ABSTRACT
Title of Dissertation: AEROMECHANICS OF A DOUBLE
ANHEDRAL TIP COMPOSITE ROTOR:
EXPERIMENT AND MODELING
Cheng Chi
Doctor of Philosophy, 2022
Dissertation Directed by: Professor Anubhav Datta
Department of Aerospace Engineering
This thesis investigates the performance and loads on a double-anhedral tip
modern composite rotor. Double anhedral tips are a recent introduction in ro-
tors with no research data available for understanding their behavior or modeling
them adequately. The objectives were to bridge these gaps. Both experimental and
analytical methods were employed to fulfill the objectives systematically. Double
anhedral blades of 5.6-ft diameter were designed and fabricated. The blades had
a uniform VR-7 airfoil profile, a D-spar, ?16? twist, a 5? dihedral from 80%R to
95%R and a 15? anhedral from 95%R to the tip. The blades were built in-house
using IM7/8552 graphite/epoxy prepreg weave. They were instrumented for strains
and structural loads measurement. A two-bladed hingeless hub was designed and
fabricated for the vacuum chamber to measure rotating frequencies (fan plot). The
hover tests were performed on the Alfred Gessow Rotorcraft Center Mach-scaled
four-bladed hingeless rig. Tests were carried out up to tip Mach number of 0.6
over a collective range of 0? to 10?. The rotor performance, blade structural loads,
pitch link loads, and surface strains were measured. A double anhedral tip is a
3-D structure. Accordingly, a 3-D model was developed with CATIA (CAD), Cubit
(hexahedral meshing), and X3D (aeromechanics). The 3-D CAD was constructed
with guidance from Boeing to ensure the geometry was representative of a modern
rotor yet generic enough to be open source for U.S. Gov-industry-academia joint
study. The meshing used 27-node solid hexahedral elements, as needed by X3D.
The pitch bearing was modeled with a joint commanded by control input. In total
there were 3427 elements and approximately 100,000 degrees of freedom. Properties
of the composite plies were acquired through in-house four-point bending coupon
tests. The aerodynamic model used in-house CFD extracted C-81 decks and a lifting
line with a refined free wake. The data acquired from tests were used to validate
the model. A 3-D model of a straight blade was also developed as a baseline for
comparison. These models have the same external and internal structure except for
the tip. By comparing the behavior of the analytical models, insights were gained
on the impacts of a double anhedral tip on the structural dynamics and aerome-
chanics in hover and forward flight. The local center of gravity offset at the tip
appeared to make the blade softer. No performance gain was predicted in hover,
however, the static flap, lag, and torsion moments at the root all decreased due to
the vertical center of gravity offset in the tip portion. Strong 3-D strain patterns and
multiple strain concentrations at the tip were predicted. In forward flight, the 4/rev
vibratory vertical hub load and hub moments were predicted to increase by 15%
and 100% respectively at tip speed ratio 0.1. Higher 1/rev oscillatory flap bending
moment and 2/rev oscillatory lag bending moments were also predicted. The key
conclusion is that the vertical center of gravity of the double anhedral tip can have
significant ramifications on blade loads - reducing the static loads while increasing
oscillatory harmonics particularly vibratory harmonics in forward flight. Systematic
wind-tunnel tests are needed in future to dissect these effects. This thesis laid the
foundations of that future through blade fabrication, vacuum and hover testing.
AEROMECHANICS OF A DOUBLE ANHEDRAL TIP
COMPOSITE ROTOR: EXPERIMENT AND MODELING
by
Cheng Chi
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2022
Advisory Committee:
Dr. Anubhav Datta, Chair/Advisor
Dr. Inderjit Chopra, Co-Advisor
Dr. James Baeder
Dr. Alison B. Flatau
Dr. Amr M. Baz
? Copyright by
Cheng Chi
2022
Acknowledgments
The graduate school experience at UMD has been the one that I will cher-
ish forever. But the journey to complete this thesis would not be as pleasant and
beneficial without the help and support of many people. First of all, I would like
to express my sincere appreciation to my advisor, Anubhav Datta. Dr. Datta has
expanded my knowledge in the field of rotorcraft research and has given me the
opportunities to engage in meaningful research projects like the Mars Helicopter.
Working with Dr. Datta, I am always motivated by his trust and expectation. And
it?s his guidance and encouragement that supported me to finish this thesis and
pursue my helicopter pilot license. I would also like to thank Inderjit Chopra, who
gave me the opportunity to join the Alfred Gessow Rotorcraft Center in the first
place. Dr. Chopra also provided many opportunities for my research skills devel-
opment, allowing me to find my field of interest. Whenever I encounter difficulties,
Dr. Chopra always reminds me to trace my way back to an anchor point, which has
become a beneficial habit of mine.
I would also like to thank the other members of my committee, James Baeder,
Alison B. Flatau, and Amr M. Baz, for their expertise and guidance throughout my
time in Maryland. It is an honor to have you on the committee. This work has
been a collaborative effort of UMD and Boeing. Without the support from Boeing
ii
and the guidance of Brahmananda Panda, Boeing technical fellow, this endeavor
would not be possible. I owe many thanks to Vengalattore T. Nagaraj. Dr. VT is
so knowledgeable about the rotorcraft industry. Every time I encountered questions
in rotor design, he always pointed me in the right direction. And I could never
thank him enough for inviting me to join the Vertical Flight Society student design
competition team.
I learned from the senior students as much as I learned from the professors. I
am very thankful to Ananth Sridharan who pointed me into the path of 3-D mod-
eling, and Bharath Govindarajan and Vikram Hrishikeshavan who instilled me in
a strong work ethic. I would also like to thank Will Staruk, Daniel Escobar, Tyler
Sinotte, and Xing Wang for teaching me all of the necessary skills to tackle engi-
neering problems. I am very grateful to have the company of Elena Shrestha, Fred
Tsai, Brandyn Phillips, Vera Klimchenko, Seyhan Gul, Ravi Lumba, Mrinalgouda
Patil, Shashank Maurya, James Sutherland, Abhishek Shastry, Wanyi Ng, Emily
Fisler, Katie Krohmaly, Peter Ryseck, and Amy Morin.
Finally, I would like to thank my family. My parents, Jiangneng Chi and
Yanjuan Lu, always support and encourage me unconditionally. My grandfather,
Yongshen Chi, cared for me deeply and always had my best interests at heart. May
he rest in peace and forgive me for not being near him in his last days. Thanks to
my grandma, Qiuqun Liao, for her optimism and encouragement. Special thanks
are due to my wife, Wei Huang, for her support and understanding, which I could
not appreciate more. Thank you for supporting me in pursuing my dreams.
iii
Table of Contents
Acknowledgements ii
Table of Contents iv
List of Tables vii
List of Figures viii
List of Abbreviations xiv
Chapter 1: Introduction 1
1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 History of Anhedral Tip on Fixed-Wing . . . . . . . . . . . . 6
1.1.2 History of Anhedral Tip on a Rotor Blade . . . . . . . . . . . 7
1.1.3 Rotor Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.1.4 Rotor Comprehensive Analysis . . . . . . . . . . . . . . . . . . 14
1.2 Objectives of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.3 Organization of the Dissertation . . . . . . . . . . . . . . . . . . . . . 19
Chapter 2: Development of Double Anhedral Tip Composite Blade 21
2.1 Blade Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Blade Mold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3 Internal Components Fabrication . . . . . . . . . . . . . . . . . . . . 28
2.4 Spar and Skin Fabrication . . . . . . . . . . . . . . . . . . . . . . . . 34
2.5 Blade Curing and Finishing . . . . . . . . . . . . . . . . . . . . . . . 36
2.6 Blade Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.7 Material Elastic Property . . . . . . . . . . . . . . . . . . . . . . . . 48
2.8 Blade Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Chapter 3: Development of Test Rigs 55
3.1 Vacuum Chamber Rig . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.1.1 Vacuum Chamber . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.1.2 Design of a New Vacuum Chamber Hub . . . . . . . . . . . . 58
3.1.3 Vacuum Chamber Hub Fabrication . . . . . . . . . . . . . . . 62
3.1.4 Vacuum Chamber Hub Stiffness . . . . . . . . . . . . . . . . . 67
3.1.5 Vacuum Chamber Instrumentation and Data Acquisition . . . 71
iv
3.2 Hover Rig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.2.1 Hover Rig Components . . . . . . . . . . . . . . . . . . . . . . 72
3.2.2 Hover Rig Instruments . . . . . . . . . . . . . . . . . . . . . . 76
3.2.3 Hover Stand Data Acquisition . . . . . . . . . . . . . . . . . . 80
3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Chapter 4: Development of 3-D Blade Model 83
4.1 Blade Geometric Model . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.2 Blade Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.2.1 Clean-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.2.2 Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.2.3 Imprinting and Merging . . . . . . . . . . . . . . . . . . . . . 94
4.2.4 Meshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.2.5 Assignment of Blocks, Sidesets, and Nodesets . . . . . . . . . 99
4.3 Blade Aerodynamic Model . . . . . . . . . . . . . . . . . . . . . . . . 107
4.4 Blade Structural Load Calculation . . . . . . . . . . . . . . . . . . . . 110
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Chapter 5: Rotor Tests and Model Validation 124
5.1 Vacuum Chamber Test . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.1.1 Test Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.1.2 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.1.3 Data Analysis and Model Validation . . . . . . . . . . . . . . 129
5.2 Hover Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.2.1 Test Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.2.2 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.2.3 Data Correlation with Prediction . . . . . . . . . . . . . . . . 139
5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
Chapter 6: Comparison of Straight and Double Anhedral Blades 149
6.1 Blade Natural Frequencies and Mode Shapes . . . . . . . . . . . . . . 150
6.2 Strains in Vacuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6.3 Hover Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
6.3.1 Rotor Performance . . . . . . . . . . . . . . . . . . . . . . . . 161
6.3.2 Blade Structural Loads . . . . . . . . . . . . . . . . . . . . . . 163
6.3.3 Blade Strain/stress . . . . . . . . . . . . . . . . . . . . . . . . 171
6.4 Forward Flight Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 176
6.4.1 Rotor Performance . . . . . . . . . . . . . . . . . . . . . . . . 176
6.4.2 Hub Vibratory Loads . . . . . . . . . . . . . . . . . . . . . . . 180
6.4.3 Blade Structural Loads . . . . . . . . . . . . . . . . . . . . . . 185
6.4.4 Blade Strain/stress . . . . . . . . . . . . . . . . . . . . . . . . 195
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Chapter 7: Summary and Conclusions 209
7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
v
7.2 Key Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
7.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
7.4 Recommendations for Future Work . . . . . . . . . . . . . . . . . . . 215
Appendix A:Engineering Drawings 217
A.1 Vacuum Chamber Hub Central Block . . . . . . . . . . . . . . . . . . 218
A.2 Vacuum Chamber Hub End Block . . . . . . . . . . . . . . . . . . . . 219
A.3 Vacuum Chamber Hub Blade grip . . . . . . . . . . . . . . . . . . . . 220
A.4 Vacuum Chamber Hub Blade Adaptor . . . . . . . . . . . . . . . . . 221
A.5 Vacuum Chamber Hub Pitch Horn . . . . . . . . . . . . . . . . . . . 222
A.6 Vacuum Chamber Hub Pitch Link . . . . . . . . . . . . . . . . . . . . 223
A.7 Vacuum Chamber Hub Pitch arm . . . . . . . . . . . . . . . . . . . . 224
A.8 Vacuum Chamber Hub Shaker Housing . . . . . . . . . . . . . . . . . 225
Appendix B:Test Data 226
B.1 Vacuum Frequency Test Data . . . . . . . . . . . . . . . . . . . . . . 226
B.2 Hover Performance Test Data . . . . . . . . . . . . . . . . . . . . . . 227
Bibliography 229
vi
List of Tables
2.1 Blade parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2 Elastic properties of IM7/8552 graphite/epoxy prepreg weave. . . . . 51
2.3 Elastic properties of the isotropic materials. . . . . . . . . . . . . . . 51
2.4 Measured weight of each component in gram. . . . . . . . . . . . . . 52
2.5 Measured center of gravity location. . . . . . . . . . . . . . . . . . . . 52
2.6 Measured density of each components in kg/m3. . . . . . . . . . . . . 52
3.1 Aluminum beam frequencies in Hz. . . . . . . . . . . . . . . . . . . . 71
3.2 Rotor parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.1 Primary variables of the parametric geometry. . . . . . . . . . . . . . 85
4.2 Secondary variables of the parametric geometry. . . . . . . . . . . . . 85
4.3 Structural analysis representation. . . . . . . . . . . . . . . . . . . . . 89
4.4 Size of blade meshes. . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
B.1 Frequency test data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
B.2 Hover performance test data (Mtip = 0.4). . . . . . . . . . . . . . . . 227
B.3 Hover performance test data (Mtip = 0.5). . . . . . . . . . . . . . . . 228
B.4 Hover performance test data (Mtip = 0.6). . . . . . . . . . . . . . . . 228
vii
List of Figures
1.1 Rotorcraft with advance tip geometry. . . . . . . . . . . . . . . . . . 2
1.2 Blade tip elementary parameters. . . . . . . . . . . . . . . . . . . . . 4
1.3 Winglet designed by Richard Whitcomb [21]. . . . . . . . . . . . . . . 7
1.4 Double vortex sytem [32]. . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 Boeing Advanced Chinook Rotor Blades. . . . . . . . . . . . . . . . . 10
1.6 Rabbott?s wind tunnel rotor test in 1956 [50]. . . . . . . . . . . . . . 11
1.7 UH-60A wind tunnel test in 2010 [51]. . . . . . . . . . . . . . . . . . 11
1.8 Model rotor with anhedral tips in TDT wind tunnel [15]. . . . . . . . 12
1.9 PF1 tip tested at ONERA [34]. . . . . . . . . . . . . . . . . . . . . . 13
1.10 Double vortex system visualized by Muller [32]. . . . . . . . . . . . . 13
1.11 Aeroacoustic test of anhedral tip rotor at NUAA [46]. . . . . . . . . 14
1.12 Rigid anhedral tip blade tested by Uluocak [48]. . . . . . . . . . . . . 14
2.1 UMD Double Anhedral Tip Blade. . . . . . . . . . . . . . . . . . . . 21
2.2 Boeing Advanced Chinook Rotor Blade [88]. . . . . . . . . . . . . . . 22
2.3 The airfoil layout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4 Blade tip geometry and planform. . . . . . . . . . . . . . . . . . . . . 24
2.5 Types of blade spar. . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.6 Blade cross-section structure. . . . . . . . . . . . . . . . . . . . . . . 26
2.7 The layout of leading-edge weights. . . . . . . . . . . . . . . . . . . . 26
2.8 Root insert design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.9 CAD model of each blade component. . . . . . . . . . . . . . . . . . . 27
2.10 CAD model of the mold. . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.11 Double anhedral tip blade mold. . . . . . . . . . . . . . . . . . . . . . 28
2.12 Root inserts fabrication. . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.13 Foam sheet inside the mold. . . . . . . . . . . . . . . . . . . . . . . . 31
2.14 Machining of the foam core. . . . . . . . . . . . . . . . . . . . . . . . 32
2.15 Blade internal components. . . . . . . . . . . . . . . . . . . . . . . . . 33
2.16 Assembly of internal components. . . . . . . . . . . . . . . . . . . . . 33
2.17 The D-spar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.18 Blade core assembly. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.19 Release film and skin. . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.20 Uncured blade. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.21 Leading-edge of the blade in the mold. . . . . . . . . . . . . . . . . . 37
2.22 Double anhedral tip composite blades. . . . . . . . . . . . . . . . . . 38
viii
2.23 Methods of strain gauge installation. . . . . . . . . . . . . . . . . . . 39
2.24 Wires for instrumentation. . . . . . . . . . . . . . . . . . . . . . . . . 40
2.25 Structural load sensors. . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.26 Strain gauge configurations for structural load sensors. . . . . . . . . 41
2.27 Structural load sensors calibration. . . . . . . . . . . . . . . . . . . . 45
2.28 Strain measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.29 Strain rosette. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.30 Strain rosette on the blade. . . . . . . . . . . . . . . . . . . . . . . . 47
2.31 Four-point bending test. . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.32 Composite coupons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.33 Measurement of blade center of gravity. . . . . . . . . . . . . . . . . . 52
2.34 Final blades. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.1 Experimental tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2 Vacuum chamber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.3 Air Pump system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.4 Vacuum chamber systems. . . . . . . . . . . . . . . . . . . . . . . . . 58
3.5 Internal setup design of the chamber test. . . . . . . . . . . . . . . . 59
3.6 Hub central block on shaft. . . . . . . . . . . . . . . . . . . . . . . . . 60
3.7 Connection of hub central block and end block. . . . . . . . . . . . . 60
3.8 Connection of end block and blade grip. . . . . . . . . . . . . . . . . 61
3.9 Connection of blade grip and blade adaptor. . . . . . . . . . . . . . . 61
3.10 Connection of blade adaptor and blade. . . . . . . . . . . . . . . . . . 62
3.11 Connection of blade grip and pitch horn. . . . . . . . . . . . . . . . . 62
3.12 Pitch mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.13 Machining of blade adaptor. . . . . . . . . . . . . . . . . . . . . . . . 63
3.14 Machining of central block. . . . . . . . . . . . . . . . . . . . . . . . . 63
3.15 Machining of blade grip. . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.16 Tension-torsion strap. . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.17 Vacuum chamber hub components. . . . . . . . . . . . . . . . . . . . 65
3.18 Assemble of pitch bearings. . . . . . . . . . . . . . . . . . . . . . . . 65
3.19 Vacuum chamber hub assembly with shaker. . . . . . . . . . . . . . . 66
3.20 Vacuum chamber hub assembly with fixed pitch. . . . . . . . . . . . . 67
3.21 Vacuum chamber hub pitch stiffness test. . . . . . . . . . . . . . . . . 68
3.22 Vacuum chamber hub pitch moment versus pitch deformation. . . . . 68
3.23 Vacuum chamber hub flap and lag stiffness test. . . . . . . . . . . . . 69
3.24 3-D model of the aluminum beam. . . . . . . . . . . . . . . . . . . . . 69
3.25 Frequency spectrum of aluminum beam strain signal. . . . . . . . . . 70
3.26 Vacuum chamber hub instrumentation. . . . . . . . . . . . . . . . . . 72
3.27 Vacuum chamber test data acquisition system. . . . . . . . . . . . . . 72
3.28 Hover test stand. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.29 Hover test stand components. . . . . . . . . . . . . . . . . . . . . . . 74
3.30 Hingeless hub. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.31 Swashplate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.32 PCB on the hub cap. . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
ix
3.33 Hover stand slip ring. . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.34 Hub balance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.35 Torque sensor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.36 Pitch link load sensors. . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.37 Pitch Hall sensor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.38 Pitch Hall sensor calibration. . . . . . . . . . . . . . . . . . . . . . . . 78
3.39 Encoder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.40 Azimuth calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.41 Optic sensor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.42 Output of optic sensor and encoder. . . . . . . . . . . . . . . . . . . . 80
3.43 Hover test data acquisition system. . . . . . . . . . . . . . . . . . . . 81
3.44 LabVIEW program. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.1 Development of 3-D Blade Model. . . . . . . . . . . . . . . . . . . . . 83
4.2 Parameterization models. . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.3 Bodies in the geometric model. . . . . . . . . . . . . . . . . . . . . . 87
4.4 Leading edge weight body; the gaps are merged in geometry for
smooth meshing but defined by material properties. . . . . . . . . . . 87
4.5 Shared surfaces between bodies. . . . . . . . . . . . . . . . . . . . . . 88
4.6 Multi-section surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.7 Composite of sliver surfaces. . . . . . . . . . . . . . . . . . . . . . . . 91
4.8 Spanwise decomposition. . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.9 Sectional decomposition; each volume has a different ply angle. . . . . 93
4.10 Leading-edge weights decomposition. . . . . . . . . . . . . . . . . . . 94
4.11 Cross-section selected to mesh. . . . . . . . . . . . . . . . . . . . . . . 96
4.12 Cross-section mesh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.13 Radial curve mesh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.14 Root insert mesh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.15 Tip portion mesh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.16 Blade meshes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.17 Blade meshes scale Jacobian quality. . . . . . . . . . . . . . . . . . . 99
4.18 Blocks of isotropic material volumes. . . . . . . . . . . . . . . . . . . 100
4.19 Blocks of spar volumes. . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.20 Blocks of skin volumes. . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.21 Aerodynamic segment sidesets (top view). . . . . . . . . . . . . . . . 102
4.22 Root boundary and strain gauge nodeset. . . . . . . . . . . . . . . . . 103
4.23 Nodset for applying static loads. . . . . . . . . . . . . . . . . . . . . . 103
4.24 The 700 class nodesets . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.25 The 800 class nodesets. . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.26 The 900 class nodesets. . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.27 Hover free wake geometry. . . . . . . . . . . . . . . . . . . . . . . . . 108
4.28 Aerodynamic panels corresponding to aerodynamic sideset. . . . . . . 109
4.29 Aerodynamic node forces. . . . . . . . . . . . . . . . . . . . . . . . . 109
4.30 Mesh and 800 class nodesets of a twisted aluminum beam. . . . . . . 112
4.31 Axial strain on a twisted aluminum beam under tip loads. . . . . . . 113
x
4.32 In-plane shear strain on a twisted aluminum beam under tip loads. . 113
4.33 Structural loads of a twisted aluminum beam under tip loads. . . . . 114
4.34 Axial strain on a rotating twisted aluminum beam. . . . . . . . . . . 115
4.35 In-plane shear strain on a rotating twisted aluminum beam. . . . . . 115
4.36 Structural loads of a rotating twisted aluminum beam. . . . . . . . . 116
4.37 Mesh and 800 class nodesets of the straight twisted blade. . . . . . . 117
4.38 Axial strain on the straight blade under tip loads. . . . . . . . . . . . 119
4.39 In-plane shear strain on the straight blade under tip loads. . . . . . . 119
4.40 Structural loads of the straight blade under tip loads. . . . . . . . . . 120
4.41 Axial strain on the rotating straight blade. . . . . . . . . . . . . . . . 121
4.42 In-plane shear strain on the rotating straight blade. . . . . . . . . . . 121
4.43 Structural loads of the rotating straight blade. . . . . . . . . . . . . . 122
5.1 Final setup of the frequency test. . . . . . . . . . . . . . . . . . . . . 126
5.2 Frequency spectrum of strain signal at 200 RPM. . . . . . . . . . . . 128
5.3 Raw strain signals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.4 Strain rosette diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.5 Fan plot of the double anhedral blade: symbols are measurements;
solid lines are predictions. . . . . . . . . . . . . . . . . . . . . . . . . 130
5.6 Arms of the vacuum chamber hub. . . . . . . . . . . . . . . . . . . . 131
5.7 Rotating strains on the top surface at 30%R: symbols are measure-
ments; lines are predictions. . . . . . . . . . . . . . . . . . . . . . . . 132
5.8 Hover stand hub balancing. . . . . . . . . . . . . . . . . . . . . . . . 134
5.9 Reflective tapes for blade tracking. . . . . . . . . . . . . . . . . . . . 136
5.10 Blade tracking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
5.11 Final setup of the hover test. . . . . . . . . . . . . . . . . . . . . . . . 137
5.12 Fan plot of the hingeless rotor; the vertical lines are the RPM selected.137
5.13 Hover test envelope. . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.14 Blade loading vs. collective. . . . . . . . . . . . . . . . . . . . . . . . 140
5.15 Power coefficient vs. collective. . . . . . . . . . . . . . . . . . . . . . 140
5.16 Power vs. Thrust. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.17 Figure of Merit vs. blade loading. . . . . . . . . . . . . . . . . . . . . 142
5.18 Flap bending moment at 40%R (test vs. prediction). . . . . . . . . . 143
5.19 Lag bending moment at 40%R. . . . . . . . . . . . . . . . . . . . . . 143
5.20 Torsional moment at 40%R. . . . . . . . . . . . . . . . . . . . . . . . 145
5.21 Pitch link load vs. collective. . . . . . . . . . . . . . . . . . . . . . . . 145
5.22 Two version of 800 class nodesets. . . . . . . . . . . . . . . . . . . . . 146
5.23 Mean Strain on the top surface of 30%R. . . . . . . . . . . . . . . . . 147
5.24 Mean Strain on the bottom surface of 80%R. . . . . . . . . . . . . . . 147
6.1 Straight and double anhedral blades; same twist of ?16? . . . . . . . 149
6.2 Fan plot of straight blade (solid lines) compared to double anhedral
blade (dotted lines). Rigid root, ? ?75 = 0 . . . . . . . . . . . . . . . . . 151
6.3 Straight blade mode 1; first flap (1.32/rev). . . . . . . . . . . . . . . . 152
6.4 Double anhedral blade mode 1; first flap (1.29/rev). . . . . . . . . . . 152
xi
6.5 Straight blade mode 2; first lag (2.62/rev). . . . . . . . . . . . . . . . 153
6.6 Double anhedral blade mode 2; first lag (2.32/rev). . . . . . . . . . . 153
6.7 Straight blade mode 3; second flap (4.07/rev). . . . . . . . . . . . . . 154
6.8 Double anhedral blade mode 3; second flap (3.8/rev). . . . . . . . . . 154
6.9 Straight blade mode 4; third flap (8.9/rev). . . . . . . . . . . . . . . . 155
6.10 Double anhedral blade mode 4; third flap (8.12/rev). . . . . . . . . . 155
6.11 Straight blade mode 5; first torsion (11.07/rev). . . . . . . . . . . . . 156
6.12 Double anhedral blade mode 5; first torsion (10.64/rev). . . . . . . . 156
6.13 Predicted axial strain ?xx distribution in vacuum for straight blade
(1522 RPM). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.14 Predicted axial strain ?xx distribution in vacuum for double anhedral
blade (1522 RPM). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.15 Predicted in-plane shear strain ?xy distribution in vacuum for straight
blade (1522 RPM). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
6.16 Predicted in-plane shear strain ?xy distribution in vacuum for double
anhedral blade (1522 RPM). . . . . . . . . . . . . . . . . . . . . . . . 160
6.17 Predicted out-of-plane strain ?zz distribution in vacuum (1522 RPM;
left: straight blade; right: double anhedral blade). . . . . . . . . . . . 161
6.18 Power versus blade loading. Mtip = 0.4. . . . . . . . . . . . . . . . . . 162
6.19 Figure of Merit versus blade loading. Mtip = 0.4. . . . . . . . . . . . . 162
6.20 Comparison of axial force.Mtip = 0.4. . . . . . . . . . . . . . . . . . . 163
6.21 Flap bending moment in hover. Straight blade versus double anhedral
blade. Mtip = 0.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
6.22 Diagram of flap bending moment on the double anhedral blade. . . . 165
6.23 Lag bending moment in hover: Straight blade versus double anhedral
blade. Mtip = 0.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
6.24 Diagrams of lag bending moment on the double anhedral blade. . . . 167
6.25 Torsion moment in hover. Straight blade versus double anhedral
blade. Mtip = 0.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
6.26 Diagrams of torsion moment on the double anhedral blade. . . . . . . 169
6.27 Pitch link load in hover. Straight blade versus double anhedral blade.
Mtip = 0.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
6.28 Propeller moment direction of the straight and double anhedral blades.170
6.29 Axial strain ?xx distribution of straight blade. CT/? = 0.117, Mtip =
0.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
6.30 Axial strain ?xx distribution of double anhedral blade. CT/? = 0.117,
Mtip = 0.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
6.31 Internal axial stress ?xx distribution. CT/? = 0.117, Mtip = 0.4. . . . 173
6.32 In-plane shear strain ?xy distribution of straight blade. CT/? = 0.117,
Mtip = 0.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
6.33 In-plane shear strain ?xy distribution of double anhedral blade. CT/? =
0.117, Mtip = 0.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
6.34 Internal in-plane shear stress ?xy distribution. CT/? = 0.117, Mtip =
0.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
xii
6.35 Out-of-plane strain ?zz distribution of straight blade and double an-
hedral blade. CT/? = 0.117, Mtip = 0.4. . . . . . . . . . . . . . . . . 175
6.36 Out-of-plane stress ?zz distribution of straight blade and double an-
hedral blade. CT/? = 0.117, Mtip = 0.4. . . . . . . . . . . . . . . . . 176
6.37 Diagram of rotor in forward flight. . . . . . . . . . . . . . . . . . . . . 177
6.38 Rotor effective lift-to-drag ratio (M ?tip = 0.4, ?s = 4 , CT/? = 0.1). . . 178
6.39 Rotor propulsive force coefficient (M = 0.4, ? = 4?tip s , CT/? = 0.1). . 178
6.40 Rotor torque coefficient (Mtip = 0.4, ? = 4
?
s , CT/? = 0.1). . . . . . . 179
6.41 Trimmed forward flight control (M ?tip = 0.4, ?s = 4 , CT/? = 0.1). . . 179
6.42 Hub 4/rev and 8/rev vibratory loads (M = 0.4, ? = 4?tip s , CT/? = 0.1).183
6.43 Non-dimensional hub 4/rev and 8/rev vibratory loads (Mtip = 0.4,
?s = 4
?, CT/? = 0.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
6.44 Flap bending moment versus azimuth (M = 0.4, ? = 4?tip s , CT/? =
0.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
6.45 Oscillatory flap bending moment versus tip speed ratio (Mtip = 0.4,
?s = 4
?, CT/? = 0.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
6.46 Lag bending moment versus azimuth (Mtip = 0.4, ?s = 4
?, CT/? = 0.1).189
6.47 Oscillatory lag bending moment versus tip speed ratio (Mtip = 0.4,
? = 4?s , CT/? = 0.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
6.48 Torsion moment versus azimuth (Mtip = 0.4, ?s = 4
?, CT/? = 0.1). . 192
6.49 Oscillatory torsion moment versus tip speed ratio (Mtip = 0.4, ?s =
4?, CT/? = 0.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
6.50 Pitch link load versus azimuth (Mtip = 0.4, ?s = 4
?, CT/? = 0.1). . . 194
6.51 Oscillatory pitch link load versus tip speed ratio (Mtip = 0.4, ?s = 4
?,
CT/? = 0.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
6.52 Axial strain ?xx distribution of straight blade (Mtip = 0.4, ?s = 4
?,
CT/? = 0.1, ? = 0.3). . . . . . . . . . . . . . . . . . . . . . . . . . . 198
6.53 Axial strain ?xx distribution of double anhedral blade (Mtip = 0.4,
?s = 4
?, CT/? = 0.1, ? = 0.3). . . . . . . . . . . . . . . . . . . . . . 200
6.54 In-plane shear strain ?xy distribution of straight blade (Mtip = 0.4,
? ?s = 4 , CT/? = 0.1, ? = 0.3). . . . . . . . . . . . . . . . . . . . . . 202
6.55 In-plane shear strain ?xy distribution of double anhedral blade (Mtip =
0.4, ? = 4?s , CT/? = 0.1, ? = 0.3). . . . . . . . . . . . . . . . . . . . 204
6.56 Out-of-plane strain ?zz distribution comparison (M
?
tip = 0.4, ?s = 4 ,
CT/? = 0.1, ? = 0.3). . . . . . . . . . . . . . . . . . . . . . . . . . . 206
xiii
List of Abbreviations
ACRB Advanced Chinook Rotor Blade
AGRC Alfred Gessow Rotorcraft Center
BVI Blade Vortex Interaction
CAD Computer Aided Design
CFD Computational Fluid Dynamics
CNC Computer Numerical Control
CSD Computational Structural Dynamics
EMI Electro Magnetic Interference
FEM Finite Element Method
FFT Fast Fourier Transform
FM Figure of Merit
GF Gauge Factor
IGES International Graphics Exchange Specification
NASA National Aeronautics and Space Administration
NUAA Nanjing University of Aeronautics and Astronautics
PCB Printed Circuit Board
PIV Particle Image Velocimetry
RCAS Rotorcraft Comprehensive Analysis System
RPM Revolutions Per Minute
SAM Structural Analysis Model
SAR Structural Analysis Representation
STEP Standard for the Exchange of Product
STL Stereolithography
xiv
TDT Transonic Dynamics Tunnel
UMARC University of Maryland Advanced Rotorcraft Code
UMD University of Maryland
VABS Variational Asymptotical Beam Sectional Analysis
3?D three dimensional
c blade chord
C.G. center of gravity
Cd0 drag coefficient at zero angle of attack
CM hub moment coefficient
CP power coefficient
CQ torque coefficient
CT thrust coefficient
CX propulsive force coefficient
E Young?s modulus
G shear modulus
L/De rotor effective lift-to-drag ratio
K? pitch stiffness
K? flap stiffness
K? lag stiffness
Mtip tip Mach number
r spanwise location
R blade radius
t ply thickness
?s shaft tilt angle
?xy in-plane shear engineering strain
?xx axial normal strain
?yy chordwise normal strain
?zz out-of-plane strain
?0 collective
?1S longitudinal cyclic
?1C lateral cyclic
?tw built-in twist
?A Anhedral angle
? tip speed ratio or Poisson ratio
? rotor solidity
?xx axial stress
xv
?xy in-plane shear stress
?zz out-of-plane stress
? azimuth angle
xvi
Chapter 1: Introduction
1.1 Background and Motivation
As a special air vehicle that has the ability to take-off and land vertically,
hover and fly slowly in any direction, rotorcraft has been an important part of the
aviation community since it was invented. Over the last century, higher cruise speed,
larger payload, and better handling qualities have been the primary pursuits of
rotorcraft designers. These design goals have been mutually exclusive to some extent
historically. Therefore, design compromises between high lift-to-drag ratio, high
Figure of Merit, and low vibration level have to be made. These design compromises
were eased as the rotor aeromechanic behavior was better understood, and new rotor
technologies were developed.
The main rotor, as the source of lift, propulsion, and control all combined,
naturally became the focus of research. Due to the slender and flexible nature
of the blade structure, the blade tip, that has the highest dynamic pressure and
complex flow also has the maximum deformation, and hence has the most powerful
impact on performance, noise, loads, and vibration. Meanwhile, due to the design
flexibility introduced by advanced composite materials and fabrication methods,
the design of blade tips became more and more innovative. The goal of these tip
1
designs is to alleviate the problems of loads, acoustics, and vibration while enhancing
performance. The objective of this thesis is to study one such special tip profile.
For decades, engineers and researchers tried various tip geometries to design
better rotor blades. Figure 1.1 shows examples of advanced tip geometries on rotor-
craft. It shows the swept tip on Sikorsky UH-60, the anhedral tip on Sikorsky S-92,
the double swept tip (Blue Edge tip) on Airbus H160, and the double anhedral tip
on Boeing CH-47, and the paddle tip (BERP tip) on AgustaWestland Merlin Mk3.
(a) UH-60 with swept tip (b) S92 with anhedral tip
(c) H160 with double swept tip (Blue Edge tip) (d) CH-47 with double anhedral tip
(e) Merlin Mk3 with paddle tip (BERP tip)
Figure 1.1: Rotorcraft with advance tip geometry.
2
All of these advanced tip geometries can be condensed into three canonical
parameters or a combination of them [1], which are planform-taper, sweep, and
anhedral (Figure 1.2). The tapered tip is the small outboard portion of the blade
that has a significant variation in chord length. According to the tests reported by
Stroub et al [2], McVeigh and McHugh [3], and Althoff and Noonan [4], a properly
designed tapered tip can improve the maximum rotor Figure of Merit in hover
and the rotor effective lift-to-drag ratio in forward flight. This effect is due to
the reduction in outboard profile drag [5, 6]. However, the tapered tip can also
be prone to premature stall and increase in vibration due to the low Reynolds
number on the retreating side as well as present difficulty in inserting tip weights
for autorotation [7].
A swept tip shifts (shears/or rotates) the blade cross-sections toward the trail-
ing edge. This type of tip geometry is driven by the pursuit of high forward flight
speed by delaying the drag divergence Mach numbers. The sweep back can delay
the onset of compressibility effects on the advancing side, which reduce drag and
unsteady pitching moments [8?12]. This can be explained by the reduction of Mach
number normal to the tip leading-edge, or equivalently by the rotated cross-sections
having a lower thickness-to-chord ratio which performs better at high Mach num-
bers. However, this advantage on the advancing side may be reduced by the early
flow separation on the retreating side. More importantly, the rearward shift of the
center of gravity and aerodynamic center on the swept tip introduces aerodynamic
and inertial couplings that have significant impacts on pitch links and blade struc-
tural loads. [13,14].
3
Anhedral tips rotate the cross-sections up or down away from the plane of
rotation. An important effect is the change in the position of the tip vortex and
hence the induced velocity field in the plane of rotation. An anhedral tip can show
improvement in hover performance, as reported by Weller [15] and Mueller [16]. The
change of tip vortex release location also changes Blade-Vortex Interaction (BVI)
which is a major source of vibration and noise [17].
Figure 1.2: Blade tip elementary parameters.
Among these three canonical geometries, the anhedral tip has seen less in-
depth investigations, and the few that were carried out all focused on aerodynamics
and noise. Recently, there have been attempts to improve hover performance by
using an anhedral tip on a production rotor. The inertial couplings may be lowered
by having both dihedral and anhedral in the tip region (called the double anhedral)
to bring the effective C.G. close to the rotating plane. Though it was reported that
this attempt has the potential of increasing the payload, excessive vibrations oc-
curred in forward flight. High vibrations shorten the fatigue life of key components,
4
degrade ride qualities, and are major detriments for a new design, particularly when
discovered late in the design cycle. This vibration problem shows that accompany-
ing performance and acoustic benefits are structural and aeromechanical behavior
that are not fully understood.
In order to understand the behavior of double anhedral tips, test data from
realistic rotor blades are vital. Good test data requires systematic step-by-step
investigation with clear documentation of not only data by also rotor properties.
The model rotor should be Mach-scaled and representative of real aircraft, so the
phenomena measured are relatable to the flight vehicles. Good research data should
be open-source, allow peer review, and open to assessment by other investigators.
None of the existing data sets satisfied these criteria. Most of the important tests
are either proprietary or documented with insufficient details to be admissible as a
benchmark for fundamental understanding or model validation.
Precise modeling is equally critical to capturing and understanding basic phe-
nomena. The aerodynamics of even a straight blade tip is complex as it is subjected
to rapidly varying conditions under unsteady 3-D transonic flow. An anhedral tip is
expected to add more complexity. The structural dynamics do not conform to the
basic assumptions of a 1-D beam near the tip. Therefore, structural models that
are not limited to beams are needed to investigate the impact of 3-D aerodynamics
on blade stresses.
In this work, Mach-scale double anhedral tip composite rotors were fabricated,
hover tested and modeled with 3-D structures to validate with test data. The
aerodynamic model was still lifting line with free wake. Once validated, the analysis
5
was extended to forward flight. Since the Glenn L. Martin wind tunnel remained
closed, the high-fidelity 3-D analysis took its place instead for the best assessment
of blade stress/strain. Ultimately the prediction will need to be validated with test
data, which remains a task for the future.
1.1.1 History of Anhedral Tip on Fixed-Wing
The concept of a non-planar endplate, or a winglet, on a lifting device to
improve aircraft performance can be traced to Frederick W. Lanchester?s patent in
1897. Later, Nagel (1924) [18], Hemke (1928) [19], and Mangler (1938) [20] carried
out theoretical investigations on lift and induced drag. One of the first applications
was carried out by Richard Whitcomb of NASA Langley Research Center [21, 22].
Whitcomb installed a fin extending both upwards and downward (Figure 1.3) of a
semi-span wing to reduce induced drag and increase the lift-to-drag ratio. This kind
of tip extension can be seen on many commercial jets today.
Theoretical analysis by Jones and Lasinski of NASA Ames Research Center [23]
confirmed that reduction of induced drag can be achieved by extending the tip
vertically. One of the more recent studies was that of Eppler, in 1997, who showed
that a dihedral angle is more beneficial than anhedral [24]. A similar conclusion
was drawn by Boeing and Aviation Partners Inc. since they developed what they
called a blended winglet [25]. A blended winglet is simply a continuous smooth
structure without a sharp edge. In 2000, Herrick designed what he called a raked
wingtip [28]. The increase in the effective span is the main target since it reduces
6
Figure 1.3: Winglet designed by Richard Whitcomb [21].
induced drag [29].
The induced power benefit of the winglets is derived from the reduction in
the strength of wingtip vortices. These are moved further away from the wing [30].
There is a secondary benefit. A component of the winglet aerodynamic force can be
pointed forward if suitably designed. This component is an additional counter to
the drag. Mary variants of winglets can be found today, including canted winglet,
vortex diffuser, blended split, sharklet, spiroid winglet, downward canted winglet,
active winglets, and tip sails [30, 31].
1.1.2 History of Anhedral Tip on a Rotor Blade
The success of winglets on fixed-wing aircraft cannot be simply carried over
to rotor blades. Rotor blades have g-loading of nearly 1000 at the tip, so structural
pieces cannot be installed without taking into consideration other effects. Moreover,
7
the induced power loss is not due to the vortex right at the tip but from the vortices
of all blades. The rapid variation of local flow, plunge, and pitch of the blade
section, and stronger tip vortex make blade tips on the rotor significantly different
from fixed-wings. The lessons learned from fixed-wing, while providing a basis, do
not transfer directly to rotors. Nevertheless, motivated by the potential benefit of
non-planar tips, researchers have conducted some investigations in the past.
The development of advanced blade tips was made possible by metal, and
then by the advent of composite materials. The discussion of advanced blade tips
on rotors can be found in an early work by Spivey in 1968 [8]. Thereafter, no tests
or studies were conducted on anhedral tips in the next ten years until Weller [15]
and Mantay and Yeager [11] considered it again in 1979 and 1983. Both studies
showed the hover performance could be improved by an anhedral tip.
At the time, the mechanism behind the performance improvement was not
clear. A study by Muller [16, 17] found there might be a double vortex system
formed by the anhedral tip (Figure 1.4), which reduces Blade Vortex Interaction
(BVI) by smoothing the vortex core and lowering the initial location of the tip
vortex [32]. More recently, anhedral tip aerodynamic studies were conducted by
Desopper et al [33, 34], Vuillet et al [35], and Tung et al [36] in the 90s. In 2001,
McAlister et al also considered the anhedral tip to reduce BVI [37]. The aeroelastic
impact of the anhedral tip on helicopter rotor blade and tilt-rotor blade was studied
by Kim and Chopra [13] and Srinivas, Chopra and Nixon [38], respectively. These
were all analyses with no data to verify or validate. Some of the analyses were too
approximate to even capture the expected 3-D effects near the tip.
8
Figure 1.4: Double vortex sytem [32].
The maturation of Computational Fluid Dynamics (CFD) for rotors in the
past 20 years [39, 40] has opened the avenue to a better understanding of anhedral
tip. Some sample optimization attempts can be found in Refs. 41?44. Interest
in anhedral tips has transitioned from performance to acoustics and flight dynam-
ics [45?48]. So far, there are far fewer variants of anhedral tips envisioned on ro-
tors due to the natural hesitation of introducing discontinuities at the tip. Boeing
adopted the double anhedral tips on Chinook CH-47 (Figure 1.5), and some analyses
were carried out jointly by Boeing and Army. However, there is limited to no data
available in public.
9
Figure 1.5: Boeing Advanced Chinook Rotor Blades.
1.1.3 Rotor Testing
There is a long and rich history of full-scale helicopter rotor tests in the US.
Bousman, in his Nikolsky Lecture [49], traced this history beginning with the pi-
oneering Langley 15.3-ft diameter teetering rotor wind tunnel tests in 1956 (Fig-
ure 1.6) [50] to the modern NASA Ames 26.8-ft diameter UH-60A Black Hawk
articulated rotor tests in 2010 (Figure 1.7) [51]. The Bousman review focused on
tests that measured airloads?the most difficult of all tests. However, there were no
anhedral tips in any of them.
There is also a vast literature on model-scale rotor tests and the story is
somewhat better there. A few cases had anhedral tips. These were: 1) the 2.743 m
radius four-bladed articulated rotor model tested by Weller at the Langley Transonic
Dynamics Tunnel (TDT) (Figure 1.8) measuring rotor performance and blade flap
and lag bending moments [15]; 2) the 0.857 m radius rotor model with PF1 tips
10
Figure 1.6: Rabbott?s wind tunnel rotor test in 1956 [50].
Figure 1.7: UH-60A wind tunnel test in 2010 [51].
(Figure 1.9) tested by Desopper at the ONERA S2 Chalais-Heudon wind tunnel
measuring rotor performance [34]; 3) the 0.5 m radius rotor model tested by Muller at
Associazione Industrie Aerospaziali wind tunnel [16] and FIBUS Research Institute
11
water tunnel [32] measuring the vortex system (Figure 1.10); 4) the 1 m radius
rotor model tested by Huang at Nanjing University of Aeronautics and Astronautics
(NUAA) acoustic chamber (Figure 1.11) measuring sound pressure level [46]; and
5) the 0.65 m radius five-bladed rigid rotor model tested by Uluocak at Middle
East Technical University (Figure 1.12) measuring flow field with Particle Image
Velocimetry (PIV) technique [48]. None of these measured blade dynamics or loads
? the fundamental barrier of anhedral blades. None of these were double anhedral
blades.
Figure 1.8: Model rotor with anhedral tips in TDT wind tunnel [15].
12
Figure 1.9: PF1 tip tested at ONERA [34].
Figure 1.10: Double vortex system visualized by Muller [32].
13
Figure 1.11: Aeroacoustic test of anhedral tip rotor at NUAA [46].
Figure 1.12: Rigid anhedral tip blade tested by Uluocak [48].
1.1.4 Rotor Comprehensive Analysis
The early helicopters had articulated or teetering rotors. And the blades are
considerably rigid due to their metal spars. So the elastic motion of the blades was
not the main consideration in engineering design at that time. It was not until 8
years after the successful maiden flight of Sikorsky?s first helicopter, the VS-300,
14
that the first elastic flap bending blade model was proposed by Flax [52]. Next,
through the efforts of Yuan and Diprima et al. [53,54], an elastic blade model with
lag and torsion degrees of freedom was conjured. Eventually, the seminal work of
Houbolt and Brooks established the flap, lag, and torsion linear dynamic model
(the nonlinear effect of the centrifugal force was reduced through tension) with a
built-in twist in 1957 [55]. The linear model dropped many flap-lag-torsion coupling
terms, consistent with the small deformation assumption. Hodges and Dowell de-
rived nonlinear flap-lag-torsion coupled equations in 1974 [56]. An ordering scheme
was used in that model to obtain manageable analytical expressions. Concurrently,
Kvaternik [57], Johnson [58], and Rosen [59] also built models of equal accuracy by
expanding on Houbolt and Brooks. Most comprehensive codes still use these models
or their more refined geometrically exact versions. The University of Maryland Ad-
vanced Rotorcraft Code (UMARC) was also developed based on these models [60].
Later, Crespo da Silva [61] and Hodges [62] developed a large deformation
beam model that does not depend on the ordering scheme. The strains are still
small, but the rotations are exact. Concurrently, Johnson [63] also extended the
beam model and unified multibody dynamics to allow exact rotation.
Next, researchers turned attention to the modeling of composite blades. From
the isotropic material to the anisotropic material, the constitutive relationship of the
material and the warping of the beam cross-section are the two aspects that change
the most. Hong and Chopra [64] studied the effect of composite laminate structure
on the blade stiffness coupling by replacing the isotropic material constitutive rela-
tion in Hodges and Dowell nonlinear blade model with that of the laminate structure.
15
Bauchau et al [65?67] focused on adding degrees of freedom for section warping to
the beam model. Hong [68] and Smith [69] combined the above two aspects of work
and carried out research on the modeling and analysis of composite blades. Ben-
quet [70] and Celi et al [71?73] analyzed the complex geometry blades with swept
and dihedral tips via coordinate system transformation and special finite element
matrix assembly method. With the development of the new rotor structural designs,
the drawbacks of simplifying the model based on the rotor system characteristics
were exposed. Whenever there was a new structural design, the model needed to
be re-derived and validated. Bauchau and Ghiringhelli [74?76] showed how general-
purpose multi-body dynamics can be used to build up systems of blades, hubs, and
pitch links while avoiding repeated re-derivation of the equations. However, all of
these models were limited to beams. The blades must be uniform and slender. The
composite formulation was applied to the cross-section. The computational power
available at the time would not allow 3-D models for rotor dynamics.
Thus, for decades, the rotor blades were analyzed by a combination of two-
dimensional cross-sectional analysis and one-dimensional beams. However, it is
obvious that when the blade profile, internal structure, and material properties
have discontinuities, the blade should be regarded as a three-dimensional structure.
Parts of the rotor that are near the hub are not even slender structures. These parts
absorb stresses and determine weight. These parts provide kinematic couplings that
determine stability. The growth of active rotors revealed further drawbacks and
limitations of analyses. Damaged blades or blades with live fire hit could not be
modeled as beams. Chordwise deformations or spanwise discontinuities like flaps
16
and slats are also hard to model. The beam models became more and more reliant
on empirical measurements made after the rotor is built and fell short of providing
a true first principal prediction.
Epps [14] studied the effect of the swept tip on the natural frequency of a
rotating beam. By comparing the experimental data and the analysis results, it was
found that when the sweep angle of the tip section increases, the error of the beam
model also increases, and the error in the higher-order frequencies are more promi-
nent. In 2005, Truong et al [77] attempted to compare the blade analysis results of
the beam model and the 3-D finite element model. In this study, the beam model
and the 3-D model in the commercial program MSC/Marc were used. The results
indicated that the difference between the natural frequencies of the blade obtained
by the 3-D finite element model and the experimental value is lower than that of
the beam model. Then Yeo et al carried out further systematic comparison [78].
The beam model, in this study, adopted the geometric accurate composite beam
model and Variational Asymptotical Beam Sectional Analysis (VABS) method in
the Rotorcraft Comprehensive Analysis System (RCAS), while the 3-D finite ele-
ment model was still MSC/Marc. The comparison of natural frequencies shows that
this beam model has good accuracy for beams with a small aspect ratio. However,
when a swept tip is present, whether it is a metal beam or a composite blade, the
difference between the beam model and the 3-D finite element model increases with
the swept angle. Even though these models were elementary and included none of
the complexities of a modern rotor that called for 3-D, these findings reveal the
value of developing 3-D structural finite element models for blades.
17
In 2008, NASA [79] identified 3-D structures as one of the requirements of
future comprehensive analysis. Datta and Johnson [80] proposed a 3-D finite element
structural analysis method for rotor blades in 2009. In 2010, they unified multi-body
dynamics with 3-D formulation [81]. But these were idealized rotors. From 2014
to 2017 Staruk et al established the analysis process and tools based on Computer-
aided Design (CAD) [82]. Ward et all established material modeling techniques for
3-D [84]. These ultimately opened the door to application on real rotors. NASA
provided the 1/4 scale V-22 model geometry to the University of Maryland to assist
in the creation of a showcase problem [83]. The 3-D methodology has matured since
then [85?87], and it is now available within the X3D solver.
1.2 Objectives of the Thesis
The objectives of this thesis are to: 1) fabricate and test a double anhedral
tip composite rotor to investigate its impact on structural dynamics and loads; 2)
develop a state-of-art 3-D model and validate it with test data.
The first objective aims to fill the lack of basic understanding of loading on the
rotor with anhedral tips. A set of Mach-scaled double anhedral composite blades
were designed in consultation with Boeing to ensure that the geometry and structure
are realistic enough to be representative of a modern rotor and yet be open source.
An in-house fabrication methodology was developed for these blades. A special-
purpose hingeless hub was designed and fabricated in-house to excite the rotating
blades in vacuum, and allow the measurement of rotating frequencies. Hover tests
18
were carried out with a hingeless rig as well.
Three-dimensional models were developed from the same CAD used in fab-
rication. Then they were meshed in Cubit and analyzed with X3D. A lifting line
aerodynamic model with free wake was used with particular attention paid to the
aero-structure interface. The correlation of the test data and the analysis not just
laid the foundation for studying the double anhedral tip, but reproduced the 3-D
workflow, and validated the 3-D model on a realistic advanced rotor. A straight
blade model was also developed as a baseline control case to explore the impact of
the double anhedral tip in forward flight. The straight blade was not fabricated,
however. Nor were forward flight tests carried out in the wind tunnel. These remain
work for the future.
1.3 Organization of the Dissertation
This dissertation contains seven chapters. These chapters are organized as
follows. Chapter one presented the background and motivation of the investigation
of the double anhedral composite blade. Prior work in fixed-wing aircraft and rotary-
wing was reviewed. The objective of the current thesis was described. Chapter two
describes the development of the double anhedral composite blade. Chapter three
covers the test rigs used in vacuum tests and hover tests. Chapter four introduces the
development of the 3-D blade model. Chapter five validates the 3-D double anhedral
composite rotor with the test data acquired from the vacuum test and hover test.
Chapter six contains the fundamental understanding of the double anhedral tip. A
19
straight blade 3-D model is used as a baseline. Chapter seven summarizes the work
and draws key conclusions. It ends with recommendations for future work.
20
Chapter 2: Development of Double Anhedral Tip Composite Blade
This chapter presents the development of the double anhedral tip compos-
ite blades (Figure 2.1). The double anhedral tip was designed with a superficial
resemblance to the Boeing CH-47F like Advanced Chinook Rotor Blade (ACRB),
as shown in Figure 2.2, with a similar but simplified tip shape. The cross-section,
twist, and structural properties are otherwise generic. Thus, in essence it is an
open-source academic research blade. The blade geometry, structure, and materials
are representative of any modern scaled composite rotor, and they are detailed in
this chapter.
Figure 2.1: UMD Double Anhedral Tip Blade.
21
Figure 2.2: Boeing Advanced Chinook Rotor Blade [88].
2.1 Blade Design
The overall parameters of the blade are shown in Table 2.1. The blade has a
span of 0.713 m and a uniform chord of 0.08 m. There is a linear built-in twist of
?16? over the radius and a non-symmetric VR-7 airfoil. The layout of the airfoil
across the span is shown in Figure 2.3. The anhedral angles are defined by a curved
quarter chord line with respect to the rotational plane. The airfoil always remains
perpendicular to the local quarter chord line. Moreover, the blade cross-sections are
rotated about the local quarter chord line to form the built-in twist.
The blade design has three main sections and two transition regions, as shown
in Figure 2.4. The straight portion extends from the root to 80%R connecting to
a 5? dihedral portion over 80 ? 95%R. The last portion has an anhedral of 15?
over the last 5%R. Two transition regions are designed at the beginning of each
anhedral portion to ensure a smooth aerodynamic contour. Each transition region
occupies the first 0.5%R of its portion. The quarter chord lines are linear outside
22
the transition region. These geometric attributes were decided in consultation with
Boeing and based on the hover tower and the Glenn L. Martin wind tunnel test
section at Maryland.
Table 2.1: Blade parameters.
Parameters English Metric
Span 28 inch 0.713 m
Chord 3.15 inch 0.08 m
Airfoil VR-7
Twist ?16?/radius
Taper Untapered
(a) Isotropic view of the airfoil layout.
(b) Rear view of the airfoil layout.
Figure 2.3: The airfoil layout.
23
(a) Rear view of the blade geometry.
(b) Top view of the blade geometry.
Figure 2.4: Blade tip geometry and planform.
As for the internal structure, the cross-section is mainly determined by the spar
type since it is the main structural member of a blade. Figure 2.5 shows four spars
considered for this design: C-spar, D-spar, box spar, and solid spar. The D-spar
was selected. Compared to the C-spar and the solid spar, the D-spar is a closed
section and therefore has a higher torsion stiffness which is beneficial to prevent
instabilities such as flap-pitch flutter and divergence. Compared to the box spar,
the D-spar provides better support for the leading-edge shape with fewer ply layups
and more space for leading-edge weights which are required for small-scale rotors.
Furthermore, the D-spar structure is a good representative of the Chinook blade
internal structure [89]. Therefore, the D-spar was chosen to be the main structural
member of the blade.
The final internal structure is shown in Figure 2.6. The width of the D-spar
is 26.8 mm (33.5%c) starting at the leading-edge. The parameter is mainly affected
by the location and size of the blade root insert. It comprises two layers of ?45?
24
Figure 2.5: Types of blade spar.
IM7/8552 graphite/epoxy prepreg weave throughout the span. Besides the D-spar,
another main structural member is the skin. The same composite material is shared
between the spar and the skin. The skin is made of one layer instead of two. A 3.6
mm long trailing edge tab is designed to obtain a better bond between the upper
and lower skins at the trailing edge. As shown in Figure 2.6, there is a leading-edge
weight inside the D-spar to bring the cross-sectional center of gravity (C.G.) to the
nominal aerodynamic center at the quarter chord. To minimize the mass and size
of leading-edge weight, it is better to use dense material and place it as close to the
leading-edge as possible. Hence, tungsten alloy was chosen. However, placing the
leading-edge weight against the internal surface of the spar requires the leading-edge
weight to have an airfoil profile, which is hard to machine in-house. Based on these
considerations, tungsten alloy rods of 13.2 mm diameter are used as leading-edge
weights, and they have located 16.1 mm ahead of the quarter chord. Instead of a
single continuous rod, there are 16 discrete rods to limit their effect on the blade
structural stiffness (Figure 2.7). Each tungsten alloy rod has a length of 38.1 mm
25
which can fit inside the 5%R anhedral tip portion of the blade. An aluminum root
insert was designed as shown in Figure 2.8 for blade connection. All of the blade
features discussed are individually modeled and are parts of a 3-D Computer-Aided
Design (CAD) model built in CATIA (Figure 2.9).
Figure 2.6: Blade cross-section structure.
Figure 2.7: The layout of leading-edge weights.
(a) Top view of the root insert. (b) Side view of the root insert.
Figure 2.8: Root insert design.
26
Figure 2.9: CAD model of each blade component.
2.2 Blade Mold
Based on the blade CAD model, a blade mold was designed (Figure 2.10) and
fabricated (Figure 2.11) by Xcentric Mold & Engineering Inc. The mold is made of
aluminum 5083 selected to limit the deformation due to the temperature change.
Figure 2.10: CAD model of the mold.
27
Figure 2.11: Double anhedral tip blade mold.
The mold can be separated into a top and a bottom part. Two pairs of ogive-
shaped positioning pins were designed to help the top and bottom surface of the
blade match precisely when the mold is closed. The length of the internal space is
longer than the blade, and the extra internal space was designed to allow the epoxy
to flow freely at the root and the tip portion. Sixteen through holes distributed
evenly on the mold are used to apply uniform pressure on the blade via bolts and
nuts. There are two opening slots on the side of the mold to help open the mold
after the curing process.
2.3 Internal Components Fabrication
The blade fabrication process essentially follows the standard University of
Maryland process [90] but is refined here for advanced blade geometry. The internal
28
components of the blade include: 1) root insert, 2) leading-edge weights, 3) fore
core, and 4) aft-core. Their fabrication is documented here.
The root insert transfers loads from the blade to the blade grip by providing
attachment points to three bolts. It was machined out from an aluminum 7075 plate
that is slightly thicker than the root insert. Its fabrication process involves drilling
and Computer Numerical Control (CNC) machining. Because the top surface of the
root insert is not flat but follows the airfoil profile (Figure 2.4(b)), the blade grip
holes need to be drilled before CNC machining to ensure the quality of the holes
(Figure 2.12(a)). The alignment and orientation of these holes are critical to the
blade as they determine if the blade has any unintentional pre-pitch and pre-lag
angles.
The G-code for CNCmachining was generated via a CAM program?SprutCAM [91]
based on the root insert CAD model. As shown in Figure 2.12(b), the CNC machin-
ing was done by Tormach PCNC1100 [92]. It is recommended that a batch of root
inserts are fabricated at the same time to reduce dissimilarity among blades and
time consumed (Figure 2.8(b)). The same is true for the other internal components.
(a) Root insert holes drilling.
29
(b) Root insert machining.
(c) Root inserts.
Figure 2.12: Root inserts fabrication.
The next step is the fabrication of the foam core. The primary function of the
foam core is to support the aerodynamic shape and hold the leading-edge weights
in place. Typically, foam with a high density is better for holding the internal
components. However, the denser foam the harder it is to work with. Rohacell 31
IG-F [93] 12.75 mm thick sheet is used as the raw material of the foam core. A
rectangular foam piece that is slightly larger than the blade contour was cut out
from the foam sheet. This prevents manual adjustment of the foam shape later and
ensures a consistent core density. The tip of the blade has a 20? bend which exceeds
30
the maximum allowable bending curvature of the foam sheet. Therefore, a separate
piece of foam is needed for the tip.
The airfoil contour of the core is formed by the mold pressure. It is challenging
to precisely set the foam pieces into the mold since this blade has a highly twisted
and curved tip geometry. Double-sided tape was used to ensure the foam stays in
a secured place. While closing the mold, it is important to make sure the leading
and trailing sides of the foam are caught by the leading and trailing edge of the
mold (Figure 2.13). This can be checked by looking from the side of the mold with
a flashlight. As long as the foam is fully caught by the mold, the internal space
of the mold will be fully filled by the foam and form a precise blade contour. The
bolts and nuts should be tightened manually, and slowly, beginning in a star pattern
to minimize the chances of relative motion between the foam and the mold. The
star pattern also helps to apply pressure evenly across the blade. Finally, an impact
wrench was used to tighten the bolts and close the mold completely.
Figure 2.13: Foam sheet inside the mold.
After closing the mold, the aerodynamic contour is formed on the foam core.
However, this is only temporary. The foam core needs to be heated to solidify the
31
shape. The oven (FREAS 645) is heated up to 177?C before the mold is put inside
and held at the same temperature for 90 minutes. After cooling down, the foam
core is removed from the mold, and the excess material at the leading-edge and
trailing-edge are trimmed and lightly sanded. Particular care should be taken while
treating the leading-edge to make sure the airfoil profile is preserved smoothly. The
leading-edge is critical for airfoil performance.
The splitting of the foam core into fore and aft-core pieces (Figure 2.9), milling
of the circular slots for leading-edge weights, and creating the space for root insert
also require CNC machining. A 3-D printed base with an internal airfoil profile is
used to untwist and level the foam core during the machining process (Figure 2.14).
The foam core is secured in the base using double-sided tape. By splitting the foam
into the fore and aft-core, a gap is created in between which accommodates the D-
spar. The leading-edge weight slots are milled from the bottom surface of the core.
The entire machining process can be done automatically and precisely by generating
a G-code based on the foam core CAD model.
Figure 2.14: Machining of the foam core.
32
At this stage, the fabrication of internal components is complete and they are
ready to be assembled (Figure 2.15). The next step is to wrap the leading-edge
weight rods with a ply of film adhesive (Cytec FM300 [94]) before inserting them
into the circular slots in the fore core. After covering the root insert with a ply of
film adhesive to enhance structural integrity, the fore foam core and the root insert
are assembled and wrapped with one additional ply of film adhesive. This assembly
becomes the mandrel of the D-spar. Similarly, the aft-core is also wrapped by a
layer of film adhesive (Figure 2.16).
Figure 2.15: Blade internal components.
Figure 2.16: Assembly of internal components.
33
2.4 Spar and Skin Fabrication
A ?45? IM7/8552 graphite/epoxy prepreg weave is the material of the main
structural members: spar and skin. This composite material is donated by Boeing.
Prior to working with carbon fabric material, gloves are required to protect the
specimen and the fabricator. Acetone is needed to clean the tools and mold. A
release film (Wrightlon 5200) cover is needed on the workspace to create a clean
dust-free environment.
In order to have precise cuts on composite sheets, a new X-ACTO blade is
used. Both the size and fabric orientation are crucial considerations. The exact
size of the composite sheet needed for the spar and skin can be extracted from the
CAD model. Instead of having a slightly larger sheet, then trim after wrapping, an
exact size allows better control over the weight. As for the ?45? fabric orientation,
it is recommended to use the white fabric bundle as a reference. Using a metal
cutting template, the composite sheets can be cut efficiently and accurately. All of
the composite sheets cut out for spar and skin should be preserved in the fridge and
the temperature kept under ?18? to prevent dehydration of the epoxy and breakage
of the fabric.
The final step of the D-spar fabrication is to wrap the mandrel with ?45?
IM7/8552 graphite/epoxy prepreg weave. The prepreg sheet is wrapped around the
mandrel twice to form the double layers starting at the back surface of the mandrel.
As the sheet wraps around the mandrel, a rubber roller is used to compress the
composite sheet to the mandrel. The wrapping should be done as tightly as possible
34
(Figure 2.17). At the anhedral tip, the mandrel is straightened and wrapped the
sheet as if it was a straight blade, then let the mold bend the blade later. As shown
in Figure 2.18, the assembly of the D-spar and the aft-core now becomes the core
of the blade.
Figure 2.17: The D-spar.
Figure 2.18: Blade core assembly.
To prevent the blade from sticking inside the mold after curing, one layer
of release film (Wrightlon 5200) is used to cover the blade and separate the blade
from the mold. To ensure the smoothness of the skin, the release film is attached
to the skin before wrapping the skin to the blade core assembly. As shown in
Figure 2.19, the skin is covered by an oversized release film. This step must be
performed carefully to remove any wrinkles and bubbles. Then the skin is flipped
35
and the trailing-edge of the blade core is pressed against the long edge of the skin.
While laying down the rest of the blade core, a roller is used to press and remove
the trapped air. By lifting the blade core and pressing it against the table, a good
bond between the D-spar and the skin can be achieved. Now the rest of the skin
is pulled across the top surface of the blade core. The trailing-edge of the top and
bottom skin needs to be bound firmly by the roller pressure. It is critical to keep
the skin smooth in this process.
Figure 2.19: Release film and skin.
2.5 Blade Curing and Finishing
The uncured blade assembly is shown in Figure 2.20. Similar to the foam
core fabrication process, double-sided tape is needed to secure the blade in the right
place inside the mold. As the mold is closing, it is vital to keep the leading-edge of
the blade aligned with the leading-edge of the mold (Figure 2.21).
The 8552 epoxy is a toughened resin that must be cured under high temper-
36
Figure 2.20: Uncured blade.
Figure 2.21: Leading-edge of the blade in the mold.
ature and high pressure. Therefore, the curing of the blade is effectively the curing
of the epoxy. Similarly to the foam core fabrication, the oven is heated up to 177?C,
then the mold is heated up from room temperature to 177?C and then held the
temperature for 150 minutes. The double anhedral tip geometry was formed by the
mold pressure.
After curing, the resin beads and unnecessary extrusions are trimmed out by
a grinder. The leading-edge is sanded manually for a smooth finish. Drilling the
bolt holes at the root is the final step. The root insert holes are covered by spar and
skin. These holes can be found by using a relatively small drill bit. Then gradually
increase the size of the drill bit until the holes are fully opened. In this study, a
total of six blades were fabricated (Figure 2.22).
37
Figure 2.22: Double anhedral tip composite blades.
2.6 Blade Instrumentation
Strain gauges are needed to measure blade structural loads. The installation of
gauges should be such that there is minimal change to structural integrity, sectional
mass, stiffness, and aerodynamic properties. To this end, multiple ways of strain
gauge installation were investigated, as shown in Figure 2.23. Method-1 binds the
strain gauge on the surface of the blade and then protects it with a layer of epoxy.
This method is easy to implement and has the minimum impact on blade structure.
However, it changes the airfoil shape. Method-2 creates an indentation on the blade
skin before curing using a thin metal shim. After installing the strain gauge, the
indentation is filled with epoxy to recover the aerodynamic shape. In contrast to
38
method-1, this method has minimum impact on airfoil shape. However, it indents
the structure. Method-3 embeds the strain gauge on the inner surface of the skin.
In this method, the strain gauge neither indents the structure nor changes the
aerodynamic shape. But the strain gauge must be installed before curing. It is
hard to find a strain gauge that can survive the heat and pressure in the curing
process. Since this study focuses on the structural loads and strain/stress of the
blade, method-1 is chosen to keep the blade structure intact.
Figure 2.23: Methods of strain gauge installation.
To limit the impact of instrumentation, the wiring of the sensor is embedded
inside the blade. As shown in Figure 2.24(a), copper wires were embedded in the
aft-core. Due to the skin being made of prepreg weave material, existing holes allow
the wires to pierce through the skin. The exposed wires are wrapped by release film
to separate them from the outer surface of the skin during curing. Then they are
trimmed to the right length and protected by epoxy (Figure 2.24(b)).
39
(a) Wires embedded in foam core.
(b) Wires pierced through the skin.
Figure 2.24: Wires for instrumentation.
There are three sets of structural load sensors on each blade to measure flap
bending, lag bending, and torsional moment at 40%R (Figure 2.25). Full Wheat-
stone bridge (Figure 2.26(a)) is used to build the sensors. VEX is the excitation
voltage, and VC is the signal voltage. This kind of circuit has a good tempera-
ture compensation feature and the ability to amplify the signal of the target load
while suppressing others. Figure 2.26 shows the strain gauge configurations for the
measurement of each load. Two parallel grid gauges (Micro-measurements, N2A-13-
S5092N-350/E5) near the quarter chord measure flap bending moment; four 1-axis
linear gauges (Omega engineering, SGD-3/350-SY43) at leading and trailing-edge
measure lag bending moment; two dual shear gauges (Omega engineering, SGT-
3JS/350-SY41) near the quarter chord measure torsional moment.
40
Figure 2.25: Structural load sensors.
(a) Full Wheatstone bridge cir-
cuit.
(b) Flap bending moment configuration.
(c) Lag bending moment configuration.
(d) Torsional moment configuration.
Figure 2.26: Strain gauge configurations for structural load sensors.
41
All of these sensors are calibrated carefully. A static loading frame is built out
of 80-20 frames to perform the calibration. Figure 2.27 shows the setup for each
load. For flap and lag bending moment, the blade root is clamped in a vise, and
static weights are hung via a pulley to create the bending moment. An in-house
fabricated load cell is used to measure the applied load accurately. For torsional
moment calibration, the torsional moment is applied by a pair of the weight-pulley
system and a moment arm. As each type of load (flap, lag, and torsion) is applied,
the moment and the voltage signals from all three sets of sensors are recorded. This
process resulted in a calibration matrix for each blade to convert analog voltage to
moment. Equation (2.1) can be used to calculate the calibration matrixK. MT ,MF ,
and ML are torsional, flap, and lag bending moments; VT , VF , and VL are voltage
signals from the torsional, flap, and lag bending sensors. This method allows three
sensors to be calibrated together and account for structural coupling. Due to the
built-in twist, it is important to define the reference frame of the measured structural
loads precisely. During the calibration, the flap bending moment was applied by a
force normal to the chord line of the blade root. Hence, the measured flap bending
moment references the root chord line. Similarly, the lag bending moment references
the root insert bolt hole axis, and the torsional moment is about the quarter chord
line of the straight portion of the blade. This means the structural loads were
measured in an undeformed blade frame that rotates with the blade pitch control
angle during testing.
42
(a) Flap bending moment calibration.
43
(b) Lag bending moment calibration.
44
(c) Torsional moment calibration.
Figure 2.27: Structural load sensors calibration.
45
?? ???? ? ? ???VT VT V? T?? ???
???K K K M 0 0
?V V V ???
11 21 31
???K K K ?
???
? ?
?? = ?
? T ??
F F F 21 22 32 ?? ??? 0 M 0 ???? (2.1)F
VL VL VL K31 K32 K33 0 0 ML
As for surface strain, there are two monitoring points: the top surface at
30%R near the root and the bottom surface at 80%R at the first anhedral junction.
A diagram is shown in Figure 2.28. Both of the measurement points are on the
quarter chord line. Metal foil strain gauge rosettes (Figure 2.29) with a relatively
small footprint are used (Micro-measurements, C5K-09-S5198-350-33F). The gauges
are protected by an epoxy coating (Figure 2.30). There are three linear strain gauges
in a rosette.
Figure 2.28: Strain measurement.
46
Figure 2.29: Strain rosette.
(a) Strain rosette at 30%R.
(b) Strain rosette at 80%R.
Figure 2.30: Strain rosette on the blade.
Quarter Wheatstone bridge (only one active element) is used to measure the
strain ?, and it is given by Equation (2.2). GF is the gauge factor. For the rosette
used in this study, the gauge factors are 1.86, 1.79, and 1.86 for each gauge, re-
spectively. Strain rosette allows the access of axial normal strain ?xx, chordwise
normal strain ?yy, and in-plane engineering shear strain ?xy. Equation (2.3) is used
47
to transform the measured strains into strains in the global blade coordinate. ?1,
?2, and ?3 are the orientation angles of the strain gauge with respect to the blade
X axis.
4 VC
V
? = ( EX ) (2.2)
GF 1? 2 VC
VEX
?? ? ? ??1? ????? xx?? ?
??? ???
cos2 ? sin21 ?1 cos ?? 1
sin ?1
? ? ??
? ????1???
?? =yy?? ??cos2 ?2 sin2 ?2 cos ?2 sin ? ???? ?2 ???? ???? (2.3)2
?xy cos
2 ?3 sin
2 ?3 cos ?3 sin ?3 ?3
2.7 Material Elastic Property
To build a reliable 3-D blade structural model, the material elastic properties
and density of each component are necessary. They are documented in the next two
sections.
The blade consists of four materials: IM7/8552 graphite/epoxy weave for spar
and skin, tungsten alloy for leading-edge weight, Rohacell 31 IG-F for foam core, and
aluminum 7075 for root insert. The elastic properties of IM7/8552 graphite/epoxy
weave are important since it is the material of the main structural member (spar
and skin). A standard four-point bending test is performed to measure the elastic
properties (Figure 2.31). The four-point bending test creates constant bending
moment and surface strain at the middle section of the beam, which is easier to
48
measure accurately.
(a) Four-point bending test setup. (b) Loading analysis of four-point bending
test.
Figure 2.31: Four-point bending test.
As per ASTM D7264 [96], sample coupons were fabricated with layups of
[0/90]6, [90/0]6, [?45]6, and [?45]6 to determine tensile moduli E1 and E2, in-
plane shear modulus G12, and major Poisson ratio ?12. The subscripts (1 and 2)
correspond to the fiber axis, and their definition is shown in Figure 2.32(a). Strain
gauges are instrumented at the mid-section of the coupon along the longitudinal x
and lateral y axis of the coupon to measure strains ?xx and ?yy (Figure 2.32(b)).
Three coupons for each layup were fabricated and tested. Equations (2.4)-(2.7)
are derived based on beam static load-strain relation, and then used for the elastic
properties calculation.
Coupon [0/90]6:
6M
E1 = (2.4)
bh2?xx
??yy
?12 = (2.5)
?xx
49
Coupon [90/0]6:
6M
E2 = (2.6)
bh2?xx
Coupon [?45]6 and [?45]6:
3M
G12 = (2.7)
bh2(?xx ? ?yy)
where M is the bending moment; b the width of the cross-section; h the height of
the cross-section; ?xx, and ?yy are strains along its corresponding axis.
(a) Definition of fiber axis.
(b) Sample coupons.
Figure 2.32: Composite coupons.
The measured properties are shown in Table 2.2. The measured values show
some differences with the product specification. The Poisson ratio ?12 and shear
modulus G12 are not supplied at all. The differences are mainly due to the difference
50
in the curing cycle. The measured properties were used in modeling. The properties
of the isotropic materials are taken from product specifications as they are fairly
standard. They are listed in Table 2.3.
Table 2.2: Elastic properties of IM7/8552 graphite/epoxy prepreg weave.
Properties Hexcel Corporation [95] Present measurement
E1, GPa 85 81.45
E2, GPa 80 72.85
?12 0.0755
G12, GPa 5.45
Cured ply thickness, mm 0.131 0.23
Table 2.3: Elastic properties of the isotropic materials.
Properties Tungsten alloy Rohacell 31 IG-F Aluminum 7075
E, GPa 650 0.036 68.9
? 0.2 0.3846 0.33
2.8 Blade Mass
The weights of the individual blade components were documented during fab-
rication for every blade. The weights are listed in Table 2.4. Blades 2, 3, 4, and 6
were then down selected as they were the most similar. The chordwise and span-wise
center of gravity locations were also measured (Figure 2.33, Table 2.5). Based on the
component weights from measurement, and the volumes extracted from the CAD,
the density of each component can be calculated (Table 2.6). Thus, the weights of
film adhesive and compressed foam are accounted for in these density data, which
is important to reduce the uncertainties in the 3-D model. Figure 2.34 shows the
final instrumented double anhedral tip composite blades.
51
Table 2.4: Measured weight of each component in gram.
Root Fore Total
ID LEW* Aft-core* Spar Skin
insert* core* Mass Discrepancy (%)
1 11.45 19.43 73.77 37.57 31.47 38.49 212.18 0.19
2 11.59 19.8 73.78 37.45 31.81 36.99 211.42 -0.17
3 11.33 19.67 73.77 37.56 31.6 37.77 211.7 -0.04
4 11.39 19.44 73.77 37.7 31.62 37.67 211.59 -0.09
5 12.34 19.68 73.77 37.21 32.19 37.17 212.36 0.28
6 11.53 19.66 73.78 37.78 30.85 37.79 211.39 -0.18
(*) including film adhesive
Figure 2.33: Measurement of blade center of gravity.
Table 2.5: Measured center of gravity location.
ID Chordwise C.G. (%c) Spanwise C.G. (%R)
2 29.8 40.2
3 30 40.6
4 28.9 40.6
6 29 40.9
Table 2.6: Measured density of each components in kg/m3.
Component Density
Skin 1415.2
Spar 1524.8
Fore foam 187.3
Aft-foam 193.2
Leading-edge weight 15287
Root insert 2750
52
Figure 2.34: Final blades.
2.9 Summary
This chapter presented the detailed design and fabrication of the double an-
hedral tip composite blade and the development of a corresponding 3-D CAD model.
The fabricated blades were gauged and calibrated for structural loads. Material elas-
tic properties were measured with coupon tests. The densities of each component
were measured. Finally, six blades were fabricated of which four most similar were
picked for testing. The key conclusions are:
1. Possible to create double anhedral tip blades with pressure molding alone.
2. Two spanwise internal cores are needed for the straight-dihedral section and
the anhedral section.
53
3. The strain gauges can be mounted on the blade surface, but they should be
connected to wires embedded in the foam core.
4. Reliable calibration is obtained by accounting for coupling.
5. Reliable component densities are acquired by weight measurement during fab-
rication and CAD model volume.
6. The composite material properties are different from the product specification.
So in-house measurements are necessary.
54
Chapter 3: Development of Test Rigs
Vacuum tests and hover tests were carried out to obtain high-quality validation
data and gain insights into the aeromechanics of the double anhedral tip compos-
ite rotor. Vacuum chamber rig (Figure 3.1(a)) was developed from scratch. The
hover rig (Figure 3.1(b)) was repurposed from the existing test stand. This chapter
presents the details of these two rigs.
(a) Vacuum test. (b) Hover test.
Figure 3.1: Experimental tests.
55
3.1 Vacuum Chamber Rig
3.1.1 Vacuum Chamber
A vacuum chamber test allows the elimination of aerodynamic couplings, and
only the structural and kinematic couplings retain. Therefore, the blade structural
integrity can be confirmed, and the rotating natural frequencies and surface strains
can be measured. These data provide insights into pure structural dynamic charac-
teristics. The vacuum chamber at UMD is shown in Figure 3.2. It is made of 1-in
thick cast iron and has a cylindrical internal diameter of 10-ft and height of 3-ft.
Figure 3.2: Vacuum chamber.
The air inlet/outlet of the chamber allows the pressure to be controlled by
an electric air pump (Figure 3.3). An analog gauge is used to monitor the cham-
ber pressure. As the chamber is fully sealed, the pressure can be reduced to and
56
maintained at 99% vacuum, approximately 0.3 inch Hg.
(a) Air pump. (b) Pump accessories.
Figure 3.3: Air Pump system.
The entire chamber is mounted on a steel structure and lifted 6 ft above the
floor. This setup creates room for the rotor drive system, data acquisition system,
and an entrance for the operator to access the rotor. As shown in Figure 3.4, the
drive system and the instruments are mounted under the rotor shaft. The rotor is
driven by an electric motor via a 1-to-1 ratio belt-pulley system. The rotor speed is
set manually by the motor controller and monitored by optic sensors. The output
voltage of the optic sensor changes every time a gear-tooth passes by, which results
in a square wave signal. The rotor speed is acquired by analyzing the frequency
57
of the signal. A 64-channel slip ring is used to control the actuator on the rotor
hub and communicate the sensor signal from the rotating frame to the non-rotating
frame. It is connected to the rotor shaft through a shaft coupling to allow for some
shaft misalignment and reduce vibration.
Figure 3.4: Vacuum chamber systems.
3.1.2 Design of a New Vacuum Chamber Hub
A new vacuum chamber hub is required to measure rotating frequencies. The
design was performed in CATIA based on the CAD of the blade and the vacuum
chamber as shown in Figure 3.5. The hub is two-bladed and hingeless. There is no
swashplate. This configuration is chosen to limit the structural complexity, improve
compactness, and obtain clean frequencies uncontaminated with complications of
58
the control system dynamics.
Figure 3.5: Internal setup design of the chamber test.
The details of the hub are described in Figures 3.6-3.11. The hub central block
is mounted on the vacuum chamber rotor shaft (Figure 3.6). Then the end block
is held in the central block. Ideally, the central and end blocks should be made in
one piece. However, considering the workspace of the Tormach PCNC 1100 CNC
milling machine, the design is separated into four pieces, two central blocks and two
end blocks, that are feasible to machine yet can be assembled as one structure easily.
The concave-convex shape (Figure 3.7) is designed to withstand the centrifugal force
naturally.
As shown in Figure 3.8, the blade grip connects to the end block through a
tension-torsion strap. The tension-torsion strap is designed to be flexible in torsion
to allow twist deformation induced by pitch motion. The blade grip tube slips on
the end block tube as a sleeve, and there are three pitch bearings between the two
tubes. Moving outboard, the blade grip and the blade adaptor are connected by two
59
shoulder bolts (Figure 3.9). The blade adapter is used to connect the test blade to
the hub (Figure 3.10). The blade adaptor in this design is interchangeable, which
means the vacuum chamber hub can test blades other than the blades in this study.
The current blade adaptor is designed to keep the radius and root cutout of the
vacuum test rotor the same as the hover test rotor.
Figure 3.7: Connection of hub central
Figure 3.6: Hub central block on shaft. block and end block.
In order to measure rotating frequency, the blade needs to be excited during
rotation. Hence, a pitch mechanism is used to excite the blade in pitch motion.
As shown in Figure 3.11, the pitch horn is mounted on the side of the blade grip.
The other end of the pitch horn is connected to a pitch link via a ball-bearing rod.
The ball-bearing allows free rotation and transfer of the linear translations. The
pitch horn dimension is designed to keep the location of the pitch link close to the
hub. There is another ball-bearing rod connecting the pitch link to the pitch arm,
which is fixed on the actuator of the shaker. This pitch horn-link-arm mechanism
60
Figure 3.8: Connection of end block and blade Figure 3.9: Connection of blade
grip. grip and blade adaptor.
(Figure 3.12) transforms the linear motion of the shaker into the pitch motion of
the blade. Because only collective pitch input is needed, the shaker is mounted in
the shaker housing on the hub, which rotates with the rotor. So the linear motion is
imported directly in the rotating frame, and no swashplate is necessary. The shaker
housing also connects two central blocks to strengthen the structure. Engineering
drawings of each component are given in Appendix A. The material of the hub
central block, end blocks, blade grips, blade adaptors, pitch horns, and pitch links
is aluminum 7075.
There are three independent load paths on this hub design. The tension-torsion
strap inside the end block tube carries the centrifugal force and passes it on to the
end block and central block. Since the tension-torsion strap allows twist deformation
and the blade grip can rotate freely about the pitch axis with the help of the pitch
bearings on the end block tube, the majority of the pitch moment is transferred via
the pitch mechanism and ends up at the shaker. The bending moments and shear
61
Figure 3.10: Connection of blade adap- Figure 3.11: Connection of blade grip
tor and blade. and pitch horn.
Figure 3.12: Pitch mechanism.
forces are carried by the pitch bearings and the end block tube. These bearings also
help keep the blade grip tube and the end block tube aligned.
3.1.3 Vacuum Chamber Hub Fabrication
The vacuum chamber hub was fabricated in-house. Drilling, milling, and lath-
ing were involved in the fabrication process of most of the components (Figure 3.13
62
and 3.14). Though the fabrication process is similar to the blade root insert, it is
much more complicated. Due to the complexity of these components, milling of
more than one side of the metal block is needed to fabricate them. The sequence of
different machining methods (drill, milling, and lathing) and ways of securing the
part on the workspace (vice clamping, fixture, etc.) were taken into consideration
when generating the G-code in SprutCAM. Furthermore, the entire machining pro-
cess was simulated virtually in SprutCAM to check for collision, tool travel limit,
and stock removing rate. The simulation also allows the estimation of the machining
time.
Figure 3.13: Machining of blade adap-
tor. Figure 3.14: Machining of central block.
For components like the blade grip and blade adaptor that have cylinder fea-
tures, the fabrication should start with a cylinder billet and lathing (Figure 3.15).
It is because concentricity is very important for those components. This ensures the
concentricity of the end block tube and blade grip tube, which aligns the pitch axis
with the blade quarter chord axis.
The tension-torsion strap used in the vacuum chamber hub was designed and
63
Figure 3.15: Machining of blade grip.
fabricated by Anand Saxena [97]. The tension-torsion strap (Figure 3.16) is designed
for the Mach-scale model rotor hub, which can withstand a centrifugal force as
high as 14000 N. The maximum rotational speed provided by the vacuum chamber
motor (1500 RPM) is much lower than the hover stand rotor speed (2400 RPM) for
which the strap was designed for. Therefore, the magnitude of safety in the vacuum
chamber is sufficient.
Figure 3.16: Tension-torsion strap.
The components of the vacuum chamber hub are laid out in Figure 3.17. Most
of the assembly steps are elaborated in the hub design section. However, a few steps
require more care during the assembly process. As shown in Figure 3.18, two types
of 3-D printing sleeves were designed to keep the pitch bearings in place. The radius
of the larger sleeve is the same as the radius of the pitch bearing outer ring, and
the smaller sleeve corresponds to the inner ring. This arrangement is critical during
64
the assembly of the end block and the blade grip. It ensures the pitch bearings
on each side of the hub have equal distances to the hub center. Lock tie glue was
applied to both the outer and inner ring of the pitch bearing to fill all the gaps
due to the machining tolerance. The length of the pitch link was designed to be
adjustable. Since blade pitch has an influence on the rotating frequency and strain,
it is necessary to set the pitch of both blades the same by adjusting the length of
the pitch link.
Figure 3.17: Vacuum chamber hub components.
Figure 3.18: Assemble of pitch bearings.
65
Figure 3.19 shows the vacuum chamber hub assembly mounted inside the
chamber. This setup was designed to excite and measure rotor blade rotating fre-
quencies. As for rotating strains, the setup was modified slightly to fix the blade
pitch. An aluminum block was designed to replace the shaker, and the pitch arm
was mounted on top of it (Figure 3.20). Due to the vacuum environment, there is
no need to perform tracking. But balancing the rotor is still critical to eliminate any
undesired vibration. The hub was balanced separately from the blades by carefully
measuring the weight of each component.
Figure 3.19: Vacuum chamber hub assembly with shaker.
66
Figure 3.20: Vacuum chamber hub assembly with fixed pitch.
3.1.4 Vacuum Chamber Hub Stiffness
Identifying the blade root boundary condition is critical for performing analysis
later. Therefore, static load tests and non-rotational frequency tests were performed
to measure the pitch stiffness, flap stiffness, and lag stiffness of the hub. The test
setup and diagram for measuring the pitch stiffness are shown in Figure 3.21. Static
load F was applied on the pitch link via a pulley and measured by an in-house
fabricated load cell. The deformation of the pitch horn ? was measured by a laser
sensor. Based on the distance h between the end of the pitch horn and the pitch
axis, the pitch moment applied, and the rotational deflection about the pitch axis
were determined (Figure 3.22), and then the pitch stiffness K? can be calculated by
Equation (3.1).
67
Figure 3.21: Vacuum chamber hub pitch stiffness test.
Figure 3.22: Vacuum chamber hub pitch moment versus pitch deformation.
Fh
K? = (3.1)
sin?1(?/h)
68
Direct measurement of the flap and lag root stiffness is error-prone as, unlike
in pitch, the stiffness is much higher. Hence, a non-rotating frequency test was
carried out, as shown in Figure 3.23. A rectangular aluminum beam was mounted
on the vacuum chamber hub. The beam response was recorded by the laser sensor
and strain gauge. Both shake tests and hammer tests were performed to measure
the beam frequency. The frequency spectrum of the beam response is shown in
Figure 3.25. The narrow peaks at the power supply frequency of 60 Hz and its
integer multiples are discarded. The remaining peaks are the beam frequencies.
Multiple tests were performed, and the measured frequencies were cross-referenced
to identify the repeated results until repeatable results were obtained.
Figure 3.23: Vacuum chamber hub flap Figure 3.24: 3-D model of the aluminum
and lag stiffness test. beam.
69
Figure 3.25: Frequency spectrum of aluminum beam strain signal.
Then a 3-D structural model (Figure 3.24) was developed for the aluminum
beam using X3D. Due to the simple and well-defined structure, the beam can be
modeled very accurately. The only parameter that can be varied in the model is the
root stiffness. The root flap and lag bending stiffnesses were varied until the pre-
dicted frequencies matched the measured frequencies. The measured and predicted
frequencies are listed in Table 3.1. The frequencies predicted with a clamped root
are also presented to show the impact of the root stiffness. The outer tube on the
blade grip and the inner tube on the end block are the main components that affect
the flap and lag bending stiffness. Flap and lag directions have the same stiffness
due to the circular cross-section of these two components. The final root stiffness
values are pitch stiffness of 75 Nm/rad, flap and lag stiffness of 900 Nm/rad.
70
Table 3.1: Aluminum beam frequencies in Hz.
Measurement Prediction Prediction
(K?=75 Nm/rad, K?=K?=900 Nm/rad) (clamped root)
10.8 (Flap) 10.8 12.7
21.5 (Flap) 20.8 79.5
58.6 (Lag) 66.5 117
118 (Torsion) 123 (used K?) 224
150 (Flap) 184 259
347 (Flap) 358 441
463 (Torsion) 486 (used K?) 720
3.1.5 Vacuum Chamber Instrumentation and Data Acquisition
A hub excitation frequency sensor is built into the rotating frame. As shown in
Figure 3.26, a single linear strain gauge is used. For this purpose, a Printed Circuit
Board (PCB) was designed and mounted on the side of the hub for the connection
of sensors and slip ring. The PCB is also a checkpoint for system debugging.
Figure 3.27 shows the function generator to power and control the shaker.
The frequency and magnitude of the shaker linear motion are determined by the
output signal of this function generator. National Instruments PXIe is used as
the data acquisition system in the vacuum chamber test. The 8-slot PXIe-1082
chassis provides housing to the PXIe-8840 controller, PXIe-6365 multifunction I/O
module for rotor speed input and function generator output, PXIe-4331 8-Channel
strain/bridge input module for blade strain outputs. A LabVIEW program was
developed for this test to interface with the PXIe hardware.
71
Figure 3.26: Vacuum chamber hub instrumentation.
Figure 3.27: Vacuum chamber test data acquisition system.
3.2 Hover Rig
3.2.1 Hover Rig Components
Unlike vacuum chamber tests, there is aerodynamic forcing in hover tests. The
test data can be used to validate the aerodynamic model for complex tips and the
aero-structural interface.
72
The hover test was carried out on the hover stand at Alfred Gessow Rotorcraft
Center (AGRC), shown in Figure 3.28. The stand is mounted on the hover tower,
which raises the rotor hub two rotor diameters away from the ground to keep the
rotor out-of-ground effect. In the present work, the blades were mounted on a
four-bladed hingeless hub. The overall parameters of the rotor are summarized in
Table 3.2. The rotor solidity is 0.1 with a root cutout of 16.4%R. The maximum
rotational speed is 2282 RPM, allowing the blade tip speed to reach a Mach number
of 0.6. The components, instruments, and data acquisition system are detailed in
the following sections.
Figure 3.28: Hover test stand.
Figure 3.29 shows the main components of the hover stand. The rotor is
driven by a hydraulic motor and a 2:1 ratio belt-pulley system. The hydraulic drive
system is chosen to prevent Electro-Magnetic Interference (EMI) and improve the
signal-to-noise ratio. The details of the drive system can be found in Ref [97].
73
Table 3.2: Rotor parameters.
Parameters
Number of Blades 4
Radius 0.853 m
Root cutout 16.4%R
Solidity 0.1
Max tip Mach number 0.6
Hub type Hingeless
Rotation direction Counter-clockwise
Figure 3.29: Hover test stand components.
The structure of the hingeless blade grip is similar to the vacuum chamber
hub. As shown in Figure 3.30, the end block is clamped by two hub plates. The
blade grip is connected to the end block via a tension-torsion strap. The end block
tube is set inside the blade grip tube. The flap and lag motions are eliminated, and
the pitch bearings between the end block tube and the blade grip tube enable the
torsion degree of freedom. The pitch horn is fixed to the blade grip and connected
with the pitch link to control the pitch input. There are no kinematic couplings
since the pitch link is located inboard of any equivalent hinge of elastic flap and lag
74
Figure 3.30: Hingeless hub.
motion. All of these components are made of steel. Therefore, the hingeless hub is
stiff enough to be considered rigid.
The blade pitch is controlled by a swashplate (Figure 3.31) which influences
the rotor tip path plane. Three electric actuators are used to tilt and or translate
the non-rotating swashplate. Then the orientation and position of the non-rotating
swashplate are transferred to the rotating swashplate via a spherical bearing, which
decouples the rotation motion. A scissor connects the rotating swashplate and the
shaft to ensure the rotating swashplate has the same rotational speed as the rotor.
The rotating swashplate connects four pitch links that change the collective and
cyclic inputs.
There are multiple sensors in the rotating frame (strain gauges, pitch sensors,
pitch link load sensors, and shaft torque sensors), which are connected to a PCB
in the hub cap (Figure 3.32). The bottom of the PCB is wired with a 150-channel
slip ring to communicate the signals between the rotating and non-rotating frames.
A shaft coupling is installed between the rotor shaft and the slip ring for protec-
tion (Figure 3.33). Aligning the slip ring with the shaft is very important. Any
75
Figure 3.31: Swashplate.
misalignment can result in undesired vibration, noisy signal, and potential slip ring
damage.
Figure 3.32: PCB on the hub cap. Figure 3.33: Hover stand slip ring.
3.2.2 Hover Rig Instruments
The base of a 6-component balance is installed on the test stand (Figure 3.34).
The rotor shaft is held by the other end of the balance. A single load path ensures
all hub loads are captured by the balance. Calibration was done in-house to account
76
for the vertical and axial offset of the hub from the center of the balance. The details
of the static load calibration are documented by Wang [98].
The yaw moment measured by the hub balance is a fixed frame moment from
shaft friction. The rotor torque is measured in the rotating frame. As shown in
Figure 3.35, a torque sensor is installed on the shaft. This torque sensor consists
of four shear strain gauges and a full-bridge circuit. The calibration process of
this sensor is similar to that of the blade torsional moment sensor. The pitch link
loads are also measured in the rotating frame. The pitch links are instrumented to
measure the axial load for pitch moment estimation (Figure 3.36).
Figure 3.34: Hub balance. Figure 3.35: Torque sensor.
The root pitch angle of each blade is measured directly by Hall effect sensors.
As shown in Figure 3.37, a Hall effect sensor is installed on the top surface of the
end block, with a magnet on the pitch horn near the blade grip. As the blade grip
rotates about the pitch axis, the magnet moves along with the blade grip, which
changes the voltage of the Hall effect sensor output signal. To calibrate the Hall
77
Figure 3.36: Pitch link load sensors.
effect sensors, an inclinometer was used to monitor the blade pitch angle while the
collective or cyclic was adjusted to vary it. Since the blades are highly twisted,
the inclinometer was clamped at 75%R to account for the slight difference in the
orientation of the blade root insert. Figure 3.38 shows the calibration data of each
blade. A third-order polynomial curve fit is used to generate the function for pitch
measurement during the hover test.
Figure 3.37: Pitch Hall sen-
sor. Figure 3.38: Pitch Hall sensor calibration.
The blade pitch angles are also needed to derive the control angles. Equa-
tions (3.2)-(3.4) can be used to calculate collective ?0, longitudinal ?1S, and lateral
78
?1C pitch given by the swashplate input. ?i is the pitch angle at 75%R of blade
i, and ? is the azimuth angle of blade one. The azimuth angle is measured by an
encoder installed at the bottom of the slip ring (Figure 3.39). The magnitude of the
encoder output signal varies linearly with azimuth angle, as shown in Figure 3.40.
?1 + ?2 + ?3 + ?4
?0 = (3.2)
4
(?1 ? ?3) sin(?)? (?2 ? ?4) cos(?)
?1s = (3.3)
2
(?1 ? ?3) cos(?) + (?2 ? ?4) sin(?)
?1c = (3.4)
2
Figure 3.39: Encoder. Figure 3.40: Azimuth calibration.
The rotor speed can be estimated with the sawtooth wave signal generated
by the shaft encoder. The optic sensor (Figure 3.41) is also used to monitor rotor
speed as a backup. As shown in Figure 3.42, the frequency of the optic sensor and
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the shaft encoder is consistent, which indicates reliable rotor speed measurement.
Figure 3.41: Optic sensor. Figure 3.42: Output of optic sensor and encoder.
3.2.3 Hover Stand Data Acquisition
Figure 3.43 shows the hardware that controls the test system, provides power
for sensors, as well as records the data. A motor control box is used to adjust
the rotor speed and monitor the motor temperature. The control sticks are for
collective/cyclic control. National Instruments SCXI system is for data acquisition,
which is detailed in Ref [97]. Due to the emphasis on blade structural loads in this
test, a LabVIEW program (Figure 3.44) is developed to store as well as process
loads data in real-time for review. The program also allows access to the hub and
structural load frequency spectrum to monitor resonance and safety of flight. The
raw data from all instruments are stored in a time array.
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Figure 3.43: Hover test data acquisition system.
Figure 3.44: LabVIEW program.
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3.3 Summary
This chapter described the test rigs used for vacuum chamber and hover tests.
A two-bladed hingeless hub was designed and fabricated for the vacuum chamber
as a part of this work. Benchtop tests were performed to determine the blade root
stiffness in flap, lag, and torsion for this new hub. The existing four-bladed hingeless
hub was needed for hover tests.
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Chapter 4: Development of 3-D Blade Model
This chapter presents the development of the 3-D blade aeromechanic model,
starting from the creation of CAD geometry to 3-D solid meshing to the aeroelastic
model, to finally 3-D stresses. An overview is presented picturization in Figure 4.1.
Figure 4.1: Development of 3-D Blade Model.
The X3D solver is used for aeroelastic predictions. X3D is a 3-D structural
dynamics solver developed specifically for next-generation Integrated 3-D analysis of
rotors [99]. X3D uses a multibody analysis framework in which flexible components
are analyzed using 3-D brick finite elements and connected by multibody joints. The
combination of the 3-D FEM with multibody dynamics, trim solution, and aerody-
namics make X3D unique. The basic 3-D blade modeling process is documented by
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Staruk in detail [100]. Therefore, only the specific steps for modeling the double
anhedral tip and the special refinements are discussed here.
4.1 Blade Geometric Model
To create a 3-D blade aeroelastic model, 3-D CAD geometry with accurate
internal structure is essential. Not every detail is essential to begin with, but the
geometry should be consistent with the principal shapes and materials identified.
The standard file formats for storing geometry are Stereolithography (STL), Inter-
national Graphics Exchange Specification (IGES), and Standard for the Exchange
of Product (STEP). The STEP format is considered to be the most suitable and
portable for sharing 3D geometric models. Therefore, as long as the geometric model
can be saved in a STEP format, it can be created with any CAD software. In this
work, the CATIA V5R20 software is used.
A systematic study requires control over the variables of the subject. Parame-
terization of the geometric model allows the designer to have complete control of all
the key shapes and features, thereby enabling precise variable control for subsequent
structural analysis. Such a geometric model also minimizes the time required for
analysis as well as subsequent mesh development. Table 4.1 lists the primary pa-
rameterized structural variables, and Table 4.2 shows the secondary variables which
relate to the primary variables via analytical formulae. All dimensions are in the SI
unit and angles in degrees.
A straight blade model is also developed as a baseline to analyze the impact
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of the double anhedral tip. These two models fall out of the same parameterized
CAD model. As shown in Figure 4.2, the only difference between the two models
is the dihedral/anhedral angle. Both of them have the same twist about the local
quarter chord.
Table 4.1: Primary variables of the parametric geometry.
Variable Notation Straight Double anhedral tip
Radius R 0.853 m 0.853 m
Root cutout rroot 16.4%R 16.4%R
Chord c 0.08 m 0.08 m
Spar width wspar 33.5%c 33.5%c
Skin layer thickness tskin 0.19 mm 0.19 mm
Number of skin layer nskin 1 1
Spar layer thickness tspar 0.19 mm 0.19 mm
Number of spar layer nspar 2 2
Location of 1st anhedral r? 80%R 80%RA1
1st anhedral angle ? 0?A1 5
?
Location of 2nd anhedral r? 95%R 95%RA2
2nd anhedral angle ? 0?A2 ?15?
Twist rate over radius ?tw ?16? ?16?
Table 4.2: Secondary variables of the parametric geometry.
Variable Notation
Transition length ltrans = 0.5%R
Root pitch ?root = ?tw(rroot/R? 0.75)
1st transition pitch ?trans1 = ?tw(r?a1/R? 0.75)
2st transition pitch ?trans2 = ?tw(r?a2/R? 0.75)
Tip pitch ?tip = ?tw(1? 0.75)
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Figure 4.2: Parameterization models.
As the geometric model is created, the same parts can be generated in multi-
ple ways. However, some are not beneficial for the finite element meshing process.
The 3-D structural dynamics model, X3D, uses hexahedral brick finite elements.
Hence, the familiarity with 3-D meshing with hexahedral brick elements is helpful
for the creation of the geometric model. Although modifications of the geometry
can be done later in the meshing software, it is not desired. Creating a geometric
model upfront that is suitable for meshing later will significantly simplify the pro-
cess. It is likely that iterations between CAD and meshing would be needed. The
characteristics of a good CAD model are described as follows.
1. The internal structure of the blade is composed of as many parts as materials.
?Bodies? in CATIA are used to create these parts. Ideally, each body is
defined with a single material. For the double anhedral blade (Figure 4.3),
skin, spar, fore core, aft-core, and root insert have their own bodies. However,
for parts that are repeated in discrete intervals like the leading edge weights,
it is beneficial to model all the leading edge weights including the foam in
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between as one body (Figure 4.4). This reduces the number of bodies and
unnecessary complexity in the geometric model. They can then be separated
into multiple volumes by the meshing process. More details related to this
step will be clarified in section 4.2.
Figure 4.3: Bodies in the geometric model.
Figure 4.4: Leading edge weight body; the gaps are merged in geometry for smooth
meshing but defined by material properties.
2. There should be no artificial gaps or overlaps between the internal structures.
In other words, interfaces should be consistent. The definition of geometric
elements such as points, lines, and surfaces between adjacent bodies should
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be identical. For example, Figure 4.5 shows the surfaces used to construct the
skin body, spar body, fore core body, and aft-core body. The skin inner and
spar outer surfaces are the same surface, similarly, the spar inner and fore core
surfaces are the same surfaces, so their definition is identical.
Figure 4.5: Shared surfaces between bodies.
3. The helicopter rotor blade is a structure with a long radial dimension in gen-
eral. For such structures, a multi-section surface is a convenient way to con-
struct bodies. In order to control the geometry between the cross-sections, it
is necessary to define suitable guidelines, as shown in Figure 4.6. For highly
twisted blades, the guidelines should be defined using helix. Using a straight
line as a guideline will make the blade chord between two cross-sections shorter
than the actual value.
The 3-D blade geometric model is used both in mold fabrication, as well as
analysis. These two critical activities of the research are sourced from the same
geometric model thus ensuring consistency.
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Figure 4.6: Multi-section surface.
4.2 Blade Mesh
Prior to meshing the blade, a Structural Analysis Representation (SAR) is
needed to determine whether a component is modeled by a flex part or a joint.
The SAR is simply a definition on paper along with a load path diagram. Because
the vacuum chamber rotor hub and the hover tower rotor hub are both hingeless,
the system can be simplified as a single flex part and a root joint. Additionally,
a tip joint is assigned for blade structural loads. The position, orientation, and
connections in the SAR are summarized in Table 4.3.
Table 4.3: Structural analysis representation.
Part Part Position (m) Orientation (?)
Name Connections
ID type x y z ?x ?y ?z
1 Joint Root holes 0 0 0 0 0 0 2
2 Flex part Blade 0 0 0 0 0 0 1, 3
3 Joint Tip connection 0.682 0 0 0 0 0 2
The Cubit v15.2 software [101] is chosen to mesh the flex part. In this study,
the blade is the only flex part. The meshing process starts with importing the STEP
file of the geometric model into Cubit. Then steps for clean-up, decomposition,
89
imprint, merge, mesh, and mesh quality estimation follow. The steps follow the
sequence alone in general, but can also be combined when necessary. These steps
are described next.
4.2.1 Clean-up
The first step in the meshing process is cleaning the geometric model. As the
geometric model is imported into Cubit, geometric elements like vertices, curves,
surfaces, and volumes (terms used in Cubit) are identified. Among these elements,
there might be sliver elements that will lead to failure in mesh generation or a
low-quality mesh. The ?Remove small features? operation in Cubit can be used
to detect the sliver elements. Normally, the smallest dimension in the geometric
model is a suitable threshold for the operation to identify sliver elements. For a
composite rotor blade, the threshold will be the thickness of a single ply of the
composite material. There are mainly two types of sliver elements that require
cleaning. The first type is created during the development of the geometric model.
These sliver elements might be too small for the designer to check with naked eyes.
Removing this type of sliver element by modifying the geometric model and then
re-starting the meshing process all over again is recommended. The second type
of sliver element is created by Cubit during STEP file import, particularly when
the geometric model is complicated. This is usually the case for rotor blades. This
type of sliver element does not exist in the geometric model. And it breaks up the
continuous element. The ?composite? function in Cubit can be used to clean this
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type of sliver element. As shown in Figure 4.7, two sliver surfaces on the leading
edge weights can be composited into a larger surface which allows better control
of meshing in the following steps. This clean-up step might need to be performed
multiple times in the entire mesh process, particularly after decomposition, imprint,
and merge.
Figure 4.7: Composite of sliver surfaces.
4.2.2 Decomposition
Decomposing the volumes is a critical step in the meshing process. The pur-
pose is not only to separate the existing geometries into meshable volumes but also
to separate regions of different material properties and help control mesh quality.
Since the double anhedral blade has two distinguish tip portions, the blade geome-
try is first decomposed into three main portions: straight, dihedral, and anhedral,
and two transition portions as shown in Figure 4.8. The sectional geometry of each
portion is the same, so, the geometries in each portion have two topologically similar
opposite faces connected by curved surfaces. This kind of volume is easily meshable
and can be meshed with the ?sweeping? algorithm.
91
Figure 4.8: Spanwise decomposition.
As mentioned previously, the skin and spar consist of composite material, and
the material property varies with the orientation of the layer. Therefore, the skin
and spar needed to be decomposed further to apply layups with different orienta-
tions. This is done by the sectional decomposition in each portion. As shown in
Figure 4.9, the skin is decomposed into three top volumes and three bottom volumes.
The spar is decomposed similarly into two top, two bottom, and one web volume.
The ?Webcutting? (Cubit decomposition operation) surface should be created using
the original vertices and curves to decompose sectional geometry efficiently. Such a
surface can decompose volume accurately without generating additional sliver ele-
ments. An example is decomposing the highly twisted skin into a top and a bottom
volume. The ?Webcutting? surface should be created based on the leading-edge
guide curves on the inner and outer surfaces of the skin volume as they share the
same twist rate as the blade. This is also an aspect that the designer should keep
in mind when defining the guidelines of the geometric model.
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(a) Leading-edge.
(b) Trailing-edge.
Figure 4.9: Sectional decomposition; each volume has a different ply angle.
Recalling the leading-edge weight body created in the geometric model is a
continuous structure combining the leading-edge weights with the foam, further
decomposition is needed now to separate them. Based on the spanwise location of
the start and end of each leading-edge weight, the entire blade geometry can be
further decomposed into smaller volumes (Figure 4.10). By decomposing the skin,
spar, and foam core along with the leading-edge weights, more authority of mesh
node placement is gained.
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Figure 4.10: Leading-edge weights decomposition.
4.2.3 Imprinting and Merging
After decomposition, each volume is more or less independent. Even if the
geometric elements (vertices, curves, and surfaces) between adjacent volumes are
completely coincident, they are not connecting the adjacent volumes. A continuous
geometry is needed to generate a continuous finite element mesh later. In order to
join the adjacent geometric elements together, the step of imprinting and merging
is needed. Imprinting refers to the identification of the common geometric elements
between adjacent volumes and the generation of the missing elements. Merging
refers to completing the fusion of adjacent and identical geometric elements. For
a complex geometry like the double anhedral tip, it is not recommended to rely
on the commands ?imprint all? and ?merge all? to perform this step automatically.
Imprinting and merging are better performed along with decomposition. Every time
a volume is separated into two, the interfaces should be imprinted and merged. For
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the radial decomposition, which is relatively clean, the imprinting can be skipped
and merge performed directly. The ?Connect volumes? operation can identify the
geometric element that fails to merge successfully. Then the geometries are ready
for mesh generation.
4.2.4 Meshing
The majority of the blade volume can be meshed with the ?sweeping? algo-
rithm. A 2-D sectional surface mesh and radial curve meshes are needed to apply
the ?sweeping? algorithm. The selection of a suitable cross-section has a significant
influence on the mesh quality. The best practice is to search for the cross-section
with the most complex internal structure. For the present blade, that will be the
cross-section at 5.58%R shown in Figure 4.11. This cross-section includes all the
internal structures of the blade: skin, spar, leading-edge weight, fore core, aft-core,
and root insert. The surfaces in this cross-section can be categorized into three
types. The first type is a logical rectangle (four edges and four corners), and it is
suitable for the ?map? algorithm. The second type is a circle, which has its own
specific algorithm ?circle?. The third type is a non-rectangle, which can be meshed
by the ?pave? algorithm. The meshing of radial curves is straightforward. The
leading-edge curves are selected and meshed as shown in Figure 4.13. The cross-
section mesh becomes the source of the ?sweeping? algorithm to mesh the volume,
whereas the curve mesh becomes the guile.
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Figure 4.11: Cross-section selected to mesh.
Figure 4.12: Cross-section mesh.
Figure 4.13: Radial curve mesh.
The cross-sectional mesh is swept inboard and outboard of 5.58%R to form the
volume mesh. For sweeping the cross-section inboard, special treatment is required
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to account for the root insert holes. The top surface of the root insert is meshed
using the ?hole? algorithm and then the surface meshes are swept vertically (Fig-
ure 4.14). The rest of the inboard volumes are meshed by sweeping the cross-section
mesh inboard to the root. As for the outboard portion, the cross-section mesh is
simply swept to the tip. Because of the special tip, it is crucial to ensure the tip
mesh matches the airfoil. The double anhedral tip airfoils are always perpendic-
ular to the local curved quarter chord line. Hence, the cross-section mesh in the
tip should be perpendicular to the curved quarter chord line as well (Figure 4.15).
This is determined by the aero-structural interface method, which will be detailed
in section 4.3.
Figure 4.14: Root insert mesh.
Figure 4.15: Tip portion mesh.
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The meshes of the double anhedral blade and the straight blade are shown in
Figure 4.16. All of the elements are converted from 8-noded hexahedral elements
(in Cubit) to higher-order 27-noded hexahedral elements needed by X3D. It can be
seen in Table 4.4 that two blade meshes have comparable sizes.
Figure 4.16: Blade meshes.
Table 4.4: Size of blade meshes.
Double anhedral blade Straight blade
No. of elements 3427 3305
No. of nodes 30,756 29,680
Degrees of freedom ? 100, 000 ? 100, 000
It is necessary to evaluate the quality of the mesh. If the mesh quality is
poor, the FEM model will generate inaccurate solutions or even be ill-conditioned.
For 27-noded hexahedral elements, the scaled Jacobian is a useful metric of quality.
This metric measures the proximity of each edge to the normal vector of its adjacent
surface. The FEM model can be solved successfully if only all elements have scaled
Jacobian greater than zero. Generally, for an 8-noded hexahedral mesh, a scaled
Jacobian greater than 0.7 is desired for good accuracy. But when converted to
27-noded element values lower than 0.7 can be sufficient. The precise value for a
27-noded hexahedral mesh is not well-established generally and requires detailed
98
study outside the scope of this thesis. For the present blade, it was observed that
a scaled Jacobian greater than 0.25 would provide an accurate solution. The mesh
quality of both blade meshes is shown in Figure 4.17. The majority of the mesh
elements have a scaled Jacobian close to 1, and the minimum value occurs at the
root insert but remains higher than 0.25.
Figure 4.17: Blade meshes scale Jacobian quality.
4.2.5 Assignment of Blocks, Sidesets, and Nodesets
The assignment of material properties in X3D requires Blocks. Volumes with
the same material properties are assigned to one block. As shown in Figure 4.18,
the root insert, leading-edge weights, the fore core, and the aft-core are assigned to
blocks 201-204 respectively. Though the fore and aft-core are both made of foam,
they are assigned to different blocks to account for the density variation due to
the film adhesive and compressed foam. For the spar and the skin, which consist
of composite plies, the material properties in the global coordinate change with
the volume orientation. So the spar or the skin cannot be assigned to one block.
The spar volumes are assigned to 12 blocks (block 205-216, Figure 4.19), four for
each portion (straight, dihedral, and anhedral). In each portion, top, leading-edge,
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bottom, and web volumes are assigned to four blocks, respectively. The volumes in
each block are assumed to have the same orientation. Similarly, the skin volumes
are assigned to 15 blocks (block 217-231, Figure 4.20).
Figure 4.18: Blocks of isotropic material volumes.
Figure 4.19: Blocks of spar volumes.
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Figure 4.20: Blocks of skin volumes.
Since the block orientation impacts the composite properties in the global
frame, it is important to extract the block orientation with respect to the X3D global
coordinate system. These angles are extracted for each block and used as inputs
later when building the Structural Analysis Model (SAM) input file. Currently, this
step is done with an excel sheet.
The only kind of sideset used in this model is the 900 class sideset. This kind
of sideset consists of the nodes on the external faces exposed to airflow (aerodynamic
surface nodes). As shown in Figure 4.21, sixteen 900 class sidesets (SS901-SS916)
are assigned. Each sideset is an aerodynamic segment. The aerodynamic forces and
moments on each segment are distributed into nodal forces and applied to the nodes
of this sideset.
101
Figure 4.21: Aerodynamic segment sidesets (top view).
Compared to sidesets, nodesets have more functions. There are four types of
nodesets defined on this blade. The first type is two 400 class nodesets identified as
NS401 and NS402. These are used to define a joint. The solution process relates
the degrees of freedom at these nodes to the joint degrees of freedom. The nodal
degrees of freedom are then eliminated. Nodeset 401 are nodes on the inner surface
of blade root holes (Figure 4.22). These are connected to the root joint for boundary
conditions and pitch control input. Nodeset 402 are nodes near the quarter chord
line in the cross-section of the first dihedral junction (Figure 4.23). A joint is defined
with this nodeset, and it is used to apply static loads for structural load calibration.
This nodeset can be placed at any radial location as long as it is outboard of the
desired load inspection point. For the double anhedral blade, placing nodeset 402 at
the end of the straight portion simplifies the calibration process. Note that unlike
the root joint this joint is not a physical bearing but rather a load sensor.
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Figure 4.22: Root boundary and strain Figure 4.23: Nodset for applying static
gauge nodeset. loads.
The second type of nodeset is the 700 class nodeset. As shown in Figure 4.24,
the nodeset 701 is defined by nodes on the leading-edge curve, nodeset 702 for the
trailing-edge curve, nodeset 703 for the top surface, and nodeset 704 for the bottom
surface. The motions of these nodes are used to determine a beam-like cross-sectional
deformation. It is critical to place the leading-edge nodes and trailing edge nodes
precisely because these two nodesets define the chord lines. However, the placement
of the top and bottom nodeset is not as strict. They define the thickness line loosely.
When placing them, there are only two requirements: 1) the nodes are in the same
cross-section as the chord nodeset, and 2) the vector joining them is not parallel
to the chord line. The number of nodes in these four nodesets must be the same.
Otherwise, there will be orphan nodes without any cross-sections.
The third type of nodeset is the 800 class nodeset. It is for structural load
103
Figure 4.24: The 700 class nodesets .
calculation. The sectional blade structural loads (axial force, flap bending moment,
lag bending moment, and torsional moment) can be calculated base on the 3-D
strain of the selected nodes in the 800 class nodesets. As shown in Figure 4.25,
this class of nodeset is also composed of four nodesets (NS801, NS802, NS803, and
NS804). The rule of placement is that NS801 and NS802 are put on the top surface,
whereas NS803 and NS804 are put on the bottom surface. Moreover, NS801 and
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NS803 should be in front of NS802 and NS804. The specific node selection varies
with the structure, and it is further discussed in section 4.4.
Figure 4.25: The 800 class nodesets.
The last type of nodeset is the 900 class nodeset. It is defined based on the 700
class nodeset (chord and thickness line) and 900 class sideset (aerodynamic surface).
The locations of NS901-NS904 are shown in Figure 4.26. Essentially these nodes
105
are the 700 class nodesets at the beginning and end of 900 class sidesets. This type
of nodeset is used to identify the sectional dynamic pressure and angles of attack
for aerodynamic force and moment calculation of the corresponding segment (a 900
class sideset).
Figure 4.26: The 900 class nodesets.
106
Finally, the mesh is exported as an I-DEAS Universal (.unv) mesh file. Then
a python code, SamBuilder, developed by Staruk [102] is used to convert the mesh
file to X3D mesh data file (.dat), joint data files (.j.dat), and the Structural Analysis
Model (SAM) input file. These are all readable ASCII files. The SAM is a Fortran
namelist file. Material properties, ply orientations, blade orientations, blade position
relative to hub, and joint properties are defined in the SAM input file. The SAM
file, mesh file, and joint files are inputs to X3D.
4.3 Blade Aerodynamic Model
The built-in aerodynamic model in X3D is a lifting-line model with 2-D un-
steady flow airfoil C81 tables and free wake. The free wake is a time-marching
version of Maryland Free Wake [103]. For the present study, a single rolled-up vor-
tex is used, released from the deformed blade tip quarter-chord. The vortex strength
equals 55% maximum circulation outboard of 50% span, and the vortex core is 10%
of the tip chord when formed with a growth factor of 0.05. These numbers are set
empirically based on experience validation with single and coaxial rotors of a similar
scale. In hover, 12 turns of wake with 15? azimuth angle discretization are used. A
full span Weissinger-L near wake model [104] is used 30? behind each blade after
which the wake rolls up. For edgewise flow, 4 turns of wake with 5? azimuth angle
discretization are used. The near wake model is turned off for edgewise flight to
avoid complications on the retreating side near the reverse flow boundary. A sample
wake geometry in hover is shown in Figure 4.27.
107
Figure 4.27: Hover free wake geometry.
An interface is needed to communicate between the aerodynamic and struc-
tural models. The sideset and nodesets described in the last section are essential for
exchanging information. In the blade aerodynamic model, 23 aerodynamic panels
are created as shown in Figure 4.28. Each aerodynamic panel has a corresponding
aerodynamic segment on the mesh (900 class sideset), to which the aerodynamic
forces and moments are supplied. More aerodynamic panels are assigned to the tip
region. The aerodynamic segmental normal force FN , chordwise force FC , and pitch
moment about the quarter chord M1/4 on the lifting line are re-distributed over the
surface to create nodal normal force fN and chordwise force fC . This re-distribution
is ad hoc at present but ensures the net moment remains the same. This is a limita-
tion of the lifting line model, not the structural model. Figure 4.29 shows the forces
108
and Equations (4.1) and (4.2) [99] give the re-distribution method. The variables
? and ? are the chordwise and normal coordinates of the surface nodes, and n is
the number of surface nodes. ?0, ?1, and ?0 are the coefficients needed to solve to
calculate fN and fC .
Figure 4.28: Aerodynamic panels corresponding to aerodynamic sideset.
Figure 4.29: Aerodynamic node forces.
?? ? ? ? ?? ??? FN ??? ??? n ? ? 0 ???????0???
???? F ? = ?C ??? ????0
2 ?? ?
? ? ?n ???????1???
(4.1)
M1/4 ? (?
2 ? ?3) ? ? ?0
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fN = ?0 + ?1?
(4.2)
fC = ?0 + ?1?
2
4.4 Blade Structural Load Calculation
Unlike the force summation method or the deflection method in a 1-D beam
model, a strain-based load calibration method is developed to extract structural
loads from the 3-D model. This method mimics the strain-based load measurement
method used during rotor tests. Instead of measured strains calculated strains are
used. As in tests, pre and post-processing are needed. In pre-processing, known
static loads (extension FX , torsion (MX), flap bending MY , and lag bending MZ)
of various magnitudes are applied to the structure one at a time. calculated strains
are output from the 800 class node and grouped as in Equation (4.3). EX , ET , EF ,
EL are axial, torsional, flap bending, and lag bending strain groups. ?xx and ?xy
are axial and in-plane shear strains. The blade structural loads can be calculated
in post-processing based on these strain groups and a calibration matrix as shown
by Equation (4.4). Since the strain groups and applied loads of each cross-section
are known, the calibration matrix K for each section can be solved. K matrix
is extracted row by row with F and M of various magnitudes, and least square
inversion is used. Similar to the strain gauge circuit of the blade structural load
sensor, this kind of strain group can enhance the strain magnitude of the correlated
load.
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?? ? ? ???EX??? ??? ? + ? + ? + ?? ? ? xxNS801 xxNS802 xxNS803 xxNS804 ?? ???ET ??
?
? ??? ?xy + ? ? ? ? ? ?? ? ? NS801 xyNS802 xyNS803 xyNS804 ?? ? = ? ???? (4.3)??EF?? ?? ?xx + ?xx ? ?NS801 NS802 xx ? ?NS803 xxNS804 ??
EL ??xx + ? ? ? + ?NS801 xxNS802 xxNS803 xxNS804
?? ? ? ????
FX ???? ????
EX?
???MX??? ???E? ? ? T ?
???
? ? = K ? ???M ?? ??E ?
?? (4.4)Y F??
MZ EL
The placement of the 800 class nodesets requires more discussion. As shown
in Figure 4.30, consider a 3-D model of a twisted aluminum beam (20? twist, 1
m long, and 0.1 m wide) and two selection of 800 class nodesets: version-1 and
version-2. Figure 4.31 and 4.32 show the axial strain and in-plane shear strain of
the beam under a combination of all four tip loads (FX = 500N , MX = 5Nm,
MY = 5Nm, MZ = 50Nm). The extracted structural loads along the span are
shown in Figure 4.33. It can be seen that two choices have a limited impact on
structural load. This conclusion also holds for a rotating beam (RPM = 955), as
shown in Figure 4.34-Figure 4.36.
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Figure 4.30: Mesh and 800 class nodesets of a twisted aluminum beam.
112
Figure 4.31: Axial strain on a twisted aluminum beam under tip loads.
Figure 4.32: In-plane shear strain on a twisted aluminum beam under tip loads.
113
(a) Axial force. (b) Torsional moment.
(c) Flap bending moment. (d) Lag bending moment.
Figure 4.33: Structural loads of a twisted aluminum beam under tip loads.
114
Figure 4.34: Axial strain on a rotating twisted aluminum beam.
Figure 4.35: In-plane shear strain on a rotating twisted aluminum beam.
115
(a) Axial force. (b) Torsional moment.
(c) Flap bending moment. (d) Lag bending moment.
Figure 4.36: Structural loads of a rotating twisted aluminum beam.
116
Now consider the present blade. Figure 4.37 shows three versions of 800 class
nodesets on the straight blade model. The third version is added to mimic precisely
the strain gauge placement during tests. Furthermore, this third version in fact uses
three distinct groups of nodesets. One each for flap, lag, and torsion.
Figure 4.37: Mesh and 800 class nodesets of the straight twisted blade.
Figure 4.38 and 4.39 show the axial strain and in-plane shear strain of the blade
under a combination of all four tip loads (FX = 500N , MX = 5Nm, MY = 5Nm,
MZ = 50Nm). The structural loads extracted using a different selection of nodesets
(Figure 4.40) are still comparable except for the 3-D effects near the root and the
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tip. However, the differences become marked in the rotating case. It can be seen
in Figure 4.43 (RPM = 993, ? ?75 = 4 ) that the structural loads extracted from the
third version of nodeset are very different from the other two versions, especially
in axial force and lag bending moment. The jumps in version-1 and -3 are due to
the presence of leading-edge weights. During pre-processing, the strain groups are
calibrated against a tip axial force, not centrifugal force. For a uniform structure
(twisted aluminum beam), the influence of centrifugal force can be captured by a
tip axial force. But not for a blade with discrete weights inside. The axial force
is applied only at the tip and then transferred to the rest of the structure, but the
centrifugal force acts everywhere. The strain concentrations caused by the weights
in presence of the centrifugal force cannot be accounted for with a static axial force
calibration. The strain patterns under a tip axial force and centrifugal force are
markedly different (Figure 4.38 and 4.41). This effect is more pronounced in the
calculation of axial force and lag bending. Moreover, the structural loads that jump
between positive and negative along the span is not physical but merely an artifact
of local strain concentration. The problem can be solved by calibrating the strain
against centrifugal force, but that is not feasible. The next best solution will be to
avoid the region of strain concentration when selecting nodes. The version-2 nodeset
is one of the solutions. The impact of these nodesets will be validated further later
with test data.
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Figure 4.38: Axial strain on the straight blade under tip loads.
Figure 4.39: In-plane shear strain on the straight blade under tip loads.
119
(a) Axial force. (b) Torsional moment.
(c) Flap bending moment. (d) Lag bending moment.
Figure 4.40: Structural loads of the straight blade under tip loads.
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Figure 4.41: Axial strain on the rotating straight blade.
Figure 4.42: In-plane shear strain on the rotating straight blade.
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(a) Axial force. (b) Torsional moment.
(c) Flap bending moment. (d) Lag bending moment.
Figure 4.43: Structural loads of the rotating straight blade.
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4.5 Summary
This chapter presented the development of the 3-D blade model. The special
features in the geometric model needed for mesh generation were highlighted. The
process for meshing the 3-D blade structural model was detailed. Structural models
for the straight blade and the double anhedral blade were formulated. The lifting line
model was set up for aerodynamic calculation. A structural load calibration method
was described with several options of sensor placement and the best placement was
identified.
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Chapter 5: Rotor Tests and Model Validation
The 10-ft vacuum chamber was used to test the blades without aerodynamic
effects. The objectives were to measure rotating natural frequencies and 3-D strains.
This was followed by hover tests. The test procedures, post-processing, and the
data acquired are detailed in this chapter. The data is used to validate the 3-D
structural model, aerodynamic model, and aero-structural interface of the double
anhedral blade systematically.
5.1 Vacuum Chamber Test
5.1.1 Test Procedure
The rotating blade natural frequencies and strains were measured with two
test procedures. For the frequency test:
1. The vacuum chamber hub was mounted on the vacuum chamber shaft via four
shoulder bolts, as shown in Figure 3.6. Then the slipring wires were connected
to the PCB on both sides of the hub. A connectivity check was performed to
the hub PCB terminals (Figure 3.26) and the slipring non-rotating end wires
with a multimeter.
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2. The hub strain gauge (Figure 3.26) and shaker were connected to the data
acquisition system via the hub PCB terminals and the slipring. The hub strain
gauge was checked at the slipring non-rotating end with a multimeter to see
if the resistance value is as expected (350 ?). Next, the function generator
(Figure 3.27) was turned on and the excitation frequency was set. As the
shaker operates, the frequencies were picked up by the hub strain gauge. This
was a check of the frequency excitation system.
3. The slipring wires connected to the hub were secured with aluminum taps.
Then the hub was spun up at a low speed. The rotational speed measured
by the RPM sensor (Figure 3.4) was checked against a tachometer. Next,
excitation frequency sweeps were performed. The sweeps were performed at
multiple rotor speeds to check if the shaker, the hub strain gauge, and the
data acquisition system work properly when the hub is spinning.
4. The blades were installed in the blade adapters with three shoulder bolts and
locknuts (Figure 3.10). Then the blade root pitch was adjusted to zero degrees
by changing the length of the pitch links (Figure 3.12).
5. The blade strain gauges were connected to the data acquisition system via
the hub PCB terminals and the slipring. All of the blade strain gauges were
checked at the slipring non-rotating end with a multimeter to see if the resis-
tance value is as expected (350 ?). Next, simple tip static load was applied
to the blade to examine if the measured strain is as expected. The wires were
secured on the hub with aluminum tapes. The final test setup is shown in
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Figure 5.1.
Figure 5.1: Final setup of the frequency test.
6. After the chamber entry and air outlet was sealed, the air pump was turned
on to vacuum the chamber. The chamber was considered vacuumed when the
chamber pressure indicated by the pressure gauge (Figure 3.3(b)) was below
0.3 inch Hg (? 99% vacuum). This process took about 20 minutes. The low-
pressure level can be maintained for at least 30 minutes, which was enough to
perform multiple tests.
7. The rotor speed was adjusted to the target value via the motor controller
(Figure 3.4). As the rotor speed became stable, an excitation frequency sweep
was performed. Meanwhile, the time history of the hub strain and blade strains
were recorded. This process was repeated for multiple rotor speeds, including
zero rotor speed.
8. Only two blades can be tested in a test. So, steps 4-7 were repeated with the
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other two blades to examine the repeatability of the test and the similarity of
the blades.
For the strain test:
1. The shaker was replaced by the aluminum block (Figure 3.20), and the blade
root pitch was fixed at 5.6?.
2. The blade installation and chamber vacuuming steps are the same as steps 3-6
in the frequency test.
3. After the chamber was vacuumed, the rotor was spun up at the lowest con-
trollable speed. A baseline case was recorded at this rotor speed. Due to the
rotation, the brush in the slipring might change the overall resistance of the
strain measurement system. Hence, the strain signal at the lowest controllable
rotor speed was used as the baseline. Because the rotor speed was low, the
centrifugal force was negligible at this point.
4. Rotation speed sweep was performed. Once the rotor speed stabilized at the
desired value, 3 seconds of strain data were recorded.
5. The position of two test blades was swapped, and then the test was repeated.
All four blades were tested eventually.
5.1.2 Data Processing
The raw data from the frequency tests were strains versus time. The data
was first passed through a low pass filter with the highest excitation frequency (300
127
Hz) as the threshold. Then frequencies were extracted using Fast Fourier Transform
(FFT). In Figure 5.2, the frequency spectrum of a blade spinning at 200 RPM is
shown as an example. The peaks at multiples of the excitation voltage (120 Hz and
240 Hz) were discarded. The remaining peaks were from blade dynamics.
Figure 5.2: Frequency spectrum of strain signal at 200 RPM.
The data from the strain test was first subtracted by the strain of the baseline
case. The subtracted raw strain data from the strain rosette at the top surface of
30%R are shown in Figure 5.3. These strain data of gauge 1-3 were measured in the
local axis (Figure 5.4), then they were transformed to axial ?xx, chordwise ?yy, and
in-plane shear ?xy strain using Equation (2.3).
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Figure 5.3: Raw strain signals.
Figure 5.4: Strain rosette diagram.
5.1.3 Data Analysis and Model Validation
The measured frequencies and the X3D predictions are shown in Figure 5.5.
The markers represent measured frequencies, and the different colors correspond to
different blades. Up to seven non-rotating frequencies and six rotating frequencies
were captured. The vacuum chamber motor limits the rotor speed range. The solid
129
lines are the predicted frequencies. The dashed lines are the constant per-revolution
frequencies. The 900 Nm/rad flap and lag root stiffness and the 75 Nm/rad pitch
stiffness were considered in the prediction. The predictions match well with the
test data except for the highest mode. The cross-over of the first two modes is also
observed. By analyzing the mode shape in X3D, each mode was identified. The
second lag frequency could not be measured. Due to the high lag stiffness, the test
could not excite the second lag mode. The test data is documented in Appendix B.1
Figure 5.5: Fan plot of the double anhedral blade: symbols are measurements; solid
lines are predictions.
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The measured strains on the top surface at 30%R are shown in Figure 5.7. Ax-
ial ?xx, chordwise ?yy, and in-plane shear ?xy strains were measured. Measurements
from multiple blades are shown (markers). The error bars illustrate the differences
introduced by ?2? of strain gauge misalignment. It can be seen that there is gener-
ally good repeatability between blades. However, large discrepancies are observed
when comparing the data from the two arms (Figure 5.6). The X3D prediction is
overlaid in the figure (lines). The solid lines are from the baseline model with no
pre-cone angle. Examination of the discrepancies revealed that the vacuum chamber
hub had in fact a ?1? to ?2? of pre-cone angle at the end block. When the pre-cone
angle was included in the model (dash line), the agreement between test data and
prediction became satisfactory. The predictions with pre-cones show that the 3-D
structural model captures the impact of such un-intended imperfections.
Figure 5.6: Arms of the vacuum chamber hub.
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(a) Vacuum chamber hub arm 1.
(b) Vacuum chamber hub arm 2.
Figure 5.7: Rotating strains on the top surface at 30%R: symbols are measurements;
lines are predictions.
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5.2 Hover Test
5.2.1 Test Procedure
The hover test procedure considers the following steps.
1. Stand sensors and actuators were connected directly to the National Instru-
ments SCXI system. These stand sensors and actuators were a hub balance, a
rotor speed sensor, an encoder, and three swashplate actuators. The rotating
frame sensors were the four pitch sensors, four pitch link load cells, and a
torque sensor. They were connected to the PCB in the hub cap. From these
goes to the slipring and thereafter the data acquisition system. The encoder
signal was calibrated against the azimuth angle by rotating the hub manually
to acquire the relation shown in Figure 3.40. The hub cap was then closed
and wires secured with tapes.
2. The motor hydraulic hoses were connected from the hydraulic pump to the
hydraulic motor, the cooling inlet hose from the water tap to the hydraulic
pump, and the cooling outlet hose from the hydraulic pump to the water sink.
A simple motor check was performed. The hub (no blades yet) was spun up at
the lowest controllable speed. The hydraulic pump temperature was monitored
to see if the cooling system works properly. The temperature should remain
below 100?F.
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3. A rotor speed sweep from 300 to 2300 RPM was performed, and hub loads were
recorded. The hub loads data was processed to look for the 1/rev component.
Then counterweights were attached on the side of the hub cap to eliminate
the 1/rev hub load. Tungsten alloy leading-edge weights were used as the
counterweights (Figure 5.8). The counterweights must be secured carefully
with aluminum tapes and superglue to withstand the enormous centrifugal
force.
Figure 5.8: Hover stand hub balancing.
4. Tests to acquire hub tare data were performed. Hub tare data is hub loads
of the isolated hub (no blades) at different rotor speeds. First, baseline hub
load signals were saved. The baseline hub loads are the hub loads when the
rotational speed is zero. Then the hub was spun up to a target rotor speed,
and the hub loads were recorded. This step was repeated from 300 to 2300
RPM. The hub tare data was acquired by subtracting the baseline hub loads
from the rotating hub loads.
134
5. The hover stand was moved up on the hover tower, which raised the rotor 12
ft (4.3R) about the ground out of the ground effect region. The high bay crane
was used to lift the hover stand. Extra care should be taken in this step to
keep the hover stand as well as the operators safe. Kevlar straps were lashed
on the stand pole (near the center of gravity) and wrapped around the hub
before being hooked on the crane. When the hover stand rested on the tower,
the connection bolts were tightened.
6. The double anhedral blades were mounted on the blade grips with three shoul-
der bolts and locknuts with an external-tooth lock washer. Then the root pitch
hall effect sensors were calibrated. The calibration method was described in
section 3.2.2. After leveling the swashplate, the length of the pitch links was
adjusted to equalize the pitch angles. The range of collective and cyclic angles
is also determined by the length of the pitch links. Next, the blade sensors were
connected to the hub cap PCB, and the signals were checked in the LabVIEW
program before securing the sensor wires.
7. The blade tracking was performed. The objective of blade tracking is to ensure
the aerodynamic similarity between blades. To this end, a tracking procedure
was followed. Reflective tapes of different colors were attached to the blade
tips, as shown in Figure 5.9. Then a high-intensity strobe light was placed on
the outside frame in the hub rotating plane and pointed at the hub center.
Due to the four-bladed configuration, the reflective tapes will appear to be
frozen at a certain azimuth angle when the strobe frequency equals four times
135
the rotational frequency. As shown in Figure 5.10, four tapes overlap closely,
indicating that the blades are well tracked. In other word, the tips are following
the same path in space. Otherwise, adjustment of pitch link length is required,
and the tracking process was repeated until all blades follow the same tip paths.
Figure 5.9: Reflective tapes for blade tracking.
Figure 5.10: Blade tracking.
8. The last step before the rotor test was fuselage assembling. An existing 3D-
printed fuselage was used as a fairing to shield the internal structure and
improve the smoothness of the flow field. The fuselage was originally printed
in four pieces: nose, two side panels, and tail, and at least two operators were
needed to assemble it safely. The fabrication of the fuselage was not part of
this research. The final hover test setup is shown in Figure 5.11.
136
Figure 5.11: Final setup of the hover test.
Figure 5.12: Fan plot of the hingeless rotor; the vertical lines are the RPM selected.
137
9. From the predicted fan plot (Figure 5.12), three rotor tip Mach numbers of 0.4,
0.5, and 0.6 were selected. The temperature and pressure were also measured.
10. Before the rotor was spun up, all of the sensor signals were recorded, and
this case was used as a baseline. Then the rotor speed was increased to the
target RPM. Once the rotor speed stabilized, the collective was adjusted to
the desired value. While adjusting collective, the rotor speed might vary as
well due to the change in rotor torque, hence, adjustment of the rotor speed
was also needed. The rotor was trimmed with cyclic controls. For a hingeless
rotor, it is hard to use blade flap motion as an indicator of rotor trim. In this
test, the 1/rev flap bending moment was used as the trim target. The rotor
was trimmed to minimize the 1/rev flap bending moment. Three seconds of
data were saved before moving on to the next collective setting. During the
test, the hydraulic pump temperature was kept below 140?F .
5.2.2 Data Processing
The tip Mach number and blade loading envelope are shown in Figure 5.13.
There are 80 test points in the collective sweep test. The raw data from each
hover test point were stored in the form of voltage. The high-frequency harmonics
(? 100Hz) were first removed by a low pass filter. There is a three-second time
history record for each test point containing 76, 95, 114 revolutions for 0.4, 0.5, and
0.6 Mtip respectively. By clocking the signals to azimuth angles, multiple revolutions
of data were merged to improve the signal-noise ratio. Then, the data from the
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baseline case (the non-rotating case) were subtracted. The voltage signals were
transferred to physical quantities by the calibration matrices. The hub tare data
was subtracted from the hub loads, while an azimuth shift was performed for pitch
link loads, blade loads, and blade stains.
Figure 5.13: Hover test envelope.
5.2.3 Data Correlation with Prediction
The rotor hover performance is shown in terms of collective, thrust CT/?, and
power CP/?. Figure of Merit (FM) is calculated from thrust and power. Figures 5.14
and 5.15 shown blade loading and power coefficient versus collective, respectively.
The markers with different shapes are test data at different tip Mach numbers. The
dashed lines are X3D predictions. It can be seen that the non-dimensional hover
performance is not sensitive over this range of tip Mach numbers. The blade loading
increases with collective linearly, and power grows quadratically.
139
Figure 5.14: Blade loading vs. collective.
Figure 5.15: Power coefficient vs. collective.
140
Figure 5.16 plots power versus thrust, and the curve fit was used to acquire Cd0
for analysis correction, which is 0.016. This model rotor is quite efficient as shown
in Figure 5.17. There is no stall observed in the test range. And the maximum
Figure of Merit (Equation (5.1)) is 0.713, which occurs at a blade loading of 0.117.
Thus a high Figure of Merit can be achieved on a scale model rotor when properly
designed. The agreement of test data and predictions is satisfactory. The test data
is documented in Appendix B.2
Figure 5.16: Power vs. Thrust.
141
3/2 ?
CT / 2FM = (5.1)
CP
Figure 5.17: Figure of Merit vs. blade loading.
Blade flap bending moments measured at 40%R are shown in Figure 5.18.
The test data is indicated by markers. Different colors represent different tip Mach
numbers. The flap bending moment is positive when the blade bends up. The flap
bending moment increases with collective due to the obvious increase in lift. But it
decreases with tip Mach number due to an increase in the centrifugal force, which
relieves the moment. The prediction captures the general trend. However, there is
discrepancies in the magnitude.
Blade lag bending moments measured at 40%R are shown in Figure 5.19.
Positive bending is toward the trailing edge. The magnitude of lag bending moment
at 40%R shows no change with collective, but it increases with tip Mach number due
142
to increased drag. However, not significant enough to impact torque. The prediction
of lag bending moments matches well with the measurements.
Figure 5.18: Flap bending moment at 40%R (test vs. prediction).
Figure 5.19: Lag bending moment at 40%R.
143
The torsional moment test data measured at 40%R, shown in Figure 5.20. It
is also not sensitive to collective but grows with rotor speed. However, unlike lag,
the prediction does not agree with the measurement. The absolute magnitudes are
close, but the trend with tip Mach number is flipped. The positive values indicate
a nose-up twist. Yet the pitch link loads are nose down in compression, as shown
in Figure 5.21. Surprisingly the prediction here agrees with the measurement. The
pitch link loads grow with both collective and Mach number. The agreement is
reasonable, though not entirely satisfactory. Based on the agreement of flap, lag
bending, and pitch link load, it is reasonable to assume the errors in torsional
moment validation are from measurements, not prediction. There are discrepancies
in the slope of the pitch link loads. More vacuum tests focused on torsion loads,
and high-fidelity 3-D CFD aerodynamics is recommended to resolve the apparent
mystery.
As discussed in section 4.4, the placement of 800 class nodesets had a large
impact on the structural load extraction. The loads predicted in Figure 5.18-5.20
were extracted with the version-3 800 class nodesets shown in Figure 5.22 (same
as version-3 Figure 4.37). These nodesets are intended to mimic the strain gauge
placement in the test. However, as discussed in section 4.4, the loads calculated (test
and prediction) based on strains extracted from these locations are contaminated
with local strain concentration. Thus, though the extracted loads from version-3
nodesets have a satisfactory agreement with test data, this nodeset was not used
in further analysis. The version-2 nodesets selected nodes avoiding concentration
region was used instead, which give more physical structural loads.
144
Figure 5.20: Torsional moment at 40%R.
Figure 5.21: Pitch link load vs. collective.
145
Figure 5.22: Two version of 800 class nodesets.
Measured Strains from the top surface at 30%R reveal a clear pattern (Fig-
ure 5.23). The axial strain ?xx decreases as the collective angle increases. The
extension generated by the centrifugal force is countered by the compression gener-
ated by the lift. As the tip Mach number increases, the centrifugal force outweighs
that of the lift. Therefore, the axial strain increases. The chordwise strain behaves
in the opposite fashion due to the local Poisson?s ratio effect. The in-plane shear
strain ?xy always remains low. The solid and dash lines are predictions of two tip
Mach numbers, respectively. The agreement is satisfactory as both magnitude and
trends are captured.
Compared to the strain near the root, measured strains on the bottom surface
at 80%R near the anhedral junction (Figure 5.24) are much lower and much harder
to predict. The data is also more scattered due to the low magnitude. However, some
trends can be identified. Both centrifugal force and the lift generate extension at this
location, which of course, grows with the rotor speed. So the axial strain increases
as the rotor speed increases. The magnitude of the in-plane shear is comparable to
the normal strains. The agreement between prediction and test data degraded at
146
this location due to the generally low magnitude of strain. But the trend was still
captured.
Figure 5.23: Mean Strain on the top surface of 30%R.
Figure 5.24: Mean Strain on the bottom surface of 80%R.
147
5.3 Summary
In this chapter, the vacuum chamber test and hover test results were described.
The test procedure of the vacuum chamber test and hover test as well as the data
processing method were described in detail. Blade natural frequencies and surface
strains were measured in the vacuum chamber test. Rotor performance, structural
loads, and strains were measured in the hover test. The test data was used to
validate the 3-D blade model developed in Chapter 4. The 3-D blade structural
model is validated with the measured fanplot and strains. The prediction of rotor
performance, flap bending moment, lag bending moment, pitch link load, and surface
strains are satisfactory. Strain-load calibration revealed the importance of sensor
placement. Complex blades have regions of strain concentration and these are to be
avoided. The torsional moment and pitch link load were inconsistent. More vacuum
tests and 3-D CFD analyses are recommended to understand this behavior. At this
point, the 3-D blade model is ready for further analysis of the influence of the double
anhedral tip.
148
Chapter 6: Comparison of Straight and Double Anhedral Blades
The comparison of the straight and double anhedral rotor is analyzed in this
chapter. Due to the lack of resources and the closure of the Glenn L. Martin wind
tunnel, no straight blades could be built, and no forward flight tests could be carried
out. So analysis remained the only option available for comparison. A straight rotor
model is used as a baseline for comparison (Figure 6.1). Frequency, performance,
structural loads, and strain/stress are studied.
Figure 6.1: Straight and double anhedral blades; same twist of ?16?
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6.1 Blade Natural Frequencies and Mode Shapes
The influence of the double anhedral tip on natural frequencies is shown in
Figure 6.2. These frequencies are generated using the 3-D structural model while
assuming the blade roots are rigid and the collective pitch at 75%R is zero. The
solid lines are the double anhedral blade frequencies, whereas the dotted lines are the
straight blade frequencies. Both blades have the same twist. The thin dashed lines
are constant per-revolution frequencies. There is a negligible difference in the first
frequency. The effect of the tip geometry starts to show from the second frequency
and becomes significant in all higher frequencies thereafter. The double anhedral
blade frequencies are lower than the straight blade frequencies. The local center of
gravity offset in the normal direction at the tip appears to make the blade softer.
The dominant motion in each mode can be identified by examining the mode
shape. A comparison of the first five mode shapes at 1522 RPM is shown in Fig-
ures 6.3-6.12. The first frequency of the straight and double anhedral blades are
1.32/rev and 1.29/rev respectively. The mode shapes of both are dominated by flap
bending. Due to the twist, there is also some lag motion in the first mode but it is
small (Figure 6.3 and 6.4, see side view). Mode two is the first lag mode (Figure 6.5
and 6.6). Here the lag motion is clearly visible. Mode three is the second flap (Fig-
ure 6.7 and 6.8), and mode four is the third flap (Figure 6.9 and 6.10). Mode five is
the first torsional mode (Figure 6.11 and 6.12). Since the magnitude of mode shape
is arbitrary, the direction of twist is immaterial. The main conclusion is that the
double anhedral tip does not appear to introduce any new mode or coupling. It is
150
the frequencies that differentiate the designs.
Figure 6.2: Fan plot of straight blade (solid lines) compared to double anhedral
blade (dotted lines). Rigid root, ? ?75 = 0 .
151
Figure 6.3: Straight blade mode 1; first flap (1.32/rev).
Figure 6.4: Double anhedral blade mode 1; first flap (1.29/rev).
152
Figure 6.5: Straight blade mode 2; first lag (2.62/rev).
Figure 6.6: Double anhedral blade mode 2; first lag (2.32/rev).
153
Figure 6.7: Straight blade mode 3; second flap (4.07/rev).
Figure 6.8: Double anhedral blade mode 3; second flap (3.8/rev).
154
Figure 6.9: Straight blade mode 4; third flap (8.9/rev).
Figure 6.10: Double anhedral blade mode 4; third flap (8.12/rev).
155
Figure 6.11: Straight blade mode 5; first torsion (11.07/rev).
Figure 6.12: Double anhedral blade mode 5; first torsion (10.64/rev).
156
6.2 Strains in Vacuum
The straight and double anhedral blades have markedly different strain distri-
butions. The strain distributions in vacuum at a speed of 1522 RPM and a collective
of 0? are shown in Figures 6.13-6.17. The comparison of axial strain ?xx, in-plane
shear strain ?xy, and out-of-plane strain ?zz are presented. The indices refer to the
rotating frame coordinate: the X-direction is oriented axially along the radius of the
un-deformed blade and positive toward the tip, the Z-direction is pointing vertically
upward in the direction of nominal thrust, and the Y-direction follows the right-
hand rule, hence in the rotating plane pointing in the direction of the leading-edge.
In each figure, the left-hand sub-figure shows the surface strain distribution, and the
right-hand sub-figure shows the cross-section strains at 30%R, 50%R, 80%R, and
95%R along with the strains in the D-spar. It can be observed that there are strong
3-D patterns in the strains. Due to the centrifugal force, the axial strain decreases
from the root toward the tip. The strain concentrations near the leading-edge are
caused by the discrete leading-edge weights. The root axial strain of the double
anhedral blade is much higher than the straight blade (Figure 6.13 and 6.14). The
double anhedral blade also has a compression region at the dihedral junction. Both
of these phenomena are caused by the vertical center of gravity (C.G.) offset of the
double anhedral tip, which introduces an additional bending moment via centrifugal
force.
157
Figure 6.13: Predicted axial strain ?xx distribution in vacuum for straight blade
(1522 RPM).
Figure 6.14: Predicted axial strain ?xx distribution in vacuum for double anhedral
blade (1522 RPM).
158
The in-plane shear strain (Figure 6.15 and 6.16) magnitudes are small in both
blades. A pair of strain concentration zones occur at the top surface near the root of
both blades. The shear strain reflects that there is a torsional moment near the root.
This torsional moment is the propeller moment. Moving outboard, there is limited
impact of the tip geometry on the strain patterns. From midspan to the tip, the D-
spar carries most of the shear strain. At the tip of the double anhedral blade, strain
concentrations appear in the dihedral portion. These concentrations indicate that
the C.G. offset also introduces additional propeller moment. Figure 6.17 compares
the out-of-plane strain distribution. Out-of-plane strain can represent inter-laminar
strain to a certain extent. This type of strain is important in a composite material as
it relates to delamination. There is no out-of-plane strain on the surface, naturally
only the internal strain is shown. The out-of-plane strain only increases at the
dihedral and anhedral junctions. The absolute magnitude is still too low to be of
any concern.
159
Figure 6.15: Predicted in-plane shear strain ?xy distribution in vacuum for straight
blade (1522 RPM).
Figure 6.16: Predicted in-plane shear strain ?xy distribution in vacuum for double
anhedral blade (1522 RPM).
160
Figure 6.17: Predicted out-of-plane strain ?zz distribution in vacuum (1522 RPM;
left: straight blade; right: double anhedral blade).
6.3 Hover Analysis
6.3.1 Rotor Performance
Hover performance is presented as power coefficient (CP/?) and Figure of
Merit (FM) variation with blade loading (CT/?). As shown in Figure 6.18 and 6.19,
the influence of the double anhedral tip on the power coefficient is negligible, and
the highest Figure of Merit is improved by a minuscule 0.7% near the blade loading
of 0.117. This might simply be an artifact of the essentially 2D nature of the lifting
line model. More differences might occur when 3D CFD is brought to bear instead
of freewake model.
161
Figure 6.18: Power versus blade loading. Mtip = 0.4.
Figure 6.19: Figure of Merit versus blade loading. Mtip = 0.4.
162
6.3.2 Blade Structural Loads
Figure 6.20 shows the axial force at 30%R, 50%R, and 70%R. The solid lines
represent the straight blade, while the dash lines represent the double anhedral
blade. The axial force is mainly the centrifugal force, hence, it decreases from root
to tip as expected, and it is not sensitive to the collective angle. The axial force
on the double anhedral blade is slightly higher because the tip mass of the double
anhedral blade is slightly higher.
Figure 6.20: Comparison of axial force.Mtip = 0.4.
In Figure 6.21, the flap bending moment at inboard (30%R), midspan (50%R),
and outboard (70%R) are compared. The positive flap bending moment indicates
a bending up. The flap bending moments near the root increase with collective
due to the obvious increase in lift. Moving outboard, the flap bending moment
of the straight blade decreases, and the sensitivity to the collective also reduce.
163
For the double anhedral blade, the bending moment is always lower, and at the
outboard portion significantly downward. The lack of variation with collective indi-
cates that the difference is not due to aerodynamics, but centrifugal force. As shown
in Figure 6.22, the vertical C.G. offset of the double anhedral portion generates a
centrifugal force which generates a downward bending moment. The inboard and
midspan flap bending moment is reduced by this downward bending moment. The
outboard moment is dominated by this downward moment.
The lag bending moment comparison is shown in Figure 6.23. The positive
lag bending moment means the blade is bending toward the trailing edge. Com-
pared to the straight blade, the lag bending moment of the double anhedral blade
decreases substantially throughout the span. The reduction decreases outboard.
This reduction is also related to the out-of-plane C.G. offset. At positive collectives,
the vertical C.G. offset generates an aft-C.G. offset, as shown in Figure 6.24. This
aft-C.G. offset generates a lead-lag moment via the centrifugal force, which counters
the lag moment from the drag.
164
(a) Flap bending moment at 30%R.
(b) Flap bending moment at 50%R.
(c) Flap bending moment at 70%R.
Figure 6.21: Flap bending moment in hover. Straight blade versus double anhedral
blade. Mtip = 0.4.
Figure 6.22: Diagram of flap bending moment on the double anhedral blade.
165
(a) Lag bending moment at 30%R.
(b) Lag bending moment at 50%R.
(c) Lag bending moment at 70%R.
Figure 6.23: Lag bending moment in hover: Straight blade versus double anhedral
blade. Mtip = 0.4.
166
(a)
(b)
Figure 6.24: Diagrams of lag bending moment on the double anhedral blade.
The situation is different for torsion moment (Figure 6.25). Throughout the
blade span, the torsion moment is nose down (negative) for both blades. In the
inboard portion, both torsion moments grow with collective due to the increase in
propeller moment. In this region, the torsion moment of the double anhedral blade
is nose up compared to the straight blade. This can be explained by the additional
propeller moment introduced by the double anhedral tip shown in Figure 6.26. Due
to the C.G. offset, there is an additional propeller moment acting at the tip which
is a nose up moment. While the rest of the blade generates a nose down propeller
moment, this nose up moment reduces the torsion moment near the root. However,
midspan out the torsion moment of the double anhedral blade is nose down compared
to the straight blade. In this region, the opposite propeller moment from the tip
and the straight portion further twist the blade, hence, increasing the blade torsion
167
moment.
(a) Torsion moment at 30%R.
(b) Torsion moment at 50%R.
(c) Torsion moment at 70%R.
Figure 6.25: Torsion moment in hover. Straight blade versus double anhedral blade.
Mtip = 0.4.
168
(a)
(b)
Figure 6.26: Diagrams of torsion moment on the double anhedral blade.
The impact of double anhedral on the blade torsion moment is reflected in the
pitch link load (Figure 6.27). The double anhedral decrease the magnitude of pitch
link load, and the reduction grows with the collective. This is also due to the nose
up propeller moment at the tip countering the nominal nose down propeller moment
from the rest of the blade (Figure 6.28).
169
Figure 6.27: Pitch link load in hover. Straight blade versus double anhedral blade.
Mtip = 0.4.
Figure 6.28: Propeller moment direction of the straight and double anhedral blades.
170
6.3.3 Blade Strain/stress
The prediction of blade axial strain ?xx distributions in hover are shown in
Figures 6.29 and 6.30. Both rotors are operating at 1522 RPM (Mtip = 0.4) and a
collective of 10? (CT/? = 0.117). The left subfigures show the blade undeformed
(dotted mesh) and deformed geometry and the surface strains. The right-hand
subfigures show the internal strain at 30%R, 50%R, 80%R, and 95%R, along with
the strains in the D-span. The main deformation is the bending up due to lift.
Therefore, there are high negative and positive axial strains on the top and bottom
surfaces respectively. Due to the drag, the positive strain at the leading-edge in the
inboard-midspan region is much higher now compared to the vacuum strains. The
double anhedral blade has a high positive axial strain region inboard of the dihedral
junction. Figure 6.31 compares the internal axial stress ?xx. In the inboard region,
the loads are shared by the skin and spar for both blades. However, the load in the
outboard portion of the double anhedral blade is mainly carried by the skin.
171
Figure 6.29: Axial strain ?xx distribution of straight blade. CT/? = 0.117, Mtip =
0.4.
Figure 6.30: Axial strain ?xx distribution of double anhedral blade. CT/? = 0.117,
Mtip = 0.4.
172
Figure 6.31: Internal axial stress ?xx distribution. CT/? = 0.117, Mtip = 0.4.
Figures 6.32-6.34 show the in-plane shear strain ?xy and stress ?xy. These
strain magnitudes are comparable to that of vacuum. But higher shear strains
occur near the trailing edge in the inboard to midspan region for the straight blade,
and this region expands to the outboard for the double anhedral blade. The strain
pattern in the tip portion of the double anhedral blade is similar to the pattern in
vacuum. The internal in-plane shear stress is shown in Figure 6.34. It is clear that
the majority of shear stress is carried by the skin, especially for the dihedral and
the anhedral junction. The out-of-plane strain ?zz and stress ?zz are examined in
Figures 6.35 and 6.36. The double anhedral tip geometry increases the strain at the
dihedral and anhedral junctions slightly, and the out-of-plane stresses are carried by
the D-spar.
173
Figure 6.32: In-plane shear strain ?xy distribution of straight blade. CT/? = 0.117,
Mtip = 0.4.
Figure 6.33: In-plane shear strain ?xy distribution of double anhedral blade. CT/? =
0.117, Mtip = 0.4.
174
Figure 6.34: Internal in-plane shear stress ?xy distribution. CT/? = 0.117, Mtip =
0.4.
Figure 6.35: Out-of-plane strain ?zz distribution of straight blade and double an-
hedral blade. CT/? = 0.117, Mtip = 0.4.
175
Figure 6.36: Out-of-plane stress ?zz distribution of straight blade and double an-
hedral blade. CT/? = 0.117, Mtip = 0.4.
6.4 Forward Flight Analysis
The influence of double anhedral tip in forward flight is studied in this section.
The rotors operate at 1522 RPM (Mtip = 0.4) with a forward shaft tilt of 4
?. At
each tip speed ratio (? = V/?R), the trim target is blade loading (CT/?) of 0.1 and
zero hub moments (CMX/? = 0, CMY /? = 0) accomplished by the collective (?75)
and cyclic (?1C , ?1S) angles.
6.4.1 Rotor Performance
The rotor power, drag, and trim controls are studied. The rotor performance
metric in forward flight is the effective lift-to-drag ratio (L/De). The definition of
this parameter is given by Equation (6.1).
176
?CL
L/De = (6.1)
CQ ? ?CX
where CL is lift coefficient, CQ is torque coefficient, CX is propulsive force
coefficient, and ? = V?/?R is tip speed ratio (Figure 6.37).
Figure 6.37: Diagram of rotor in forward flight.
Figure 6.38 presents the effective lift-to-drag ratio variation with advance ratio.
The solid line is the straight rotor, while the dash line is the double anhedral rotor.
In this range of tip speed ratio (0.05-0.3), the effective lift-to-drag ratio increases
with forward flight speed as is typical of any rotor. The performance of the straight
rotor is higher, and the difference worsens with tip speed ratio. At the tip speed ratio
of 0.3, the L/De of the straight rotor is 16.7% higher. These differences is mainly
due to the higher propulsive force of the straight rotor, as shown in Figure 6.39. The
rotor torque between two rotors is very similar (Figure 6.40). The control angles
needed to trim the rotors are shown in Figure 6.41. The control angles are very
similar throughout the advance ratio range.
177
Figure 6.38: Rotor effective lift-to-drag ratio (Mtip = 0.4, ?s = 4
?, CT/? = 0.1).
Figure 6.39: Rotor propulsive force coefficient (Mtip = 0.4, ?s = 4
?, CT/? = 0.1).
178
Figure 6.40: Rotor torque coefficient (Mtip = 0.4, ?
?
s = 4 , CT/? = 0.1).
Figure 6.41: Trimmed forward flight control (M = 0.4, ? = 4?tip s , CT/? = 0.1).
179
6.4.2 Hub Vibratory Loads
The hub H force FH and side force FY are combined into in-plane hub force
F , and roll moment MX and pitch moment MY into a net hub moment M as shown
in Equations (6.2) and (6.3).
?
F (?) = FH(?)2 + FY (?)2 (6.2)
?
M(?) = MX(?)2 +M (?)2Y (6.3)
The dimensional and non-dimensional vibratory hub loads are shown in Fig-
ures 6.42 and 6.43. The hub loads are non-dimensionalized by the mean thrust.
The solid and dash lines represent the straight rotor and the double anhedral rotor
respectively. Since both rotors are four-bladed, only 4/rev (black lines) and 8/rev
(red lines) hub loads are shown.
Figures 6.42(a) and 6.43(a) shows the in-plane vibratory hub force variation
with tip speed ratio. Both rotors have the same trend of 4/rev and 8/rev compo-
nents. The 4/rev in-plane vibratory hub force increase initially and reach a peak at
the tip speed ratio of 0.1, then decrease with the tip speed ratio. As for the 8/rev
component, it grows as the tip speed ratio increase, but the magnitude is negligi-
ble compared to the 4/rev component. The vertical vibratory hub force is given in
Figure 6.42(b). The trend is similar to the in-plane force, but the magnitude is 5
times higher. This is typical of rotors. The 4/rev of the double anhedral rotor is
180
15% higher at the low tip speed ratio peak. Greater differences between two rotors
appear in the vibratory hub moment (Figure 6.42(c)). At a tip speed ratio of 0.1,
the 4/rev vibratory hub moment of the double anhedral rotor is twice as high as the
straight rotor. Vibratory loads at a high tip speed ratio require 3-D tip transonic
pitching moments which are beyond the capability of lifting line models. Never-
theless, the increase in ?1S and consequent 3/rev lift gives rise to a 4/rev moment
at high tip speed ratios. The trend of 4/rev vibratory torque typically follows the
vertical force, which increases by 18% with the double anhedral tip.
(a) In-plane force
181
(b) Vertical force
(c) Hub moment
182
(d) Torque
Figure 6.42: Hub 4/rev and 8/rev vibratory loads (Mtip = 0.4, ?s = 4
?, CT/? = 0.1).
(a) Non-dimensional in-plane force
183
(b) Non-dimensional vertical force
(c) Non-dimensional hub moment
184
(d) Non-dimensional torque
Figure 6.43: Non-dimensional hub 4/rev and 8/rev vibratory loads (Mtip = 0.4,
? ?s = 4 , CT/? = 0.1).
6.4.3 Blade Structural Loads
Structural load is an important aspect of design, especially for a hingeless
rotor. The flap bending moment azimuthal variations in Figure 6.44 are extracted
from 30%R (black lines) and 50%R (red lines). The solid lines are the straight blade,
while the dash lines are the double anhedral blade. The mean flap bending moment
of the double anhedral blade is lower than the straight blade at both 30%R and
50%R, which is consistent with the conclusion drawn from hover analysis.
The oscillatory flap moments at 30%R and 50%R variation with tip speed ratio
are shown in Figures 6.45. The solid and dash lines are the straight blade and the
double anhedral blade respectively. At 30%R, flap bending moments are dominated
185
by a 1/rev component when the tip speed ratio is low. The double anhedral blade
1/rev component is much stronger than the straight blade at ? = 0.1. As the tip
speed ratio increases, 1/rev and 2/rev components are comparable. The higher
harmonics components (3/rev and 4/rev) always remain at a low level. At 50%R,
the flap bending moments are dominated by the 1/rev component except for the
lowest tip speed ratio case. The impact of the double anhedral tip is limited at this
spanwise location. These indicate that the high vibratory hub load of the double
anhedral blade at a tip speed ratio of 0.1 is due to the high 1/rev flap bending
moment.
The legends used in Figures 6.46 and 6.47 are the same as in Figures 6.44
and 6.45. The peak-to-peak magnitude of lag bending moment increase with the
tip speed ratio (Figure 6.46). Regardless of the spanwise location, the lag bending
moments are dominated by the 2/rev component as shown in Figure 6.47. Its
magnitude at 30%R first decreased by 20% when ? = 0.1 then increased by 2.5 times
when ? = 0.3. The double anhedral blade always has a higher 2/rev oscillatory lag
bending moment.
186
(a) ? = 0.1
(b) ? = 0.3
Figure 6.44: Flap bending moment versus azimuth (Mtip = 0.4, ? = 4
?
s , CT/? =
0.1).
187
(a) r = 30%R
(b) r = 50%R
Figure 6.45: Oscillatory flap bending moment versus tip speed ratio (Mtip = 0.4,
?s = 4
?, CT/? = 0.1).
188
(a) ? = 0.1
(b) ? = 0.3
Figure 6.46: Lag bending moment versus azimuth (Mtip = 0.4, ? = 4
?
s , CT/? =
0.1).
189
(a) r = 30%R
(b) r = 50%R
Figure 6.47: Oscillatory lag bending moment versus tip speed ratio (Mtip = 0.4,
?s = 4
?, CT/? = 0.1).
190
Figure 6.48 shows the azimuthal variation of torsion moment. The double
anhedral blade has a lower mean and peak-to-peak torsion moment. In Figure 6.49,
the oscillatory torsion moments are from 30%R and 50%R. At 30%R, the straight
blade torsion moment is dominated by the 2/rev component regardless of the tip
speed ratio. The double anhedral blade is also dominated by the same harmonics
component, however, the magnitude is much lower. At 50%R, the double anhedral
blade has a much lower 2/rev component.
The pitch link loads are shown in Figure 6.50. The pitch link is always in
compression while the tip speed ratio is low, and the highest magnitude occurs at
an azimuth angle of 180?. At a 0.3 tip speed ratio, there is an extension pitch link
load on the retreating side of the rotor. The 1/rev and 2/rev components have
similar magnitudes. The double anhedral blade has a higher oscillatory pitch link
load (Figure 6.51).
191
(a) ? = 0.1
(b) ? = 0.3
Figure 6.48: Torsion moment versus azimuth (Mtip = 0.4, ? = 4
?
s , CT/? = 0.1).
192
(a) r = 30%R
(b) r = 50%R
Figure 6.49: Oscillatory torsion moment versus tip speed ratio (Mtip = 0.4, ?s =
4?, CT/? = 0.1).
193
(a) ? = 0.1
(b) ? = 0.3
Figure 6.50: Pitch link load versus azimuth (Mtip = 0.4, ? = 4
?
s , CT/? = 0.1).
194
Figure 6.51: Oscillatory pitch link load versus tip speed ratio (M = 0.4, ? = 4?tip s ,
CT/? = 0.1).
6.4.4 Blade Strain/stress
The axial strain ?xx, in-plane shear strain ?xy, and out-of-plane strain ?zz are
examined in forward flight. There are a large amount of detailed data available, but
only the strain distributions at 0?, 90?, 180?, and 270? of the 0.3 tip speed ratio case
are shown.
Figures 6.52 and 6.53 show the axial strain of the straight blade and the double
anhedral blade at various azimuth angles. In each subfigure, the left side shows the
undeformed (dotted mesh) and deformed geometry as well as the surface strains.
The right side shows the internal strains at 30%R, 50%R, 80%R, and 95%R along
with the strains in the D-span. At 0? and 180? azimuth, both blades have high
positive axial strains near the root at the trailing edge. At 90? and 270? azimuth,
195
high negative axial strains appear near the root at the trailing edge, while high
positive axial strain present at the leading-edge. These strain patterns are consistent
with the flap and lag bending moment. The double anhedral tip expands all of the
high axial strain regions at the trailing edge and leading-edge. Meanwhile, the tip
geometry introduces strain concentrations near the anhedral and dihedral junction
at 90? and 270? azimuth respectively.
The in-plane shear strain distributions are shown in Figures 6.54 and 6.55.
The in-plane shear strain is mainly carried by the skin. The leading-edge weights
introduce shear strain concentrations near the leading-edge. And the highest con-
centrations near the root occur at 90? and 270? azimuth for both blades. The double
anhedral tip changes the in-plane shear strain patterns in the tip portion. And the
magnitude in the tip region is comparable to the root region, which is quite high.
As shown in Figure 6.56, the pattern of the internal out-of-plane strain of two
blades is compared. The variations of strain near the root for the two blades are
similar. The only difference resulting from the tip geometry occurs at the anhedral
junction which is the same as in hover.
196
(a) ? = 0?
(b) ? = 90?
197
(c) ? = 180?
(d) ? = 270?
Figure 6.52: Axial strain ?xx distribution of straight blade (Mtip = 0.4, ?s = 4
?,
CT/? = 0.1, ? = 0.3).
198
(a) ? = 0?
(b) ? = 90?
199
(c) ? = 180?
(d) ? = 270?
Figure 6.53: Axial strain ?xx distribution of double anhedral blade (Mtip = 0.4,
? = 4?s , CT/? = 0.1, ? = 0.3).
200
(a) ? = 0?
(b) ? = 90?
201
(c) ? = 180?
(d) ? = 270?
Figure 6.54: In-plane shear strain ?xy distribution of straight blade (Mtip = 0.4,
? = 4?s , CT/? = 0.1, ? = 0.3).
202
(a) ? = 0?
(b) ? = 90?
203
(c) ? = 180?
(d) ? = 270?
Figure 6.55: In-plane shear strain ?xy distribution of double anhedral blade (Mtip =
0.4, ?s = 4
?, CT/? = 0.1, ? = 0.3).
204
(a) ? = 0?
(b) ? = 90?
205
(c) ? = 180?
(d) ? = 270?
Figure 6.56: Out-of-plane strain ?zz distribution comparison (Mtip = 0.4, ?s = 4
?,
CT/? = 0.1, ? = 0.3).
206
6.5 Summary
In this chapter, the 3-D models of the straight blade and the double anhedral
blade are used to study the impacts of the double anhedral tip. Analysis of fre-
quencies and strains in vacuum, performance, vibration, loads, and strain/stress in
hover and forward flight were conducted. Based on this investigation, the following
conclusions are drawn:
1. For a hingeless rotor, the effect of the double anhedral tip starts to show from
the second frequency and becomes significant in all higher frequencies. The
double anhedral blade frequencies are lower due to the tip center of gravity
offset appearing to make the blade softer.
2. In vacuum, the vertical center of gravity offset of the double anhedral blade in-
troduces additional bending moment via centrifugal force which increases the
root axial strain magnitude and strain compression concentration at the dihe-
dral junction. Meanwhile, a pair of in-plane shear strain concentrations in the
dihedral portion also result from the additional propeller moment generated
by the tip geometry.
3. In hover, the influence of the double anhedral tip on rotor performance is
limited. The highest Figure of Merit only increased by 0.7%.
4. The tip center of gravity offset of the double anhedral tip reduces the root
flap, lag, and torsion moment in hover.
207
5. In forward flight, the straight rotor has a higher effective lift-to-drag ratio due
to its higher propulsive force.
6. At a tip speed ratio of 0.1, the strong 1/rev flap bending moment of the double
anhedral blade causes a 15% higher 4/rev vibratory hub vertical load.
7. Regardless of the spanwise location, the lag bending moments are dominated
by 2/rev components in forward flight. And the double anhedral blade always
has a higher oscillatory lag bending moment. As for torsional moment and
pitch link load, the double anhedral blade also has more oscillatory loads.
208
Chapter 7: Summary and Conclusions
7.1 Summary
This study investigated the aeromechanics behavior of a Mach-scaled double
anhedral composite rotor. Both experimental and analytical methods were employed
to investigate the subject systematically. Double anhedral tips are a recent intro-
duction in rotors with no research data available for understanding their behavior
or modeling them adequately. The objectives were to bridge these gaps.
Double anhedral blades of 5.6-ft diameter were designed and fabricated. The
blade has a D-spar, and there is a 5? dihedral portion from 80%R to 95%R and a
15? anhedral portion from 95%R to the tip. They were instrumented for strains and
structural loads. A two-bladed hingeless hub was designed and fabricated for the
vacuum chamber to measure rotating frequencies (fanplot). The hover tests were
performed on the AGRC Mach-scaled hingeless rig. And the tests were carried out
up to tip Mach number of 0.6, collective range of 0?-10?. The rotor performance, hub
loads, blade structural loads, pitch link loads, and surface strains were measured.
A double anhedral tip is a 3-D structure. Accordingly, a 3-D model was devel-
oped with CATIA (CAD), Cubit (hexahedral meshing), and X3D (aeromechanics).
The 3-D CAD was constructed jointly with Boeing to ensure the geometry was
209
representative of a modern rotor yet generic enough to be open source for U.S.
Gov-industry-academia joint study. The meshing used 27-node solid hexahedral el-
ements, as needed by X3D. The pitch bearing was modeled with a joint commanded
by a control input. In total there were 3427 elements and ? 100, 000 degrees of free-
dom. Properties of the composite plies were acquired through in-house four-point
bending coupon tests. The aerodynamic model used C-81 decks and a lifting line
with a refined free wake. The data acquired from tests were used to validate the
model.
A 3-D model of a straight blade was also developed as a baseline for com-
parison. This model had the same external and internal structure except for the
tip. Ideally, such a model should be fabricated, but fabrication was not pursued
due to the lack of resources. By comparing the behavior of the analytical models,
important insights could be gained. The models were also used to study forward
flight loads. Wind-tunnel tests were planned but were shelved due to the prolonged
shut-down of the tunnel.
7.2 Key Conclusions
This thesis is one of the first systematic studies of a double anhedral tip com-
posite rotor in the public domain. Based on the study, the following key conclusions
were drawn. The conclusions are given in the order they were learned, not impor-
tance.
1. Composite blades with double anhedral tip were successfully fabricated using
210
mold pressure alone. There is no additional treatment needed for the skin and
the spar, but the foam core should be carefully separated at the tip junctions
and assembled separately. The fabrication process documented in this study
allows all test blades to have a high degree of similarity (?0.3% of mass).
2. The strain-load static calibration for blade structural loads can be contami-
nated by the strain concentration from the segmented leading-edge weights.
Therefore, some points should be avoided for strain gauge placement. The
location of strain sensors in the 3-D model should also avoid these strain con-
centration regions accordingly.
3. There were seven non-rotating frequencies and six rotating frequencies cap-
tured in the vacuum chamber from 0? 1200 RPM. These frequency data were
limited only by the motor RPM, yet the cross-over of the first flap and lag
modes were captured. The second lag frequency was missed. The 3-D model
predictions had a satisfactory agreement with the measured frequencies.
4. The 3-D model was validated with blade surface strains measured in vacuum.
The agreement was satisfactory once the pre-cone angle of the vacuum chamber
hub was taken into account. The pre-cone angle was small, approximately
?1 to ?2?, and a small deviation from the intended design. This activity
demonstrated that 3-D was capable of capturing the true behavior of the
rotor, as-built, including un-intended imperfections of the test setup.
5. In the hover test, a maximum Figure of Merit of 0.713 was observed at all Mtip
211
(0.4-0.6) near a blade loading of CT/? = 0.117. This indicated that relatively
high hover performance can be achieved for a model-scale rotor when designed
properly. A proper design has smooth leading and trailing edges, smooth
transition region, identical blade weight, and center of gravity location. The
3-D model had a satisfactory agreement with performance data.
6. The prediction of the flap and lag bending moments at 40%R, pitch link loads,
and surface strains at 30%R and 80%R captured the trends generally, over the
collective and tip Mach number range. The prediction of the torsional moment
at 40%R does not agree with the measurement. Based on the comparison with
pitch link load and the simplicity of the control system, it might be reasonable
to assume the measurement was incorrect. But the reasons were not clear, so
this remains to be resolved in the future.
7. When compared with the predicted fanplot of the straight blades, only the first
frequency of the double anhedral blade was identical. The frequencies were
all different from the second to the higher modes. The double anhedral blade
frequencies were lower. The local center of gravity offset at the tip appears to
make the blade softer.
8. Limited improvement in hover performance was predicted by the double an-
hedral blade. The maximum Figure of Merit was increased by a negligible
0.7% at a blade loading of 0.12. The lifting line model with a single tip vortex
wake is not expected to capture any 3-D tip flow effect precisely. The data
acquired however would provide CFD researchers a baseline to pursue this
212
problem.
9. In hover, the inboard and midspan flap bending moments decrease for the
double anhedral blade. The double anhedral tip also leads to a reduction in
lag bending moment though out the span. In the inboard region, the torsional
moment of the double anhedral blade is lower. However, it is higher at the
midspan. The double anhedral tip also decreases the pitch link load, and the
reduction grows with the collective. The main source of these effects is the
vertical center of gravity offset of the tip, which generates additional bending
moments and propeller moments with significant ramification inboard.
10. Strong 3-D patterns are observed in predicted strain on the double anhedral
blade. In hover, midspan axial strain can be higher both externally and inter-
nally. There is also a compression zone at the tip dihedral junction. In-plane
shear strain concentrations also appear in the dihedral region, due to an ad-
ditional propeller moment introduced by the C.G. offset there. Out-of-plane
strains increase at the dihedral and anhedral junctions.
11. In forward flight, the performance of the straight rotor is higher, and the
difference worsens with the tip speed ratio. At the tip speed ratio of 0.3, the
effective lift-to-drag ratio of the straight rotor is higher by 16.7%. However,
the controls needed to trim the rotor remain the same with or without the
double anhedral tip.
12. The vibratory hub loads in forward flight are significantly influenced by the
213
double anhedral tip. Of the two high vibration regions, the one at low speed,
near the ? = 0.1 transition, can be predicted by lifting line with free wake.
At that tip speed ratio, the 4/rev vibratory vertical hub force, hub moment,
and hub torque increase by 15%, 100%, and 18% respectively with the double
anhedral tip.
13. The inboard oscillatory flap bending moment in forward flight is dominated
by the 1/rev component at a low advance ratio, and the double anhedral blade
has a high magnitude. As the tip speed ratio reached 0.3, the inboard 2/rev
component outweighs the 1/rev. The double anhedral blade has a lower 2/rev
moment.
14. Regardless of the spanwise location, the lag bending moments in forward flight
are dominated by the 2/rev component. Its magnitude at 30%R first decreased
by 20% when ? = 0.1 then increased by 2.5 times when ? = 0.3. The double
anhedral blade always has a higher 2/rev lag bending moment.
15. The double anhedral blade has a lower mean and peak-to-peak torsion mo-
ment. At 30%R, the straight blade torsion moment is dominated by the 2/rev
component regardless of the tip speed ratio. The double anhedral blade is also
dominated by 2/rev, however, the magnitude is much lower.
7.3 Contributions
The main contributions of this thesis are the following.
214
1. The successful development of a double anhedral Mach-scaled rotor model.
It is a joint industry-academia open-source model. The design and fabrica-
tion method for advanced geometry blades, such as double anhedral tip, was
developed in Maryland.
2. A vacuum chamber hub was developed that would allow the measurement of
rotating frequencies. The excitation mechanism was designed specially and
fabricated in-house. Combined with pressure control, the test system can be
used for vacuum, seal-level, high-altitude, and even Mars conditions. This
facility is new in Maryland and unique in academia.
3. A unique set of test data on a double anhedral tip was acquired. Including
frequencies, strains, rotor performance, structural loads, and strains well doc-
umented and freely available to U.S. Government, industry, and academia.
These data will be used by Boeing to insert X3D into their workflow. This
data will also be used by U.S. Army Helios to understand double anhedral tip
flow.
4. The data will support the exploration of advanced 3-D CFD/CSD fluid-structure
interface mythologies of the future.
7.4 Recommendations for Future Work
This investigation is the first step in understanding the aeromechanics behav-
iors of double anhedral tip composite rotor. Important works remain for the future.
215
The source of high vibration in forward flight and its potential remedy remain to
be resolved. The current rotor provides a suitable base for launching into that
endeavor. The roadmap for that task ahead is listed below.
1. First, the forward flight tests that have been postponed by the Glenn L. Martin
wind tunnel closure must be carried out as soon as possible. It remains a
crucial part of this project. The performance, blade structural loads, pitch
link loads, surface strains, and hub vibratory loads must be measured. In
addition, significant effort must be devoted to measure aerodynamic pressures
and airloads near the tip. Airloads would require the placement of at least 5
surface taps on either side of the airfoil.
2. The current tests and analysis were all carried out for a hingeless rotor. It is
recommended to repeat the same investigation on an articulated hub. This
would be a good training exercise for a new student. The same blades can be
used only the hub will need to be changed.
3. The high fidelity 3-D structural model should be coupled with a 3-D CFD
model to perform an Integrated 3-D (I3D) analysis. The true flow field of the
double anhedral tip particularly in forward flight required 3-D CFD for precise
resolution of the surface pressures and shear stresses.
4. Once the vibratory loading problem is resolved, attention should be paid to
stability measurements, particularly at slowed RPM, and high-speed/high-?
conditions.
216
Appendix A: Engineering Drawings
List of engineering drawings:
A.1 Vacuum Chamber Hub Central Block
A.2 Vacuum Chamber Hub End Block
A.3 Vacuum Chamber Hub Blade grip
A.4 Vacuum Chamber Hub Blade Adaptor
A.5 Vacuum Chamber Hub Pitch Horn
A.6 Vacuum Chamber Hub Pitch Link
A.7 Vacuum Chamber Hub Pitch arm
A.8 Vacuum Chamber Hub Shaker Housing
217
A.1 Vacuum Chamber Hub Central Block
218
A.2 Vacuum Chamber Hub End Block
219
A.3 Vacuum Chamber Hub Blade grip
220
A.4 Vacuum Chamber Hub Blade Adaptor
221
A.5 Vacuum Chamber Hub Pitch Horn
222
A.6 Vacuum Chamber Hub Pitch Link
223
A.7 Vacuum Chamber Hub Pitch arm
224
A.8 Vacuum Chamber Hub Shaker Housing
225
Appendix B: Test Data
B.1 Vacuum Frequency Test Data
Table B.1: Frequency test data.
RPM Frequency (Hz) RPM Frequency (Hz)
0 8.7 0 222.2
0 8.8 0 239.3
0 8.9 0 334.7
0 18.3 0 341.9
0 19.2 200 9.8
0 19.5 200 9.8
0 52.2 200 9.8
0 52.4 200 19.5
0 53 200 20
0 111.2 200 53.1
0 112.1 200 54.7
0 112.7 200 116.2
0 132.2 200 134.8
0 133.8 200 136.7
0 134.2 200 140.2
0 221 200 208
226
RPM Frequency (Hz)
RPM Frequency (Hz)
200 224.3
600 56.6
400 11.7
600 129.9
400 13.2
600 221.4
400 19.5
600 225.6
400 19.5
600 227.9
400 20
800 18.1
400 55.7
800 222.6
400 107.9
800 231.4
400 132.8
1000 16.6
400 142.6
1000 21.9
400 142.9
1000 227.5
400 212.3
1000 229.5
400 214.4
1000 235.3
400 240.3
1200 25.4
600 20
1200 251.9
600 20.2
B.2 Hover Performance Test Data
Table B.2: Hover performance test data (Mtip = 0.4).
?75 CT/? CP/? FM
1 0.0182 0.002565 0.2138
1 0.0185 0.002578 0.2179
2.9 0.0348 0.003624 0.4008
3.1 0.037 0.003684 0.432
5 0.0572 0.0057 0.59
5 0.0578 0.00526 0.577
7 0.08 0.0077 0.66
7 0.082 0.0078 0.68
9 0.1087 0.0113 0.711
227
Table B.3: Hover performance test data (Mtip = 0.5).
?75 CT/? CP/? FM
2.9 0.0353 0.00355 0.417
2.98 0.0362 0.00362 0.4248
3 0.0362 0.00361 0.4252
4.9 0.0561 0.0052 0.5707
5.08 0.0591 0.00542 0.5926
6.98 0.0827 0.00795 0.6685
7.03 0.0847 0.0081 0.6802
8.9 0.1128 0.01188 0.7126
Table B.4: Hover performance test data (Mtip = 0.6).
?75 CT/? CP/? FM
1 0.0182 0.00254 0.216
2 0.0277 0.0031 0.335
2.7 0.0348 0.0036 0.404
3 0.0377 0.0037 0.441
4 0.0474 0.00451 0.512
4.9 0.0596 0.00554 0.5879
6 0.0742 0.00691 0.6534
228
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