes for Numerically national Machine Tool Technical Conference, McLEAN, C. R., 1986, The vertical workstation of the Controlled Machines AMRF: software integration. ASME Symposium on Intelligent NC Numerical Controlled NIST National Institute of Science and Technology and Integrated Manufacturing, Chicago, IL. NAU, D. S., GRAY, M. 1986, SIPS: An application of hier- PADL Solid Modeller archical knowledge clustering to process planning. Proceed- PDES Product Data Exchange Specification PMF Part Model Format ings, Sympos£um on Integrated and Intelligent Manufacturing, PP_SCP ASME Wmter Annual Meeting, Anaheim, CA, Process Plan_System Control Program PP_CCP Process Plan_Cell Control Program pp. 219-225. RPP ONO, Y., 1987, Cell Control Systems. Rapid Prototyping Protocol Robotics & Computer- Rapid Prototyping Protocol for Design Integrated Manufacturing, 3 (4) 389-393. RPP/D RICKERT, Jr., W. K., 1987, The use of IGES in automated RPP/M Rapid Prototyping Protocol for Manufacturing CNC machining. M. S. Thesis, Mechanical Engineering, SCP System Control Program College Park, University of Maryland, February. SIPS Semi-Intelligent Process Selector SMITH, B., and WELLINGTON, j., 1986, Initial Graphics UIS User Interface Shell Exchange Specifications (IGES), Version 3.0, Report No. VMC Vertical Machining Center NBSIR 86-3329, National Bureau of Standards VWS2 Vertical Workstation Gaithersberg, Maryland. ' WECK, M_-, KIRATLI, G., 1987, Applicability of expert systems to flexible manufacturing. Robotics & Computer-Integrated Manufacturing, 3, (1), 97-103. Page 1183 Final Prototype of Magnetically Suspended Flywheel Energy Storage System D. K. Anandt, J. A. Kirkt, R. B. Zmood:j:, D. Pangt, C Lashleyt tDepartment of Mechanical Engineering University of Maryland, College Park, MD 20742, U.S. A. :j:Department of Communication and Electrical _Eng~neering . Royal Melbourne Institute of Technology, Melbourne, Victoria 3000, Austraha ABSTRACT store the maximum kinetic energy, a multi-ring A prototype of a 500 WH magnetically suspended composite flywheel is used. In addit!on, the energy flywheel energy storage system was designed, built an~ losses in the electronics associated with the charge and tested at the University of Marylan~. The srstem design discharge cycles must be minimized. ~ high ef~ic_iency utilized new innovations of composite materials, motor/generator is desired to accomplish an efficiency of magnetic suspension and permanent magnet brushless 90% for each cycle. motor/generator: t~chnology. ,:\_ design goal o~ the system is to maximize the specific energy density (SED) Two permanent magnet/elec~romagnet_ (PM/EM) to exceed a value of 20 WH/Kg for spacecraft bearings are used for magnetic ~usp~ns10n of the . . applications. This paper presents the work done ~nd flywheel. The bearing electromcs will not only mamtam includes the following: ( 1) a final design of magnetic a uniform gap betw~en the rotor and the ~tator but bearing, control system, and motor/ge?e~ator, (2) withstand 1 g load disturbances. Mecham~al tou~hdown construction of prototype system consistmg of !he bearings are utilized to protect the magnetic bearings magnetic bearing stack, flywheel, motor, contamer, an~ and motor/generator from failure ~f the magnetic display module, (3) experim.ental results of the magnetic suspension. . The touchdown gap 1s set t_o be le_ss than bearings, motor and the entire system. Th~ successful the linear operation range of the magnetic bearmgs. completion of the prototype system .has achieved_: .( 1) The mechanical bearings will also ensure the system to manufacture of tight tolerance bearmgs, (2) stab.1hty and recapture the flywheel after a l_oss i? suspension. A. spin above the first critical frequency, (3) 1:1se of m~1de container of the whole system 1s bmlt for the protect10n sensors to eliminate runout problems, ( 4) mtegration of of satellite equipment due to any failures at high speed. the motor and magnetic bearings. BACKGROUND INTRODUCTION The flywheel energy storage system ~hown in Figure 1 A magnetically suspended flywheel ener~ storag~ was first built and tested as an experimental prototype. system was designed to inte~rate the n_ew mnovat10ns of The system used two pancake magnetic bearing~ . composite flywheel, magnetic suspension, and assembled in a stack arrangement. A commercial off- permanent magnet brushless motor/generator the-shelf DC brushless motor was mounted between two technologies. Based on the review of recent bearings. Mechanical touchdown bearings were located developments of technolog)'., the flywh~el energy storage between the top of the lower bearing and bottom of system is a viable and superior alternative to bat_tery for upper bearing. A aluminium flywheel was used to prove spacecraft appli~a.tions [1 ]. Th~ system can easily this system design. External eddy current transducers achieve the specific energy density (SED) of 20 \YH/kg were placed on the support structure to measure the which exceed a typical 14 WH/kg of electrochemical motion of the flywheel. The control systems suspend system. Also, the flywheel system has a long lifetime of the flywheel with a uniform gap. 10 to 15 years and possible usage of attit~de control. For attitude control of a spacecraft, multiple flywheels When this prototype was spun slightly above its first must be used to achieve motion control in all angular critical frequency ( 4500 rpm) a touchdown w<;mld occur. degrees of freedom. The proposed 500 WH flywheel . It was sometimes observed that the system failed to self- energy storage system was designed for a low ~arth orbit suspend or exhibited unstable oscillations when the satellite with a 90 minute cycle. The flywheel 1s control system was initially turned on. After repeated accelerated during 60 minute interval ( charge cycle) . efforts of debugging and analysis, the_ problems were when the satellite is exposed to sunlight: The flywheel 1s ascertained to be as follows: ~ 1) _th~ Im ear range of ~he spun down during 30 minute interval ( discharge cycle) displacement of the flywheel 1s hm1te? ~ue to el~ctrical when the satellite is exposed to the darkness. The and magnetic saturations. (2) th~ ex1stmg bearing has a flywheel energy storage systew during this darkness must small linear range because some important compon_ents supply at a constant voltage of 150+ 2% volts DC. To could not be held to a tight tolerance. (3) the location of the touchdown bearing magnifies the motion at the Page 1184 pole face where the linear range is crucial. ( 4) The A computer aided design program JEYCAD [2] and an mductance of the bearing affects the transient response optimization methodology [3] have been developed and of the overall system. An improved design of the used to achieve these design goals. The optimization flywheel energy storage system was proposed to correct method is used for a preliminary design to satisfy the these problems. Moreover, the external position design requirements and maximize the stable range traducers were replaced by the inner ones to cancel the without a detailed bearing information. The JEYCAD radial growth of the flywheel at high speed. To achieve program is applied for a detailed design by inputting all a higher efficiency, a state-of-the-art permanent magnet geometric dimensions and magnetic information. The DC brushless motor was specially designed and program will analyze the magnetic properties of the fabricated. These improvements lead to a better bearing and check if there is saturation occurring in the understanding and design of the overall system. critical sections. The JEYCAD program also includes a control system design which will be discussed later. The flywheel energy storage system is considered to consist of five key components, viz: magnetic bearings, The permanent magnets are made of Recoma 20, a control system, motor/generator, flywheel and support cobalt-rare earth material, with a typical remanance Br structure. Each component was designed to meet its of 0.9 tesla and a coercive force of 8.8 KOersted. The specifications and maximize its performance. All B-H curve of each magnet is tested and the magnets components were carefully fabricated and tested before with similar properties are arranged at the same axis of being assembled together. A final prototype was built the bearing. Because of the high speed and large flux along with a display panel which includes all control density of the bearing, the magnetic material requires a electronics and a data acquisition system. high saturation flux density and a low core loss at high frequency. Carpenter high permeability 49 alloy, a 48% MAGNETIC BEARING nickel-iron alloy, was chosen for its good magnetic The magnetic bearin~s applied in the flywheel energy pr~perties which include a relative permeability of 10 3 - 10 , the saturation value of 1.5 tesla after hydrogen storage sxstem combmes usage of the permanent (PM) annealing and the core loss of 1 W/lb at 400 Hz (24000 magnet and electromagnetic (EM) coils. The rpm). bearing has the characteristics of radially active control and axially passive support. The permanent magnets The final design of the magnetic bearing is shown in generate a bias flux through the air gap to support the Figure 3. The magnetic flux plates have 8 dowel pins weight of the flywheel. This bias flux will cause a added to prevent relative motion. To improve the destabilizing force if the flywheel moves away from the rigidity of the plates, ribs are added to the slot which center. The control system senses this motion and sends separate adjacent quadrants. The thin ribs are designed a control current through the EM coils which results in a to saturate at very low flux to ensure there is little flux corrective flux. By adding the flux at the small gap side and subtracting the flux at the large gap side, the bearing flow between the quadrants. In the stack design, two produces a corrective force. The net restoring force is magnetic bearings and a motor/generator are assembled with a central rod to keep tight tolerance in the radial the combination of the corrective force and the destabilizing force. direction. A sleeve made of non-magnetized material is designed to mate the rod and the flux plates with tight tolerance. The slots in the control flux plates are used The characteristics of the PM/EM bearing were tested to facilitate electrical wiring. The positioning experimentally with typically experimental results shown transducers in the stack design have been moved from in Figure 2. Curves A and C are plotted as force and the outside of the flywheel to the inside and are control current responses verse displacement at a lower mounted on aluminum cover cups. The outer cover gain of the control system. Curves B and D are plotted cups also hold the mechanical touchdown bearings. at a higher gain. It shows the net restoring force reaches its peak when the power amplifier becomes The new bearing was built using the pole face thickness saturated and can not supply more current. The of 0.12 inch and the permanent magnet diameter of 1.25 distance between the center and the peak is called the inch. The original bearing and the new bearing were linear range where the bearing should be operated. tested for their performance and the experimental Notice that the linear range is dependent on the gain of results are shown in Table 1. We draw the following the control system, the maximum control current of the conclusions: power amplifier, and the magnetic saturation of the material. The bearings should be designed to have a (1) The new bearing can stand 1 g load (7 lbs) at both maximum linear range with a proper load carrying radial and axial direction. capability. (2) When both bearings have almost the same linear range due to the same gain in the control system, the The design goals of the bearing are new bearing exhibits a higher active stiffness and a (1) The bearing withstand at least 1 g axial load in both greater radial force. axial and radial direction. (3) Both bearings show a similar active stiffness when (2) The axial drop be less than 20% of the pole face the new bearing has a gain at 125 KOhms and the thickness. original bearing at 250 KOhms. The linear range of (3) The linear range must be greater than the the new bearing is almost doubled. touchdown gap of the mechanical bearing. ( 4) Both bearings have a similar axial drop around 20% of the pole face thickness at 1 g load. Page 1185 Both bearing were tested with the pancake flywheel and the EASY5 is applied for the nonlinear models of system by spinning up to 3400 rpm. They both the pancake and stack system. demonstrated very good performance with less than 0.8 mil displacement throughout the speed range. The new Two design methods, component design and parameter bearing shows impressive performance in the radial design, have been developed for the pancake bearing direction and satisfactory in the axial direction. It was flywheel system . The parameter design adjusts the chosen for the final 4" stack magnetic bearing system to values of the critical parameters to satisfy the gain be delivered to NASA. margin and the phase margin specifications for a robust control system. The parameters can be derived by the CONTROL SYSTEM selections of the resistances and/or capacitance in the The pancake bearing flywheel system with a single electrical circuits. The component design in the bearing has 2 degrees of freedom. The motion of the JEYCAD program allows user input of the component system can be represented by two translation dynamics data of the control system, and computes the transfer equations in 2 orthogonal axes X and Y. The model is functions and the active stiffness etc. Incorporated with based upon the fact that the bearing has a negative the CC program, the component design tool can plot the spring constant -Kx due to bias flux of the permanent frequency and time responses of the control system and magnet and the flywheel is symmetric without mass compare to the specifications in the parameter design. imbalance. It is also assumed that the translation motion in the X and Y direction are independent. A Figure 4 shows experimental results of the frequency proportional and derivative control system is used for response of the stack bearing flywheel system. The the magnetic bearing flywheel system and it has been overall frequency response is smooth and flat, although extensively explained previously [1,2,5]. a little rise occurs around the first critical frequency. In the stack spinning test the flywheel spins over 4500 rpm The stack system with two magnetic bearings has 4 with a maximum excursion of 1 mil. The experimental degrees of freedom with the flywheel spinning about the tests proved that the control system achieves the stated axial direction. Four independent control systems are design requirements. used to center the flywheel. Since the system has two translational motions and two rotational motions with MOTOR/GENERATOR gyroscopic effects, the dynamic equations become The motor/generator design considerations for the nonlinear and complicated. Jayaraman [4] has derived prototype include the following: these equations and studied the stack dynamic performance and shown that they have minimal effects (1) The motor/generator is sandwiched between two at the speeds under consideration. magnetic bearings. The geometric size of the overall system limits the available space of the There are three control system models developed to motor/generator with a maximum diameter of 4.5 study the behavior of the magnetic bearing flywheel inch and a maximum length of 2.5 inch. system. First is the linear model of the pancake bearing (2) In the 60-minute charge cycle, the motor has a flywheel system. Second is the (nonlinear) model of the constant power of about 600 W from the solar cells. stack bearing flywheel system. third is a nonlinear The motor spins from 33000 to 66000 rpm with the model of the pancake bearing flywheel system [5]. In applied voltage changing from 70 to 140 Volts. In the third model, the inductance of the EM coils, the the 30-minute discharge cycle, the generator delivers saturation of the power amplifier, and the physical the power for the satellite. Neimeyer [6] has limitation of the flywheel movement are introduced to designed and specified the input and output voltage study the self-suspension and limit cycle oscillation and power profiles for these cycles. phenomenon. Analysis and simulation have shown that the reduction of the inductance of the EM coils can (3) Since the torque, speed and applied voltage of the improve the robustness of the control system. When motor .is known, the motor torque constant Kt, which the number of turns of the EM coils was reduced by half, is the same value as the voltage constant Kv, is the bearing stability improved and the limit cycle chosen to be 0.02025 N-m/A. oscillation disappeared. ( 4) The motor design includes the power loss due to the armature resistance, the eddy current, and The design goal of the control system are as the hysteresis. To achieve the maximum efficiency, the following: core lamination, the magnetic materials, the (1) A bandwidth of the control system must be greater permanent magnets and the core winding are than the first critical frequency. specially designed. The overall motor efficiency was (2) A maximum excursion of the flywheel should be less calculated to be around 94%. than the mechanical touchdown bearing gap. (3) The transient response should have little oscillation The motor is designed to have rotating permanent or final error. It is desired to have a gain margin of magnets and a surface wound armature, which is at least 6 dB and a phase margin of 30 to 60 degrees. mounted in the air gap and attached to the stator laminations. The armature winding is a three phase Two simulation tools, Classical Control (CC) and delta connection design with an overlap of one-third of EASY5 programs, are used tD'analyze the control the pole pitch in each phase. The lamination material system. The CC program is used for the linear model for the armature is chosen to be Carpenter HyMu 80 with a thickness of 6 mil. The laminations are Page 1186 individually laser cut and insulated with a silica coating. DISPLAY PANEL The permanent magnets for the motor are Neodymium- Iron Boron with a high energy product of 32 MGauss- The display panel provided with the flywheel energy Oersted. These powerful magnets can produce a flux storage system is an integrated unit designed to handle density of 0.4 tesla in the large air gap required for the all sys!em control, monitoring and diagnostic functions. surface wound armature configuration. The display panel unit , shown in Figure 6, is divided into four panels: the DC power supply, the temperature A commercial brushless DC motor controller, measurement, the motor/generator controller and the Automation LC-4C, was selected to operate and control bearing control system. the motor/generator. Optical sensors, which have a faster response time and accurate waveform, were used The DC power supply panel has two +24 V 7.5 Amp to provide the necessary signals . power supply units used for magnetic bearing control system. This panel includes four DC voltage meters and After the motor/generator was fabricated, it was tested four current meters, which monitor the voltage and to compare actual performance with design values. The current output. motor torque constant Kt was measured to be 0.0284 N- m/A and a similar result is independently obtained by The temperature measurement panel displays three experimentally measuring the voltage constant Kv. This pyrometer outputs, which indicate the temperatures value is approximately 40% greater than the design measured by thermocouples at two magnetic bearings calculation. This can be explained by the 37% increase and the motor/generator. The operating temperature of the stack is designed to be less than 100 °c. in the air gap flux density over the design value. The motor/generator was successfully spun up to 9000 rpm in the test-rig before being assembled in the stack. The motor/generator controller panel includes: the motor/generator operation mode switch, the FLYWHEEL Automation motor controller, the AC voltage and current meters, the DC voltage meter, and the rpm The flywheel, used to store kinetic energy, is one of the meter. There are three operation modes of the most important components in the system. One of the motor/generator: the charge, coast and discharge modes. design goal of the system is to maximize the specific In the charge mode the motor/generator is operating as energy density (SED). For 500 WH energy storage a motor and the flywheel speed is increasing. In the system, the SED must be greater than 20 WH/Kg in coast mode the controller is turned off and the flywheel order to compete with any electrochemical system. To essentially spins at constant speed. In the discharge increase the SED the only way is to design the flywheel mode the motor/generator acts as a generator and using the high strength composite materials. For a discharges energy which is dissipated in a resistance spacecraft application, the composite flywheel has the network in the controller. The AC voltage and current advantages of both a higher SED and a longer life span meters are used to measure the RMS line voltage and (10 to 15 years). A composite flywheel design was current into the controller. The rpm meter is used to proposed by Ries [7] but will be implemented in a future display the speed of the flywheel. The DC voltage research project. meter is used to indicate the motor supply voltage. For this prototype a cylindrical aluminum flywheel is The bearing control system panel has four independent used. A motor permanent magnet ring, two return rings control systems and four adjustable resistors for the and four aluminum spacer are assembled into the center reference voltage inputs. There are four connecters for of the flywheel with a locational fit. Very tight the voltage input to the control systems and four tolerances are specified in an attempt to control the connecters for the outputs from the positioning sensor concentricity of every part to within 1 mil. The total signals. They can be used to measure the frequency .f lywheel weight is approximately 14 lbs. response of the system and to monitor the motion of the flywheel. SUPPORT STRUCTURE TESTING Support structure for the stack bearing flywheel system contains a center rod, a container and two mechanical During and after the construction phase of the touchdown bearings. The central rod is used to ensure prototype, the following tests were conducted: the concentricity of the magnetic bearings, the motor/generator and the mechanical touchdown (1) Measurement of various parts of the magnetic bearings with extremely close location fits (LC-1 ). The bearing flywheel system, prototype stack design is shown in Figure 5. The (2) Determination of the characteristics of individual container includes a cylindrical tube as well as top and magnetic bearings, bottom plates. The container provides not only the 3l Suspension and spinning test of individual bearings, support but the safety protection of the stack. The 4 Determination of the characteristics of the motor, mechanical bearings are intend to support the flywheel 5 Spinning test of the motor, when the system is switched off or loses magnetic !6 Suspension and testing of the entire stack. suspension. The touchdown gap, which must be within the linear range, is 5 mil. Since the stack bearing flywheel system operates in a small linear range, various parts in the system are designed with tight tolerance design. The quality control of the parts becomes critical to ensure the Page 1187 success of the assembly and operations. The PM/EM "Design Optimization for Magnetic Bearings", to be bearings were individually tested for their characteristics published m IECEC, 1991. including Kx, Ki, Ka, linear range, stable range, and axial and radial load capabilities. These bearings were [4] Jayaraman, C. P., Kirk, J. A., Anand, D. K. and individually suspended with their designated control Anjanappa, M., "Rotor Dynamics of a Flywheel systems and spun over 3400 rpm. The motor also was Energy Storage System", J. of Solar Energy Eng., tested for its characteristics including K,, Kt, armature Vol. 113, pp. 11-18, Feb., 1991. resistance and inductance. The motor was spun over 9000 rpm in the test-rig. [5] Zmood, R. B., Pang, D., Anand D. K., Kirk, J. A., "Improved Operation of Magnetic Bearings for The testing and measurement of the individual bearings Flywheel Energy Storage System", Proc. of 25th and the motor/generator indicate the experimental IECEC, pp. 469-474, 1990. results were sufficiently close to design parameters and therefore no changes were necessary. Consequently the [6] Neimeyer, L. H., Studer, P.A., Kirk, J. A., Anand, D. two bearings and the motor/generator were finally K. and Zmood, R. B., "A High Efficiency assembled into a stack configuration. Motor/Generator for a Magnetically Suspended Flywheel Energy Storage System", Proc. of the 24th The stack configuration, once connected to the IECEC, pp.1511-1516, 1989. display/control panel, was suspended so that the control current in the EM coils was a minimum. The flywheel [7] Ries, D. M., "Manufacturing Analysis for a Multi- was spun over 4500 rpm (the first frequency is around ring Composite Flywheel", M.S. Thesis, Univ. of 2700 rpm) with stable performance. Higher spinning MD, 1991. speed can be achieve only in a vacuum chamber. The overall frequency response of the system was measured and found to be flat and smooth. Table 1 Experimental Results of Two Bearing Design CONCLUSIONS Bearing Type Original New A prototype of a magnetically suspended flywheel Pole Face Thickness (in) 0.065 0.120 energy storage system was successfully built and tested. Mean Radius (in) 2.018 2.080 Specially we achieved the following: Air Gap (in) 0.048 0.040 Passive Radial Stiff. (lb/in) 900 1460 (1) Manufacture of tight tolerance bearings. Force/Current Stiff. (lb/A) 5.8 14.2 (2) Stable performance by spinning test above the first Maximum Current (A) 1.9 1.9 critical frequency. Stable Range (in) 0.013 O.D18 (3) Use of the sensor inside the flywheel thereby Maximum Axial Load (lb) >16 >16 eliminating runout problem. Axial Stiffness (lb/in) 650 330 Axial Drop Ratio(%) 19 20 ( 4) Successful integration of PM brushless DC motor Current/Displ. Ratio (A/in) with PM/EM magnetic bearings. at Rl7=125 KOhms 191 191 at R17=250 Kohms 382 382 There are, however, some problems that need further Active Stiffness (lb/in) rells earch and development. These include at R17=125 KOhms 360 1440 at Rl7=250 KOhms 1580 4160 Testing in a vacuum chamber to high speed, Max. Radial Force (lb) !2 Testing with a composite flywheel, at R17= 125 KOhms 2.6 10.9 3 System integration. at R17=250 KOhms 6.7 15.4 4 Re-evaluation of the analytical basis of the magnetic Linear Range (in) bearing design to include nonlinearities and at Rl7=125 Kohms 0.0096 0.0094 saturations. at R17=450 Kohms 0.0045 0.0047 ACKNOWLEDGEMENTS This work was supported by a research grant from the NASA Goddard Space Flight Center under contract NASS-30091 and under the technical direction of Ernest G. Rodriguey. REFERENCE [1] Kirk, J. A. and Anand, D. K., "The Magnetically Suspended Flywheel as an Energy Storage Device", NASA Pub. 2484, "Space Electrochemical Research and Technology (SERT)", pp. 137-146, 1987. [2] Jeyaseelan, M., "A CAD Approach to Magnetic Bearing Design", M.S. Thesis, Univ. of MD, 1988. [3] Pang, D., Kirk, J. A., Anand, D. K. and Huang, C., Fig. 1 First Prototype of Stack System Page 1188 LEGEND A: KA (Rl7= 125 KOhms) B: KA (Rl7= 250 KOhms) C: Current Output for A Mag D: Current Output for B (dB) -30 L,LJ..UJ.1-_1..-JL-J....J..l..J..1..Ul---'-...J-.J....l...LL.l.LL-~ 240 ....... ,...,.,..,,.-.,.......,....----......- ·-~~......,,.-----,---, Phase (Deg) -80 .....,_.......,.....__ IO JOO Freq (Hz) Fig. 4 Frequency Response of Stack Fig. 2 Experimental Test of the Bearing Outer Cover Plate Control Flux Plate Upper Control Pins EM Coils Magnet Plate Fig. 5 Final Prototype Design Permanent Magnets Bearing Control Panel Lower Control Pins Temperature Monitor MIG Controller Panel Inner Cover Plate DC Power Supply Fig. 3 Final Design of Magnetic Bearing Fig. 6 Display Panel Page 1189 DESIGN OPTIMIZATION FOR MAGNETIC BEARING D. Pang, J. A. Kirk, D. K. Anand, C. Huang Department of Mechanical Engineering University of Maryland, College Park, MD 20742, U.S. A. ABSTRACT IM: Maximum supply current ( = 1.9 A) !max: Maximum control current to EM This paper proposes an optimization design Ka: Active stiffness ( = CKi - Kx) methodology for the PM/EM radially ac~ive magnetic Ki: Force/current sensitivity of EM bearing developed at the Advanced J?esig!1 and Kx: Passive radial stiffness Manufacturing Laboratory of the Umversity of Kz: Passive axial stiffness Maryland. The bearing is used in the flywheel energy Lm: Length (thickness) of PM storage system to ~a$netically suspend_ t~e r~tating flywheel without fnctlon loss. The opt1mizat10n model N: Number of turns for one EM is based on the stiffness and permeance models of the NM: Maximum number of turns for one EM ( = 750) Pt: Permeance of total flux at magnetic circuit magne~ic bearin$· . The objective _of the optimization design is to maximize the st~ble displacement.range, Pu: Permeance of useful flux which directly affects the stt1fness, load capa~ity ~nd Pu/Pt: Useful flux ratio ( = 0.3) operating range of the bean~g. The coi:stramts i~clude Rmean:Mean radius of magnetic bearing the bearing load, the mag1.1et!c ~ux. density, the axial load RM: Maximum mean radius ( = 2 in) and stiffness, the geometnc ltm1tat1on, and the power tpf: Pole face thickness . . amplifier and the contr~I syste~. Xlin: Linear range of magnetic beanng ( = Imax/C) There _are a total of Xstb: Stable range of magnetic bearing 12 design variabJes, 11 mequaltty co_nstramts and 6 equality constramts. The problem is solved by _three Xl: Air gap ("'.'go), in . . . X2: Mean radms of magnetic beanng ( = Rmean ), m different optimization methods: the monotomc1ty analysis the generalized reduced gradient method and X3: Pole face thickness ( = tpf), in X4: Number of turns for one EM ( = N), turns the augi'nented Lagrange multiplier method .. The XS: Maximum control current to EM ( = lmax ), A design methodology not only can help to achi~ve the X6: Diameter of PM ( = Dm ), in design goals. and ~etter perfor~ance ~ut specify the X7: Corrective flux density by EM ( = BEM), tesla important dimens10ns and design var!ables ?f the bearing. A case study of the magnetic beanng flywheel XS: Bias flux density by PM ( = Bu), tesla system design is demonstrated. These three methods X9: Axial drop of flywheel ( = dp ), in yield results with less than 1% error. XlO: Passive radial stiffness ( = Kx), lb/in Xu: Force/cur~ent ~ensitivity (=Ki), Jb/A NOMENCLATURE X12: Pas~ive axial stiffness ( = kz), lb/m WA: Weight of flywheel ( = 9 lb) Ac: Cross section area of pole face ( = 21rRmeantpf) µ.o: Permeability of free space ( = 41r X 1o -7 H/m) Am: Cross section area of PM(= 1rDm2/4) BEM: Corrective flux density by EM at pole face INTRODUCTION Bm: Operating flux density of PM ( = 0.85 tesla) Magnetic be~~ings having t~e advan_tage _of no friction Br: Remanence = loss, high eff1C1ency, lo'Y nmse and v~bra_tion, and large Bsat: Saturation flux density of material ( 1.5 tesla) load capacity are used m ma1.1y ap_phcatlons [1-5). The Bu: Bias flux density by PM at pole face bearing developed at the Umversity of M~ryland, C: Current/displacement ratio of control system ori$inally designed by Studer [1 ], has a umque feature Dm: Diameter of PM which combines a permanent magnet a1_1d elec~romagnet dp:. Axial drop of flywheel for stabilization. The Pancake Magnetic Bearmg [3] drat: Axial drop/pole face thickness ratio ( = 0.1) = shown in Figure 1 includes a stator and a rotor. The FA: Axial load ( 18 lb) stator has 4 permanent magnets (PMs ), 8 FR: Radial force by EM ( = 18 lb) electromagnetic coils (EMs ), 2 magnet plates, ~ control Frad: Restoring radial force ( = Kif - KxX) . = flux plates and 8 control pins .. The !otor c?ntams a gmach: Minimum clearance for air gap ( 0.01 m) return ring and a flywheel, which spms at ~1$h s_peed and go: Air gap stores energy. The bearing has active positlonmg He: Corrosive force of PM control in the radial direction and passive support Page 1190 capability in the axial direction. The bearing is divided Stiffness Model into 4 quadrants to decouple the flux produced by an adjacent quadrant. The flux paths are separated into 2 The static behavior of the bearing is rel'resented by independent axes, east-west and north-south axes. Each force equilibrium equations. In the axial direction, the axis has its own control system without any coupling. bearing passively supports the axial load of the flywheel. The magnetic flux (bias flux) from the permanent FA= Kzdp (1) magnets supports the weight of the flywheel. If the flywheel is not in the center, the permanent magnets will In the radial direction, the flywheel is affected by two cause a destabilizing force to pull away the flywheel forces: the destabilizing force from permanent magnets farther from the center. A control system responds to and the corrective force from electromagnetic coils. the motion by sendin$ a control current through the coils The combined restoring radial force of the bearing is which results in additmnal corrective flux. The Frad = Kil - KxX (2) corrective flux adds to the bias flux on the small gap 'side and subtracts from the bias flux on the large gap side. Figure 2( a) represents the radial forces of the bearing The result of these flux combination produces a net including the destabilizing force, the corrective force, restoring force. and the combined force. Figure 2(b) shows the control current output from the power amphfier. The STATOR corrective force reaches its peak when the power amplifier becomes saturated and cannot supply more current. Simultaneously the restoring force also reaches the peak and begins to decline as the destabilizing force continues to increase and the corrective force stays ~~~~~~~~~~ constant. When the restoring force is zero, the corrective force equals the destabilizing force. The Flywheel :..J maximum displacement of flywheel is defined as the I,.. maximum stable range and given by go Xstb = Kilmax/Kx (3) Radial Forces Rmean Linear Region Saturation Region Corrective Force Fig. 1 Pancake Magnetic Bearing Kilmax MAGNETIC BEARING MODELLING KaXHn · The mathematical model of the pancake magnetic bearing can be represented by both a stiffness model and a permeance model. The stiffness model uses force equilibrium equations and the stiffness of the bearing to -KxXlin present a static behavior of magnetic bearing. The dynamic behavior of the bearing can be simply revised I by adding a mass and acceleration term. The stiffness (a) derived from magnetic force equations and magnetic Contro!Cunent lz: field theory can be described by a function of magnetic flux or flux density. The stiffness model is useful for lmax=CXlin - - - I understanding the bearing performance but offers little help for the design of a bearing. The permeance model . I however calculates all the possible flux paths in the K------------- Fly~~c:~:~:~~ent (b) bearing and describes a magnetic circuit which is useful for design. Applying the permanent magnet strength Fig. 2 Radial Forces and Control Current Response and the parameters of the electromagnetic coils, the model can calculate the flux and the flux density in any Notice that from equation (3) the stable range of section of the bearing. By combining the results of the flywheel is related to the maximum control current of stiffness and permeance modelling the bearing power amplifier and the characteristics of permanent performance can be predicted. In additions the magnet and EM coils but independent of the control geometric dimensions, the permanent magnet and the system. There is a maximum displacement range the electromagnetic coils can be selected and designed. flywheel can travel without current saturation. The maximum range Xlin is called the linear range of the The properties of the bearings are assumed to be linear bearing. over the operating range except the control current to the EM coils in the control system. The control current Xlin = lmax/C. ( 4) is linear until the saturation of the power amplifier, after In the linear range, the force equilibrium equation (2) which it is held constant. TheJimitation of control can be written as current is important because the bearing design should avoid the magnetic saturation of materials. Frad = KaX = Kil- KxX (5) Page 1191 This active stiffness of bearing can be represented by bearing due to high intrinsic coercive forces. The B-H Ka = CKi - Kx (6) demagnetization curve can be presented by a line between the remanence Br on the Y axis and the The linear range is determined not only by the maximum coercive force He on the -X axis. Once the total control current to the EM coils but by the permeance is known a loading line of the magnet can be cur!ent/?isplacement ratio ~ of the control system. The drawn on the B-H curve. The intersecting point with active stiffness and the maXImum restoring force are also the demagnetizing curve is the operating point of the dependent on the current/displacement ratio C. A magnet. The operating flux density of the permanent lower current/displacement ratio means a larger linear magnet Bm is range, a lower active stiffness and a smaller maximum restoring ~orce. F?r a ~agnetic bearing, a larger linear Bm= Br l + BrAm (11) range, a higher active stiffness and a greater maximum LmPtHc restoring force are desired. A good bearing system must balance all of these performance requirements. The total ~ux from the permanent magnet in one quadrant 1s a constant BmAm. The bias flux across the Figure 1 also shows important geometric dimensions of air gal? is the total _flux multiplied by the useful flux ratio. the bearing. The length and the cross section area of The bias flux density Bu can be written as the air gap have major effects on the magnetic flux and Bu= (Pu/Pt)(BmAm/Ac) (12) t~e magnetic force because the flux directly across the air gap of two pole faces helps to support the weight as The flux generated by the electromagnetic coils can be well as center the flywheel. The bias flux from the ·t reated as independent from the flux of the permanent permanent magnet contributes the axial stiffness Kz and magnet. The four EM coils of one axis are connected in the radial stiffness Kx. The flux from both the parallel to the power amplifier. Therefore the permanent magnet and EM coils influences the magnetomotive force (m.m.f.) of the EM c~ils in each force/current sensitivity Ki. The Kz, Kx and Ki values ~s is Nlmax. The EM flux used to center the flywheel can be obtained from experiments or a theoretical 1s the permanence of the useful flux multiplied by the analysis. m.!11.f.. The ma&netic flux density generated by EM cmls across the a1r gap BEM is The ~al stif!ness of the magnetic_ bearing derived by . BEM = µ,oNimax/( 4go) (13) Sabms [2] usmg the Schwartz-Chnstoffel transformation ' demonstrates that Since the flux and permeances of all paths are known the flux density of any section of the bearing can be ' Kz = 4Bu2Rmean/,uo (7) analyzed and checked for magnetic saturation. Zmood, Iwaskiw et al. [3] developed the following Furthermore, the information from the permanence formulas for the radial stiffness and the force/current model can be used in conjunction with the stiffness sensitivity: model to calculate characteristics of the magnetic bearing such as Kx, Ki and Kz. Kx = 2,rBu2Rmeantpf/(µ,ogo) (8) Ki = -vlBuRmeantpfN/go (9) DESIGN GOALS The design goals for the bearing in the flywheel energy Permeance Model sltol rage system are: Jayaraman, Jeyaseelan et al. [4] applied the magnetic circuit theory to build a permeance model for the the bearing has 2 g axial load capacity. pancake magnetic bearing. This includes a detailed !2 the be!lring ca~ withstand 2 g radial force. study of all possible flux paths to analyze the 3 the axial drop 1s less than 10% of pole face thickness. per:me~nces of these paths. . The permeance of a flux, 4 the stable range of the bearing should be maximized. which 1s analogous to electncal conductance, is a function of the geometry and the material of the The magnetic bearings are expected to handle a 2 g load magnetic circuit. . of the flywheel at both the axial and radial direction. The axial drop ratio requirement is based on past work P = µ,oNL (10) that sh~ws that the large axial drop will reduce the useful There is a total of 8 flux paths analyzed in the model. magnetic flux and affect all the magnetic properties of The flux path, which passes through the air gap between the bearing [5]. The last requirement seems to be hard two pole faces, is the useful flux and the rest paths are to obse!"e because the bearing should be designed for a the leakage fluxes. Nickle iron, used as the magnetic larger lmear range, a higher active stiffness and a greater m:;\teria\has a high relative permeability of the order of radial force. Notice that the linear range active 1()-' to 10 so that the permeances of the magnetic stiffness and radial force are dependent o~ the control material can be neglected. Only the permeances of air system design and impose conflicting requirements. For gaps are calculated in all flux paths. The useful example, a control system with a larger linear range will permeance compared to the total permeance is called ~ave a lower active stiffness. In order to fundamentally the useful flux ratio presented as an efficiency index. improve the properties of the bearing, the stable range Typical useful flux ratio is around 30% in the pancake which is independent of the control system should be as bearing design. large as possible. Cobalt-rare earth permanent magnets are used in the Page 1192 OPTIMIZATION MODEL constraints, variables, and parameters of the simplified An optimization model was developed mainly based on model are rewritten shown in Table 2. the mathematical model of the magnetic bearing. In order to keep the desi~n problem manageable, the Table 1 Optimization Design Objective and Constraints scope of the optimizat10n is concentrated on the most important dimensions and design variables of the Obi.e ctt.v e: M ax.i mum Xs Kilmax tb=~ bearing. The permeance model is simplified with the Design Constrains: assumption that the useful flux ratio Pu/Pt and the 1. Magnetic Flux Density 5. Power Amp & Control System operating flux density of the permanent magnet Bm are BEMSBu lmax SIM constant. Except the geometric dimensions related to Bu + BEM $ Bsat NSNM the useful flux at the pole face , the other dimensions are left for further detailed design. The stiffness model is 2. Bearing Load Capacity 6. Magnetic Bearing Model 2 also simplified in order to study the bearing FA= 2WA S 1t Bu2Rmeango Bu_BmPu Dm2 - 2Pt Rmeantpf performance without considering the control system. µo The stable range, Xstb, is chosen as the objective FR = 2WA $ -4"2 BuBEMRmeantpf BEM = µo Nlmax 4 go function to achieve the best radial performance. µo 3. Axial Drop & Axial WA Stiffness dp= Kz The objective of the optimization is to maximize the dp drat tpf = 0.1 tpf Kx = 21t Bu2Rmeantpf $ stable range of the bearing, Xstb, given by equation (3). µo go There are 12 design variables in the model: the mean go$ tpf Ki = ..f2BuRmeantpfN r!,ldius of the bearing Rmean, the air gap go, the pole face go thickness tpf, the maximum control current lmax, the 4. Geometry Kz = _£ Bu2Rmean µo number of turns in one electromagnetic coil N, the bias Om $ 2Rmean - go flux density Bu, the corrective flux density BEM, the "2+1 permanent magnet diameter Dm, the axial drop dp, the gmach $ go axial stiffness Kz, the radial stiffness Kx and Rmean$RM force/current sensitivity Ki. Equations (11) and (12) in the permeance model and equations (1 ), (3), (7), (8) and (9) m the stiffness model are used in the optimization Table 2 Simplified Optimization Model model. . . Mini" . 1 1tBmPu X62 In these equations there are parameters in the model Ob~ecuve: nuze X s tb = ~.,,2µ0Pt X2X3X4X5 that must be specified by the designer. These Design Constraints: parameters includes the weight of the flywheel WA, the l: ~ X4X5 _ BmPu X~ s maximum mean radius of the bearing RM, the useful flux g 4 0 XI 2Pt X2X3 ratio Pu/Pt, the operating flux density of the permanent µo X4X5 BmPu X62 g2: magnet Bm, the saturation value of the magnetic 4Xl+ 2Pt X2X3-Bsat$O material Bsat, the maximum axial drop ratio drat, the g3: FA_ 1tBm2pu2 X64X1 < O 2 maximum current output IM, the maximum number of 2µoPr.2 X2X3 - turns for the EM coil NM, and the minimum air gap for g4: F _ BmPu X62X4X5 $ O assembly gmach. R ..f2Pt XI g5: µoW AJ>t2 X2X3 - drat$ 0 The design constraints of the bearing include: the Bm2Pu2 X64 2 1 magnetic flux density of materials, the load, the axial g6: X6 - ..f2+l X2 + ..f2+l Xi$ 0 stiffness, the axial drop, the geometry, the power g7: Xi -X3SO amplifier and control system, and the magnetic bearing gs: X5-IM$0 mathematical model. There are a total of 11 inequality g9: X4-NM $ 0 constraints and 6 equality constraints which means 12 g!O: X2 - RM $ 0 design variables can be further simplified to 6. The gll: gmach - XI $ 0 equations for the objective function and the design constraints are shown in Table 1. All the design parameters and variables are listed in the nomenclature. OPTIMIZATION METHODS Simplified Optimization Model Three optimization methods, the Monotonicity analysis, the Generalized Reduced Gradient (GRG) method and By substituting 6 equality constraints into the the Augmented Lagrange Multiplier (ALM) method, optimization model, the problem of 12 design variables have been applied to find the optimal design of the are simplified into 6 independent variables, Xl to X6, magnetic bearing [6-8]. The monotonicity analysis can and 6 dependent variables, X7 to X12. It is easy to check if the optimization model is well-bounded. The analyze the problem since some design constramts are procedures are first to examine monotonic functions of decoupled. All 6 dependent variables can be drop off the objective function and the design constraints of the the calculation initially and studied later. The resulting model, and then apply two monotonicity principles listed computer program is simpler .and the errors can be in Appendix. If all design variables are bounded, the easily debugged, but the physical meaning of the model is well defined. This analysis can improve the constraints becomes difficult to recognize. The design modelling of the problem and satisfy the necessary Page 1193 condition of existence of a solution before trying to Table 3 Monotonicity Table for Simplified Model compute the solution. Xl X2 X3 X4 Xs X6 X1 xs x, X10 Xll X12 The GRG and ALM methods are used to solve the Obj. - - - - nonlinear constraint problems numerically. The GRG + g1 - method utilizes a linear approximation to find a descent + + + + -g2 - direction (reduced gradient) of the function and solve an - - + + + gi optimal design. A commercial software GRG2 - + + - g4 developed by Lasdon [7] is used in the optimization + - - - gs process. + + - g6 + - + The ALM method is a kind of penalty algorithm to solve g7 + - a constrained optimization problem as an unconstrained gs + problem [8]. This method design is based upon a g9 + pseudo-objective function combining the constraints, g10 + penalty R and Lagrange multiplier A. To avoid a g11 - numerically ill condition, the R and A will be updated hl + + + + during the optimization process. As the penalty h2 + + =F + increases the variables converge to an optimal point. A h, + =F + + computer program is developed using the ALM method, h4 + + + + + the Fletcher-Reeves conjugate direction method, and hs + + + + the golden section method to find the optimal point of h6 + + + + the pseudo-objective function. The orders of magnitudes of the constraints and their gradients should be approximately the same, otherwise it will cause problems in the optimization process. Table 4 Results for Three Optimization Methods CASE STUDY AND RESULTS u~n~ r.,or.,? 1'T.U" Xstb 0.027954 0 027953 0. 027944 The bearing model is designed for a 2 inch mean radius Xl 0 03854 0 03851 0 0•949 of the bearing with the weight of the flywheel being 9 X2 2 2 2 pounds The operating flux density of a permanent Yo o oon9 0 30238 0 302?R X4 750 750 750 magnet is assumed to be 0.85 tesla for a Samarium XS l 9 1 9 , Q Cobalt magnet. The magnetic bearing has a typical X6 1 6409 1.6409 1. 6409 30% useful flux ratio and the saturation flux density of X7 0 45744 o 4sn1 0 '"794 Xe 0 56765 0 56767 0 56784 1.5 tesla for the nickel-iron materiaL Using the existing X9 0 03025 0 03024 0 03023 control system and power amplifier, the maximum X10 3668 3669 3673 v,, ., 02 control current is 1.9 Ampere and the maximum number 53.97 53 99 X12 297 53 297 55 297 74 of turns in each EM coil is 750 turns. The maximum Gl Inactive :Inactive Inactive clearance of the air gap is 0.01 inch and the allowable G2 Inactive Inactive Inactive axial drop is restricted to within 10% of the pole face. G3 Active Active Active G4 Inactive Inactive Inactive The monotonicity analysis demonstrates that the model Gs Active Active Active G6 Active Active Active is well-bounded and the monotonicity table is shown in G7 Inactive Inactive Inactive Table 3. All the design variables in the objective Ga Active Active Active Active Active Active function are bounded by at least one constraint. The G9 G10 Active Active Active design variable Xl is not in the objective function but its Gll Inactive Inactive Inactive relevancy can be established by the second monotonicity principle. If any of the constraint gl, gz, g3, g4, g6 or g7 1s active, the Xl will be relevant. From past experience The results show the constraints of the axial stiffness, the g3, gs, g9 and glO are always active, so the model can be axial drop, the control current limitation, the number of simplified further. By an exhaustive search, the turns for the EM coil, the space limitation for the constraints g3, gs, g6, gs, g9 and gm are active. The permanent magnet, and the maximum diameter of the variable Xl is proven to be relevant and bounded by the . bearing are active. It comes as no surprise that the axial constraints g3 and g6. performance requirement are dominant for the radial active bearing, because the axial direction has passive The results from these three methods are shown in control and its performance is limited. The control Table 4 and are within 1% error. The same result is current output is restricted by the existing power achieved using the GRG2 program for both the original amplifier but the objective function can be improved by and the simplified models. Notice that the ALM relaxin~ this constraint. The number of turns for the method is very sensitive to the penalty R, and the EM coll is restricted by the stability of the control multiplier A and the initial points. Also the number of system. The geometric limitations for mean radius of the function evaluation for the ALM method is much bearing and the permanent magnet are inherited from larger than the GRG2 program. The GRG2 program is the design of the flywheel system so the restrictions are proven to be more robust an(ifaster. hardly to ease physically. Page 1194 CONCLUSIONS [8] Vanderplaats, "Numerical Optimization Techniques An optimization model, based on the stiffness model for Engmeering Design", McGraw Hill, NY, 1984. and the permeance model of the bearing, is used to maximize the bearing radial performance by maximizing APPENDIX the stable displacement range. The performance The First Monotonicity Principle: In a well-constrained requirements and physical considerations comprise the objective function every increasing ( decreasing) variable design constraints. Three optimization methods are is bounded below (above) by at least one active implemented for a case study. The GRG2 software constraint. applying the GRG method is the most robust and fastest method. The monotonicity analysis can be used to The Second Monotonicity Principle: Every monotonic check if the problem is well-bound and to cancel the nonobjective variable in a well-bounded problem is redundant constraints. A computer program using the either ALM method is developed but appears overly sensitive to initial conditions. (1) irrelevant and can be deleted from the problem together with all constraints in which it occurs, or The simulation results of the optimization methods (2) relevant and bounded by two active constraints, one allow the following observations: from above and one from below. (1) Although exhaustive search is used in the monotonicity analysis, it is very time-consuming and unrealistic in complicated problems. (2) The axial load and axial stiffness constraints become dominant in the optimization model. It has a physical meaning because a radial active bearing has a large restoring force in the radial direction and a limited ability in the axial direction. From a design point of view, the radial bearing should not be used for the applications of large axial loads. (3) The limitation of the control current in the power amplifier is over-constrained in the case study. This constraint should be relaxed by allowing the power amplifier to increase the current output until a magnetic saturation. REFERENCES [1] Studer, P.A., "Magnetic Bearings for Instruments in the Space Environment", NASA Technical Memorandum 78048, 1978. [2] Sabnis, A. V., "Analytical Techniques for Magnetic Bearings", PhD Dissertation, Univ. of California, Berkeley, 1974. [3] Iwaskiw, A. P., "Design of a 500 WH Magnetically Suspended Flywheel Energy Storage System", Master Thesis, Univ. of MD, 1987. [4] Jeyaseelan, M., "A CAD Approach to Magnetic Bearing Design", Master Thesis, Univ. of MD, 1988. [5] Plant, D. P., Anand, D. K., Kirk J. A., Calomeris, A. J., Romero, R. L., "Improvement in Magnetic Bearing Performance for Flywheel Energy Storage", Proc. of 23rd IECEC, Denver, CO, Vol. 2, pp. 111- 116, 1988. [6] Papalambros, P. Y., Wilde, D. J., "Principles of Optimal Design", Cambridge University Press, Cambridge, England, 1988. [7] Lasdon, L. S., Waren A. D,, Margery W. R., "GRG2 User's Guide", 1983. Page 1195 PED-Vol. 55 SENSORS, CONTROLS, AND QUALITY ISSUES IN MANUFACTURING presented at THE WINTER ANNUAL MEETING OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS ATLANTA, GEORGIA DECEMBER 1-6, 1991 D D sponsored by - - THE PRODUCTION ENGINEERING DIVISION, ASME edited by T. I. LIU CALIFORNIA STATE UNIVERSITY C.H. MENQ OHIO STATE UNIVERSITY N. H.CHAO AT&T BELL LABORATORIES - c... c... THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 East 4 7th Street • United Engineering Center • New York, N.Y. 10017 Page 1196 AN INTEGRATED APPROACH TO CALIBRATE AN UNTENDED MACHINING SYSTEM J.E. Parker, G.M. Zhang, J.A. Kirk and D.K. Anand Department of Mechanical Engineering and Systems Research Center University of Maryland College Park, MD 20742 ABSTRACT This paper presents a new methodology for the calibration of an untended machining system. The methodology requires the calibration conducted under both static and dynamic loading conditions. The transformation matrix method was used to establish the mapping function between the performance measure of Interest (input) and the control signal (output). A prototype system, building on a CNC machining center equipped with a magnetic spindle, was developed to demonstrate a strategy for monitoring the tool wear progress through the cutting force prediction. The effect of phase distortion due to the presence of time lag on the output prediction was studied. A performance index to characterize the phase distortion error was suggested for further improvement of untended machining. 1 . INTRODUCTION Today's technological innovations in manufacturing are driven by demands to maintain a consistent, high level of product quality in the modern manufacturing environment. At the same time, the ever increasing competition in the world market pushes the manufacturing industry to reduce production costs and to increase productivity. These challenges are forcing the manufacturing industry to consider untended machining as one of the major technical innovations to succeed in the modern manufacturing environment. The effectiveness of utilizing untended machining has attracted great attention from the manufacturing industry. Its impact on the improvement of production automation and machining accuracy are evident. Under untended machining, the operator is not in a position to sense the operation. To replace the operator, an on-line monitoring system is used to ensure the product quality. It is expected that the on-line system, as an integral part, is built In the machine tool. Consequently, the success of an untended machining system is entirely dependent on the methods to perform sensing and control during machining. During the past 30 decades, various sensors, based on force, torque, power, vibration, acoustic emission, and vision, have been developed. Many of them have been successfully applied in monitoring the machining process. The availability of sophisticated computers further enables us to incorporate signature analysis techniques into untended machining for the control of machining processes. The adaptive control system reported in (Tlusty et al., 1978) was used in a CNC milling machine. A dyrfamometer was attached to the spindle. Its on-line monitoring of the milling operation was through the detection of cutting force. A control algorithm was developed to adjust the table movements for keeping the dynamic variation of the cutting force within a preset level. It was reported in (Lan and Naerbeim, 1985) that chipping of the cutting tool during machining 1 Page 1197 was deiected through an on-line monitoring of cutting force. The detected cutting force at each sampling instant was used as an input to a discreet autoregressive model that estimated the status of tool wear during machining. A common characteristic in the previous approaches is that the sensors were attached to the machine tool and were not built in the machine tool. Consequently, these researchers performed the calibration process, which is a complex undertaking, on their own. It is felt that the complexity involved in the calibration process and in the determination of monitoring strategy has slowed down the wide acceptance of untended machining significantly. There has been a deterministic trend that a new generation of machine tools should be built to carry out untended machining. In these machine tools, sensors are built to function as an integral part for the on-line monitoring of various aspects of machining such as tool wear, tool breakage, material handling, and in-process inspection. It can be expected that the success of building these machine tools is heavily dependent on the availability and capability of the built-in sensors, or the built-in monitoring system. One of the major issues involved in designing the monitoring system is its calibration because the calibration data provides a basis for diagnostics of the machining process. The work reported in this paper is the calibration of an on-line monitoring system built ,in a Matsuura CNC machining center. The on-line monitoring system mainly consists of a S2M magnetic bearing spindle with an Intel based data acquisition system and a control system (Zivi, 1989, Zivi et al., 1990). During machining, the magnetic bearing spindle is subjected to the cutting force. The S2M control system reacts to the cutting force by varying the currents in the built-in electromagnetic coils to maintain the spindle in the center of its air gaps, both horizontally and vertically. To carry out a specific monitoring target such as tool wear, an indirect model-based method is used (Koren et at., 1989, Danai and Ulsoy, 1987). Through the detection of the cutting force variation, the tool wear progress during machining is retraced. we need to know the dynamic variation of the cutting force present during machining. Therefore, the calibration between the cutting force and the coil currents, or the air gaps, or both forms a basis for the establishment of a quantitative mapping function between them. In section 2 of this paper, calibration under static loading is presented. The transformation matrix method used to establish the transfer function between the coil currents and the cutting force is discussed. Section 3 presents calibration under dynamic loading to characterize the dynamics of the magnetic bearing spindle in relation to the coil current variation. The integration of the two calibration processes forms a systematic approach to perform the calibration of an untended machining system. 2 . CALIBRATION UNDER STATIC LOADING 2 . 1 Description of the Equipment for Untended Machining In order to carry out an intended machining process, a Matsuura 500 Vertical Machining Center was retrofitted with an S2M magnetic bearing spindle in place of the conventional spindle (Zivi, 1989). The basic structure of the S2M spindle is shown in Fig. 1. There are two sets of magnetic bearing coils located in two horizontal planes and one set in the vertical axis. When electrical currents flow through these coils, the generated magnetic forces maintain a uniform air gap around the spindle. During machining, the magnetic spindle is subjected to the generated cutting force. As a result, the air gap becomes uneven. At the same time, the position sensors, which are shown in Fig. 1, detect such changes and send feedback signals to the controller. The controller adjusts the coil currents to recover the uniform air gap. This monitoring cycle provides the capability of performing an untended machining process. 2 . 2 Cutting Force Measurement During an untended machining process, there is always a need to replace the cutting tool when it becomes worn. It has been known that direct measurements of tool wear seem difficult (Koren et al., 1989). On the other hand, indirect and model-based ~e~surement_ methods to retrace tool wear through the cutting force measurement seem promising (Dana1 and Ulsoy, 1987, Chryssolouris et al., 1987, Park and Ulsoy, 1989). It has been reported that the thrust force acting on the drill during machining is a good indication for drill reP,lacement 2 Page 1198 MAGNETIC POSITION FEEDBACK SPINDLE COIL CURRENT S2M AMB CONTROLLER C8J c::::J jg! ~ MAGNETIC - " BEARING GAA~PR / COILS - / ~ 0 COIL CURRENT = '--.... ----'"--.. POSITION SENSOR 1'<----t --1-MECHANICAL BEARING USED FOR CALIBRATION TABLE 0/A CONVERTER INTEL WEIGHT DATA ACQUISITION SYSTEM Figure 1 Matsuura 500 Machining Center equipped with the S2M Magnetic Bearing Spindle and the Experimental Setup for Static Loading Calibration. (Bandyopadhyay aria Wu, 1985). Therefore, it is imperative to study the reiation between the cutting force, such as the thrust force, and the coil currents in order to carry out the untended drilling process on the retrofitted CNC machining center. The necessity to calibrate this relation can also be felt when machining composite/steel laminate materials. An on-line adjustment for feedrate and spindle speed during machining is needed when the drill reaches the boundary between the composite and steel materials. A reliable signal to actuate this adjustment would be again the thrust force. 2. 3 Calibration under Static loading Since the magnetic bearing spindle functions as a sensing system, ii is a common practice to apply a known and static force at the end of the spindle during the calibration process. When the force is applied, the·corresponding changes in the coil currents are recorded. By increasing, or decreasing, the applied force, the relationship between the applied force and the coil currents, or the transfer function of the sensing system, can be established (Zhang and Kapoor, 1986). 3 Page 1199 . . It should be pointed out that the cutting force generated during machining is a vector in the three-dimensional space. The cutting force acts on the spindle. Consequently, there exist reaction forces at the bearing locations. As indicated in Fig. 2, the two reaction forces at the two radial bearings balance the two components of the cutting force acting in the horizontal plane (x-y plane), i.e., Fx and Fy . From the modeling viewpoint, each of the two reaction forces can be treated as a sum of two components, namely, the pair of F1x and F1y, or the pair of F2x and F 2y. In the vertical plane, the reaction force at the thrust bearing balances the vertical component of the cutting force, F2 • Therefore, the calibration process requires analysis of the force transmission and establishment of the transfer functions between the applied force and the coil c.urrents. In gen-era-l,_ -the- ca-lib-rat-ion process consists of the following four steps. d1= 0.499m -----'"1 d2= 0.216m----- d3 = 0.283m--...... fr .............." "-F,:?i F1z Fx F2x Fix X )--, y Figure 2 Decomposition of the Reaction Force Components when Subjected to the Applied Loads Step 1: Transfer ·the cutting f?rce, or the applied calibration force, into the five (5) components of_ th~ reaction forces at the three bearing locations. This means that the apphed force ,s first decomposed into its three components i e Fx , Fy , and F I •• , Z· Then, the three components are transferred into F1 x, F1y , F2x, F2y, and Fz. ( 1 ) where d1 and d2 are distances between the applied force and the two radial bearings, and d3 is the distance between the two radial bearings. They are shown in Fig. 2. Step 2: Identify the transfer function between the corresponding coil current and the reaction force component for each of the five pairs, i.e., (Coil Current)1 x I 1 x TF1x = (Applied Force)1 x =~ (Coil Current)1 y ~ TF1y = (Applied Force)1 y = F 1 y (Coil Current)2 x 12 X = ( 2) TF2x (Applied Force)2 x = F2x (Coil Current)2 y ~ TF2y = (Applied Force)2y = F2 y 4 Page 1200 (Coil Current)z lz TFz = (Applied Force)z = r=;- .Step 3: Assemble the five identified transfer functions into a transformation matrix. The transformation matrix is a diagonal matrix, assuming that there does not exist any cross-talking among the coil currents when subjected to the cutting force. 0 0 [ TF J = [ T~1x T~1y J2, 0 ( 3) 0 0 0 TF2y 0 0 0 1] 0 Step 4: Combine Eqs. (1), (2), and (3) to derive the mapping function between the cutting force components and the coil currents. The mapping function in a matrix form is given below. l [ 0 0 0 0 1l11 xy TF01 x TF1y 0 0 0 l2x = 0 0 TF2x 0 0 (4) [ l2y 0 0 0 TF2y lz. 0 0 0 0 lJ 0 1 In the present work, the calibration process was carried out in three separate directions. For example, when the applied force is oriented in the x direction, the force vector T is equivalent to [ Fx O O J • This enables us to estimate TF1 x and TF2x· Using the relation indicated in Eq. (1 ), we identify the two reaction forces In the x-direction, i.e., F1 x and F2x· 11 has been observed that, among the five magnetic coils, only two magnetic coils respond to the applied force acting in the x-direction. Through the recording of the two coil currents, i.e., 11 x • 11 X and 12x , the two transfer functions can be established by the two raltos, TF 1 x = F x and TF2x 1 = 12 x where 11 x and 12x are the recorded coil currents during the calibration. Figure 1 · F2x illustrates the experimental setup of static loading to identify the five diagonal elements in the transformation matrix. During the calibration process, known weights were gradually added, from 10 Newton~ to 5~ 0 Newtons with -an interval of 50 Newtons in ihe x direction. The curren! changes rn the five coils were recorded. Linear relations between the applied force and the coil ?urr~nts were observed .. The solid line shown in Fig. 3 is the plot of the applied force in the x d1rect1on Fx .vs. the coil current 11 x· Consequently, the slope of the line through , I . h . = 611 X regression ana ys1s c aractenzes the transfer function TF1 x F x . In a similar manner, 6 1 we estimate TF1 y and TF2y when applying the static loading in the y direction, and estimate TFz when applying the static loading in the z direction. During mac}lining, the detected signals from the on-line monitoring are the five coil currents. The corresponding three cutting force components can be known from the following matrix multiplication. Page 1201 1 0 0 0 0 TF1x _1_ 0 0 0 0 [~ ;] · p 0 - 1 0 TF1y 11 y _1_ 1 0 - 1 ~ J 0 0 0 0 [,, , l TF2x l2x F 0 0 0 0 2 _1_ 0 0 0 0 l2y TF2y 1 lz. 0 0 0 0 TF2 ( 5) It is worth noting that special cares have been taken during the calibration under static loading. First, a mechanical ball bearing was attached to the end of the magnetic spindle, as shown in Fig. 1. The calibration force was directly applied to the mechanical ball bearing, then- . transmitted to the spindle. This attachment allowed the calibration process to be carried out while the spindle was rotating in order to more closely mimic the machining environment. Second, the calibration process was duplicated at five different spindle speeds to study possible effects of the spindle speed on the transformation matrix. Among the five calibration data sets, three were plotted in Fig. 3. They represent the three calibration processes where the spindle speeds were set at 1000 rpm, 3000 rpm, and 5000 rpm, respectively. Examining the data shown in Fig. 3, there appears to be only a single straight line due to the fact that the estimated slope and intercept of each of the three calibration lines are so close to each other. The difference among them can be hardly displayed by the scale used in Fig. 3. Although the three lines are not exactly collinear, using the calibration line at spindle speed setting 1000 rpm for ·o ther spindle speed settings can be justified from the statistical point of view. Consequently, · this observation could justify using one transformation matrix when the spindle is under operation from 1000 rpm to 5000 rpm. X1 -Axis Calibration 0.7 0.6 c 0.5 .!1: :5 (.) ·5 0.4 (.) "O ~ ::, ""'' .0.3 0 1000 rpm Ill Cl) ::iE L 3000 rpm 0.2 D 5000 rpm 0.1 0 50 100 150 200 250 300 350 Applied Force (Newtons) Figure 3 Calibration Data Plot to Illustrate the Determination of Transf~r Function ~. F1x p Page 1202 3. CALIBRATION UNDER DYNAMIC LOADING The need to perform a calibration under dynamic loading comes from the need to identify patterns of the dynamic variation of the cutting force. It has been reported that methods of using pattern recognition in the frequency domain are effective In detecting the tool wear progress during machining (Bandyopadhyay and Wu, 1985). In order to perform the dynamic analysis of the cutting force variation in the frequency domain, and detect the dynamic variation of the cutting force during machining , the calibration process was also carried out under dynamic loading. The concern for calibrating the magnetic bearing spindle dynamically arises from the observation from previous research (Park and Ulsoy, 1989) that tool wear can be detected by monitoring the frequency components of the cutting force. The calibration under dynamic loading consists of three parts, namely, the impulse response test, the frequency response test, and the phase distortion test. Each test is designed to perform specific tasks, such as identification of natural frequency, damping coefficient, gain factor, and phase shift. An integration of these test results presents a comprehensive description of the system dynamic~. of t~e magnetic bearing spindle in the .!requency domain. The impulse response test was used to determine the natural frequency and th.e damping ratio of the magnetic bearings. Figure 4 is the plot of the response of the magnetic bearing spindle to impulsive loading. The response pattern shown in Fig. 4 strongly suggests that the dynamic characteristics of the magnetic bearing spindle can be modeled as a second-order system. The recorded time interval for a single cycle is approximately equal to 0.008 second. The natural frequency of the magnetic bearing spindle is estimated to be 125 Hz. The damping coefficient, equal to 0.13, is also estimated from the decay envelope. impulse test 2.0 1.5 ,~ooa,~ 1.0 C: 0.5 Cl) Before applied 1::,.-... U::, oll impulse () :::> 8'-' Point of / -0.5 Impulse -0.13wn --e -1.0 -1.5 -2.0 1.75 1.8 1.85 1.9 Time (sec) Figure 4 Experimental Data Recorded during the Impulse Test 7 Page 1203 To perform the frequency response test, a HP Digital signal analyzer and a shaker amplifier were used. The experimental setup is illustrated in Fig. 5. The signal analyzer injected while noise into. the shaker amplifier to generate an excitation characterized with a flat frequency spectrum. Figure 6 presents the Bode plot from the signal analyzer. The r~sponse pattern is typical of a second-order system when subjected to white noise excitation. Al the low frequency range from o Hz to 80 Hz, the gain factor is almost kept at a unity (db) level. At the high frequency range, the gain factor decreases as the excitation frequency increases. At the frequency range between 80 Hz and 200 Hz, the gain factor changes dramatically, indicating that the excitation frequency is closed to the natural frequency of the magnetic bearing spindle. POSITION FEEDBACK MAGNETIC SPINDLE COIL CURRENT S2M AMB CONTROLLER tEJ c::J [2J ~ ~ ~' MAGNETIC BEARING GAA~PR ..i- COILS ~ COIL CURRENT 4-l-POSITION SENSOR SHAKER AMPLIFIER MILLING MACHINE TABLE DIGITAL SIGNAL ANALYSER D WHITE NOISE INPUT EXCITATION OUTPUT ! FORCE TRANSDUCER OUTPUT Figure 5 Experimental Setup for Dynamic Loading Calibration 8 I Page 1204 As shown in Fig. 6a, the resonance frequency is about 125 Hz, which matches the experimental . results obtained during the impulse response test. These observations confirm the validity of· using a second order model to predict the response of the magnetic bearing spindle in the : frequency domain. Examining the Bode plot carefully, the gain factor remains close to unity · between O and 80 Hz. The gain factor increases significantly when the excitation frequency approaches 125 Hz. Figure 6b is the phase shift plot. It indicates that the phase shift is relatively constant between O and 80 Hz. The phase shift angle Is about 12.50 . This shift angle. indicates that the response of the magnetic bearing spindle, or the dynamic variations of the coil currents, lag behind the dynamic variation of the cutting force during machining. The time lag is given by the phase shift angle divided by the angular frequency 21tf (Rao, 1990). It is evident that the time lag in the frequency range from O lo 80 Hz varies and decreases as the excitation frequency increases. Consequently, the dynamic variation of the coil currents may not give an accurate picture of the dynamic variation of the cutting force during machining. This indicates that the distortion in the wave form of the applied force with respect to the recorded wave form of the coil currents is likely to occur. a) Gein 100 ~.;_;.-1-___ ;__...J___,c_i----;~..;-.;.+----,----;---;,-I- ,-I- ;-I -I; -I~ ,~,-+----+----t--.---j I I I I I I I I 125 Hz I I I I I I I I I I I I I I ! I I I I I I I I 1 Hz lOHz lOOHz 500Hz b) Phase 160 I I. I I I 12.s 0 I I I, I I I I I I 0 I I I I I I I I I 1 I -160 I I I I I I I I I I I I I I -320 I I I I I I I I I I I I I I -480 1 Hz 10Hz lOOHz 500 Hz Figure 6 Plots of Amplitude and Phase Angle of the Coil Currents vs Excitation Frequency 9 Page 1205 In order to verify just how faithfully the magnetic bearing spindle sensing system will be recording the dynamic cutting force during machining, the phase distortion test was designed to quantify the time lag under different excitation frequencies. When the time lag is known, the difference between the recorded coil currents and the actual cutting forces can be evaluated. The actual cutting force can be recovered from the recorded coil currents. Figure 7 shows the experimental set up used. Two function generators were connected in parallel to the shaker amplifier. They excited the shaker with sinusoidal waves of two specified and different frequencies. As a result, the excitation force generated by the shaker amplifier consisted of two frequency components. II was expected that the recorded coil currents also contained the same frequency components. During the test, the excitation force acting on the spindle and the resulting coil current signals were recorded by an Haitachi 20 MHz digital storage oscilloscope, and down loaded into an IBM/AT. The input and output wave forms were then compared in the time domain. Figure 8 shows the input wave as a dotted curve and the output wave as a solid curve. The excitation frequencies were 10 Hz and 30 Hz. The time lag between the input and output was measured through a shifting process to mate the two patterns. As illustrated in Fig. Ba, the time lag is 10.5 ms. After shifting the output curve to the left for mating the input pattern, the areas between the two curves shown in Fig. 8b reflects the distortion between the input and output. POSITION FEEDBACK MAGNETIC SPINDLE COIL CURRENT S2M AMB CONTROLLER MAGNETIC " BEARING / COILS COIL CURRENT / ~--POSITION SENSOR OSCILLOSCOPE FORCE TRANSO cm- SHAKER AMPLIFIER ., MILLING MACHINE TABLE FUNCTION GENERATORS 0 'V\; 0 v' Figure 7 Experimental Setup for Testing the Phase Distortion 10 Page 1206 10 Hz end 30 Hz Excitation Frequencies 20 15 10 -.. 5 0 > - 0 e -5 -10 - Output signal -15 ·-·-· Input signal -20 0.1 0.12 0.14 0.16 0,16 0.2 0.22 0.24 Time (sec) (a) Oelermlnallon or Shirl Time 20 15 10 5 !) 0 > - 0 E -s -10 -15 -20 0.12 0.14 0.16 0.16 0.2 0.:!2 0.24 b) Error Due lo Phase Olslorllon Figure 8 Shift of the Coil Current Response with Respect to the Excitation Signal Consisting Two Frequencies (1 O Hz and 30 Hz) Page 1207 4 . DISCUSSION OF RES ULT S - 4. 1 A Case Study: On-Line Monitoring of Tool Wear In order to demonstrate the on-line monitoring of tool wear during machining, a prototype system was developed using an indirect model-based method. We assumed that the magnitude of the cutting force would increase as tool wear progressed. In addition, a sudden drop in the magnitude of the cutting force would also indicate the occurrence of tool breakage. Therefore, as long as the magnitude of the cutting force varied within two preset limits during the monitoring, the machining process should continue on. Otherwise, human intervention should be called in. Because of the availability of the transformation matrix through the calibration process, the monitoring of tool wear can be performed through the on-line detection of the coil currents. The machining process was to mill slots in a composite material. The end mill diameter was 12.7 mm. The cutting parameters were set at spindle speed = 1000 rpm, feedrate = 60 mm/min, and depth of cut = 4 mm. Table 1 is a list of the measured coil currents in a consecutive time order. The three predicted cutting force components are calculated using the calibrated transformation matrix. As an example, the three cutting force components listed in row 1 were calculated using Eq. (4). 0 0 0 99.66 0 0 00 ][ -..1 115 J 0 158 0 0 .06 0 0 151 0 - 21 0 0 0 86.5 .24 Table 1 Measured Coil Currents and Predicted Cutting Forces Current Measered at Bearings (Volts) Calculated Cutting Forces O'cwtons) lxl lyl lx2 ly2 Fzl Fx Fy Fz 0.11 ·0, 15 0.06 -0.21 0.24 ·0.48 -51.45 ·90.44 ·0.03 ·0.03 0.00 0.04 ·0.13 11.52 -10. 72 48.61 0.00 ·0.09 0.04 0.09 0.31 -19.25 -13.26 ·118.63 ·0,04 0.02 0.07 -0.02 -0.02 ·19.63 5.71 9.15 0.05 0.01 -0,01 0.02 0.10 ·10.17 ·11.34 ·39.70 0.08 -0.01 ·0.05 0.07 0.04 3.17 ·30.78 ·17 .15 -0.05 0.01 -0.07 0.01 ·0.28 51.18 -7.49 101.75 0.04 -0.09 0.05 0.23 0.34 ·35.45 ·81.43 ·129.90 ·0.06 0.03 -0.02 0.03 -0.30 28.32 ·25.96 116. 26 -0.06 ·0,05 0.12 0.05 0.14 ·40.66 -7.71 -52.86 0.01 0.02 -0.01 0.05 -0.58 2.19 -29.13 223 .37 0.00 0.02 -0.04 --0.02 0.31 18.58 1.86 -1:s.~ 0.07 ·0.05 ·0.04 0.06 1.37 -0.27 -13.89 ·528.27 ·0.01 ·0.04' ·C.02 0.06 0.26 15.55 ·13.09 -101.71 -0.05 -0:-16 0.06 0.17 1.05 -13.36 -29.17 -404.25 L2 Page 1208 Figure 9 was the control chart designed for monitoring the thrust force acting on the end mill. The center line of the control chart was determined by the mean value, -65.12 Newtons, calculated from the 15 detected thrust forces (note: the_ Ume period should be longer for calculating this mean value in a practical application). The upper and lower control limits were established using the ±. 3s principle where parameter s stands for the standard deviation of the thrust force about its mean level and is equal to 229 Newtons calculated from the 15 detected thrust forces. The decision-making policy was that the milling should be stopped when the on-line detected thrust force(s) beyond the upper limit, or below the lower limit. 4 . 2 Evaluation of Phase Distortion Effect For an accurate monitoring of the cutting force during machining, it would be desirable to quantitatively evaluate the effect of the phase distortion on the cutting force prediction, and, if possible, to compensate the error for the recovery of the true cutting force signal (Rao, 1990). A performance index to characterize the phase distortion error was developed In this research. As shown in Fig. Sa, the displayed Input and output signals were recorded directly from the oscilloscope during the phase distortion test. In Fig. Sb, the output signal was shifted to the left to match the input signal pattern. The shifted distance represents the time lag, which Indicates that the dynamic variation of the measured coll currents lags behind the excitation force. By integrating the two curves to get the two covered areas and subtracting the two areas, a quantitative measure of the phase distortion error can be obtained. For comparison, the evaluated difference was normalized with respect to the time period used during the integration process. The normalized difference· was used as the performance index to characterize the phase shift effect. The larger the difference, the greater the phase shift error. Several calculated normalized difference is listed below. Combination of 5 & 6 10 & 30 50 & 55 Frequencies Normalized Difference 0.1 28.5 0.2 Examining the listed values, it is evident that the normalized difference increases as the difference between the two combined frequencies. The research is going on at the University of Maryland, is to compensate the phase distortion error to recover the true cutting force signal for further improvement of on-line monitoring. Upper Control Limit = F + 3 cr J_ 11111 --------- ., t Ill Ill • • .. ... II • • /\ ,, I \ \ I , ,I \ J \ r 'I Center Line = F i ' I 1 j I 1• .Jl 1111 -----------~ '· H Ill Ill 111 II 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 J J l I J J l I I l l I I I J I J J Recorded from On-Line Monitoring Lower Control Limit= F - 3 cr Figure 9 Control Chart Designed for Monitoring the Thrust Force during the Machining of a Composite Material Page 1209 V. CONCLUSIONS 1 . A CNC machining center equipped with a magnetic bearing spindle was used as a test bed to perform untended machining. In order to monitor the dynamic variation of the cutting force during machining, a strategy of measuring the coil currents in the magnetic bearings was used. The dynamic variation of the cutting force was being indirectly monitored through the detection of the coil current variation. A calibration procedure was developed to establish the relationship between the three componen\s of the cutting force and the coil currents for the purpose of performing untended machining. 2. Calibration under static loading was carried out to identify ,the transfer function between the statically applied force and the coil currents. The matrix transformation method was used. The force decomposition matrix establishes the relationship between the applied force and the reaction force on each of the magnetic bearing locations. The mapping function matrix establishes the relationship between the reaction forces and the coil currents. Combination of these two matrices leads to the identification of the system transfer function under static loading. 3. Calibration under dynamic loading identified the dynamic characteristics of the coil current variation in relation to the dynamic characteristics of the magnetic bearing spindle. II has been found that system dynamics of the magnetic bearing spindle can be represented by a second order system with a natural frequency equal to 125 Hz and a damping coefficient equal to 0.13. The most significant finding is the distortion in the wave form of the applied force with respect to the recorded wave form of the coil currents. Time lags were experimentally determined to quantify the effect of phase distortion on the prediction accuracy of the cutting force through the measurements of the coil currents. 4. As a demonstration example, a prototype system to perform an on-line monitoring of the tool wear progress was presented. Using the indirect model-based method, the coil currents were detected during machining to predict the culling force, which retraced the tool wear status during machining. A system performance index, called normalized phase distortion error, was developed to characterize the phase distortion effect on the prediction accuracy, showing good promise for further improvement of monitoring sensitivity. ACKNOWLEDGEMENTS The authors acknowledge the support of the Systems Research Center at the University of Maryland at College Park under Engineering Research Centers Program: NSFD CDF 8803012. They also express their gratitude to the College of Engineering for the financial support through Minta Martin funding. They wish to thank Dr. M. Abdulhamid for his technical support in this research. REFERENCES Bandyopadhyay, P., and Wu, S., "Signature Analysis of Drilling Dynamics for On-Line Drill Life Monitoring", Sensors and Controls for Manufacturing, ASME, San Fransico, CA, November 17-22, 1985, pp.101-110. Chryssolouris, G., Guillot, M., and Domroese, M., "Tool Wear Estimation for Intelligent Machining", Intelligent Control, ASME, Boston, MA, December 13-18, 1987. pp.35-43. Danai, K., and Ulsoy, A., "An Adaptive Observer for On-Line Tool Wear Estimation·in Turning, Part I and ii," Mechanical System and Signal Processing, 1987, pp. 211-240. Koren, Y., Ko, T., Danai, K., and Ulsoy, A., "Methods for Tool Wear Estimation from Force Measurements Under Varying Cutting Conditions", Control Issues in Manufacturing Processes, ASME, Miami Beach, FL, December 10-15, 1989, pp.45-53. 14 Page 1210 Lan, M. and Naerheim, Y., "In-Process Detection of Tool Breakage in Milling", Sensors and Controls for Manufacturing, ASME, San Fransico, CA, November 17-22, 1985, pp. 49-56. Park, J., and Ulsoy, A., "On-Line Tool Wear Estimation Using Force Measurement and a Nonlinear Observer", Control Jssues in Manufacturing Processes, ASME, Miami Beach, FL, December 10-15, 1989, pp.55-63. Rao, s., Mechanical Vibrations. second edition, Addison Wesley, 1990, pp. 501-502. Tlusty, J., Cowley, A., and Elbestawl, M., "A Study of an Adaptive Control System for Milling with Force Constraint",Sixth NAMRC Proceedings, Society of Manufacturing Engineers, .1978, pp. 364-371. Zhang, G., and Kapoor, S., "Development of An Instrumented Boring Bar Transducer," The 14th North American Manufacturing Research Conference Proceedings, pp. 194-200, May 1986. Zivl, E., "Robust Control of a Magnetic Bearing Spindle for Increased Milling Tool Accuracy," Ph. D. Thesis, University of Maryland, 1989 Zivi, E., Anand, D., Anjanappa, M., and Kirk, J., "Magnetic Bearing Spindle Control for Accuracy Enhancement in Machining," 1990 ASME Winter Annual Meeting, Dallas, Texas, November 1990. 15 Page 1211 NAVY TRIBOLOGY USNA WORKSHOP Held at the U.S. Naval Academy 11 - 13 May, 1992 UNCLASSIFIED: Distribution limited to workshop attenpees and to those individuals and organizations designated by the sponsoring agencies Page 1212 Tribological Interaction in Machining Aluminum Oxide Ceramics G.M. Zhang, T.W. Hwang, and D.K. Anand Department of Mechanical Engineering and Systems Research Center University of Maryland College Park, MD 207 42 S. Jahanmir, Ceramics Division National Institute of Standards and Technology Gaithersburg, MD 20899 I. Introduction Due to the achievement of high strength and fracture toughness through improved processing methods used in the manufacture of ceramic materials, new interests in the use of ceramic materials for structural applications are remarkably increasing. Although most of ceramic parts are manufactured to near net size by pressing and sintering processes, precision machining is now required to achieve a high degree of the geometrical accuracy of ceramic components. The high cost of machining has been the major barrier to widespread introduction of advanced structural ceramics. Our research effort is to study the fundamentals of ceramic machining focusing on the tribological interaction in machining, to search cost-effective, novel processing methods with emphasis on chemical-assisted machining, and to develop a sensor-based system for in-process quality assessment. Particularly, the effect of the chemical additives on the cutting force, surface finish and integrity, and the tool wear will be investigated. This paper presents an experimental study of the turning of a ceramic material - aluminum oxide (Al20 3). The machining tests were performed on a CNC machining center, as shown in Fig. 1. Diamond coated tools were used. The cutting force during machining was measured using a dynamometer. The surface finish was inspected using a profilometer. SEM technique was used to study the mechanism of the surfa ce formation in microscale. Special attention was paid to the investigation of chemo-mechanical effects of using different types of cutting fluids on these performance measures of interest. Results from this experimental study provides rich information on the cutting mechanisms during the machining of aluminum oxide (A!03) and the effect of the tribological interaction occurred on the interface between the diamond cutting tool and aluminum oxide (AI20 3). " Figure 1 Experiment Setup 1 Page 1213 II. Tribological Interaction Three important observations from comparison between the machining process using distilled water and the machining process using certain chemical additives. 1. Reduction of the tangential cutting force and increase of the feed cutting force while maintaining a constant level of the resultant cutting force. As illustrated in Fig. 2, the change in the direction of the resultant cutting force keeps the tool staying in the cutting zone and attenuates tool vibration effectively. 2. A stabilized tool motion leads to a better surface quality regarding surface finish and micro- cracks formed on the machined surface. Tool Vibration Resultant Force (a) A Large Ratio of the Feed Cutting Force to the Tangential Cutting Force when Using Distilled Water as Cutting Fluid Cutting Tool Tool Vibration Workpiece (Al203) (b) A Small Ratio of the Feed Cutting Force to the Tangential Cutting Force when Using Distilled Water as Cutting Fluid Fig. 2 Chemo-Mechanical Effect when Using certain chemical additives during machining 2 Page 1214 III. As.__-.essment of Machining Quality Comparison of Suiface Appearances ne correspondence with the actual structure of approach by implementing statistic principles to determine the the S2M B25/500 magnetic spindle system. Toe simulation includes characteristics of geometric positioning errors. This same control signal and coil current limits, coil current rate limits, magnetic methodology has been applied by Zhang et al [1985) to improve the saturation, nonlinearities, and losses, air gap reluctance variations and accuracy of coordinate measuring machines at the National Institute constant flux compensation. The modelling of amplifier dynamics was of Standards and Technology. In [Anjanappa et al 1988) it was based on time and frequency domain experimental data and builds on shown that cutting force independent errors can be measured and the steady state parameter identification. Equations for spindle rotor pre-compensated on a vertical machining center reliably. was derived from a simple inertial mode~ subjected to small angle gyroscopic effects. Detailed description of the building of analytical Toe on-line correction (primarily used to correct transient portion of model is available in [Zivi 1990]. CFD errors) schemes, typically, monitor the machining status and adaptively control the appropriate machining parameters. For Model validation was performed using experimental large signal step example, DeVor et al [1983] present a model descn'bing the response and small signal frequency response data. As shown in Fig. compliance due to cutting forces of a thin web work piece. Watanabe 3, the simulation closely tracks the experimentally observed large and Iwai [1983] reports application of adaptive control to increase the signal step response. Toe small signal simulation validation results of accuracy of the finished surface in end milling. Toe deflection of the Figure 4 compare e:,:perimental and simulation closed loop Bode spindle nose is used to compute the necessary change required in frequency response. To obtain the experimental frequency response feedrate to maintain the error within limits. characterization, an HP 3582A spectrum analyzer was used to inject Several researchers have investigated the application of incremental small (25 mVnns) sinusoidal excitation, into the S2M PID controller displacement actuators for error compensation. Kouno [1984] feedback loop through the customary user spindle position command implemented a piezoelectric incremental error compensation using interface. Spindle displacement response was measured using the L VDT measured position feedback. Anjanappa et al [1987) modeled S2M sensed spindle position instrumentation interface. Simulation the cutting process as a discrete stochastic system and an on-line based frequency response was obtained from a linear state space optimal controller was developed for maintaining surface roughness model extracted from the nonlinear simulation using the ACSL within specified values. numerical Jacobian solver. Prior to computation of the Jacobian, the ACSL equili'brium finder was used to ensure that the simulation was The on-line correction techniques discussed so far are found effective properly trimmed to steady state conditions with a null input in reducing machine tool errors. However, the requirement of command. Toe resulting state space linear model was imported into attaching highly sensitive instruments to moving machine elements in the MATLAB linear analysis environment to compute the Bode a manufacturing environment makes the approaches difficult, response. Toe gain increase in the 125 Hz range results from the expensive, and hence, impractical for many applications. derivative feedback and the spindle rotor first bending mode. To overcome these limitations, the research facility setup at the University of Maryland uses the two unique features of the RESEARCH FACIUTY magnetically suspended spindle which provides an ideal situation for error minirniza tion. To accomplish the objectives of this project, first of al~ a CNC machine fitted with a magnetic spindle was needed. In addition, such The error minimization methodology developed for this work is a system must provide an user interface whereby the user can tap into shown in Figure 6. The error correction is achieved by superimposing the current status and be able to command the translation and tilt of magnetic bearing spindle movements (high resolution and wide band the spindle rotor on-line in real time. As there is no such machine width incremental movements) upon nominal machine table available, an S2M-B25/500 magnetic spindle was retrofitted to an movements. Toe post processed M&G codes are downloaded to the existing Matsuura MC500 CNC machining center at the University of machine controller, which sends out motion commands for x. y, and Maryland. z movements. The real time position information from the machine controller is fed to the error minimization controller to generate Considerable effort was invested in the establishment of the magnetic incremental motion signals proportional to the error (taken from a spindle research facility. Figure 5 shows the primary elements of the priori obtained error map) at that position. The displacement-bias facility along with their interconnections. Hardware interfacing thus induced is used to translate and tilt the spindle-tool system details has been reported in [Woytowitz et al 1989]. The functional within its air gap to achieve enhanced accuracy. This methodology requirements can be summarized as, providing the operational control requires resolution of several issues: necessary to operate the CNC mill with the magnetic bearing spindle, implementation of safety interlocks, communication interfacing On-line determination of (apparent) ool path errors, necessary for real-time process monitoring. and coordination Calculation of corrective action, necessary to imple;~ent the error correction scheme. Actuation of corrective action, and Coordination of machining and compensation. Central to this research is the implementation of the error minimization controller which will be discussed in detail in a later Error determination is based on pre-calt'brated representations section of this paper. Various on-line process parameters are codified in an 'error map' formulation. On-line monitoring of the provided to the error minimization controller as inputs to the control x. machining process, using interfaces descn'bed in earlier section, algorithm. Available input parameters include, y, and z axis 36 Page 1220 provides the independent parameters, used to extract real-time error a.'cis error plot. estimates, from the error map representation. These perturbational corrective actions are implemented by displacing the spindle within Using the data from these tests a linear model of the thermal the magnetic bearing air gap. Since the machining process is deformation error along the y-axis based on the change in the bulk reviewed as a sequence of tool path trajectories, coordination is spindle temperature and the change in the ambient machine provided by downloading a representation of the part program to the temperature was constructed. By monitoring the above two error minimization controller. Inclusion of handshaking functions, temperatures, the quasi-static thermal error can be compensated by allows the CNC and error minimization controllen to operate in a moving the spindle shaft inside the air gap of the research facility. coordinated fashion. Figure 7 shows the physical structure of the system. The portion of VALIDATION the figure, above the dotted line, represents the conventional CNC milling machine. The accuracy enhancement. shown below the dotted Several error compensation experiments were performed using the line, includes the error minimization controller the magnetic spindle research facility to demonstrate and evaluate the error minimization system, and the required integration and coordination logic. methodology. Non-rutting terminal point error (CFl errors) compensation was performed first using the geometric position error The error minimization controller has been implemented using an map generated earlier. The HP 5528A laser metrology system was Intel 80386-based real-time computer system. Real-time input/output used to measure milling machine table position during this test. The is provided by analog-to-digital and digital-to-analog boards. The laser optics were affixed to the spindle tool holder, providing a direct control program is partitioned into two primary components. Non measurement of relative axial table position. From machine home, real-time processing is coded in Intel FORTRAN and supports the the table position command was stepped. in 25.4 mm increment$, primary operator interaction and processing of files. Real-time across the positioning range. Figure 8 presents the measured x-axis processing is accomplished using Intel PUM language. The errors before and after compensation at a nominal feedrate of 2.54 FORTRAN main program calls PUM procedures to transfer data mlmin. The result indicates terminal point accuracy improvement structures and initiate real-time processing. Once the real-time factor of about fJVe. Although Woytowitz et al [1989] reported the processing has completed, the FORTRAN main program resumes. standard deviation of the terminal point errors to be approximately one tenth the magnitude of the error, the positional behavior, shown The currently defined error representations are: in Fig. 8, retains larger systematic errors. Since the cahbrated 3 Terminal point error = f(position, nominal feedrate) sigma positional uncertainty of the spindle position is approximately Trajectory error = {(position, feedrate) 2.54 micron, these systematic compensation errors were as,umed to Ramp error = f(position, feedrate) be caused by long term drift in the error phenomena. To evaluate the short term terminal point error compensation capability, the laser Dynamic error = f(position relative to activation) metrology procedure of error map generation was repeated at a single, 2.54 mlmin feedrate. Wiih a one day tum around. between In the current implementation. the first three error representations metrology and compensation, the results of Figure 9 were obtained. are mutually exclusive while the fourth provides an additive y-axis This shows more than an order of magnitude improvement. correction. The first three error representations are implemented as Continuing metrological investigations, by other researchers, are two dimensional error maps defining a a."dal or ramp error in the currently in progress to refme the error characterization. terms of the position and velocity along the axis. The control task has been developed as a distinct, self contained module to facilitate One CFD error compensation demonstrated is the correction of a future enhancements and extensions. linear distortion of a prismatic part. As shown at the top of Figure 10, the nominal test part geometry is rectangular, 25.4 mm by 11430 mm. However, the the programmed shape was distorted into a trapezoid EXPERIMENTAL WORK which specifies a linear variation in width from 25.60 mm ( +100 micron.s per side) to 25.20 mm (-100 micron, per side). The error The net tool position displacement relative to the machine table for map, required to remove the distortion. specifies a simple linear y-axis each axis is determined from seven error terms, which are measured error as a function of x-axis position and direction of feed. Bottom under static conditions using the Hewlett Packard 5528A-based laser of Fig. 10 shows the error compensation results. measurement system. Although there are 18 error terms for a true 3-axis simultaneous motions, only 7 terms are needed for motions in This work has reported initial error compensation experiments and two axis (x and y axis) which covers most of the prismatic part demonstrated a general accuracy enhancement methodology. Future machining operations. Four types of measurements were coi.iducted, qualitative improvements resulting from metrological refinements and viz, axial position. straightness, angular, and Squareness (see enhanced magnetic spindle performance are anticipated. reference Anjanappa et al 1988 for details) to obtain all the seven error terms. Each error term was measured at 0.0254m increments Accuracy enhancement performance is limited by the quality of the of table motion at fJVe commonly used feed rates (0.254, 0.762, 1.27, error representation and by the ability to effect the proper 2.54 m/min and Rapid (5.0&n/min)) in positive and negative compensation. Using a priori obtained error map, the quality of the directions. Six sets of data are recorded at each feed rate and the error representation is dependent on two primary factors, viz; standard deviation are computed to assure that the averages of the identification of the error phenomenon independent parameters and errors represent a repeatable error. statistical properties of the error phenomenon. Recent metrological experience indicates that the CFl error repeatability may approach The resulting geometric position errors were represented in the form values of an order of magnitude better than the CFl accuracy. of an error matrix. This matrix consists of scale and straightness However, in order to exploit this fully under realistic conditions, errors for each axis for each node for fJVe feedrates and for positive improved error characterization is required. and negative approaches. Since error data at several feedrates is present. errors due to the servo drive and electronic control system Compensation implementation limitations may be characterized in are included in the map. In summary, the geometric position errors terms of bandwidth and accuracy. Relative to tool path trajectory possess a position. direction, and feedrate dependence. More dynamics ( <10 Hz'), the 125 Hz bandwidth of the existing S2M detailed information on experimental data can be obtained from B::?5/500 is sufficient for effective error compensation. In order to reference [Woytowitz et al 1989]. improve the error compensation capability, of magnetic spindles, the effective stiffness must be improved. Thermal deformation induced errors, with the magnetic spindle, is complicated since it has air cooling and extensive cooling water circuits around the magnetic coils. Tests were performed to CONCLUSIONS determine the thermal deformation errors along the x and y axis. Only the errors due to changes in ambient conditions and servo This research has, for the first time, established the ability of a motor beat sources were found to be of importance. Further, since magnetic hearing spindle to provide accuracy enhancement through the spindle bore/tool is centered about the x-axis of spindle housing. incremental error compensation. It is shown that they can provide only the y-a.x:is errors are discussed. Several 'recovery from cool simultaneous high speed, error compensation. and process monitoring down' and servos on 'warm up' tests were conducted to obtain they- capabilities. A general and fleXIble accuracy enhancement 37 Page 1221 methodology bas been fonnulated implemented and demonstrated. The hierarchical control structure, using an AMB spindle, is an effective method for both static and transient dynamic error compensation. ACKNOWLEDGEMENTS Deterainistic Error Classification This project was supported by the National Science Foundation through grant NSF 8516218 and the Engineering Research Center at the University of Maryland. In addition, this project was supported, Cutting Force Independent En-or Cutting Force Dependent Error in part, by the David Taylor Research Center Independent Research Program, sponsored by the Office of the Chief of Naval Research under task area ZR-()()()..01-01. Contnbutions from Dr. JA. Kirk. Dr. E.L Zivi. M. Woytowitz and S. Shyam towards this project is acknowledged. REFERENCES Transient and Steaa; State Trajectory Aggarwal, T. (1984). Research in Practical Aspects of High Speed Errors Milling of Aluminum, Cincinnati Milacron Technical Report. Anand, D.IC., Kirk. JA., and Anjanappa, M. (1986). Magnetic Bearing Spindles for Enhancing Tool Path Accuracy, ~ Manufacturing Processes, 1:121-134. Anjanappa, M., Kirk. JA., Anand, D.IC. (1987). Tool Path Error Fig. 1. Tool Path Error Classification Control in Thin Rib Machining. Proc. of 15th NAMRC, Bethlehem, PA. 485-492. Anjanappa, M., Anand, D.IC., Kirk. J.A., Shyam, S. (1988). Error Correction Methodologies and Control Strategies for Numerical Controlled Machining. Control Methods for Manufacturing Processes, DSC-Vol 7, ASME publications, 41-49. DeVor, R.E., Sutherland, J.W., Kline, WA (1983). Control of Error in End Milling. Proc. of 11th NAMRC. 356-362. Donmez, M. A (1985). A General Methodology for Machine Tool Accuracy Enhancement Theory-Application and Rea-w:tm,nbaltbtiril1J Implementation, Ph.D. Dissertation, Purdue University. !Inst lm'i"J jX)Si tim sersr Dufour, P .. Groppett~ R. (1980). Computer Aided Accuracy Improvements in Large NC Machine Tools, Proc. of 21st Int. !!rust ...,.ti, belrirq MTDR, 611-618. Ru ralial jX)Sitim.....,. , Field, M., S.M. Harvey, J.R. Kahles (1982). High Speed Machining Pa-nidial ""'l"ticlm'illJ Update, 1982: Production Experiences in the USA., ~ Research Associates Inc .. Cincinnat~ Ohio, USA. Kouno, E. (1984). A Fast' Response Piezoelectric Actuator for Servo Correction of Systematic Errors in Precision Machining. ~ of CIRP, 33:369-372. Frml nidiel ""!"lie lui"J Nimphius, JJ. (1984). A New Machine Tool Specially Designed for fnJtt radial belri"J ....,,. Ultra High Speed Machining of Aluminum Alloys, High Speed fttnl lcu:trl,,n ball btiri11J Machining. ASME Publications, 321- 328. Schultz, H. (1984). High-Speed Milling of Aluminum Alloys, !!lgh Speed Machining. ASME publications, 241-244. SKF (1981). Active Magnetic Bearing Spindle Systems for Machine Tools, SKF Technology Services Report. Fig. 2. Magnetic Bearing Spindle Configuration 11usty, J. (1971). Techniques for Testing Accuracy of NC Machine Tools, Proc. 12th Int. MTDR Conf., 333-345. Watanabe, T., Iwa~ S. (1983). A Control System to Improve the Accuracy of Finished Surfaces in Milling. Journal of Engineering for Industry, Transactions of ASME, 105:192-199, Woytowitz, M .. Anand, D.K., Kirk. JA., and Anjanappa, M. (1989). Tool Path Error Analysis for High Precision Milling with a Magnetic Bearing Spindle, Advances in Manufacturing Svstems Engineering. PED-Vol 37, ASME Publications, 129-142. Zhang. G .. Veale, R .. Charlton, T., Borchardt, B., Hocken, R. (1985). Error Compensation of Coordinate Measuring Machines,~ of CIRP, 34: Z~ E. (1990). Robust Control of Magnetic Bearing Spindle for Milling Tool Path Error Minimization, Ph.D. Dissertation, Univ. of Maryland, USA '' ·• ··•l '----------------------' Fig. 3. Spindle Step Response Horizontal: Time (m.r) Vertical: Displacement ( x2S.4 microns) 38 Page 1222 f'f.."r•t. .N.a.4 1at ·,. •. ·t ..,.,,,;. -10 ·H -,oL---~----~------.-.. ~--......., 10• 10• ... »•t• a,1.rku-s. deaot.e Fig. 7. Physical Structure of the System cs~ri. . •Ul. r•••lt.a -uo <> uncompensated, mean=6.60, std=S.59 Fig. 4. Spindle Frequency Response " compensated, mean=t.27, std=l.78 Horizontal: Frequency (Hz) improvement factor=5.19 20 E Vertical: Top-Magnitude (dB) r r Bottom-Phase (tkgrwc) 15 0 r 10 in 5 rn >--+f,C:J.n-('.l'd.......,::l.w"~.rc;::::::...._ _~ 0 I C Oigi tal Signals -0.5 r -5 0 Magnetic H?ts';)Ura ~;:::::::::::::::::~ Error n Spindle M111 rng Minimization -10 s '-'-~~-1 Machine with Controller Signal Table slide position (m) Yasnac Conditioning Computer Controller Fig. 8. X-axis, 2.54 mlmin, Terminal Point Error Compensation Spindle Bearing Force. Position Controls .--~~-an.d. ,C ommand Volkman S2H Spindle Excitation <> uncompensated, mean=226, std=7.11 Controller Controller " compensated, mean=l.78, std=l.27 improvement factor= 126 40 Er r Levitation Power and Feedback 30 f in Fig. 5. Primary Elements of Research Facility 20 rn I 10 ~ 0 n s -0.55 -0.4 -0.25 -0.1 -+- Table slide position (m) Fig. 9. Short Term X-uis, 2.54 m/min Terminal Point Error Compensation Coapensat.d Spindle Trajectory Error Controller : \:I 0 Slide Move111ent Magnetic 11~.))-~n Bearing 25.20 oa Controller 25 40 oa a, C "Baseline <> Compensated C O Magnetic p e _,., 25.7 Spindle a :Oz 0 r e Movement t 25.6 w 25.5 Incremental ~ motion t 25.4 h in Accuracy 25.3 i Enhanced mm 25.2 Part 0 20 40 60 BO 100 120 140 Position Along Part ~ngth (mm) Fig. 6. Error Minimization Methodology Fig. 10. Trapezoidal Test Part and Error Compensation Results 39 Page 1223 PROCEEDINGS OF THE THIRD INTERNATIONAL SYMPOSIUM ON MAGNETIC BEARINGS EDITED BY PAUL E. ALIAIRE July 29-31, 1992 Radisson Hotel at Mark Center Alexandria, Virginia SPONSORED BY The Center for Magnetic Bearings, University of Virginia CO-SPONSORED BY Virginia's Center for Innovative Technology (CIT) Electric Power Research Institute (EPRI) National Aeronautical and Space Administration (NASA) a,1111 TECHNOMIC PUBLISHING CO .. INC. T, ANCASTER • BASEi' Page 1224 Physical Modelling of High Speed Magnetic Bearing Systems R. G. JOHNSON, D. PANG, J. A. KIRK AND D. K. ANAND ABSTRACT Magnetic bearings offer significant advantages due to their non-contact operation. Higher speeds, no friction, no lubrication, precise position control, and active damping make them far superior to mechanical bearings. The University of Maryland has developed a combination electro/permanent magnet bearing that axially supports a flywheel and provides active radial displacement control. A vertically stacked system integrates two bearings and a motor/generator for kinetic energy storage applications. The current aluminum flywheel is designed to rotate at 15 kRPM, with a composite follow-on reaching 80 kRPM and capable of storing 500 watt-hours. Because of nonlinear effects, a closed solution analysis is practically impossible. Permeance modelling, empirical data, finite element analysis, and other numerical methods are generally used to determine the characteristics of such device. In the PM/EM bearing, high rotational speeds cause flywheel deformation and air gap growth. Gyroscopic effects and dynamic imbalance in the flywheel couples the two radial axis motion. Pole face misalignment due to the flywheel weight decreases axial stiffness. The cycling magnetic fields caused by flywheel rotation increases hysteresis and eddy current losses. This paper discusses the physical modelling of nonlinear high-speed factors: dynamic motion, displacement sensor error, pole face misalignment, disturbance force, gyroscopic motion, and air gap growth. Part of the modelling includes a computer simulation of the bearing magnetic circuitry which analyzes nonlinear magnetic and geometric effects. The program functions as a design tool for future prototype development. INTRODUCTION The flywheel energy storage (FES) system [1] shown in Figure 1 relies on two magnetic bearings to suspend a flywheel against gravity and destabilizing radial forces. Because the bulk of magnetic flux is provided by permanent magnets, power Department of Mechanical Engineering, University of Maryland, College Park, MD 20742 USA 474 Page 1225 Physiail Modelling of High Speed Magnetic Bearing Systems 475 requirements are reduced to that of a motor/generator for energy conversion and electromagnets for stabilization. The system's high efficiency, high specific energy density, and low environmental impact make it a more viable alternative to other forms of stored energy. Limiting factors include material strength of the flywheel, torque generating capacity of the motor/generator, control system response frequency, and bearing force capabilities. The composite flywheel currently being developed will withstand speeds up to 80 kRPM and the motor/generator has been designed to commutate at that speed in the vacuum. The last two factors, however, are more difficult to assess when considering high-speed operation. A block diagram of the bearing operation is shown in Figure 2. Voltage feedback from the control system is combined with disturbance force F d and sensor noise 71. The actuator consists of the power amplifier and electromagnets, which provide additional flux in the air gap where needed to stabilize the bearing. Rotor dynamics results from the rotational inertia and the destabilizing radial force from the permanent magnet flux distribution. DISTURBANCE CONSIDERATIONS A single magnetic bearing system has four centers: geometric center, mass center, magnetic center and sensor center. Ideally, the four centers are coincident Eccentric errors will introduce disturbances into the system. We assume the rotor is a geometrically perfect cylinder. The eccentric errors of the other centers will cause a mass imbalance, magnetic imbalance, and sensor error. At low speed the magnetic bearing will force the rotor to spin at the sensor center. At high speed the rotor will spin along the inertia axis. A mass imbalance is caused by the rotation of an eccentric mass. The imbalance force can be written as (1) where du is the distance between the mass center and the rotating center, and n is the rotating speed. The magnetic imbalance due to uneven magnetic flux distribution in the air gaps of the magnetic bearing will cause a fluctuating force even at very low speed of F =K d eJCt (2) "1n a,,. where Ka is the active stiffness of the magnetic bearing, and dm is the distance between the magnetic center and the rotating center. The sensor center is the intersection of two axes of the displacement sensors, which maintain an uniform gap to the rotor. The sensor error can be represented as (3) where ds is the distance between the sensor center and the rotating center. Errors will be further compound by imperfect geometries of the bearing and Page 1226 476 BEARING MODELING rotor components and an axial misalignment between pole faces of the stator and rotor. Because the FES system consists of two magnetic bearings and a motor/generator it becomes very difficult to experimentally differentiate between error sources. ROTOR DYNAMICS The rotor dynamic modelling includes the mechanical dynamic behavior of the stator and rotor with their inherent destablizing force from the permanent magnets. Lashley et. al. [2] conducted a model test of a four inch prototype aluminum flywheel system. An impact test of the freely suspended flywheel shows its first natural frequency is 4.35 kHz. Because this value is substantially above the maximum operating speeds (1.33 kHz), rigid body motion analysis is valid. The support structure has four natural frequencies below the maximum operating speed, but it is feasible to alter the dynamic characteristics via the structural design. For a proposed composite flywheel the first natural frequency is calculated to be 2.14 kHz, which is also above the maximum operating speed. For a single magnetic bearing the rotor dynamics can be viewed as planar motion, a problem with two degrees of freedom. Because of axis symmetry, the rotor dynamics can be further simplified to be one degree of freedom problem. The dynamic equation becomes Mx-K-r=-F +F (4) :C C d where F c and F d are the corrective and disturbance forces. The flywheel spins on the Z axis at a rate of n rad/s. The flywheel has four degrees of freedom, X1, X2, Y1 and Y2, which are the displacements of the flywheel measured at the magnetic bearing planes. The dynamic equations of gyroscopic effects show X and Y coupled at high speed: M(i1+~) 2 -Kx(x1 +x2)=-(Fa 1+Fa 7.)+(Fa xi+Fd x2) M(j1+Y2) -Kz;Rn (15) Wµ=f~12µ = ~ -2- The first derivative of this function with respect to the Z direction yields the axial force, and the second derivative yields the axial stiffness ~. The three material permeability curves in Figure 5 are programmed: DC, 60 Hz, and 400 Hz ( corresponding to 0, 3600, and 24000 RPM) to represent the eddy current effects in the core material. The flywheel speed determine which two curves to interpolate between, as well as setting the gap growth factor due to centripetal forces. The bearing's maximum axial support can thus be fixed from geometry and speed. Axial force eJ}"or between experimental data and simulation results ranges between 0.2 and 3.0 lb (0.9 and 13.3 N) on the low side so it provides for a margin of Page 1230 480 BEARING MODELING safety. Figure 6 illustrates a comparison of the theoretical and experimental axial force for the current bearing. The axial stiffness Kz ranges from over 300 lb/in (52.5 N/mm) near zero displacement, decreasing to 200 lb/in (35.0 N/mm) farther down. It is desired that the misalignment be no more than 20% of the pole face thickness, which corresponds to 0.024 in (0.61 mm). CONCLUSION This paper presents a physical model of the magnetic bearing system for high speed applications. The FES system becomes nonlinear due to gyroscopic motion, air gap growth, pole face misalignment, nonlinear permeability, and eddy current effects. The model includes these nonlinear factors as well as system disturbances such as eccentric mass, magnetic imbalance forces, and displacement sensor error. To analyze the nonlinear effects on the bearing computer simulation software called AMBER has been developed. AMBER applies magnetic circuitry, finite element analysis, and a coenergy method to calculate bearing axial force and stiffness. There is good correlation between simulation results and experimental data from existing bearings. REFERENCES 1. Anand, D. K., Kirk, J. A., Iwaskiw, P., "Magnetically Suspended Stacks for Inertial Energy Storage Flywheel", Proceeding of 22th IECEC, 1987. 2. Lashley, C.M., Ries, D.M., Zmood, R.B., Kirk, J.A., Anand, D.K., "Dynamics Considerations for a Magnetically Suspended Flywheel", Proceeding of 24th IECEC, 1989. 3. Zmood R.B., Anand, D.K., Kirk, J.A., "The Influence of Eddy Currents on Magnetic Actuator Performance", Proceedings of IEEE, Vol. 75, No. 2, February 1987. 4. Johnson, R.G., Computer-Aided Modelling and Simulation of a Magnetic Bearing System, M.S.Thesis, University of Maryland, College Park, 1991. NOMENCLATURE a flux density correcting factor ~ air gap pole face cross-sectional area Aui permanent magnet cross-sectional area Br permanent magnet remanence ic control system-induced EM current J mass moment of inertia N number of electromagnet coils Rm permanent magnet reluctance µ 0 permeability of free space Page 1231 MAGNETIC BEARING COMPOSITE MATERIAL FLYWHEEL MOTOR GENERA TOR Figure 1 Flywheel Energy Storage System Tl X* Gpa(s) Gpr(s) Gps(s) -- Actuator Rotor Dynamics Sensor Gc(s) Control System Figure 2 System Block Diagram EM Ni fil 4 4 Rm Rm Rg t RL PM PM RL t Rg BrAmRm BrAmRm + Ni 4 t EM Figure 3 Magnetic Bearing Electrical Analog 481 Page 1232 Carpenter Steel Magnetization 105~-----.-------.----..,......----, DC 0 00 >. 0 104 ·- a 60Hz [J a a Ill Q) a a • E I I I. Q) I a. (I) 103 > 0 0 0 .., II -Ill a (I) a: CARRIAGE RAIL «S EYE ..J ..J <( <( .... UUZ 1-ti-lUJ ZC:l: FIBER REINFORCEMENT ___,4 ----9- UJ..JC l:LULU MANDREL Figure 3 Two Axis Filament Winding Process for Rotor Fabrication 566 Page 1242 --2 HR.- COOL DOWN 350" t AT s• F/HIN TEMPERATURE I --1 HR,......., 11s· F/HIN VACUUM= 25 In Hg Figure 4 A Typical Epoxy Cure Cycle Using Vacuum Bagging Technique o"r(r) = A+ Br -(K+l) + CrK·l a9 (r) = A- BK.r -(K+l) + CKr K·l §a whereK2 = Er A = -a [ -1 - -1 l, a = angle of separation or overlay 2-r E9 Er b-(K+l)-a{K+l) l C =-A [ aK·l b-(K+l) .b1(·1 a -(K.+1) Figure 5 Residual Stresses in a Wound Composite Ring [7] 567 Page 1243 . ' , ·~ chnology for En rgy Efflci ncy In th 21st Century' Page 1244 HOST SOCIETY COMMITTEES Society of Automotive Engineers 400 Commonwealth Drive CONFERENCE COMMITTEE Warrendale, PA 15096-0001 Telephone: (412) 776-4841 General Chairman: ............................................................... Dr. Bury/ McFadden Facsimile: (412) 776-5760 Program Chairman: .................................................................... Timothy J. Bland l 1991-1992 IECEC STEERING COMMITTEE l A MESSAGE FROM THE 1992 IECEC Society of Automotive Engineers (SAE) CHAIRMEN Dr. Bury/ McFadden, Wright-Patterson AFB, OH Timothy Bland, Sundstrand Corporation, Rockford, IL American Chemical Society (ACS) IECEC is returning to San Diego after six years. The combina- HamidArastoopour, Illinois Institute of Technology, Chicago, IL tion of pleasant August weather and many attractions make this Dr. Joe W. Hightower, Rice Univ., Houston, TX one of the more popular sites for a conference, and this year, American Institute of Aeronautics and Astronautics (AIAA) when budgets are tight, the conference locale offers reasonable A. Warren Adam, Sundstrand Corporation, Rockford, IL hotel rates. We have assembled an exciting technical program Robert C. Winn, Consulting Engineer, Colorado Springs, CO covering many different topics to challenge your intellect, and we also offer several social functions to help you enjoy San American Society of Mechanical Engineers (ASME) Landis Kannberg, Battelle Pacific NW Laboratories, Richland, WA Diego's tourist attractions while giving you the opportunity to Yogi Goswami, Univ. of Florida, Gainesville, FL meet old friends. Institute of Electrical and Electronics Engineers (IEEE) As we get ever closer to the 21st Century, ourneed to emphasize William Jackson, HMJ Corporation, Kensington, MD energy efficiency increases. Growing worldwide recognition of William Billerbeck, MRJ Incorporated, Oakton, VA the need to protect the environment and conserve finite re- American Institute of Chemical Engineers (AIChE) sources, while improving quality of life, will certainly require Elton Cairns, Lawrence Berkeley Laboratory, Berkeley, CA every effort to minimize the energy consumed per unit produc- Paul Nelson, Argonne National Laboratory, Argonne, IL tion by industry. In addition, improved efficiency in the area of creature comforts can play a significant role in these vital areas. American Nuclear Society (ANS) David Black, Westinghouse Electric Corporation, Washington, DC Patrick Bailey, Lockheed Missiles and Space Co., Sunnyvale, CA We will open the conference on Monday morning with a keynote address by Dr. Stuart Fordyce of NASA entitled, "Promises to Keep." This year we plan to offer a conference dinner on TOPICAL COORDINATORS Tuesday evening at which our conference speaker will address issues associated with the theme of Energy Efficiency. Having AEROSPACE POWER SYSTEMS a dinner on Tuesday evening leaves Wednesday afternoon A. Warren Adam, Sundstrand Corporation, Rockford, IL William J. Billerbeck, MRJ Inc., Oakton, VA completely free for other activities, including the numerous committee meetings, which we always hold in conjunction with CONVERSION TECHNOLOGIES IECEC, and time to visit the San Diego attractions. We will be William Jackson, HMJ Corporation, Kensington, MD offering an evening trip to Tijuana, a harbor tour on a charter boat, and a guided tour of the zoo. ELECTROCHEMICAL CONVERSION Albert R. Landgrebe, DOE, Washington, D.C. The chairmen, the Steering Committee, and especially the ENERGY SYSTEMS topical coordinators and organizers have worked hard to provide M. Mitchell Olszewski, Martin Marietta Energy Systems, Oak Ridge, TN you· with the best possible program for your enjoyment. In particular, the staff at SAE has done an outstanding job behind POLICY ISSUES Sampat Sridhar, Atomic Energy Commission of Canada, Ontario, Canada the scenes at coordinating all the details. Finally we must not forgetthe authors, without whom none of this would be possible. NEW TECHNOLOGY We are excited about the program and look forward to meeting Patrick Bailey, Lockheed Missiles and Space Co., Sunnyvale, CA you there. RENEWABLE RESOURCES Steven G. Hauser, National Renewable Energy Lab., Golden, CO Bury/ McFadden, General Chairman STIRLING CYCLES Jeffrey Schreiber, NASA Lewis Res. Ctr., Cleveland, OH Tim Bland, Technical Program Chairman Page 1245 MONDAY, AUGUST 3 The Principle Correction Factors in the Expression of 929027 A Computer Analysis of Regenerator Losses in a Stirling 929038 Stirling Engine Power Cryocooler with Multiple Expansion Stages Paolo Lista, Vincenzo Maso, Univ. of Rome, lvo Kolin, Prof., Israel Urieli,Kuo-Chiang Tang, Ohio Univ. Univ. of Zagreb Free-Piston Stirling Coolers for Intermediate Lift 929039 HFA ST - A Harmonic Analysis Program for Stirling Cycles 929028 Temperatures S. C. Huang, Analyst, Mechanical Technology, Inc. David M. Berchowitz, ChiefEngr., Sunpower, Inc. Comparison of GLIMPS and HFA ST Stirling Engine Code 929029 Predictions with Experimental Data Steven M. Geng, Res. Engr., Roy C. Tew, Res. Engr., DOMESTIC POLICY NASA Lewis Res. Ctr. (Session Code: Pil) Simple Vector Analysis of Stirling Machine's Basic 929030 Sierra Room 1:30p.m. Performance Naotsugu lsshiki, Prof., Nihon Univ. A session describing policy aspects of energy in both the U.S. and other nations. Summary of Simulation Models for Stirling and Vuilleumier 929031 Organizer and Chairperson--Herbert lnhaber, Prin. Sci., Westinghouse Cycle Machines and Characteristic Analyses Savannah River Co. Hiroshi Sekiya, Fasao Terada, Sanyo Electric Co., Ltd., lwao Yamashita, Mechanical Engineering Laboratory Paper No. A Linear Model of a Free Piston Vuilleumier Machine 929032 Contemporary U.S. Domestic Policy on Energy Future 929040 Compared to Experimental Results of a Prototype Miro Todorovich, Exec. Dir., Scientists and Engineers for S. Schulz, Prof., B. Thomas, Res. Asst., Univ. of Dortmund Secure Energy Is Migration-Induced Warming Greater than the Physical 929041 Greenhouse Effect? Herbert lnhaber, Prin. Sci., Westinghouse Savannah STIRLING REFRIGERATORS/HEAT PUMPS AND River Co. CRYOCOOLERS (Session Code: SC2-A2) Sustainable Energy Development 929042 Steven Ebbin, V. P., Ahmad Ghamarian, Tech. Dir., Inst. of Sunset Room 1:30p.m. Intl. Education Stirling refrigerators/heat pumps and cryocoolers. A Total System Approach for Electric Vehicles 929043 Mario Cardul/o, Roger LeGassie, Technology and Management Organizer--Graham Walker, Prof., Univ. of Calgary Services, Inc. Chairpersons--Ronald Fiskum, Dept. of Energy, Theodor Finkelstein, Stirling Associates Intl. Paper No. ENERGY STORAGE TECHNOLOGY & MAGNETIC BEARING APPLICATIONS Engineering Model Cryocooler Test Results 929033 (Session Code: ES7) Martin A. Shimko, W. Dodd Stacy, Creare Inc. Mesa Room 1:30p.m. Dynamic Behavior and Load Matching Analysis of the Mark II 929034 Free-Piston Stirling Engine Heat Pump This session addresses high speed rotating devices and the use of Magnetic Ronald J. Vincent, Sr. Mech. Engr., Mechanical Technology Inc. Bearings to suspend and control these systems. Papers will address Rotor- Bearing System interactions and advanced techniques for diagnostic and control Stirling, Near-Ambient Temperature Refrigerators: 929035 of rotating systems. In addition, manufacturing techniques to greatly enhance Innovative Compact Designs high speed performance of composite material flywheels will be presented. Graham Walker, Prof., Graham Reader, Prof., Rod Fauvel, Assoc. Prof., E. R. Bingham, The Univ. of Calgary Organizer--James A. Kirk, Prof. of Mech. Engrg., Univ. of Maryland Chairperson--Da-Chen Pang, Res. Assoc., Univ. of Maryland Simulation Program for Multiple Expansion Stirling 929036 Cryocoolers Paper No. Graham Walker, Prof., Marvin Weiss, Graham Reader, Prof., Rod Fauvel, Assoc. Prof., E. R. Bingham, The Univ. of Calgary Influence of Magnetic Bearing Operating Constraints on 929044 Rotor-Bearing System Performance Calorimetric Thermal-Vacuum Performance 929037 Ronald B. Zmood, Prof. of Elec. Engrg., Royal Melbourne Inst. Characterization of the BAe 80 K Space Cryocooler of Technology, J. Krookiewski, Prof., Univ. of Melbourne V. Y. Kotsubo, Engr., D. L. Johnson, Engr., R,,G. Ross, Jr., Grp. Supvr., Jet Propulsion Laboratory Computer-Aided Modelling and Analysis of a Magnetic Bearing 929045 System ( continued next column) Ryan G. Johnson, Res. Asst., D. Pang, Res. Assoc., James A. Kirk, Prof., D. K. Anand, Prof., Mech. Engrg., Univ. of Maryland ( continued next page) 11 Page 1246 MONDAY, AUGUST 3 Versatile Diagnostic Device for Use with Magnetic Bearings 929046 TERRESTRIAL BATTERIES Il Robert H. Hwnphris, Prof., Univ. of Virginia (Session Code: ECl-B) Neural Network Controller Design for a Magnetic Bearing 929047 Adobe Room 1:30p.m. Flywheel Energy Storage System Roger L. Fittro, Res. Asst., D. K. Anand, Prof., Mech. Engrg., Organizer and Chairperson--Michael D. Eskra, Mgr., Advanced Battery Univ. of Maryland Systems, General Motors Corp. Design and Manufacturing for a Composite Multi-Ring Flywheel 929048 Paper No. Douglas M. Ries, Mech. Engr., FARE, Inc., James A. Kirk, Prof., Univ. of Maryland Final Report on the Development and Operation of a 929054 1MW/8MWh Na/S Battery Energy Storage Plant Eiichi Nomura, Kazumasa Matsui, Asao Kunimoto, Koichiro Takashima, Yuji Matsumaru, Yuasa Battery Co., Ltd., AQUIFER THERMAL STORAGE Shigeru lijima, Yasushi Matsuo, NGK Spark Plug Co., Ltd., Toshihiko Hirabayashi, Shigenobu Furuta, New Energy and (Session Code: ES2-B) Industrial Technology Development Organization, NEDO El Camino Room 1:30p.m. lOOOkW Sodium-Sulfer Battery Pilot Plant: Its Operation 929055 Experience at Tatsumi Test Facility The long-term performance of a number of heat and chill AIBS systems are T. Tanaka, A. Miyoshi, T. Tada, Y. Yano, Y. lguchi, The Kansai presented in this session. Electric Power Co., Inc., S. Furuta, T. Hirabayashi, New Energy and Industrial Technology Development Org. Organizer--£. A. Jenne, Sr. Staff Scientist, Pacific Northwest Laboratory Chairperson--Edward Morofsky, Public Works Canada Nickel Hydrogen Batteries for Terrestrial Applications 929056 Jeff Zagrodnik, Ken Jones, Johnson Controls Battery Grp., Inc. Paper No. Long-Term Performance of an Air-Conditioning System Based 929049 on Seasonal Aquifer Chill Energy Storage K. C. Midkiff, C. E. Brett, K. Balaji, Y. K. Song, Dept. of HEAT ENGINES AND ADVANCED CYCLES Mechanical Engrg., Univ. of Alabama (Session Code: CT3-B) Experience with a Solar Heating ATES System for a University 929050 Padre Room l:30p.m. Building Erich Hahne, Prof., Director, Martin Hornberger, Asst., The first paper describes analysis and results for a device which extracts Univ. of Stuttgart mechanical work from the temperature dependent stress/strain relationship for nickel-titanium alloy. The remaining three papers are devoted to diesel engines. Results of the Third Long-Term Cycle at the University of 929051 Two of them discuss the development of a diesel engine which can operate Minnesota Aquifer Thermal Energy Storage (ATES) Field independent of the atmosphere. The third describes the design and performance Test Facility of a diesel engine incorporating a mechanism which makes possible an expan- Marcus G. Hoyer, Scientist, Raymnnd L. Sterling, Dept. of Civil & Min. sion stroke that is longer than the compression stroke. Engrg., Univ. of Minnesota Organizer and Chairperson--Char/es H. Marston, Assoc. Prof., Villanova Univ. Heat Storage at SPEOS (Swiss ATES Pilot Plant): Chemical and 929052 Microbiological Aspects and Problems Paper No. Lucia Jollien, Chemist, Sabine Remnnnay, Chemist, Firouzeh Miserez, Mgr., ICC lngenieurs Chimistes-Conseils SA Shape Memory Alloy Engine 929057 Makoto Tanaka, MITI, JAPAN High-Temperature ATES at the State University of Utrecht, 929053 The Netherlands A Thermodynamic Model of an Air Independent IDI Diesel 929058 L.JM . van Loon, Heidemij Adviesbureau, K. van der Holde, Engine System Univ. of Utrecht M. Zheng,/. J. Potter, G. T. Reader, R. W. Gustafson, Dept. of Mech. Engrg., Univ. of Calgary Development of an IDI Diesel Engine Test Facility for Use with 929059 Nonconventional Atmospheres I. J. Potter, M. Zheng, G. T. Reader, R. W. Gustafson, Dept. of Mech. Engrg., Univ. of Calgary Alternative Mechanical Arrangements for Diesel and 929060 Spark-Ignition Engines Employing Extended Expansion Strokes J. A. C. Kentfield, Dept. of Mech. Engrg., Univ. of Calgary 12 Page 1247 IECEC-92 San Diego, CA August 3-7, 1992 Proceedings of the 27th lntersociety Energy Conversion Engineering Conference P-259 • Volume 4 •.l.!! f-J-!-A-~- Energy Systems New Technologies Aquifer Thermal Storage Energy Storage Technology and Magnetic Bearing Applications New Technologies for Energy Utilization: Superconductivity +. Thermal Storage Nuclear Fission and Fusion Power Thermal Management of Energy Systems IEEE Marine Energy New Technologies for Energy Utilization: Advanced and Innovative Concepts Alternative Fuels Society of Automotive Engineers, Inc. 400 Commonwealth Drive• Warrendale, PA 15096-0001 Page 1248 929045 Computer-Aided Modelling and Analysis of a Magnetic Bearing System Ryan G. Johnson U.S. Navy Da-Chen Pang, James A. Kirk, and Davinder K. Anand University of Maryland 1. The pennanent magnets offer a bias flux and the feedback ABSTRACT controlled electromagnets add or subtract flux in the air gap in order to keep the flywheel centered. The bearings radially AMBER (Active Magnetic Bearing Evaluation control the position of the flywheel as it rotates and suspend it Routine) is a computer algorithm developed for the University axially through the passive bi~ flux. of Maryland pancake magnetic bearing, which supports and controls af lywheel in a kinetic energy storage system. Because of the gap growth due to centrifugal forces at high speed, the bearing axial load capability degrades and the axial characteristics become critical in the bearing design. AMBER applies magnetic circuit theory, magnetic material saturation curves, coenergy theory, and finite permeance- based elements to solve the air gap flux density and coenergy over a series of incremental axial displacements. Differentiation of the coenergy of the magnetic field yields axial force and stiffness characteristics. An axial test machine is constructed to conduct experiments to verify the flux distribution and axial forces predicted by the model. MAGNET PLATES User interaction with AMBER allows modification of the bearing geometry and composition to optimize future prototypes. NOMENCLATURE B: Flux Density ~: Axial Stiffness R: Reluctance of Flux Paths vol: Volume of Air Gap W'M Coenergy of Magnetic Field 4,: Magnetic Flux Figure 1 Pancake Magnetic Bearing µ: Permeability The current energy storage system includes a INTRODUCTION flywheel and a vertical stack which sandwiches a motor/generator between two magnetic bearings [1]. In order Magnetic bearings have advantages over to store and deliver energy, the flywheel is designed to cycle conventional mechanical bearings, including high speed, no between low and high speed rotation (40,000 RPM to 80,000 friction, no lubrication and precision control. The University RPM). In addition to dynamic effects, the air gap increases of Maryland uses magnetic bearings to suspend a high speed up to 40% of the nominal value due to centripetal forces [2]. flywheel in a kinetic energy storage system. The magnetic The air gap growth has nonlinear effects on the bearing flux bearing combines pennanent magnets (PMs) and distribution, axial load and radial control capability. The electromagnets (EMs) for high efficiency as shown in Figure bearing behavior in the axial direction deteriorates and becomes critical in the system design. 4.23 Page 1249 Sabnis [3] using field theory and the Schwarz- with an internal resistance. The permanent magnets used in Christoffel transformation derives the axial stiffness of finite- the pancake bearing are made of samarium-cobalt (SmCo5) width rectangular pole face geometry. The stiffness can be with a remanence of O. 9 T, coercive force of 700 kA/m, and determined by the air gap flux density and its geometry. The maximum energy density of 160 kJ/m3. derivation ignores flux changes and saturation effects with ELECTROMAGNETS - An electromagnet can also pole face misalignment. The axial stiffness }'-z is in error by be modelled as a voltage source which is a function of current 30% to 155% over the experimental values, depending on the and the number of coil turns. In the pancake bearing, two axial displacement of the bearing. This method is therefore electromagnets add or subtract flux from each quadrant as only useful as a first approximation. dictated by the control system response to off-center The purpose of this work is to illustrate a tool - a displacement. Ferromagnetic flux control plates are used to computer model - based on experimental data and magnetic transfer flux across two opposing quadrants. There are a total theory that accurately predicts axial characteristics of a of four electromagnets connected in parallel by each control magnetic bearing. Using permeance modelling, empirical channel. data interpolation, and finite element meshing, the flux FERROMAGNETIC MATERIALS - Nickel-iron through each path of the model is determined for a given steel, although expensive, is a very good ferromagnetic state. Evaluation of the air gap flux density through an material with high permeability and saturation flux density of incremental series of axial pole face misalignments provides 1.3 T. Three material permeability curves (4] shown in information on the rate of change of coenergy and axial force. Figure 2 are tested at frequencies of DC, 60 Hz, and 400 Hz The axial force and stiffness assist in determining the design (corresponding to 0, 3600, and 24000 RPM) and represent the of the bearing and flywheel. Changes in geometry and eddy current effects on the core material. The permeability of rotational speed are substituted into the model to estimate the core material can be accurately represented by a third- high-speed behavior and possibilities for optimization. order polynomial below the flux density of 1 T and a continuous, decaying exponential above 1 T. Depending on MAGNETIC CIRCUIT APPROACH the flywheel speed the permeability is calculated by interpolating between the appropriate two curves. Magnetic bearing~ can be modelled using magnetic circuit or finite element approaches. The magnetic circuit method is easy and quick to implement and offers an approximate solution. The finite element method is good for a detailed study in a complicated system. Because of the ex: 0~ 00 magnetic bearing design, the finite element model must be 0 three dimensional with both cylindrical and Cartesian C 601-!Z coordinates. Also, despite symmetry sufficient resolution 0 0 ...... , 0 I I requires a large number of wavefront degrees of freedoms. In 0 a • I 4001-!Z light of the high cost of equipment and software licensing, the ooO[! I • • 0 0 uncertainty of any improvement over current modelling a I ... techniques detracts from the feasibility of employing the finite ••• oO • • II element approach. 0 However, the concepts behind finite element analysis can be applied to the magnetic circuit approach, providing 411 .. , ... definite improvements. For the pancake magnetic bearing, a '" '" 1 major source of magnetic nonlinearity is the permeability 10·B(T) curve of the ferromagnetic material. Material permeability quickly decreases to near that of free space when the flux Figure 2 Nickel Iron Permeability Curve density in a ferromagnetic material is too high. Refined meshing is used to study the smaller cross-sections which are FLUX PATHS - There are three basic flux paths in more apt to saturate, and cause nonlinearities and prediction the bearing: useful flux, fringing flux, and leakage flux. The error. To detect possible saturation, the ferromagnetic core first two flux paths occurring around the air gap between two parts are meshed appropriately with the smaller cross-sections pole faces are the most important for magnetic bearing being given higher priority. performance. The useful flux, the perpendicular connection PERMANENT MAGNETS - Rare-earth permanent between the pole faces, is responsible for radial control of the magnets are used because of their high energy density and bearing. Fringing flux paths above and below the useful flux high intrinsic coercivity. These permanent magnets are very path provide the passive axial support for the return ring and difficult to demagnetize and the relationship between an flywheel. Leakage flux is any magnetic flux that deviates imposed magnetic field 8in and the produced flux density Bm from the intended path between the pole faces by short- is very close to linear. Additionally, recoil occurs along the circuiting though air. The amount of the leakage flux will same line as well. Because the magnet permeability is on the determine the efficiency of the bearing. same order of magnitude as that of free space, the permanent Pole face misalignment critically affects the useful magnet places a large reluctance in the circuit. A permanent flux by decreasing the useful flux area and causing useful flux magnet can be modelled as a constant voltage source (battery) to be diverted into fringing paths. It also increases the 4.24 Page 1250 reluctance around the air gap. Because the flux "prefers" the Figure 4 illustrates a simplified quadrant symmetry useful region over fringing path the flux through the useful version of AMBER's magnetic circuit. The M.1BER program region decreases more slowly than the cross-section area until inputs the data of bearing geometry, permanent magnet saturation occurs at the pole faces. Therefore, the useful path strength, control current settings, and ferromagnetic material reluctance continually increases until the reluctance of the permeability. It iteratively finds the flux and flux density closest fringing path becomes equivalent. distnbutions in the network of over 500 fixed and variable Jeyaseelan [51 using Roters' spherical quadrants reluctances based on Kirchhoff's principles. An initial method [6] calculates all flux paths in a magnetic bearing. permeability is assumed in all core materials of the bearing. To study the nonlinear effect of the ferromagnetic material Based on the reluctance established by the mean path length, the flux paths are further separated into 8 segments in each cross-sectional areas and permeabilities, the flux through quadrant as shown in Figure 3. The reluctance of the useful each path is calculated. The resulting flux density is and fringing flux varies due to pole face misalignment but substituted into the material permeability curve polynomial most leakage flux does not. In the magnetic circuit there are and a second permeability is determined. The adjusted 4 constant voltage sources (PMs), 8 variable voltage sources permeability is calculated with a blending factor that auto- (EMs), 458 fixed value resistors, and 100 variable resistors. detects convergence or divergence of the cumulative errors and increases its own value. ~ ~'<,~Cl~ ~e~~ pole face Figure 3 Magnetic Plate Flux Paths Figure 4 M.1BER Electrical Analog with Quadrant COENERGY Symmetry The coenergy of the magnetic field in the air gap The magnetic circuit is solved over a range of axial region can be calculated as pole face misalignments. The coenergy of the magnetic field in the air gap region is calculated for each Z value and the B2 #regions ¢1;,R,, data pairs are curve-fit via linear regression with a fifth-order W'fld= J-= I: _n_ polynomial. The axial force and stiffness are obtained by vol2µ n=l 2 differentiating the coenergy polynomial. The data is stored in a disk data file for importation into a spreadsheet or other The coenergy of the air gap can be calculated over a graphing/analysis program. range of incremental axial drops. The resulting coenergy data can be curve-fitted into a fifth order polynomial. The EXPERIMENTATION first derivative of the polynomial with respect to the Z direction yields the axial force and the second derivative The pancake magnetic bearing flywheel system is yields the axial stiffness. suspended in the space by 4 solid rods mounted on the base plate as shown in Figure 5 for the axial force test. Three steel AMBERPROGRAM wires are used to connect the flywheel and the strain ring. During testing the flywheel is centered via the control system. M.1BER is written in QuickBASIC for an IBM- As the lead screw is tightened, the wires displace the compatible PC with 512k main memory running DOS 2.0 or flywheel. The force is measured from the strain ring and the later versions. Two data files are used which contain the axial displacement from a depth micrometer and dial gage. specifications of the pennanent magnets and the bearing Displacement measurements are taken at each of the three geometry. If desired, the user may enter his own parameters connection points to ensure the :flywheel plane is maintained and save them on disk for later recall. The most critical level with the plane of the pancake bearing. The air gap flux selections are always prompted: control currents, axial drop, density of the bearing is also measured using a Hall-effect and drop increment. The user may also request the display of flux probe. the flux densities of critical ferromagnetic cross-sections at each displacement to check for saturation. 4.25 Page 1251 N/mm) near zero displacement, to 200 lb/in (35.0 N/mm) Flywheel Magnetic Bearing farther down. It is desired that the misalignment be no more than 20% of the pole face thickness, which corresponds to 0.024 in (0.61 mm). 0.8 fBOTTOM I It-,.. 0.7 I" n I ' 0 ~ r ..., I \ 'I \ I ,\ 0.8 E J 0.5 \ J '\ Ii \ I Strain Ring Lead Screw f , r:1' V \..Li ~ 0.4 ' I o.3 I 0.2 AXIS DIFFERENCE I 0.1 0 - -- - r - - A V ' -0.!150 ·100 .50 0 50 100 150 200 250 Figure 5 Axial Test Apparatus Reference Angle (degrees, O=north) Three experiments are conducted to evaluate the test Figure 6 Flux Density Distribution of Top and Bottom Pole condition and verify the AMBER model. The first is a Faces measurement of flux density distribution of the bearing. This data provides an indication of the base operating condition of 0.8 I I the bearing. The second test is a measurement of flux density ~ 0.75 :increased Axial Drop I 11"'1 as a function of reference angle and axial drop. The third test j - ',:ZS. 0.7 determines the relationship between axial force and pole face E ,vr f f} ~ misalignment. The last two tests are used to compare the 0.85 u I \ prediction from the AMBER program. ~ 0.6 1 There are some limitations to the accuracy of this I ~ 0.55 experiment. First, sensor dimensions of the flux probe is j 0.5 \ I 0.120 in x 0.060 in (3.05 mm x 1.52 mm) which is large ~ ':, 0.45 J' '\ comparing to the pole face thickness of 0.125 in (3.18 mm) ' for pinpoint measurements. If the air drop is over 0.005 in 0·iso -200 .150 -100 .50 o 50 100 1so (0.13 mm), the flux probe measures a proportion ofboth Reference Angle (North = o degrees) useful and fringing flux. The second inaccuracy is that the flux densities at the top and bottom pole faces are different. Figure 7 Flux Density Variation Due to Axial Displacement Except for the first test, only the maximum flux densities at the top pole face are recorded. Third, the accuracy of the 0.8 axial displacement measurement is 0.25 mils (0.006 mm) for H El I I A A 0.75 1 the dial gage and 0.5 mils (0.013 mm) for the depth , fl 1ncraa,sed A~ ,xi al Drop, ~ micrometer. Forth, the flux density probe is accurate to 0.01 E .?; 0.7 T. Finally, structural vibration becomes excessive at a pole r! ~ 0.65 face misalignment ofO.l in (2.54 mm). !:§ Figure 6 shows the flux densities of different radial ii: 0.6 angles at both the top and bottom air gap. The difference in j 0.55 l magnitudes between the two gaps is attributed to bearing j 0.5 I I l I manufacturing errors and component inequality. In Figure 7, I t:: t::::l t=I I the flux density is noted to increase slightly with increased 0.45 ·50 0 50 100 150 200 250 300 350 axial drop. The flux density begins to drop after an axial Reference angle (degraes, o • north) displacement of0.017 in (0.43 mm). The AMBER prediction shown in Figure 8 has a large flux density increase. Figure 8 AMBER Results for Flux Density Variation Unfortunately, the theoretical model cannot be verified ex-perimentally due to the limitation of the flux probe. The axial forces of pole face misalignment from the AMBER prediction and experimental data are plotted in Figure 9. The axial force error between experimental data and simulation results ranges between 0.2 and 3.0 lb (0.9 and 13.3 N) on the low side providing for a margin of stability. The axial stiffness Kz ranges from over 300 lb/in (52.5 4.26 Page 1252 bearing. The air gap flu.x distribution of axial pole 20.00 misalignment is difficult to verify due to the large size of the 18.00 flux probe. a The pole face of the bearing is a primary region for 16.00 a saturation, and directly affects the radial and axial stiffness. a ,., H.00 w ia These two parameters cannot be maximized together, thus the Coc,ne ExPE imen al ~ n Al8 R !! 12.00 pancake bearing can either have mediocre performance in ... a V a both directions or have a severe deficiency in one. The Gl10.00 V - AMBER analysis suggests that since axial performance is I. ~ 8.00 .. a D severely degraded in the operational speed range of the 0 0 6.00 ~... •. - existing system, the future system should add a thrust bearing that passively carries the axial load and allows the pancake ~ uo ~ ......; ii bearings to radially control the position of the flywheel. 2.00 0.00 /i REFERENCE 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 Axial Displacement (in) 1. Anand, D. K., Kirk, J. A., Zmood, R. B., Pang D., Lashley C. M., "Final Prototype of Magnetically Suspended Flywheel Figure 9 Axial Force Comparison Energy Storage System", Proceeding of 26th IECEC, 1991. 2. Lashley, C. M., Ries, D. M., Zmood, R. B., Kirk, J. A., Anand, D. K., "Dynamics Considerations for a Magnetically PREDICTIVE SIMULATIONS Suspended Flywheel", Proceeding of 24th IECEC, 1989. 3. Sabnis, A. V., Analytical Techniques for Magnetic Bearings, Figure 10 predicts axial force capabilities of the Ph.D. Dissertation, University of California, Berkeley, 197 4. bearing at high rotational speeds. Because the centrifugal 4. Carpenter Technology Corporation, "Carpenter High forces cause the air gap to increase quadratically, gap Permeability 49 Alloy", 1988. reluctance is greatly increased. Also, the cycling of magnetic 5. Jeyaseelan, M., "A CAD Approach to Magnetic Bearing flux from the electromagnets at the same speed as the Design", M.S. Thesis, University of Maryland, College Park, flywheel causes hysteresis in the ferromagnetic core and 1988. decreases the permeability of those regions. Therefore, axial 6. Roters, H. C., "Electromagnetic Devices", John Wiley & force capability and axial stiffness generally decrease with Sons, 1941. speed. The trends depicted by AMBER correlate to this hypothesis, but no correlation can be made for the actual experimental data. 18 / J 18 _,,,.l..121" 14 g ~ 12 g / __. 10 V -- .... ... 8 J / v-- _... 8 __. ....... - - 4 .,......,._..._ _ V~ - 1.-«-i...-- L.-a-- -2 ~ 00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Axial drop (In) j-e- 0 RPM -- 5000 RPM ....tr- 10000 RPM -- 15000 RPM Figure 10 AMBER Prediction for Axial Force at High Speed CONCLUSION & DISCUSSION AMBER applies magnetic material saturation curves, magnetic circuit analysis, finite element analysis, and the coenergy method to analyze axial bearing characteristics and flux density distribution. There is a good correlation of axial force between the simulation model and the existing 4.27 Page 1253 IECEC-92 San Diego, CA August 3-7, 1992 Proceedings of the 27th lntersociety Energy Conversion Engineering Conference P-259 • Volume 4 ·...·,1-!11-!1-!%-. Energy Systems New Technologies Aquifer Thermal Storage Energy Storage Technology and Magnetic Bearing Applications New Technologies for Energy Utilization: Superconductivity Thermal Storage + Nuclear Fission and Fusion Power Thermal Management of Energy Systems IEEE Marine Energy New Technologies for Energy Utilization: Advanced and Innovative Concepts Alternative Fuels Society of Automotive Engineers, Inc. 400 Commonwealth Drive• Warrendale, PA 15096-0001 Page 1254 929047 Neural Network Controller Design for a Magnetic Bearing Flywheel Energy Storage System Roger L. Fittro and Davinder K. Anand University of Maryland ABSTRACT The conttol and analysis of magnetic bearings has been primarily based upon classical linear conttol theory. This approach does not allow for some important system complexities and nonlinearities to be taken into account. The resulting simplifications degrade the overall system performance. This paper investigates the use of a neural network to control a magnetic bearing flywheel energy storage system. A plant simulation is developed as well as a neural network emulator and conttoller. INTRODUCTION The University of Maryland has developed a combination electro/permanent magnet bearing system for use in flywheel energy storage. The bearing design used in this application can be seen in figure 1. This design has been thoroughly investigated and reported on in the literature. [l] Identical independent controllers are used to control each degree of freedom of the system. In the case of a single bearing. there are two degrees of freedom (x & y axes) and two corresponding Figure 1: Pancake Magnetic Bearing separate controllers. A vertically stacked system of two pancake bearings has also been developed in order alleviate tilt follows. A position transducer senses the position of the problems. In this design, a total of four independent flywheel and sends a signal to the linear controller; composed conttollers are used. of a compensation netwOJ:k, low-pass filter, and various gains. Because there is no physical contact between moving The resulting control signal is then fed into the power parts, the only frictional loss in the system is due to wind amplifier which in turn powers the electromagnetic coils resistance, which can be eliminated by operating in a vacuum. producing the appropriate stabilizing force. The flywheel The only other energy losses are due to eddy currents and response is then sensed by the position transducer and the cycle hysteresis in the ferromagnetic material and resistive losses in starts all over again. Unfortunately from a system design the electromagnetic coils. These losses can be made to be standpoint, there are a number of !l()nlinearities and quite small and therefore, a very highly efficient system complexities in this system which must be thoroughly results. Because of this high efficiency and the high specific understood and dealt with in order to achieve an optimal energy density capability of the flywheel, this system should design. However, at this stage in the research, this is not prove to be a far more favorable form of energy storage than possible and therefore approximations, linearizations, and any other presently available. simplifications have to be made. One of the main areas of uncertainty. and also an area SYSTEM DESIGN greatly affecting the system performance, is the air gap region. System response is very sensitive to a number of parameters A model of the magnetic bearing system has been related to this area. Of primary concern is an understanding of developed. And as can be seen in figure 2, it operates as the exact strength and path taken by the magnetic flux. The 4.37 Page 1255 stabilizing force is directly related to the flux density squared to necessary simplifications is the linearization of the and therefore a detailed understanding of this parameter is operating region. The destabilizing force (F< V• related to the necessary for development of a proper design. However, off-center displacement, dynamic imbalance, and other because this remains to be an area of major uncertainty disturbances, and the corrective force (Fc ), related primarily to approximations are necessary. Also tied to the air gap region are imperfections introduced during manufacturing and the coil current, are both approximately linear only within a \ assembly. These imperfections result in the presence of four small operating range. This is known as the linear region. bearing centers: geomettic center, mass center, magnetic However, even though the system is stable well beyond this center, and sensor center. For best results, these four centers point, the operating range is limited to this region because of should coincide exactly. But this is a practical impossibility. the necessity of linearization. (See figure 3) Many other In fact, even knowledge of their exact locations cannot be similar system simplifications likewise reduce overall accurately determined. Related to these noncoincident centers performance. Therefore, the objective is to develop a is a dynamic imbalance problem. This imbalance causes an controller which will produce improvements in system unknown disturbance force in the system, which must be performance characteristics such as: operating range, transient overcome in order to maintain stability. response, and robustness to parameter variation and external In addition to these uncertainties, there are system disturbances. nonlinearities which add complexity. There are two main sources of these nonlinearities. First, there are nonlinearities FORCE associated with the magnetic properties of the ferromagnetic material. These include nonlinear permeability, hysteresis, and Linear Region I Corrective Force eddy current effects. And second, there are nonlinearities associated with the physical limitations of components, namely the saturation of the power amplifier and coils. Further, there are a number of system complexities which must be taken into account A couple of these have to do with Flywheel high speed performance. At very high speeds, the x-y axes Displacement that were assumed to be independent become coupled. Also, E;..._-'""""'~,---.....,..~..,.-----1...,._ material deformations caused by high rotational speeds produce an air gap growth which changes flux characteristics and consequently performance. [2] r--------PL-AN-T·- --------1 ·---------,• r ---------.,. ~m 11 I + Fp II 1 w ili:r 1• 1• Figure 3: Operating Region 1• LL - - - - - - - - -, ------, I K'"4l~----i ~ticm ___.. ..1.__.; y-, I I __________ J NEURAL NETWORKS 1 -----Lin-ear- Con-llO-Uer ------- One alternative to solving these problems may prove to Figun: 2: Magnetic Bearing System Desill!' be the use of artificial neural networks in control system Because of these uncertainties, nonlinearities, and design. What is an artificial neural network? It is a massively complexities; approximations, linearizations, and parallel system of densely interconnected simple processing simplifications have to be made in order to develop a linear elements which work together to adaptively produce a complex controller and overall working system. Consequently system input-output functional relationship through a learning performance is compromised in many ways. For example, process. There are two basic configurations in which neural there are two system parameters related to the air gap region: networks can be found: feed-forward networks and recurrent radial stiffness ulse Torque motor T• • 0.832 lb.ill.oee. (K • 500 loll @ 60000 rpm) Umu: x-ua (sec), y.ua \mils) • spin testing of motor • suspension and testing of the entire stack. The measured and design parameters of the physical bearing and associated system is given in Table 1. It is noted that the manufactured hardware is well within the tolerances specified. Typical plots of results of testing individual bearings is shown in Fig. 7. This LEGEND A:lowOain B:lllpOaln C: Current Amplifier Output for A D: Curren! Amplifier Oolput fur II Dl•plattm•nl ,----~r-T:.-:-~-~ ·- . r-_ _...._;.__:_.,-1·-t-· ,-i. -!. / . I • : 1 - ···-- ----· ----· -------- Fig. 7 Acllve sum,ess for Top N-S Bearing Page 1265 information was used to derive~~. and KA which is shown in Table 2. This table also shows the linear and stable ranges. We note that a linear range of around 0.004" can be achieved and is necessary for self-capture. The bearings were individually suspended and spun to over 1000 rpm. The results were quite robust although the gain was on the low side, thereby having a relatively soft suspension. The testing of the motor/ generator has been discussed at length in ref. 5. We simply note that~ and K1 values were fairly close to those that were predicted. The stack configuration, shown in Figure 8, once connected to the display/ control panel, was suspended so that the bias current in the coils was a minimum. The flywheel was spun at over 5000 rpm (the first rigid body critical is around 4200 rpm) to yield stable performance. Higher spin rates can be achieved only in a vacuum chamber. Although such a chamber was constructed, the bearing has not yet been tested in a vacuum owing to time constraints. The experimental program, that will continue, will cover this testing phase. CONCLUSIONS The successful completion by this project establishes a viable technology and engineering base for designing and construction of a prototype magnetic bearing flywheel energy storage system. Specifically, we have proven the manufacture of tight tolerance bearings, stability and spin above first critical, use of sensors inside the bearing thereby eliminating runout problems, successful integration of surface wound brushless de motor with EM/PM magnetic bearings, and finally established the analytical basis of magnetic bearing design including nonlinearities and saturation. ACKNOWLEDGEMENTS This research was supported by NASA Fig. 8 Prototype Sirucrure through a GSFC Contract No. NASS-30091. REFERENCES 1. Anand, D.K, Kirk, J.A, Zmood, R.B., Studer, P.A. and Rodriguez, G.E., "System Considerations for a Magnetically Suspended Flywheel," Proceedings of the 21st Intersociety Energy Conversion Engineering Conference, August 25-29, 1986, San Diego, California, pgs. 2.449-2.453. 2. Kirk, J.A., Anand, D.K., Evans, H.E. and Rodriguez, G.E., "Magnetically Suspended 1 Page 1266 Flywheel System Study," NASA Conference Publication 2346, "An Assessment of Integrated Flywheel System Technology, Dec. 1984, pgs. 307-328. 3. Anand, D.K, Kirk, J.A and Iwaskiw, P., "Magnetically Suspended Stacks for Inertial Energy Storage Flywheel," Proceedings of the 22nd Intersociety Energy Conversion Engineering Conference, August 10-14, 1987, Philadelphia, Pa., Vol. 2, pgs. 769-774. 4. Kirk, J.A and Anand, D.K, "Satellite Power Using a Magnetically Suspended Flywheel Stack,'l Journal of Space Power, Vol. 22, Issue 3&4, March 1988. 5. "Magnetically Suspended Flywheels for Inertial Energy Storage", GSFC/NASA Contract NAS5-30091, January 1991. E-W N-S Top Bottom Top Bottom Spring Constant (lb/in) -1538 -1545 Electromagnetic Coil (lb/A mp) 14.1 12.3 13.1 11.3 System Gain (Amp/in) 185 375 196 399 Active Stiffness (lb/in) 1067 3349 1337 3962 Max Amplifier Current (Amp) 1.84 1.85 2.16 2.2 Max Force (lb) 6.4 13.4 8.9 15.3 Linear Range (mil) 9.1 4.6 10.7 5.3 (Stable Range (mil) 14 13.9 17.1 17 Table 1: Final Test Results .8 Page 1267 4" New Bearing Magnet Plate Bearing A Bearing B Design Dbp 4.121 4.122 8120+0.001 Sleeve Go Go 1.ooo_:0-0005Lc1 Fit. Dowel Pin Go Go 0.1875 +0.0007LC3Fit -0 Control Pins 0.375 Go 0.375 Go o.375+0.00l4LC6 Fit -0 Pole Face 0.118-0.119/0.120 0.120 /0.120-0.121 0.120+0.001 Thickness 0.178/0.181 0.179 /0.177 1.800 + 0.005 Flywheel A B Design OD 4.680 4.683-4.679 4.68o+0 -0.001 .ID 0.198 4.202 4.200+0.0005 Thickness 0.540 0.540 0.540+0.001 Lip Thick 0.120 0.120 0.120+ 0.001 Control Plots A B Thick 0.365 /0.364 0.365 /0.364 0.365 + 0.001 OD 2.849 /2.843-2.849 2.847 /2.847 2.846+0.002 Control Pin 0.376 Go 0.376 Go 0.376 +0.0012 -0 Central 0.374 Go 0.374 Go 0.3743 + 0.0002 Table 10-1. Measured and Designed Physical Dimensions Page 1268 PROCEEDINGS OF THE 1993 NSF DESIGN AND MANUFACTURING SYSTEMS CONFERENCE VOLUME 1 The University of North Carolina at Charlotte Mechanical Engineering and Engineering Science Department Precision Engineering Laboratory Charlotte, North Carolina January 6-8, 1993 Sponsored by Published by National Science Foundation Society of Manufacturing Engineers Design and Manufacturing Systems One SME Drive Engineering Division PO Box 930 Washington, DC 20550 Dearborn, Michigan 48121 Page 1269 Chemo-Mechanical Effects on the Efficiency of Machining Ceramics G.M. Zhang, T.W. Hwang, D.K. Anand University of Maryland Abstract This paper presents an experimental study of the turning of a ceramic material - aluminum oxide (Al20 3). Emphasis is given to gain a comprehensive understanding of the cutting mechanism. This study explores the utilization of cutting f1uids with chemical additives to develop a novel machining process. The machining tests were performed on a CNC lathe. Polycrystalline diamond compact tools were used. The cutting force during machining was measured using an instrumented tool holder as a dynamometer. The surface finish was inspected using a profilometer. SEM technique was used to study the mechanism of the surface formation in microscale. Results from this experimental study provides rich information on the cutting mechanisms during ceramics machining and the chemo-mechanical effects on the machining efficiency. 1. Introduction The work presented in this paper is an experimental study of the cutting mechanism during the machining of ceramics. The The need for high-strength materials at hig!l temperature experimental work is based on a single-point turning process, a applications has led to the development of advanced ceramics. Today fundamental element of machining operations. In this study, the industries, such as aircraft, automotive, and micro-electronics, are workpiece material used was aluminum oxide (Al20 3). The cutting finding increasing applications for ceramic materials. Machining of tools used were polycrystalline diamond compact tools. Method of a ceramics has been a rapidly growing field. However, ceramic two-level experimentation design was emplo,Yed to study the effects of materials are hard to be machined. Although most of ceramic parts are machining parameters such as f~ed, depth of cut, and cu'.u~g speed. on manufactured to near net shape size by pressing and sintering the machining performance with respect to surfa~e f1msh quality. processes, precision machining is now required to achieve a high Special attention was paid to the collection .of evidence. wh1c.h can degree of the geometrical accuracy of ceramic parts after the pressing support the theories assumed to be the cutting mechanisms m the and sintering processes. material removing process. To apply these findings, or more importantly, to develop new and innovative machining methods based The traditional technology to machine ceramics is grinding. on these findings, chemical-assisted machining processes were By means of making very small chips produced by the cutting edges explored to achieve a better m.achining per~ormance. The .paper is of abrasive particles, the grinding process removes ceramic material organized as follows. Section 2 of this paper describes the with a low productivity. With the ever increasing number of ceramic experimental procedures. The experimental evidence and results ~re materials in the market place, there is a pressing need to improve reported in Section 3. Section 4 presents the study of cutting traditional methods to machine ceramic materials for cost reduction mechanism with emphasis on the tribological interactions in machining and quality assurance in order to achieve the full potential of ceramics. aluminum oxide (Al20 ) when selected chemicals were added to the As reported in [l), a "laser lathe" was developed in MIT where the 3applied cutting fluid. Section 5 contains concluding remarks. dual beam principle was applied to remove ceramic materials in liquid form. However, the surface damage and sub-surface damage induced during machining are issues remaining unsolved. In abrasive jet machining, the high pressure abrasives wash and pierce ceramic materials away [2). But, the availability of new equipment and economic factors have limited its wide use on the shop f1oor. With the 2. Experimental Procedures availability of making abrasive grain consistently to high levels of 2. 1 General Description of Experimental Setup performance and accurate size, the grinding process has maintained its popularity in a world of machining operations. Grinding wheels made of hard structural ceramic materials such as Si N SiC and alumina In this study, the ceramic material selected to b~ mach~ned.is 3 4, aluminum oxide (A! 0 (hot pressed silicon nitride ceramics) are capable of achieving high 2 3 ). The purchased 99.8% A120 3 1s a cyhndnal quality of micro finishing. It was reported that the roughness average bar with diameter= 19.0 mm and the length= 76.2 mm. The material value (R.) of the surface ground by wheels of #140-200 mesh size is noted as a strong, dense recrystallized high-alumin~ ceramics ..I n order to machine aluminum oxide (Al 0 ), the tool msert material diamond abrasive was about O.lto 2 µm [3]. However, little work 2 3selected is polycrystalline diamond compact. Some material properties has been conducted in the study to gain a comprehensive of the ceramics are listed below. Note that the hardness of understanding of the cutting mechanjsm during the machining of polycrystalline diamond compact is, at least, five times as har~ as that ceramic materials. Lack of such knOwledge has slowed down the of aluminum oxide material to ensure that the cutting tool will have development of new and innovative machining processes that may revolutionize the machining technology of advanced ceramic materials. sufficient length of tool life to perform the experimental study. 421 Page 1270 aluminum polycrystalline test depth feed spindle tool property item unit oxide diamond compact condition of cut rate speed insert number (mm) (mm/min) (rpm) 2 3 Hardness kg/mm2 1100-1200 6000-9000 Modulus of Elasticity GPA 345 725-1049 1 - (0.1) - (5) - (400) Compressive Strength Mpa 2071 8200 2 +(0.2) - (5) - (400) Fracture Toughness MP a*-{;; 4.0 3.4 3 - (0.1) +(10) - (400) 4 +(0.2) +(10) - (400) Figures la and I b show the experimental setup. The machine 5 - (0. I) - (5) +(600) tool used was a CNC Slater lathe. The aluminum oxide bar was 6 +(0.2) - (5) +(600) mounted in the spindle. The cutting tool was fixed on the rotatory tool 7 - (0.1) +(10) +(600) post attached to the lathe. Strain gages were attached to the tool holder 8 +(0.2) +(10) +(600) which convert the strain induced by the cutting force generated during machining into an electrical signal for the cutting force measurement. As illustrated in Fig. 1b , a pc-based computer data acquisition was In order to block experimental errors due to the variation used for on-line recor.ding the cutting force signal. among the tool insert quality, a single tool insert was used to cut 16 tests, 8 tests for the pure distilled water conditions and 8 tests for the chemical added conditions. To get fair estimates, three tool inserts (a) were used to duplicate the 16 tests. Whenever a new tool insert was used, the method of tossing a coin was employed to determine which of the two sets of 8 tests should be performed first to randomize the effect of tool wear on the machining performance when the experimental study was in progress. 3. Experimental Results and Evidence The experimental study consisted of three phases. In the first phase, the cutting force generated during machining at each of the 8 tests for a give cutting fluid was on-line recorded. Figure 2 presents two cutting force signals measured during machining and indicates that the average value and its standard deviation are calculated from the recorded data. Figure 3a and Figure 3b display the measured cutting force at each of the 8 tests for the distilled water cutting fluid and the cutting fluid with the selected chemical additive, respectively. A comparison between two corresponding comers reflects the effect of the selected chemical additive on the magnitudes of the two cutting force components measured during machining. (b) CNC Slanter Tangential Cutting Force (Cutting Fluid: Distilled Water) Lathe Lathe Spindle 10 Cutting Fluid g <> 5 ~ Diamond Compound 0 Tool Insen and 0 0.02 Force Transducer 0 0.04 0.06 0.08 0.1 0.12 Time (sec) Microcomputer Tangential Cutting Force (Cutting Fluid: Distrilled Water+ Chemical Additive 10 Figure 1 Experimental Setup and Its Schematic Diagram @: <> 5 ] 0 2. 2 Setting of Machining Conditions 0 0.02 0.04 0.06 0.08 0.1 0.12 In order to investigate the cutting mechanism, the factorial Time (sec) design, based on the principle of orthogonal array, was employed. The three parameters under investigation were feed, depth of cut, and Figure 2 Cutting Force Signals Recorded during Machining cutting speed. The following design matrix lists their settings used in the experimental study. In order to explore the possibility of using cutting fluids as an In the second phase, the machined surface of the ceramic bar efficient means to achieve satisfactory machining performance, four was examined using a scanning electronic microscope. Photos were types of cutting fluids were used during the study. They are a type of taken to gain a qualitative information on topography of the machined traditional mineral oil, an oil-based water soluble coolant, pure surface in micro-scale. Figure 4 displays the appearances of two distilled water, and a mixture of distilled water and a selected chemi_cal machined surfaces under an identical machining conditions except the additive. In this experimental study, our finding was that the cuttmg cutting fluid type. The picture depected in Fig. 4a show the fluid with the selected chemical additive performed surprisingly well topography of the surface formed during the machined with pure regard the machining performance. 'Therefore, i~ the p~per we present distilled water, and the picture depected in Fig. 4b with the selected the experimental results from two types of cuttmg flmds. T~ese t"".o chemical additive. The geometrical shape and size of the visible marks types are the cutting fluid of pure distilled water and the cuttmg flmd and the contrasts between the lightest and darkest parts of these two with the selected chemical additive. pictures signify a fact that the surface conditions shown in Fig. 4b are 422 Page 1271 a. Cutting Fluid Type: Distilled Water 0.2 0.2 I e a .as 'o 'o ! ! 0.1 0.1 (·) 5.0 Feect,r- flow and lateral cracking (7). a lateral fracture threshold loading When the force Data Acquisition developed dming is below the loading Microcomputer '----o-1 System threshold, plastic occurs. the other hand, lateral cracking occurs when the developed force is above the loading threshold. The Figure l Experimental Setup for Machining interplay between the dynamic characteristics of a Alumina machining process the micro-fracture mechanisms of the workpiece material at A dynamometer was attached· to the molecular level calls a systematic study of the toolpost and the tool holder was fixed on the physics behind material removal process dynamometer. During machining, polycrystalline during machining of ceramics. This research diamond tipped carbide inserts, with nose radius focuses on an investigation, which 0.25 mm and -7 ° rake angle, were used to consists of three components: machine the alumina bars. In order to absorb the heat generated during machining, distilled water 1. Machining of ceramic material for sample ... ,.,,.,,.,,,.., was used as cutting fluid during machining. Chips are collected in a funnel shaped device with 2. Profilometric measurements of a built-in filter to separate chip from the cutting machined surfaces. fluid. The dynamometer measured the cutting 466 Page 1283 force both directions. The data were 2. a PC-based data acquisition For setting selecting feed, of cut, factorial design method (8) Table 1 lists the eight three machining parameter measured cutting force speed and feed directions. listed as Test 5 in Table 1 means: (1) (2) measured the cutting average of two HH.,U! and 6.7 N); (3) The measured from 1 Test 2 0.012 0.772 11. 22.46 22.68 4.98 4.93 1.92 Test3 0.012 0.264 67. 3.83 3.71 2.16 2.05 4.32 1.05 Test 4 0.012 0.264 11. 3.24 5.03 1.47 1.99 4.48 1.15 Test 5 0.051 0.772 67. 13.94 16.49 6.16 6.67 16.51 2.17 Test6 0.051 0.772 11 21.34 23.99 8.72 8.75 2.30 Test 7 0.051 0.264 67. 4.24 3.93 3.08 1.51 Test 8 0.051 0.264 11. 5.76 5.14 2.61 2.20 1.70 !+6 7 Page 1284 deep valleys along the feed direction. (mm) The deepest valleys are found in the case of high 0.035 feed and large depth of cut (Fig. 2d). These narrow deep valleys suggest occurrence of 0.025 brittle fracture during the chip formation. O.Dl5 (mm) ..,...,.....,,....,.,.,........,..,.......,.,..,.,........,.,....,....... 0.035 B++H-H++t+!+- 0.005 ............................................................. ....... 0.0 0.1 0.2 0.3 0.4 0.5 0.6 (mm) Ra= 2.30 µm O.Dl5 (d) Test 6: f=0.051 mm/rev, d = 0.772 mm, v= 11 m/min 0.005 --------- 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Figure 2 Surface Profiles Measured from the (mm) Machine Surfa ce Ra= 1.05 µm 2.3 SEM Examination (a) Test 3: f=0.012 mm/rev, d = 0.264 mm, v= 67 m/min To understand the process of chip formation during machining and identify the (mm)..,..,....,..,.,.,......,..,.,..,.,.,.,..,........,,...,...,...,,,.....,..., relationship between the fracture mode and the O.D35 n++.++!+-++H+-*¾+++w+-*'*-H-H microstructure of the materail, a detailed examination and analysis of the fracture surface is required. In this research, an environmental 0.025 scanning electron microscope (ESEM) was used to obtain high-magnification images that provide O.Dl5 details about the geometry of the formed chips and the topography of the machined surfaces. 0.005 .............................................. ...... Another advantage of using ESEM is that no 0.0 0.1 0.2 0.3 0.4 0.5 0.6 conductive coating is required as in the case of (mm) ordinary SEM. This allows a direct identification Ra= 1.35 µm of macro- and micro-cracks induced by machining without the influence of applied (b) Test 1: f=0.012 mm/rev, coating. d = 0.772 mm, v= 67 m/min Figure 3 presents a set of electron (mm)....,.,,,...,.,.,......,,......,,.....,..,......,........,......,..,.,.,..... micrographs of the chips collected during O.D35 machining. Figure 4 presents a set of -N-l-t-Mtt~-rtt"i't-H'-i{x) are the,"' mode shape function about Fig.2. Comparison of tip angle with one. two and three DOF x-axis and z-axis, respectively, and q/(t) and q:(t) are called the z""' generalized displacement of x-axis and z-axis, respectively. The Also, the simulation work showed that the dynamic equations can tip position vector can be similarly defined by be decoupled if motion is very small. Based on the observation made here, the translational motions will be added to the R, - (:.-, -X(t)]i + y,j - [z, +z(r)J.t (7) manipulator after the tip approaches the desired angle for the where, control of tip position. x, -.%(/), Y, - £:,

7(1:-1)0(.t-1) (15) dynamic equation is given by, w h e r e 0(.l:-l)-[a ,"':,, .. ·,a,, bl'b2, ... ,b.J7 a n d 1 (}+ .. ) im!+Xm,~ 7 lo) r 0 -L' ,_, m,'q/ ~ T:.+ .. 4>(A:-l) T - [y(k-1), ... ,y(.l:-n),u(.1:-1), ... u(k-n)] whet~ n is the delay. {F) (q~ ., [mul [OJ {OJ 10) - {F ) 10) ~ •• ~ [mul {m,~ i ,-mg M 0 f symmetric M The governing three DOF equations (12) can be simplified by decoupling the larger ''.lmplitude rotational motion from small amplitude translational motions. Therefore. eq. (1) reduces to a one DOF equation for rotational motion only as, Fig.3. Block diagram of the identification process Vol.8-184 Page 1309 The parameter vector A is estimated from measurements of where u(k) and y(k) are the input and output respectively and z·1 input and output. Following Gauss. the unknown parameters of is the backward shift operator.. T he transfer function is given by., a model are chosen in such a way as to minimize the loss function. 1 • , .[ 6 (.t)z- r, G(z-')-y(k) _ B(lc.:. 1) __,_ ,_ _ 1__ V{ll.kl - ..!. e<,1' (16) (22) 2 ,_, u(k) A(k • .,l • ~ l•.[dtk)z·' where. e(r)-y(i)-j(z)-y(i)-,j,T(i-l)A(i-1).· Herc y(i) are the 1-1 observation output and j(r) are the estimated output. As a result where, 41 and 61 are the estimates of a, and b,. of minimization of the loss function, the estimate parameters are, -P(k)[±. From Fig. 4, one can formulate the following (Sung et al 1981). 8(1:) ,_, cl>(i-l)y(r)l (17) (Q(z-')A(k.::· 1)-K(l:.:: ·')A(.t,:: · 1)-H(.t,::· 1)B(.t.::-1))y(k)-Q(z· 1)1iO P(k)-[±,_,. $(i-l)'(i-l)]·' (18) (23) Let Aj,1:,::·1) y(k) - li(.t,::·1) w(k) be the desired closed-loop To make eq.(18) computationally efficient, the least squares system such that the polynomial 2 estimate can be shown to be given in a recursive form by, Ajk.z-')-1 +a1dz·' +a,.,:· +---+a..,z·• has the desired set of Act) - &(1:-1) • P(k)$(1:-!jy(k) - ip7(.!:-l)A(k-1)] (19) poles. The coefficients of A(.t,::·') and B(l:.z;-1) are not known 7 and are obtained as estimates from the identification algorithm. P(k) _ _!_[PO:-I) _ P(k-l)cl>(k-1)¢ (.1:-l)P(k-1)] (20) If the polynomials K(k,z·'J and H(k,z" 1) arc chosen to satisfy, µ µ + ¢'(.t-l)P(k-1)$(.!:-1) K(k,z" 1)A(k,z·') + H(t,z·')B(l:.z · 1)-Q(z-'l(A(.t.z·1) -A,,(k,.z· 1) )(ll) Hereµ, the forgetting factor ranging from Oto !, can be selected then, the following desired relationship would he satisfied, based upon speed of convergence desired. For proper Aj.t.z·')y(k) - B(.t.:·')w(.!:). (25) identification, the input should excite all the modes of the The coefficients, K(k,: 1) and H(k,z·'J can be shown to be, system. This is satisfied by choosing the input signal as a 10 ... 00 0 periodic square wave. The two main factors that are taken into consideration in speeding up the convergence of the a, 6, 0 ... 0 identification scheme are the initial gain matrix P(O) and the • -a,., forgetting factor,µ. Details of this is given in Sung et al (1987). a1 a, 61 G, 0 -a,. Although, while the equivalent linear model has to be at least a fourth order system. identification studies were conducted on 3"' a. a,._1 ... (26) 6. 6,_, 6, • -a*' to 6'' order equivalent linear models to achieve a better understanding of the effects of P(O), µ(O), and a on the speed of 0 a. 0 b:., 62 0 convergence. Reasonably good results were obtained when the 0 0 ... 0 0 6) 0 . manipulator was identified by a 3•• order model, with µ(0)-0.7, a.-0.97, P(0)-10-[I]and k,=10. However, for the 4'' and 5'' order models. a had to be increased to 0.98 and 0.985 By solving eq.(26), the coefficients of polynomials K(k,z·'J and for the best convergence. See (Sung et al 1987) for more details. H(k,z·'J are obtained. Hence, this control scheme performs satisfactorily only when the model is exact and all disturbances 4. CONTROL METI:IODOLOGY are also modeled. However, it is desirable for the system to be robust against minor errors in the process model. One way to A self-tuning adaptive controller was chosen to control the eliminate this steady state error is to introduce an integrator as rotational motion in one DOF. Since. the linear motions are shown in Fig. 4. This closed-loop system is of order (n+ 1 ). For small a linear time-invariant ?ID controller was chosen. Fig. 4 an overall desired pole locations, it can be shown that, shows the block diagram of the three DOF motion control. 0 0 ... 0 6, ,+I Id -1 0 ... 0 G1 P1 0 -1 1 ... 0 61 "' P, (27) 0 o o ... G, 0 0 0 ... -1 0 ;J Thus, with a desired choice of the overall closed-loop poles given by D(z·'J and the coefficients ofli(.t,::· 1), the coefficients ofA,(k.z· 1 ) and c(k), would be obtained by solving eq.(27). With coefficients of A,(k,z·1; thus obtained. eq.(26) can be solved for K(k,z·'J and H(k,z·1J. It may, however, be difficult to specify all the desired closed-loop pole locations. One possibility is to specify only the dominant poles and require that the remaining poles be close to the origin (in the discrete time framework). In practice, it is often Fig.4. Control structure of the three DOF motion satisfactory to choose D/:: 1 ) .D(z-')-1 •p,z-' •P2=-2 (28) 4.1 Self-Tuning Pole Placement Control for rotational motion where, Pi·-2e-,H•cosf.,w~). p,-e-u..i., w is the natural frequency, ( the damping ratio, and h is the sampling period. While a variety of configurations can be found in the literature (Elliot et al 1979; Goodwin et al 1985) for pole placement, the 4.2 Implementation of the Self-Tuning Control Scheme Luenberger observer structure was chosen. From Fig. 4, the relationship between input and output is, The equivalent linear model is assumed to be of 4th order. A(z- 1)y(k) - B(z-')u(.t) (21) The experimental setup included a rectangular cross-section Vol. 8-185 Page 1310 beam driven by a computer controlled torque motor at its hub in Table 1: Fundamental Frequencies (unit: rad/sec) a horizontal plane. The tip angle was measured in real time with a video camera. The mass of payload is considered to be the payload Rectangular cross- main cause of change in the dynamic effects of manipulators. By Rectangular cross- sectional beam(x) implementing the self-tuning adaptive control, a satisfactory sectional beam(z) performance can he achieved even when a high load to weight 5% 23.540 612.183 ratios are encountered. 10% 21.778 566.297 L- - . ----,---··- 20% 19.184 498.833 , -""' Ir ....-.-..· ,, ",1 .". ,,, .. , 30% o 17.316 450.268 ~ 100% 11.428 -· 29i.150 ,. ... t~ J-v-mi;l Table 2: Cvcle Time for Various Pavloads (Unit: seconds) l,J l.0,4Slb payload 5% 10% 20% 30% cycle time 2.6i 2.69 2.79 3.30 • .. .... 11/ .. :. ~ ,_::: •. : , fI . ~ !ffl~ 1 , ~- !_ , •. , l __ ,. ··-•- .• J •••• l ... , .. _,_J. ___ , :>e.eM Ht ••a 1a1.H" ilH.01:1 lM(!SEC) ref an;. Fig.5. Commanded and actual tip angles with fixed parameters tro al'lQ(Jradlsec) hp anot21"adfsec) c.•11• trc, eng(3.5ta 50. Although TOR, CTOM and OARM all characterize the functions fi(t) and the chatter data, the robustness and computational efficiency of TOR recommends it. The elements of matrices R, Q and r 2 are functions of third order cumulants. Singular values of the C and S matrices associated with AR approximations by cumulants of arbitrary order are studied as a function of matrix size or maxlag. It is shown that the associated C and S ratios characterize cubically phase-coupled test functions. The R, Q, and rrratios have a potential application in the control of orthogonal cutting in which quadratic phase coupling is present. The C and S ratios may be useful in the control of cutting systems in which cubic or higher order phase coupling is present. 2. THIRD ORDER RECURSION The following definitions and theorems [22, 24] provide a background in higher order spectral theory for a subsequent application. Let m" (r 1 ,r2 , ... ,rn-i) the nth order moment of a real nth order stationary random process X(k), k = 0, ± 1, ± 2, .... Then, (1) Page 1319 CUTTING STATE IDENTIFICATION 353 E is the expected value, which may be estimated by +m mn(r1,T2,···,'n-1)=(1/2m+l) L X(k)X(k+r1)···X(k+, 11 -i), (2) k= -m where m-+ + oo. For a set of random variables {x1, x 2, ... , xn} the joint cumulants Cum[x 1, x 2, ... , x»J of order n are given by Cum[x1, X2, ... ' Xn] = I(-1t-1(P -1) !E {n X;}E {.n X;} ... E {n X;}, (3) p lES1 lES2 lESp where summations extend over all partitions (s1, s2, ... , sP) p = 1, 2, ... , n of the set of integers (1, 2, ... , n). Let c~(r1, T2, ... , 'n-1) = Cum[X(k), X(k + , 1), ... , X(k + 'n-1)J. (4) Then equations (1), (3) and (4) imply that C1 = m1, (5, 6) These expressions take a simpler form if m1 = 0. In the subsequent computations the mean, m1 is always subtracted from the time series. Then, (8) In general, the cumulant c~(r1,r2, ... ,rn-d, equation (4), is symmetric for any permutation of its arguments [24]. Third order cumulants satisfy further symmetries [21], including (9) and (10) The (n -l)th order spectrum of X(k), Cn(r1, r 2, ... , 'n-i), is defined by +oo +oo +oo Cn(w1,W2,···,Wn-1)= !1IG0,2ICO···,J1~-co cn(T1,T2,···,'n i) (11) Xexp[-j(W1T1 + WzT2 + ··· + Wn-l'n-dJ. Consider an AR estimation of the bispectrum, C3 (w1, w2 ), equation (11) [21, 25]. A Pth order AR process is described by p X(n) + I a(i)X(n - i) = W(n), (12) i= 1 Page 1320 354 B. S. BERGER ET AL. where it is assumed that W(k) is non-Gaussian, E(W(k)) = 0, E(W 3 (k)) = /3. Multiplying through equation (12) by X(n - k)X(n - t), summing and noting equation (2) gives p c~(-k, - t) + L a(i)cW- k,i t) = f3b(k,t), (13) i= 1 the third order recursion equation, where k ~ 0, t ~ 0. b(O, 0) = 1 and b(k, t) = 0 for all other positive values of k and t. Three algorithms TOR, CTOM and OARM, have been proposed for the determination of the AR coefficients a(i) [20, 21, 23]. The singular values of matrices associated with these algorithms provide a basis for the identification of the cutting state. 3. TOR The TOR algorithm, for the determination of the AR coefficient a(i), follows from the third order recursion equation (13), letting k = t, k = 0, ... , P. This yields P + 1 equations for the P + 1 unknowns a(i) and /3; P + 1 = maxlag. In matrix notation, Ra =b, (14) where g(O, 0) g(l, 1) g(P, P) g(-1, -1) g(O, 0) g(P 1, P -1) R= (15) g(-P, - P) g(- P + 1, - P + 1) g(O, 0) and where g(i,j) =c ~(i,j), a= [1, a(l), ... , a(P)Y and b =[ /3, 0, ... , O]T. R is, in general, a non-symmetric Toeplitz matrix. Sufficient conditions for the representation in equation (14) to exist are given in reference [22]. The bispectrum corresponding to equation (13) is given by references [20, 22] (16) where H(w) = 1 / (1 + "t a(i)exp(-jwn)) (17) and H*(w) = complex conjugate of H(w). An estimate of the R matrix, equation (15), for a data set X(i), i = 1, ... , N, may be formed [20] as follows: (1) Segment the data set into K records of M samples each. X;(k), k = 1, 2, ... , M, are data points associated with the ith record. (2) Compute cL(m, n) for the ith record as b cL(m, n) = (1/M) L x 60, Figure l(b). Similar behavior is exhibited by the singular values of Q. Although the magnitudes of the singular values of Q differ from those of R by a factor of 103 the Q-ratio oscillates with a small amplitude about a value of 2, Figure 2(a) and 2(b). For f 1 (t), the singular values of r 2 versus maxlag differ from those of R and Q, Figure 3(a). However, the Q-ratio converges to a value of 2 for maxlag > 80, Figure 3(b). It is evident that the number of pairs of singular values equals the number of different frequency components in j 1 (t). Functionf2 (t), equation (33), exhibits phase coupling of 90 and 100 Hz components. The coupling of side bands to the central 100 Hz frequency component has been observed in the experimental data associated with light and medium cutting. The R-ratios forf2 (t) and light cutting data are similar [19]. Singular values of Rand Q matrices and the Rand Q-ratios as functions of maxlag, Figures l(c) and 2(c), l(d) and 2(d) are identical. For maxlag = 100 the Rand Q-ratios, equal 1 and are bounded between 1 and 1·2 for maxlag > 100. The rrratio is similar to the R and Q-ratios, reaching a minimum of 1·2 for maxlag = 100 and is bounded between 1·2 and 1·25 for maxlag > 100, Figure 3(c) and 3(d). The number of pairs of singular values, 3, is seen to equal the number of different frequency components inf2 (t). Functions f 3 (t), equation (34), is the sum of a phase-coupled component at 100 and 110 Hz and a phase coupling of 90 and 100 Hz components. The R-ratios for j 3 (t) and medium cutting data are similar [19]. Singular values of R and Q matrices and R and Q-ratios, Figures l(e) and 2(e), l(f) and 2(f) are nearly identical. For the Rand Q-ratios, Page 1324 358 B. S. BERGER ET AL. 3·5 ,---------------~ (b) 3·0 0 2·5 ·~ ci:: 2·0 1·5 ] ·0 .___ ___, ___ ___. .L_ ___ _, 0 50 100 150 Maxlag Maxlag 8---------------~ 3·5 --------------~ (d) 7 3·0 0 2·5 ·_p ~ i:,: 2·0 2 1·5 1· 0 L__ ___L __ ___ .:,dL__ ___ __, 50 100 150 0 50 100 150 Maxlag Maxlag 3·5 --------------~ (f) 50 3·0 g 40 1 0 2·5 ·~ 130 ';< c,: 2·0 Cl'J 20 10 1· 0 '------'------"-----~ 50 100 150 0 50 100 150 Maxlag Maxlag Figure 1. f;(t) with n samp = 1024, J samp = 1024 Hz, n record= 15. For i = 1: (a) singular values and (b) R-ratio versus maxlag; for i = 2: (c) singular values and (d) R-ratio versus maxlag; for i = 3: (e) singular values and (f) R-ratio versus maxlag. respectively, at maxlag = 100, minimums of 1· 46 and 1· 52 are attained and 1-46 < R < 1· 62, 1·52 < Q < 1·63 for maxlag > 100. The rrratio is similar to the R and Q-ratios reaching a minimum of 1·28 at maxlag = 100 and is bounded between 1·28 and 1-50 for maxlag > 100, Figure 3(e) and 3(f). Five pairs of singular values are evident which correspond to the five frequency components present inf3 (t). Page 1325 CUTTING STATE IDENTIFICATION 359 9000 ,-----------------, 3·5 ~--------------, (b) 8000 7000 3·0 3000 2000 1-5 1000 1 ·O '------'------.1,___ ___ _, 50 100 150 0 50 100 150 Maxlag Maxlag 8000 ~-------------~ 3·5 ~---------------, (c) (d) 7000 3·0 6000 ~ 5000 > 0 2·5 ·;:i ~ 4000 :.:sI ~ 3000 Cll 2·0 Cl) 2000 1·5 1000 l·O ~----~---~~---~ 50 100 150 0 50 100 150 Maxlag Maxlag 4 xl0 6 3·5 ,r---------------, (e) (f) 3·0 0 2·5 -~ Cll 2·0 1·5 1· 0 L,__ ___, ___ ___. 1,__ ___ _, 0 50 100 150 Maxlag Maxlag Figure 2. f;(t) with n samp = 1024, f samp = 1024 Hz, n record= 15. For i = 1: (a) singular values and (b) Q-ratio versus maxlag; for i = 2: (c) singular values and (d) Q-ratio versus maxlag; for i = 3: (e) singular values and (f) Q-ratio versus maxlag. Rapid identification of the current cutting state is essential for the on-line control of the cutting process. To this end, parametric studies were carried out in which sampling rates, record size and number were varied. Three data sets were formed consisting of f;(t), i = 1, 2, 3 sampled at 1024 Hz and arranged in three records of 256 samples each for a time series 0·75 s in length. The singular values of the R, Q and r2 matrices and the R, Q and Page 1326 360 B. S. BERGER ET AL. 9000 ,---------------~ 3·5 -------------~ (a) (b) 8000 7000 3·0 g 6000 1 5000 0 2·5 ~ ·~ 4000 .S J...N 2•0 U'.l 3000 2000 1· 5 1000 0 1·0 '-----~----~---~ 0 50 100 150 0 ~ 100 1~ Maxlag Maxlag 4000 .---------------~ 3·5 ,----------------, (c) (d) 3500 3000 3·0 "g' 2500 1 .g 2·5 ~ 2000 1 *,._N 2•0 1500 U'.l 1000 1·5 500 O L.......i11111111111111:. l·O ~---~----~---~ 0 50 100 150 0 50 100 150 Maxlag 4 Maxlag X 10 14 -------------~ 3·5 .-,---------------, (e) (f) 12 3·0 10 "g' 1 8 ~ i 6 .s U'.l 4 1·5 2 1· 0 '-----------'------'-------' 100 150 0 50 100 150 Maxlag Maxlag Figure 3. f,(t) with n samp = 1024, f samp = 1024 Hz, n record= 15. For i = 1: (a) singular values and (b) r,-ratio versus maxlag; for i = 2: (c) singular values and (d) r,-ratio versus maxlag; for i = 3: (e) singular values and (f) r,-ratio versus maxlag. rrratios were computed by averaging the appropriate functions over the three records associated with eachf;(t). Figures 4 and 5 show the results of the computation. Comparison of Figure 4(a) and 4(b) for f 1 (t) with Figure l(a) and l(b), singular values of R matrices and the R-ratios for 15 records of 1024 samples each sampled at 1024 Hz, shows the figures to be identical. Figure 4(c) and 4(d), for f 2 (t), is nearly identical to Figure l(c) and l(d). The minimum of the R-ratio for f 3 (t), Figure 4(f), at maxlag = 100 is 1·56, while for the more Page 1327 l I CUTTING STATE IDENTIFICATION 361 10 ,------------------, 3·5 r,----------------, 9 (b) 8 3·0 :rJ 7 0 ] 6 0 2·5 ~ 5 ·~ ], .s 4 C,:: 2·0 r Cl) 3 2 1· 5 1·0 ~-~--~-~--~-~~-~ 20 40 60 80 100 120 0 20 40 60 80 100 120 Maxlag Maxlag 5·0 ---------------~ 3·5 ,-,----------------, (c) (d) 4·5 4·A-+----------.s!- "".=.. - -'. ...... 3·0 00 3·5 i 3·0 0 2·5 ~ 2·5 ·~ ".s 2·0 c,:: 2·0 Cl) 1 ·5 1·0 1· 5 0·5 1·0 L__.....J..._ __JL__ _.L__ __J_ _::,~,=."'-l 20 40 60 80 100 120 0 20 40 60 80 100 120 Maxlag Maxlag 3·5 ,--,.---------------, (f) 50 3·0 00 40 i 0 2·5 ~ 30 ], l a 2·0 20 1·5 10 1·0 ~-~--~-~--~-~--~ 20 40 60 80 100 120 0 20 40 60 80 100 120 Maxlag Maxlag Figure 4. f,(t) with n samp = 256, fsamp = 1024 Hz, n record= 3. For i = 1: (a) singular values and (b) R-ratio versus maxlag; for i = 2: (c) singular values and (d) R-ratio versus maxlag; for i = 3: (e) singular values and (f) R-ratio versus maxlag. accurate result shown in Figure 1 (f) the minimum is 1- 46. Figure 5 displays the singular values of Q matrices and the Q-ratios for f;, i 1, 2, 3 based on the reduced data set of three records each of 256 samples. A comparison with Figure 3 shows the superposition of oscillations on the more accurate result. However, the approximation is sufficiently accurate to characterize the functions f;. Page 1328 362 B. S. BERGER ET AL. 3·5 --------------- (a) \ (b) 500 3·0 "' 400 ~ 0 2·5 I ti! -~ 300 ] 6 \/\ 2,0 \ \/\,J"\,.l'\. . r\. . FV'\J\fV\J en 200 1-5 100 l ·O .___.....,__--'---'----'---",- -_ _, 20 40 60 80 0 20 40 60 80 100 120 Maxlag Maxlag 900.--------------~ 3·5 --------------- (c) (d) 800 700 3·0 ~ 600 2-5 ] 500 0 ! -~ 400 a Ol 2·0 300 200 1-5 100 0 1·0 L__...L.._.....,.L_ _j ___ _L_ _:::£1,e'.,__ _J 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Maxlag Maxlag 9000 --------------~ 3·5 ~-------------- (f) 8000 3·0 7000 "' 6000 ~ 0 2·5 > 5000 ·_p ti! ~ ], 4000 Ol 2·0 a 3000 2000 1000 0 0 20 40 60 80 100 120 20 40 60 80 100 120 Maxlag Maxlag Figure 5. f;(t) with n samp = 256, fsamp = 1024 Hz, n record= 3. For i = 1: (a) singular values and (b) Q-ratio versus maxlag; for i = 2: (c) singular values and (d) Q-ratio versus maxlag; for i = 3: (e) singular values and (f) Q-ratio versus maxlag. For k?; 3 the cumulants ck(,1, , 2, ... , 'k-i), equations (2), and (7), are known to be insensitive to added Gaussian noise for sufficiently large values of min equation (2) [22, 24]. The magnitude of error, for a givenf;(t), in the numerical computation of singular values of the R, Q, and r 2 matrices occasioned by additive Gaussian noise is shown to be a function of the magnitude of the noise variance and m. Gaussian noise with a variance = 1 was added Page 1329 CUTTING STATE IDENTIFICATION 363 18 ~-------------~ 3·5 ~-------------~ (a) 16 (b) 14 3·0 0 2·5 ! 2·0 ~------------------1 4 1·5 2 1· 0 '--------'------'------' 50 100 150 0 50 100 150 Maxlag Maxlag 10 .----------------~ 3·5 ~-------------~ (d) 9 8 3·0 0 2·5 -~ ~ 2·0 1·5 1·0 ~---~----~~----' 50 100 150 0 50 100 150 Maxlag Maxlag 70 .------------------, 3·5 ~-------------~ (f) 3·0 ., 2·5 ~ 2·0 1·5 1· 0 '--------'------'------' 0 50 100 150 Maxlag Maxlag Figure 6. f,(t) + Gaussian noise of variance= 1 with n samp = 1024, f samp = 1024 Hz, n record= 15. For i = 1: (a) singular values and (b) R-ratio versus maxlag; for i = 2: (c) singular values and (d) R-ratio versus maxlag; for i = 3: (e) singular values and (f) R-ratio versus maxlag. to thef;(t) functions. Three data sets were formed forf;(t), i = 1, 2, 3 sampled at 1024 Hz and arranged in 15 records of 1024 samples each. The corresponding singular values of the R matrix, equation (15) and the R-ratios are shown in Figure 6. Figure 6(a) and 6(b) forf1 (t) plus noise is identical to Figure l(a) and l(b) for the noiseless case. The qualitative behavior of the R-ratio for f 2 (t) plus noise, Figure 6(d), is similar to the noiseless case, Figure l(d), Page 1330 364 B. S. BERGER ET AL. 3·5 ,--,----------------, (b) 3·0 @ 10 000 1 ~ §i a sooo 1·5 l·O ,___ ___, ___ ___, ___ ___ _, 50 100 150 0 50 100 150 Maxlag Maxlag 10000 ~-------------~ 3·5 ~-------------- 9000 (d) 8000 3·0 7000 6000 0 2·5 ·~ C)l 2·0 3000 2000 1000 l·O '------'------'""""-----' 50 100 150 0 50 100 150 Maxlag Maxlag 7~-------------~ 3·5 r,---------------, (e) (f) 3·0 l·O '------~----'-------' 0 50 100 150 Maxlag Maxlag Figure 7. f;(t) + Gaussian noise of variance= 1 with n samp = 1024, f samp = 1024 Hz, n record= 15. For i = 1: (a) singular values and (b) Q-ratio versus maxlag; for i = 2: (c) singular values and (d) Q-ratio versus maxlag; for i = 3: (e) singular values and (f) Q-ratio versus maxlag. decreasing to a minimum of 1 for maxlag = 100. Figure 6(e) and 6(f) forf3 (t) plus noise is nearly identical to Figure l(e) and l(f) for the noiseless case. As in the case of the R-ratio, the Q-ratio, equation (25), associated with CTOM, gives ratios for f;(t) plus noise, Figure 7, which are qualitatively similar to those found for the noiseless case, Figure 2. Similar calculations of the R and Q-ratios based on the reduced data set with added Gaussian noise of variance = 0·50 displayed qualitative similarities Page 1331 CUTTING STATE IDENTIFICATION 365 11 X 10 14 4·0 (b) 12 3·5 " 8 ·0a t;; = ~ 2·5 6 bJJ ~ .esn 2·0 4 2 1· 5 1·0 50 100 150 0 50 100 150 Maxlag Maxlag 14 X 10 14 4·0 (d) 12 3·5 <"l)' 10 " 3·0 .;' 0 >.... 8 -~ 2·5 ="' 6 6 .sbJJ 2·0 V\,~ ---en 4 2 1·5 l·O 50 100 150 0 50 100 150 Maxlag Maxlag 25 X 10 7 4·0 (e) (f) 6 3·5 " 50. Previous studies of the measured tool acceleration chatter data [19] have shown that an R-ratio ? 2 is associated with the chatter state. Page 1332 366 B. S. BERGER ET AL. 8. AR APPROXIMATION BY CUMULANTS OF ARBITRARY ORDER The previous discussion has been limited to Toeplitz matrices of third order cumulants, c3 (, 1 , i- 2), associated with AR approximation. For systems with cubic or higher order non-linearities, algorithms based on third order cumulants would fail. Two algorithms for the determination of ARMA parameters [28-30] provide matrices of cumulants of arbitrary order suitable for singular-value analysis. Consider the causal ARMA model p q L a(j)y(i j) = L b(j)w(i - j), (35) j=O j=O where y(i) is the output and the input w(i) is stationary, zero mean, i.i.d., non-Gaussian with kth order cumulant rk. Since w(i) is i.i.d. its kth order cumulant may be expressed as (36) where 6(i1, i 2 , ••• , ik_ 1) denotes the Kronecker delta function. The kth order output cumulants are then given by [28, 29] + 00 cW1, i2, ... , ik-1) = ri:' I h(i)h(i + i1) ... h(i + ik-d, (37) i=O where h(m) = ARMA response function. Let ck(m, n) = ck(m, n, 0, ... , 0) (38) for k ?= 3. Substituting equation (38) into equation (37) gives 00 k-2 cJ:(m, n) = y;:' L h(i) h(i + m)h(i + n). (39) i=O It can be shown [28] that p h(i + m) = - _I a(j)h(i + m - j) + b(i + m). (40) j= 1 Combining equations (39) and (40) gives p cf (m, n) + I a(j)cf (m - j, n) = rn::::it (41) j=l where Q = y;:I,;: k-2 h(i) b(i + m)h(i + n). Letting n = q p, ... , q, m = q + l, ... , q +pin 0 equation (41) gives p(p + 1) equations for the coefficients a(i), i = 1, ... , p [28]: Ca= b, (42) Page 1333 CUTTING STATE IDENTIFICATION 367 where (q + 1 - p, q - p) (q, q - p) (q + 1 - p, q) (q, q) C= (43) (q, q - p) (q + p - 1, q - p) (q, q) (q + p - 1, q) a = [a(p), a(p 1), ... , a(l)]r and b = [(q + 1, q p), ... , (q + 1, q), ... , (q + p, q - p), ... , (q + p, q)]r. cnm, n) = (m, n). Taking the product of the p(p + 1) x p matrix C with er gives (44) where Csq = ere is p x p. Assumptions inherent in the deviation of equation (42) are given in references [28, 30]. The singular values of Csq will be examined subsequently. A second algorithm for ARMA parameter estimation [30] follows the derivation of reference [28], equations (35)-(41). In reference [30], equation (41) is written in the form p I a(j)cf (m - j, n) = 0 (45) j=O for m > q, where n = q p, ... , q and m = q + 1, ... , q + p + M, M:;,: 0. Expressing equation (45) as S a= 0, Ssq is defined as (46) For a proper choice of p, q and M, the AR parameters, a(j), are identified by equation (45), [30]. In practice, the true ARMA orders, p and q are not usually known. Assuming that these parameters are overestimated by P :;,: p and Q :;,: q, letting n = - P, ... , Q and m = Q + 1, ... , Q + P will include a sufficient amount of data in providing a robust estimate of the singular values of the S matrix. The elements of the C and S matrices may be estimated by averaging over K records of M samples each; equation (19). 9. CUBIC PHASE COUPLING Relationships between cubically phase-coupled trigonometric functions and the singular values of the Csq and Ssq matrices were considered through a study offunctionsg;(t), i = 1, 2: g 1 (t) = 0·25 cos(2n lOOt + 0i) + 0·25 cos(2n lOOt + 02) + l·Ocos(2nl30t + 03) + 0·86cos(2n330t + 01 + 02 + 03), (47) g2 (t) = l·Ocos(2nl00t + 0i) + l·Ocos(2n110t + 02 ) +l·Ocos(2n160t+03)+0·15cos(2n370 1 1.1 11. +/)1), (48) Page 1334 368 B. S. BERGER ET AL. 16 000 (a) 5·0 (b) 14 000 4·5 12 000 4·0 "0)' " 10 000 ';;J' 3·5 > 0 "'"' 8000 -~ 3·0 '3 'c 0l) (_) .s 6000 2·5 f/) 4000 2·0 2000 1·5 0 0 10 20 30 1·0 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 Maxlag Maxlag 4 X 10 2·0 3·5 (c) 1·8 1·6 3·0 1-4 "0)' "' 1-2 2·5 ';;J > ·~ :. 1·0 'c ], 0·8 U 2·0 .s f/) 0·6 0·4 1-5 0·2 0 1·0 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 Maxlag Maxlag Figure 9. g,(t) with n samp = 512, f samp = 512, n record= 15. For i = 1: (a) singular values and (b) C-ratio versus maxlag; for i = 2: (c) singular values and (d) C-ratio versus maxlag. where the phases Bi are mutually independent and uniformly distributed over [O, 2n]. Two data sets were constructed consisting of cubically phase-coupled test functions gi(t), i = 1, 2; equations (47) and (48), sampled at 512 Hz and arranged in 15 records of 512 values each. The singular values of the C and Ssq matrices equations (43) and (46), and the C and Ssq ratios were found by averaging the appropriate function over the 15 records associated with each gi(t). g 1 (t) is the sum of two components at 100 Hz together with components at 130 and 330 Hz. Three pairs of singular values of the C matrix are evident in Figure 9(a). The C-ratio is seen to approach a value of c::,, 3·2 in Figure 9(b) for maxlag = 100. The singular values and C-ratio verses maxlag for gi(t) are qualitatively similar to those for the quadratically phase-coupled functionf1 (t); equation (32), Figure 3(a, b). The modulated function g2 (t), equation (48), is the sum of four components at 100, 110, 160 and 370 Hz. Four pairs of singular values of the C matrix appear in Figure 9(c). The C-ratio approaches a value of l·O at intervals of 50 maxlags. Three of the largest pairs of singular values have a common value of maxlag = 50 which corresponds to approximately 10 Hz, the modulation frequency, with a sampling rate of 512 Hz. A similarity is evident between Figures 9(c, d) and 3(c, d) for the quadratically coupledf2 (t); equation (33). An analysis of gi(t) based on the Ssq matrix gave the results identical to those shown in Figure 9. Page 1335 CUTTING STATE IDENTIFICATION 369 10. CONCLUSIONS In references [21, 22], the algorithms CTOM and OARM were shown to resolve the peaks in the bispectrum of a set of phase-coupled test functions more accurately than the TOR algorithm. The present study demonstrates that for a set of phase-coupled test functions modelling the orthogonal cutting of stiff metal cylinders [19] and an example of experimentally measured cutting tool accelerations, ratios of singular values associated with TOR, CTOM and OARM identify the test functions and cutting state. However, the relative computational simplicity and speed of TOR together with its invariance in the presence of high levels of Gaussian noise indicate greater effectiveness than CTOM and OARM in the on-line control of cutting states. The above algorithms detect quadratic or second order phase coupling but not third or higher order coupling. In the present study, ratios of singular values associated with matrices of fourth order cumulants were shown to identify test functions with cubic phase coupling. ACKNOWLEDGMENTS The authors acknowledge the support of the National Science Foundation through GER-9354956. The encouragement of H. L. Russell of the University of Maryland, College Park, P. Grootenhuis and D. J. Ewins of the Imperial College of Science, Technology and Medicine, London, is very much appreciated. M. Rokni read the manuscript, making a number of important suggestions. The assistance of T. Miller in the presentation of the manuscript has been invaluable. REFERENCES 1. J. TLUSTY 1979 CIRP Annals 27, 583-589. Analysis of the state of research in cutting dynamics. 2. I. KOENIGSBERGER and J. TLUSTY 1971 Structure of Machine Tools. New York: Pergamon Press. 3. M. WECK 1985 Handbook of Machine Tools, Vol. 4. New York: John Wiley. 4. H. R. TAYLOR 1977 Proceedings of the Institute of Mechanical Engineers 191, 257-270. A comparison of methods for measuring the frequency response of mechanical structures with particular reference to machine tools. 5. K. J. KIM, E. F. EMAN and S. M. Wu 1984 International Journal of Machine Tool Design and Research 27, 161-170. Identification of natural frequencies and damping ratios of machine tool structures by the dynamic data system approach. 6. M. E. MERCHANT 1945 Journal of Applied Physics 16, 267-275. Mechanics of metal cutting process I. 7. D. W. Wu 1989 Transactions of the American Society of Mechanical Engineers, Journal of Engineering for Industry 11, 37-47. A new approach to formulating the transfer function for dynamic cutting processes. 8. J. S. LIN and C. I. WENG 1990 International Journal of Machine Tools and Manufacturing 30, 53-64. A nonlinear model of cutting. \ 9. T. Y. AHN, K. F. EMAN and S. M. Wu 1985 Trqnsaction of the American Society of Mechanical Engineers, Journal of Engineering for Industry Hp, 91-94. Cutting dynamics identification by dynamic data system modeling approach. ' 10. J. PETERS, P. VANDERCK and H. VAN BRUSSEL 1971 CIRP Annals 20, 129-136. The measurement of the dynamic cutting coefficient. 11. T. DELIO, J. TLUSTY and S. SMITH 1992 American Society of Mechanical Engineers, Journal of Engineering for Industry 114, 146-157. Use of audio signals for chatter detection and control. 12. I. GRABEC 1986 Physics Letters 117, 384-386. Chaos generated by the cutting process. 13. I. GRABEC 1988 International Journal of Machine Tools and Manufacturing 28, 275-280. Chaotic dynamics of the cutting process. Page 1336 370 B. S. BERGER ET AL. 14. M. K. KHRAISHEN, C. PEZESHKI and A. E. BAYOUMI 1995 Journal of Sound and Vibration 180, 67-87. Time series based analysis for primary chatter in metal cutting. 15. B. S. BERGER, I. MINIS, K. DENG, Y. s. CHEN, A. CHAVALI and M. ROKNI 1996 Journal of Sound and Vibration 191, 986-992. Phase coupling in orthogonal cutting. 16. B. S. BERGER, I. MINIS, J. HARLEY, M. ROKNI and M. PAPADOPOULOS 1998 Journal of Sound and Vibration 213, 813-827. Wavelet based cutting state identification. 17. I. N. TANSEL, A. WAGIMAN and T. TZIRANIR 1991 International Journal of Machine Tools and Manefacturing 31, 539-552. Recognition of chatter with neural networks. 18. J. GRADISEK, E. GOVEKAR and I. GRABEC 1998 Journal of Sound and Vibration 214, 941-952. Using coarse-grained entropy rate to detect chatter in cutting. 19. B. S. BERGER, I. MINIS, M. ROKNI M. PAPADOPOULOS, K. DENG and A. CHAVALLI 1997 Journal of Sound and Vibration 200, 15-29. Cutting state identification. 20. M. R. RAGHUVEER and C. L. NIKIAS 1985 IEEE Transactions on Acoustics, Speech and Signal Processing ASSP-33, 1213-1230. Bispectrum estimation: a parametric approach. 21. M. R. RAGHUVEER and C. L. NIKIAS 1986 Signal Processing 10, 35-48. Bispectrum estimation via AR modeling. 22. C. L. NIKIAS and A. P. PETROPULU 1993 Higher-order Spectra Analysis. Englewood Cliffs, NJ: Prentice-Hall. 23. G. K. AN, S. B. KIM and E. J. POWERS 1998 Proceedings of ICASSP, New York, 2392-2395. Optimized parametric bispectrum estimation. 24. D. R. BRILLINGER 1981 Time Series. San Francisco: Holden-Day Inc.; expanded edition. 25. C. L. NIKIAS and A. P. MENDEL 1993 IEEE Signal Processing Magazine July, 10-37. Signal processing with higher-order spectra. 26. G. H. GOLUB and C. F. VAN LOAN 1993 Matrix Computations. Baltimore, MD: The Johns Hopkins University Press. 27. R. A. HORN and C. R. JOHNSON 1991 Topics in Matrix Analysis. Cambridge: Cambridge University Press. 28. G. B. GIANNAKIS 1990 Transactions on Automatic Control 35, 18-26. On the identifiability of non-Gaussian ARMA models using cumulants. 29. A. SWAMI and J.M. MENDEL 1990 IEEE Transactions on Acoustics, Speech and Signal Processing 38, 1257-1264. ARMA parameter estimation using only output cumulants. 30. A. SWAMI and J. M. MENDEL 1992 IEEE Transactions on Automatic Control 37, 268-273. Identifiability of the AR parameters of an ARMA process using cumulants. Page 1337 QTH . ~TERNATIONAL CONGRESS ON SOUND AND VIBRATION The Hong Kong Polytechnic University The lnlcmational Institute of Acoustics and Vibration Environmental Protection Department The Government of the HKSAR The American Society of Mechanical Engineers (Hong Kong Section) The Hong Kong Institute of Acoustics The Hong Kong Institution of Engineers The Institution of Mechanical Engineers (Hong Kong Branch) l \!J • H l Page 1338 Abstracts The Multibound Digital Regulator Synthesis of the soundproof facilities is conducted for the prediction of Stabilization System of the Technological Space noise impact of the KTX (Korea Train Express) and for Platform optimizing noise barriers in order to eliminate the noise L.A. Rybak by high speed train. A number of computer simulations Time: 12:30 and measurements are carried out in order to determine They observe in this paper the problem of active control the specification of noise barrier on test track. of the vibration isolation platform position for realizations of space technological experiments. The Considerations upon Attenuation of Acoustic Waves principles of control of platform position concerning the by Screens basis of the load-carrying structure of a space according Vasile Bacria, E. Jebelearnu the signals of accelerometers and gauge of relative Time: 12:10 position make a methodical basis. The separate task The attenuation of acoustic waves by means of screens includes development the principle of the work of high- containing several elements separated by air layers resolution accelerometer. This kind of the differs from the attenuation corresponding to the simple accelerometers arc intended for a measurement in type of screen. The former one is also influenced to a conditions of microgravity of levels of vibration great extent, by the absorbent layers which are applied on accelerations of the order mcg. The movements of drive the screen. In this paper the authors deal with the study mechanisms between the platform and the basis ensures of sound attenuation by means of screens built up of control of the platform position in space. The regulator several nonadjacent elements as well as of screens coated treats an information from gauges and sends pilot signals with absorbent layers. The authors establish, for each to the electric drive, which one actuates an the drive type of screen described in the paper, the expression of mechanism. The regulator is designed as multivariable, attenuation, emphasizing the factors influencing it, the combining analog and digital control. Depending on an authors also presents the results of the experimental allowable level of relative movement the variable measurements. structure of a system of management is offered. The control algorithms are constructed. These algorithms (E2-S3) Machine Tool Vibration combine as invariant management, which one ensures a zero level of accelerations on object, and management on Room: M114 feedback. The outcomes of experimental researches are Date: Thursday, 5 July 2001 indicated. Toeplitz Matrices and Cutting State Identification B. Berger, C. Belai, D. Anand Time: 11:30 (E2-S2) Noise Barriers II Properties of the singular values of a Toeplitz matrix, R- Room: TUI01 matrix, are examined as a function of matrix size. The Date: Thursday, 5 July 2001 R-matrix arises in the TOR algorithm for parametric bispectrum estimation and has recently found application Scale Model Measurements of the Sound Field due to in the identification of cutting states in connection with Dipole Sources in the Presence of a Barrier the orthogonal cutting of short circular cylinders. M. Burel, K. M. Li, K. Attenborough Numerical studies, of phase coupled functions for which Time: 11:30 exact expressions for the third order cumulant elements Dipole sources are of particular interest in the context of of the R-matrix are known or estimated from measured transportation noise. Scale model measurements of cutting tool acceleration data, show the presence of diffraction by a barrier have been carried out using singular value trajectories. The trajectories provide an piezo- ceramic transducers as dipole sources. The alternative means for ordering the singular values, each measurements have been used to compare with the being associated with a frequency, and are shown to be predictions of new models. They give insight into the related to frequency components of the bispectrum. The effects of source directivity on the 3D sound field, noise suppressive properties of third order cumulants and particularly in the transverse direction. The new models singular value decomposition result in robust algorithms use an adaptation to a dipole source of Pierce's for state identification. calculation of the diffraction of the sound field due to a point source by a half-plane. Complex Approach to Vibration Based Cutting Tool Diagnostics Soundproof Facilities for the Korea High Speed Train Andrzej Sokolowski, Jan Kosmol H. S. Na, K. H. Kim, S. H. Hyun, J. P. Clairbois Time: 11:50 Time: 11:50 The paper presents research on developing a tool flank This paper introduce the study of the soundproof wear diagnostic strategy based on machine tool vibration. facilities (noise barriers) to be placed on the Seoul-Pusan The main goal of the research is to work out a strategy, H.S.T. project. High speed railroad noise is one of the which makes possible far reaching independence of the main causes of environmental impact. Whenever HST wear symptoms on cutting conditions. The description project is planned or a housing project near an existing shown in the paper follows major steps of the railroad is proposed, an estimate of the relevant noise investigations conducted. First, a general analysis of levels is usually required. For this, it is necessary to vibration spectral characteristics is performed. Then, quantify those parameters that affect the railroad noise. several signal processing methods are applied to In this paper, the present state of environmental calculate symptoms that are expected to be independent conservation for H.S.T. noise is described, including on the influence of cutting parameters. At the first step, noise regulations and laws. Then we conduct the various RMS (root mean square) values are calculated for the study to reduce H.S.T. noise along track. The design of data representing different tool wear VB levels. Next, Page 1339 The 8th International Congress on Sound and Vibration 2-6 July 2001, Hong Kong, China TOEPLITZ MATRICES AND CUTTING STATE IDENTIFICATION B. Berger, C. Belai, D. Anand Department of Mechanical Engineering University of Maryland, College Park, MD 20742 U.S.A e-mail: berger@eng.umd.edu Abstract Properties of the singular values of a Toeplitz matrix, R-matrix, are examined as a function of matrix size. The R-matrix arises in the TOR algorithm for parametric bispectrum estimation and has recently found application in the identification of cutting states in connection with the orthogonal cutting of short circular cylinders. Numerical studies, of phase coupled functions for which exact expressions for the third order cumulant elements of the R-matrix are known or estimated from measured cutting tool acceleration data, show the presence of singular value trajectories. The trajectories provide an alternative means for ordering the singular values, each being associated with a frequency, and are shown to be related to frequency components of the bispectrum. The noise suppressive properties of third order cumulants and singular value decomposition result in robust algorithms for state identification. INTRODUCTION Recently developed signal processing methodologies including neural nets, [8], wavelets, [5], higher order spectra, [2], and information-theoretic functionals have been utilized in the analysis and control of cutting dynamics. The on-line identification of cutting states, associated with the orthogonal cutting of stiff steel cylinders, was realized in [2] through an analysis of the behavior of the singular values of a Toeplitz matrix, R, of third order cumulants of tool acceleration measurements. In the following properties of the singular value trajectories ofR are investigated numerically. TIIlRD ORDER RECURSION Let ci1:1,1:2) = the third order cumulant of the third order stationary random process X(k), k=0,±1,±2, .... If the mean of X(k) vanishes, then ci1:1,1:J = m3(1:1,1:J where mi1:1,1:2) = E(X(k) X(k+1:1)X(k+tJ); Eis the expected value, which may be estimated by :1877 _ Page 1340 +n ~(ri,r2 ) = (1/2n) LX(k)X(k+ r1)X(k+ r2), (1) k=-n where n ... + 00• The bispectrum of X(k), Ciw1, w2), is defined by +co +co CiO J I' OJ z) = L L C3 ( r i, r z) exp [- j (O J i r i + OJ zr 2)] . (2) 'I =-co '2 =-CO A p-th order AR process is described by p X(k) + La(n)X(k- n) = W(k) (3) n=I where W(k) is non-Guassian, E(W(k)) = 0 and E(W3(k)) = p. Multiplying through (3), summing and noting (1) gives p c;(-k,-e) + Ia(n)c;(n- k,n- e) = f3 8(k,e) (4) n=I where k,Q ~O. Setting k=Q in the third order recursion, TOR, equation (4) with k=O, ... ,p gives p+ 1 equations for the p+ 1 unknowns a(n) and p. p+ 1 = maxlag. The matrix form of the TOR algorithm, (4 ), is Ra=b (5) where (0,0) (1,1) (p,p) (-1,-1) (0,0) (p-1,p-1) R= (6) <. (-p,-p) ( - p + 1, - p + 1) (0,0) (nj) = c/(nj), a= [l,a(l), ... ,a(p)f and b = [P,O, ... ,Of. A sufficient but not necessary condition for the representation in ( 5) to exist is the symmetry and positive definiteness oft he Toeplitz matrix R, [6,7]. · If A is a real mx.n matrix, then there exists orthogonal matrices U e Rmxn and V e Rmxn such that - 1978 - Page 1341 (7) where q = min(m,n), 0 1 ~ 0 2 L.Oq 1 + <1>2 and <1> 1,<1>2 are independent and uniformly distributed over [0,21t] then (8) where G1(A1,A2,k) = 2(cos (A1k) + cos (A2k) + cos (A1 + A2)k). Consider the self phase coupled test function f1(t) = cos(21t·l00t+1) + cos(21t·lOOt + 1+¢2)). If m = sampling rate in Hz, then A1 = A2 = 1, A3 = 0.2, A.1 = A2 = 21t·lOO/m and A3 = 21t·200/m. The singular values ofToeplitz R-matrices, with elements consisting of sums ofc osine functions, occur in intertwining pairs as a function of maxlag. Denote a singular value over an interval a ::: maxlag ::: b by SV(i,a,b) = Oj and a mean singular value by MSV(i,a,b) = (o i+oi+1)/2, omitting the maxlag argument for brevity. Denote a singular value trajectory by SVT(n,a,b) where n = a positive integer identifying a singular value trajectory. The mean singular value trajectory MSVT(Q,a,b) = (SVT(q,a,b) + SVT(r,a,b))/2 where SVT(q,a,b) and SVT(r,a,b) intertwine and Q identifies MSVT(e,a,b). In Fig. l(a), the4 non-zero singular values off1(t) vs. maxlag are shown withm=lOOO Hz., MSV(l,1,150) = (01+02)/2 and MSV(3,l,150) = (o3+o4)/2. Identify the intertwining pairs 0 1, o2 ando3, o4 withi=l,2, respectively. Then theupperMSVT(l,1,150) =MSV(l,1,150) and the lower MSVT(2,1,150) = MSV(3,l,150). Fig. l(b) shows the R-ratio vs. maxlag forf1(t) forwhichR=2.0 for maxlag > 50. Values of R~2.0 identify the chatter state for the orthogonal cutting of short circular steel cylinders, [2]. A plot of SV(l,93,135) and SV(2,93,135) is shown in Fig. l(c). The distance between intersection points is!:,. maxlag = 5 which is exactly equivalent to the low frequency, 100 Hz, 10 lags/cycle, componentoff1(t). The difference SV(3,l,150)- SV(4,1,150) is plotted in Fig. l(d) as a function ofmaxlag. Points of intersection, corresponding to minimum values of the difference, due to a lack ofresolution alternate between 2 and 3 lags apart. The mean oft he distance between minima is A maxlag = 2.5 which is exactly equivalent to the high frequency, 200 Hz, 5 lags /cycle, component off1(t). Then the two pairs ofSVT are each separately associated with one oft he two --:-r&79- Page 1342 frequency components of f1(t). A computation identical to the foregoing except that values of c/(k,k) are estimated by averaging over subsets of the time series for f1(t) yields essentially identical results. Somewhat more complex behavior is observed in the phase coupled function fz(t) = 0.9 cos (21t·90t+q>1) + cos (21t·lOOt+2) + 0.2 cos (21t·190t+(1+q>2)) where q> 1, 2 are independent and uniformly distributed over [0,21t]. The A1 = 0.9, A2 = 1.0, A3 = 0.2, A1 = 21t·90/m, A2 = 21t· 100/m and ).3 = 21t· 190/m. In Fig. 2(a) the 6 non-zero singular values offz(t) vs. maxlag are shown with m=l900 Hz. A plot ofSV(l,98,140) and SV(2,98,140) vs. maxlag is shown in Fig. 2(b). Points of intersection alternate between 9 and 11 lags apart. The mean of the distance between intersections is A maxlag = 10 which is exactly equivalent to a frequency of 95 Hz. Fig. 2( c) shows the difference SV(3,l,150) - SV(4,l,150) as a function of maxlag. The mean of the distance between minima is A maxlag = 5.0 which is exactly equivalent to the high frequency, 190 Hz, 10 lags/cycle, component of f1(t). A plot of SV(5,l,150) - SV(6,l,150) vs. maxlag is shown in Fig. 2( d). The distance between minima alternates between 9 and 11 lags giving a mean which is A maxlag = 10 which is exactly equivalent to 95 Hz, 20 lags/cycle. In Fig. 2(a) let MSVT(l,1,190) = MSV(l,1,190), MSVT(2,l,190) = MSV(3,l,190) and MSVT(3,l,190) = MSV(5,l,190). The three MSVT intersect in a single point, off of the figure, for which A maxlag = 190 lags which corresponds exactly to a frequency of 5 Hz. For fz(t), c3" (k,k) = 0.09 (cos (90·a·k) + (cos (lOO·a·k) + cos (190·a·k)) where a= 21t/1900. This may be re-written as c3"(k,k)=0.09(2·cos(5·a· k)-cos (95·a·k) + cos (190·a·k)). As shown previously the intertwining and modulation frequencies along MSVT(l, 1,190) and MSVT(3, 1,190) correspond exactly to the 95 Hz and 5 Hz frequency components appearing in the above expression for c/(k,k). In the case of f1(t) and fz(t) the elements of the R-matrix, c3" (k,k), are exact and consequently noise free. As a test oft he algorithm's robustness consider the measurements of tool acceleration of the March 5 chatter experiment for which spindle speed = 37 1 rpm, depth of cut= 2.8 mm, feed rate= 0.007 in/rev, surface speed= 90 m/min, and sampling rate= 1024 Hz. This is a case of the orthogonal cutting of short steel circular cylinders. Fig. 3(a) shows the largest 10 singular values vs. maxlag. Fig. 3(b) shows the corresponding R-ratio which is:::: 2 thus identifying the chatter state. A plot of SV(l,68,140) and SV(2,68,140) is shown in Fig. 3(c). The average distance between intersection points is A maxlag = 5.46 which is equivalent to a frequency of93.8 Hz associated with MSVT(l,68,140). A plot of SV(3,63, 135) and SV( 4,63, 135) vs. maxlag is shown in Fig. 3( d). The average distance between intersection points is A maxlag = 2. 70 which is equivalent to a frequency of 189 .4 Hz. The frequency associated with the intertwining pair SV(5,67,139) and SV(6,67,139) was found to be 95.1 Hz. The bispectrum displays well defined peaks at (93.02 Hz, 93.02 Hz), (JOO. Hz, 93.02 Hz) and (93.02 Hz, 100. Hz). The (93.02 Hz, 93.02 Hz) peak's components correspond closely with the 93.8 Hz frequency associated with MSVT(l,68,140). Self coupling as in f1(t) is suggested. The bicoherence associated with (93.02 Hz, 93.02 Hz) is"' 1.0. The average of (100. Hz, 93.02 Hz) is 96.51 Hz, which approximates the frequency component 95.1 Hz associated with MSVT(3,68,140). There is some simularity to the behavior of fz(t). CONCLUSIONS A numerical study of the singular values of the Toeplitz R-matrix as a function of matrix size, - 1880 - Page 1343 max.lag, has demonstrated the presence of trajectories of pairs of singular values each associated with a frequency component of the bispectrum. The global behavior of the trajectories clearly identifies differences in the frequencies of phase coupled cosine functions. ACKNOWLEDGMENTS The authors acknowledge the support oft he National Science Foundation through GER-9354956. The encouragement ofH. L. Russell of the University of Maryland, College Park, P. Grootenhuis and D. J. Ewins of the Imperial College of Science, Technology and Medicine, London, is very much appreciated. The assistance of T. Miller in the preparation of. the manuscript is acknowledged. REFERENCES 1. G. K. An, S. B. Kim and E. J. Powers, ,,Optimized Parametric Bispectrum Estimation," Proceedings of ICASSP, New York, 2392-2395 (1988). 2. B. Berger, I. Minis, M. Rokni, et al., ,,Cutting state identification," J. of Sound and Vibration, 200, 1, 15-29 (1997) 3. B. Berger, J. A. Manzari, D. K. Anand and C. Belai, ,,Auto-Regressive SVD algorithms and cutting state identification," J. of Sound and Vibration, to appear. 4. G. H. Golub and C. F. VanLoan,Matrix Computations. (Johns Hopkins Univ. Press, Baltimore, MD, 1993). 5. M. K. Khraishen, C. Pezeshki and A. E. Bayoumi, ,,Time series based analysis for primary chatter in metal cutting," Jour. Of Sound and Vibration 180, 67-87 (1995). 6. C. L. Nikias and J.M. Mendel, ,,Signal processing with higher-order spectra," IEEE Signal Processing Magazine, 10-37, July (1993). 7. C. K. Nikias and A. P. Petropulu, Higher-order Spectra Analysis. (Prentice Hall, Englewood Cliffs, NJ., 1993). 8. I. N. Tansel, A. Wagiman and T. Tziranir, ,,Recognition of chatter with neural networks," Inter. Jour. Of Machine Tools and Manufacturing, 31, 4, 539-552 (1991) -::-r&81 - Page 1344 20,------------,------------.------------, "' 15 ~ 7o > 10 (a) 0) C: i:i5 5 50 100 150 Max Lag 3.---.-------------,-----------~------------, 2.5 (b) 0 -~ 2 I a: 1.5 1 ~-------------''--------------'------------' 0 50 100 150 Max Lag s12crossat84 69 94 99 104 109 114 119 124 fr-100 13,----,,----,----,----,------,----.------,----,----;*.-, "g' ' 12 ·;;; 2 (C) (.) 11 Cl> ~ 10 > ci, C: 9 i:i5 8'-----'-----'------''------'-----'-----'-----'-----''------' 80 85 90 95 1 00 105 11 0 115 120 125 F1 TOR Fsam~%6"89nin of diff of s34 0.2 .--------------,------------------------, lfl 0.15 ::, (d) «i > g> 0.1 i:i5 0 00 0.05 0'----'----..J---'---,..___ _....____. __. ..__ _____. ...,. _____. __. ....~ __,-_...,_, 0 50 100 150 Max Lag Figure 1: Fl ExaC't: (a) Singular Values (b) R-ratio (c)a12 Crossings (d) tr:3 - 0"4 Page 1345 10 8 Cl) Q) :::l (a) ni 6 > d, C: 4 en 2 50 100 150 Max Lag s12 cross at 28 39 48 59 68 79 88 99 108 a.------.-----.-----.------.-lr=-9-5 ---,,--------------.------, Cl) g> 7 ·u; (b) u8 6 ~5 ni >4 13 220 ~---~---~---~-----'-----~---~---~---~---~ 30 40 50 60 70 80 90 100 110 Max Lag F2 TOR Fsamp-1900 min of diff of s34 0.2 ,--------------.---------------------------, (C) gj 0.15 :::l ni > g> 0.1 en 0 '° 0.05 50 100 150 Max Lag F2 TOR Fsamp~1900 min of diff of s56 0.2c-------------.---------------------------, ~ 0.15 (d) ~ g> 0.1 en 0 '° 0.05 O'----;-<=-.lf--"""41i<----'----4'. ......- -""'"_ _. .__ ____. ..__ _. L-__..___ ___ _,o;._ __~ -= 0 50 100 150 Max Lag Figure 2: F2 Exact: (a) Singular Values (b) 0'12 Crossings (c) 0'3-0'-1 (cl) O'r,-0'6 - 1883 - Page 1346 11 X 10 15 "Q') .=2 10 >"' ~ :5 0, C 5 i.i5 0 0 50 100 150 Max Lag 3 2.5 0 ~ i 2 a: 1.5 20 40 60 80 100 120 140 Max Lag s12 cross at 68 74 79 85 12 X 10 fr=93.7465 1.4 "g'> 1.3 ·;;; l!l 1.2 c'3 g 1.1 "iii > 0) ~ 0.9 0.8 60 70 80 90 100 110 120 130 140 Max Lag s34 cross at 63 66 68 71 7 4 11 X 10 frE 1 89 .3699 6 ."~' 5.5 ""'' ue 5 :C:l>, "iii 4.5 > 0) C 4 i.i5 70 80 90 100 110 120 130 140 Max Lag Figure 3: :\fard1,j experiment 1 TOR: (a) Singular Values (b) R-ratio (c)CCQ_.,,. ...1 .- i½ technology is applied to the miniaturization and integration of conventional devices. MEMS accelerometers are used extensively in the automotive industry for controlling airbags, figure 8. Silicon microfabrication technology, and more specifically Figure 9. MEMS Market Share Estimate. silicon micromachining, has been a key factor for the rapid progress of microsensors, and now microactuators and Market segments expected to outpace the collective MEMS MEMS. Silicon micromachining, which refers to fashioning market growth include optical MEMS, bio-MEMS and RF microscopic mechanical parts out of a silicon substrate or on devices. These high growth technologies will be driven by a silicon substrate, has emerged as an extension of telecommunication and biomedical market segments. integrated circuit fabrication technology. Micro machining is Products include optical switches and tunable optical used to fabricate a variety of mechanical microstructures of components applied to fiber based communication great diversity including beams, diaphragms, grooves, networks. Within the biomedical market, MEMS enabled orifices, sealed cavities, pyramids, needles, springs, products are anticipated for drug delivery and drug complex mechanical suspensions, gears, linkages, and discovery. micromotors. These microstructures, with and without integrated electronics, have been used successfully to realize 393 Page 1392 Area AI!I!lication MEMST:y:I!e Market Share Automotive Airbag, ABS, tires, engine air-intake Acceleration , flow and pressure %31 gauges sensors Computer Data storage devices MEMS actuators for probe %26 tip read/write heads Industrial Machine condition monit9ring Accelerometers, MEMS based %25 gyroscopes Medical Infusion pumps, respirators, kidney Pressure, temperature and flow sensors. % 16 dialysis machines, blood pressure Micro pumps measurement, drug delivery systems (BioChip) Table 1. Commercial MEMS applications. Flight Batt~ Rocket Motor Unitary Payload Height Of Burst (HOB) Sensor Safe and Arm Device INS with GPS Guidance · Figure 1. Cutout illustration of the ERGM unit 394 Page 1393 Unitary Warhead With Height of Burst Sensor Establish Glide for Maximum Range Figure 2. Illustration ofERGM flight path {~mard Control Guid.1tKe Figure 5. Excalibur round with the MEMS GPS/IMU navigation system. 395 Page 1394 Figure 6. Illustration of an Excalibur launch. Diameter of Earth lA stronomical Unit Light Year 10" I 108 1118 1010 1012 1014 1016 1011 1020 meter meter ~@:Zm:Z~~0;,;;zm:;;;w:;;;~fl=======~w;;2W,;~0ama:v/2a1/...mau::::::=]~~m~,;,-,00~:z¼¼~~m~~c::::::Jf!"9~@~w~/2%~0:;-.;:1//2~0~~r::=::::J10~0~m~w~0~m~m~m 10"16 10"U '10"12 10"10 1041 10'6 10-4 10"2 108 102 tD iameter of Proton tH •Atom Diameter tH uman Hair Nanodevices Typical Man-Made Devices Figure 7. Scales of Things in Meters. 396 Page 1395 ICMA 2004 Proceedings of the International Conference on Manufacturing Automation Advanced Design and Manufacturing in Global Competition October 26-29, 2004 Wuhan, People's Republic of China Edited by Professor X Y Shao and Dr C Deng Professlonzil Engineering Publlshlng Professional Engineering Publishing Limited Bury St Edmunds and London, UK Page 1396 First Published 2004 This publication is copyright under the Berne Convention and the International Copyright Convention . All rights reserved. Apart from any fair dealing for the purpose of private study, research, criticism or review, as permitted under the Copyright, Designs and Patents Act, 1988, no part may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, electrical , chemical, mechanical, photocopying, recording or otherwise, without the p rior permission of the copyright owners. Unlicensed multiple copying of the contents of this publication is illegal. Inquiries should be addressed to: Academic Director, Professional Engineering Publishing Limited, 1 Birdcage Walk, Westminster, London SW l H 9JJ, UK. CO 2004 Professional Engineering Publishing Limited, unless otherwise stated. ISBN 1 86058 468 3 A CIP catalogue record for this book is available from the British Library. Printed and bound in Great Britain by Antony Rowe Limited, Chippenham, Wiltshire, UK. Toe Publishers are not responsible for any statement rn.ade in this publication. Dam, discussion, and conclusions developed by Authors are for infomi.ation only and are not intended for use v..-ithout independent substantiating investigation on the part of potential users. Opinions expressed are those of c.hc Auilio~s and :u=: not necessarily those of the In.stirurion of Mechanical Engine~rs or ics Publishers. Page 1397 Design and operation of a storage facility in a virtual environment Z TUNCALI, SK GUPTA, and DK ANAND Department of Mechanical Engineering, University of Maryland, USA ZYAO Department of Automation and Computer-Aided Engineering, The Chinese University of Hong Kong, People's Republic of China ABSTRACT This paper demonstrates the design, visualization and analysis of a warehouse in virtual environments. Our motivation is to create an interactive simulation program that allows engineers to create and test their own warehouse configurations with a fairly inexpensive and practical method, i.e. Virtual Reality (VR). Our program allows the user to create the floor plan from scratch, construct the designed structure, optimally store and retrieve incoming items, and finally analyze the design with respect to various performance criteria. 1 INTRODUCTION Virtual Reality (VR) is a computer-generated environment that gives the illusion of being immersed in a real system (1-2). The utility of applying VR technologies in various design applications as well as facility layout design has been proven to be of considerable benefit in the area of industrial engineering research and practice (3 ). The Surface Warfare Center Division in Indian Head (NAV SEA) has recognized the potential of VR as a tool to improve design and manufacturing processes in the future and is beginning to invest in the development of industrial VR applications. The Laboratory for Design and Visualization in Virtual Environments at the University of Maryland is seeking the solutions ofs·ome riiaJor engineering problems ~n VR. fhe research anu ·ueVt:liJpment activities in this · laboratory focus on engineering applications of VR and have already produced remarkable results; some of them sufficiently mature for introduction in practical design tasks. As stated in ( 1-2), the expected benefits of industrial VR applic3.tions include savings in cost and time, better market response through reduced design cycles, and improved products or facilities. 1004/179/2004 © Professional Engineering Publishing 2004 521 Page 1398 Warehousing and distribution systems play a maj or role in the "service economy." The motivation in this study, however, is the storage and retrieval of hundreds of different CADIP AD (Cartridge/Propellant Actuated Devices) devices used by the DOD (Department of Defense). Their timely availability for insertion in ships, aircrafts, etc. makes it important lo optimize the " supply chain." The design and operation of a warehouse entails many challenging problems such as the orientation of the storage racks, the allocation of space among compcting users. and the overall configuration of the facility. Because of the reasons stated above, a storage facility layout designer may have to go through multiple intermediate prototypes before reaching the optimal solution or even make significant modifications to the final design. This is a quite tedious and economically inefficient way of designing a storage facility. In this paper we would like to present an interactive simulation program that allows engineers to create and test their own warehouse configurations wi th a fairly inexpensive and practical method, i.e., Virtual Reality (YR). Our program allows the user to create the floor plan from scratch, construct the designed structure, optimally store and retrieve incoming items, virtually walk around inside the warehouse, pick up any part and look at it in more detail and finally analyze the design with respect to various performance criteria. The storage of an item is performed by an unmanned forklift, which is guided by optimal path find ing algorithms within the program. A carrier vehicle that is navigated to follow the shortest path within the existing floor plan also manages the retrieval of an item. l;,,l4l'k tJ.L., on Automated storage/retrieval ~--- tha !loorb ..u• (AS/R) systems are also of strong interest due to such R•rroV'II benefits as lower bui lding will, 4rd '}..h. ... , f:x1»..1d•: and land cost, labour Bh,, tilt,., ,h.«lf savings, reduced inventory L Red ':il.:, ..u will levels, and an improved throughput level, among y _;::::,-.------- -----, others (4) . References (5-8) present various studies that have been made to improve storage/retrieval [/0 l=•bon d...t.-.f"orS /R. performance inside the C .aJcu 1.... tio rs 1----.. Allow \,,Uer b pi.:kup U"d. IT0......,. e-=----+-l~=:.:.. ?~ ' CAD warehouse design, storage P•l"1c:r:rrn..u-c• m.cxi•lJ .a.rd .UWy-,U ,tor • dAU. assignment and automated SIR systems, visualization in a virtual environment has d...,,. f'orSIR c:.Jcul..ation., not been employed. i he _::>-=-------i~:::i::.. P.ub' txpl.CW l.On research reported here p•rf"CIZ":T\.U"Ce ~y,U k.=udu,d ,tor • d....t.a investigates this new idea. F i g ur e l: T h e flowchart of the virtual wa r eho u si n g process in a virtual environment. 522 1004/179/2004 © Professional Engineering Publishing 2004 Page 1399 2 THE PROBLEM OF "VIRTUAL WAREHOUSING" The critical result of this study is the ability to design, visualize and analyze warehousing in virtual environments. This reqmres the development of the following: • Interactive floor plan development utility; • Utility for construction of the warehouse; • Optimal storage assignment and retrieval of items; • Analysis and display of simulation results; • Utility for picking up storage items for a d~tailed visual inspection; • Necessary interface for visualization in a CAVE (Computer Automated Virtual FiguN 2; \Var~house floor-base during the design .stsge. Environment); • A systematic mapping of software generated from a SGI workstation to a CAV E; • Performance optimization strategies in order to render a very large database of 3D objects with an acceptable frame rate. The research reported here tackles all these activities stated above. 3 METHODOLOGY The methodology for design and analysis of a warehouse in a virtual environment is shown in the flowchart of Figure 1. The storage items, Figure 3: The floor plan has bu:n extruded. which are detailed CAD models stored in STL (stereolithography) format, have been generated external to this work. A computer aided modeling software, Pro/E, has been used for most of the part models, which belong to the Naval Research Center inventory. Virtual storage racks and the walls of the virtual warehouse are also imported into the database as separate STL files, then scaled and cloned to form the internal and external structure of the warehouse. The CAV E user may select from the interactive list of six main executive commands depending on the current operational status of the program. The six options mentioned above are: BUILD, COLLAPSE, PARTS ON, PARTS OFF, ANALYZE and SThifULATION. A brief discussion of the overall chart follows. 3.1 Design of a Warehouse Our "Virtual Warehouse" program allows the CAV E user to design the facility layout by marking the floor tiles with the wand (a baseless joystick). The marked tiles aUocate space for shelves and walls on the floor grid, where the red and blue tiles represent the location of the walls and shelves respectively as shown in Figure 2. Launching the "BUILD" command from the main menu removes the marked· floor grid and places. the walls and the storage racks Oil° the virtual floor creating a 3D storage facility as shown in Figure 3. The CAVE user/users can now walk around inside the facility or even fly over it, exploring a structure that doesn't even 1004/179/2004 © Professional Engineering Publishing 2004 523 Page 1400 exist yet. After viewing the warehouse from various standpoints and angles, the user may decide to modify his/her design. This can easily be done by just executing the "COLLAPSE" command, which removes the whole JD structure and brings back the marked floor. The floor plan can now be modified by erasing the marked tiles or painting new ones. This operation either removes some of the existing walls and racks or adds new ones to the structure as soon as the "BUILD" command is rep:ated. 3.2 Optimal Storage Assignment Once the designer is convinced with the overall warehouse configuration, he/she can now proceed with the operation of optimally placing the storage items on the storage racks by just giving the "PARTS ON" command. This process accepts some part specific inventory data as well as part CAD models to display inside the warehouse as shown in Figure 4. A simple text file containing the following information is traversed by the appropriate file parsing algorithms: 1. Part index number 2. Name of the part model file and it's location in the database 3. Total quantity of the storage item 4. Storage/ retrieval FOR (frequency of request) data Different storage assignment methods have been considered for this study and dedicated storage has been selected for its higher system throughput performance (6) . Throughput capacity of a storage facility is defined as the maximum ho urly rate at which the storage system can receive and put loads into storage and/or receives and delivers loads to the output station (7). As stated in (8), to maximize throughput capacity, we assigned SKUs (Stock . Keeping Units) to storage locations based on the ratio of their activity (FOR) to the num ber of openings or slots assigned to the SKU. The SKU having the highest ran.king is assigned to the preferred openings, and so on; with the lowest-ran.king SKU is assigned to the least preferred openings. Since " fast movers" are up front and "s low movers" are in back, throughput is maximized. The number of slots assigned to the SKU is determined by first finding the smallest encapsulating box for each part model and multiplying its volwne by quantity. The storage racks are also ranked from the most preferred to the least preferred by comparing their minimum distance to the VO point. A shortest path finding method based on Dijktra's algorithm is used. The most efficient pick-up location is found for each storage rack to calculate the minimum distance to the VO point. After the best location is found for each item within the warehouse, the associated item 1s scaled to a predetermined unit size and placed on the storage rack. Since the items may F ii: ure "= Parts are placed oa the s he l ves. The user is pickln: u p a p ar t witb 1b.e wand ro look at it clo1cl y . He ca n turn lbe part in J .axes to Jee all around ir. be fairly diverse in 524 1004/179/2004 © Professional Engineering Publishing 2004 Page 1401 size, the scaling operation helps the CA VE user to have a better view of the parts and thus perform a better visual inspection. With the items placed on the racks, the designer now has a feel for what the loaded warehouse will look like in the future . A prel iminary judgment about the size of the facility can be made at this moment. There may be too many empty slots or some items could not be assigned to a slot due to the shortage of storage space inside the warehouse. The designer may then click on "PARTS OFF" to remove all the storage items off the shelves, and modify the design as explained in 3.1 . 3.3 Storage Performance Analysis The design of a storage faci lity has a crucial influence on its operational performance (5, 9) . The location and orientation of storage racks, support structures such as columns, walls or protective bunkers for explosive storage applications, play a significant role in performance measures such as throughput performance or fire hazard rate. In order to address this issue, our "Virtual Warehouse" program performs three different kinds of performance analysis: storage density, system throughput and explosion/fire safety. Storage uensity is defined as the volumetric space avai lable for actual storage relative to the total vo lumetric space in the storage facility and can be assessed by using the floor plan. A high storage density is important since unnecessarily large faci lities, i.e. large aisle space :tnd redundant walls increase land and constructional costs. However, as storage density is increased, accessibility, the capability to access any storage item or pallet is adversely affected. System throughput capacity is an important performance measure from the operational point of view. High throughput levels mean easier and faster storage and retrieval of the items, and help reduce the facility's operational costs. Assuming that the AGV or the order-picking vehicle has a constant speed and performs the vertical movement while travelling towards/from the pick-up location, we define the system throughput performance as the ratio of the pick-up distances. The sum of the minimum distance of each pallet to the VO point is divided by the sum of each pa llet - VO distance assuming that there are no obstacles, i.e., other shelves or walls, inside the warehouse. As a result of this evaluation, a v. ..· arehouse configuration with easi ly accessible storage spaces brings a high throughput perfom1Uncc. On the other hand, an unorganized, labyrinth like structure makes the pick-up vehicle travel more, thus causes a lower performance. Fire safety assessment is for special applications where the faci lity is used for storing explosive or combustible materials. Our current application involves the storage of CAD/PAD (Cartridge/Propellant Actuated Devices) products. CAD/PAD products contain high explosives, blasting agents · and detonators and thus possess a potential ·-:!xplosion.. :1azard. This ass~ssment is based on an idea of penalizing such designs where storage racks are placed next to each other Figure 5: Storage ef1iclency and opuation~I performance without having any open space or separator i• displayed ~ftcr the paru have been ploceJ. 1004/179/2004 © Professional Engineering Publishing 2004 525 Page 1402 walls in between th.e storage pallets. Explosive containers that are placed sufficiently away from other explosives or having a separator wall in between are consider safe and do net decrease the fire hazard rate of the facility. The minimum separation distance for each substance has been obtained from the Explosive Storage Distance Table within the Reclamation Safety and Health Standards (RSHS), which was prepared by Bureau of Reclamation. U.S. Department of Interior. The analysis process is started by giving the "ANALYZE" command from the main menu, after the storage items are placed on the shelves. The analyzing algorithms are executed consecutively and the results of this process are displayed on a percent scale on the 30 analysis display chart as shown in Figure 5. 3.4 Simulation of Pick-up Process While the storage items are being placed on the shelves, certain information regarding the location and quantity of each item is kept as inventory data to be used in order to retrieve a desired item. Our program is capable of simulating the pick-up operation of a storage item using the inventory data. While walking around inside the virtual warehouse, the user may want to observe how a particular item will be retrieved from the rack and delivered to the I/0 point. This simulation gives the CA VE user an idea about the optimal path to be taken, the best pick-up location for one rack as well as the accessibility of one part. The CAV E user selects the desired item by simply pointing at it with the CAV E wand and clicking a wand button. This action allows the user to hold the part with the wand, mov·e it around, and rotate around two axes with the CAV E buttons for a better visual inspection. After selecting the storage item to be retrieved, an unmanned carrier vehicle is guided to travel from the I/0 point to the pick-up location and back. The best pick-up location is determined by running the minimum distance finding algorithm for both sides of the storage rack and the closest side of the shelf to I/0 point is found. The carrier vehicle follows the closest path to and from the pick-up location. Our shortest path finding algorithm uses Dijktra's method and travels on a path connecting the central points of the tiles on the aisle floor. 4 VISUALIZATION INSIDE THE "CAY E" The CAV E (Computer Automatic Virtual Envirorunent) at the University of ;,.-1aryland, College Park is a projection-based VR system that surrounds the viewer with 4 screens. The screens are arranged in a cube (8ft x 8ft x 8ft) made up of three rear-projection screens for walls and a down-projection screen for th.e floor; that is, a projector overhead points to a mirror, which reflects the images onto the floor. A viewer wears stereo shutter glasses and a six-degrees-of-freedom head-tracking device. As the viewer moves inside the CAV E, the correct stereoscopic perspective projections are calculated for each wall. A second sensor and buttons in a wand held by the viewer provide interaction with the virtual envirorunent. A Silicon Graphic:./ONYX2 Infini(e Reality Compute1 performs all of the neces~ary calculations for real time visualization. 526 1004/179/2004 © Professional Engineering Publishing 2004 Page 1403 The Virtual Warehouse has been created on a Silicon Graphics Octane2 workstation. Octane2 runs on IRIS 6.5 operating system, which is compatible with Unix environment. Our workstation incorporates a 32MB "ODYSSEY" graphics unit that is optimized for OpenGL graphics applications. C++ has been chosen as the primary programming language for it>s easily expandable infrastructure. SGI's OpenGL Performer graphics libraries have been used to create the virtual warehouse environment. OpenGL Performer incorporates significantly fast loading and rendering capabilities, which are the key factors in the creation of real time graphical applications. Navigation inside the C.AVE, from the programming point of view, is quite different than PC or workstation applications due to the physical nature of the CAV E environment. The navigation algorithm applies the necessary transformations only to the database while the camera, which happens to be the user, remains steady in the middle of the CAV E. With the help of the appropriate reverse transformations, a realistic illusion of a flying-camera is generated. A head tracker and a wand perform the interaction and communication with the program inside the CAV E, i.e. navigation and menu selections. The necessary communication between these navigation devices and the software is performed using various cailback functions at each program execution cycle. The head tracker is a position sensor mounted on the user's head. The wand is a 3D joystick, which also incorporates a position and orienlation sensor for feed back of the location and heading direction of the wand. The navigation module on the wand allows the user to travel towards the wand's heading direction. Our Virtual Warehouse software program has been created and tested on the CAV E Simulator. The Simulator is a software developer environment, which allows testing the source codes specially developed for the VR. The navigation devices of the CAVE are mapped on to the workstation hardware, i.e., mouse and keyboard, so that navigation inside the CAV E can be simulated on the workstation. The monitor also displays individual images that will be mapped onto the CAVE's walls. The Simulator is a safe testing environment, which is widely used in order to protect the expensive CAV E equipment from unexpected runtime errors and crashes during the development stage of VR programming. 5 CONCLUSIONS Al~D FUTURE WORK The current version of our "Virtual Warehouse" program includes the following utiiities: • Interactive floor-base structure to create a simple 'blueprint' of the storage facility. • Operation selection widgets for a 3D environment. • Algorithms for optimal part placement. • Algorithms for performance assessment of a storage facility • Shortest path finding algorithms have been assembled to guide the order-picking robot. The above utilities are assembied to the main program as separate modules and are able to operate in harmony with an acceptable frame rate. Various performance enhancement operations for VR programming have been discussed and the importance of these precautions has been considP-red. Dedicated storage methods have been used in our aopHcation, however randomized storage is also a ·widely used method and preferred in many storage facilities where significant fluctuations in inventory levels are observed ( l 0). Random storage assignment algorithms should and can easily be added on to our existing software. 1004/179/2004 © Professional Engineering Publishing 2004 527 Page 1404 Our "Virtual Warehouse" program allows the CA VE user to build a virtual warehouse from scratch and is currently capable of assessing an existing warehouse for operational performance. However, it is knmvn that the greatest expectations from a computer are far beyond the assessment of an already existing design. Instead, facility design experts would like the computer to come up with an optimal warehouse design that would assume certain weight parameters and minimize a given cost function. We are currently working on an optimization module that would perform this operation and let the CA VE user start with a good design and eventually reach a superior result by ma.1<.ing some certain modifications in a virtual environment. ACK.t'fOWLEDGEMENTS This research is supported by Center for Energetic Concept Development at the University of Maryland. The authors would like to thank the K.C. Wong Education Foundation (Hong Kong) and National Nature Science Foundation of China (NSFC) for the supporting. REFERENCES 1. Cruz-Neira, C., Sandin, D.J., DeFanti, T.A., (1993) Surround-screen projection-based virtual reality: the design and implementation of the CA VE. Computer Graphics (Proceedings of SIGGRAPH '93), ACM SIGGRAPH, August 1993, pp. 135-142. 2. Kenyon, R.V. and Afenya, M.B., (1995) Training in virtual and real environments. Ann Biomed Eng (United States), Jul-Aug 1995, 23(4), pp. 445-55. 3. Smith, R.P. and Helm, J.A., (2000) Virtual facility layout design: the value of an interactive three-dimensional representation. 1ntemational Journal of Production Research (UK); 37; 17; pp. 3941-3958. 4. Considerations for Planning and Installing an Automated Storage/Retrieval System. Material Handling Institute, Inc., AS/RS Document-I 00 7M, 1977. 5. Cormier, G., ( 1997) A brief survey of operations research models for warehouse design and operation. versions franc;;aise et anglaise. CO RS-SCRO Bulletin 31, 3, pp. 15-20. 6. Hausman, W.H., Leroy, B.S., Graves, S.C., (1976) Optimal storage assignment in automatic warehousing systems. Management Science, Vol.22, Issue 6. 7. Groover, M.P., (2001) Automation, Production Systems, and Computer Integrated Manufacturing, 2nd. Edition, Prentice-Hall. 8. Salvendy, G., (1982) Handbook of Industrial Engineering, New York: Wiley. 9. Bozer, Y.A. and White, J.A., ( 1984) Travel time models for automated storage and retrieval system. IIE Transactions 16(4), pp. 329-338. 10. Roodbergen, K.J., Petersen, II C.G., ( 1999) How to improve order picking efficiency with routing and storage policies. Progress in Material Handling Practice, pp. I 07-124. 528 1004/179/2004 © Professional Engineering Publishing 2004 Page 1405 THE SCIENCE AND ENGINEERING WORKFORCE AND NATIONAL SECURITY Robert A. Kavetsky Energetics Technology Center La Plata, MD rkavetsky@etcmd.org Davinder K. Anand, Ph.D. Center for Energetic Concepts, University of Maryland College Park, MD dkanand@umd.edu Michael Marshall Physicist, Department of Navy (Retired) mmarshall l 3@triad.rr.com ABSTRACT their start-up. The Jet Propulsion Laboratory provided an This article identifies concerns about the U.S. defense early model of a university-operated facility, while the industry's difficulty in maintaining the level of skilled labor RAND Corporation was an early model for many of the force necessary to sustain it in all phases of science and non-profit technical centers, the so-called "think tanks." technology, from research and development to design and Both extend the capabilities of the DOD in-house effort manufacturing, required to support the country's economic through their ability to attract top technical and managerial and military needs. The challenges cited include a national talent to work on national security problems, which they do shortage in technologically prepared workers; the inherent under broad charters to their DOD sponsors. national security risks in the increasing number of foreign graduates with advanced technological degrees; the degree Universities or privately organized, not-for-profit of outsourcing to the defense industry; a reduction in corporations operate FFRDCs through long-term contracts partnerships between academia and the government's with the Federal government. DOD currently sponsors defense programs; declining resources; ill-advised personnel eleven FFRDCs managed by eight parent organizations. reductions and private industry's focus on immediate and Each falls under one of three categories: studies and analysis short range financial interests. The above-mentioned centers, systems engineering and integration centers, and concerns will require government, military and defense research and development laboratories. industry leaders to consider new approaches to secure and maintain the necessary talent in order to support the UARCs came into being when the DON entered into a technology required to ensure economic and national number of memoranda of understanding with certain security. universities to establish and host laboratories to support research in important areas. In the 1990s the DON Key words: science and engineering workforce, national reaffirmed its strategic relationship and commi~ent to four security, defense S&T university laboratories to serve as centers of excellence for critical DON and national defense science, technology, and INTRODUCTION engineering. These four are the Applied Physics Laboratory The defense technology base consists of three sectors: at Johns Hopkins University, the Applied Research academia and not-for-profits, industry, and in-house Laboratory at the Pennsylvania State University, the government laboratories and centers. As the defense Applied Physics Laboratory at the University of technology base developed, the DOD set up agreements Washington, and the Applied Research Laboratories at the with several University Affiliated Research Centers University ofTexas,Austin. (UARC)s and established several Federally-Funded / Research and Development Centers (FFRDCs). FFRDCs The other crucial partners in the defense technology base are had expertise in such emerging areas as radar, space, companies from both the defense and commercial industrial satellites, and operations research, and were often operated sectors. DOD's in-house laboratories and centers are highly by major universities, since faculty played a major role in mission-oriented and generally concerned with the entire Page 1406 life cycle of weapons or warfare systems, but only industry with the Naval Air Systems Command (NA VAIR), NSWC manufactures, on a large-scale basis, the products that are anc;l NUWC with NA VSEA, and the SSCs with SP AW AR. the ultimate objective of the development and acquisition The NRL reports through the Chief of Naval Research process. And while intellectual value is available from a (CNR) to the Office of the Secretary of the Navy wide range of sources, industry is best equipped to field (SECNA V). Both the centers themselves and their missions hardware and support it long term. In the past, industry has are products of a long and complex evolution resulting from provided a number of comparative advantages to DOD. changes in the defense environment throughout and since Examples include: the end of the Cold War. • Integrated technology, systems engineering, and manufacturing expertise, leading to faster fielding of The SECNAV established a two-tiered group mechanism to improved capabilities oversee and coordinate this community, Figure 1. First, the • A wide range of technological, design, engineering, and Navy Laboratory/Center Coordinating Group (NLCCG) manufacturing skills ( developed for civilian as well as consisted of the military commanders and civilian directors military products), expanding the range of ideas and of the warfare/systems centers and the NRL. Second, options for solving military problems members of the Navy Laboratory/Center Oversight Council (NLCOC), chaired by the ASN (RDA), included the Vice • Non-governmental international connections, increasing Chief of Naval Operations, the Assistant Commandant of the availability of technologies and reducing the the Marine Corps, the commanders of the naval systems possibility of technological surprise commands, and other senior DON representatives. Its main • Flexible access to top talent job was to provide broad oversight of the RDT&E, in- • An ability to project needs. service engineering, and fleet support efforts of the NLCCG. In November 2002, the NLCCG membership was expanded The last key element of the defense technology base, but by to include the ASN (RDA) and the commanding general and no means the least, is the commun~---oL,,i~ouse TD of the Marine Corps W arfighting Laboratory which laboratories and centers operated by the ~tary S~es. reports to the Marine Corps Combat Development They have a rich history, the roots of some stretclfmg back Command (MCCDC). more than 150 years. Historically, the Navy early on understood the importance of S&E in the conduct of war. It was also among the first to recognize that "the nature of CHIEF OF NAVAL OPERATIONS scientists and 'big science requires institutional environments to foster creativity and support formulation of ideas and discovery." Accordingly, early on it began establishing a community of engineering centers, test stations, proving grounds, weapons laboratories, and similar facilities to cultivate these creative environments. -AIR ·sURPAJ.::E· UNDERSEA· SPACE&NAvAiWARFARE -RE:SEARc·H· WARFiGHT1N \V ARl•"ARE ·wARV ARE .WARF ARE. . .. SvS'.I'EMs' CENTERS. . . l,i\BORATOR LABo"RATbR DCIEVNl,8T:E19R! ~ ·C ENTER . CENTER '_SA('l[!IE_GO_,·C.H~Rf,!!S}'f~M · THE DON LABORATORY/CENTER COMMUNITY Today, a community of geographically dispersed warfare and systems centers, along with the NRL, provides most of the internal technical competence to support DON efforts to Figure 1: NLCCG Organizational Relationships develop, acquire, and support weapons and weapons systems for the Navy and Marine Corps. This community The DOD's S&T program consists of three Budget includes the Naval Surface Warfare Center (NSWC), Naval Activities: Basic Research (BA 1) , Applied Research (BA Undersea Warfare Center (NUWC), Naval Air Warfare 2), and Advanced Technology Development or ATD (BA Center (NAWC), and the Space and Naval Warfare System 3). Even though S&T funding is only about six percent of Command (SP AW AR) Systems Centers (SSCs) in San the centers' total business base, it still represented $843 Diego, California and Charleston, South Carolina. million in FY 2004 dollars. About a quarter of the centers' total business base comes from the defense RDT &E When they created this technical community, planners appropriation, Figure 2. envisioned each warfare/system center would embody within its respective area all the in-house capabilities Regardless of its size, the centers' S&T funding is crucial to necessary to support naval systems throughout their life their ability to meet their uniquely-assigned roles and cycle-from S&T all the way through to in-service missions. It provides the "seed corn" for both the manpower engineering of deployed systems. and ideas that lead to next-generation military capabilities. Put another way, S&T historically is where new Having a unique mission in a specific warfare or technologies and their potential applications are explored, programmatic area, it was decided to assign each center to developed, and transitioned. It is also vital in that it supplies the systems command with which its mission most closely much of the funding centers use to attract and retain top- aligned. The NA WC was therefore organizationally aligned quality S&Es, particularly those with Ph.D.s. Page 1407 20 10 Business Base -.._ +7"/o % 96 98 04 06 08 10 • 10 -20 -30 ·.. Personnel ··········,. * Civilian & Military -40 ............... :.:::''.'~~ ........... ::::::~~;;;:;::::::·::::::·t .............. l -50 Figure 2: FY 04 Center Business Base by Appropriation ($13,982 million) (Source: NLCCG data base) Figure 3: NLCCG Community Personnel and Workload Trends (Source: NLCCG data; OSD Comptroller Green In spite of their importance, the warfare/system centers have Book of April 2005) been buffeted by several rounds of consolidation, closure, realignment, and personnel downsizing, as many in DOD believe the private sector should do work once considered inherently governmental. While many of the personnel cuts following the end of the Cold War were inevitable, the way they were implemented was problematic. Most cuts followed the rules of the -20 DOD's industrial-era Civil Service System (CSS), making it all but impossible to target staff reductions and reshape center workforces strategically. Moreover, most of the -40 • • • • • • • • • • • • • • • • • • • • • • ••••• A. vcrage - 44 '½1 downsizing focused on efficiency-cutting costs. Little attention was paid to the impact of the cuts on -60 -58'% effectiveness-performing missions. Nor was there much concern over the impact of these reductions on the Figure 4: Personnel Reductions for Warfare/Systems remaining human capital in the centers. Figure 3 compares Centers and NRL (FY 1991 - FY 2009) changes in the NLCCG business base from FY 1991 FY 2004. After an initial decline, the funding has rebounded Between FY 1991 and FY 2004, the overall NLCCG vigorously along with the rest of the defense budget, so that civilian workforce was reduced by 43 percent. Over this by FY 2002, the community had a business base in same time, the S&E workforce was reduced 20 percent, as inflation-adjusted dollars that actually exceeded its FY 1991 shown in Figure 5. total. Over this same period, however, the workforce ( civilian plus military) followed a different path. Initially, 80000 its decline mirrored the decline in the center's business base ....n u. .................T otal Civilian Workforce u ..........u .......n ................. l 60000 as would be expected in an industrial fund setting. * _4301,, -44'% However, instead of tracking the tum-around in workload, 40000 -------..t. ........................... . workforce numbers continued to fall, reaching a reduction ................................................................ -20% 20000 of about 43 percent relative to the FY 1991 baseline. In part, Scientists And Engineers Only this disparity between business and workforce base trends 92 94 96 98 00 02 04 06 08 JO reflects the DOD's increased emphasis on outsourcing. It FY also reflects a common belief among many defense policy makers that the centers could sustain additional cuts without Non S&Es losing effectiveness. 46% Figure 4 breaks down the personnel reductions for each of the centers and for NRL over this same timeframe. The NA WC experienced the largest reduction (58 percent) in personnel followed by the NUWC (47 percent). These Figure 5: NLCCG Community Civilian Workforce Trends numbers largely reflect the declines in emphasis in air and (Source: NLCCG data base) submarine warfare relative to other warfare areas following the end of the Cold War. The&e reductions have affected The Internet bubble hiring boom in the private sector also support personnel more than the science and engineering hampered the NLCCG community's recruitment of high- (S&E) workforce. quality S&Es. It was especially difficult to hire at the Ph.D. level in many of the specialties of growing importance, such Page 1408 as nanoscience. In fact, some of the community's best and AYERAQ:EAQ:E brightest S&Es left during this period, enticed by higher II FY91 38,2 YRS 1111 FYOI 42.7 YRS wages, better benefits, and often by more exciting and The "Bow Wave" 10000 D FYOZ 42.4 YRS challenging work. For example, in a span of just 18 \ ISl FYOJ 42.2 YRS months, DOD lost a key part of its 24-year old ability to ~ 8000 0 FY04 42.4 YRS perform fiber optics research when industry hired away 26 -.~. T .;j 6000 of NRL's best researchers. At the time, NRL was the o,l Department's only laboratory with this world-class defense j 4000 capability. .=~ ~ "' 2000 As they have in the past, larger historical events are also 0 driving this trend. Figure 6 displays a number of events that <31 31-40 41-50 51 -60 >60 produced increased hiring at the centers or their predecessor Age (yrs) organizations. Although not shown in this figure, the SOURCE: DTJC/DMDC (DEFENSE CIVJLIAN PERSONNEL DATA SYSTEM, JAN 05) Soviet's launch of SPUTNIK in 1957 led to a jump in hiring as a result of widespread fear that the U.S. was falling Figure 7: NLCCG Community S&E Age Trend (Source: DTIC, DMDC, DCPDS data) behind in the space and missile race. Other hiring spurts occurred during the Vietnam War era and during the defense build-up led by President Reagan. The downsizing These sizeable multi-year cuts and the consequent aging of of the 1990s, on the other hand, was the result of the end of the S&E population have had serious consequences for the the Cold War and the search for a "peace dividend." defense S&T effort, and threaten more ominous Recently, President George W. Bush has overseen a major consequences in the long-term. For example, as many defense build-up spurred in large part by the events of analysts are discovering, downsizing alone often carries September 11, 2001. Since then, pressure from the growing with it a host of negative effects. These include, to name Federal budget deficit and GWOT costs are again but a few, adverse effects on employee loyalty, the loss of threatening hiring at the centers, as some of the systems invaluable corporate memory, organizational instability, and, paradoxically, high costs. commands turn once more to cost-cutting measures, including limited hiring freezes aimed at shedding personnel. SHRINKING S&E WORKFORCE The demographic trends in the warfare/systems centers are in fact indicative of a much wider problem. Comparable troubles are affecting all the Services, other Federal 1400 'GWOT' Reagan Build-up departments and agencies that operate laboratory systems t::: l ,., FY91 (such as DOE and NASA), and a growing number of = defense and aerospace companies in the private sector. lllJ FY04 f;o;l ,.i 800 :i ".Q 600 Sean O'Keefe, until recently the NASA Administrator, discussed these trends in his testimony before the House .~ 400 r,:, Science Committee in July 2002. Within NASA's S&E 200 workforce, the over-60 population outnumbered the under- 0 ,' 30 population by almost 3 to 1. The age contrast was even 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 more dramatic at some of NASA's field centers. For Age example, at the Marshall Space Flight Center only 62 Missing Generation 'Peace Dividend' engineers out of a 3,000-person workforce were younger than 30. Similar proportions prevailed at the Glenn and Figure 6: NLCCG Community S&E Demographic Profile Langley Research Centers, where the corresponding ratios and Trends (Source: Defense Technical Information Center were 5: 1 and 7: 1 respectively. 0 'Keefe noted that by (DTIC), Defense Manpower Data Center (DMDC) ) contrast, "in 1993 the under-30 S&E workforce was nearly double the number of over-60 workers. This is an alarming Figure 7 shows how the various BRACs and mandated trend that demands our immediate attention with decisive reductions have increased the average age of S&Es in the action if we are to preserve NASA's aeronautics and space NLCCG community, contributing to a "bow-wave" effect of capabilities." a generation of experienced technologists moving through the system, without adequate replacements behind the Figure 8, taken from O'Keefe's testimony, shows how the wavefront Perhaps one of the most important trends to note demographic profile for NASA S&Es has changed from is the steady decline in S&Es in the 30 to 40 age group. 1993 to 2002. These data clearly demonstrate that the space There were 6,920 S&Es in this age group in FY 1991, but agency has significantly fewer young S&Es than ten years by FY 2004 this number had dwindled to only 4,801. ago. Page 1409 -~ I the United States Aerospace Industry, issued in November 2002. Even more recently the AIA has proposed steps to 2500 address the difficulties, as have others. :i 2000 DECLINING S&T RESOURCES ~" Unlike the NLCCG community's civilian workforce, other 1500 .i,i, components of the DON enterprise have experienced a more 5 1000 positive reversal of fortune over the last few years. We have z= already noted that the overall business base of the NLCCG 500 declined from FY 1991 to FY 1996. Thereafter, it grew markedly, reflecting increases in the overall DON budget <20 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70+ measured in terms of TOA. Figure 9 illustrates that DON I~-•-<· DistnDuti.ml TOA also declined significantly from FY 1991 to FY 1997. 1993 Age Distnbufon ~2002 Age It then began to increase and by FY 2003 had returned to its Figure 8: NASA S&E Demographic Profile and Trends inflation-adjusted FY 1991 level. In fact, the latest budget (Source: Congressional testimony by Sean O 'Keefe) projections suggest TOA in FY 2010 will be about 2 percent greater than in FY 1991. Figure 9 also shows that while Demographic data gleaned from the DOE laboratory workforce levels in the defense industrial sector track these community tell a similar story, as that Department has budget changes, those in NRL and in the warfare/systems begun to experience hiring, recruitment, and retention centers do not. This is partly a result of factors already problems within its laboratory system. This community discussed, and partly a result of mandated workforce includes the so-called national laboratories, which have key reductions imposed on the centers. missions in basic science, national security, energy resources, and environmental quality. These laboratories have long been regarded as among the most eminent in the DOD Industry world, and have also been a critical factor in helping the 30 Workforce U.S. maintain its worldwide leadership in generating 20 FY - +24% 10 scientific knowledge and discovery. %0 Navy .J() TOA -4% Recently, however, the DOE laboratories, like those in NASA and DOD, have experienced critical challenges -30 Civilians regarding their S&E workforces: The Department -40 •••••.•• , .............................., _ NRL&Navy Centers established a task force to recommend actions for -50 -43% consideration by management, an effort involving almost all of the DOE laboratories. Though there are differences Figure 9: Civilian and Defense Industry Workforces and among individual and among groups of laboratories ( for DON Budget (Source: NLCCG data base; OSD Comptroller example national security versus science laboratories), the Green Book of April 2005) task force focused on the high degree of commonality across the laboratories on workforce issues. Table 1 shows how the DON Basic Research, Applied Research, and ATD dollars have changed from FY 1992 to The demographic trends that imperil DOD's laboratories FY 2004. Overall, S&T dollars increased, in significant and centers also threaten a growing number of private sector measure the result of additions by the Congress during its defense and aerospace companies, and this too has serious mark-up process. However, as a percentage of TOA, S&T implications for U.S. economic and national security. still remains well below the overall DOD goal-three Responding to this problem, the Air Force asked the percent of TOA. Most of the growth in S&T has occurred National Research Council (NRC) of the National in the ATD account, which grew by almost 260 percent over Academies to ''provide a report that addresses the effects of the period FY 1992 to FY 2004. U.S. defense industrial base shrinkage and the aerospace industry's ability to continue to attract and maintain Table 1: DON S&T Funding Trends in Millions of Constant requisite aerospace engineering talent ... to produce cutting- FY 2004 Dollars edge military products" the DOD needs. Fiscal Year 1992 2004 Basic Research The report emphasizes how current trends threaten the inter- 476 468 generational transfer of specialized, crucial technical Research knowledge and skills, a point that also directly applies to the Advanced Technology Development in-house laboratories and centers. Various other reports __ Science_and.,rechnology ____ ... have discussed these and similar problems in the aerospace Science and Technology Percent of DON 1.24 1.79 industry. One commentary is in the report of the TOA congressionally-established Commission on the Future of Page 1410 Another feature of the centers' S&T funding has to do work overall business base of the sites. An example is in Table 3, carried out in-house versus that contracted out to the private which shows the size of the IED program at NSWC's sector. Of the approximately $491 million in DON S&T Dahlgren Division for FY 1989 through the last year of the they received in FY 2004, the centers expended some 56 program. Note that most projects received about $100,000, percent on work done in-house and contracted out the other enough on average to support one scientist or engineer for a 44 percent. It should be noted that the percentages vary year. across the three S&T budget activities, as shown in Table 2. Table 3: Independent Exploratory Development Funding at Table 2: Who Performs the Centers' DON Science and NSWC's Dahl ren Division Technology Work? FY FY FY FY FY ($ millions of FY 2004 1989 1990 1991 1992 1993 Percent dollars) Funding Center Budget Performed Activity In- I Out-of- I (thousands 2600 2412 2880 1437 1219 Total In-House House House of dollars) Basic Research 20.3 4.3 24.6 83 Number of Projects 24 22 13 Applied 105.1 -- - --v .... CJ l u / .'+ ~ V -.-J Average Advanced per project 108 110 115 96 94 Technology 147.9 150.7 298.6 50 (thousands Development of dollars) Total S&T 273.3 217.3 490.6 56 In sum, despite the relatively modest sizes of both the ILIR Discretionary funds are allocations laboratory and center and IED programs, they have in the past served important directors use, with some constraints, as they see fit. These functions, including: funds give directors more flexibility in pursuing promising • Providing funding to the centers for basic and applied projects, and therefore more opportunities to attract high- research in areas important to their missions quality personnel. The steady decline in such funding over • Enabling innovation the last dozen years is further eroding capabilities to carry • Developing and maintaining a cadre of S&Es capable of out work that only defense laboratories and centers can do, tracking and evaluating the rapidly growing global data and which is critical to national security. base of research and new knowledge in order to apply it to problems of naval interest Despite the broad agreement on the importance of • Promoting the hiring and development of S&Es discretionary funding in general, and ILIR and IED funding in particular, both programs suffered erosion in their • Encouraging and supporting cooperation with universi- funding base beginning in the late 1960s. From FYs 1967 ties, industry, the NRL, and other DON and DOD labs. through 1980, ILIR funding at the Navy's RDT&E centers decreased by 59 percent, while IED funding decreased by Both programs also have proven track records of 74 percent (adjusted for inflation). Although the DOD productivity, measured in terms of output metrics such as budget guidance mentioned above specified that ILIR and technical papers published, patents applied for or received, IED should not constitute more than five percent of a and awards and honors. Metrics for the ILIR program are laboratory's funds, only in 1967 did the two programs even shown in Table 4. Even more important is the overall approach five percent. In fact, ILIR and IED expenditures, impact of these programs over the years in transitioning the as a percent of the total budgets of the Navy RDT &E results of new discoveries and inventions into weapons and centers, declined significantly after that-between 1967 and warfare systems. 1980, these programs dropped from 3.8 percent of total funds to just 1.5 percent. The impact of these reductions on the S&Es with advanced degrees is significant. From 1995 to 1999, the centers The cancellation of the IED program in 1993 had a experienced a 15 percent reduction in the number of S&Es particularly adverse impact on the centers' discretionary with advanced degrees (M.S. and Ph.D.). Figure 10 funds. In part, an overall reduction that year of the DON illustrates the decline in Ph.D.s as a percentage of new S&E S&T account caused the termination. However, it was also hires in both the warfare/centers and NRL. For example, the result of a historically demanding defense of the among the new hires in FY 1997, 45 percent at NRL were program to Congress. It was always difficult to explain to Ph.D.s while only 5.6 percent of those at the centers had congressional staff why the IED program involved only doctorates. For the class of FY 2004, these percentages had after-the-fact review and oversight. dropped to 39 percent and 3 percent respectively. While the NRL data show several ups and downs in Ph.D. hiring The IED program, like ILIR, was a relatively small account, patterns, the data for the warfare systems centers show a usually around $25 million a year for the DON. Moreover, slow but steady decline in the percentage of new S&E hires when this was divided among the various center sites, the with doctorates. In fact, from FY 1997-FY 2004 that individual allotments were quite modest in proportion to the percentage declined by about 46 percent. Page 1411 Table 4: ILIR Program Metrics Output Metric '93 '94 '95 '96 '97 '98 '99 '00 '01 '02 '03 No. Transitions 38 35 41 33 38 44 49 50 32 68 No. Projects 181 197 218 214 206 192 183 195 198 151 Published Papers 393 270 259 225 250 261 270 202 203 2 77 Submitted Papers 110 90 82 74 59 17 19 54 Books/Chapters 52 7 20 19 6 8 13 16 Patents/Patent Applications 79 67 69 72 93 98 99 105 94 9 38 Government Reports 76 62 68 56 38 27 20 8 19 0 8 Dissertations 37 3 3 2 2 Presentations 417 248 234 229 220 198 76 Aw ards/Honors 79 41 39 19 14 39 15 Funding (Millions of dollars) 15.4 13.7 13.1 14.2 14.4 15.6 14.0 the need for this internal competence is growing. As has 60% been seen, the centers already outsource a large percentage 45%, 50% / of their S&T effort to obtain support for the in-house 40% component. To assess that work, they must be able to PHDs/ Class 30% interface, peer-to-peer, with their private sector colleagues 20% conducting it. 5.{io/~ 10% =/ 0% =========::==:::;::====J'O-/o- -= Centers IN-HOUSE S&T CAPA BILITY 97 98 99 00 01 02 03 04 Although S&T resources, especially discretionary resources, Class going to the warfare/systems centers are declining, there are SOURCE: DT!C several reasons to believe the demand for center capability Figure 10: Ph.D. Hiring Trends at the Centers and NRL will grow in the future. (Source: NLCCG data base) One reason to believe this demand for S&T effort will In FY 2004, the NLCCG community's civilian workforce increase is that the continued growth in outsourcing will included 20,795 S&Es, but only 1,702 of them had Ph.D. eventually require a commensurate strengthening of the degrees- slightly more than 8 percent. Table 5 shows the centers' yardstick competence. The Federal Government percent change in the Ph.D. populations at the must have objective technical advice about the quality, warfare/system centers and at NRL from FY 1997 to FY military relevance, and overall worth of the contracted work. 2004. The community as a whole experienced almost a 15 This can be obtained only through sources insulated from percent decline. pressures to profit. Otherwise, it cannot be an intelligent consumer of private sector products. Indeed, the absence of Table 5: S&Es with Ph.D. Degrees at the Centers and NRL such advice could waste precious defense resources or, Percent Lab/Center FY 1997 FY 2004 worse yet, undermine national security. Chane NAWC -19.1 A second factor indicating a future increased demand for NSWC -12.2 center S&T capability is the growing reluctance of defense NUWC -12.6 companies to invest their own resources in long-term, high- SSC -19.4 risk research. This is part of a general trend that has Center Total -15.3 NRL -14.5 affected most commercial technology companies, and it NLCCG could mean the DOD will have to look elsewhere, including Community Total 2,001 1,702 -14.9 to its own Service laboratories and centers, for many of the innovations needed in the global war on terrorism and other The loss of staff with advanced degrees, left unchecked, will conflicts. A recent article in the press addressed this issue, also reduce the centers' ability to judge the products the noting, "It is not unusual to hear defense officials complain DON receives from the private sector. In other words, their that contractors are too focused on their financial bottom yardstick role in emerging areas of science, engineering, lines, rather than on the quality of their new products and and mathematics will become more difficult at the very time the needs of the customer. They also blame the industry's Page 1412 rapid consolidation into a handful of conglomerates for a Each of these factors is discussed in more detail in the perceived decline in technical innovation." following sections. Whether or to what extent any or all of them will have the impact suggested is yet to be determined. A third factor involves the remolding of the industrial base Nevertheless, they seem to increase the likelihood that the by the on-going process of defense transformation Secretary DON warfare/system centers will need more, not less, in- Rumsfeld has begun. The point here is that the effort could house S&T capability in the months and years ahead. result in less DOD investment in big-ticket weapon systems and platforms, a development that would jeopardize the INCREASED OUTSOURCING funding base of today's major defense contractors. This Over the last 50-plus years, there have been innumerable could, in turn, pressure these companies to further reduce all authoritative statements regarding the proper roles of investments, including those in R&D. Even more DOD's in-house laboratories and centers; these statements dramatically, it could force a number of them out of show a high level of consensus with respect to several of business. The implication in either case is that other sources those roles. Table 6 summarizes a few examples, but there may have to take up the slack, which could shift work back are many others, most containing variations of the same or to the laboratories and centers. similar themes. For example, almost all studies contend that the laboratories and centers exist to: A fourth factor that could interest defense policy makers in increased in-house performance of S&T is an inability, or in Enable the DOD to be a "smart buyer" in the systems some cases reluctance, in academia to pursue certain kinds acquisition process of defense research. In part, this is due to causes stemming Provide technological expertise in areas of limited from the events of September 11, 2001, such as increased interest to the private sector scrutiny of foreign students at both the graduate and Provide an immediate response in time of crisis undergraduate levels and reductions in student visas. (wartime, for example) A final factor that militates in favor of increased in-house performance of S&T is the globalization of the technology Maintain a corporate research and development memory base. Most likely this will intensify demands on the Maintain and provide specialized equipment and centers' capability to track, assess, and apply this rapidly facilities impractical for the private sector to provide for growing base of new research and knowledge. itself Table 6: Examples of Roles Performed by DOD Laboratories and Centers White House Report Director of Navy Labs Federal Advisory Commission White House Report (1994) (1979) Report (1980) (1991) • Yardstick or smart • Yardstick or smart • Yardstick or smart buyer • Lowest cost to the Sponsor Buyer buyer • Infuse "art of possible" into • Improve planning and avoid • Mission-oriented • Advanced capability in defense planning technological Surprise studies, tech areas of limited interest • Act as principal agent in • Rapid/quick Response analyses and to private sector maintaining tech base Capability evaluation • Rapid/quick response • Avoid technological surprise & • Flexibility and • Corporate memory capability ensure technological innovation Responsiveness • Independent test & • Provide large/unique • Support the acquisition process • Inherently governmental tasks evaluation facilities not commercially feasible • Provide large/unique R&D • Corporate memory • Rapid/quick facilities not commercially response capability • Infuse "art of the • Technology and systems feasible • Mandated in-house possible" into defense integration performance planning • Rapid/quick response • Reducing management capability responsibilities • Provide full-spectrum complexity capability • Be a constructive advisor for • Provide • Continuity of Personnel and DOD directions and programs large/unique R&D Facilities Across a System's based on technical expertise facilities not Lifecycle commercially • Support the user in the • Long-term/low pay-off feasible application of emerging and essential military R&D new technology • Translate user needs into technology Requirements for industry • Serve as S&T training ground for civilian and military acquisition personnel Page 1413 Jim Colvard, a prominent former Navy laboratory TD, In "The Case Against Privatizing National Security," Ann Deputy Chief of Naval Material, and Deputy Director of the Markusen, a university professor and member of the Office of Personnel Management during the Reagan Council on Foreign Relations, also discusses how and why administration, has written extensively about in-house many defense officials are beginning to reexamine their laboratories, often about their smart buyer role. He notes faith in outsourcing: that while many in the DOD today believe you can go directly to industry with a problem, it is not that simple-a [Privatizing] military research and development is fact attested to by the billions of dollars DOD has poured especially problematic. Traditionally, the United States into contractor claims and get-well programs over the years. has maintained strong in-house research and development laboratories to work on sensitive and Paradoxically, DOD's increased outsourcing of technical pressing technical issues. These laboratories have work makes it more difficult for the centers to assess contributed to the technological superiority of the technical competence, because to do so, they must be American military.... They have acted as reservoirs of knowledgeable performers of hands-on technical work expertise than can be used to oversee, evaluate, and themselves. The more work contracted out, the greater the compete with private-sector research and development importance of a basic level of in-house technical efforts, a "yardstick" function that economists and proficiency. In the increasingly complex world of S&T, this defense experts have always considered appropriate for means having S&Es who are themselves experts in fields government. Yet in 2000, the Defense Science Board relevant to the DOD's current and future needs. recommended that the services hire scientists and engineers 'from universities, industry, and nonprofits for The loss of this internal technical competence means loss of a majority of the professional staffs of the defense control over outsourced work, which can have catastrophic laboratories. ' This is considered dangerous by insider consequences for any business, public or private. Colvard critics, because it will degrade the ability of the defense cites several examples of what can happen when such laboratories as performers of research and as evaluators technical capability is lost or technical advice ignored. of for-profit research performance [leaving] the military dependent upon advice that is not insulated from • ValuJet lost technical control of its fleet and was commercial interests. grounded after one of its jets crashed in the Florida Everglades in 1996. The company had contracted out A final indication the privatization trend may be winding all maintenance and lost the ability to recognize its down is that the revivalist fever it engenders is sure to abate technical troubles. Further, there are reports that the as it always has in the past, every time the evangelists of government inspector who monitored ValuJet was not outsourcing manage to reap a new wave of temporary technically qualified. converts. This is especially the case once the shortcomings • NASA decided to go through with the doomed and excesses of the new movement become apparent. In Challenger launch in 1986, despite technical advice to fact, an examination of the historical record discloses that delay it because of cold weather's effects on the space today's faith in privatization is just another swing in a shuttle's 0-rings. The decision was managerial, not recurring historical cycle. As has been noted, the pendulum technical. It was reported that the contractor's regional may already be once again swinging back in favor of manager suggested to the engineer who provided the rebuilding DOD's capacity to do more in-house work. technical advice that the company not appear uncooperative, since the contract was coming up for DEFENSE COMPANIES AND LONG-TERM/HIGH- rebid. Barbara Romzek and Melvin Dubnick, authors of RISK RESEARCH American Public Administration: Politics and the A second major factor that argues in favor of increased in- Management of Expectations (MacMillan, 1991), say house performance of S&T in certain areas of defense is a "there has been a shift in NASA from a system of growing unwillingness in the private sector to engage in professional accountability, which emphasizes deference technical work that involves long-term and/or high-risk to expertise within the agency, to a management system investments of their own money. Commercial companies, incorporating bureaucratic accountability. " including many in the technology sector, are primarily • interested in a quick return on investment to boost profits The Navy lost its surface-launched missile engineering and please shareholders. This is equally true as regards the capability, at least for the short term, in a defense industry shakeout that followed the Cold War. General defense industry, where large companies are focusing their Dynamics Corp. operated the Navy Industrial Reserve dwindling in-house R&D efforts on things like risk reduction and cost containment, with little of their own Ordnance Plant in Pomona, Calif, for years. The organization ultimately moved to Tucson, Ariz., after money going toward developing innovative technologies. being shifted from General Dynamics to General Electric to Raytheon. Many people who had worked for A report by Booz Allen Hamilton discusses in some detail years building Navy missiles did not relocate. this trend of disinvestment in research by defense companies. It points out there are basically three sources of R&D funds for the defense industry: Page 1414 • The U.S. Government for funded development programs technologies designed to meet emerging security threats ( contract research and development) including countering bioterrorism, developing new non~ • Company-sponsored research and development lethal and kinetic energy weapons, and fostering joint service science and technology efforts." • Independent Research and Development (IR&D) paid for by the government, but spent at the discretion of the The potential impact of defense transformation is also the contractor subject of another recent article that examines how changing defense investments may fundamentally reshape the defense With respect to the third funding source-IR&D (also industrial base. One source quoted is Suzanne Patrick, abbreviated as IRAD)-the report points out a few Deputy Undersecretary of Defense for Industrial Policy, problems, including a growing national security risk. First, who believes "we'll have a completely different set of "discretionary IR&D funds are becoming less actors ... in terms of corporations that we will draw on.... Of discretionary; simply put, the 'I' in 'IR&D' is slipping the current companies that exist, there may be a modest away." Second, IR&D is increasingly "aligned toward near-term programs or used to warrant the development of subset of_the primes that still will be recognizable." Perhaps more ommously, she also predicts that two or three of these a specific deliverable rather than long-term independent companies "will go belly up, " while three to five "may research and development. While the near-term risks to the change quite dramatically, getting into other activities and contractor haven't increased, the long-term risks to the U.S. tasks" that suit the soldiers' needs. and its citizens have increased even more." In 1996 for example, 75 percent of the IR&D investments by space It remains to be seen whether the small number of major companies fell in the discretionary category, a figure that defense and aerospace companies we have today will declined to just 23 percent by 2000. Instead, more IR&D weather the change promised both by budget cuts and was directed toward near-term programs-from 20 percent budget restructuring in response to defense transformation. in FY 1996 to 45 percent in 2000-and toward developing a If, however, they falter, where will the DOD look for the specific deliverable-from just 5 percent in FY 1996 to 32 technology products it relied on them to produce? Again, percent in FY 2000. Long-term independent R&D one source may well be its own in-house laboratories and decreased proportionately. centers. Regardless of the cause, the defense industry is investing ACADEMIA AND DEFENSE SCIENCE AND less of its own money in new, innovative technologies. TECHNOLOGY Unless the trend is reversed, defense companies will be less As discussed early in this chapter, historically the DOD has and less able to provide solutions the DOD requires, with relied on academia to perform much of its basic and applied the result that the Department's in-house laboratories and research. In fact, academia performs the largest share of the centers may become an increasingly attractive alternative. Department's overall defense basic research program. According to National Science Foundation (NSF) data, U.S. TRANSFORMATION AND DEFENSE INDUSTRIAL universities and colleges performed 56 percent of all BASE federally funded basic research in 2002. A third factor that may well impact in-house versus out-of- house performance of defense basic and applied research is There are, however, reasons to believe it may become more DOD's on-going defense transformation effort. At issue is difficult to get universities to undertake defense work at the following question: how will transformation affect the least in certain areas. If so, alternative sources will' be ability of the major defense companies to provide new required, and these could include DOD's in-house technologies? laboratories and centers. There are several reasons for this postul_ated chan~e, but most can be attributed to the security- Some observers are beginning to suggest the shift away consc10us environment growing out of the events of from the acquiring major weapon systems and toward September 11, 2001. developing new technologies that address terrorist threats may imperil these companies' long-term survival. For Even ~efore "9/11," there were several long-standing example, some defense officials and analysts believe that constrai~ts to unfettered performance of defense S&T by proposed funding cuts in such major programs as Lockheed acaderma. Many of these were, and remain, self-imposed. Martin's F/A-22 stealth fighter and Northrup Grumman's For one, most colleges and universities prefer to focus on shipbuilding and repair programs may foreshadow other fundamental (basic and applied) research, the results of cuts to big-ticket programs. which can be published without restriction. For another academia prefers to eschew classified work, which whe~ One defense industry source quoted in a recent story on this subject said such changes "raise the question of how large done is often confined to off-campus facilities. The MITRE Corporation is an example of an off-site organization set up defense contractors will stay in the game as the Pentagon to do classified work related to defense research performed puts _less emphasis on buying big platforms such as aircraft by the Massachusetts Institute of Technology (MIT) on earners and stealth fighters in quantity and more on behalf of the Air Force. Another historical constraint Page 1415 involves the cost of facilities and/ or equipment which are, in GLOBALIZATION many cases, so large as to prohibit private ownership. Globalization is a much talked about subject, especially its impact on the ability of the U.S. to remain a world leader in After 9/11 the constraints on academic performance of innovation. Discussions of globalization and technological research became even more restrictive, and significantly so. innovation often include three aspects: technological These new circumstances promise to curb the growth of generation, technological exploitation, and technological academic performance of defense S&T in some areas by collaboration. All of these are important in the context of threatening the four principal values under which most this book, because globalization of sources of new research universities operate. According to Eugene Skolnikoff, and knowledge will place new demands on the S&Es in the emeritus professor of political science at MIT, these values DON warfare/systems centers concerning their ability to are "commitment to openness, resistance to classified track, assess, and, when appropriate, apply this rapidly research, maintaining open relationships between growing knowledge to military problems. The challenge of universities and industry (including foreign industry) and, globalization to American technical leadership is of growing ofc ourse, relations with foreign students." concern to U.S. policy makers, especially its economic and national security implications. The issue of foreign graduate students and national security is another factor affecting academia's ability to do defense- An important point to note regarding collaboration is that related research. This is all the more true because, while today, only a handful of firms and other organizations can American students are rejecting graduate study in innovate alone. More and more frequently, innovation mathematics, engineering, and the physical sciences, the requires a network of organizations working together. This numbers of international graduate students in these areas is especially true in the case of the most valuable, has increased. Today, for example, in the U.S. more knowledge-intensive, and complex technologies, such as engineering doctorates are awarded to international than computers, semiconductors, telecommunications equipment, domestic students. According to NSF data, the number of aircraft, and biotechnology. Moreover, the ever more rapid new U.S. doctorates earned by students on temporary visas dispersion of scientific knowledge around the world means rose from about 4,300 in 1986 to about 8,000 in 1991, a an increasing percentage of what many refer to as figure around which it has fluctuated for a decade. innovation networks involves a mix of global partners. Significantly, foreign students, both temporary and permanent visa holders, earn a larger proportion of Already, these trends are affecting U.S. research outputs doctorates than at any other degree level. relative to the rest of the world. The "Task Force on the Future of American Innovation," which examined this issue Aside from the question of whether foreign students remain in detail, points out that the U.S. share of S&E papers in the U.S. and contribute to our S&T resources, there are published worldwide declined from 38 percent in 1988 to 31 concerns about admitting large numbers of them to percent in 2001, with Europe and Asia being responsible for American universities and allowing many of them to stay the bulk of recent growth in scientific papers. In fact, the after graduation. Issues surrounding this controversy burst Task Force notes that Western Europe's output passed the into the open in the spring of 2002, when DOD proposed a U.S. in the mid-nineties, and Asia's share is rapidly new policy aimed at the handling of unclassified research in growing. Moreover, from 1988 to 2001, "the U.S. increased both DOD and private-sector laboratories. According to its number ofp ublished S&E articles by only 13 percent. In Science, the proposed policy "would have Pentagon contrast, Western Europe increased its S&E article output program managers decide if DOD-funded studies at by 59 percent, Japan increased by 67 percent and countries universities, companies, or military laboratories involve of East Asia, including China, Singapore, Taiwan, and critical research technologies, or critical program South Korea, increased by 492 percent." information. If so, the institutions and researchers conducting the work would have to prepare detailed The downward trend in U.S.-authored scientific and security plans, label documents as protected, obtain prior technical articles is evident in most fields, with the greatest review of publication and travel plans, and decide whether decrease occurring in engineering and technology articles to place restrictions on any foreign scientists involved in the (down 26 percent between 1992 and 1999). Other declines project." Many of the areas that such a policy would affect over this period included articles in mathematics, physics, are precisely those in which additional talent is needed. chemistry, and oceanography, all of which are important to the DOD. Figure 11, which is taken from a slide in an April As with the effects of defense transformation on major 2005 briefing by the DDR&E illustrates a striking example defense companies, the effects of these changes remain to of the increase in publications in physics from countries be seen. They are, however, further reasons the DOD other than the U.S, a field of critical import to the DOD. should retain a highly trained S&T workforce capable of performing work in areas academic researchers no longer Consider just one example-technological globalization's pursue. threat to the electronics sector. According to an unpublished report by the distinguished Pentagon Advisory Group on Electron Devices (AGED), the "Department of Defense Page 1416 faces shrinking advantages across all technology areas due currently stable situation may well be heading into one of to the rapid decline of the U.S. electronics sector.... off- instability. shore movement of intellectual capital and industrial capability, particularly in microelectronics, has impacted CONCLUSION the ability of the U.S. to research and produce the best Changes in the environment in which its laboratories and technologies and products for the nation and the centers will be operating in the 21 st century have begun to warfighter.... DOD is forced to rely on perceived system undermine the approaches the DOD previously used to integration advantages to maintain superiority." The group maintain technological superiority over our adversaries. argues this could force the DOD to obtain the most The rapid spread of capabilities derived from new advanced technologies from overseas, a situation that could technologies, now widely available on a global basis, raises assign those nations both political and military leverage. important new questions. For one, how can the DOD mine According to the AGED, "In the area of battlefield and employ these technologies to maintain its technological communications and data networks, the global availability dominance? For another, will the DOD's current of wireless communications and high data rate fiber optical approaches to the process of technological innovation, landlines has greatly reduced this advantage even against especially those that appertain to the D&I phases, sustain us the less sophisticated terrorist threat. Use of best in the 21st century? commercial chips and processors levels the playing field for allies and adversaries. " Clearly, more in-house S&T capability than we have today will be needed. In fact, it will have to be increasingly s::JURCE: MIERICAN PHY~CAL :£JCJETY sophisticated for the DOD to remain a peer-player on the global technology scene. Regrettably, however, just as these demands are growing, the very S&T workforce the 20 +----------------r.---1 Physical DOD needs is dwindling and in urgent need of renewal, Review especially in light of its recent deterioration. Indeed, some & 15+---- Physical policy-makers have recognized this need, and proposed new Review initiatives aimed at bolstering the S&T workforces in the in- house laboratories and centers, but these are far from Total Submissions 5 sufficient. It is nearly axiomatic that an organization remains "world- 1983 1985 1987 1989 1991 1993 1995 1997 1999 class" by hiring and retaining productive, high-quality I• United States Iii Western Europe D Rest ofWorldj people, including a few-the top IO-percent-who have Figure 11: Trends in the Publications of U.S. Physics exceptional talent. This is especially true of cutting-edge Papers (Source: April 2005 briefing by DDR&E base on S&T organizations. Thus, if the DOD S&T enterprise is to American Institute of Physics data) remain world-class, it needs the flexibility to do whatever is necessary to hire, train, and retain a cadre of the best and A related consequence is that while many U.S. companies brightest scientific and engineering talent available-world- are downsizing at home, they are boosting hiring at their class talent. laboratories in India, China, and even Eastern Europe. This drains high-tech investment capital away from the U.S. and What is needed is a fresh look at the entire innovation into these countries, a point Battelle makes in its most process, and in particular, the role of the DOD's in-house recent R&D funding forecast: "the U.S. industrial laboratories and centers and their workforces. community will be strained to invest in U.S. R&D as China, India, and other Asian economies develop their own REFERENCES technological capabilities and draw off investments to This paper has used material available in Chapter two of support their own burgeoning markets that might normally From Science to Seapower, pp. 7-52. See Kavetsky, R., go to U.S. facilities." Marshal, M., and D.K. Anand, From Science to Seapower: A Roadmap for S&T Revitalization, CALCE EPSC Press, As a result, there is a growing consensus among U.S. University of Maryland, College Park, MD, 2006. government and many business leaders that off-shoring Footnotes and quotations can be found there. threatens economic and national security. A recent report by the PCAST voiced concerns that "while not in imminent jeopardy, a continuation of current trends could result in a breakdown in the web of innovation ecosystems that drive the successful U.S. innovation system." That is to say, while a snapshot might suggest all is well, the trends tell a different story-there is no room for complacency. The story told by the "slope" of the trend lines suggests a Page 1417