ABSTRACT
Title of dissertation: DEVELOPMENT OF THE
MARYLAND TILTROTOR RIG (MTR)
AND WHIRL FLUTTER
STABILITY TESTING
Frederick Tsai
Doctor of Philosophy, 2022
Dissertation directed by: Professor Anubhav Datta
Department of Aerospace Engineering
Tiltrotor aircraft encounter an aeroelastic instability called whirl flutter at
high speeds. Whirl flutter is caused by the complex interaction between the aerody-
namics and dynamics of the rotating proprotor blades, hub, and the wing. Current
tiltrotors are limited to about 280 kt in cruise. While many computational analyses
have been performed to assess potential improvements in whirl flutter stability, few
have been validated by test data. There is a scarcity of publicly available test data
along with documented model properties. A new tiltrotor rig is developed in this
work to address this gap. The new rig, henceforth called the Maryland Tiltrotor Rig
(MTR), is a semi-span, floor-mounted, optionally-powered rig with a static rotor tilt
mechanism, capable of testing 3-bladed proprotors of up to 4.75-ft diameter in the
Glenn L. Martin Wind Tunnel (7.75- by 11-ft section with 200 kt maximum speed).
The objective is to experimentally characterize the parameters that affect the on-
set of whirl flutter which is vital to validating computational models and analyses.
The MTR supports interchangeable hubs (gimballed and hingeless), interchangeable
blades (straight and swept tip), and interchangeable wing spars, to allow a system-
atic variation of components important for tiltrotor flutter and loads. The vision
for this rig is to conduct research towards flutter-free tiltrotors capable of achieving
400 kt and higher speeds in cruise. This dissertation lays the groundwork toward
that vision by describing the test and evaluation of a baseline gimballed hub model.
The features, controls, instrumentation, data acquisition, and all supporting equip-
ment of the rig are described. A simple whirl flutter analysis model is developed,
verified, and used for pre-test stability prediction of the MTR. The damping mea-
surement methods are detailed. The first whirl flutter tests of the MTR were carried
out at the Naval Surface Warfare Center-Carderock Division wind tunnel between
26 October - 2 November, 2021. Frequency and damping data were measured for
four parametric configurations of wing on versus wing off, gimbal free versus gimbal
locked, freewheel versus powered rotor, and straight versus swept-tip blades. The
tests were conducted up to 100 kt windspeed, restricted only by the tunnel pre-
cautionary measures. Since the baseline model is loosely a 1/5.26-scale XV-15, 100
kt translates to a full-scale speed of 230 kt. It was observed that the baseline rig
was stable up to 100 kt with an average wing damping lower than 1% critical in
beamwise and 1.5% critical in chordwise motion. The effect of wing aerodynamics
was insignificant up to 100 kt. Locking the gimbal affected mostly the chord mode
and increased is damping significantly. Powering the rotor also affected mostly the
chord mode and increased its damping significantly. The swept-tip blades showed
interesting trends near 100 kt but higher speeds are needed for definitive conclusions.
Overall, the MTR allowed the controlled variation of parameters that are important
for fundamental understanding and analysis validation, but are impossible to carry
out on an actual aircraft.
DEVELOPMENT OF THE
MARYLAND TILTROTOR RIG (MTR)
AND WHIRL FLUTTER STABILITY TESTING
by
Frederick Tsai
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:
Professor Anubhav Datta, Chair/Advisor
Professor Inderjit Chopra
Professor Olivier Bauchau
Professor James Baeder
Professor Christoph Brehm
Professor Amr Baz
? Copyright by
Frederick Tsai
2022
Acknowledgments
I am indebted to many people for their support and guidance during my grad-
uate experience and this section is a small token of my gratitude.
First and foremost, I am grateful to my advisor and committee chair, Professor
Anubhav Datta, for believing in my abilities before I believed in them myself and
for giving me the opportunity to conduct research on such a rewarding project. It
is my good fortune to have been in his first cohort of students.
I must thank Professor Inderjit Chopra, who was the first person I talked to
about returning to graduate school, and who guided me to Dr. Datta?s research
group when I was accepted into the graduate program. Thanks are also due to Pro-
fessor Olivier Bauchau, Professor James Baeder, Professor Amr Baz, and Professor
Christoph Brehm for serving on my thesis committee and for sparing their time to
review the manuscript.
My colleagues at the tiltrotor laboratory: James Sutherland, Chris O?Reilly,
Amy Morin, Seyhan Gul, Cheng Chi, Akinola Akinwale, Nathan O?Brien, and
Xavier Delgado, have been great sources of conversation and laughter in our daily
tasks, and their roles and expertise during our wind tunnel tests have been invalu-
able. To everyone in Dr. Datta?s research group, the rotorcraft center, members of
my Student Design team, the cube farm regulars, and many others - I am grateful
for all the group meetings, meals, and events that made graduate school all the more
enjoyable.
ii
I owe my deepest thanks to my family - my wife, Joanna, and my son,
Theodore, who arrived when I was halfway through my studies. Their love and
support continue to drive me to improve myself every day. I must recognize the
contributions of my parents-in-law, Howard and Meiling, who lived with us for over
a year and greatly eased the difficulties of balancing childcare, work, and sleep, and
all during a pandemic no less. To my mother, Karen, my father, Chris, and my
sister, Cecilia, words are not enough to express my sincere appreciation for your
lifelong support.
I gratefully acknowledge the financial support from the Office of Naval Re-
search (ONR) and Vertical Lift Research Center of Excellence (VLRCOE) and tech-
nical support from Army Research Lab (ARL), NASA Langley, NASA Ames, and
Calspan Systems on all the projects discussed herein.
It is impossible to list every individual that has made an impact on me these
last several years, and I apologize to those I?ve omitted. Know that I am truly
thankful for all the interactions I have had. This thesis is the proud manifestation
of those connections.
iii
Table of Contents
Acknowledgements ii
Table of Contents iv
1 Introduction 1
1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Summary of Previous Work . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.1 Full-Scale Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.2 Model-Scale Tests . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 Model Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.4 Damping Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.4.1 Logarithmic Decrement . . . . . . . . . . . . . . . . . . . . . . 23
1.4.2 Prony Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.4.3 Moving-Block Method . . . . . . . . . . . . . . . . . . . . . . 37
1.5 Scope and Contribution of Present Work . . . . . . . . . . . . . . . . 48
1.6 Overview of Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . 49
2 Flutter System Development Model 51
2.1 FSD Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.2 FSD Pylon and Hub . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.3 FSD Blade Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.4 FSD Wind Tunnel Test . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.5 Chapter Summary and Conclusions . . . . . . . . . . . . . . . . . . . 60
3 Design of the Maryland Tiltrotor Rig 61
3.1 Features of the New Rig . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.2 Overview of the New Rig . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.3 Size and Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.4 Rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.5 Blades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.6 Hub and Shaft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.6.1 Gimballed hub . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.6.2 Hingeless hub . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.7 Drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.8 Pylon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.9 Wing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
iv
3.10 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.11 Chapter Summary and Conclusions . . . . . . . . . . . . . . . . . . . 81
4 The Maryland Tiltrotor Rig 82
4.1 Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.2 Wing Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.3 Pylon Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.4 Electric Drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.5 Rotor Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.6 Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.7 Measured Rig Characteristics . . . . . . . . . . . . . . . . . . . . . . 114
4.8 Pylon Center of Gravity and Inertia . . . . . . . . . . . . . . . . . . . 122
4.9 Chapter Summary and Conclusions . . . . . . . . . . . . . . . . . . . 128
5 Model Instrumentation and Calibration 130
5.1 List of Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.2 Load Cell Hub Forces and Moments . . . . . . . . . . . . . . . . . . . 132
5.3 Calibration Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.4 Calibration Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.5 Triaxial Accelerometer . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.6 High-Bandwidth Electric Actuators . . . . . . . . . . . . . . . . . . . 142
5.7 Blade Pitch Encoders . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
5.8 Shaft Torque Strain Gauge . . . . . . . . . . . . . . . . . . . . . . . . 154
5.9 Pitch Link Strain Gauges . . . . . . . . . . . . . . . . . . . . . . . . . 156
5.10 Gimbal Angle Hall Effect Sensors . . . . . . . . . . . . . . . . . . . . 157
5.11 Azimuth Hall Effect Sensor . . . . . . . . . . . . . . . . . . . . . . . . 162
5.12 Wing Strain Gauges . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
5.13 Data Acquisition System . . . . . . . . . . . . . . . . . . . . . . . . . 164
5.14 Chapter Summary and Conclusions . . . . . . . . . . . . . . . . . . . 168
6 Whirl Flutter Analysis 171
6.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
6.2 Rotor Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
6.3 Wing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
6.4 Whirl Flutter Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . 189
6.5 Model Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
6.6 Validation and Predictions . . . . . . . . . . . . . . . . . . . . . . . . 200
6.7 Comprehensive Analysis Parameters . . . . . . . . . . . . . . . . . . . 203
6.8 Chapter Summary and Conclusions . . . . . . . . . . . . . . . . . . . 206
7 Wind Tunnel Testing 208
7.1 Glenn L. Martin Wind Tunnel . . . . . . . . . . . . . . . . . . . . . . 208
7.2 Navy Subsonic Wind Tunnel . . . . . . . . . . . . . . . . . . . . . . . 212
7.3 Test Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
7.4 Test Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
v
7.5 Flutter: Baseline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
7.6 Flutter: Wing Off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
7.7 Flutter: Gimbal Locked . . . . . . . . . . . . . . . . . . . . . . . . . 236
7.8 Flutter: Powered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
7.9 Flutter: Swept-Tip Blades . . . . . . . . . . . . . . . . . . . . . . . . 246
7.10 Flutter Analysis: 9 DOF Model . . . . . . . . . . . . . . . . . . . . . 250
7.11 Chapter Summary and Conclusions . . . . . . . . . . . . . . . . . . . 253
8 Summary and Conclusions 258
8.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
8.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
8.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
Appendices 1
A Technical Drawings
B Matlab Codes
C MTR Pin Connections
D LabVIEW Block Diagram
E Derivations
Bibliography 269
vi
List of Tables
1.1 Comparison of features between helicopters, traditional tur-
boprop planes, and tiltrotors. . . . . . . . . . . . . . . . . . . . . 2
1.2 Similarity parameters for model testing. . . . . . . . . . . . . . 19
1.3 Properties of heavy gas compared to air. . . . . . . . . . . . . . 21
1.4 Prony-estimated amplitudes, frequencies, and damping for
various model numbers on a 1 second duration signal of 1000
samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.5 Window function equations; N is length of the response sig-
nal minus 1, n is the sample count in the response signal. . . 41
1.6 Damping results for run N1.78 for different window func-
tions on block size of 512. . . . . . . . . . . . . . . . . . . . . . . 41
1.7 Correction factors for amplitude for different window func-
tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
1.8 Damping results for N1.78 using moving-block method with
different block shifts for a block size of 512 samples. . . . . . 45
1.9 Damping results for N1.100 beam mode using moving-block
method with different block shifts for a block size of 512
samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.1 FSD wing properties. . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.2 Purchased parts for FSD swashplate. . . . . . . . . . . . . . . . 55
2.3 FSD blade materials. . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.1 Top level MTR specifications. . . . . . . . . . . . . . . . . . . . . 64
3.2 MTR rotor speeds (in revolutions per minute (RPM)) com-
pared to previous Bell (gimballed) and Boeing (hingeless)
tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.3 Blade root flap moment in hover. . . . . . . . . . . . . . . . . . 70
3.4 Blade root flap moment in hover for 2? pre-cone. . . . . . . . . 70
3.5 Nominal stiffness and mass properties for gimballed rotor
blades; EIN and EIC are the normal and chord-wise flexural
stiffnesses and m the mass per span; 1 Nm2 = 2.42 lbf-ft2;
full-scale values from Bell 25-ft diameter model (XV-15 ro-
tor), x=r/R, approximate mean values are taken; s = model
length/full-scale length = 1/5.26. . . . . . . . . . . . . . . . . . 72
vii
3.6 Nominal stiffness and mass properties for hingeless rotor
blades; EIN and EIC are the normal and chord-wise flexu-
ral stiffnesses and m the mass per span; 1 Nm2 = 2.42 lbf-
ft2; full-scale values from Boeing 26-ft diameter model (Bo
105 rotor), x=r/R, approximate mean values are taken; s =
model length/full-scale length = 1/5.47. . . . . . . . . . . . . . 72
3.7 Wing-pylon frequencies normalized with cruise RPM. . . . . 78
3.8 MTR on-rig instrumentation . . . . . . . . . . . . . . . . . . . . 80
4.1 MTR Size Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.2 Wing assembly fasteners. . . . . . . . . . . . . . . . . . . . . . . . 87
4.3 Wing-pylon frequencies normalized with cruise RPM; MTR
RPM shown is Froude-scale RPM for flutter tests. . . . . . . 91
4.4 Electric motor specifications. . . . . . . . . . . . . . . . . . . . . 97
4.5 Power electronics components. . . . . . . . . . . . . . . . . . . . 102
4.6 MST140-200 motor controller specifications. . . . . . . . . . . 105
4.7 MTR weight breakdown. . . . . . . . . . . . . . . . . . . . . . . . 113
4.8 ANSYS results for interface post frequencies. /rev values
shown for Froude and Mach-scale speeds. . . . . . . . . . . . . 114
4.9 Comparison of spar frequencies for first beam, first chord,
and first torsion modes. . . . . . . . . . . . . . . . . . . . . . . . . 115
4.10 Measured damping ratios for spar alone and spar with rib. . 120
4.11 Measured frequencies and damping ratios for MTR in GLMWT,
no wind, unpowered. . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.12 Measured frequencies and damping ratios for MTR in Navy
SWT, no wind, unpowered. . . . . . . . . . . . . . . . . . . . . . 122
4.13 Results of CG and MOI tests at NASA Langley. . . . . . . . . 126
4.14 Tare measurements of interface plate at NASA Langley. . . . 126
4.15 Pylon assembly properties. . . . . . . . . . . . . . . . . . . . . . 127
5.1 MTR on-rig instrumentation. . . . . . . . . . . . . . . . . . . . . 131
5.2 ATI original calibration matrix. . . . . . . . . . . . . . . . . . . 133
5.3 ATI calibration matrix transformed to hub location. . . . . . 135
5.4 UMD calibration matrix. . . . . . . . . . . . . . . . . . . . . . . . 141
5.5 Comparison of wing strain gauge FFTs and accelerometer
measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
6.1 Bell 25-ft diameter rig and MTR properties used for whirl
flutter analyses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
6.2 Full-rig MTR properties, compiled after Carderock test in
2021. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
7.1 MTR freewheel RPM measurements; average temperature
= 63.3?F , average pressure = 29.85 Hg, average density =
0.002343 slugs/ft3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
7.2 Straight blade set 1 freewheel collective data. . . . . . . . . . . 220
viii
7.3 Straight blade set 2 freewheel collective data. . . . . . . . . . . 221
7.4 Straight blade set 1 powered collective data. . . . . . . . . . . 221
7.5 Swept-tip blades freewheel collective data. . . . . . . . . . . . . 222
7.6 Swept-tip blades powered collective data. . . . . . . . . . . . . 222
7.8 Test sequence at Navy SWT. . . . . . . . . . . . . . . . . . . . . 224
7.9 Straight blades, gimbal free, wing on, and freewheeling flut-
ter results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
7.7 Test conditions at Navy SWT. . . . . . . . . . . . . . . . . . . . 230
7.10 Straight blades, gimbal free, wing off, and freewheeling flut-
ter results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
7.11 Straight blades, gimbal locked, wing off, and freewheeling
flutter results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
7.12 Straight blades, gimbal locked, wing off, and powered flutter
results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
7.13 Swept-tip blades, gimbal free, wing on, and freewheel flutter
results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
ix
List of Figures
1.1 Modern day tiltrotors in both military and commercial spaces. . . . . 2
1.2 Diagrams of primary forces for traditional helicopters and tilrotors in
forward flight. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Diagrams of flow for rotor in edgewise flight and proprotor in axial
flight. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Lockheed L-188 C Electra II turboprop aircraft. . . . . . . . . . . . . 5
1.5 Propeller whirl mode model. . . . . . . . . . . . . . . . . . . . . . . . 6
1.6 Tiltrotor whirl flutter model. . . . . . . . . . . . . . . . . . . . . . . . 7
1.7 Bell XV-3 in NASA Ames 40- by 80-ft wind tunnel. . . . . . . . . . . 10
1.8 Full-scale semi-span models by Bell and Boeing, respectively, in the
NFAC 40- by 80-ft wind tunnel. . . . . . . . . . . . . . . . . . . . . . 10
1.9 Bell XV-15 in NASA Ames 40- by 80-ft wind tunnel. . . . . . . . . . 11
1.10 NASA Tiltrotor Test Rig (TTR) in NFAC 40- by 80-ft wind tunnel. . 12
1.11 Boeing Vertol 1/4.622 M222 model in Boeing V/STOL wind tunnel
(BVWT). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.12 Boeing Vertol 2.8-ft diameter Froude-scale model in MIT Wright
Brothers wind tunnel. . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.13 Bell 1/5th scale V-22 semi-span model at NASA Langley?s Transonic
Dynamics Tunnel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.14 Wing and Rotor Aeroelastic Test System in NASA Langley?s Tran-
sonic Dynamics Tunnel (TDT). . . . . . . . . . . . . . . . . . . . . . 15
1.15 Sikorsky?s Variable Diameter Tilt Rotor Model. . . . . . . . . . . . . 16
1.16 Tiltrotor Aeroacoustic Model. . . . . . . . . . . . . . . . . . . . . . . 17
1.17 TiltRotor Aeroelastic Stability Testbed (TRAST) in NASA Transonic
Dynamics Tunnel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.18 N1.78 chord mode response, 1 second duration, 1000 samples. . . . . 26
1.19 N1.78 mean removed from original signal, y-axis centered at zero. . . 26
1.20 N1.78 peaks of signal determined. . . . . . . . . . . . . . . . . . . . . 27
1.21 Prony method using model number of 400 to produce fitted curve on
original signal in run N1.78. . . . . . . . . . . . . . . . . . . . . . . . 35
1.22 Effect of model number on Prony approximation of signal. . . . . . . 36
1.23 Moving-block method applied to run N1.78 chord mode trial. . . . . . 37
1.24 Comparison of window functions. . . . . . . . . . . . . . . . . . . . . 40
1.25 Moving-block method with Hanning window applied to run N1.78
chord mode. Block sample size of 512. . . . . . . . . . . . . . . . . . 40
x
1.26 The natural log of amplitude plots with linear fit dotted line for large
block sizes. Data from run N1.78 chord mode. . . . . . . . . . . . . . 44
1.27 The natural log of amplitude plots with linear fit dotted line for vary-
ing block shifts. Data from run N1.78 chord mode. . . . . . . . . . . 45
1.28 Run N1.100 beam mode with markers for where the response increases
in amplitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
1.29 The natural log of amplitude plots with linear fit dotted line for vary-
ing block shifts. Data from run N1.100 beam mode. . . . . . . . . . . 47
2.1 2-ft diameter flutter system development model. . . . . . . . . . . . . 52
2.2 FSD wing tip assembly. . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.3 FSD actuators assembly. . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.4 FSD rotor model and components. . . . . . . . . . . . . . . . . . . . 55
2.5 FSD wing tip assembly. . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.6 FSD blade molds: straight, twisted, and twisted with swept-tips. . . . 57
2.7 FSD base mount, 3D-printed on Markforged Mark 2. . . . . . . . . . 58
2.8 FSD in GLMWT test setups. . . . . . . . . . . . . . . . . . . . . . . 59
3.1 The Maryland Tiltrotor Rig (MTR) inside Glenn L. Martin
wind tunnel test section (7.75- by 11-ft); dimensions in inches;
dashed line is Center Line of tunnel. . . . . . . . . . . . . . . . 64
3.2 The Maryland Tiltrotor Rig (MTR) inside Glenn L. Martin
test section (7.75- by 11-ft); isometric view. . . . . . . . . . . . 65
3.3 Tip clearances from top and bottom of the wind tunnel as
function of rotor radius; the symbol shows the present con-
figuration with R = 2.375 ft and clearances of 0.3 R and 0.96
R from the bottom and top respectively. . . . . . . . . . . . . . 66
3.4 Predicted MTR performance used for design: torque, power,
thrust and collective pitch (at blade root) versus rotor speed;
CTOS is blade loading CT/? and mu is tip speed ratio ?. . . . 76
4.1 Maryland Tiltrotor Rig in the Glenn L. Martin wind tunnel; Novem-
ber 2019. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.2 Maryland Tiltrotor Rig; all dimensions in inches. . . . . . . . . . . . 84
4.3 Maryland Tiltrotor Rig in cruise, transition, and hover regimes. Free-
wheel state is same configuration as cruise. . . . . . . . . . . . . . . . 85
4.4 MTR designed for the Glenn L. Martin wind tunnel test section. . . . 86
4.5 Maryland Tiltrotor Rig Wing Assembly: (A) Baseplate and wing spar
with spacers (B) Wing ribs attached (C) Segmented fairings attached
on right side (D) Fairings completed and coupling plate attached on
spar tip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.6 Wing assembly fairings and ribs. . . . . . . . . . . . . . . . . . . . . . 89
4.7 Wing fairing details. . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.8 Spacers used to fill gap between wing spar and wing ribs. . . . . . . . 92
4.9 Wing-pylon connection through coupling plates. . . . . . . . . . . . . 94
xi
4.10 Pylon assembly with rotor components removed. . . . . . . . . . . . . 95
4.11 Pylon assembly components. . . . . . . . . . . . . . . . . . . . . . . . 96
4.12 Pylon assembly load paths. . . . . . . . . . . . . . . . . . . . . . . . . 98
4.13 Linear actuators connection and load path. . . . . . . . . . . . . . . . 99
4.14 Features of Plettenberg NOVA 30 with water cooling. . . . . . . . . . 101
4.15 Motor power diagram from wind tunnel supply to DC power supplies
to motor controller; green dotted wire is ground. . . . . . . . . . . . . 102
4.16 Motor power connections from power supplies to motor controller. . . 103
4.17 MTR gimballed hub section view. . . . . . . . . . . . . . . . . . . . . 107
4.18 Rotor assembly parts. . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.19 MTR gimballed hub. . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.20 Individual components of the gimballed hub. . . . . . . . . . . . . . . 110
4.21 Swashplate and yoke mounted on rotor shaft. . . . . . . . . . . . . . 111
4.22 Pitch case and gimballed hub component. . . . . . . . . . . . . . . . . 111
4.23 Rotor assembly mounted to pylon. . . . . . . . . . . . . . . . . . . . . 112
4.24 A gimbal lock plate is installed between the yoke and rotor to fix the
gimbal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.25 Results of impact testing for spar without rib. . . . . . . . . . . . . . 116
4.26 Results of impact testing for spar with rib. . . . . . . . . . . . . . . . 117
4.27 ANSYS modal analysis of baseline spar; first six modes shown to-
gether with the undeformed model wireframe. . . . . . . . . . . . . . 118
4.28 ANSYS modal analysis of spar with single rib; first four modes shown
together with the undeformed model wireframe. . . . . . . . . . . . . 120
4.29 KSR CG/MOI machine at NASA Langley; Pylon mounted in yawing
configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.30 Pylon testing in pitch orientation. . . . . . . . . . . . . . . . . . . . . 124
4.31 Pylon testing in yaw orientation. . . . . . . . . . . . . . . . . . . . . 124
4.32 Tare runs on the interface plate and brackets. . . . . . . . . . . . . . 127
5.1 On-rig instruments and sensors. . . . . . . . . . . . . . . . . . . . . . 132
5.2 Load cell coordinate system orientation: red dotted axes - as installed,
yellow solid axes - desired orientation for positive forces in pylon axes. 134
5.3 Load cell coordinate system orientation: yellow solid axes - desired
load cell orientation, green dotted axes - pylon coordinate system. . . 135
5.4 Calibration setup for Fz testing. . . . . . . . . . . . . . . . . . . . . . 139
5.5 Calibration setup for My, front view. . . . . . . . . . . . . . . . . . . 139
5.6 Calibration setup for My, side view. . . . . . . . . . . . . . . . . . . . 140
5.7 Calibration setup for Mz. . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.8 All forces and moments measured for an applied force in Fx. Blue -
ATI calibration, orange - UMD calibration, black - ideal output. . . 143
5.9 All forces and moments measured for an applied force in Fy. Blue -
ATI calibration, orange - UMD calibration, black - ideal output. . . 144
5.10 All forces and moments measured for an applied force in Fz. Blue -
ATI calibration, orange - UMD calibration, black - ideal output. . . 145
xii
5.11 All forces and moments measured for a pure moment in Mx. Blue -
ATI calibration, orange - UMD calibration, black - ideal output. . . 146
5.12 All forces and moments measured for a pure moment in My. Blue -
ATI calibration, orange - UMD calibration, black - ideal output. . . 147
5.13 All forces and moments measured for an applied moment inMz. Blue
- ATI calibration, orange - UMD calibration, black - ideal output. . . 148
5.14 Triax accelerometer mounted to rear bulkhead of pylon, shown in red
outline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
5.15 High bandwidth electric actuators for high frequency swashplate in-
puts. Ultramotion A2. . . . . . . . . . . . . . . . . . . . . . . . . . . 150
5.16 Actuators max stroke length. . . . . . . . . . . . . . . . . . . . . . . 151
5.17 Peak to peak collective amplitude due to actuator motion as a exci-
tation frequency increases. . . . . . . . . . . . . . . . . . . . . . . . . 151
5.18 Pitch encoder sensor on the hub. . . . . . . . . . . . . . . . . . . . . 153
5.19 Side view of pitch encoder, green light denotes proper working con-
dition with magnetic track within acceptable distance. . . . . . . . . 153
5.20 Shaft torque gauge calibration frame. . . . . . . . . . . . . . . . . . . 155
5.21 Shaft torque gauge calibration results for three trials with errors bars
displaying twice the standard deviation. . . . . . . . . . . . . . . . . 155
5.22 Pitch link calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
5.23 Gimbal Hall effect sensor 1 mounted on the bearing housing. . . . . . 157
5.24 Gimbal Hall effect sensor 2 mounted on the inside of the hub. . . . . 158
5.25 Gimbal Hall effect sensor calibration setup. . . . . . . . . . . . . . . . 159
5.26 Gimbal Hall effect sensor calibrations. . . . . . . . . . . . . . . . . . . 160
5.27 Azimuth Hall effect sensor. . . . . . . . . . . . . . . . . . . . . . . . . 161
5.28 Wing strain gauges on the wing spar. . . . . . . . . . . . . . . . . . . 163
5.29 MTR systems support rack. . . . . . . . . . . . . . . . . . . . . . . . 165
5.30 Flutter excitation of wing modes through swashplate actuation. . . . 167
6.1 Tiltrotor whirl flutter model. . . . . . . . . . . . . . . . . . . . . . . . 171
6.2 Validation of analysis with Bell 25-ft model frequencies (/rev) and
damping ratio. Red - present analysis; Blue circle - Johnson. . . . . . 201
6.3 MTR frequency and damping results from simplified model. . . . . . 202
7.1 MTR installed in GLMWT 7.75 by 11-ft subsonic wind tunnel. Novem-
ber 2019. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
7.2 MTR mounted to custom post in GLMWT. November 2019. . . . . . 210
7.3 MTR alignment using laser sheet. . . . . . . . . . . . . . . . . . . . . 211
7.4 MTR installed in NSWCCD 8- by 10-ft subsonic wind tunnel. Octo-
ber 2021. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
7.5 Interface post for MTR and T-slot table. . . . . . . . . . . . . . . . . 213
7.6 RPM variation with collective at windspeed of 60 kt. . . . . . . . . . 214
7.7 Collective variation with speed. Comparison of two straight blade
sets; data from Tables 7.2 and 7.3. . . . . . . . . . . . . . . . . . . . 216
xiii
7.8 Collective variation with speed: powered versus freewheel. Data from
Tables 7.2 to 7.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
7.9 Collective variation with speed; swept-tip blades. Data from Table 7.5.218
7.10 Collective variation with speed; powered versus freewheel for swept-
tip blades. Data from Tables 7.5 and 7.6. . . . . . . . . . . . . . . . . 219
7.11 Stability results for baseline configuration at 1050 RPM. . . . . . . . 231
7.12 Stability results for straight blades, gimbal free, wing off, and rotor
in freewheel at 1050 RPM . . . . . . . . . . . . . . . . . . . . . . . . 235
7.13 Comparison of damping for wing on and wing off configurations. . . . 237
7.14 Stability results for straight blades, gimbal locked, wing off, and rotor
in freewheel at 1050 RPM. . . . . . . . . . . . . . . . . . . . . . . . . 239
7.15 Comparison of damping for gimbal free and gimbal locked configura-
tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
7.16 Stability results for straight blades, gimbal locked, wing off, and pow-
ered rotor at 1050 RPM. . . . . . . . . . . . . . . . . . . . . . . . . . 242
7.17 Comparison of damping for powered and freewheel configurations. . . 245
7.18 Stability results for swept-tip blades, gimbal free, wing on, and rotor
in freewheel at 1050 RPM. . . . . . . . . . . . . . . . . . . . . . . . . 250
7.19 Comparison of damping for swept-tip blades and straight blade base-
line configurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
7.20 Predictions and test data for baseline configuration: straight blades,
wing on, gimbal free, and rotor in freewheel at 1050 RPM. . . . . . . 252
1 GLM Wind Tunnel Interface Post Drawing . . . . . . . . . . . . . . . 1
2 Carderock Wind Tunnel Interface Post Drawing . . . . . . . . . . . . 2
3 Hover Tower Drawing . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4 Baseline Wing Spar . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
xiv
Chapter 1: Introduction
This chapter introduces the background of tiltrotor aircraft and the primary
features that differentiate tiltrotors from traditional helicopters and turboprop air-
craft, which are summarized in Table 1.1. The concept of whirl flutter is also
presented. Then, the history of full-scale and model-scale experimental tiltrotor re-
search is summarized. An in-house-built, small-scale, tiltrotor model is also shown
as a task performed in preparation for the present research. The scope and contribu-
tions of the current research are presented, and lastly, an outline of the dissertation
is provided.
1.1 Background and Motivation
Tiltrotors combine the vertical takeoff and landing capability of helicopters and
the high-speed forward flight of conventional fixed-wing planes. These platforms can
be seen in Fig. 1.1.
Of all tiltrotor vehicles, only the Bell-Boeing V-22 Osprey is in operational
service. The Bell V-280 Valor is a technology demonstrator and Bell?s offering
for the US Army?s Future Long Range Assault Aircraft (FLRAA) program. The
Leonardo?s AW-609 is aiming to be the first commercial tiltrotor and is currently
1
Table 1.1: Comparison of features between helicopters, traditional turbo-
prop planes, and tiltrotors.
Helicopter Turboprop Plane Tiltrotor
VTOL CTOL VTOL
Flexible/flapping blades Rigid blades Flexible/flapping blades
Low twist blades High twist blades High twist blades
Cyclic controls N/A Cyclic controls
Large rotors for hover Small propellers Large proprotors for hover
High Speed Phenomenon
Retreating blade stall Propeller whirl flutter Tiltrotor whirl flutter
(a) MV-22 Osprey tiltrotor. (b) V-280 Valor tiltrotor.
(c) AW-609 tiltrotor. (d) Joby S4 tiltrotor.
Figure 1.1: Modern day tiltrotors in both military and commercial spaces.
2
undergoing flight certification requirements. Joby?s Urban Air Mobility (UAM)
vehicle is also undergoing certification tests at the time of writing this thesis.
The appeal of tiltrotors starts with the elimination of runways and the require-
ments for vast real estate. For UAM, vertiports, essentially an assembly of helipads,
reduce the landing zone footprint and can be placed on rooftops or above parking
garages. In terms of performance, tiltrotors are much faster and have greater range
than traditional helicopter at the price of lower payload.
In broad terms, all aircraft have to overcome weight and drag forces to fly
forward by using lift and propulsive thrust, respectively. Traditional helicopters
do so by using one device for both lift and thrust: the main rotor. A tiltrotor
can decouple these forces in forward flight by having a wing carry the lift and the
proprotor providing the thrust. This means engine power is primarily concentrated
on overcoming the drag component only. This concept is shown in Fig. 1.2(b).
(a) Single main rotor helicopter. (b) Tiltrotor wing and proprotor.
Figure 1.2: Diagrams of primary forces for traditional helicopters and tilrotors in
forward flight.
3
Helicopters encounter a fundamental limitation in speed due to an asymmetric
edgewise flow along the rotor disk shown in Fig. 1.3(a). On the advancing side of
the rotor which is the upper part of the diagram, the windspeed seen by the blade
tip is the speed of the blade tip plus the speed of the oncoming wind. The sum
of these velocities can reach transonic speeds, close to the speed of sound, where
compressibility effects, such as shockwaves, occur. On the retreating side of the
rotor, which is the bottom half of the diagram, the windspeed seen by the blade
is the speed of the blade subtracted the oncoming wind. The faster helicopter is,
the slower the windspeed on the retreating side, and this can cause dynamic stall
near the tips and a reverse flow region forms on the inboard portion of the blade.
These asymmetric effects create large vibrations and ultimately limit the speed of
an edgewise rotor.
(a) Single main rotor in edgewise flow. (b) Tiltrotor proprotor axisymmetric flow.
Figure 1.3: Diagrams of flow for rotor in edgewise flight and proprotor in axial flight.
4
Tiltrotors in forward flight see an axisymmetric flow, shown in Fig. 1.3(b).
meaning the flow by one blade on one side of the disk is the same everywhere around
the disk. This condition reduces the number of adverse flow effects seen by the rotor.
However, tiltrotors cannot reach the same speeds as conventional fixed wing
airplanes because the heavy nacelles and large flexible proprotors at the wing tips
bring with them an aeroelastic instability called whirl flutter at high speeds. This
phenomenon is far more severe from propeller whirl flutter because of the larger
and more flexible rotors required for helicopter mode hover and low-speed edgewise
flight.
The first recorded case of whirl flutter occurred on a Lockheed L-188 C Electra
II turboprop aircraft, shown in Fig. 1.4, owned by Braniff Airways in 1959 [1]. Less
than a year later, another Lockheed L-188 C Electra II owned by Northwest Airlines
crashed due to the same phenomenon [2].
Figure 1.4: Lockheed L-188 C Electra II turboprop aircraft.
5
This caused Lockheed to initiate the Lockheed Electra Action Program (LEAP)
to investigate the problems and find solutions. It was found that a propeller whirl
mode was exacerbated by weakened mounting of the propeller nacelles to the wing
which caused larger than designed deformations and subsequent structural failure
of engine and wing structures. A model diagram [3] of this propeller whirl mode is
shown in Fig. 1.5.
Figure 1.5: Propeller whirl mode model.
This model has two degrees of freedom in pitch, ?, and yaw, ?. ? is the
propeller RPM, R is the radius of the propeller disk, aR is the length of the rotor
shaft, Ix is the propeller mass moment of inertia about the rotational axis. The
support structure is represented at the origin with stiffness, K, and damping, C,
constants in pitch and yaw and In denotes the structural mass moment of inertia.
This model assumes the propeller to be rigid. Only the pitch or yaw modes can
go unstable and there is no coupling with other parameters. Through this simple
model, it was determined that stiffening the support structure and adding additional
6
damping components, in other words, increasing K and C, were enough to alleviate
the instability.
For tiltrotors, the whirl mode is much more complicated. To model a tiltrotor
rotor and wing [4, 5], at least nine degrees of freedom are required. Figure 1.6
shows the simplest model for a tiltrotor.
Figure 1.6: Tiltrotor whirl flutter model.
Three modes for the wing: q1 beam bending, q2 chord bending, and p torsion.
Six rotor modes because the rotor has flexible blades with a gimballed hub, so
the rotor can flap and lag and the rigid assumption is not valid. The variables
?0, ?1C , ?1C denote the collective flap, longitudinal flap, and lateral flap motions,
respectively. The variables ?0, ?1C , and ?1S denote the collective lag, longitudinal
lag, and lateral lag motions, respectively. The flapping motion occurs out of plane of
the hub, whereas the lagging motion occurs in plane. The flapping motion affects the
rotor in-plane forces generated as a result of wing perturbation and has a primary
7
influence in tiltrotor whirl flutter. Tiltrotor whirl flutter derives its name from
propeller whirl flutter but the mechanism is far more complicated. As a result, the
solution is also more drastic which in turn limits tiltrotor cruise performance below
a propeller aircraft.
The current solution to delay whirl flutter on tiltrotors is to use very thick
wings, around twice as thick as a propeller aircraft; for example, V-22 wing is
23% thickness-to-chord as compared to a typical 14% for a turboprop. This is the
manifestation of increasing the stiffness K of the support structure. However, this
creates a significant amount of drag and, ultimately, limits tiltrotors from achieving
high speeds. Current tiltrotors are limited to about 280 kt whereas their turboprop
airplane counterparts can achieve up to 400 kt and higher. To realize higher speeds,
tiltrotor wings must be made thinner without adverse impact on whirl flutter.
Many numerical studies have been conducted to investigate methods to allevi-
ate tiltrotor whirl flutter. Advanced concepts have been explored such as composite
tailoring [6, 7], tip anhedral [8, 9], and sweep with inertial tuning [10, 11]; many of
which have shown to increase flutter speed. However, none have been experimentally
verified.
Therefore, the University of Maryland developed a new laboratory and a new
generic tiltrotor model called the Maryland Tiltrotor Rig (MTR) to obtain funda-
mental understanding of tiltrotor whirl flutter and to explore alternate configura-
tions with interchangeable hubs, wing spars, and advanced geometry blades. The
motivation is to eliminate the whirl flutter boundary so tiltrotors can finally achieve
speeds up to 400 kt and higher.
8
1.2 Summary of Previous Work
Tiltrotor tests began with Bell?s XV-3 aircraft in the 1950s. Full-scale tests on
the XV-3, and its successor, the XV-15, continued into the late 1970s and model-
scale tests occurred from the 1970s to the late 1990s [12]. Since then, there has
been a gap in tiltrotor tests, however, new full-scale and model-scale rigs have been
developed in the 2010s. A review of previous tiltrotor experiments is presented in
this section, separated by full-scale and model-scale tests. Details of a small-scale,
tiltrotor model built in-house for risk reduction are also provided.
1.2.1 Full-Scale Tests
Full-scale tiltrotor tests began with the experimental Bell XV-3 tiltrotor at
the NASA Ames National Full-Scale Aerodynamics Complex (NFAC) 40- by 80-
foot wind tunnel in 1957-1958 and again in the 60s, shown in Fig. 1.7.
The XV-3 had experienced an unstable rotor-pylon backward whirl mode at
high advance ratios. So the pitch-flap coupling delta-3, control modifications, and
flapping restraints were investigated to prevent the instability [13, 14]. It was found
that the damping of the low frequency whirl mode increased with swashplate stabi-
lization, pylon stiffness, and hub restraint.
Full-scale semi-span models built by Bell, Model 300 [15] (25-ft diameter gim-
balled hub), and Boeing, Model 222 [16] (26-ft diameter hingeless hub), were tested
in the NFAC 40- by 80-ft tunnel in the late 60s and early 70s, shown in Fig. 1.8.
9
Figure 1.7: Bell XV-3 in NASA Ames 40- by 80-ft wind tunnel.
(a) Bell 25 ft. gimballed hub proprotor. (b) Boeing 26 ft. hingeless hub proprotor.
Figure 1.8: Full-scale semi-span models by Bell and Boeing, respectively, in the
NFAC 40- by 80-ft wind tunnel.
10
Properties and data were both documented and available to the public. The
dataset, however, is limited. No parametric evaluations of model features were
performed.
These led to full-scale tests of the XV-15 Tilt Rotor Research Aircraft (TRRA)
in the NFAC 40- by 80-ft tunnel in 1978 [17], shown in Fig. 1.9.
Figure 1.9: Bell XV-15 in NASA Ames 40- by 80-ft wind tunnel.
The XV-15 test focused on lift characteristics with nacelle angles, flap effec-
tiveness with a flap tab, autorotation capability, yaw characteristics with an H-tail,
drag measurements, and flow separation visualizations. However, no aeroelastic
flutter data was provided.
In the 2010s, a new Tiltrotor Test Rig (TTR) was developed by U.S. Army and
NASA Ames. Its first test was in 2017 in the NFAC 40- by 80-ft wind tunnel [18].
Figure 1.10 shows the TTR with a three-bladed proprotor in the test section. While
11
the state-of-the-art TTR will certainly inform future proprotor designs, it is not a
flutter model.
Figure 1.10: NASA Tiltrotor Test Rig (TTR) in NFAC 40- by 80-ft wind tunnel.
1.2.2 Model-Scale Tests
There is also a rich history of small-scale tiltrotor tests. While full-scale tests
were conducted to represent real aircraft flight, small-scale models were used for
fundamental understanding and to produce empirical databases for validation of
the analyses being developed.
In the late 60s through the 70s, Boeing Vertol developed a 1/4.622 Froude-
scale, two 5.5 ft diameter props, full-span (6.78 ft rotor center to rotor center),
powered, hingeless tiltrotor model[19, 20] and tested it in the Boeing V/STOL wind
tunnel (20- by 20-ft test section), shown in Fig. 1.11. The model was based on
12
a conceptual tiltrotor designated Model 150/160 in competition with Bell?s XV-15
tiltrotor.
Figure 1.11: Boeing Vertol 1/4.622 M222 model in Boeing V/STOL wind tunnel
(BVWT).
This model was used to obtain performance, stability, and loads on the blades.
No flutter data were obtained but blade modal frequencies and damping variation
with RPM were acquired.
Boeing Vertol Company also built two 2.8-ft diameter Froude scale models,
designated M301 and M222, and tested at MIT in the Wright Brothers wind tunnel
(elliptical test section: 7.5 ft minor and 10 ft major axes) in 1975 [21, 22], shown in
Fig. 1.12.
While they were dynamically scaled, these two models were used to investigate
gust response and alleviation methods. No flutter data were recorded.
13
Figure 1.12: Boeing Vertol 2.8-ft diameter Froude-scale model in MITWright Broth-
ers wind tunnel.
Bell built a series of 1/5th scale V-22 models and carried out a series of com-
prehensive tests at NASA Langley?s Transonic Dynamics Tunnel (TDT) from 1983-
1987 [23] as part of the V-22 development program, shown in Fig. 1.13.
The right-hand rotor of this model later evolved into the Wing and Rotor
Aeroelastic Test System (WRATS) [24, 25], shown in Fig. 1.14(a). The WRATS
tests investigated the effect of control system stiffness and pitch-flap coupling. A
four-bladed, semi-articulated, soft-in-plane rotor system was also tested for aeroe-
lastic stability, shown in Fig. 1.14(b). While these models published some flutter
data, the model properties are not available to the public.
Novel concepts were also tested at a small-scale such as the Variable Diameter
Tilt Rotor (VDTR) developed by Sikorsky in 1993 which had a 8.2-ft diameter in
14
Figure 1.13: Bell 1/5th scale V-22 semi-span model at NASA Langley?s Transonic
Dynamics Tunnel.
(a) 3-bladed, gimballed hub WRATS model. (b) 4-bladed, semi-articulated WRATS model.
Figure 1.14: Wing and Rotor Aeroelastic Test System in NASA Langley?s Transonic
Dynamics Tunnel (TDT).
15
hover and reduced 5.4-ft diameter in cruise [26], shown in Fig. 1.15. Neither model
properties nor flutter data are available to the public.
Figure 1.15: Sikorsky?s Variable Diameter Tilt Rotor Model.
Two 1/4 scale V-22 models ? one isolated-rotor (sting mounted) and another
full-span rotor-airframe ? were designed and fabricated with powered rotor and
conversion mechanism during the late 1990s at NASA Ames [27]. These were the
Tiltrotor Aeroacoustic Models (TRAM) shown in Fig. 1.16. None of these models
were tested for flutter.
For almost all of these successful models, the tests were in support of the
development of the next iteration of the tiltrotor which culminated in the V-22.
Model properties and data sets were either extremely limited or were not released in
the public domain. Almost all models were also single-point design configurations:
mostly straight blades with gimballed hub. Thus, there is a lack of parametric flutter
16
Figure 1.16: Tiltrotor Aeroacoustic Model.
data that are not specific to a particular aircraft but compares a variety of wings,
blades, and hubs systematically.
In parallel with the present effort, the U.S. Army has developed a new model-
scale tiltrotor rig, called the Tilt Rotor Aeroelastic Stability Testbed (TRAST) [28],
shown in Fig. 1.17.
Figure 1.17: TiltRotor Aeroelastic Stability Testbed (TRAST) in NASA Transonic
Dynamics Tunnel.
17
TRAST focuses on the variation of pylon pitch spring and yaw spring stiff-
nesses as well as pitch-flap coupling, delta-3. As of this thesis, TRAST has had one
wind tunnel test and results are waiting to be published.
1.3 Model Scaling
For scaling of models, there is a need to satisfy similarity requirements [29],
so that results at the small-scale are representative of full-scale models.
For aeroelastic scaling, six basic similarity parameters must be matched be-
tween model and full-scale: Mach number, M (ratio of inertia and fluid elastic
forces), advance ratio, ? (ratio of forward speed and rotor tip speed ?R), Lock
number, ? (ratio of aerodynamic and inertial forces), Froude number, Fr (ratio of
inertia and gravity forces), Strouhal number, St (related to oscillatory frequency of
a periodic motion), and Reynolds number, Re (ratio of inertia and viscous forces).
Additionally, model configuration should be similar to the full-scale system meaning
all important degrees-of-freedom must be included.
If all six of the similarity parameters are equal to full-scale then the model is
aeroelastically scaled; meaning the frequencies of oscillations with air on are identical
to their full-scale counter part, and all measurements on the model can be interpreted
to full-scale behavior. This, however is never achieved. In a conventional wind tunnel
with air as the test medium, up to four out of the six parameters can be simulated.
Advance ratio and Lock number must always be simulated. Strouhal number can
be simulated for rotors. If compressibility effects are important Mach number must
18
be simulated. Otherwise Froude number must be simulated. Reynolds number is
not prioritized over Mach or Froude number, so it is typically not simulated. With
the use of variable-pressure or heavy gas as a test medium, such as in the NASA
Langley Transonic Dynamics Tunnel (TDT), both Mach number, Froude number,
and Reynolds number can be simulated for some selected flight conditions and model
sizes.
These parameters for similitude are shown in Table 1.2.
Table 1.2: Similarity parameters for model testing.
Parameter Expression
Advance Ratio ? V?R
Lock Number ? ?acR4
Ib
Strouhal Number St ?c
V
Mach Number M V
a
Froude Number Fr V 2
gl
Reynolds Number Re ?V c
??
For the parameters with characteristic lengths in their expression, a scale factor
is defined as s, where model scale = s ? full-scale length. Therefore s = lM . By
lFS
matching the similarity parameters, a scale factor can be determined for a properly
scaled model.
To achieve a Mach-scale model, where compressibility effects must be ac-
counted for,
V
M MM = aMV = 1 (1.1)M FSFS aFS
19
Then,
VM = aM (1.2)
VFS aFS
Where subscripts M denotes the model-scale and FS denotes full-scale. Speed of
sound, a, changes with altitude and the ratio of model windspeed to full-scale wind-
speed, VM is directly proportional to the ratio of model test medium speed of sound
VFS
and full-scale speed of sound, aM . So if the full-scale vehicle?s operating regime is
aFS
at sea level, and the model is being tested at sea level, then the tunnel speed for the
model must be at the same speed as the full scale vehicle?s test speed.
To match Strouhal number at the same Mach number,
? c
St M MM = VM = cMVFS?M = cMaFS?M = aFS?Ms = 1 (1.3)
St ?FScFSFS cFSVM?V FS cFSaM?FS aM?FSFS
Then,
?M = 1 aM (1.4)
?FS s aFS
So if a full-scale vehicle?s operating regime is at sea level, and the Mach-scaled model
is being tested at sea level, then the model frequency of oscillation must be higher
than the full scale by the inverse of the scale factor.
Pertaining to rotors, Strouhal number can be evaluated with V = ?R and
l = R.
= ?l = ?R = ?St (1.5)
V ?R ?
Thus the frequencies to be kept the same are the non-dimensional frequencies relative
the rotor speed, i.e., frequencies in /rev. This is particularly important for tiltrotors:
20
the wing-pylon frequencies of the model must be kept the same relative to the rotor
speed of the model.
To match Reynolds number and Mach number,
?MVM cM
ReM = ?? = cMVM M?M??FS = aM?M??FS? V c s = 1 (1.6)Re FS FS FSFS cFSVFS?FS?? a ?? M FS FS??? MFS
Then,
aM?M?? 1FS = (1.7)
aFS?FS?? sM
So, if full scale vehicle?s operating regime is at sea level, and the model is being
tested at sea level, then in order to match Re, the scale factor must be 1. If the
model can be tested in heavy gas, such as R-134a used in NASA TDT, then it is
possible to obtain a smaller model. Heavy gas properties for R-134a as compared
to air are shown in Table 1.3.
Table 1.3: Properties of heavy gas compared to air.
Property Unit R-134a Air
Molar mass kg/kmol 102.03 28.97
Speed of sound, a m/s 165 340
Density, ? kg/m3 5.22 1.225
Viscosity, ? ?5 ?5? Pa-s 1.076? 10 1.81? 10
However, even with heavy gas, only 1/3 scale models can be achieved when
Mach number is matched; still quite large.
21
To develop a Froude-scale model, Froude number must be matched.
V 2
Fr M 2M = g V l gM lM = M FS FS = 1 (1.8)
F V 2 V 2FS FS FSlMgM
gFS lFS
Then, ?
VM = gMs (1.9)
VFS gFS
where g is the gravitation acceleration at altitude. In order to match Mach number
with this relationship: ?
s gMMM = gFSa (1.10)M MFS aFS
Since, on Earth, gM ? gFS, the only way to match Mach and Froude is to have
s = ( aM )2. Using R-134a, this can be achieved with a 1/4-1/5 scale model.
aFS
When Froude is matched, then Reynolds number scales as:
?
s3/2 gM ?MReM = gFS ?FS (1.11)
Re aMFS aFS
So when Froude is matched, Mach and Reynolds cannot be matched. If Froude
?
number is simulated, Mach number is lower by s, and Re number by s3/2, when
atmospheric conditions are the same. The Mach number similitude can be main-
tained with heavy gas but only for a particular s ? 1/5. The Re number similitude
cannot be achieved. Recall, with heavy gas, Re number and Mach number simili-
tude requires s ? 1/3, and for this size scale Froude number similitude cannot be
22
achieved. Typically, Re is not simulated, but every attempt is made to keep it near
1 million.
1.4 Damping Measurement
There are various approaches to measure damping of a physical system. Three
common methods are described in this section: the textbook logarithmic decrement,
Prony method, and the moving-block method. The moving-block method was se-
lected in post-processing to obtain the frequencies and damping of the wing beam
and wing chord modes.
The MTR was deliberately designed with high bandwidth electric actuation to
introduce perturbation at a specified frequency. Thus, the frequencies of response
need not be identified or separated from a transient response; the response is already
at the specified frequency. Thus, the moving block method was used to extract
damping. This method is also robust to measurement noise. Damping was also
extracted by the other methods for a few selected points. It confirmed that the
selection of methods made no difference in the results.
1.4.1 Logarithmic Decrement
The Logarithmic Decrement is applicable to a single frequency signal of the
form:
x = Aest (1.12)
23
?
Where, s = ??j?, ? = ???n, and ? = ? 1? ?2n . It is also known the signal
period, T , is related to the frequency ? by the relation T = 2? or T = ?2? .
? ?n 1??2
Then the natural frequency of the signal can found:
= ?2?/T?n 2 (1.13)1? ?
To obtain damping ratio, ?, first select a starting peak on the decay envelope:
x = Ae?tt . Then pick another peak after nT periods: xt+nT = Ae?(t+nT ), where n
is the number of periods the second peak is away from the first peak. Divide the
amplitude of the first peak by the second peak:
xt = e??nT (1.14)
xt+nT
Then solve for the exponential term:
( )
? = 1 xt?T ln (1.15)
n xt+nT
Where the left hand side is ??T = ?? T = ?? ?2? = ?2??n n . The right
?n 1??2 1??2
hand side is the logarithmic decrement, ?, the natural log of the ratio of amplitudes
of successive peaks.
( )
= 1 xt? ln (1.16)
n xt+nT
Solving for ?:
24
? = ? 1( ) (1.17)2
1 + 2?
?
The log dec method works well when the decay envelope is easy to identify,
which is typically the case for a single frequency signal with no noise. For a signal
with multiple frequencies, the log dec method may be used in conjunction with a
band-pass filter to isolate the frequency of interest. For noisy signals, applying a
moving average would help mitigate the noise.
The raw signal must be manipulated before log dec can practically be applied.
The mean of the signal must be ascertained reliably, and removed from the raw
signal. The log dec method only applies to the perturbation signal. If the signal has
a large positive offset, the log dec method will show an incorrect low damping ratio,
?. If the signal has a large negative offset, the log dec will show an incorrect negative
damping ratio, ?. Thus, it is important, obviously, that only the perturbation be
taken.
If the offset varies with time such that peaks start positive but successive peaks
are negative, the log dec, ?, will result in incorrect complex numbers. These are
issues that do not arise in theoretical analysis, but are unavoidable in experimental
data.
Figure 1.18 shows the raw signal for run N1.78 chord mode trial (see Section 7.4
for naming convention). Figure 1.19 is the same signal with the mean removed.
Figure 1.20 shows the amplitudes of each peak found. The log dec, ?, is calculated
for each pair of successive peaks such that n is 1 for each calculation, i.e. peaks
25
Figure 1.18: N1.78 chord mode response, 1 second duration, 1000 samples.
Figure 1.19: N1.78 mean removed from original signal, y-axis centered at zero.
26
Figure 1.20: N1.78 peaks of signal determined.
1-2, peaks 2-3, peaks 3-4, etc. Then the mean of the damping ratios is calculated
to obtain the final damping ratio of the response which in this case is 1.53%. Once
? is known, natural frequency, ?n, is identified from Eq. (1.13), where T is the time
between peaks.
1.4.2 Prony Method
When there are multiple frequencies in a signal, Prony method can be used
to decompose them into superpositions of damped sinusoids. It is essentially the
Fourier transform equivalent for damped oscillations. It is irrelevant for MTR as
the response frequency is already known but covered here for completeness and
comparison.
27
First, start with a signal, say, with three frequencies for the sake of illustration.
x = A es1t + A es2t + A es2t1 2 2 (1.18)
Then pick seven equidistant points in the signal, where 7 = 2 ? 3 frequencies
+ 1. Let them be related linearly through a relation of the following form
xtP0 + xt+1P1 + xt+2P2 + xt+3P3 + ...+ xt+6P6 = 0 (1.19)
where xt+n are the known signal values, and Pn are some unknown coefficients.
Then, it follows
(A es1t + A es2t + A es2t1 2 2 )P0
+(A es1(t+1) + A es2(t+1) + A es2(t+1)1 2 2 )P1
+(A es1(t+2) + A es2(t+2) + A es2(t+2)1 2 2 )P2
(1.20)
+...
+(A es1(t+6)1 + A2es2(t+6) + A es2(t+6)2 )P6
= 0
28
This is rewritten as
A es1t(P + P es11 0 1 + P2e2s1 + P3e3s1 + ...+ P6e6s1)
+A es2t1 (P0 + P es21 + P 2s2 3s2 6s22e + P3e + ...+ P6e )
(1.21)
+A es3t s31 (P0 + P1e + P2e2s3 + P e3s3 + ...+ P e6s33 6 )
= 0
For nontrivialA s t s t s t1e 1 , A2e 2 , A3e 3 , the expressions in parentheses in Eq. (1.21)
must be zero.
This implies es1 , es2 , es3 are simply the roots of the sixth order polynomial
P0 + P 2 3 61x+ P2x + P3x + ...+ P6x = 0.
This allows 6 roots, and in general, 3 complex conjugate pairs. Only the
coefficients P0, P1....P6 are left to be determined.
Note, one of the coefficients, say P6, can be set to 1 or -1, without any loss of
generality. Because:
P 2 30 + P1x+ P2x + P3x + ...+ P6x6 = 0 (1.22)
and
1 (P + P x+ P x2 + P x30 1 2 3 + ...+ P x66 ) = 0 (1.23)
P6
have the same roots.
29
Going back to Eq. (1.19), by setting P6 = ?1, it is rewritten as:
xtP0 + xt+1P1 + xt+2P2 + xt+3P3 + ...+ xt+5P5 = xt+6 (1.24)
This form is widely used. To calculate the 6 unknown coefficients, it only
remains to find 6 equations. These are found by applying the same relation for xt+5,
xt+4,..., xt+1. The assumption is Eq. (1.19) is valid for any seven consecutive points
on the signal. This is valid for any signal that is a result of an underlying partial
differential equation. It is indeed the basis for any finite difference approximation.
In matrix form
?? ?? ? ? ???? xt xt?1 xt?2 xt?3 xt?4 xt?5???
?????
??
? ??
P5???? ????xt+1? ? ???
?
? ??xt+1 xt xt?1 xt?2 xt?3 xt?4? ??
???P4? ?xt+2?????? ???? ???? ????????xt+2 xt+1 xt xt?1 xt?2 xt?3????????P3???? ????xt+3?? = ?? ?? (1.25)?????
xt+3 xt+2 x
?? ?
t+1 xt xt?1 xt?2
???
??????
??P? 2????
?? ?
???x ?? t+4????
??xt+4 xt+3 xt+2 xt+1 xt x ?t?1????P1?? ???x ?? ?? ? ? t+5????
xt+5 xt+4 xt+3 xt+2 xt+1 xt P0 xt+6
Then solve for the coefficients P0, P1, P2, P3, P4, P5.
This has the form:
AP = x (1.26)
Where A is a Toeplitz matrix if it is square, P is the prediction coefficients
vector and x is the observation vector.
30
If A is square then P = A?1x. However, in test data, more than 7 observations
points are desired. Then A is not square, and there are more equations than than
the prediction coefficients. In this case, solve in the least square sense:
ATAP = ATx
(1.27)
P = (ATA)?1ATx
Which minimizes the error norm
||x? AP ||2 (1.28)
Finally, P0, P1, P2, P3, P4, P5 are obtained.
Now that the coefficients are known, solve for the roots of Eq. (1.22) with
P6 = ?1. This has the following form.
x6 ? P5x5 ? P4x4 ? P3x3 ? P 22x ? P1x? P0 = 0 (1.29)
From root x, find s from x = es. The root s is complex. The imaginary
part of s is unique only up to multiples of 2?k, where k is an integer. This is
because es = es?j2?k. So care must be taken to extract the frequency, but there is
no ambiguity in ?.
? = Re(s)
(1.30)
? = Im(s)? 2?k
31
where k can be zero or any integer.
The damping ratio and natural frequency, ? and ?n, can now be found. For a
complex conjugate pair s1 = ?1 ? j?1:
s11 = ?1 + j?1
(1.31)
s21 = ?1 ? j?1
Then A s t1e 1 becomes A s t11e 11 +A es21 21t. Find A11 and A21 separately, because
if s11 and s21 are complex conjugates, then A11 and A21 must also be complex
conjugates. For 3 pairs of complex conjugates:
?? ?? ? ? ??????
es11t es21t es12t es22t es13t es23t ????????A11??? ???x1???? ? ? ?? es11(t??t) es21(t??t) es12(t??t) es22(t??t) es13(t??t) es23(t??t) ????? ? ? ????? ?
????A21???? ????x2????
?es11(t?2?t) es21(t?2?t) es12(t?2?t) es22(t?2?t) es13(t?2?t) es23(t?2?t)?????? ?????
? ? ?
A12???? ????x3??? = ?
?
? ??es11(t?3?t) es21(t?3?t) es12(t?3?t) es22(t?3?t) es13(t?3?t) es23(t?3?t)????A ? ? ?? 22? ?
x4?
????
?????? ??? ??? ???
es11(t?4?t) es21(t?4?t) es12(t?4?t) es22(t?4?t) es13(t?4?t) es23(t?4?t)?????A ? ?x ?? ( ?5? ) ( ?5? ) ( ?5? ) ( ?5? ) ( ?5? ) ( ?5? )?
???? 13???? ???? 5????
es11 t t es21 t t es12 t t es22 t t es13 t t es23 t t A23 x6
(1.32)
Let
1
A = C ej?111 2 1 (1.33)
1
A ?j?121 = 2C1e
32
Then
A1e
s1t = C1 cos(?1t+ ?1) (1.34)
where C1 is the magnitude and ?1 is the phase content of the first frequency. C1
and ?1 can be found from A11 and A21. Thus, finally the signal is fully decomposed.
To apply Prony method numerically, the following steps are carried out.
1. Create a Toeplitz matrix, T , representation of the data, where the first column
is the damped signal and each subsequent column is the signal shifted down
one sample. Like so:
?? ???? x0 0 0 . . . 0? ?
?
? ?? ?? ?? x1 x0 0 . . . 0 ?? ?T =
????
??
x x ?2 1 x0 . . . 0
?? ?
?? (1.35)
? .? . .
. ?. . ... . . . . . .
? ???
??
xN?1 xN?2 xN?3 . . . x0
Here it is assumed the signal starts at x0. Prior values are all zero. T is an
N ?N square matrix where N is the number of samples in the signal.
2. Choose a model number, M , which represents the number of polynomial co-
efficients P0, P1, P2, ..., PM . M is typically around 30%-40% of the number
of samples, N .
3. Select portions of the the Toeplitz matrix using the model number, M , such
that x=T (M :N -1,1), and A=T (M :N -1,2:M). Note that this procedure starts
33
at an index of zero for the first element, whereas Matlab convention for index-
ing starts at 1. Adjust Matlab code accordingly.
4. Solve for the coefficients vector P in the form AP = x. Matlab operation
P = [?1;A\x] provides the least squares solution. Recall from Eq. (1.24), PM
is set to -1 and is the first element in the coefficient array. If PM is set to 1,
then P = [1;?A\x] is the coefficient array.
5. Determine the roots of the coefficient array P . The roots are in the form e(s?t),
so take the natural log of the roots then multiply by the sampling frequency
of the signal, f , to obtain s.
6. Take the absolute value of the imaginary part of s to obtain normal frequencies,
?n in radians/s.
7. The real part of s is the damping factor ???n, where ? is the damping ratio.
Dividing the real part by the frequencies in the prior step will result in the
damping ratios.
8. For a large model number (number of coefficient terms), find the indices of the
frequencies of interest and match them to the damping ratios.
If the frequency is already known, the above steps are all that is needed to
obtain the damping ratio. If the frequency is not known, sorting the amplitudes in
descending order brings the most important modes to the forefront. A numerical
code for Prony?s method is given in the appendix.
34
Figure 1.21 shows Prony?s method applied to run N1.78 chord mode trial for
a model number of 800 in a 1000 sample signal of 1 second duration. The Prony
approximation signal is in very good agreement with the original signal. Figure
1.22 shows a sensitivity study for the Prony approximation signal for various model
numbers. The results of frequencies and damping ratios extracted from the model
numbers are shown in Table 1.4
Figure 1.21: Prony method using model number of 400 to produce fitted curve on
original signal in run N1.78.
Table 1.4: Prony-estimated amplitudes, frequencies, and damping for var-
ious model numbers on a 1 second duration signal of 1000 samples.
Model Number Amplitude (??) Frequency (Hz) Damping (% critical)
20 79.40 9.77 16.39
100 71.14 9.45 1.64
200 69.98 9.47 1.58
300 52.13 9.46 1.56
400 69.53 9.47 1.57
500 71.12 9.45 1.55
800 95.67 9.47 1.50
35
Figure 1.22: Effect of model number on Prony approximation of signal.
Increasing model number (number of coefficient terms, P ) improves accuracy,
however, model numbers approaching the number of samples in the signal will result
in incorrect values of amplitude and damping. This is because the procedure in step
3 uses the number of coefficients to predict N ?M terms in the signal, x. If the
length of the signal is 1000, and the model number is 999, x becomes a single
term, and the coefficients are not unique. on the other hand, low model numbers
result in incorrect amplitude, frequency, and damping because there are not enough
coefficients to capture the behavior of the signal. Thus, a model number about
30%-40% of the number of samples should be used as a starting point.
It is obvious Prony is an excessive method when the response contains a single
specified frequency. A high model number is needed to converge to the same solution
as the other methods. However, the method is generic and useful if there are multiple
frequencies in the perturbation response.
36
1.4.3 Moving-Block Method
The Moving-Block method belongs to a broad class of modern block processing
techniques of digital signal processing that emerged during the 1960s. The imple-
mentation here generally follows Refs. [30?32]. It is used to calculate the frequency
and damping of the MTR. Generally, the moving block method is very effective
for noisy signals and for low damped signals less than 5% of critical damping. An
example for run N1.78 chord mode demonstrates the procedure, shown in Fig. 1.23.
(a) Full signal with truncated signal selected. (b) Truncated signal with first block selected.
Sample size 512.
(c) FFT for first block of sample size 512. (d) Natural log of the max FFT amplitude and
linear fit for consecutive moving blocks.
Figure 1.23: Moving-block method applied to run N1.78 chord mode trial.
37
The raw data at 10 kHz is downsampled to 1 kHz for ease of processing. The
downsampled signal from the wing chord strain gauge is shown in Fig. 1.23(a). A
region of the decaying signal is selected starting from the end of excitation (4.225
sec) and for a duration of 3 seconds. This region is shown in Fig. 1.23(b). It
contains 3000 samples over 3 seconds. A Fast Fourier Transform (FFT) is taken of
this signal to determine the key frequency, and equated to ?n. Then, the signal,
denoted as x, is split into moving blocks of 512 samples in the form shown below.
First block:
[x0 x1 x2 ... x511]
Second block:
[x1 x2 x3 ... x512]
Third block:
[x2 x3 x4 ... x513]
And so on until the last block, where N is the length of the signal:
[xN?512 xN?511 xN?510 ... xN?1]
These are the so-called moving blocks. On each block, an FFT is performed.
The FFT of the first block is shown in Fig. 1.23(c). The FFT is performed with zero
padding (appending zeros to the end of the block) which increases the resolution of
the FFT bins and, as a result, the peak is more precise with side lobes that appear
smooth and continuous. The peak amplitude of the frequency of interest is stored.
In this example, the amplitude is 57.3. The next block of 512 samples is treated the
same way. This continues for all the blocks in the signal such that an array of (N-
512) amplitudes is produced. A plot of the natural log of the amplitude array versus
38
starting time of the block is generated and the result is an oscillating signal that
decreases linearly with time. The slope from a least-squares fit over this oscillating
line is equal to ???n where ?n is the frequency calculated from an FFT of the
three-second signal and ? is the damping ratio. It is assumed the damped frequency
?d = ?n because the damping ratio is known to be less than 5%. Figure 1.23(d)
shows the results of the natural log and the least-squares fit over a one second time
duration. In this example, ?n = 9.5 Hz and ? = 0.0141. If the damping is in %
critical, it is 1.41%.
The block mentioned above is nothing but a rectangular window, also called
a boxcar. A window essentially connects the end of the block with the beginning of
the block. The accuracy of the moving-block method can be enhanced by using non-
rectangular windows [33], which avoid the jump at the ends of the blocks. A study
of windowing functions was performed with several other windows namely Hanning,
Hamming, Flat Top, and Blackman-Harris windows. These window functions are
shown in Fig. 1.24.
The equations for these windows are shown in Table 1.5.
By multiplying the response signal with one of these windows, then performing
an FFT on the output avoids the spurious frequency and amplitude generated by
the edges of the rectangular window, called side-lobes seen in Fig. 1.23(c). This
is especially true for signals with multiple modes with close-proximity frequencies.
The results of the moving block method with the Hanning window are shown in Fig.
1.25. The truncated signal used in this example is the same as Fig. 1.23(b).
39
Figure 1.24: Comparison of window functions.
(a) FFT for first block of size 512 with Hanning (b) Natural log of the FFT amplitudes with lin-
window applied. ear fit.
Figure 1.25: Moving-block method with Hanning window applied to run N1.78 chord
mode. Block sample size of 512.
40
Table 1.5: Window function equations; N is length of the response signal
minus 1, n is the sample count in the response signal.
Window Equation
Boxcar w(n) = 1, 0 ? n ? N
( ( ))
Hanning w(n) = 1 1? cos 2? n2 , 0 ? n ? N(N )
Hamming w(n) = 0.54? 0.46 cos 2? n , 0 ? n ? N
N ( )
Flat Top w(n) = 0.21557895? 0.416(63158)cos 2? n +N
0.27(72631)58 cos 4? n ?N ( )
0.083578947 cos 6? n + 0.006947368 cos 8? n ,
N N
0 ? n ? N
( )
Blackman- w(n) = 0.3(5875?) 0.48829 cos 2(? n +NHarris )0.14128 cos 4? n ? 0.01168 cos 6? n ,
N N
0 ? n ? N
Table 1.6: Damping results for run N1.78 for different window functions
on block size of 512.
Window Type Damping (% critical)
Boxcar 1.40
Hanning 1.44
Hamming 1.44
Flat Top N/A
Blackman-Harris 1.43
41
The damping ratios obtained from the various windows are shown in Table
1.6. Damping results are similar between all the window functions with a maximum
difference of 3%. The flat top window applied to the 512 sample block suppressed
the signal to the point where no peak was detected in the FFT; therefore, larger
block sizes are needed for the flat top window to be applied. While non-rectangular
windows, generally, result in more accurate results for frequencies and damping, they
are most beneficial for separating frequencies in close proximity. For the baseline
MTR model, the frequencies are already well separated, but future variations of the
model may require these window functions.
Note when using non-rectangular functions, the amplitude of the resulting
FFT will not be the same as the rectangular window. FFTs of non-rectangular
window functions must be multiplied by correction factors to be compared one-to-
one with a rectangular window. A list of correction factors are given in Table 1.7. For
the purposes of extracting damping ratio, amplitude corrections are not necessary
as the solution relies on the ratio of amplitudes so these factors are canceled out.
However, for comparing the FFT amplitudes between different trials or different test
conditions, these correction factors are necessary.
Table 1.7: Correction factors for amplitude for different window functions.
Window Type Amplitude Correction Factor
Boxcar 1
Hanning 2
Hamming 1.852
Flat Top 4.639
Blackman-Harris 2.381
42
Block size is a key parameter. Too small a block size will not capture the signal
frequency peaks accurately, and too large a block size may cause the damping to
skew to lower values. Natural systems can also display complex nonlinear damping
over time due to phenomenon such as free play and contact. The initial free decay
response of the wing, within the first few seconds, normally has the proper aeroelastic
damping that is of interest.
Figure 1.26 shows the calculation of the natural log of amplitudes for block
sizes of 1024 and 2048 for N1.78 chord mode using the default Boxcar window. The
baseline of 512 samples has been shown in Fig. 1.23(d). As can be seen, larger
block sizes tend to lower damping values. This is due to higher damping seen at
the beginning of the response and over time the damping decreases as the structure
reaches a steady state oscillation.
Block sizes of 256 and smaller could not acquire a max amplitude in the
FFT between 8 and 11 Hz. So for the N1.78 signal with 9.5 Hz frequency and
sampling rate of 1000 samples/second, a block size of 512 samples is the minimum
size required. It is recommended practice to choose a block size which incorporates
at least 4 cycles of the response signal.
A sensitivity study was conducted to investigate the effect of shifting the blocks
by more than 1 sample. Shifting blocks by more than 1 sample speeds up post-
processing. Figure 1.27 shows the natural log of the FFT amplitudes plot for each
block shift condition. These are applied to run N1.78 with the default boxcar win-
dow.
The damping calculated from different block shifts are shown in Table 1.8.
43
(a) Block size of 1024 samples. 1.35% critical damping.
(b) Block size of 2048 samples. 1.25% critical damping
Figure 1.26: The natural log of amplitude plots with linear fit dotted line for large
block sizes. Data from run N1.78 chord mode.
44
(a) Block shift by 32 samples. (b) Block shift by 64 samples.
(c) Block shift by 128 samples. (d) Block shift by 256 samples.
Figure 1.27: The natural log of amplitude plots with linear fit dotted line for varying
block shifts. Data from run N1.78 chord mode.
Table 1.8: Damping results for N1.78 using moving-block method with
different block shifts for a block size of 512 samples.
Block Shift (samples) Damping (% critical)
1 1.41
32 1.40
64 1.40
128 1.45
256 1.41
45
The different block shifts for the N1.78 runs shows good agreement. Notice the
N1.78 signal is clean from noise, occurs at a single frequency due to the actuation
system, and the response does not increase in amplitude as time elapses. Caution
must be used because sometimes the response does increase in amplitude seemingly
from random disturbances as time elapses. Figure 1.28 from run N1.100 is an ex-
ample. Here, the beam mode shows sudden, though slight, increases in amplitude
at multiple points.
Figure 1.28: Run N1.100 beam mode with markers for where the response increases
in amplitude.
When this occurs, for large block shifts, the resolution is lost between the
blocks and can skew the results to lower damping. This is shown in Fig. 1.29. The
damping results for these block shifts are shown in Table 1.9.
While the large block shifts may result in slightly decreased damping val-
ues, they are reasonable as a first pass calculation. Therefore, to save computing
46
(a) Block shift by 32 samples. (b) Block shift by 64 samples.
(c) Block shift by 128 samples. (d) Block shift by 256 samples.
Figure 1.29: The natural log of amplitude plots with linear fit dotted line for varying
block shifts. Data from run N1.100 beam mode.
Table 1.9: Damping results for N1.100 beam mode using moving-block
method with different block shifts for a block size of 512 samples.
Block Shift (samples) Damping (% critical)
1 0.79
32 0.75
64 0.75
128 0.65
256 0.79
47
time during wind tunnel tests, large block shifts can be used; however, it is rec-
ommended to use single sample shifts during postprocessing to obtain the most
accurate, validation-quality results.
1.5 Scope and Contribution of Present Work
The present work has one main objective: to acquire reliable whirl flutter data
from the Maryland Tiltrotor Rig (MTR). Much of the experimental work focused on
model hardware and software integration, instrument calibrations, power electronics
integration, and wind tunnel test setup. Key contributions are listed below:
1. This work obtained the first flutter test data for the Maryland Tiltrotor Rig.
The tests were conducted up to a max speed of 100 kt. Parametric variations
of model features were compared for wing on versus wing off, gimbal free ver-
sus gimbal locked, powered rotor versus freewheeling rotor, and straight blades
versus swept-tip blades. Results showed that wing aerodynamics had minimal
effect on damping up to 100 kt, locking the gimbal increased wing chord damp-
ing but did not affect beam damping, powered rotor increased chord damping
further compared to freewheeling rotor and produced an unexpected peak be-
tween 20-30 kt, and swept-tip blades had minimal effect on damping for the
baseline configuration of wing on, gimbal free, and freewheeling rotor.
2. This work developed a new calibration stand to calibrate the MTR load cell
directly on the rig. The new stand was used to calibrate Fx, Fy, Fz, Mx, and
My in the laboratory. Mz was calibrated on a separate stand dedicated to
48
isolated load cell testing. During calibration, it was found that there were two
load paths, one of which did not pass through the load cell. Results showed
that thrust and torque were minimally affected by the secondary load path.
3. This work evaluated logarithmic decrement, Prony, and moving block meth-
ods as candidates for flutter test implementation. The moving block method
was used for postprocessing the data and obtaining the final damping values
reported in this thesis.
4. This work documented integration of MTR hardware and the data acquisition
system using LabVIEW.
5. This work prepared a Test Readiness Review document for the flutter test of
the MTR. This document covered the model features, predicted performance,
test execution, test matrix, safety criteria and procedures, and personnel roles.
This document was needed for access to the NSWC-Carderock wind tunnel
and gives a template for what might be needed for future tests at any U.S.
Government facility.
1.6 Overview of Dissertation
Chapter 1 introduces the background and motivations of research into tiltrotor
whirl flutter. A literature review provides a state-of-art overview on experimental
tiltrotor tests, including previous wind tunnel tests and computational analyses. The
scope and contribution of the current study are highlighted at the end of chapter.
49
Chapter 2 describes a 2-ft diameter tiltrotor model that was built for risk-
reduction and to explore flutter actuation system methods. The development and
fabrication of the model and wind tunnel test in the Glenn L. Martin wind tunnel
are detailed.
Chapter 3 shows the design of the Maryland Tiltrotor Rig (MTR) for teh
Glenn L. Martin wind tunnel. Desired features and capabilities are listed for the
rotor, hub, blades, and wing.
Chapter 4 describes the properties and features of the fabricated MTR as well
as the electric drive components.
Chapter 5 details the instruments on the MTR and their calibration. The load
cell, accelerometer, electric actuators, pitch encoders, shaft torque gauge, pitch link
gauges, gimbal hall effect sensors, shaft hall effect sensor, and wing strain gauges
are covered. Off-rig instruments for data acquisition are also described.
Chapter 6 describes the methodology to evaluate whirl flutter for a 9 DOF
tiltrotor model. Verification results are shown and compared to a Bell 25 ft model.
Results for the MTR are also shown and discussed.
Chapter 7 presents the first flutter test results. The test location, conditions,
procedures, damping measurement method, and parametric results are shown.
Chapter 8 summarizes the current work, draws key conclusions, and recom-
mends works for future research.
50
Chapter 2: Flutter System Development Model
A 2-ft diameter, three-bladed, unpowered, gimballed hub tiltrotor model was
developed as a risk-reduction model to gain experience for fabrication of blades,
and testing of whirl flutter in the Glenn L. Martin Wind Tunnel (GLMWT). The
Flutter System Development (FSD) model was fabricated in-house with only the
swashplate and pitch linkages purchased off-the-shelf.
2.1 FSD Description
A picture of the FSD, designed to be 1/12.5-scale XV-15, is shown in Fig. 2.1.
The FSD wing is a NACA 0012 airfoil with Rohacell 31 foam, one bi-directional
carbon fiber ply for the skin, and 16 unidirectional carbon fiber plies for the spar.
The FSD wing is actually a re-purposed rotor blade normally used for the Alfred
Gessow Rotorcraft Center?s hover stand. The wing properties are shown in Table
2.1.
51
Figure 2.1: 2-ft diameter flutter system development model.
52
Table 2.1: FSD wing properties.
Parameter Value
Length, in. 28
Chord, in. 3.15
EI , N ?m2beam 24.5
EI 2chord, N ?m 250
GJ , N ?m2 23.5
2.2 FSD Pylon and Hub
The pylon assembly of the FSD consisted of a wing tip insert that had three
microservo actuators mounted to it, and the main shaft running through the tip.
Pictures of the wing tip insert and its assembly are shown in Fig. 2.2
(a) Exploded view of the wing tip com- (b) Wing tip insert assembled.
ponents.
Figure 2.2: FSD wing tip assembly.
53
Adafruit microservos were used to actuate the swashplate. The servos were
mounted to a 3D-printed part that was then fixed to the wing tip insert. A CAD
model of the servo cage and the resulting servo assembly is shown in Fig. 2.3.
(a) 3D-printed servo cage, made of ABSplus ma- (b) Servos mounted to cage.
terial.
Figure 2.3: FSD actuators assembly.
A CAD model of the FSD hub is shown in Fig. 2.8(a). The hub was fabricated
in-house on a manual mill and lathe. The swashplate was the only part bought off-
the-shelf from a 3-blade RC helicopter. A list of the purchased parts are shown
in Table 2.2. The linkage lengths had to be modified, so long threaded rods were
trimmed to the required lengths and used, instead of the rods that came with the
linkage set.
The assembly of the FSD actuators and hub to the wing tip insert is shown in
Fig. 2.5.
54
(a) CAD model of the FSD gimballed hub. (b) Physical hub components.
(c) Off-the-shelf RC helicopter swashplate and
in-house fabricated linkages.
Figure 2.4: FSD rotor model and components.
Table 2.2: Purchased parts for FSD swashplate.
Part # Description Price ($)
OXY3-091-SP OXY Heli Qube 3-Blade Ultra Swashplate 20.49
OXY3-001-SP OXY Heli Carbon Steel Main Shaft Set 9.99
OXY3-037 OXY Heli Servo Linkage Set 8.29
OXY3-036 OXY Heli Servo Arm Set 5.59
55
(a) Wing tip insert with servo cage mounted to (b) Swashplate connected.
rear.
(c) Hub attached.
Figure 2.5: FSD wing tip assembly.
56
2.3 FSD Blade Fabrication
The FSD had three sets of proprotor blades. Straight, ?45 deg linear twist,
and ?45 deg linear twist with swept-tips. The blades were 10.75 inches in length
and 1.32 inches in chord. These blades were fabricated in blade molds shown in Fig.
2.6.
Figure 2.6: FSD blade molds: straight, twisted, and twisted with swept-tips.
Table 2.3 shows the materials used for blade fabrication. At this scale, there
was no requirement for adhesive tape, leading edge weights, or a blade spar. Unlike
the pre-preg carbon fiber plies for the wing, two layers of fiberglass plies had to be
laid on top of each other and then epoxy resin was poured and spread over the area.
Extra care needed to be taken to ensure the fiberglass plies did not slide significantly
between each other. For root inserts, two small pieces of aluminum sheet metal are
used to reinforce the blade root. The sheet metal is pressed into the foam, the foam
is wrapped with the fiberglass skin, placed in the mold, then cured with the blade.
Once the curing process is complete, the blade is trimmed and holes are drilled into
the blade root.
57
Table 2.3: FSD blade materials.
Blade Part Description Part # Vendor
Foam Rohacell 31 IGF RF3124 CST
Skin E-glass Fiberglass Cloth 1080-50 Aircraft Spruce
Adhesive PR2032/PH3660 Gallon Kit 01-42150 Aircraft Spruce
2.4 FSD Wind Tunnel Test
Figure 2.7 shows a 3D-printed stand made out of 100% filled Onyx on the
Markforged Mark 2 printer. The stand was printed in two halves so it could clamp
the blade like a clamshell. The stand had holes for the root insert of the wing and
holes along the edges to clamp the wing and bolt to the wind tunnel post.
Figure 2.7: FSD base mount, 3D-printed on Markforged Mark 2.
For data acquisition, the FSD used an NI compactDAQ-9174 chassis with NI-
9401 Digital I/O module for microservo control, an NI-9237 Strain/Bridge Input
58
module for wing strains, and an NI-9207 Voltage and Current module for hall effect
RPM sensor.
(a) FSD straight blade test up. (b) FSD swept-tip blade test up.
(c) FSD flutter test setup: back view. Safety string on right, flutter
string on left.
Figure 2.8: FSD in GLMWT test setups.
The FSD was tested at the GLMWT in December 2018 for straight-twisted
and twisted with swept-tip blades. The test setups are shown in Fig. 2.8. First,
the FSD was characterized by mapping the RPM to collective and windspeed. The
model was tied down with cables to the wind tunnel floor and turnbuckles used to
59
tighten the cables. Damping was extracted for wind beam mode only. During the
test, the swashplate actuators were not able to excite the rig at the wing frequency,
therefore, a string was attached to the FSD wing tip interface and pulled from
outside the test-section to impart an impulse. The wing strains were recorded and
moving-block method applied to extract the wing damping.
2.5 Chapter Summary and Conclusions
This chapter provided an overview of the 2-ft diameter Flutter System Devel-
opment (FSD) model. It covered the details of the following.
1. A description of the wing properties and dimensions.
2. A description of the pylon and hub assemblies including off-the-shelf compo-
nents.
3. A description of the design and fabrication of small-scale blades.
4. A summary of wind tunnel preparation and testing.
The key conclusions are the following.
1. The FSD confirmed that blade fabrication procedures were adequate for the
larger scale model and no alternative methods were required.
2. The FSD wind tunnel test revealed that, at the larger scale, actuators must
be high frequency to provide flutter actuation for all wing modes.
60
Chapter 3: Design of the Maryland Tiltrotor Rig
This section describes the design of the Maryland Tiltrotor Rig. The Prelimi-
nary Design Review (PDR) occurred in June 2017, and the Critical Design Review
(CDR) occurred in October 2017 at Calspan. A summary is published in Ref. [34].
3.1 Features of the New Rig
The new Maryland Tiltrotor Rig (MTR) is characterized by the following
special features.
1. A hub with interchangeable gimballed and hingeless options.
2. A drive capable of powered and unpowered operations.
3. The rig is capable of supporting loads of Mach-scale rotors of 4.75-ft diameter.
4. A pylon that can be tilted from 90? to 0? at increments of 5?.
The gimballed hub, representing all current generation tiltrotors, is considered
the baseline. The rig is simple but robust, easy to maintain, and easy to expand
over time.
A comparison of the general features with other models clarifies its unique-
ness. The MTR is different from the unpowered, floor mounted, semi-span, hub
61
interchangeable models of the 1970s ? model scale Boeing M222 and Bell M301,
because of the following features:
1. powered rotor
2. pylon tilt
3. straight wing
4. high bandwidth electric actuation of swashplate
5. direct electric drive on the pylon
6. modern instrumentation, including load cell on the pylon.
The MTR is different from the powered, wall mounted, semi-span, gimballed
models ? WRATS (Langley TDT), TRAM (NASA Ames) and VDTR (Sikorsky)
since then, because of the following features:
1. interchangeable hub
2. motor located in pylon (simulating the engine)
3. floor mounted
4. straight wing
5. load cell on pylon (unlike WRATS and TRAM)
6. flutter rig (TRAM and VDTR measured loads, not flutter)
62
The extensive 1/5 scale gimballed hub Bell models tested during the 1980s
were several generations of development models specific to the V-22 aircraft with
restricted properties and datasets.
3.2 Overview of the New Rig
The rig consists of the wing frame, motor drive, rotor shaft, hubs (gimballed
and hingeless), swashplate (three-bladed), and major instrumentation hardware (see
later). The blades and wing spars can be inserted in and out depending on the
nature of investigation. The blades can be Froude- or Mach-scaled; Froude- for
whirl flutter and Mach- for loads. The rig is designed to allow Mach-scaled rotors,
which means adequate power from the motor, and adequate structure to withstand
the higher loads. The detailed design and construction of the rig is carried out by
Calspan Systems. The composite blades and wing spars are designed and fabricated
in-house at Maryland.
The overall specifications are given in Table 3.1.
3.3 Size and Scale
The dimensions of the rig are shown in Figs 3.1 and 3.2 placed inside the Glenn
L. Martin wind tunnel test section.
The wall clearances from the blade tip are determined by the rotor radius and
the vertical placement of the hub. Figure 3.3 shows the possible tip clearances for a
given rotor radius as the hub is moved down (left of curves) or up (right of curves).
63
Model Parameters Maximum
Rotor radius R 2.375 ft
Height above ground 3.0875 ft
Rotor speed 2750 RPM
Number of blades 3
Type of hub Gimballed and hingeless
Pre-cone 2?
Pitch-flap ?3 ?15?, for gimballed only
Thrust 300/? 70 lbf
Hub Moments 198 ft-lbf
Centrifugal retention per blade 2430 lbf
Weight of blade 0.66 lb
Weight of hub-pylon 65 lb
Power Electric motor, water cooled
20 HP at 2660 RPM
Table 3.1: Top level MTR specifications.
Figure 3.1: The Maryland Tiltrotor Rig (MTR) inside Glenn L. Martin
wind tunnel test section (7.75- by 11-ft); dimensions in inches; dashed line
is Center Line of tunnel.
64
Figure 3.2: The Maryland Tiltrotor Rig (MTR) inside Glenn L. Martin
test section (7.75- by 11-ft); isometric view.
The V-22 tip clearance from fuselage in cruise is around 0.105 R. With this clearance
at the bottom, a radius of 2.375 ft would leave a clearance of 1.16 R at the top.
The baseline position is to leave a clearance of 0.3 R at the bottom and 0.96 R at
the top. This still allows a radius of clearance at the top while leaving ample space
below for future needs.
The maximum rotor radius is presently set at R = 2.375 ft. So the scale factors
are:
1/8.00 V-22
1/2.00 TRAM (which is similar to a 1/4 scale V-22)
1/5.26 full-scale Bell 25-ft dia gimballed rotor tested at Ames 40- by 80-ft
(XV-15 rotor)
65
1.8
1.6
1.4
1.2
R = 2.00 ft
1
0.8 2.25
0.6 2.50
0.4
2.75
0.2
3.00
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Bottom clearance in R
Figure 3.3: Tip clearances from top and bottom of the wind tunnel as
function of rotor radius; the symbol shows the present configuration with
R = 2.375 ft and clearances of 0.3 R and 0.96 R from the bottom and top
respectively.
1/5.47 full-scale Boeing 26-ft dia hingeless rotor tested at Ames 40- by 80- ft
(Bo 105-like rotor)
1.69/1 of model Bell M301 gimballed and model Boeing M222 hingeless 2.8-ft
dia
The design is loosely anchored to Bell 25-ft gimballed (XV-15) and Boeing 26-
ft hingeless (Bo 105) rotors where possible. The primary departure is in the pylon
inertia (weight, C.G., moments of inertia). This is unavoidable because electric
motors do not scale as engines, and the pylon includes the load cell and slip ring
? components essential for model testing. The increase in inertia can be partially
countered through the placement of wing frequencies but expected (and confirmed)
66
Top clearance in R
to reduce the flutter frequencies nonetheless. Flutter at low speeds, if encountered,
would be considered a positive feature for research purposes as long as the properties
are well documented.
The MTR rotor speeds are compared to the Bell (gimballed) and Boeing (hin-
geless) rotors in Table 3.2.
Scale Full-scale Froude-scale Mach-scale
Factor RPM RPM RPM
Bell full-scale 25-ft dia 1 458 - -
Bell model M301 2.8-ft dia 1/8.89 - 1366 -
MTR gimballed 4.75-ft dia 1/5.26 - 1050 2409
Boeing full-scale 26-ft dia 1 386 - -
Boeing model M222 2.8-ft dia 1/9.244 - 1174 -
MTR hingeless 1/5.47 - 903 2111
Table 3.2: MTR rotor speeds (in revolutions per minute (RPM)) compared
to previous Bell (gimballed) and Boeing (hingeless) tests.
For the MTR, a rotor speed of 2660 RPM will achieve the same tip Mach
number MT = 0.59 as V-22 in cruise, and a rotor speed of 3200 RPM will achieve
the same tip Mach number MT = 0.71 as V-22 in hover. The latter is deemed too
high; a lower tip Mach number MT = 0.61, similar to the TRAM model, is set as
the maximum RPM of the MTR. This requires a lower maximum RPM of 2750.
At Froude-scale, flight speeds of 360 and 400 kt of the V-22 will translate
into tunnel speeds of 130 and 140 kt respectively, which are well within the 200 kt
maximum limit of the Glenn L Martin tunnel.
67
3.4 Rotor
The maximum rotor radius R is 2.375 ft ( 0.7239 m ). Airfoil profiles are
assumed to begin at 0.1R for sizing calculations but likely near 0.2 ? 0.3R for
the actual blades. The solidity is ? = 0.1. The maximum twist is linear ?45?:
? = ?33.75? ? 45?t (x ? 0.75) where x = r/R and r is the radial dimension. The
maximum sweep is 20? (sweep back) over 20% from 0.8 R outboard. At flat pitch,
the sectional angle is 29.25? at 0.1R, 0? at 0.75R, and ?11.25? at the tip. With
three blades (Nb = 3), and with solidity defined as projected blade area at flat pitch
divided by disk area, the mean chord (? ? R/Nb) is 0.0758 R. Taper is zero. A single
airfoil is assumed across entire span ? the VR-7 with no tab. The maximum RPM
is 2750.
These assumptions produce a hover power of 50 HP (37 kW) at a collective
angle (?75) of 16? and thrust of 318 lbf (1.42 kN). This is considered the maximum
power hover point. This represents the maximum power of the Maryland hover
tower. The tiltrotor rig is not required to supply this power but is designed to
withstand loads up to this point so the rotor head can be tested separately on the
hover tower in future. The vertical shear at the root of each blade is 106 lbf (472 N).
The inplane shear is 23.4 lbf. The centrifugal force at the root requires weight of each
blade; the maximum weight considered is 0.66 lb (mass 0.3 kg), which gives 2024 lbf
(8.9 kN). For the swept tip blade, a maximum of 20% of the blade mass is assigned
to the swept portion, offset from the hub center, inplane, with center of gravity
located at 0.9 R (center of the swept portion) along a 20? sweep line. Assuming the
68
twist to be about local quarter-chord and center of gravity on quarter-chord there
is no vertical offset. So the sweep introduces an additional inplane shear of 33 lbf
toward the trailing edge.
The bending moment at the root in hover is moment due to aerodynamic force
?
(lift) MA = r dL minus a relief from the centrifugal force in presence of blade
flapping. Assuming a spanwise mass distribution m kg/m, and blade flapping ? rad,
?
the relief is ?2 ? mr2 dr. The moment at the root is k? ? where k? is an equivalent
root spring in N-m/rad.
? ?
k? ? = r dL? ?2 ? mr2 dr
= MA ? I 2? ? ?
MA is 175 ft-lbf at the maximum hover point. I? is the flapping moment
of inertia which for a uniform blade is I = 1 3? 3 mR = 1.2434 lb/ft
2 where m =
0.66/2.375 = 0.278 lb/ft. The spring is related to the rotating flap frequency ??
(non-dimensionalized with rotor RPM, in /rev) as k? = (?2??1) I? ?2. The blade root
bending moment is then related to the flap angle and flap stiffness as in Table 3.3.
Greater the allowed flapping angle, lower the moments at the root, but the blade root
must be softened to allow flapping, which means a softer spring and flap frequency
nearer to 1/rev. If for example, a flapping of 3? is allowed, the net moment at the
root is only 7.3 ft-lbf, and the corresponding flap frequency would be 1.022 /rev.
69
Aero moment Flap angle Centrifugal relief Net moment Root spring Flap frequency
MA ? due to flapping at root k? ??
ft-lbf degree ft-lbf ft-lbf ft-lbf/rad /rev
175 0 0 175 locked rigid
175 1 56 119 6824 1.77
175 2 112 63 1811 1.25
175 2.25 125.8 49 1254 1.18
175 2.5 139.7 35 808 1.12
175 3 167.7 7.3 140 1.022
175 3.13 175 0 free 1.00
Table 3.3: Blade root flap moment in hover.
Aero moment Flap angle Centrifugal relief Net moment Root spring Flap frequency
MA ? due to flapping at root k? ??
ft-lbf degree ft-lbf ft-lbf ft-lbf/rad /rev
175 2 112 63 locked rigid
175 2.25 125.8 49 11285 2.13
175 2.5 139.7 35 4041 1.50
175 3 167.7 7.3 420 1.064
175 3.13 175 0 free 1.00
Table 3.4: Blade root flap moment in hover for 2? pre-cone.
If the blade is pre-coned at an angle, then the same moment can be absorbed
by less flexibility at the root. The moment balance with pre-cone is
k? (? ? ?P ) = M 2A ? I? ? ?
With a pre-cone of ?P = 2?, the root moment is related to the flap angle and flap
stiffness as in Table 3.4. The moment from a 3? flap angle (7.3 ft-lbf) is now absorbed
by spring deflection of only ? ? ? = 1?P , so a stiffer hub can be used. The pre-cone
allows higher flap frequencies to be achieved without increasing the root moment.
Pre-cone is also an important parameter for whirl flutter. A pre-cone of ?P = 2?
70
will be used for the present rig. The maximum root moment is then 63 ft-lbf in flap
up direction (considering a rigid hub, but likely lower due to flexibility). The root
moment in the lag direction is 32 ft-lbf. The root moment in the pitch direction is
a nose down 2 ft-lbf. The nose down moment sizes the pitch link and actuators.
The target flap frequency, non-dimensionalized with rotor RPM (in /rev), is
?? = 1.85 for the gimballed hub, although frequencies in the range ?? = 1.20? 1.85
(TRAM to XV-15) are acceptable. This is the collective frequency (with gimbal
locked), the cyclic frequency is always 1.0 /rev without a hub spring. The target
flap frequency for the hingeless hub is between ?? = 1.30? 1.50.
3.5 Blades
The blades are interchangeable and many different blade geometries will be
tested on the rig. They are likely all carbon fiber composite blades with either
rectangular or D-spars. For the baseline blades, the primary flap and lag frequencies
were intended to remain within the following range:
??0 = 1.20? 1.85 ?? = 1.20? 1.80 gimballed, with gimbal locked (collective)
?? = 1.20? 1.50; ?? = 0.70? 0.80 hingeless
(3.1)
However, the lag frequency of the fabricated blades were significantly higher near
5/rev at the Froude-scale RPM of 1050. This was due to limitations of the carbon
fiber material and construction of the blade root arm.
71
Property Full scale Froude Value Mach Value
approx scaling scaling
EI 2 5 4N Nm s s
0.1 < x < 0.3 8? 105 198.7 1046
0.3 < x < 0.5 1.5? 105 37.3 196.1
0.5 < x < 1.0 0.5? 105 12.4 65.4
EI Nm2 s5 s4C
0.1 < x < 0.3 7? 105 173.8 915
0.3 < x < 0.5 20? 105 497 2614
0.5 < x < 1.0 12? 105 298 1567
m kg/m s2 s2
0.0 < x < 0.2 55 1.99 1.99
0.2 < x < 1.0 10 0.36 0.36
Table 3.5: Nominal stiffness and mass properties for gimballed rotor
blades; EIN and EIC are the normal and chord-wise flexural stiffnesses
and m the mass per span; 1 Nm2 = 2.42 lbf-ft2; full-scale values from Bell
25-ft diameter model (XV-15 rotor), x=r/R, approximate mean values
are taken; s = model length/full-scale length = 1/5.26.
Property Full scale Froude Value Mach Value
approx scaling scaling
EI 2 5 4N Nm s s
0.0 < x < 0.08 3? 105 61.3 335
0.08 < x < 0.2 0.5? 105 10.2 56
0.2 < x < 1.0 0.2? 105 4.1 22.3
EI Nm2 s5 s4C
0.1 < x < 0.3 3? 105 61.3 335
0.3 < x < 0.5 3? 105 61.3 335
0.5 < x < 1.0 12? 105 245 1341
m kg/m s2 s2
0.0 < x < 0.08 114 3.8 3.8
0.08 < x < 1.0 5 0.17 0.17
Table 3.6: Nominal stiffness and mass properties for hingeless rotor blades;
EIN and EIC are the normal and chord-wise flexural stiffnesses and m the
mass per span; 1 Nm2 = 2.42 lbf-ft2; full-scale values from Boeing 26-ft
diameter model (Bo 105 rotor), x=r/R, approximate mean values are
taken; s = model length/full-scale length = 1/5.47.
72
The gimballed frequencies represent the state of the art range from V-22 and
TRAM -like to XV-15 -like proprotors. The hingeless frequencies are expected to
produce interesting air resonance instability. The hub can be rigid in flap and still
absorb flap loads (first row in Table 3.4) so blades with very high flap frequencies
(2/rev and higher) can be investigated.
The nominal targets for blade structural properties are given in Tables 3.5
(gimballed) and 3.6 (hingeless) based on the Bell 25-ft and Boeing 26-ft diameter
rotors respectively. The discontinuities near the root are due to hub connections
(blade grip, pitch case, hub) and are not expected (or required) to be reproduced.
The baseline blades will target average properties from 0.3 R to the tip.
3.6 Hub and Shaft
The hub consists of blade retention, pitch mechanism, and shaft connection.
A simple construction with a single load path is desired for both gimballed and
hingeless hubs.
The hub contains sensors for motion (gimbal angle and blade root pitch), slip
rings for data transmission, a 6-component load cell, a torque transducer, and a
tachometer and 1/rev pulser for rotor speed and position.
The hub holds three blades (Nb = 3) and allows a configuration change between
gimballed and hingeless rotors. The pitch links are on the trailing edge side to
provide a negative pitch-flap coupling for the gimballed rotor. A flap up about the
gimbal by an angle ?? would pitch the blades down by an angle ??, so ??/?? is
73
negative and quantified by an angle ?3 such that ??/?? = ? tan ?3. The nominal
dimensions are: pitch horn location at 0.019 R, pitch horn radius 0.078 R (behind
blade), and a pitch link length of 0.144 R (based on TRAM data). The pitch links
are actuated by a conventional swash-plate.
Both hubs have a pre-cone of 2?. The specific features of each hub are given
below.
3.6.1 Gimballed hub
A constant velocity joint was desired, but deemed not essential because of the
cost and complexity involved. Simplicity was an over-riding factor for this research
rig. The gimballed hub is therefore an universal joint, similar to the XV-15 hub
? essentially a stiff in-plane hingeless hub sitting on a gimbal. An universal joint
will produce a 2/rev excitation from the RPM so the wing-pylon natural frequencies
must steer clear of this region. There is no gimbal undersling or torque offset by
intent. A small undersling might be a fall-out from the construction.
Gimbal spring is also zero by intent. The full scale Bell 25-ft rotor had a hub
spring of 2700 in-lb/?. With scale factor s = 1/5.26 the maximum allowable model
spring would be 2700 s2 = 97.6 in-lb/?.
Ideally, pitch-flap coupling should produce the same effect on flap frequency as
full-scale, so ? tan ?3 should remain constant, not ?3, where ? is the Lock number.
The ?3 angle also varies with the cosine of collective away from nominal setting. For
this rig, the nominal value is set as ?3 = ?15? at flat pitch ? = 0?75 .
74
3.6.2 Hingeless hub
Pitch-flap coupling is not needed for the hingeless hub.
The construction of the hingeless hub is simple by itself. The hub/blade as-
sembly can slide into the shaft as a push fit. Rotor torque can be transmitted to the
shaft by a key. The hub can be secured axially with a nut. But the requirement for
configuration changeover, from gimballed to hingeless, or vice versa, introduces cer-
tain considerations. The changeover would follow a certain step by step procedure.
An example of the basic steps would be:
1. Installing or removing instrumentation needed only for the gimballed rotor
(gimbal flapping).
2. Installing or removing wing spar ballast weight if needed for the hingeless
rotor (the hingeless hub might be lighter and ballast weight might be needed
to recover same wing-pylon frequencies).
3. Relocating swashplate scissors.
4. Re-configuring spinner and other shaft end item.
5. Re-calibrating collective and cyclic controls.
75
70 36
32 Cruise mode
60
160 kn (airplane)
28 CTOS = 0.025
50 V = 160 kn 
C  / s 24
T
40 0.03 Mach Tip 20 V = 130 kn 
130 kn 0.59
V?22
16 Conversion30
(Helicopter)
12 CTOS = 0.1
20 mu = 0.15 Mach Tip
8 V = 61 kn 0.59
V?22
10
C  /s  0.002 4 V = 100 kn 
T
0 0
0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000
RPM RPM
(a) Torque versus rotor speed (b) Power versus rotor speed
60 80
70
50 160 kn
60 270 ft/s
82 m/s
40 C  / s
T 160 kn Mach Tip 50
0.03 270 ft/s 0.59
82 m/s V?22
30 40
130 kn
219 ft/s
130 kn 30 67 m/s
20 219 ft/s
67 m/s
20
Mach Tip
10 0.59
C  /s  0.002 10
T V?22
0 0
0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000
RPM RPM
(c) Thrust versus rotor speed (d) Collective pitch versus rotor speed
Figure 3.4: Predicted MTR performance used for design: torque, power,
thrust and collective pitch (at blade root) versus rotor speed; CTOS is
blade loading CT/? and mu is tip speed ratio ?.
3.7 Drive
The drive supplies the rotor with a maximum of 20 HP at 2660 RPM and
can be operated down to at least 900 RPM. In general it can function continuously
down to 0 RPM. Three possible options were explored:
1. an electric motor, mounted on the pylon, driving the rotor directly or through
a gear-box,
76
lb ft?lb
Collective, degree HP
2. an electric motor, located below the rig, with a high powered shaft through
the wing, and
3. a hydraulic motor, located outside the rig, with high pressure fluid lines
through the wing.
Option 1 offered the best solution.
Option 2 was too complex, costly, less safe and not conducive to frequent spar
swaps.
Option 3 was feasible but an electric drive was preferred for its higher band-
width.
The motor was chosen based on the predicted torque- and power-speed en-
velopes, Figs 3.4(a) and 3.4(b) respectively, and constraints of pylon weight and
dimensions. Hydraulic motors were discarded due to their slow response, but also
difficulty in passing high pressure fluid lines through the deforming wing. Electric
motors from eleven vendors and pneumatic motors from two vendors were consid-
ered. An electric motor with suitable speed and torque control was selected ?
Plettenberg NOVA 30. This is a water cooled permanent magnet motor operating
at 80 ? 140 V (nominal 110 V), maximum speed of 5000 RPM, maximum torque
of 80 Nm (59 ft-lbf), maximum continuous power of 30 kW (22.4 HP), efficiency of
90% (including controller), diameter of 20.2 cm (7.56 inches), and total weight of
6.8 kg (15 lb) without the controller. The controller (and water tank) will be housed
outside the pylon in the tunnel control room.
77
V-22 XV-15 Bell 25 ft Bell M301 Boeing 26 ft Boeing M222 MTR
aircraft aircraft full scale 1/8.89 full scale 1/9.24 nominal
Froude Froude
Radius R ft 19 12.5 12.5 1.4 13 1.4 2.375
Cruise RPM 333 517 458 1366 386 1174 1050
Beam per rev 0.53 0.45 0.42 0.38 0.36 0.42 0.35-0.45
Chord per rev 0.80 0.86 0.70 0.66 0.62 0.73 0.60-0.86
Torsion per rev 1.04 1.07 1.30 1.36 1.43 1.58 1.04-1.60
Table 3.7: Wing-pylon frequencies normalized with cruise RPM.
Figures 3.4(c) and 3.4(d) show the range of thrust and collective pitch angles
(root pitch angles) required for cruise flight. High collectives are required at lower
RPM, which is typical of tiltrotors, due to the high blade twist.
3.8 Pylon
The pylon consists of a slip ring, the electric actuators, the electric motor, the
load cell (6-component rotating balance on the rotor drive shaft), the shaft, and a
set of couplings, adapters, and fairings.
The pylon is integrally mounted on the wing spar through two coupling plates.
The plates have holes drilled in a verniered arrangement, every 15? on the wing side
and every 20? on the rotor side, providing a 5? resolution of static pylon tilt. The
total pylon weight for the gimballed hub is estimated to be 65 lb (pylon body 8.5,
fairings 2.8, three actuators 9, load cell 6, motor 15, slip ring 4.5 and the rotor head
without blades 19 lb).
78
3.9 Wing
The wing is straight (departure from XV-15 or V-22 and similar to V-280),
untwisted, and 18% thick with a simple profile (NACA 0018). The state of the art
thickness being 20? 23% (approximately) and the target being 14% this is deemed
an appropriate intermediate baseline. The wing has no flaps.
The wing is a critical part of the rig. The coupled wing-pylon natural frequen-
cies (including hub but excluding blades) in bending (beam-wise and chord-wise)
and torsion must achieve certain targets to simulate whirl flutter. The wing-pylon
natural frequencies for several rigs in previous flutter tests, normalized with rotor
RPM, are given in Table 4.3, together with the MTR targets. There is some flexi-
bility in the targets, although attempts will be made to remain near the Bell 25-ft
and Boeing 26-ft frequencies. These rotors (and their model-scale versions M301
and M222) have the precedence of being tested on the same wing and might allow
historical insights.
The frequencies can be met with a simple spar as in the previous model-scale
flutter tests (for example an aluminum box beam from tunnel attachment to pylon
coupling plate). The key difference is the powered rotor and hub instrumentation
that changes the pylon weight and hence the dimensions. The Bell and Boeing
full-scale tests used a thinner 13.5% thick wing; the choice of 18% thickness here is
deliberate, it provides ample space for parametric variations of the spar for future
needs. The spar is the important piece, the outer profile can always be replaced.
The spar attachment to the pylon coupling and to the floor attachment are simple
79
and robust (bolted) and provide more than 5 Factors of Safety margin in for all
operating loads, steady state and oscillatory.
The wing structural damping is also an important parameter. This value will
be measured after assembly of the hardware.
Measurement Sensor Quantity Leads Mounting
Blade pitch angle Hall sensor 3 12 1 per blade
Gimbal tilt angle Hall sensor 2 8 1 per blade
Rotor speed and position 1/rev 1
Rotor torque Strain gauge 8 8 Two full bridges
on the shaft
3-axis forces Load cell 1 on pylon bulkhead
and moments near motor
Vibration Tri-ax accel 1 pylon frame
Slip ring 1 64 channels/leads,
16 measurements,
4 leads per measurement
Absolute pitch angle inclinometer 1 tool mounted at
blade attachment
Fixed system actuation integrated below swashplate
Table 3.8: MTR on-rig instrumentation
3.10 Instrumentation
The rotor, pylon, and wing will all be instrumented. The major instrumenta-
tion on the rig are listed in Table 3.8. Minor instrumentation like sensors on the
80
wing, standard equipment like wind tunnel balances, and out of rig equipment like
track and balance, VICON, or PIV are left out.
3.11 Chapter Summary and Conclusions
This chapter covered the conceptual design of the Maryland Tiltrotor Rig. It
covered the following.
1. An illustration of the overall dimensions of the rig and the clearance as installed
in the GLMWT.
2. A description of the architecture of the subassemblies.
3. A description of the load limits on the rotor for hover.
4. A description of the motor requirements and the considerations for motor
options.
5. A list of the on-rig instrumentation.
6. A description of the target properties, loosely scaled to the XV-15.
In conclusion, the design of the MTR has matured to the level where fabrica-
tion can begin. The following chapter describes the actual rig after fabrication.
81
Chapter 4: The Maryland Tiltrotor Rig
This chapter describes the Maryland Tiltrotor Rig (MTR). It covers the MTR
dimensions, and overviews of the wing assembly, pylon assembly, and rotor assembly.
4.1 Dimensions
The Maryland Tiltrotor Rig (MTR) is a 3-bladed, semi-span, floor-mounted,
optionally-powered, tiltrotor rig. The first installation was in November 2019 at the
Glenn L. Martin Wind Tunnel (GLMWT). Figure 4.1 shows a photograph of the
installation. Figure 4.2 shows the CATIA model of the MTR in its baseline airplane
mode cruise configuration. The principal dimensions are shown in this figure. The
dimensions are also listed in Table 4.1. Figure 4.3 shows the configuration in all
three modes - cruise, transition, and hover.
The baseline rotor and wing spar of the MTR is loosely a Froude-scale model
of the Bell XV-15 wing and 25-ft diameter proprotor. With a rotor diameter of 4.75
ft, the MTR is a 1/5.26 scale model of the full-scale proprotor. The design was
constrained to fit within the wind tunnel test section dimensions of the GLMWT
(11-ft wide by 7.75-ft tall), as shown in Figure 4.4, while keeping ample margins
from the wall.
82
Figure 4.1: Maryland Tiltrotor Rig in the Glenn L. Martin wind tunnel; November
2019.
Table 4.1: MTR Size Overview
Dimension Value (in) Value (cm) x/R
Baseplate to Pylon Center 36.5 92.71 1.28
Tunnel Floor to Pylon Center 34 86.36 1.19
Wing Fairing Span 27.5 69.85 0.96
Wing Chord 15.45 39.24 0.54
Pylon Length 34.02 86.41 1.19
Pylon Diameter 8.58 21.79 0.30
Rotor Radius 28.5 72.39 1.0
Root Cutout 7.55 19.18 0.26
83
84
34.02
7.55 9.58
28.5
34 36.5 27.5
2.88 15.45
Tunnel Floor
Front view Left view
Y
8.58
Z X
Bottom view
Isometric view
Figure 4.2: Maryland Tiltrotor Rig; all dimensions in inches.
85
Cruise Transition Hover
Figure 4.3: Maryland Tiltrotor Rig in cruise, transition, and hover regimes. Freewheel state is same configuration as cruise.
Figure 4.4: MTR designed for the Glenn L. Martin wind tunnel test section.
The MTR is a research rig with interchangeable wing spars, rotor hubs, and
rotor blades. The baseline configuration of the MTR has a rectangular, solid alu-
minum wing spar and an XV-15-like gimballed hub. This section will describe the
major features of the baseline rig starting from the base of the model to the rotor
hub.
4.2 Wing Assembly
The wing assembly is shown in Figure 4.5. The wing is straight (a departure
from the XV-15 and V-22 but similar to the V-280), untwisted, and has a 18%
thickness to chord (t/c) ratio with a NACA 0018 profile. With the current state-of-
the-art thickness being 20? 23% and the ultimate target being 14%, a thickness of
18% was deemed an appropriate intermediate baseline.
86
The primary requirement for the wing assembly is to allow for interchangeable
spars, which necessitated easily removable wing ribs and fairings, shown in Figure
4.6. The wing ribs and fairings were designed to be non-structural, so while they
add mass, they minimally affect the stiffness of the wing. The wing also provides
a channel for power cables and coolant hoses and instrumentation wires to run to
the pylon. The segmented fairings are made with a foam core wrapped in fiberglass
skin. Slots are cut into the foam for the ribs and aluminum anchors are placed in
locations for screws shown in Figure 4.7. The aluminum anchors in the fiberglass
are threaded so screws can keep the two halves of the fairings together. The ribs and
fairing fasteners are listed in Table 4.2. The ribs to spar connection uses two long
screws with barrel nuts on the other side to clamp the ribs to the spar. Attention
must be given to the bored holes on the ribs: one side is bored a little deeper for
the barrel nuts to sit in, the other side is slightly shallower for the screw heads.
Table 4.2: Wing assembly fasteners.
Connection Screw Type Tool Type
Spacer to spar 10-32 3/8? flat cap 1/8? Allen key
Ribs to spar 10-32 2.25? socket cap 5/32? Allen key10-32 barrel nut 3/16? Allen key
Ribs to ribs (forward 3 holes) 10-32 5/8? socket cap 5/32? Allen key
Ribs to ribs (trailing edge) 10-32 1/2? socket cap 5/32? Allen key
Fairings to ribs (forward 3 holes) 10-32 3/8? flat cap 1/8? Allen key
Fairings to ribs (trailing edge) 10-32 1/4? flat cap 1/8? Allen key
Fairings to fairings (leading edge) 6-32 3/4? socket cap 7/64? Allen key
Fairings to fairings (trailing edge) 6-32 5/16? socket cap 7/64? Allen key
87
88
(A) (B) (C) (D)
Figure 4.5: Maryland Tiltrotor Rig Wing Assembly: (A) Baseplate and wing spar with spacers (B) Wing ribs attached (C)
Segmented fairings attached on right side (D) Fairings completed and coupling plate attached on spar tip.
(a) Wing fairings: left to right corresponding to bottom to top of model.
(b) Wing assembly ribs: left to right corresponding to bottom to top of model.
Figure 4.6: Wing assembly fairings and ribs.
89
(a) Half the wing fairing; the top fairing is cut to make clearance for cables and
coupling plates.
(b) Top wing fairing with materials labeled.
Figure 4.7: Wing fairing details.
90
The baseline wing spar was designed to the Froude-scale frequencies of the XV-
15 wing. A comparison of different model frequencies is shown in Table 4.3. The
resulting MTR frequencies are somewhat lower than the other models; however, this
leaves some clearance for lighter spars in the future. The baseline solid aluminum
spar is heavy. Dimensions of the spar can be found in the appendix of Technical
Drawings. To facilitate the interchangeability of the spar, spacers are used to bridge
the gap between the spar and the wing ribs as shown in Figure 4.8. For future spars
with different dimensions, new spacers must be fabricated to match them.
Table 4.3: Wing-pylon frequencies normalized with cruise RPM; MTR
RPM shown is Froude-scale RPM for flutter tests.
Full-scale V-22 XV-15 Bell 25 ft Model Bell M301 Model MTR
1/8.89 Froude 1/5.26 Froude
Radius R ft 19 12.5 12.5 1.4 2.375
Cruise RPM 333 517 458 1366 1050
Beam per rev 0.53 0.45 0.42 0.38 0.29
Chord per rev 0.80 0.86 0.70 0.66 0.53
Torsion per rev 1.04 1.07 1.30 1.36 1.06
The MTR steel baseplate, which clamps the wing spar, is bolted to the top
of the tunnel post. Two large shoulder bolts hold the wing spar to an L-shaped
support on the baseplate.
The spar tip is attached to a coupling plate using three 1/4-inch diameter
shoulder bolts. The coupling plate is the connection between the wing spar and the
pylon, as shown in Fig. 4.9. Two guide pins on the spar coupling plate slide into
91
Figure 4.8: Spacers used to fill gap between wing spar and wing ribs.
92
a slot in the pylon-side coupling plate to assist in alignment of the holes, shown in
Fig. 4.9(a). The spar-side coupling plate has 24 holes spaced 15? apart while the
pylon-side plate has 18 holes spaced 20? apart. This verniered design allows for 5?
of static tilt increment of the pylon from 0? to 90? with exactly six shoulder bolts
clamping the two plates together in any setting. This coupling plate connection is
made deliberately rigid and does not allow for free-play or stiffness adjustments.
4.3 Pylon Assembly
The pylon is a housing that contains the rotor shaft, a water-cooled electric
motor, a 6-axis load cell, 3 electric linear actuators, and a 64-channel slip ring.
Figure 4.10 shows the pylon mounted to the wing spar. The components can be
seen in Figure 4.11.
The motor is water-cooled. The inlet hose is connected to city water supply
in the wind tunnel balance room underneath the test section. The outlet hose
runs straight down to a drain pipe in the ground on the balance room. The motor
properties are shown in Table 4.4.
While the MTR was designed to have all primary load paths go through the
load cell, the pylon does have a secondary load path that bypasses the load cell.
The load path is described in Figure 4.12. The effect of the secondary load path
on load cell calibration is minor, but explored clearly in the Calibration chapter
later. Figure 4.12(a) shows the section view of the pylon assembly and labels the
major components. Figure 4.12(b) shows the primary load paths that travel from
93
(a) Spar-side coupling plate bolted to spar.
(b) Pylon-side coupling plate attached in cruise configuration.
Figure 4.9: Wing-pylon connection through coupling plates.
94
Figure 4.10: Pylon assembly with rotor components removed.
95
(a) Omega160 load cell and Plettenberg NOVA 30 electric motor.
(b) Fabricast 64-channel slip ring and Ultramotion A2 linear actuators.
Figure 4.11: Pylon assembly components.
96
Table 4.4: Electric motor specifications.
Parameter Imperial Units SI Units
Motor weight 15 lb 6.8 kg
Motor diameter 7.8 in 197 mm
Motor length 3.7 in 93 mm
Max power 40 hp 30 kW
Max torque 59 ft-lb 80 N-m
Max RPM 2500? 5000
Flow rate minimum 1 gal/min 63.09 cm3/s
Pressure range 0.5? 2 bar7.25? 29 psi 50? 200 kPa
the shaft and from the actuators to the motor. The loads progress into the load
cell which is mounted to forward bulkhead, into the outer case and then down into
the coupling plate and wing. Figure 4.12(c) shows the secondary load path taking
some loads from the actuators and shaft and passing them into the slip ring through
a flex coupling. The slip ring is mounted to the rear bulkhead, so the loads pass
through the bulkhead and the outer case into the coupling plate and wing from the
rear. Figure 4.13 shows the linear actuators mounted directly to the rear side of
the electric motor. This was to ensure that all loads and moments affecting the
actuators are also captured by the load cell. The motor does not directly touch
the rear bulkhead at any location; the only points of contact on the motor are the
mounts to the linear actuators, the motor shaft to flex coupling of slip ring, motor
shaft to main rotor shaft, and the connector part to the load cell.
In terms of hub forces, thrust passes through the shaft into the motor and
pushes or pulls on the load cell through the connector component, so it is not
97
(a) Pylon assembly section view of major components.
(b) Designed load path.
(c) Secondary load path.
Figure 4.12: Pylon assembly load paths.
98
(a) Linear actuators are attached at two points: the rod-end to swashplate and the mount to the
motor.
(b) Load path from swashplate to motor; pylon housing and rear bulkhead removed for clarity.
Figure 4.13: Linear actuators connection and load path.
99
affected by the secondary load path. For the hub in-plane forces, they travel down
the shaft and into the motor which wants to translate with the hub forces. Therefore,
the in-plane hub forces do get transferred into the secondary load path and causes
inaccurate measurements. For moments, torque is transferred through the shaft
and into the motor which causes a torque on the connector and subsequently the
load cell, so it is not affected by the secondary load path. For pitch and yaw hub
moments, they travel from the shaft into the motor and the connector transfers the
moments to the load cell. These moments are also affected by the secondary load
path because while the flex coupling should act as a pinned support, in reality, some
resistance to rotation is present. For pitch links, the control loads travel into the
swashplate, through the actuators, and into the base of the actuators mounted to
the rear face of the motor. Control loads are affected by the secondary load path.
Only the thrust and torque are relatively unaffected by the secondary load path.
4.4 Electric Drive
The proprotor is driven directly by a Plettenberg NOVA 30 motor shown in
Fig. 4.14. This is a three-phase, brushless DC, inrunner motor with water-cooling
option. The motor controller, MST 140-200, is delivered with the motor and housed
separately. The motor operates at 80 ? 140 V (nominal 110 V), has a maximum
speed of 5000 RPM, maximum torque of 80 Nm (59 ft-lbf), maximum power of 30
kW (40.2 h.p.)at 5000 RPM, max efficiency of 90% (including controller), diameter of
197 mm (7.76 inches), length of 93 mm (3.7 inches), and weight of 6.8 kg (15 lb). The
100
Type:?Nova?30?with?water?cooling
1 2
6
3
4
5
Figure 4.14: Features of Plettenberg NOVA 30 with water cooling.
motor controller is housed outside the pylon in the tunnel control room, connected
to a DC power supply. It uses six step commutation, also known as trapezoidal
commutation, in connection with three 120? hall sensors for communication. The
motor controller allows freewheeling of the motor with no load in freewheeling mode
by driving the motor to a zero-current state.
The flow of power from the tunnel to the motor controller is explained in Fig.
4.15, with the components listed in Table 4.5. The physical connections are shown
in Fig. 4.16.
The rig draws power from the building. The GLMWT supplies 480 VAC/100A.
This is equivalent to 340 VDC/100A, hence 34 kW of power. The MTR is expected
to use 15 kW in the powered cruise condition.
101
Current Motor Power Diagram
D3 D1, D2: Flyback Diode
Power? D3: Blocking DiodeC: 600 ?? capacitor
Supply
60V D2
Tunnel 250A
To motor
3?phase Distribution? Motor?
480VAC Block
C Controller
100A Power?
Supply
60V D1
250A
Figure 4.15: Motor power diagram from wind tunnel supply to DC power supplies
to motor controller; green dotted wire is ground.
5
Table 4.5: Power electronics components.
Component Description Quantity
AC to DC Converter Sorensen SGX Series 60V/250A 2
Flyback Diode Vishay UFL130FA60 1
Blocking Diode Vishay VSKE236/16PBF 1
DC-Link Capacitor Cornell Dubilier 947D601K901DCRSN 1
Heatsink C&H Technology CHEHK18-180MM 1
102
Figure 4.16: Motor power connections from power supplies to motor controller.
103
From the building power to the rotor, all components are part of the MTR.
The building power is first connected to two Sorensen SGX Series 60V/250A DC
power supplies to convert AC to DC. From Fig. 4.15, the 3-phase power from the
building is run to a distribution block with one phase to each wire and one ground
wire. The distribution block splits each wire into two so each power supply gets its
own set of power cables. On the output side of the power supplies, they are shown
to be connected in series to add the voltage up to 120V/250A. This setup requires
flyback diodes, D1 and D2, in case only one power supply is used. The D1 and D2
diodes are two separate diodes but physically placed on the same component. A
blocking diode, D3, is implemented as well to protect the power supplies in case of
reverse current from the motor in a freewheeling condition. All diodes are mounted
to a heat sink with thermal resistance of 0.12 ?C/W to assist in power dissipation.
This means the heat sink will have a change in temperature of 0.12?C per watt of
heat dissipated. A 600 ?F capacitor is connected to smooth out any voltage spikes
in the power supplies. The capacitor has a rated voltage of 900 VDC and a current
of 102 A at an ambient temperature of 55?C. The DC power is connected to the
motor controller which uses Six-Step Commutation in connection with three 120?
hall sensors for the communication to the motor. The node at the bottom of D1 in
Fig. 4.15 is also connected to tunnel ground (green dotted line) which eliminated
some noise seen in the sensors on the MTR.
As of this thesis, the cables running from the power supplies to the motor
controller are 10 AWG, which limit the maximum current draw to 40 amps, limiting
the total power for the motor to 4.8 kW. In Fig. 4.15, all cables to the right of the
104
power supply and to the left of the capacitor are 10 AWG. Correspondingly, in Fig.
4.16, all cables on the left hand side of the image leading to the capacitor are 10
AWG. By upgrading these cables to 2 AWG, the max current draw would increase
to 130 amps, and therefore, the total power would increase to 15.6 kW. The cables
would need to be even thicker to allow for higher current and more power. Thicker
cables require larger lugs at the cable ends, so the current diodes may need to be
replaced with larger diodes due to limited space at the diode terminals. The main
focus for these connections is to screw in the cable lugs without any cross-contact
with other lugs.
Specifications of the motor controller are provided in Table 4.6.
The motor has a brake that can be switched on in an emergency; it is off by
default. The emergency brake switch is a large red button on the graphical user
interface which instantly brings the brake voltage to 2V out of a maximum of 5V. To
Table 4.6: MST140-200 motor controller specifications.
Feature Unit Value
Weight kg (lb) 1.3 (2.87)
Max Continuous Power kW (hp) 30 (40.23)
Max Short Term Power kW (hp) 39 (52.3)
Supply Voltage V 30-140
Max Continuous Current @ 25?C Ambient Temp A 220
Max Continuous Current @ 50?C Ambient Temp A 180
Max Continuous Current @ 75?C Ambient Temp A 125
Throttle Voltage V 0-5
Brake Voltage V 0-5
Accessories Voltage V 5
105
prevent damage from a sudden arrest, the brake is not set to the maximum voltage.
A physical red button is also wired to the DAQ that will trigger the brake to 2V
when pressed as a redundant safety measure.
The motor controller has an RS-232 terminal that outputs motor parameters
such as motor temperature, controller temperature, motor voltage and current, and
rotational speed. The motor and controller temperatures are monitored throughout
the test and testing will pause if the temperatures exceed 140?F or 60?C. High motor
temperatures can affect load cell measurements as they are both encased within the
pylon without air circulation.
4.5 Rotor Assembly
The rotor assembly consists of the shaft, the hub, blade retention, pitch mech-
anism, and shaft connections. The design of the MTR rotor allows for different hubs
to be installed on the main shaft. The rotor hub is located 34%R ahead of the wing
spar which is nominally considered to be the wing elastic axis. Figure 4.17 shows a
section view of the gimballed hub model. The components of the baseline gimballed
hub are shown in Figure 4.18.
The gimbal is a universal joint, for which the details are explained via CAD in
Fig. 4.19. It is inspired by the XV-15 hub. The spider component, in Fig. 4.19(a),
is the gimbal that allows the hub to have two unconstrained rotational degrees
of freedom relative to the main shaft. A V-22-like constant velocity joint was also
pursued during the design phase but proved difficult to achieve within the constraint
106
Spinner Plate
Figure 4.17: MTR gimballed hub section view.
Figure 4.18: Rotor assembly parts.
107
of resources. Of note, a universal joint will produce a 2/rev oscillation in rotor speed
if the hub is not perpendicular to the main shaft, and avoiding this 2/rev frequency
was important in the rest of the pylon design due to historical reasons. Also, by
design, no gimbal spring was provided to zero out moment transmission. Note,
however, the shaft was still designed to carry moments due to the interchangeable
nature of the hub where a hingeless rotor will be mounted in the future. The hub
has a built-in 2? pre-cone angle to relieve hover stresses. Figure 4.19(b) shows how
the torque and loads are transferred from and to the shaft.
For a powered condition, as the shaft is rotated by the motor, the torque is
passed through the yoke (1). The yoke is locked to shaft by a spanner nut which
requires a spanner wrench to tighten. Two bearing housings (2) are bolted to the
yoke which transfers torque into the spider component through journal bearings
(3). Another pair of bearing housings (4) are slipped onto the spider component
and then bolted to the hub housing (5). This is how torque is transferred from the
motor to the hub. Loads from the hub travel to the motor in the reverse direction.
By design, there is no undersling.
The hub holds three blades (Nb = 3) and allows for configuration changes be-
tween gimballed and hingeless as long as the number of blades remain the same. The
pitch links are on the trailing-edge side of the blades to provide a negative pitch-flap
coupling for the gimballed rotor. A flap up about the gimbal by an angle ?? would
pitch the blades up by an angle ??, so ??/?? is positive and quantified by an angle
?3 such that ??/?? = ? tan ?3. The MTR has ?3 = ?16.5? by construction. The
pitch links are actuated by a conventional swashplate. Figures 4.20 and 4.21 show
108
(a) Gimballed hub CAD and spider component.
(b) Description of load path in hub assembly: (1) Through yoke on shaft, (2) Bearing
housings on one axis of spider, (3) Journal bearings in housing, (4) Through spider into
journal bearing housings on second axis, (5) Through bolts from bearin housings to hub.
Figure 4.19: MTR gimballed hub.
109
the individual components of the hub and swashplate while Figures 4.22 and 4.23
show the assembled hub. With this construction, the swashplate motion is limited
below by the load cell adapter plate seen on the left of Figure 4.23 and by the hub
assembly above. The swashplate motion translates to a collective range from ?2?
to 60? for a total of 62?. The swashplate cyclic range is limited to ?16? by the
spherical bearing in the swashplate. The gimbal flapping is physically limited to
?8? by the spinner plate.
A specially-cut aluminum plate is used to lock the gimbal such that the hub
plane remains perpendicular to the rotor shaft during operation. This is shown in
Fig. 4.24.
Figure 4.20: Individual components of the gimballed hub.
110
Figure 4.21: Swashplate and yoke mounted on rotor shaft.
Figure 4.22: Pitch case and gimballed hub component.
111
Figure 4.23: Rotor assembly mounted to pylon.
(a) Gimbal free. (b) Gimbal locked.
Figure 4.24: A gimbal lock plate is installed between the yoke and rotor to fix the
gimbal.
112
Table 4.7: MTR weight breakdown.
Assembly Component Weight (lb)
Wing Spar 8.95
Spar Coupling Plate 0.68
Aluminum Ribs 5.50
Foam Fairings 8.70
Wing Total 23.83
Pylon Slip Ring 4.5
Linear Actuators 15
Motor 15
Load Cell 6
Body & Fairings 16.36
Pylon Total 56.84
Rotor Hub 14.33
Blades 2.04
Rotor Total 16.37
Full Rig Total 97.04
4.6 Weights
Table 4.7 shows the weight breakdown of the MTR. The relatively heavy pylon
mass (compared to a scaled XV-15 pylon) is driven by the motor, electric actuators,
load cell, and slip ring, which are essential research components non-existent in the
actual aircraft, hence impossible to scale. The sub-components in the hub such as
the swashplate, hub yoke, spinner, and linkages were not measured individually,
however, the pylon and hub assembly together have a total weight of 71.4 lb, and
113
subtracting the pylon assembly from the total gives the hub weight. The twisted
proprotor blades [35] were measured to be about 308 grams or 0.68 lb, including the
blade grip. Note how the hub is heavy, driven largely by the gimbal construction.
4.7 Measured Rig Characteristics
This section describes the frequency, damping, and mode shapes of relevant
parts and assemblies, measured systematically with gradual build-up.
Frequencies of the interfacing post were obtained using ANSYS and shown in
Table 4.8. The goal was to ensure the post was stiff and would not interfere with
the frequency and stiffness of the MTR.
Table 4.8: ANSYS results for interface post frequencies. /rev values shown
for Froude and Mach-scale speeds.
Harmonic Frequency (Hz) /rev /rev1050 RPM 2300 RPM
1st 315.2 18.0 8.2
2nd 315.5 18.0 8.2
3rd 1129.3 64.5 29.5
4th 1536.3 87.8 40.1
5th 1537.5 87.9 40.1
The next step was to bolt the baseline spar to the baseplate. Beam and chord
bending responses were acquired. The time histories and frequency responses are
shown in Figure 4.25. Data was collected from a set of strain gauges located at the
base of the spar. Details of the strain gauges are found in Section 5.12.
114
Torsion response could not be easily detected with the spar alone, so a single
rib was attached near the tip of the spar and used as an arm to excite the torsion
mode. This configuration changed the spar inertia; therefore, all frequencies were
re-acquired. Figure 4.26 shows the time histories and frequencies of the spar with
rib. The beam mode frequency of 35.1 Hz is also detected in chord and torsion
gauges. The chord response shows the first chord mode at 66.64 Hz but also detects
small amplitudes of frequencies around 160 Hz, 200 Hz, and 250 Hz. The torsion
response captures the torsion frequency at 200 Hz and another one at 250 Hz.
Predicted frequencies were verified both using simple Rayleigh-Ritz (using shape
function ? = (x/L)2 for beam and chord bending, ? = x/L for torsion), as well as
detailed analysis with ANSYS. Results are shown in Table 4.9.
Table 4.9: Comparison of spar frequencies for first beam, first chord, and
first torsion modes.
Mode Measured (Hz) Analytical (Hz) ANSYS (Hz)
Baseline Spar Beam Bending 40.38 49.31 44.46
Chord Bending 77.87 101.50 87.32
Torsion ? 817.07 791.29
Spar With Rib Beam Bending 35.1 40.82 38.53
Chord Bending 66.64 83.21 74.71
Torsion 199.90 248.65 223.97
With the rib attached to the spar, the measured frequencies decreased as
expected due to additional mass. The beam frequency decreased from 40 Hz to 35
Hz while the chord frequency reduced from 78 Hz to 67 Hz. The torsion frequency,
115
(a) Beam and chord response for spar.
(b) Frequency responses.
Figure 4.25: Results of impact testing for spar without rib.
116
(a) Beam and chord response for spar with rib.
(b) Frequency responses.
Figure 4.26: Results of impact testing for spar with rib.
117
(a) First beam bending mode at 44.46 Hz. (b) First chord bending mode at 87.32 Hz.
(c) Second beam bending mode at 277.18 Hz. (d) Second chord bending mode at 533.87 Hz.
(e) Third beam bending mode at 768.76 Hz. (f) First torsion mode at 791.29 Hz.
Figure 4.27: ANSYS modal analysis of baseline spar; first six modes shown together
with the undeformed model wireframe.
118
predicted to be near 800 Hz for the bare spar, dropped to 200 Hz measured with
addition of the rib.
The analytical results and ANSYS predictions have consistently higher fre-
quencies than experimental results. The analytical method assumed a uniform beam
without spacers, hence a lower mass, so higher frequencies. ANSYS overpredictions
can be attributed to the practical differences in clamping condition of the model
and the physical spar and baseplate. With an imperfect clamp, the rig would be
expected to be slightly softer (lower frequencies) in all modes, and Table 4.9 shows
roughly 10% overprediction by ANSYS across all modes, whereas the analytical
method overpredicts the experiment by about 20% or more for each mode. Fig-
ures 4.27 and 4.28 show all the mode shapes of the spar through the first torsion
mode for the bare spar and spar with rib, respectively.
ANSYS also predicted a rib bending mode shown in Fig. 4.28(c) at about 180
Hz. The rib bending mode is actually captured in the experimental chord response
in Fig. 4.26(b) with a frequency of about 160 Hz. A fifth mode was detected in the
chord and torsion responses around 250 Hz. ANSYS predicted this to be a coupled
beam/torsion mode at 279 Hz.
The overall results were consistent enough to proceed to structural damping
measurements.
The damping ratios for the spar alone and spar with rib are shown in Table
4.10. The results show that damping ratios between the spar alone and spar with
rib are very similar and quite low. Minimal structural damping is desirable as it
allows for measuring small aerodynamic damping later. The moving block method
119
(a) First beam bending mode at 38.53 Hz. (b) First chord bending mode at 74.71 Hz.
(c) Rib bending mode at 180.04 Hz. (d) First torsion mode at 223.97 Hz.
Figure 4.28: ANSYS modal analysis of spar with single rib; first four modes shown
together with the undeformed model wireframe.
Table 4.10: Measured damping ratios for spar alone and spar with rib.
Damping Ratio Spar Alone (%) Spar with Rib (%)
Beam 0.15 0.23
Chord 0.48 0.51
Torsion ? 0.37
120
(see Section 1.4.3), is used to calculate damping ratios. The moving block method
begins with a block of data at the beginning of the time history of response. Then
the same-sized block is shifted in time and the amplitude of the frequency response
is calculated again. After a number of blocks, the log of the array of amplitudes is
plotted over time. A line fitted through the result gives a slope which is ???n, where
? is the damping ratio and ?n is the natural frequency. The method is implemented
in MATLAB and ran immediately after a test point is acquired so the damping
ratio can be monitored during wind tunnel testing. The moving block method was
sufficient since the response contained only one frequency at a time.
The previous results shown were from tests conducted in the tiltrotor lab with
the wing spar mounted to the baseplate and clamped to a 500 lb t-slot table. The
tests in the lab supported the method of extracting frequency and damping for the
rig using strain gauges and the moving block method. The frequencies and damping
ratios of the full rig mounted to the interface post and installed in the wind tunnel
are shown in Tables 4.11 and 4.12.
Table 4.11: Measured frequencies and damping ratios for MTR in
GLMWT, no wind, unpowered.
Mode Frequency (Hz) Damping Ratio (%)
Beam 5.06 0.53
Chord 9.3 0.54
Torsion 15 0.2
With the wing, pylon, and rotor assembled, but without blades, the heavy
masses brought the wing-pylon frequencies much lower, as expected, with the beam
121
Table 4.12: Measured frequencies and damping ratios for MTR in Navy
SWT, no wind, unpowered.
Mode Frequency (Hz) Damping Ratio (%)
Beam 5.06 0.4
Chord 9.65 0.57
Torsion 14.4 ?
mode around 5 Hz, the chord mode around 9.5 Hz, and the torsion mode around
14.5 Hz. The results between the GLMWT and Navy SWT are very similar for
frequency and damping with the exception of the torsion damping in the Navy
tunnel. The torsion gauges at the Navy tunnel were damaged, including the back
up gauges, so the torsion response was actually taken from the chord strain gauges.
The amplitudes were large enough to get an accurate measurement for frequency,
but the damping could not be accurately obtained.
4.8 Pylon Center of Gravity and Inertia
Center of gravity (CG) and mass moment of inertia (MOI) properties of the
pylon (including the rotor assembly) were measured using a Space Electronics KSR
CG/MOI machine at NASA Langley Research Center, shown in Fig. 4.29. The
orientations of the pylon are shown in Figs. 4.30 and 4.31.
The machine is a rotating table resting on an air spherical bearing, which
eliminates friction, and connected to a vertical torsion rod which allows the table to
rotate. It has one moment transducer at a fixed location on the machine. To measure
the CG of a test article, four measurements are taken, one at each orthogonal axis
122
Figure 4.29: KSR CG/MOI machine at NASA Langley; Pylon mounted in yawing
configuration.
123
Yp Zp
?Ym
?Xm
MCL
(Machine?Center?Line)
Figure 4.30: Pylon testing in pitch orientation.
2.96?
Base
MCL
Figure 4.31: Pylon testing in yaw orientation.
124
as the table rotates. By acquiring both the mass of the pylon and the moments
from each of the measurements, the moments divided by mass result in distances
and the resultant of these distances is the CG location. This calculated distance
is relative to the machine center line (MCL), so it is important to set a reference
point on the test article to identify the CG location relative to the test article. The
reference point on the pylon was the center of the coupling plate which coincides
with the location of the spar.
For inertia measurements, the torsion rod is clamped on the end near the floor,
given an initial offset as a starting position, then released. The torsion rod acts as
a spring and the entire table becomes a torsional pendulum. The machine is able
to measure the period of oscillation T and, from the known spring constant of the
torsion rod ?, the moment of inertia is calculated using:
I = ?T 2
where the torsion stiffness of the rod ? = 4686.624 lb-in2/sec2, T is the period of
oscillation in seconds, and I is the mass moment of inertia in lb-in2. The inertias
were converted to kg-m2 afterward. Results from the Langley tests are shown in
Table 4.13.
The distance from MCL to pylon base in the yaw configuration is 2.96?0.01
inches. The distance from pylon base to the rotor shaft axis is 5.388?0.002 inches.
Note, the pylon could not simply be placed on the table for testing. An
interface plate was required between the machine and the pylon and this was milled
125
Table 4.13: Results of CG and MOI tests at NASA Langley.
Property Unit Pitch Yaw
Part Weight lb (kg) 71.16 (32.28) 71.26 (32.28)
CG (X) wrt MCL in (cm) -0.0223 (-0.06) 1.282 (3.26)
CG (Y) wrt MCL in (cm) 1.294 (3.29) -2.370 (-6.02)
Period, T sec 1.37388 1.4136
I about CG lb-in2 (kg-m2) 4284.98 (1.25) 4275.41 (1.25)
I about MCL lb-in2 (kg-m2) 4404.15 (1.29) 4791.89 (1.40)
out of aluminum. Steel brackets were used to orient the pylon sideways for yaw
inertia. The plate orientations are shown in Fig. 4.32. Figure 4.32(a) shows the
plate sitting flush on the machine. The pylon coupling plate is mounted directly
over the MCL. Figure 4.32(b) shows the plate mounted vertically. This orientation
allows the pylon yaw moment to be measured. The results for the isolated plate are
shown in Table 4.14. Table 4.13 already has the tares accounted for in the results.
Table 4.14: Tare measurements of interface plate at NASA Langley.
Property Unit Pitch Yaw
Period, T sec 0.973554 0.987828
I about MCL lb-in2 4442.02 4573.23
All measurements from the machine were relative to the axis of rotation on
the table. Using parallel axis theorem, the pylon CG and moments of inertia about
the wing spar center were obtained. The final values of the extracted properties are
shown in Table 4.15.
126
(a) Interface plate in pitch configuration. (b) Interface plate mounted to steel brackets for
yaw configuration.
Figure 4.32: Tare runs on the interface plate and brackets.
Table 4.15: Pylon assembly properties.
Parameter Units Measurement
Mass kg 32.38
Zcg cm -3.27
Ycg cm -0.147
Xcg cm 0.06
IPX kg-m2 1.286
IPY kg-m2 1.289
127
4.9 Chapter Summary and Conclusions
This chapter described Maryland Tiltrotor Rig and its physical features and
key characteristics. It covered the details of the following.
1. A description of the overall rig dimensions. With a rotor diameter of 4.75 ft,
the MTR is a 1/5.26 scale model of a full-scale 25 ft diameter Bell XV-15-like
proprotor.
2. A description of the wing assembly and spar design. The MTR wing spar was
loosely designed to the Froude-scale frequencies of the XV-15 wing but, with
the interchangeability of the spar, there is flexibility built into the design for
future excursions.
3. A description of the pylon assembly and load paths. There are two load paths
from the rotor to the wing root. The primary load path runs through the load
cell and a secondary load path is unmeasured. Rotor thrust and torque are
minimally affected by the secondary load path.
4. A description of the electric motor features and power supply components.
The electric motor controller power is limited by the cable thickness from the
DC power supplies to the motor controller. Increasing the cable thickness to
2 AWG or thicker will allow up to 130 amps at 120 V for 15.6 kW.
128
5. A description of the rotor assembly and gimbal hub components. The rotor
uses a universal joint as the gimbal and has a ?8? gimbal flap due to physical
constraints.
6. A list of assembly and component weights. The total weight of the rig is less
than 100 lb. This does not include the hoses and cables that run from the
MTR equipment rack to the pylon.
7. The frequency and damping measurements for spar only. Measured results,
analytical calculations, and ANSYS models were in agreement.
8. The frequency and damping measurements for spar with one rib. Measured
results, analytical calculations, and ANSYS models were in satisfactory agree-
ment.
9. The frequency and damping measurements for the full rig installed in GLMWT
and Navy SWT. The results were in agreement between tunnels with wing
beam frequency of about 5 Hz and damping of about 0.5% critical, wing chord
frequency of about 9.5 Hz and damping of about 0.5% critical, and wing torsion
frequency of about 14.5 Hz and damping of about 0.2% critical. However, the
torsion damping at the Navy SWT was not acquired due to broken wing strain
gauges.
10. The pylon mass, CG, and MOI measurements obtained from testing at NASA
Langley. These properties were used in analysis and predictions.
In conclusion, the MTR is now ready to be instrumented for whirl flutter tests.
129
Chapter 5: Model Instrumentation and Calibration
This chapter describes the instruments and sensors on the rig and details
the calibrations performed to prepare them for testing and data acquisition. A new
calibration stand was developed for the rig. A section on the data acquisition system
is also presented.
5.1 List of Instruments
The major instrumentations on the rig that are available for all tests are listed
in Table 5.1 and shown visually in Fig. 5.1. Off-rig sensors such as track and
balance, VICON, or PIV equipment are not included in this list.
A custom-built slip ring is used for acquiring signals in the rotating frame.
The slip ring has 64 rings, 4 rings for each signal (2 for power, 2 for signal), which
allows for 16 signals to be acquired. There are 10 standard measurements taken
in the rotating frame: blade pitch (3), pitch link loads (3), gimbal tilt (2), and
torque (2), which leaves 6 additional rotating frame measurements. These additional
measurements will be strain gauges on the blades for measuring bending and torsion
moments.
130
Table 5.1: MTR on-rig instrumentation.
Measurement Sensor Quantity Slip RingLeads Mounting
Blade pitch angle Magneticencoder 3 24 1 per blade
Pitch link loads Strain gauge 3 12 1 per pitch link
Gimbal tilt angle Hall effectsensor 2 6 1 per tilt axis
Rotor torque Strain gauge 1 4 On shaft
Blade loads Strain gauge 4 16 2 full-bridges per blade
Rotor speed and Hall effect
position sensor 1 On shaft
6-axis forces and On pylon bulkhead
moments Load cell 1 directly above couplingplate
Vibration Tri-axaccelerometer 1 On pylon frame
Slip ring 1 64 channels
Fixed system Electric
actuation actuators 3 Below swashplate
Wing
beam/chord/torsion Strain gauge 3 3 full-brides attached
strains near the wing spar root
131
MTR Instrumentation
ATI?Omega160
Load?Cell Pitch?Link?Gauges?(3)
RPM?and?Azimuth?
Hall?Sensor
Gimbal?Angle?
Hall?Sensor?
(2)
Blade?Pitch?Encoders?(3)
Triax?Accelerometer Shaft?Torque?GaugeHigh?Bandwidth?
Electric?Actuation
Wing?Strain?Gauges
42
Figure 5.1: On-rig instruments and sensors.
In the non-rotating frame, an ATI Omega160 Transducer is used for loads and
torque measurements. The load cell provides forces and moments about all three
axes. There is a strain gauge to measure shaft torque on the shaft independent from
the load cell. Wing bending and torsion strains are also separate measurements.
5.2 Load Cell Hub Forces and Moments
The ATI Omega160 load cell measurements at the hub were determined to
be inaccurate during the first checkout test. ATI provided a calibration matrix for
measurements at the load cell surface. A transformation of the calibration matrix
could be performed to measure the loads and moments at a point not on the surface
of the load cell. For the MTR, the loads and moments were measured at the hub,
about 7.5 inches away from the load cell surface. The original, untransformed ATI
132
calibration matrix is shown in Table 5.2. Each column is dot multiplied to the load
cell voltages to obtain the corresponding forces and moments. For example, the first
column will output Fx by
Fx = ?0.96014V1+0.24773V2+4.54453V3? 57.60398V4? 0.95628V5+65.18886V6
(5.1)
These calibration matrices are unique to each load cell. For the MTR load cell, the
official ATI calibration file is FT18654.cal.
Table 5.2: ATI original calibration matrix.
Fx Fy Fz Mx My Mz
V1 -0.96014 -0.46179 102.29309 0.56981 297.62589 4.97159
V2 0.24773 73.28008 -1.26585 60.79710 -3.93646 -144.57342
V3 4.54453 1.09967 101.56629 -254.00843 -151.74245 5.37580
V4 -57.60398 -33.16828 0.81479 -29.79184 47.18046 -131.68102
V5 -0.95628 0.86957 102.35840 256.22731 -147.66212 1.80703
V6 65.18886 -38.08432 -1.79533 -35.55609 -51.35803 -149.91018
The orientation of the load cell coordinate system is not the same as the
pylon/hub coordinate system. Figure 5.2 shows the load cell orientation in the
pylon with the load cell axes X ? and Y ? in dotted red arrows. The Z axis is directed
toward the hub along the main shaft. The pylon axes are shown in Fig. 5.3 in
dotted green arrows, denoted XP and YP . To measure forces and moments along
the pylon axes, the load cell coordinate system must be oriented in the yellow solid
133
axes show in both figures. If the load cell axes were oriented in the pylon axes, a
positive force on the hub along the pylon axis would show up as a negative force
from the load cell. This is due to the hub forces traveling to the motor and the
motor acting on the rear side of the load cell, shown in Fig. 4.12(b). The load cell is
not directly connected to the shaft. The forward surface of the load cell is mounted
to the forward bulkhead, and the rear surface is mounted to the connector to the
motor. Figures 5.2 and 5.3 display the load cell with the forward bulkhead removed.
The transformation is a 17? clockwise rotation of the original axes about the Z-axis
such that the Y-axis of the load cell is in the downward direction and the X-axis is
to the left. The coordinate system also had to be translated 7.5 inches forward to
be located at the center of the hub. After this transformation, the ATI matrix is
shown in Table 5.3.
Load?Cell
X
X?
Y?
Y
???
Figure 5.2: Load cell coordinate system orientation: red dotted axes - as installed,
yellow solid axes - desired orientation for positive forces in pylon axes.
134
YP
Load?Cell
X XP
Y
Figure 5.3: Load cell coordinate system orientation: yellow solid axes - desired load
cell orientation, green dotted axes - pylon coordinate system.
Table 5.3: ATI calibration matrix transformed to hub location.
Fx Fy Fz Mx My Mz
V1 -0.78317 -0.72233 -102.29308 -91.88996 290.66141 4.97163
V2 -21.18812 70.15052 1.26584 585.42029 172.92178 -144.57341
V3 4.02444 2.38032 -101.56631 -180.69186 -249.56026 5.37583
V4 -45.38854 -48.56046 -0.81478 -406.48776 376.82263 -131.68105
V5 -1.16874 0.55199 -102.35844 292.34348 -57.53086 1.80705
V6 73.47520 -17.36083 1.79535 -149.19308 -610.57349 -149.91016
135
Under loading, a 1? 6 array of raw voltages, v, from the load cell is acquired
which is then multiplied by the 6 ? 6 calibration matrix to obtain a 1? 6 array of
six loads, f , containing three forces and three moments. Thus, vTC = fT .
From the check-out tunnel entry, it was clear the in-plane forces and moments
were not accurate, being off by as much as 50% of the load applied. Therefore,
calibration tests were conducted to extract a new 6? 6 calibration matrix, C. The
goal was to obtain the new calibration matrix based on measurements of v and f
from loads applied at the hub.
Consider a force, fr, where r = 1, 2, ..., 6 is an entry of f . This force would
produce a voltage vector, v, which, when multiplied with the rth column of the C
matrix, produce fr.
vT cr = fr (5.2)
Now if six different fr are imposed and six different voltage vectors v obtained, then
putting the voltage vectors in rows would give
V cr = fr6 (5.3)
Where V is the 6? 6 voltage matrix, cr is the 6? 1 calibration vector, and fr6 is a
6? 1 force vector containing the six different fr.
In this case, solve for cr:
cr = V ?1fr6 (5.4)
136
For proper accuracy, N different fr should be imposed
V cr = fr (5.5)N
which are N equations but still six unknowns in cr. Here V is a N?6 voltage matrix
of measurements, cr is an unknown 6 ? 1 calibration vector, and fr is the knownN
N ? 1 force vector. Each row of V corresponds to 6 voltages in one time sample.
The vector fr is either in units of pounds for loads or inch-pounds for moments.
To obtain the calibration vector cr, multiply by the transpose of V to get square
matrices:
V TV cr = V Tfr (5.6)
Then, solve
cr = (V TV )?1V Tfr (5.7)
which is the least squares error solution or the Moore-Penrose inverse.
These steps can be invoked numerically by using Matlab?s left-matrix-divide
operator \ shown in eq. 5.8.
cr = V \fr (5.8)
This process is repeated for all r = 1, 2, ..., 6 loads to produce the full C matrix of
r columns. To obtain cr accurately, there must be at least six independent rows in
V in Eq. (5.4), which is very hard to accomplish in measurement. So, in general,
N ? 6 and Eq. (5.8) must be used which results in a least squares solution for C.
137
5.3 Calibration Setup
The load cell calibration was performed in two ways. For Fx, Fy, Fz forces, and
Mx and My moments, the load cell was mounted in the MTR pylon to mimic test
conditions. Due to the difficulty attaching components to the precise hub location,
these forces and moments were applied at the shaft tip, 10 inches away from the
load cell surface that is bolted to the forward bulkhead. The Mz moment could not
be tested on the rig because the shaft could not be locked to allow for a transfer
of torque. The load cell had to be removed from the rig and mounted to a second
calibration frame specifically to calibrate the Mz moment. The Mz moment was
applied at the hub location relative to the load cell surface, 7.5 inches away.
An 8020 frame was built around the MTR to apply the loads and moments.
Figures 5.4, 5.5, and 5.6 show different configurations of the frame for testing in the
principal directions.
For the Mz calibration tests, the load cell was removed from the pylon and
mounted to a separate test stand, shown in Fig. 5.7. The weights were placed 7.5
inches ahead of the load cell surface and tested at two moment arm locations: 12
inches and 18 inches. The moment applied was not a pure moment so shear forces
were accounted for in the X and Y axes in the direction of the desired coordinate
transformation. The orientation of the load cell on the calibration frame was with
X ? axis pointed down and Y ? axis pointed to the right. Then for a shear force in
the X ? direction, the force was split into X = X ? cos(17?) and Y = X ? sin(17?).
138
Figure 5.4: Calibration setup for Fz testing.
Figure 5.5: Calibration setup for My, front view.
139
Figure 5.6: Calibration setup for My, side view.
Figure 5.7: Calibration setup for Mz.
140
5.4 Calibration Results
The final calibration matrix, C, is shown in Table 5.4. Note the calibration
matrices shown in this thesis must be multiplied on the right-side of an 1?6 voltage
reading to get a 1 ? 6 force and moment vector, in the form vTC = fT . If the
voltage is written as a 6?1 vector, the calibration matrix should be transposed and
pre-multiplied on the left-side of the voltage vector, in the form CTv = f . So the
matrix C in Table 5.4 should be transposed if it is to be multiplied by a voltage
vector to obtain loading f .
Table 5.4: UMD calibration matrix.
Fx Fy Fz Mx My Mz
V1 -12.03905 0.25538 -107.84150 -148.84551 402.61671 18.91641
V2 -21.74887 54.43504 -0.48623 504.46099 191.98466 -163.76769
V3 13.24228 -7.91720 -103.15160 -356.06921 -439.44723 -3.87865
V4 -48.07172 -42.26899 0.29361 -432.21865 405.17254 -115.70941
V5 -3.26362 13.46089 -115.24546 500.00744 37.47586 2.17141
V6 77.57090 -10.55649 2.78257 -57.56705 -667.76574 -134.70993
Figures 5.8 to 5.13 show all six measurements for an applied force or torque in
its axis direction. When Fx is applied, the voltage reading should ideally give zero
loads in Fy, ...,Mz. However, this is not the case. Both ATI and UMD matrices show
some cross-coupling. Blue denotes the ATI calibration predictions, orange denotes
141
the UMD calibration predictions, and the black lines are the ideal loads ? with
zero off-axis readings.
5.5 Triaxial Accelerometer
The accelerometer is epoxied onto the rear bulkhead of the pylon shown in
Fig. 5.14. It is a product of Endevco, part number 2270M7A/2771A-10, and it is
used in conjunction with a charge amplifier made by PCB Piezoelectronics, part
number 422E02. The accelerometer is connected to the charge amplifier through a 3
meter long 10-32 cable. The charge amplifier is connected to the PXIe-4492 module
through a 20 ft BNC/BNC cable.
The frequencies measured from the accelerometer were compared with the
frequencies measured from the wing strain gauges and are shown in Table 5.5. The
results show adequate agreement.
Table 5.5: Comparison of wing strain gauge FFTs and accelerometer mea-
surements.
Mode Strain Frequency Accelerometer
Hz Hz
Wing Beam 5.3 5.3
Wing Chord 9.0 9.8
Wing Torsion 15.0 14.7
5.6 High-Bandwidth Electric Actuators
The swashplate is actuated by high-bandwidth electric actuators. This is a
key innovative feature of the rig. The swashplate not only tilts but can have high
142
Figure 5.8: All forces and moments measured for an applied force in Fx. Blue - ATI
calibration, orange - UMD calibration, black - ideal output.
143
Figure 5.9: All forces and moments measured for an applied force in Fy. Blue - ATI
calibration, orange - UMD calibration, black - ideal output.
144
Figure 5.10: All forces and moments measured for an applied force in Fz. Blue -
ATI calibration, orange - UMD calibration, black - ideal output.
145
Figure 5.11: All forces and moments measured for a pure moment in Mx. Blue -
ATI calibration, orange - UMD calibration, black - ideal output.
146
Figure 5.12: All forces and moments measured for a pure moment in My. Blue -
ATI calibration, orange - UMD calibration, black - ideal output.
147
Figure 5.13: All forces and moments measured for an applied moment in Mz. Blue
- ATI calibration, orange - UMD calibration, black - ideal output.
148
Figure 5.14: Triax accelerometer mounted to rear bulkhead of pylon, shown in red
outline.
frequency motions. The three Ultramotion A2 linear actuators seen in Figure 5.15.
These actuators perform the conventional functions of trimming the rotor ? thrust
and flapping (or moments) when the rig is powered and RPM and flapping (or mo-
ments) when the rig is in freewheel. They also perform flutter actuation at any
specified frequency. During whirl flutter testing, a sinusoidal input from these actu-
ators will be used to excite the fixed-frame wing-pylon frequencies. The actuators
have a full stroke of 3.75 inches for an analog input voltage of ?10 V, as shown in
Fig. 5.16, which adequately covers and, in fact, exceeds the allowable travel of the
swashplate in the assembly.
The root pitch at zero actuator stroke (zero volts) is 73?. The root pitch at the
highest actuator stroke is 17?. Since the pitch link is located at the trailing edge,
the highest stroke gives the lowest pitch. For the MTR proprotor blades with ?37?
linear twist, the root pitches of 17? to 73? translate to ?75 of ?1? to 55?.
149
Figure 5.15: High bandwidth electric actuators for high frequency swashplate inputs.
Ultramotion A2.
150
Figure 5.16: Actuators max stroke length.
Figure 5.17: Peak to peak collective amplitude due to actuator motion as a excitation
frequency increases.
151
To assess the actuator?s ability to actively control and perturb the rotor, the
actuators were subjected to a 1 V sinusoidal input at a range of frequencies with
no external load applied. Figure 5.17 shows for a 1 V input signal, the amplitude
decreases as the excitation frequency increases. This is mainly due to the controller
internal to the actuator which limits the rise time of the response. The gains are
tunable so the the amplitude can be increase in the future, if desired. At the wing
beam bending frequency of 0.3 /rev at 1050 RPM, the actuators provide a collective
pitch oscillation of 5.4? peak to peak. At the wing chord bending frequency of
0.53 /rev, peak-to-peak amplitude is about 2?. At wing torsion frequency of 0.83
/rev, the peak-to-peak amplitude is about 0.1?. Later, under loading, the torsion
frequency could not be excited.
5.7 Blade Pitch Encoders
The blade pitch encoders on the MTR are contactless high-speed incremental
linear magnetic (LM) sensors of rotary motions. They were procured from Rotary
and Linear Motion Sensors (RLS). The part number is LM13-IC-10B-E-A-10-F-00.
These use quadrature signals to determine the angle based on the relative position
of the magnetic track and have a precision of 0.01153?. The encoder and track can
be seen in Figs. 5.18 and 5.19.
These linear magnetic (LM) encoders do not allow for detection of a reference
mark on the track, meaning once the encoders are turned on, they read the angles
relative to the initial angle that is preset in the LabVIEW VI. If the pitch encoders
152
Blade Pitch Encoders
Encoder
Pitch case
Hub
? Encoder?measures?relative?angle? Root?Pitch ?75
from?start?up?position deg deg
? Set?initial?position?to?minimum?
Pitch HorTnop?Limit 17 ?1swashplate?position
Bottom?
? 0.01153? precision Limit 73 55
48
BFigluared5.1e8: PPitcihtecnchod erEsennsocr oon dtheehurbs.
Magnetic Track
Encoder
? Encoder?measures?relative?angle? Root?Pitch ?75
from?start?up?position deg deg
? Set?initial?position?to?minimum? Top?Limit 17 ?1
swashplate?position
? 0.0F1i1gu5r3e?5.p19r:eSciidseiovinew of pitch encoder, green light de
BnoottLimt
oeis
m?
t proper wor7k3ing condition55with magnetic track within acceptable distance.
49
153
lose power at some non-initial position, then regain power, the readings would auto-
reset to the initial angle regardless of the magnetic track position. It is recommended
that in the future, these encoders should use RLC2IC or RLM printheads which can
detect reference marks. Then the user can power on the encoders, manually sweep
the collective and the encoders automatically set the correct angle consistently every
time.
5.8 Shaft Torque Strain Gauge
To calibrate the shaft torque gauge, the main shaft had to be removed from the
MTR and mounted to a fixed frame shown in Fig. 5.20. This allowed for a torque
to be applied without the shaft rotating. Yellow arrows in Fig. 5.20(a) shows the
load direction about the pulley. The moment arm allows a pure torque to be applied
about the shaft; however, as the torque increases the moment arm rotates slightly
as seen in Fig. 5.20(b). The result is a shortened moment arm which was accounted
for in the calibration.
Figure 5.21 shows the calibration results for the shaft torque strain gauge.
The measured strains were very small for the applied torques and the signal to noise
ratio is generally low as well. The error bars show twice the standard deviation
of the signal which is 95% of data within the bars. The conclusion is the shaft
torque gauge is not more accurate than the load cell; however, it can be a secondary
verifying signal. After combining all the trials, the relationship between the strains
and applied torques was calculated to be 161.5 in-lb/??.
154
(a) Side view. (b) Front view.
Figure 5.20: Shaft torque gauge calibration frame.
Figure 5.21: Shaft torque gauge calibration results for three trials with errors bars
displaying twice the standard deviation.
155
During testing, the wires on the strain gauge broke at the junction of the shaft
and yoke. It was not essential for the whirl flutter test, so repair was postponed.
This should be repaired before future tests.
5.9 Pitch Link Strain Gauges
Each pitch link strain gauge was calibrated for tensile loads up to 6 kg (13.23
lb). Tests were conducted with loading and unloading weights to observe for hys-
teresis. Results are shown in Fig. 5.22.
Figure 5.22: Pitch link calibration.
Minor hysteresis was observed for pitch link 2. Fitting a line through the
results gives the conversion between strain to pounds. Pitch link 1 factor is 0.5699
lb/??, pitch link 2 factor is 0.6262 lb/??, and pitch link 3 factor is 0.5778 lb/??.
156
5.10 Gimbal Angle Hall Effect Sensors
The gimbal angle Hall effect sensors are from Melexis Technologies MLX90316-
DC. One board is attached to the bearing housing, as shown in Fig. 5.23, and reads
a diametrically magnetized magnet installed in the gimbal spider component. This
is gimbal sensor 1. The other board is attached on the inner surface of the gimballed
hub housing, as shown in Fig. 5.24, also reading a magnet on an orthogonal arm of
the spider component. This is gimbal sensor 2.
Shaft
Spider
Gimbal?Sensor
Bearing?Housing
Yoke
Figure 5.23: Gimbal Hall effect sensor 1 mounted on the bearing housing.
The gimbal sensors were calibrated with the rotor upright, gimbal locked, and
with the pitch encoder plate removed, as shown in Fig. 5.25. The hub arms have a
2? pre-cone built-in and there were no flat surfaces perpendicular to the main shaft
along the hub arms for pitch gauge placement. Thus, the hub had to be disassembled
157
Gimbal Sensor Broken
Hall sensor
Hub housing
? IntegFrigaurtee5d.2?4c: iGrcimubiatl?Hbarlol ekffeec?tosefnfs?olrik2emlyou?ndteudroinntgh?eriensaidsesoefmthebhluyb?.
ofd?otwhneto?hthuebsteel hub housing where the pitch gauge could magnetically adhere to
13
the flat rim on top. The pitch gauge was placed above the location of the gimbal
sensor within the hub. Figure 5.26 shows the mapping of the gimbal voltage to the
pitch gauge measurements.
For the sensor on the bearing housing, the mapping equation is:
Dg1 = 107.3262Vg1 ? 261.1206 (5.9)
For the sensor on the hub housing, the equation is:
Dg2 = ?70.3976Vg2 + 212.2174 (5.10)
where Vg1 and Vg2 are the gimbal sensor voltages and Dg1 and Dg2 are the output
angles in degrees. The mapping equations were found by rotating the gimbal, reading
the pitch gauge measurement, and recording the voltage given by the sensors for
158
GimbGailm Cbaalli bCraltibornation
Shaft Shaft
Hub Hub Pitch GaugePitch Gauge
Pitch Case Pitch Case
(a) Hub housing. (b) Magnetic pitch gauge placed on flat surface.
? Pylon??mPoyulonnte?md?oveuFringtutireeca5d.2l?5lv:yeG?tirmotbi?acwlaHoallllryek?fftecoat ?bswenlesoorrckaltibarabtiolnesetup.
? Remo?veRde?aPmmCionBivm?aeumndod?fP?tpChriBetec?tarhina?lsed.n?Wpchioitlecdthehe?reg?ipnmblcaaoltwdeae?stfrore?ep?atlocarctoeta?tsetsoi?nh?aauncybcd?eirsesuctsiro?fnha,ucbe?surface
? Lock?g?imLobicasoklla??ftgionigrmo?nzbeesaernols?of?rdobeyr?grzorteaetrineog?radleoenfggeornee eanxicsrewafsenrotednifficceult.
? Digita?l?pDiticghit?agTlah?peuseigtgecimh?bma?gl eanagulsegsuear?eemcsone?vteaortse?wdutroietfihsxe?idtnof?ra0?mw.e1igt?idmhbeiangl a?r0neg.le1s,s?d?1seagndre?1ec,s 3 3
in conjunction with the azimuth sensor. Lateral flap, ?1s, is about the X-axis of the
rotor. Longitudinal flap, ?1c, is about the negative Y-axis of the rotor. To calculate
?1s and ?1c, the following relations can be used.
?1s = Dg1 cos(?)?Dg2 sin(?)
(5.11)
?1c = ?Dg1 sin(?)?Dg2 cos(?)
where ? is the rotor azimuth in radians. Zero azimuth is when blade 1 is aligned
with the positive X-axis.
159
(a) Calibration for gimbal sensor 1 on bearing housing.
(b) Calibration for gimbal sensor 2 on hub housing.
Figure 5.26: Gimbal Hall effect sensor calibrations.
160
Note, the Hall effect sensors are sensitive to input power. A DC power supply
provided a steady 5.00 V power to the sensors during calibration. The same power
supply was used for wind tunnel testing. AzAimziumthu tShe Snesnosror
MountiMnogu nting 
BrackeBtracket MountMinogu Bnrtiancgk eBtracket
Slip Slip 
Ring Ring
MagneMtagnet
Hall EfHfeacllt  Effect 
SensoSr ensor
43 43
(a) Rear view of slip ring. (b) Side view.
Figure 5.27: Azimuth Hall effect sensor.
161
5.11 Azimuth Hall Effect Sensor
The azimuth Hall effect sensor is the same device as the gimbal Hall effect
sensors. A magnet is mounted to the end of the slip ring shaft and the sensor board
is mounted to a plate that is attached to the slip ring, as shown in Fig. 5.27.
The azimuth sensor voltage ranges from 0.548V to 4.413V and this is initially
mapped to 0? to 360? azimuth. However, the true zero azimuth position is when
blade 1 on the hub is aligned in the positive X-axis direction, as shown in Fig. 4.2.
This position is ?40.117? from the initial mapping. The azimuth sensor generates
a sawtooth signal and the RPM is determined from the number of peaks detected
per minute.
5.12 Wing Strain Gauges
The wing strain gauges are the most elementary of all sensors yet the most
crucial. These sensors will ultimately measure flutter data. The metal foil gauges
are attached near the root of the wing spar, as shown in Fig. 5.28.
Two sets of gauges are available with the lowest set located at 4.38% of the
wing span for beam and chord, and 6.93% for torsion; the second set is located
at 13.72% for beam and chord gauges, and 18.1% for torsion. The wing span is
measured from the top surface of the base clamp bracket to the center of the pylon,
which is 34.25 inches. Only one set of beam, chord, and torsion gauges are recording
during testing, usually the lowest set. The second set of gauges is for redundancy in
162
2 Sets of Strain Gauges
Wing Spar
Torsion
Beam Chord
Torsion
Beam Chord ? Gauges?located?%?wing?
span:
? Beam/Chord
? 4.38%?and?13.72%
? Torsion
? 6.93%?and?18.1%
Figure 5.28: Wing strain gauges on the wing spar. 3
163
the event the first set of gauges malfunction. These gauges are used for frequency
and damping extractions so they were not calibrated for loads.
The beam and chord gauges are double linear strain gauges which are two
strain gauges laid parallel to each other. With a double linear strain gauge adhered
on opposite faces of the spar, a Wheatstone full-bridge circuit is obtained. The
torsion gauges used are dual-grid shear gauges, also adhered to opposite faces of the
wing spar. Integrating the strain gauges into the data acquisition system was done
by referring to Ref. [36]. A full-bridge circuit provides the highest measurement
accuracy and the most resistance to temperature changes compared to quarter- or
half-bridge circuits.
5.13 Data Acquisition System
This section details the hardware off-rig and on the equipment rack shown
in Fig. 5.29. Two chassis are used for data acquisition: NI PXIe-1082 and NI
CompactDAQ-9174. Data is acquired at 10 kHz.
The PXIe-1082 chassis has a collection of installed modules: PXIe-8840 Quad
Core Embedded Controller, two PXIe-4331 8-Ch Bridge Analog Input modules,
PXIe-4492 Sound and Vibration, PXIe-4322 8-Ch Analog Output, PXIe-8430/8
RS232, and PXIe-6365 Multifunction I/O. The cDAQ-9174 chassis holds two NI-
9401 Digital I/O Input modules.
The PXIe-4331 acquires the strain gauge measurements for four blade loads,
three pitch link loads, one shaft torque, and three wing strains, with five extra chan-
164
Figure 5.29: MTR systems support rack.
165
nels available. The PXIe-4492 acquires the tri-axial accelerometer measurements.
The PXIe-4322 module provides the voltage to control the electric actuators, motor
throttle, and brake. The PXIe-8430/8 module uses four ports to read motor data
(1 port) and actuator positions (3 ports). The PXIe-6365 module reads the analog
voltage signals of the two gimbal Hall effect sensors, the shaft speed and position
Hall effect sensor, and the six load cell measurements. The NI-9401 modules acquire
the pitch encoder digital pulse signals.
Two regulated DC power supplies are on the shelf below the DAQs to provide
5V power to sensors. One supply powers the two gimbal Hall sensors and the load
cell, and the other powers the three pitch encoders.
There are three dedicated power supplies to power each Ultra Motion A2
actuator. Each Ultra Motion unregulated DC power supply can provide 36V/360W
continuous output with high burst current, and has an integrated shunt for over-
voltage protection.
The front of the rack has a shelf that holds the pilot controller. The pilot
controller was fabricated in-house. There are two dials, a switch, and a joystick.
One dial controls the motor throttle, while the other dial controls the collective
angle of the blades. The switch toggles the motor throttle to be active or inactive
for the freewheeling condition. The joystick is used as a rate controller for the cyclic
motion of the swashplate.
The rotor control system was divided into manual control for trimming and
automated control for dynamic excitation. Manual control was performed through
the joystick and dials on the physical controller on the equipment rack. The operator
166
was able to adjust the dial for collective and use the joystick to trim the gimballed
hub to zero cyclic first harmonic flapping by monitoring a plot of lateral flapping, ?1s,
versus longitudinal flapping, ?1c. Due to the manual nature of this control, there
was difficulty in forcing the gimbal to achieve precisely zero flapping. Therefore,
gimbal flapping was trimmed to ?2.5? or less. The cyclic control was necessary only
for the gimbal free conditions.
(a) Wing beam response due to a 5 Hz longitu- (b) Wing chord response due to a 9.5 Hz collec-
dinal cyclic excitation. tive excitation.
(c) Wing torsion response due to a 14.5 Hz lon-
gitudinal cyclic excitation.
Figure 5.30: Flutter excitation of wing modes through swashplate actuation.
167
Flutter excitation was performed through the LabVIEW interface. The DAQ
operator was able to select collective, longitudinal or lateral cyclic, input frequency,
input voltage, and the number of cycles. Once the manual control trimmed the
rotor, the DAQ operator pressed a start button to activate the excitation of the
swashplate according to the parameters. Figure 5.30 shows the wing responses from
the swashplate excitation. The excitation is shown as a blade pitch oscillation.
Figure 5.30(c) shows the torsion mode was difficult to excite and the response was
not substantial enough to obtain an accurate measurement of damping.
5.14 Chapter Summary and Conclusions
This chapter described the instrumentation on the Maryland Tiltrotor Rig,
the calibration of the instruments, as well the data acquisition system. It covered
the details of the following.
1. The development of a new calibration stand for the load cell. This stand
allowed for calibration to be performed while the load cell was mounted in the
pylon, creating a test-like environment.
2. An explanation of the load cell calibration results, showing that thrust and
torque were the most accurate and most unaffected by the secondary load path
present in the pylon.
3. A description of the gimbal Hall effect sensors and azimuth Hall effect sensor.
These are used to map the rotating hub to fixed frame ?1S and ?1C angles.
168
4. A description of the wing strain gauges used to measure the frequency and
damping of the rig. All gauges were full-bridge circuits which provide the
highest accuracy and most resistance to temperature changes. There were two
sets of full-bridge circuits for each wing mode. However, only one set recorded
data during testing, the other set was for redundancy and backup.
5. A description of the data acquisition system. Various NI modules were used
to acquire data at 10 kHz for all the rotating and stationary sensors on the
MTR.
The chapter concludes the following.
1. The MTR is now fully instrumented and calibrated for testing. In total, it has
22 sensors.
2. The high frequency electric actuators allowed for a range of 56? in blade col-
lective pitch. These are the principal instruments to activating flutter at the
wing-pylon frequencies.
3. The shaft torque gauge was not sensitive enough to provide an accurate mea-
surement for torque with a 161.5 in-lb/?? calibration, but it can be used as a
backup measurement device.
Some recommendations for the future are provided.
1. The blade pitch encoders measured the blade root pitch. The actual ?75 angle
should be directly measured for each new blade set due to fabrication discrep-
ancies in the blade root insert.
169
2. If an instrument is replaced, rewired, or its power supply is replaced, a recali-
bration should be performed to ensure accuracy.
3. The shaft torque gauge was left unattached for future students to use as backup
load cell torque readings.
4. The rotary magnetic encoders should be upgraded in the future for automatic
zero-setting capability.
170
Chapter 6: Whirl Flutter Analysis
A simplified model was developed to determine the flutter boundary and the
behavior of rotor and wing modes as a function of windspeed. This model was
meant for pre-test assessment, not detailed validation. This chapter will describe
the model methodology, the derivation of which can be found in Johnson [4], and
the input parameters for the model.
Figure 6.1: Tiltrotor whirl flutter model.
171
6.1 Methodology
The model consists of a straight wing and gimballed rotor in cruise flight with
the shaft always parallel to free stream velocity V , thus the rotor is in pure axial
flow. The wing is cantilevered at the wing root. A large, heavy pylon is rigidly
attached to the wing tip. The rotor is mounted to the pylon with the hub forward
of the wing elastic axis, with the rotor shaft parallel to V . The rotor has three
blades, with first mode flap and lag motion for each blade. The rotor hub forces
and moments are transmitted through the pylon to the wing tip. Nine degrees of
freedom are used to model the wing and rotor, as shown in Fig. 6.1. There are three
modes for the wing: q1 beam bending, q2 chord bending, and p torsion. There are
six rotor modes because the rotor has flexible blades with a gimballed hub. ?0, ?1c,
?1s denote the collective flap, longitudinal flap, and lateral flap, respectively. ?0,
?1c, and ?1s denotes the collective lag, longitudinal lag, and lateral lag, respectively,
which occurs in-plane of the hub. The lag motions move the rotor center of gravity
denoted as cg shown in the figure.
The nine equations of motion are in the form:
M?x?+Cx? +Kx = 0 (6.1)
172
where M, C, and K are 9?9 matrices for mass, damping, and stiffness, respectively,
and the degree-of-freedom vector is:
? ?
?????1c?? ?? ?? ?? ???1s?? ?? ?????1c????
?????? ?
?
? 1s????? ?x = ???0 ???? (6.2)?? ???? ?0 ?????
?
??
??
q1 ????
??
??? q ?2 ????
p
6.2 Rotor Equations
There are three flap equations and three lag equations for a total of six rotor
equations. Terms with ? are the azimuthal derivative of the parameter. Terms with
? overhead are non-dimensional lengths, normalized by blade radius R. The three
173
rotor flap equations in multiblade coordinates are
( )
? ?? 2 ? ??
I?0 ?0 +??0 ?0 + S? z?P = ? M?0
[ ]
? ?? ? ( ) ? (
+2 2 ?? ?
)
I? ?1C ?1S + ?? ? 1 ?1C + I? ? ?Y +2 ?X = ? M?1C
(6.3)
[ ]
? ?? ? ( )2 ? (?? ? )
I? ?1S ?2 ?1C + ?? ? 1 ?1S + I? ?X +2 ?Y = ? M?1S
where the right-hand side perturbation flap moments are
M?0 =M? ((?0 ?KP )?0)+
? ?
M?? ?Z ? ?0 +
(6.4)
?
M? z?P +
?
M?? ?0
M?1 =MC ? ((?1C ?KP ?1C)+
? ?
)
M? ?h? ?X + y?P +?? +( ) X (6.5)?
M?? ? ?( 1C
??1S +
? )
M?? ?1C +?1S?
?
?Y
174
M?1 =M? ((?1S ?KP ?1S)+S
? ?
)
M? ?h? ?Y ? x? +?? +( ? )
P Y
(6.6)
M?? ? ?1S +?( 1C
+
? )
M?? ?1S ?
?
?1C+ ?X
The three rotor lag equations in multiblade coordinates are
(
? ??
)
2 ? ??
I?0 ? 0 +??0 ?0 ? I?0 ?Z = ? M ?0
[
? ?? ? ( ) ] (2 ? ?? )
I? ? 1C +2 ?1S + ?? ? 1
??
?1C + S? ? y?P +h? ?X = ? M ?1C
(6.7)
[
? ?? ? ( ) ] ( )2 ? ??
I? ? 1S ?2 ?1C + ?? ? 1 ?1S +
??
S? x?P +h? ?Y = ? M ?1S
where the right-hand side perturbation lag moments in fixed coordinates have the
same form as the flap moments, only theM -coefficients are changed toQ-coefficients.
175
M ?0 =Q? ((?0 ?KP? )
?0)+
?
Q?? ?Z ? ?0 +
(6.8)
?
Q? z?P +
?
Q?? ?0
M ?1 =Q? ((?1C ?KP ?C 1C)+? )
? ?Q? h? ?X + y?P +??X +( (6.9)? )
Q?? ? ?1C ??( 1S
+
? )?
Q?? ?1C +?1S? ?Y
M ?1 =Q? ((?1S ?KP ?1S)+S ? )?
Q? ?h? ?Y ? x?P +?? +( ? )
Y
(6.10)
Q?? ? ?1S +?1C +( ? )?
Q?? ?1S ??1C+ ?X
176
6.3 Wing Equations
The three wing equations of motion in matrix form are
?? ?? ??? ?? ??Iq +mP 0 Sw ????? ?
??
q 1 ??
? ? ?? ? ? ? ?? ??? 0 Iq +
?
I ?2PX ? +mP ?
??
Sw ?w2 ????? ?????? q 2 ???? ? ? ?
? + ??
?
Sw ? Sw ?w2 ??Ip ?IPY p
?? ???Cq1 0 0? ?
?
? ??
?? ?q1 ???
+???
? ?
0 C 0 ?????
? ? ??
q2 ????? q2 ?? ? ??
?
? 0 0 Cp p? ?? ?????
?
Kq1 0 0 ???? q1 ??
+
????
???? ? ??
0 K ?? ?q2 0 ?????? q2 ???
? ? ? ?? ?
? Cpq ??(?2CT?/?a) ?Cpq ? (?2CT/?a)?w2 Kp p
????
?
?
M ? ? ? ?
(6.11)
q1aero ??
?? ???? ??
?? ? ?w3 (1? ?) ?? ?w2
? ?? ????
??
???? ?2CM /?a ?? ? ? ? Y= ??? M
+ ? ? ? ?
q2aero ??? ??
?? ?w1 (1? ?) ?? ?? ?2CM /?aX
? Mpaero ?1 ??w1 (1? ?)
???
?
? ? ? ?? ? h?(1? ?) ??? ? h?+ ? ? (1? ?2 ?w3 w2 w1 )?? ?? ???
?
+ ? ?
2CH/?a ??
?
???? ?
? ? 2 ?? ?
w2 + ? ?w3 h?(1? ?) ?? h?+ ? ?w3 (1? ? ) ????? ??2CY /?a
?h? ? ?w1 h?(?1? ?)? ???? 2?
?
???? ???? ?2? ?w2 ????
+?
????
? ?2?? ? ?C /?a+ ? ? ?C /?aw2 ??? Q? ???? ?2? ??
T
??
2 ?w3 (1? ?) ?2? ?w1?
177
where shape functions ?(y) = y2/yT and ??(y) = 2y/yT are evaluated at the wing
tip y . These result in ?(y ) = y and ??T T T (yT ) = 2. Furthermore, ? is normalized by
R because the input parameters are non-dimensional, so ? = y?T . The wing dihedral
angle is ?w1 , ?w2 is the wing incidence angle of attack, and ?w3 is the wing sweepback
angle (for forward swept wing, ?w3 is negative) in radians. For the MTR, these wing
angles are set to zero, which simplifies Eq. (6.11) to
178
?? ?? ????
? ? ?
Iq +mP 0 Sw ??
? ????????
??
q 1 ??
? ?? ? ? ? ?? ??? 0 Iq + IPX ?
?2 +m 0 ?????? q ????P
? ? ? ?? 2?? ?
Sw 0 Ip + IPY p
?? ?? ???
?
?Cq1 0 0 ?? ?q1 ?
+ ???
???? ??
? ?? ? ?
?? 0 C
?? ?
q2 0 ???????? q2 ???? ? ?
? 0 0 Cp p? ?? ?? ??? Kq1 0 0? ??? ? ??
??
???
??? q1 ?
+? 0 K 0 ????? q ?
???
? q2 2 ???? ? ?? ?
? Cpq ? (??2CT/??a) 0 ?Kp p? (6.12)? ??? M q1? aero ?
?
? ? ?
?? 0 0 ????? ?
= ? ? ? ? ??
?2CM /?a ?Y ?
?? M ??
??+ ? ???? 0 ????q2aero ? ? ????
?? ??
? 2CM /?aX
Mpaero? ??1 0
???
???? 0 ???????
? ?
??? 2CH/?a+ ? ? ? ?? ?
?
??0 ?? h??? ??2CY /?a
? h? 0? ? ? ????2?
?
??? ?? ?
???? 0 ????
+?
??? 0 ??
??C /?a+ ? ?????2?????Q CT/?a? ? ?
0 0
Equations 6.11 and 6.12 notation for ?(yT ) and ??(yT ) are shortened to ? and
?
?? for convenience. The constant C ?pq = 2/3 is a term that accounts for the bending
179
motions of the wing creating a torsion moment due to the movement of the rotor
thrust. The wing aerodynamic coefficients on the right-hand side are
?? ? ? ?? ????
? ?
M q1aero ???? ????C? C? C? ?? q ?? ? ? q1q?1 q1q?2 q1p???????
1 ??
?? ? ?? = ?? ??? M q2aero ?? ??C
? C ??? C? ?? q
q2q?1 q2q?2 q2p??????? 2 ?
?
???
? ? ?
Mpaero ? C? C? C?pq?1 pq?2 pp?? ?
p
??? ?? (6.13)???C? C? C? q? q1q1 q1q2 q1p????????
1 ????+ ? ? ?
????C C C ?? q ?q2q1 q 22q2 q2p?????? ???
C? C? C? p
pq1 pq2 pp
180
These coefficients are
C? = ?d
q q? 13 ?CL1 ?
e2
1
C? = ?d13 ?CL eq q? O 21 2
C? = ?d12 ?2 ?q q w3 CL? e31 1
C? = ?d 2
q q 12 ? [?w2 3 CL eO 31 1 3 ( )]= xAC? d w
q 221p? 2 ? 4 + CL e4c ?w
C = d 2?
q p 12 ? CL? e41
C? = ?d13 ? (CD? ? 2CL ) eq q? 22 1 O
C? = ?d13 ? (2CD ? ?w2 C ) eq q? O D? 22 2
C? = ?d 2
q q 12 ? ?w3 (CD? ? 2CL ) eO 32 1
(6.14)
C? = ?d 2
q q 12 ? {?w3 (2CD ?2 2 1 [1 (
O )?]w2 CD?) e3 }
= xA 1C? d w22 2 ? 2 + (CD? ? 2CL )? 4CL eq 42p? c O Ow
C? = d 2
q p 12 ? ((CD?)? CL ) e2 O 4
= xAC w? d
pq? 22 ? CL e41 c ?w
C? = ?d ?2C e
pq? 22 mac 42
C? = d 212 ? C fpq m 21 ac
C? = ?d ?2C
pq 12 [L fO 22 ( )]
C? = ? 1 1 1 xAd ? w
pp? 31 2 ( 4
+ C f
)2 L 3c ?w
= ? 2 xAC? d ? w C
pp 21 L f3c ?w
181
where CL and CD are the aircraft trim lift and drag coefficients and CL? and CO O D?
are their derivatives with respect to angle of attack. For the MTR wing, a NACA
0018 airfoil at 0? incidence angle of attack: CL = 0, CL? = 5.73, CD = 0.4,O O
CD? = 0. The distance the aerodynamic center is behind the elastic axis is non-
dimensionalized by the chord length as xAw/cw, and Cmac is the moment coefficient
about the aerodynamic center. The constant dnm = c?n y?mw T /(??a) accounts for the
difference in the normalization of the wing and rotor coefficients. Constants en and
fn are approximated from integrals of the wing mode shapes and are given as:
e1 ?= 1/3
e2 ?= 1/5
e3 ?= 1/2
e4 ?= 1/4 (6.15)
f1 ?= 1/2
f2 ?= 1/12
f3 ?= 1/3
182
For ?w1 , ?w2 , and ?w3 equal to zero, the final wing equations become
?? ?? ?????
? ? ?
Iq +mP 0 Sw ???? ?
?? ??q 1 ???
? ? ?0 + ?2 + ? ?? ?? Iq IPX ? mP 0 ??????
?? ???? q 2 ???
???
? ? ?
S?w 0
??
Ip + I?PY p? ? ?? ?? ??Cq1 ? ? C? 0 ?? C?? q1q?1 q1p? ?
??? q1 ??
+????
???? ?? ? ?0 C ?? ?q2 0 ???????? q2 ?????
? 0 0 Cp ?
?
? C? p
pp?
? ?? ?? ??? Kq1 0 ?? C? ???????? q1 ?? q1p? ?
??
+
??
?
? 0 Kq2 0 ???????
?? q ?2 ???
? ? ? ?
Cpq ? (??2CT/?a)? 0 Kp p? (6.16)??? 0 0? ?
?
? ?
?? ??2CM /?a ?
= ?
???
?? Y ?
0 ????????? ?? ?2CM /?aX
??1 0? ????? 0
? ?
????? 2CH/?a ?
+ ? ?? ????0 ???? h????
???? ?
?
?2CY /?a
? h? 0? ?? ?? ?????2? 0 ?
+? ???
??? ??? ???
?? 0 ??
?
??
CQ/?a+ ? ??? ????2????
CT/?a
?
0 0
183
The rotor force equations are
C ??T CTaero ? ? ??? = ? ? S? ? ? M b z? P
? a ? a 0
CQ C
? = Q? aero
??
? ??? + ?Z
? a ? a 0 (6.17)
CH C
( )
Haero ? ??= ? + ?? 1
? ??
? ? M b x?P h? ?Y ? S? ?
? a ? a ( ) 2 1S
CY CYaero ? ??= ? ? ?? 1
? ??
? ? M b y?P h? ?X + 2 S? ?? a ? a 1C
where
CTaero =
? a
T? ((?0 ?KP )?0)+
? ?
T ?Z ? ?0 + (6.18)??
?
T? z?P +
?
T?? ?0
CQaero =
? a
Q? ((?0 ?KP )?0)+
? ?
Q (6.19)?? ?Z ? ?0 +
?
Q? z?P +
?
Q?? ?0
184
C
2 Haero =
? a
H? (?1S ?K(P ?1S)+ ? )
(H? +R?) ?
?
h? ?
( ) Y
? x?P +??Y +
(6.20)
?
H?? ? ?1S +?1C +( ? )
H?? ?1S ??1C+
?
?X
? 2CT ?1C
? a
C
2 Yaero =
? a
?H? (?1C ?(KP ?1C)+
? ?
)
(H? +R?) h? ?X ? y?P ???( ) X
+
(6.21)
?
?H?? ? ? ?? +( 1C 1S? )
?H?? ?1C +
?
?1S? ?Y
? 2CT ?1S
? a
where the inflow ratio ? = Vc/?R + ?i. The induced inflow, ?i, is negligible in
high inflow conditions so the inflow ratio is simply ? = Vc/?R. Pitch-flap coupling
KP = tan(?3) where ?3 is the angle the pitch link location makes with the flap hinge.
The rotor aerodynamic coefficients: blade thrust T , blade flap momentM , blade in-
plane force H, blade torque moment Q, and blade radial force R, are approximated
by only retaining cl? terms and neglecting drag cd terms. The blade radial force
is denoted as R? to avoid conflict with the blade radius R. The subscripts denote
185
the contribution due to perturbations in those parameters; advance ratio, ?; lagging
velocity, ??; flapping velocity, ??; inflow ratio, ?; and blade pitch, ?. These coefficients
evaluate to
M = ?f H = ?2? 2 ? f0
M?? = ?f 23 H?? = ? f1
M?? = ?f4 H?? = ??f2
M? = ?f3 H? = ??f1
M? = g2 H? = ?g0
T? = ?f 21 Q? = ? f1 (6.22)
T?? = ?f2 Q = ?2?? f2
T?? = ?f3 Q?? = ??f3
T? = ?f2 Q? = ??f2
T? = g1 Q? = ?g1
R? = 0
186
where
( ? )
= 1 1 + 1 + ?
2
f0 2 ln ?
1 ?
f1 = 2 ( 1 + ?
2 ? ?)
?
= 1 1 + 2 ? 1f ? ?22 4 2 f0
1 ?
f3 = 26 [ 1 + ? (1? 2?
2) + 2?3]
(6.23)
?
f4 =
1 1 + ?2 (2? 3 3?2) + ?416 8 f0
?
= 1 1 + 2 + 1g0 4 ? 2?
2f0
1 ?
g 3 31 = 26 [( 1 + ? ) ? ? ]
1 ? 1
g 2 42 = 16 1 + ?
2 (2 + ? )? 8? f0
The hub moment equations are
?2 CM
?
Y = 1 2I? (?
? a ? ?
? 1) ?1C
(6.24)
2 CM 1
?
X = 2I? (?? ? 1) ?1S? a ?
187
The relationship between the wing degrees of freedom q1, q2, and p to the rotor
shaft displacement and rotation (xP , yP , zP , ?x, ?y, ?z) is
? ?x = ?q2 ? (yT )
?y = p ?(yT )
?z = ?q1 ??(yT )
(6.25)
xP = q1 ?(yT )
yP = 0
zP = ?q2 ?(yT )
Then the derivatives are simply
? ?
? = ?q ?x 2 ? (yT )
? = ??y p ?(yT )
?
?z = ?
?
q1 ?
?(yT )
(6.26)
? = ?xP q1 ?(yT )
?
yP = 0
? ?
zP = ?q2 ?(yT )
188
and
??
?x = ?
??
q 2 ?
?(yT )
??
?y =
??
p ?(yT )
?? = ????z q ?1 ? (yT )
(6.27)
?? = ??xP q 1 ?(yT )
??
yP = 0
?? = ???z P q 2 ?(yT )
The wing vertical bending q1 produces ?z (yaw) and xP (longitudinal) motions
of the hub. The wing in-plane bending q2 produces ?x (roll) and zP (vertical)
motions of the hub. So the wing motion couples the rotor longitudinal and lateral
groups: ?y, xP , zP , and ?x, ?z, yP , respectively. Mode shape functions ? = y/yT
for torsion and ? = y2/yT for bending are used, where y = yT at the wing tip. Note,
all length parameters are non-dimensionalized by the radius R.
6.4 Whirl Flutter Evaluation
The whirl flutter matrices for M, C, and K are shown in Eqs. 6.28, 6.29, and
6.30, respectively. For convenience, all superscripts ? and ? are dropped; ? is written
for ?(y ?T ) and ? is written for ??(yT ). ?(yT ) evaluates to yT and so all yT in the
matrices are written as ?. In Johnson [4], the property yT and the calculation of
?(yT ), while the same value, are shown as separate parameters. Note, all length
properties are non-dimensional, meaning h is h/R, cw is cw/R, yT is yT/R.
189
190
?? ????I? 0 0 0 0 0 0 0 ?I ???? ?
??
?? 0 I 0 0 0 0 0 ?I ?? 0 ?? ? ? ??? ?????? 0 0 I? 0 0 0 0 ?
? 0 ?S?? h ?
???? 0 0 0 I ?
???
? ?
0 0 S?? 0 S?h ?
? ?????
?
0 0 0 0 I ?
? ?0
0 0 ?S?0? 0 ???? ?? ?? 0 0 0 0 0 I
?
?0 I?0? 0 0 ?
M = ?? ??
?
(6.28)
??? 2Mb?
2 + 2??2 ?S ?W
0 0 0 ?S?? 0 2?? 0 ?
???? + + +2 ?
?
? Iq mp Mb?h ????
???? 2 2 + 2 ?2 2 ?? Mb? Mb? h ??? 0 0 ?S ?
?
? h 0 ?2S?? 0 0 0 ??
??
?
+I ?2P ? + Iq +m ?? X p ???????? SW 2M 2 ?? b
h ?
0 0 0 S?h 0 0 0 ???
+2Mb?h +IP + IY p
191
?? ???? ?2I??
?
?? ?
?
? ?M?? 2I? ?M?? 0 0 0 0 ?M ??? ???M ?? ?? h ?
???? ???? 2I? ? ?
???
? ?2I? ??M?? 0 ?M?? 0 0 ?M ? ?M ?? ?
???
? ?? ?
? ?+?M?h ???? ??? ? ?? ??Q?? 0 ?Q?? 2I? 0 0 0 ??Q?? h ?Q?? ???????
?
? 0
?
??Q?? ?2I? ?Q?? 0 0 ?Q?? ?Q ???? ?Q?h
? ?
??
???
?
? 0 0 0 0 ? ??M?? ?M?? ?M???? ?M?? 0 ?????
???
? 0 0 0 0 ?
?
?Q?? ?Q?? ?Q
?
??? ?Q?? 0 ???C = ?? ? (6.29)?? ??2(H? +R ? ?? ?
) ?H???? ?
? ( ?? ??h H? +R?)?? 0 ??H ? 0 ?H ? ?2?Q ?? ? ?? ?? ?? ?? 2?Q??? +2?Q ?2 ?? ??
? ??Cq1q?2 ?
? ?? ??Cq1p? ???
?
+?C ? C ?q? +2?Q ?? ????q1 q1 1 ?????? ?2?T??
2
?? ??C ??C ?
???
q2q?1 q? ? 2
p? ?
??H??? h 0 ??H??? h 0 2?T??? ?2?T? ??
? + ????2h2(H? +R?) ?
?? ?? ?2?T ? ? ?? ??
?? ??H??? h ??
?? +Cq2 ? ?Cq2q?2 ?? ??? ??? ??h(H +R ) ?H ?? 2 ?? ? ? ??
h ?h (H? +R?)?
0 ??H??h 0 ?H??h 0 0 ???
??Cpq?1 ??Cpq?2 +Cp ? ?Cpp?
192
?? ??? 2? I ??(?? ? 1) ? ??? ??M 0 ?M 0 0 0 ?M?? ? 0 ???? ???? + ?? ?KPM??? ?
???
2 ?
?? I?(?? ? 1) ???
?
?M?? ??M?? 0 0 0 0 0 ?
?
?M?? ?
? ?? +?KPM ?? ? ???????? ?KPQ? ??Q?? I?(?2? ? 1) ?Q?? 0 0 0 ?Q???? 0 ????
???? ?? ?Q?? ?KPQ ??Q I (?
2
? ?? ? ? ? 1) 0 0 0 0 ??M?? ?
?? ?
?????? I
2 ?
?0??
?? 0 0 0 0
0 0 0 0 0 ??
????
?
+ ??KPM? ????
???? 0 0 0 0 ?KPQ I
2
? ?0??0 0 0 0
??
K = ? ?????? 2??(H??/2 K ?? q1
??Cq1p ?
? ?KPH?? ???H?? 0 2?KPQ??? 0 ??C ?? q1q2 ???
?
+CT/a?) ??C ?q1q1 ????(H? +R?)?
? ??? ???
?
K ?q2 ?
??? I??
?(?2? ? 1)
???
?? ??h?(H?????K
?
PH?? h +2???h(H /2 0 ??H ??h ?2?KPT?? 0 ??Cq q ??Cq p ???
? ??
?? 2 1 2 ?
+ ?R ?2?)? ??
????
??? +C /a?) ??T ? ??Cq2q2 ?
? ??? ??? I 2? ?
(?? ? 1) Kp ??
?? ??
?
??+2?h(H /2 ?KPH?h ??H??h 0 0 0 ??Cpq1 ??Cpq2 ??C ?? ?? pp ????
+CT/a?) ???h(H? +R?)
(6.30)
Substituting these matrices into Eq. (6.1) gives the system equation. The
right-hand side of the system equation is set to zero to determine the damping
behavior from the homogeneous solution. The linear system of equations is solved
by obtaining the eigenvalues using the matrix method
x? = Ax (6.31)
193
where x is the state vector, and x? is the derivative
?? ?? ?? ?????1c? ? ?
?
?1 ?c?
??
?????
??? ??? ? ?? ???1s?? ???1 ??s??? ????1c?? ?
?? ? ??
?? ???? ???
?1c
? ??
???
? ? ??? ?? 1s? ?? ? ?
??1s??
?? ?? 0? ?
??? ???? ? ?? ? ? ?? ? 0 ?? ???? ????
?0
? ???
?? ???? ? ??? 0 ???
??
?
q1 ?
? ?? ?
??? q1 ???
???
?? ? ?
q2 ????? ???
???? ? ?? q2 ?????
x = ????
? ?? ? ?p
? ? ?
? ? p ?
?? ????
x = ?????
? ?
??
? ??
??? (6.32)? 1c 1c????
? ?
? ?
? 1s????
???? ???? ??? ?? 1s? ?
?
? ? ?? ???? ???? ? ??? 1c? ? 1c???? ? ?? ???? ??
????
?1s
? ??
??
? ? ???
?? 1 ?s
? ???? ??
???0 ? ?? ? ?? ?? ? ???
?
? ????
?0 ???
??
?? ?0 ?? ? ? 0 ?
??
? ???
?
?
? q ?? 1 ?? ????
???? ??q ??1 ??
???
?
q
? 2 ?
??? ??? ?? ?? ? q ?
?
? ? 2 ???? ?? ?
p p
194
and A is an 18? 18 square matrix of the form
?? ???? 0 I ?A = ??? (6.33)
?M?1K ?M?1C
The eigenvalues of A are nine pairs of complex conjugates in the form s =
???n?j?d. So the damped frequency is the absolute value of the imaginary part and
the damping ratio, ?, can be found from the real part. The natural frequency ?n =
?
?d 1? ?2. The eigenvalues of A are obtained for each velocity V and frequencies
and damping were calculated.
6.5 Model Properties
MTR properties are listed in Table 6.1 along with the Bell 25-ft diameter
gimballed hub model properties used to validate the model and the ratio between
the two rigs. The table only includes the parameters necessary to solve the model.
Starred parameters are non-dimensionalized by N 2Ib unless otherwise noted./
Table 6.1: Bell 25-ft diameter rig and MTR properties used for whirl
flutter analyses.
Bell MTR Ratio
MTR/Bell
Rotor
Rotor radius (m) 3.82 0.7239 0.1895
Continued on next page
195
Table 6.1 ? continued from previous page
Bell MTR Ratio
MTR/Bell
Rotor solidity, ? 0.089 0.0776 0.8719
Nb 3 3 1
Air density, ? (kg/m3) 1.225 1.225 1
Lock number, ? 3.83 2.8939 0.7556
Pitch/flap feedback, KP -0.268 -0.268 1
Lift curve slope, a 5.7 5.9358 1.041
Rotational speed, ? (rad/s) 48 (458 RPM) 109.96 (1050 RPM) 2.29
Blade frequencies ?
? 1 + 0.0355(600)2? ? 1.0583R
??0 1.85 1.7882 0.967
?? ?0.1389( V? )
3 + 0.6123( V 2? ) 5.07876R R
?1.068( V? ) + 1.88R
??0 0 0
Blade inertias
Ib (kg-m2) 142 0.0552
?
M b 6.16 13.7824 2.237
?
I? 1 1 1
?
I?0 0.779 1 1.284
Continued on next page
196
Table 6.1 ? continued from previous page
Bell MTR Ratio
MTR/Bell
?
I? 0.67 1 1.5
?
I?0 1 (autorotation) 1 1
?
S? 1.035 2.6288 2.54
?
S? 1.212 2.6288 2.17
Wing
Semispan, y/R 1.333 1.202 0.902
Chord, c/R 0.413 0.542 1.31
Thickness ratio, t/c 13.5% 18% 1.33
Aspect ratio 6.6 4.99 0.756
Mast height, h? = h/R 0.261 0.3362 1.29
Pylon CG, z?cg = zPcg/R 0.05 -0.0452 -0.9
?
mP 76.9 259.9217 3.38
?
IPx 1.086 15.5314 14.3
?
IPy 1.206 15.5676 12.9
?
Iqw 4.03 20.5314 5.1
?
Ipw 0.141 2.1377 15.16
?
Sw 2.88 -11.091 -3.85
Torsion mode shape ?(yT ) 0.535 1 1.87
Continued on next page
197
Table 6.1 ? continued from previous page
Bell MTR Ratio
MTR/Bell
Bending mode shape ??(yT ) 1.74 2 1.15
Sweep, ?w3 -6.5? 0?
Angle of attack, ?w2 0? 0?
Dihedral, ? ? ?w1 0 0
Aerodynamic center, xAw/cw -0.01 0
Moment coefficient, Cmac -0.005 0
Full stiffness wing
Kq1 , N/m 9.2 x 106 2.62 x 104
Kq2 , N/m 2.5 x 107 1.159 x 105
Kp, Nm/rad 1.77 x 106 1.52 x 104
Cq1 , Ns/m 9030 (? = 1%) 7.7330 (? = 0.53%)
Cq2 , Ns/m 27300 (? = 1.8%) 17.7085 (? = 0.54%)
Cp, Nms/rad 955 (? = 1.5%) 0.6853 (? = 0.2%)
?
Kq1 18.72 26.1719 1.4
?
Kq2 50.7 115.7757 2.28
?
Kp 3.595 15.1837 4.22
?
Cq1 0.88 0.8494 0.97
?
Cq2 2.67 1.9451 0.73
Continued on next page
198
Table 6.1 ? continued from previous page
Bell MTR Ratio
MTR/Bell
?
Cp 0.093 0.0753 0.81
Resulting frequencies
q1 3.2 Hz (0.42/rev) 5 Hz (0.29/rev)
q2 5.35 (0.70/rev) 9.3 (0.53/rev)
p 9.95 (1.30/rev) 15 (0.86/rev)
The inflow ratio, ?, is V? . For Bell?s flap frequency ??, ?R = 600 ft/s. TheR
non-dimensional pylon mass is obtained from ?mP = m 2 NbP yT/( 2 Ib); the bending
?
torsion coupling term is obtained from = ?Sw mP (zPcg/R)/yT . For mode shapes,
Johnson [4] uses an approximation with ? = y/yT for torsion and ? = y2/yT for
bending. These simple shape functions are adequate for basic dynamics. MTR
analysis uses the same mode shapes, however it is unclear how Johnson obtained
?(yT ) = 0.535 and ??(yT ) = 1.74. The wing stiffness and damping terms are non-
? ?
dimensionalized by Nb I ?22 b to obtain K and
Nb
2 Ib? to obtain C.
Wing stiffnesses were designed to obtain the target wing frequencies. Wing
structural damping terms were measured through RAP tests using the moving-block
method. These measurements were taken in the GLMWT in 2019. Later, another
set of measurements were taken at the Navy wind tunnel in 2021. The measurements
agreed and are documented in Section 4.7.
199
6.6 Validation and Predictions
Figure 6.2 verifies prediction of the present analysis against Johnson for the
Bell 25 ft model. The parameters used are in Table 6.1. The frequencies are in
agreement. The damping for wing beam q1 and torsion p are over-predicted although
the trends are well captured. Notice in the frequency plot, the crossings of the rotor
regressive lag mode with the wing chord and wing beam modes. These frequency
crossings cause interesting features in the damping such as the weak trough in wing
chord damping around 80 kt and a strong peak in wing beam damping around 180
kt. These frequency crossings are main actors in the stability behavior.
With the code verified, the MTR parameters were substituted. Figure 6.3
shows the predicted frequencies and damping for the MTR. While the MTR will
only be tested up to 200 kt, the plot is extended to 600 kt to show the predicted
flutter point. The baseline MTR rig will not flutter up to 200 kt. Notice the rotor lag
modes are extremely high, do not cross the wing modes below 400 kt, and therefore,
the damping shows monotonic behavior until frequencies start to coalesce. Later,
during actual testing, data obtained for the chord mode, q2, showed a trend that
required a higher fidelity analysis to capture, proving the value of the dataset. The
wing beam mode, q1, was satisfactory and because it was the lowest damped mode
up to 60 kt, its satisfactory prediction helped clear the test.
200
Flutter Analysis Validation XV-15: Damping
? ?
? ?
?
?
? ?
??
??
? ?
8
(a) Frequency.
15
?
10
5 ??
??
0
0 100 200 300 400 500 600
28
(b) Damping.
Figure 6.2: Validation of analysis with Bell 25-ft model frequencies (/rev) and damp-
ing ratio. Red - present analysis; Blue circle - Johnson.
201
7
? ?
6
5
? ?
4
3
? ?
2
?
1 ?
?
? ??
0 ? ?
0 100 200 300 400 500 600
26
(a) Frequency.
10
?
? ?
8 ? ?
??
? ?
6
??
4
??
?
2
0
0 100 200 300 400 500 600
27
(b) Damping.
Figure 6.3: MTR frequency and damping results from simplified model.
202
6.7 Comprehensive Analysis Parameters
A new table of properties (Table 6.2) was generated after the 2021 Carderock
wind tunnel test. These parameters are more than what can be used in the simpli-
fied analysis in the previous section, but will be needed for detailed comprehensive
analysis. Many parameters overlap with the simplified model list, however, new
properties are the rotor root cutout, pre-cone, gimbal limit, cyclic limit, updated
delta-3 angle, blade linear twist, and updated wing stiffnesses.
Table 6.2: Full-rig MTR properties, compiled after Carderock test in 2021.
Parameter Unit Value
Rotor
Number of blades 3
Radius m 0.7239
Root cutout %R 27
Geometric solidity ratio, ? 0.078
100% RPM (Froude-scale XV-15) 1050
Tip speed m/s 79.56
Pre-cone deg 2
Gimbal limit (flap stop) deg ?8
Collective root pitch range, ?0 deg 17 to 73
Cyclic pitch limit deg ?16
Continued
203
Table 6.2 ? continued from previous page
Parameter Unit Value
Pitch horn location %R 2.8
Pitch horn length cm 6.84
?3 deg ?16.5
Blade
Airfoil section VR-7
Chord cm 8
Thickness % chord 12
Blade linear twist deg/span -37
Blade inertia I kg-m2b 0.0552
EIN N-m2 20.1
EI N-m2C 937
GJ N-m2 62
Wing/pylon
Pylon mass (including hub, no blades) kg 32.28
Airfoil section NACA 0018
Semi-span/R 1.202
Chord/R 0.542
Mast h/R 0.3362
EIN N-m2 8.8 ? 103
Continued
204
Table 6.2 ? continued from previous page
Parameter Unit Value
EI 2 4C N-m 3.51 ? 10
GJ N-m2 8.5 ? 103
?B Hz 5.06
?C Hz 9.65
?T Hz 14.4
?B % critical 0.4
?C % critical 0.57
?T % critical 2
The blade stiffnesses EIN , EIC , GJ are the stiffnesses of the blade, however,
comprehensive analysis would require variation with span including blade grip, pitch
case, and hub. These details can be found in Ref. [37, 38]. For the wing-pylon
parameters, the pylon mass, frequency, and damping were all measured. The mass
was measured at NASA Langley, and the frequency and damping of the rig were
extracted from RAP tests at Carderock. The 2% damping of the torsion mode
was actually extracted from the chord mode strain gauge signal because the wing
torsion gauges were damaged during the test. This meant the torsion amplitude
on the chord gauges was low; it was high enough to capture the torsion frequency
accurately, but perhaps too low for a consistent measurement for damping. Despite
that, the torsion damping is provided here for completeness. The wing stiffness
205
values, EIN , EIC , and GJ , were tuned to obtain the measured frequencies but were
not directly measured through static load tests.
6.8 Chapter Summary and Conclusions
This chapter described the whirl flutter analysis and input parameters used to
predict basic trends of the MTR. It covered the following details.
1. A description of a simplified 9 degree of freedom (DOF) flutter model. The
wing has three motions: vertical bending, chord bending, and torsion. The
rotor has six motions in multiblade coordinates: collective flap, collective lag,
longitudinal flap, longitudinal lag, lateral flap, and lateral lag.
2. A comparison of Bell 25 ft diameter rotor and the MTR parameters.
3. A verification of the simplified model predictions using Bell 25-ft diameter
model. While the results were in agreement for frequencies, the wing damping
values did not fall perfectly on top of the predictions provided by Johnson.
However, the major features and trends were captured in damping.
4. The flutter prediction for the baseline MTR configuration - wing on, gimbal
free, freewheel rotor, and straight blades. The MTR is not predicted to flutter
below 200 kt. The model frequencies are all separated with the blade lag modes
very high. Wing beam, q1, damping starts around 0.5% damping and quickly
increases to 2% by 120 kt and 3.7% by 200 kt. Wing chord, q2, damping starts
around 1.2% at zero velocity and shows a slightly decreasing trend, dropping
206
to about 0.9% at 200 kt. Wing torsion, p, damping starts around 0.25% based
on the GLMWT test, and steadily rises to 1.2% at 200 kt.
5. An updated list of parameters compiled after the Carderock flutter test for
new comprehensive analysis.
This chapter documented a simple flutter model and listed the properties re-
quired to calculate flutter. While the model is simple, it provides a quick assessment
of gross behavior, which was useful for pre-test clearance.
207
Chapter 7: Wind Tunnel Testing
The Maryland Tiltrotor Rig (MTR) had a systems checkout test in the Glenn
L. Martin Wind Tunnel (GLMWT) in November 2019. Preliminary freewheeling
data was also acquired with baseline blades up to 60 kt. The rotor speed in RPM,
collective, and windspeed were recorded.
While the MTR was designed for the GLMWT, due to pandemic closures,
subsequent tunnel breakdown and overhaul of the drive system, a different test site
was needed. In October 2021, the MTR was tested at Naval Surface Warfare Center
Carderock Division (NSWCCD) in the Subsonic Wind Tunnel (SWT). This was the
first research test of the MTR. Whirl flutter data was acquired with baseline and
swept-tip blades up to 100 kt. A complete set of measurements were recorded.
7.1 Glenn L. Martin Wind Tunnel
The GLMWT is a closed-circuit, subsonic wind tunnel with a test section that
is 7.75 ft. high, 11 ft. wide, and 13 ft. long. Maximum windspeed is 230 mph
(200 kt). A six-component balance is located below the floor with several mounting
locations for test articles. The balance is not used for rotor tests, rotor rigs have their
own special dedicated balance. Stainless steel floor panels are used to cover up the
208
Figure 7.1: MTR installed in GLMWT 7.75 by 11-ft subsonic wind tunnel. Novem-
ber 2019.
test section floor and Masonite boards are used to cover any remaining irregularly
shaped areas around mounting points. Figure 7.1 shows the MTR installed in the
test section.
The MTR steel baseplate is mounted to an interfacing post fabricated es-
pecially for the GLMWT. The post dimensions can be found in the appendix of
Technical Drawings. The post material is stainless steel 304L. It was fabricated to
order by 3DHubs. The bottom flange of the post is mounted to the right pad on
the wind tunnel balance. The bolt pattern is specifically designed to interface with
the right pad. The wind tunnel balance is supported on jacks and is treated as a
fixed support. Grade 8 or higher bolts and washers are used to mount the post to
the pad. A picture of the MTR on the post is shown in Fig. 7.2.
209
Figure 7.2: MTR mounted to custom post in GLMWT. November 2019.
For alignment of the model, a laser sheet was projected down the centerline of
the test section, shown in Fig. 7.3. The wind tunnel balance was rotated until the
model was adequately aligned.
The checkout test in November 4-8, 2019, was the first full system test of the
MTR. Many issues were discovered with the sensors and hardware integration which
were subsequently resolved. For freewheel tests, collective was varied for windspeeds
up to 60 kt and RPM was recorded up to 2116. Since this was the very first test,
only low collectives were used. The results are shown in Table 7.1.
Even though the rotor speeds easily reached target values for Froude and Mach
scales, post test comprehensive analysis showed that the collective range was too
low and not representative of tiltrotor cruise. The rotor was in fact operating in the
reverse stall regime - a curious and useful regime for analysis validation but of no
210
(a) GLMWT laser sheet projected onto pylon. (b) GLMWT laser sheet projected on wing.
Figure 7.3: MTR alignment using laser sheet.
Table 7.1: MTR freewheel RPM measurements; average temperature =
63.3?F , average pressure = 29.85 Hg, average density = 0.002343 slugs/ft3
Windspeed (kt) Collective, 75%R (deg)0 1 2 2.5 3 4 5 6 7 8
25 0 400 591 780
35 350 453 647 696 820 1127 1220 1222
40 590 780 960 1130 1461 1525 1535 1524
45 772 814 966 1073 1567 1706 1723 1695
50 725 840 1043 1224 1693 1824 1926 1938 1904
55 842 995 1216 1355 1710 2011 2116
60 845 985 1220 1349 1733 2011
211
practical significance. Higher collectives, from 10? to 50?, would be needed later to
establish the correct operating regime for all future tests.
7.2 Navy Subsonic Wind Tunnel
The Naval Surface Warfare Center Carderock Division (NSWCCD) subsonic
wind tunnel (SWT) is a closed-circuit design with a closed test section measuring 8
ft. high, 10 ft. wide, and 14 ft long. The tunnel wind speed range is 6.8 to 187.5
mph (6 to 163 kt). It has a built-in balance that is suited for six-component force
and moment measurements. As with the GLMWT, the MTR uses its own dedicated
balance, so the Navy tunnel balance was locked and used as a fixed support. Unlike
the GLMWT, where floor plates are placed around the MTR, the SWT uses a
continuous circular plate with a 6-inch diameter central hole. This requires the
MTR wing spar to be mounted without the pylon or wing assembly, so the circular
cover plate can be inserted around the wing spar. Any excess space from the central
hole is covered with tape before testing begins. Figure 7.4 shows the MTR installed
in the test section.
An interfacing post was also fabricated to connect the MTR baseplate to the
SWT balance T-slot table, shown in Fig. 7.5. It was fabricated to order by Xometry.
The interface post is 3.5 inches below the tunnel floor which allows the baseplate
and clamping bracket to sit below the test section floor. An engineering drawing of
this post is found in the appendix.
212
Figure 7.4: MTR installed in NSWCCD 8- by 10-ft subsonic wind tunnel. October
2021.
Figure 7.5: Interface post for MTR and T-slot table.
213
For alignment, the Navy tunnel uses a couple of plumb bobs hung from the
ceiling to reference the test section centerline. The bobs point to a centerline drawn
on the MTR pylon and the whole model with post is translated along the T-slot
table until the line is approximately under the bobs. There is no yaw rotation of
the T-slot table, therefore, slight rotations of the post is made by exploiting the
tolerance of the bolt holes and slots on the T-slot table.
7.3 Test Conditions
All whirl flutter tests were performed at 1050 RPM. The blades were tracked
and balanced near zero collective (?75). For the freewheeling rotor, at each tunnel
speed, the collective was trimmed to achieve 1050 RPM. For example, at 60 kt, the
RPM varied with collective as shown in Fig. 7.6. At this speed, a collective of about
26? was required to achieve 1050 RPM.
Figure 7.6: RPM variation with collective at windspeed of 60 kt.
214
A similar plot can be obtained for each speed, with greater collectives needed
for the same RPM at higher speeds. The collective needed to maintain 1050 RPM for
30-100 kt is shown in Fig. 7.7. The collective is 10? at 30 kt, 26? at 60 kt, and reaches
40? at 100 kt. This high collective makes tiltrotor trim special and different from
helicopter trim and results from high cruise inflow through the rotor. The agreement
between blade sets 1 and 2 is excellent, which implies the conclusions made for one
set will be applicable to the other. For the freewheeling rotor with gimbal free, the
cyclic angles were trimmed concurrently to achieve zero first harmonic flapping. In
practice, within ?2.5? maximum across all flight conditions was deemed acceptable.
Trim is accomplished manually through a cyclic stick. A precise control will require
an automatic controller in the future. Note that 30 kt was the minimum speed
to allow for adequate cyclic margins to maintain zero gimbal tilt. Below 20 kt,
there was no collective setting which could achieve 1050 RPM. Between 20-30 kt,
maintaining zero gimbal tilt proved difficult.
Figure 7.8 shows the comparison of the straight blade in freewheel versus
powered condition. Only straight blade set 1 was tested in the powered condition
due to time constraints. However, the results of the freewheel collective versus
speed show that blade set 1 and blade set 2 perform identically. For the powered
rotor, the rotor speed was set to the target 1050 RPM and the collective was set
to a value predicted by analysis for zero thrust. The predicted value was needed
because, at the powered condition, electromagnetic interference (EMI) prevented
reliable measurements of the thrust in real-time. It is believed that the EMI was due
to the motor and load cell assembled close to each other without insulating material
215
Figure 7.7: Collective variation with speed. Comparison of two straight blade sets;
data from Tables 7.2 and 7.3.
216
between them, but this is under investigation. All powered tests were performed
with gimbal locked because the gimbal hall effect sensors were also affected by EMI,
which made trimming the gimbal difficult. Some of the noise could be filtered but
this being the first test of the MTR, and indeed one of the first flutter tests at SWT,
no chances were taken.
Figure 7.8: Collective variation with speed: powered versus freewheel. Data from
Tables 7.2 to 7.4.
217
Figures 7.9 and 7.10 show the freewheel collective versus speed and the com-
parison with the powered condition, respectively, for the swept-tip blade set. The
collective for the powered condition were set based on prediction as with the straight
blade set. The swept-tip blades perform similarly to the straight blades in terms of
collective.
Figure 7.9: Collective variation with speed; swept-tip blades. Data from Table 7.5.
There was a difference in the root pitch angle between the blade sets which
was accounted for when reporting the pitch at 75%R ?75. The pitch case angle and
218
Figure 7.10: Collective variation with speed; powered versus freewheel for swept-tip
blades. Data from Tables 7.5 and 7.6.
219
the blade grip is not naturally the same for all sets. The blade twist is the same
for all blades. However, movement of the root insert during fabrication causes the
angle they make with the blade grip to vary slightly by a few degrees. Therefore,
the blade root installation into the blade grip causes inaccurate predictions of ?75.
It is important to physically measure ?75 for each installed blade set to avoid any
uncertainty. Straight set 1 had a root angle 1.5? higher than predicted. Straight set
2 had a root angle 3? higher, and swept-tip set had a root angle 0.5? higher. The
plots in Figs. 7.6 to 7.10 show the accurate ?75 after accounting for this offset. The
data for those plots are tabulated in Tables 7.2 to 7.6. Table 7.2 is from sweep 3 in
Table 7.7. Table 7.3 is from sweep 1 and 2. Table 7.4 is from sweep 4. Table 7.5 is
from sweeps 5-7. Table 7.5 is from sweep 8.
Table 7.2: Straight blade set 1 freewheel collective data.
V ?75
kt deg
30.5 11.3
40.4 17.2
50.6 22.1
60.5 26.4
7.4 Test Procedures
Whirl flutter tests are inherently risky particularly because the wing bending
mode can be easily less than 1% damped. The test plan emphasized safety, which
determined the sequence of the runs and ultimately limited the maximum speed
up to which the tests were permitted. Datapoints were recorded for increasing
220
Table 7.3: Straight blade set 2 freewheel collective data.
V ?75 V ?75
kt deg kt deg
30.3 9.9 30.4 10.4
40.5 17.6 40.4 17.3
50.6 22.3 50.3 22.4
60.3 26.7 60.2 26.5
64.4 28.2 65.3 28.6
69.1 30.0 70.3 30.5
73.4 31.2 74.6 31.7
77.9 32.8 79.2 33.4
81.0 34.1 83.0 34.6
84.9 35.4 86.5 35.9
89.1 36.8 89.9 36.8
92.3 37.5 93.8 37.9
96.2 38.8 97.5 39.1
99.4 39.8 100.8 40.1
Table 7.4: Straight blade set 1 powered collective data.
V ?75
kt deg
3.7 3.2
19.9 11.4
30.1 15.8
40.1 20.7
50.1 25.2
59.8 28.9
221
Table 7.5: Swept-tip blades freewheel collective data.
V ?75 V ?75 V ?75
kt deg kt deg kt deg
30.8 13.3 30.3 11.9 30.4 11.1
40.4 18.9 40.3 17.8 40.4 17.1
50.7 23.5 50.6 22.0 50.5 22.1
60.1 27.4 60.4 26.4 60.5 26.5
65.3 29.5 65.1 28.8 67.1 29.1
70.1 31.2 70.1 30.8 71.9 31.4
74.0 32.4 74.5 32.5 76.5 32.7
78.1 34.3 78.3 33.8 80.7 34.3
81.7 35.2 82.2 35.1 84.8 35.1
85.7 37.1 86.1 36.3
89.1 37.9 89.6 37.8
92.7 39.0 93.2 38.7
96.2 39.9 96.8 39.6
99.6 40.7 100.1 40.6
Table 7.6: Swept-tip blades powered collective data.
V ?75
kt deg
3.8 3.4
20.5 13.0
30.5 16.9
40.5 21.6
50.5 25.9
60.6 29.7
222
windspeeds; there were no decreasing windspeed runs. At each windspeed, repeat
trials were taken for each wing mode before moving on to the next speed.
The first step was to acquire the damping of the model with the tunnel off, i.e.
at zero velocity. Thus, a powered test had to be performed first. It was not expected
predictions would match the data, since validation and refinement of analysis was
the point of the test. As a precautionary measure, the go-ahead condition was that
the damping measurement must be higher than prediction at least for the lowest
damped mode. This tedious process was accomplished by testing during the day
and analyzing the data at night to petition a speed increase the next day. Once the
measurements were confirmed to be close to prediction, the test was cleared up to
60 kt.
After successful demonstration up to 60 kt, clearance was obtained to proceed
to 80 kt and thereafter to 100 kt. The starting configuration was powered, gimbal-
locked, wing off with straight blade set 1. Thereafter, clearance was obtained one
by one for powered to freewheel, gimbal locked to gimbal free, and wing off to wing
on. Furthermore, blade set change-outs were performed three times. All operations,
including installation in and out of the tunnel, were accomplished within only five
days. In total, 525 test points were collected. Of these, 486 were whirl flutter points.
These are tabulated in Table 7.7. Flutter data were collected for the wing beam and
wing chord mode. Three trials were performed per mode. The naming convention
uses the tunnel, the sweep, and the velocity. For example, N1.78 refers to the test
point at Navy tunnel for sweep 1, which was collected at 78 kt. Future tests at
223
Maryland may use MX.Y convention to refer to test points at the Maryland tunnel
for sweep X at speed Y kt.
The data is organized into 8 sweeps in a logical sequence. However, this is not
the order in which they were tested. The test sequence is shown in Table 7.8 and
was based on clearance, risk assessment, and time windows available. The tunnel
speeds and ?75 are nominal values. Thus the sweeps in Table 7.7 have different
maximum and minimum speeds.
Table 7.8: Test sequence at Navy SWT.
Run Blades V RPM ?75 Gimbal Mode Wing
Type kt deg
Clearance obtained up to 60 kt
Hover Straight 0 700 2, 4, 6, Locked Powered Off
Set 1 8, 10
Hover Straight 0 1050 2, 4, 6 Locked Powered Off
Set 1
Flutter Straight 0, 20, 30, 1050 2, 11, 16, Locked Powered Off
Set 1 40, 50, 60 20, 24, 28
Flutter Straight 30, 40, 1050 10, 16, Locked Freewheel Off
Set 1 50, 60 21, 25
Hover Straight 0 1050 6, 8, 10, 12, Locked Powered Off
Set 1 14, 16, 18
Hover Swept-tip 0 1050 2, 4, 6, 8 Locked Powered Off
Flutter Swept-tip 0, 20, 30, 1050 2, 11, 16, Locked Powered Off
40, 50, 60 20, 24, 28
Continued
224
Table 7.8 ? continued from previous page
Run Blades V RPM ?75 Gimbal Mode Wing
Type kt deg
Flutter Swept-tip 30, 40, 50, 60 1050 10, 16, 21, 25 Locked Freewheel Off
Clearance obtained up to 82 kt
Flutter Swept-tip 65, 70, 74, 1050 28, 30, 31, Locked Freewheel Off
78, 82 33, 34
Flutter Swept-tip 30, 40, 50 ,60 1050 10, 16, 21, 25 Free Freewheel Off
Clearance obtained up to 100 kt
Flutter Swept-tip 65, 70, 74, 78, 1050 28, 30, 31, 33, Free Freewheel Off
82, 86, 89, 92, 34, 35, 36, 37,
96, 100 38, 39
Flutter Straight 30, 40, 50, 60, 1050 10, 16, 21, 25, Free Freewheel Off
Set 2 65, 70, 74, 78, 28, 30, 31, 33,
82, 86, 89, 92, 34, 35, 36, 37,
96, 100 38, 39
Flutter Straight 30, 40, 50, 60, 1050 10, 16, 21, 25, Free Freewheel On
Set 2 65, 70, 74, 78, 28, 30, 31, 33,
82, 86, 89, 92, 34, 35, 36, 37,
96, 100 38, 39
RPM Straight 60 400, 600, 52, 41, 35, 29, Free Freewheel On
Sweep Set 2 750, 950, 27, 24
1050, 1200
RPM Swept-tip 60 400, 600, 52, 41, 35, 29, Free Freewheel On
Sweep 750, 950, 27, 24
1050, 1200
Continued
225
Table 7.8 ? continued from previous page
Run Blades V RPM ?75 Gimbal Mode Wing
Type kt deg
Flutter Swept-tip 30, 40, 50, 60, 1050 10, 16, 21, 25, Free Freewheel On
65, 70, 74, 78, 28, 30, 31, 33,
82, 86, 89, 92, 34, 35, 36, 37,
96, 100 38, 39
7.5 Flutter: Baseline
The baseline configuration of the MTR consists of straight blades, gimbal free,
wing on, and the rotor in freewheel. Wing on refers to the full-up wing with airfoils,
ribs, and fairings installed, whereas wing off is the exposed spar alone. This variation
allows for investigations into aerodynamic damping and stiffness, which enter only
if the airfoil profile is in place. Figure 7.11 shows the frequency and damping of this
baseline configuration. The values are listed in Table 7.9.
Table 7.9: Straight blades, gimbal free, wing on, and freewheeling flutter
results.
Wing Beam Wing Chord
Speed, kt
Frequency Damping Frequency Damping
(Hz) (% critical) (Hz) (% critical)
30 5.024 0.5 9.523 1.09
30 5.035 0.64 9.502 1.53
Continued
226
Table 7.9 ? continued from previous page
Wing Beam Wing Chord
Speed, kt
Frequency Damping Frequency Damping
(Hz) (% critical) (Hz) (% critical)
30 5.03 0.35 9.507 1.44
40 5.024 0.6 9.502 1.43
40 5.024 0.64 9.518 1.4
40 5.024 0.67 9.513 1.32
50 5.014 0.62 9.518 1.33
50 5.019 0.8 9.513 1.35
50 5.014 0.6 9.513 1.38
60 5.03 1.1 9.507 1.46
60 5.03 0.9 9.507 1.48
60 5.019 0.78 9.513 1.5
65 5.019 0.78 9.528 1.26
65 5.019 0.89 9.544 1.43
65 5.014 0.87 9.539 1.26
70 5.004 0.98 9.539 1.29
70 5.035 0.77 9.533 1.5
70 5.019 1.13 9.539 1.37
74 5.035 0.94 9.497 1.69
Continued
227
Table 7.9 ? continued from previous page
Wing Beam Wing Chord
Speed, kt
Frequency Damping Frequency Damping
(Hz) (% critical) (Hz) (% critical)
74 5.03 0.98 9.502 1.38
74 5.024 0.84 9.507 1.49
78 5.035 0.99 9.502 1.47
78 5.03 1 9.507 1.41
78 5.035 1.13 9.513 1.37
82 5.009 1.2 9.497 1.39
82 5.03 0.98 9.492 1.31
82 5.035 1.13 9.486 1.41
85.5 5.024 1.27 9.46 1.44
85.5 5.024 1.23 9.46 1.36
85.5 5.05 1.49 9.46 1.45
89 5.019 0.87 9.46 1.37
89 5.024 1.02 9.455 1.27
89 5.03 1.1 9.455 1.32
92.4 5.03 0.73 9.45 1.38
92.4 5.019 1.09 9.45 1.36
92.4 5.045 0.57 9.455 1.26
Continued
228
Table 7.9 ? continued from previous page
Wing Beam Wing Chord
Speed, kt
Frequency Damping Frequency Damping
(Hz) (% critical) (Hz) (% critical)
95.7 5.056 0.69 9.46 1.28
95.7 5.03 1.11 9.455 1.36
95.7 5.024 0.93 9.455 1.19
99 5.014 0.75 9.45 1.29
99 5.035 0.95 9.445 1.15
99 5.035 1.4 9.445 1.32
Wing beam damping begins around 0.5% at 30 kt with a scatter of ?0.15%
over 3 trials. The damping then steadily increases up to 80 kt and shows a small
peak between 80 to 90 kt of about 1.4%. After 90 kt, there is more scatter between
the trials, with up to ?0.35% at 100 kt, but shows an increasing trend overall. The
wing chord damping starts at 1.3% with a scatter of ?0.2% at 30 kt. It remains
relatively steady without any increase in scatter up to 100 kt and features a small
peak perhaps around 75 kt. The wing chord damping remains between 1% and 1.5%
throughout the sweep.
229
Table 7.7: Test conditions at Navy SWT.
Sweep V ?75kt deg Gimbal Mode Wing
Straight blades
Set 2
30, 40, 50, 9.9, 17.6, 22.3,
60, 65, 70, 26.7, 28.2, 30.0,
1 74, 78, 82, 31.2, 32.8, 34.1, Free Freewheel On
86, 89, 92, 35.4, 36.8, 37.5,
96, 100 38.8, 39.8
30, 40, 50, 10.4, 17.3, 22.4,
60, 65, 70, 26.5, 28.6, 30.5,
2 74, 78, 82, 31.7, 33.4, 34.6, Free Freewheel Off
86, 89, 92, 35.9, 36.8, 37.9,
96, 100 39.1, 40.1
Set 1
3 30, 40, 50, 11.3, 17.2, 22.1,60 26.4 Locked Freewheel Off
4 4, 20, 30, 3.2, 11.4, 15.8,40, 50, 60 20.7, 25.2, 28.9 Locked Powered Off
Swept-tip blades
30, 40, 50, 13.3, 18.9, 23.5,
60, 65, 70, 27.4, 29.5, 31.2,
5 74, 78, 82, 32.4, 34.3, 35.2, Free Freewheel On
86, 89, 92, 37.1, 37.9, 39.0,
96, 100 39.9, 40.7
30, 40, 50, 11.9, 17.8, 22.0,
60, 65, 70, 26.4, 28.8, 30.8,
6 74, 78, 82, 32.5, 33.8, 35.1, Free Freewheel Off
86, 89, 92, 36.3, 37.8, 38.7,
96, 100 39.6, 40.6
30, 40, 50, 11.1, 17.1, 22.1,
7 60, 65, 70, 26.5, 29.1, 31.4, Locked Freewheel Off
74, 78, 82 32.7, 34.3, 35.1
8 4, 20, 30, 3.4, 13.0, 16.9,40, 50, 60 21.6, 25.9, 29.7 Locked Powered Off
230
(a) Frequency.
(b) Damping.
Figure 7.11: Stability results for baseline configuration at 1050 RPM.
231
7.6 Flutter: Wing Off
The wing airfoils along with the ribs and fairings are now removed from the
baseline. The configuration is straight blades, gimbal free, wing off, and freewheel.
So the wing provides structure (exposed spar), but no aerodynamics. Figure 7.12
shows the frequency and damping for the wing off configuration. This is an example
of a parametric variation that is not possible in flight but important for valida-
tion. It provides insight into the damping and stiffness contribution of the wing
aerodynamics. The results are listed in Table 7.10.
Table 7.10: Straight blades, gimbal free, wing off, and freewheeling flutter
results.
Wing Beam Wing Chord
Speed, kt
Frequency Damping Frequency Damping
(Hz) (% critical) (Hz) (% critical)
30 5.05 0.48 9.46 1.27
30 5.05 0.53 9.492 1.51
30 5.05 0.52 9.492 1.46
40 5.045 0.51 9.429 1.37
40 5.045 0.45 9.434 1.31
40 5.045 0.49 9.434 1.38
50 5.04 0.67 9.445 1.24
50 5.04 0.73 9.44 1.3
Continued
232
Table 7.10 ? continued from previous page
Wing Beam Wing Chord
Speed, kt
Frequency Damping Frequency Damping
(Hz) (% critical) (Hz) (% critical)
50 5.035 0.62 9.424 1.27
60 5.035 0.71 9.455 1.25
60 5.024 0.91 9.455 1.24
60 5.035 0.71 9.455 1.29
65 5.045 0.79 9.455 1.34
65 5.035 0.66 9.46 1.27
65 5.04 0.62 9.455 1.31
70 5.05 0.83 9.466 1.13
70 5.05 0.72 9.466 1.09
70 5.05 0.97 9.481 1.19
74 5.03 0.79 9.471 1.12
74 5.035 0.89 9.481 1.21
74 5.035 0.83 9.476 1.25
78 5.061 0.9 9.481 1.27
78 5.056 0.66 9.486 1.39
78 5.04 0.81 9.481 1.43
82 5.035 0.79 9.466 1.3
Continued
233
Table 7.10 ? continued from previous page
Wing Beam Wing Chord
Speed, kt
Frequency Damping Frequency Damping
(Hz) (% critical) (Hz) (% critical)
82 5.045 0.8 9.46 1.25
82 5.056 0.83 9.455 1.25
85.5 5.056 1.17 9.455 1.23
85.5 5.055 0.61 9.455 1.2
85.5 5.056 0.94 9.45 1.27
89 5.05 1.26 9.46 1.22
89 5.03 1.03 9.466 1.25
89 5.056 1.04 9.466 1.08
92.4 5.04 0.53 9.45 1.06
92.4 5.035 0.62 9.44 1.01
92.4 5.04 0.94 9.434 1.19
95.7 5.056 0.91 9.408 1.13
95.7 5.05 0.88 9.434 1.21
95.7 5.056 1.36 9.419 1.1
99 5.087 1.01 9.388 1.1
99 5.082 0.76 9.382 1.12
99 5.061 0.89 9.398 1.22
234
(a) Frequency.
(b) Damping.
Figure 7.12: Stability results for straight blades, gimbal free, wing off, and rotor in
freewheel at 1050 RPM 235
The wing beam damping starts at 0.5% at 30 kt with minimal scatter of
?0.02% over 3 trials. It steadily increases to around 1% at 100 kt with more
prominent scatter of ?0.25%. The wing chord damping starts at 1.4% with small
scatter of ?0.12% at 30 kt. It decreases slightly to around 1.16% at 100 kt with
even less scatter of ?0.06%.
The damping of the wing beam mode is only marginally reduced without the
wing. Around 85 kt, variability between trials appear to increase and it is difficult
to discern whether the damping will increase, decrease, or remain level. The chord
mode damping starts similar to the wing on configuration and as velocity increases
the damping decreases marginally with a slight peak perhaps around 80 kt.
Figure 7.13 shows the wing beam and chord modes for the wing off damping
compared to the wing on damping. A key conclusion is that wing aerodynamics has
a minimal effect on the model damping, and certainly not important up to 100 kt.
There is no sign of interference either. The rotor still dominates and the dynamics
is determined by the structure.
7.7 Flutter: Gimbal Locked
The gimbal is now locked. The configuration is straight blades, gimbal locked,
wing off, and freewheel. The locked gimbal is an effective method of obtaining,
essentially, a very stiff-in-plane hingeless hub. Figure 7.14 shows the frequency and
damping for straight blades, gimbal locked, wing off, and rotor in freewheel. The
236
(a) Beam damping.
(b) Chord damping.
Figure 7.13: Comparison of damping for wing on and wing off configurations.
237
gimbal locked tests was performed early on, when Navy clearance was available only
up to 60 kt; hence, the data stops there. The data is tabulated in Table 7.11.
Table 7.11: Straight blades, gimbal locked, wing off, and freewheeling flut-
ter results.
Wing Beam Wing Chord
Speed, kt
Frequency Damping Frequency Damping
(Hz) (% critical) (Hz) (% critical)
30 5.057 0.31 9.497 2.13
30 5.055 0.44 9.483 2.07
30 5.054 0.23 9.497 2.13
40 5.057 0.43 9.485 1.93
40 5.057 0.6 9.483 1.91
40 5.045 0.49 9.489 2.07
50 5.057 0.48 9.463 1.86
50 5.043 0.55 9.456 2.02
50 5.051 0.47 9.46 1.84
60 5.047 0.5 9.441 1.68
60 5.043 0.62 9.45 1.76
60 5.051 0.63 9.446 1.77
The wing beam damping starts around 0.33% with scatter of?0.1% at 30 kt. It
steadily increases to 0.57% with scatter of?0.07% at 60 kt. The wing chord damping
starts at 2.1% with scatter of ?0.03% at 30 kt and steadily decreases to 1.73% with
238
(a) Frequency.
(b) Damping.
Figure 7.14: Stability results for straight blades, gimbal locked, wing off, and rotor
in freewheel at 1050 RPM. 239
scatter of ?0.04% at 60 kt. Figure 7.15 shows the damping of individual wing modes
in the gimbal locked configuration compared to the gimbal free configuration.
The damping of the wing beam mode is now the lowest of the configurations,
although it still increases with speed. The wing chord damping is the highest. It
increased significantly from 1.2% for the gimbal free configuration to about 1.8%
with gimbal locked at 60 kt. However, there is a steeper decline in wing chord
damping relative to the previous configurations.
7.8 Flutter: Powered
Finally, the rotor is powered on. The configuration is straight blades, gimbal
locked, wing off, and powered rotor. This means the lower speeds can now be
populated. This condition was also performed when clearance was available only up
to 60 kt. Figure 7.16 shows the frequency and damping for straight blades, gimbal
locked, wing off, and powered rotor. Table 7.12 shows the tabulated data. The
powered data shows a small velocity of about 4 kt for a nominal test point at zero
velocity due to recirculation in the wind tunnel from the powered rig.
240
(a) Beam damping.
(b) Chord damping.
Figure 7.15: Comparison of damping for gimbal free and gimbal locked configura-
tions.
241
(a) Frequency.
(b) Damping.
Figure 7.16: Stability results for straight blades, gimbal locked, wing off, and pow-
ered rotor at 1050 RPM. 242
Table 7.12: Straight blades, gimbal locked, wing off, and powered flutter
results.
Wing Beam Wing Chord
Speed, kt
Frequency Damping Frequency Damping
(Hz) (% critical) (Hz) (% critical)
4 5.066 0.55 9.441 2.36
4 5.044 0.43 9.384 2.33
4 5.046 0.69 9.458 2.2
20 5.04 0.34 9.439 2.76
20 4.995 0.71 9.47 2.94
20 5.04 0.32 9.46 2.66
30 5.06 0.6 9.421 2.78
30 5.057 0.61 9.4712 2.99
30 5.044 0.39 9.448 2.74
40 5.046 0.8 9.434 2.74
40 5.042 0.45 9.45 2.44
40 5.061 0.6 9.474 2.44
50 5.054 0.49 9.436 2.04
50 5.04 0.79 9.457 2.36
50 5.034 0.55 9.447 2.37
60 5.05 0.51 9.443 2.07
Continued
243
Table 7.12 ? continued from previous page
Wing Beam Wing Chord
Speed, kt
Frequency Damping Frequency Damping
(Hz) (% critical) (Hz) (% critical)
60 5.048 0.84 9.44 2.44
60 5.035 0.81 9.463 2.13
The wing beam damping starts around 0.55% at 4 kt with scatter of ?0.13%.
Then there seems to be a very slight dip with damping measurements as low as
0.32% at 20 kt. It steadily increases after that to 0.68% with scatter of ?0.17%
at 60 kt. The wing chord damping starts 2.28% with scatter of ?0.08% at 4 kt,
increases to about 2.86% at 30 kt, then decreases to 2.25% with scatter of ?0.19%
at 60 kt.
Figure 7.17 shows the wing mode damping measurements of the powered con-
dition compared with the previous freewheel condition. The wing beam damping is
marginally higher than the freewheel condition. However, the wing chord damping
shows a peak at the lower speeds that is missed by the freewheel configuration.
The peak is significantly higher, showing an increase from 2.1% for freewheel to
2.8% at 30 kt. The chord mode generally stays above 2% critical through 60 kt.
The low-speed peak is of academic interest. Though a real aircraft will never be
in airplane mode at these low speeds, the results are important for analysis valida-
tion. For example, it is not clear why the chord damping behaves the way it does,
showing a 30-40% increase in damping in powered mode. Powered rotor introduces
244
(a) Beam damping.
(b) Chord damping.
Figure 7.17: Comparison of damping for powered and freewheel configurations.
245
the dynamics of the drive, which in this case is electric, and it is important for the
future of electric aviation to understand the mechanism. In this case, the effect on
damping happens to be beneficial.
7.9 Flutter: Swept-Tip Blades
Of particular importance are the swept-tip blades. Going back to the baseline,
the full configuration is swept-tip blades, gimbal free, wing on, and freewheel rotor.
Swept-tip blade is a separate and dedicated companion Ph.D. thesis by Sutherland
[39]. Research on the blade design and development, testing, and results are given
in Ref. [40]. Figure 7.18 shows the frequency and damping of swept-tip blades
configuration. Data is tabulated in Table 7.13. Swept-tips are envisioned to im-
pact stability at high speeds, but the baseline tests were limited to only 100 kt.
Nevertheless, some interesting trends are already visible around 100 kt.
Table 7.13: Swept-tip blades, gimbal free, wing on, and freewheel flutter
results.
Wing Beam Wing Chord
Speed, kt
Frequency Damping Frequency Damping
(Hz) (% critical) (Hz) (% critical)
30 5.03 0.44 9.497 1.49
30 5.024 0.55 9.497 1.41
30 5.03 0.61 9.502 1.42
Continued
246
Table 7.13 ? continued from previous page
Wing Beam Wing Chord
Speed, kt
Frequency Damping Frequency Damping
(Hz) (% critical) (Hz) (% critical)
40 5.024 0.56 9.502 1.43
40 5.024 0.56 9.486 1.49
40 5.019 0.6 9.507 1.4
50 5.019 0.82 9.518 1.44
50 5.019 0.73 9.513 1.58
50 5.014 0.75 9.518 1.46
60 5.019 0.91 9.513 1.52
60 5.014 0.78 9.507 1.66
60 5.014 0.84 9.507 1.63
65 5.014 0.8 9.486 1.54
65 5.019 0.69 9.497 1.54
65 5.024 1.29 9.486 1.64
70 5.009 1.13 9.518 1.6
70 5.03 1.02 9.492 1.49
70 5.014 0.88 9.513 1.41
74 5.009 1 9.507 1.44
74 5.014 1.1 9.497 1.45
Continued
247
Table 7.13 ? continued from previous page
Wing Beam Wing Chord
Speed, kt
Frequency Damping Frequency Damping
(Hz) (% critical) (Hz) (% critical)
74 5.014 0.84 9.492 1.42
78 5.024 0.87 9.46 1.44
78 5.024 1.23 9.46 1.35
78 5.024 0.87 9.44 1.36
82 5.024 0.96 9.445 1.48
82 5.019 1.02 9.45 1.46
82 5.03 1.01 9.45 1.46
85.5 5.03 1.14 9.434 1.55
85.5 5.024 1.11 9.434 1.33
85.5 5.05 1.11 9.455 1.42
89 5.03 1.03 9.445 1.47
89 5.03 1.17 9.45 1.47
89 5.03 1.18 9.45 1.32
92.4 5.04 0.87 9.445 1.39
92.4 5.03 1.02 9.46 1.45
92.4 5.045 1.03 9.44 1.35
95.7 5.04 1.11 9.445 1.3
Continued
248
Table 7.13 ? continued from previous page
Wing Beam Wing Chord
Speed, kt
Frequency Damping Frequency Damping
(Hz) (% critical) (Hz) (% critical)
95.7 5.014 1.01 9.45 1.35
95.7 5.03 1.36 9.44 1.27
99 5.045 1.31 9.445 1.31
99 5.03 1.05 9.445 1.23
99 5.04 1.5 9.471 1.11
The wing beam damping starts at 0.53% with scatter of ?0.08% at 30 kt.
It steadily increases with speed, reaching around 1.28% with scatter of ?0.23% at
100 kt. The wing chord damping starts at 1.45% with scatter of ?0.04% at 30 kt.
It remains relatively steady through 70 kt, then slightly decreases to 1.21% with
scatter of ?0.1% at 100 kt.
Figure 7.19 shows the comparison of damping measurements between the
swept-tip blades and straight blades. Compared to the baseline straight blades,
the swept-tip wing beam damping shows less scatter especially at higher speeds.
The wing chord damping shows the same magnitude and trend as the straight blades
with marginally lower damping at the higher speeds. Overall, swept-tip blades show
little effect on the model damping under 100 kt. However, it does not deteriorate
the stability of the beam mode. An expansion of the windspeed envelope and RPM
envelope is required to fully explore the impact of swept-tip blades.
249
(a) Frequency. (b) Damping.
Figure 7.18: Stability results for swept-tip blades, gimbal free, wing on, and rotor
in freewheel at 1050 RPM.
7.10 Flutter Analysis: 9 DOF Model
Using the nine degree of freedom simplified Johnson model[4], the frequency
and damping of the MTR were predicted for the baseline configuration of wing on,
gimbal free, and freewheeling rotor. Such an analysis appears adequate for a quick
and preliminary assessment of basic trends to first order.
This Johnson model consists of rigid flap and lag, linear aerodynamics (Cl =
Cl??), assumed wing mode shapes, and variation of lag and flap frequency with
collective pitch based on root spring orientation. The Johnson model used measured
values of lag and flap frequencies with speed. Here, it is slightly refined to calculate
them based on predicted collective ?75 at any speed.
250
(a) Beam damping.
(b) Chord damping.
Figure 7.19: Comparison of damping for swept-tip blades and straight blade baseline
configurations.
251
The predictions are overlaid with the test results in Fig. 7.20. The prediction
was carried out for initial assessment of data and it confirms the general magnitude
and trend of the data.
(a) Beam and chord frequencies.
(b) Beam damping. (c) Chord damping.
Figure 7.20: Predictions and test data for baseline configuration: straight blades,
wing on, gimbal free, and rotor in freewheel at 1050 RPM.
252
The frequency predictions remain static with velocity and, as expected, in
agreement with test data. The damping is more complicated. The wing beam mode
damping is overpredicted although the general trend of increase in damping with
speed is captured. The chord mode damping is underpredicted but again the general
trend of constant to slight reduction with speed is captured. The simplified model
does not capture the basic magnitudes let alone details in the data like the peak
in the beam mode at 85 kt, or the peak in chord mode at 75 kt. A comprehensive
model with airfoil tables, flexible blades, finite element wing, and pylon yaw and
pitch stiffnesses would be required to gain further insights. A separate and dedicated
companion Ph.D. thesis by Gul [38], deals with the development of such an analysis.
7.11 Chapter Summary and Conclusions
This chapter described the first wind tunnel tests of the MTR. It covered the
following details.
1. The details of the first checkout test at the GLMWT where systems were ver-
ified for operations and a characterization of the freewheeling RPM to wind-
speed and collective was conducted for low collectives only.
2. A description of the installation of the MTR at the Navy subsonic wind tunnel.
3. A description of the flutter test conditions.
4. A description of the flutter test procedures and test requirements.
253
5. A demonstration of three damping extraction methods applied to run N1.78
data. These methods were logarithmic decrement method, Prony method, and
the moving block method.
6. A sensitivity study conducted on four windowing methods used for the moving
block method. These were Hanning, Hamming, Flat Top, and Blackman-
Harris windows. Block size and sample shifts of the moving blocks were also
covered.
7. The flutter results for the baseline configuration: straight blades, free gimbal,
wing on, and freewheel rotor were provided.
8. The flutter results for straight blades, free gimbal, wing off, and freewheel
rotor were provided.
9. The flutter results for straight blades, locked gimbal, wing off, and freewheel
rotor were provided.
10. The flutter results for straight blades, locked gimbal, wing off, and powered
rotor were provided.
11. The flutter results for swept-tip blades, free gimbal, wing on, and freewheel
rotor were provided.
12. A prediction of the baseline configuration with a simplified 9 DOF model.
Based on these, this chapter reached the following key conclusions.
254
1. The checkout test was imperative to gain familiarity with the MTR and to
resolve any issues with the rig instruments before performing any dynamic
tests. It also revealed the correct collective regime where the final test were
to be conducted.
2. The design of the MTR allowed it to interface with the Navy subsonic wind
tunnel easily.
3. The MTR straight blade sets performed identically, however, direct measure-
ment of ?75 must be performed on the blades after installation for precise
measurement. The designed blade grip angle and blade twist do not suffice
as the twisted blade root inserts can always have a small angular discrepancy
from design intent.
4. The baseline configuration of straight blades, free gimbal, wing on, and free-
wheel rotor showed low beam damping of 0.5% at 30 kt but increased to a
peak of about 1.4% around 80-90 kt. Chord damping was relatively steady
between 1%-1.5% up to 100 kt.
5. The straight blades, free gimbal, wing off, and freewheel rotor configuration
showed wing aerodynamics was not a major factor in the model stability, at
least up to 100 kt. Beam damping was around 0.5% at 30 kt and steadily
increased to around 1% at 100 kt. The wing chord damping started around
1.4% at 30 kt and it decreased slightly to around 1.16% at 100 kt.
255
6. The straight blades, locked gimbal, wing off, and freewheel rotor configuration
showed turning the gimbal into a stiff-in-plane hingeless hub had little effect on
the wing beam damping, but increased the wing chord damping significantly
between 30-60 kt. Beam damping started around 0.33% at 30 kt and steadily
increased to 0.57% at 60 kt. Chord damping started around 2.1% at 30 kt and
steadily decreased to 1.73% at 60 kt.
7. The straight blades, locked gimbal, wing off, and powered rotor configuration
showed the powered rotor had a major and unexpected positive effect on the
wing chord damping at low speeds while the wing beam damping was unaf-
fected up to 60 kt. Beam damping started at 0.55% at 4 kt. It dipped slightly
to 0.32% at 20 kt, then steadily increased to 0.68% at 60 kt. Chord damping
started at 2.28% at 4 kt, increased to about 2.86% at 30 kt, then decreased to
2.25% at 60 kt.
8. For swept-tip blades, free gimbal, wing on, and freewheel rotor configuration,
stability of the beam and chord modes were similar to the the straight blade
configuration up to 100 kt. Beam damping started at 0.53% at 30 kt. It
steadily increased to around 1.28% at 100 kt. Chord damping started at
1.45% at 30 kt. It remained relatively steady through 70 kt, then slightly
decreased to 1.21% at 100 kt.
9. A simplified 9 DOF model was used to confirm the basic trends of the stabil-
ity data. The trends were in agreement, but the model fell short of reliable
magnitudes, as expected.
256
Lastly, a speed of 100 kt for the MTR corresponds to 230 kt at full-scale. This
is far short of the envisioned 400 kt objective and future tests should proceed up to
200 kt at the GLMWT.
257
Chapter 8: Summary and Conclusions
This chapter provides the summary and conclusion of the thesis. A section on
future recommendations is also provided.
8.1 Summary
The Maryland Tiltrotor Rig (MTR) was developed by the University of Mary-
land and fabricated by Calspan Systems. The MTR was designed for testing in the
Glenn L. Martin wind tunnel (GLMWT). The rig is a semi-span, floor mounted,
3-bladed, flutter model with gimballed hub and straight blades as the baseline con-
figuration. It was designed to test Froude- and Mach-scaled proprotors of up to
4.75-ft diameter. Compared to full-scale tiltrotors, the MTR is 1/5.26 scale XV-15
and 1/8 scale V-22, but it is not tied to those or any other particular aircraft. It has
interchangeable wing spars, hubs, and proprotor blades. Unique features of the rig
includes high bandwidth electric actuation, a fully electric direct-drive, and static
pylon tilt mechanism.
The MTR wing spar was loosely designed to the Froude-scale frequencies of
the XV-15 wing but, with the interchangeability of the spar, there is flexibility in
the design of future spars. The MTR non-rotating frequencies and damping were
258
obtained at both the GLMWT and Navy subsonic wind tunnel (SWT). The results
were in agreement between tunnels with wing beam frequency of about 5 Hz and
damping of about 0.5% critical, wing chord frequency of about 9.5 Hz and damping
of about 0.5% critical, and wing torsion frequency of about 14.5 Hz and damping
of about 0.2% critical. However, the torsion damping at the Navy SWT was not
accurately acquired due to broken wing strain gauges.
There are two load paths from the rotor to the wing root. The primary load
path runs through the load cell and a secondary load path is unmeasured. Rotor
thrust and torque are minimally affected by the secondary load path and so flutter
tests could commence.
The electric motor controller power is limited by the cable thickness from the
DC power supplies to the motor controller. Currently, with 10 AWG cables, the
maximum current is 40A. With a power supply voltage of 120V, the max power
available for the motor controller is 4.8kW.
Frequency and damping results for the MTR installed in GLMWT and Navy
SWT were in agreement between the tunnels. The wing beam frequency was about
5 Hz and damping about 0.5% critical. Wing chord frequency was about 9.5 Hz
and damping about 0.5% critical. Wing torsion frequency was about 14.5 Hz and
damping about 0.2% critical. However, the torsion damping at the Navy SWT was
not accurately acquired due to broken wing strain gauges.
A new calibration stand was developed for the load cell. This stand allowed for
calibration to be performed while the load cell was mounted in the pylon, creating
a test-like environment. The load cell calibrations showed that thrust and torque
259
were the most accurate, and most unaffected by the secondary load path present in
the pylon.
High-bandwidth electric actuators allowed for a range of up to 56? in blade
collective pitch. They also allowed for higher harmonic inputs and were the principal
instruments to activating flutter at the wing-pylon frequencies.
Blade pitch encoders measured the blade root pitch. The actual ?75 angle
should be directly measured for each new blade set due to fabrication discrepancies
in the blade root insert.
The shaft torque gauge was not sensitive enough to provide an accurate mea-
surement for torque with a 161.5 in-lb/?? calibration, but it can be used as a backup
measurement device.
The gimbal Hall effect sensors and azimuth Hall effect sensor are used to
determine the rotating hub ?1S and ?1C angles.
The wing strain gauges were attached near the root end of the wing spar and
were used to measure the wing response. All gauges were full-bridge circuits which
provide the highest accuracy and compensate for temperature changes. There were
two sets of full-bridge circuits for each wing mode. However, only one set recorded
data during testing, the other set was for redundancy and backup.
A 9 DOF model was developed for simple whirl flutter analysis. It is a semi-
span wing with a gimballed rotor in cruise flight. The wing has three motions:
vertical bending, chord bending, and torsion. The rotor has six motions: collective
flap, collective lag, longitudinal flap, longitudinal lag, lateral flap, and lateral lag.
Six rotor equations of motion: three flap and three lag equations, and three wing
260
equations of motion are used to build the model system. The wing mode shapes
were ? = y2/yT for bending and ? = y/yT for torsion.
Both the Bell 25 ft rotor parameters and the MTR parameters are used for
comparison. The results for Bell 25 ft data was shown for verification. Frequencies
were in agreement, but the wing damping values did not fall perfectly on top of the
9 DOF model predictions. However, the major features and trends were captured
in damping. The results for the baseline MTR configuration: wing on, gimbal free,
freewheel rotor, and straight blades, did not predict any flutter below 200 kt. The
model frequencies were all separated with the blade lag modes very high. Wing
beam, q1, damping started around 0.5% damping and quickly increased to 2% by
120 kt and 3.7% by 200 kt. Wing chord, q2, damping started around 1.2% at zero
velocity and showed a slight decreasing trend, dropping to about 0.9% at 200 kt.
Wing torsion, p, damping started around 0.25% and steadily rose to 1.2% at 200 kt.
Checkout testing at the GLMWT occurred in November 2019. The first flutter
test occurred at Navy SWT in October 2021. Test conditions showed that the blades
sets used on the MTR performed identically in the SWT. Test procedures were
developed to obtain clearance for higher windspeeds at 60 kt and 82 kt. A total of
8 sweeps were completed.
Three damping extraction methods, logarithmic decrement method, Prony
method, and the moving block method, were applied to run N1.78 chord mode as
a demonstration. The moving block method considered four windowing methods.
These were Hanning, Hamming, Flat Top, and Blackman-Harris windows. Block
size and sample shifts of the moving blocks were also covered.
261
Frequency and damping results for the beam and chord modes were shown for
the configurations listed below.
1. The baseline configuration consists of straight blades, free gimbal, wing on,
and freewheel rotor.
2. The straight blades, free gimbal, wing off, and freewheel rotor configuration
which investigated the effect of wing aerodynamics on stability.
3. The straight blades, locked gimbal, wing off, and freewheel rotor configuration
which effectively turned the hub into a stiff-in-plane hingeless hub.
4. The straight blades, locked gimbal, wing off, and powered rotor configuration
with showed the difference between a freewheeling and powered rotor.
5. The swept-tip blades, free gimbal, wing on, and freewheel rotor configuration
which gave a glimpse of the effect of advanced geometry blades on stability.
6. The baseline configuration results were overlaid with a simplified 9 DOF model
prediction to determine trends.
8.2 Conclusions
Based on the present research, the following key conclusions were drawn.
1. The MTR nominal wing spar and gimballed hub were fully characterized. The
MTR was fully instrumented and calibrated for wind tunnel testing.
262
2. There were two load paths from the rotor to the wing, but the thrust and
torque measurements were minimally affected by the secondary load path.
Flutter testing could commence with these primary measurements.
3. The 9 DOF simplified model showed that the MTR blade lag frequencies were
too high and the frequencies did not coalesce with other modes. This indicated
that it would not achieve a flutter point under 200 kt. While the model
produced the gross trends reasonably, a high-fidelity model is obviously desired
to accurately capture the finer details of the magnitudes and trends from 0-
200 kt. Indeed, it is the objective of this dataset to be used for validation of
high-fidelity models.
4. The checkout test in the GLMWT was imperative to gain familiarity with the
MTR and to resolve any issues with the rig instruments before performing any
detailed dynamic tests. It also revealed the correct collective regime where the
flutter test were to be conducted.
5. The MTR straight blade sets performed identically at Navy SWT, however,
direct measurement of ?75 must be performed on the blades after installation
for precise measurement. The designed blade grip angle and blade twist are
not sufficient to derive ?75 as, during fabrication, the twisted blade root inserts
can have a small angular discrepancy from design intent.
6. The baseline configuration of straight blades, free gimbal, wing on, and free-
wheel rotor showed low beam damping of 0.5% at 30 kt but increased to a
263
peak of about 1.4% around 80 to 90 kt. Chord damping was relatively steady
between 1% to 1.5% up to 100 kt.
7. Straight blades, free gimbal, wing off, and freewheel rotor configuration showed
wing aerodynamics was not a major factor in the model stability, at least up
to 100 kt. Beam damping was around 0.5% at 30 kt and steadily increased to
around 1% at 100 kt. The wing chord damping started around 1.4% at 30 kt
and it decreased slightly to around 1.16% at 100 kt.
8. Straight blades, locked gimbal, wing off, and freewheel rotor configuration
showed turning the gimbal into a stiff-in-plane hingeless hub had little effect
on the wing beam damping, but increased the wing chord damping significantly
between 30-60 kt. Beam damping started around 0.33% at 30 kt and steadily
increased to 0.57% at 60 kt. Chord damping started around 2.1% at 30 kt and
steadily decreased to 1.73% at 60 kt.
9. Straight blades, locked gimbal, wing off, and powered rotor configuration
showed the electric drive had a major and unexpected positive effect on the
wing chord damping at low speeds while the wing beam damping was unaf-
fected up to 60 kt. Beam damping started at 0.55% at 4 kt. It dipped slightly
to 0.32% at 20 kt, then steadily increased to 0.68% at 60 kt. Chord damping
started at 2.28% at 4 kt, increased to about 2.86% at 30 kt, then decreased to
2.25% at 60 kt.
264
10. For swept-tip blades, free gimbal, wing on, and freewheel rotor configuration,
stability of the beam and chord modes were similar to the straight blade
configuration up to 100 kt. Beam damping started at 0.53% at 30 kt. It
steadily increased to around 1.28% at 100 kt. Chord damping started at
1.45% at 30 kt. It remained relatively steady through 70 kt, then slightly
decreased to 1.21% at 100 kt.
11. A simplified nine degree of freedom model was used to confirm the basic trends
of the stability data. But, it fell far short of reliable magnitudes as expected.
8.3 Future Work
The University of Maryland, Alfred Gessow Rotorcraft Center, now has a
new unique tiltrotor facility. This facility should be used over the next decade
to advance tiltrotor technology as well as electric-VTOL technology. First, some
necessary model improvements and facility recommendations are considered.
1. Electromagnetic interference (EMI) from the electric motor is intense enough
to overwhelm the gimbal sensors and makes it impossible to trim the gimbal
during powered operation. It also affects the load cell, so resolving this issue
should be the top priority before commencing powered tests.
2. The GLMWT has been unavailable for over two years due to the COVID-19
pandemic and unexpected mechanical issues. The tunnel must be repaired and
upgraded as soon as possible. Upgrades should include modern acoustic liners
265
so acoustic studies can be performed and upgraded electric power sources for
eVTOL tests.
3. Carderock SWT facility is an excellent back-up facility with a max windspeed
of 168 kt. Should the GLMWT be unavailable for an extended period, this
partnership should be leveraged so tests that can continue and data collection
can proceed up to 168 kt.
4. NASA Langley Transonic Dynamics Tunnel (TDT) is a facility that would
allow for concurrent Froude- and Mach-scale tests using heavy gas medium.
Matching these similitude parameters at scale increases the quality of aeroe-
lastic tests of the MTR.
Currently, the hingeless hub is being fabricated by Calspan and will be the
focus of studies for the next five years. Recommendations for MTR testing of the
next five years pertains to both the gimballed and hingeless hubs.
1. MTR should be tested at least up to 175 kt and perhaps 200 kt if possible.
2. Center of gravity of the pylon should be moved forward to help lower the
flutter boundary.
3. Wing pressures and airloads should be measured for interference.
4. Rotor airloads should be measured. The slip ring must be updated to provide
more channels for pressure taps.
5. Flight dynamic derivatives should be measured.
266
6. Methods to delay or eliminate instabilities should be invented and tested.
It is impossible not to think about what the future may bring beyond the next
five years. Future research on the MTR is really unlimited in scope because the
flexibility of having interchangeable parts allows for all kinds of studies, small and
large. The following recommendations only touch on a few interesting topics.
1. More advanced blade shapes should be developed and tested such as chord
variations and composite couplings. Besides their effect on performance and
stability, the acoustics should be explored for these advanced blade geometries.
2. With hub interchangeability, a rigid hub with individual blade control (IBC)
can be investigated. This would eliminate the need for swashplate actuators,
swashplate, and pitch linkages.
3. Adding a shroud to open rotors has always been a promising design and an
unrealized vision for VTOL designers. The question of how to mount it on the
MTR and how to fabricate it would be a challenging and relevant problem.
267
Appendices
268
Technical Drawings
1
Figure 1: GLM Wind Tunnel Interface Post Drawing
2
ALL DIMENSIONS IN INCHES 4 Top view
TOLERANCES: DRILL AND TAP 3/4-10
X          =     ?0.01 9 THRU ALL
X.X        =     ?0.01 70% THREAD MIN
X.XX       =     ?0.01 6 PLACES
X.XXX      =     ?0.005
5.55
7.500
5.55 0.125 A 1
9
4 7 6
6
Section view A-A A
Front view 1 Isometric view
4
17
32
6
12 DRILL THRU ALL14 FOR 1/2 INCH BOLTS
3 16 PLACES
14 Bottom view
Figure 2: Carderock Wind Tunnel Interface Post Drawing
3
8
7.63
7
Bottom view
Scale:  1:2 Isometric view 6
Scale:  1:2
4.75 3.07
2.65
5
2 2
Front view 4.75
4
Right view Scale:  1:2 Left view Rear view
Scale:  1:2 0.75 Scale:  1:2 Scale:  1:2
0.33 3
2
DESIGNED BY:
NOTE: Fred Tsai I _DATE: H _
7/10/2019
ALL DIMENSIONS IN INCHES. CHECKED BY: G _XXXTop view DATE: F _XXX
SIZE E _
Scale:  1:2 A1 DASSAULT SYSTEMES D _
SCALE WEIGHT (kg) DRAWING NUMBER SHEET C _ 1
  1:1 4.09 1/1 B _Hover Adapter
This drawing is our property; it can't be reproduced or communicated without our written agreement. A _
P O N M L K F E D C B A
Figure 3: Hover Tower Drawing
1 2 3 4 5 6 7 8
P
O
N
M
0 . 3 3
7 . 6 3
L
K
J
I
0 . 7 5
H
G
F
E
D
C
B
A
4
1.5
1.08
Bottom view
1.5 1.98 2.35
0.45
0.6 1
4.6
0.8 0.257
0.8 1.17 4.6
2.4
26.8 4.6
0.201 30.8
4.6
1 0.531
4.6
0.7
1 5.45
2.25 1.83 1.98
1.25 Right view Front view Left view
0.94
Top view
1.502
TITLE: BASELINE WING SPAR
TOLERANCES (UNLESS OTHERWISE SPECIFIED) PROJECT: MARYLAND TILTROTOR RIG - BASELINE
XX..XX X                                                                              ==                      ++//--  ..00055 i nin. . DATE:     3  0    M    A  R   C   H     2  0  1  9        SCALE:   1  : 1        UNITS: INCHES
ITEM         QTY                DESCRIPTION                               MATERIAL X.XXX    JAMES SUTHERLANDXA.NXGXUXLXA  
  
R  
     
      
                                                =            = 
                     ++//--  ..0000015 i nin. . DESIGNED & DRAWN:
001 1 BASELINE WING SPAR ALUMINUM 6061-T6 SURFACE FINISH 
                          ==                      +N/A- .1    U  N   I  V   E  R   S AITLYFR OEFD M GAERSYSOLAWN RDO, CTOOLRLCERGAEF TP ACREKN,T MERD 20742
Figure 4: Baseline Wing Spar
Matlab Codes
Code for logarithmic decrement method. The code will take an average of the
log decrements of consecutive peaks in the signal.
1 %% Test with log dec method
2 signaltime = 1000; % signal duration in samples
3 [Ypk,Xpk,Wpk,Ppk] = findpeaks(s(sig_start:sig_start+signaltime),?
?? MinPeakProminence?,20);
4
5 % Plot signal and the peaks
6 figure;
7 ee = plot(Time(sig_start:sig_start+signaltime),s(sig_start:sig_start
?? +signaltime)-mean(s(sig_start:sig_start+signaltime)),Time(Xpk+
?? sig_start),Ypk-mean(s(sig_start:sig_start+signaltime)),?dr?);
8 xlabel(?Time, sec?)
9 ylabel(?Strain, \mu\epsilon?)
10 set(gca,?FontSize?,12,?FontWeight?,?Bold?);
11 set(ee,?Linewidth?,3);
12
13 n_peaks = numel(Xpk); % Determine the number of peaks
14
15 %Vector length of interest
16 t_new = Time(Xpk);
1
17 y_new = Ypk-mean(s(sig_start:sig_start+signaltime)); % Remove mean
?? of the signal
18
19 %Calculate Logarithmic Decrement, undamped natural frequency,
?? damped natural frequency, damping ratio
20 Log_Dec = zeros(length(n_peaks)); % Initialize
21
22 for nn = 1:n_peaks-1
23 Log_Dec(nn)= log(y_new(nn)/y_new(nn+1)); % computed n = 1
?? periods apart
24 end
25
26 Mean_dec = mean(Log_Dec); %Calculate Average Logarithmic Decrement
27
28 % Damping calculation
29 damp_ratio_logdec = 1/sqrt(1+((2*pi/(Mean_dec))?2)); %Assesses
?? Damping Constant
2
Simple code for Prony Method. Signal has sampling frequency of 1000 samp/s.
The signal is a 1 second duration of a damped response from N1.78 from the MTR
Carderock test. Model number was chosen based on the 1000 sample signal used.
For signals with more or fewer samples, change the model number accordingly.
1 f = 1000; % samples/sec
2 M = 400; % model number
3 test_sig = s(sig_start:sig_start+1000);
4 N = length(test_sig);
5
6 % Perform Prony method
7 T = toeplitz(test_sig,zeros(1,N));
8 x = H((M+1):N,1); % N-M by 1
9 A = H((M+1):N,2:(M+1)); % N-M by N
10 P = [-1;A\x].?; % M+1 by 1
11 p = roots(P);
12
13
14 % Obtain frequency, and damping
15 spoles = log(p)*f;
16 sigma = real(spoles); % Sigma term
17 omega = imag(spoles); % Frequency omega rad/s
18 frequency = abs(omega/(2*pi)); % Hz
3
19 damping = (sigma)./(-frequency*2*pi)*100; % in %critical
4
Code for Prony Method using Matlab functions. Signal has sampling frequency
of 1000 samp/s. The signal is a 1 second duration of a damped response from N1.78
from the MTR Carderock test. Model number array was chosen based on the 1000
sample signal used. For signals with more or fewer samples, change the model
numbers accordingly.
1 f = 1000; % samples/sec
2 M = [20 100 250 400 800]; % loop through model numbers
3 test_sig = s(sig_start:sig_start+1000);
4
5 figure
6
7 % Perform Prony method for each model number
8 for i = 1:length(M)
9 [inumz,idenz] = prony(test_sig,M(i),M(i));
10 [iapp,tapp] = impz(inumz,idenz,length(test_sig),f); % Used to
?? plot of prony time signal
11 ff = plot(tapp,iapp,?o?);
12 hold on;
13 plot(tapp,test_sig);
14 ylim([-200 100]);
15
5
16 [r,p,k] = residuez(inumz,idenz); % Obtain residue, poles, and
?? direct terms. Only r and p needed.
17
18 % Obtain amplitude, frequency, and damping
19 a_list = r;
20 prony_amp = abs(2*a_list); % amplitude
21 spoles = log(p)*f;
22 tau_list = real(spoles); % Sigma term
23 omega_list = imag(spoles); % Frequency omega rad/s
24 frequency = abs(omega_list/(2*pi)); % Hz
25 damping = (tau_list)./(-frequency*2*pi)*100; % in %critical
26
27 % Sort results in descending order in amplitude.
28 [prony_amp_sorted, ISort] = sort(prony_amp);
29 ISort_desc = ISort(end:-1:1);
30 prony_amp_sorted = prony_amp_sorted(end:-1:1);
31 frequency_sorted = frequency(ISort_desc);
32 damping_sorted = damping(ISort_desc);
33
34 % Display first ten results of each model order
35 disp([prony_amp_sorted(1:10) frequency_sorted(1:10)
?? damping_sorted(1:10)]);
6
36 end
37
38 % Plot settings
39 xlabel(?Time, sec?)
40 ylabel(?Strain, \mu\epsilon?)
41 set(gca,?FontSize?,12,?FontWeight?,?Bold?);
42 set(ff,?Linewidth?,3);
43 legend(?Model # = 20?,?Model # = 100?,?Model # = 250?,?Model # = 400
?? ?,?Model # = 800?)
7
Code for moving block method using a simulated signal.
1 close all; clear all; clc;
2
3 %Calculate damping ratio using the moving block method for a simple
?? simulated
4 %signal
5 %1) Use raw transient strain data, determine the frequencies of
?? interest.
6 %2) FFT a window of that data - ideally use 2?n number of samples
?? like 512, 1024, etc.
7 %3) Find the amplitude of the frequencies of interest and store
?? those scalars
8 %4) Shift window down one sample and repeat step 3
9 %5) Plot the log(amplitude) vs time. Time is based on sampling
?? frequency,
10 %if you are sampling at 100 samp/sec then each sample shift is 0.01
?? second.
11 %6) Fit a line through the plot and the dampling ratio, zeta, is
?? calculated as
12 % slope = -zeta*omega_n
13
14 %% Create Damped Signal
8
15 % Simulated Signal
16 A = 10; % Amplitude 1
17 f = 1000; % sampling frequency samp/sec
18 n = 3000; % multipler to get full signal length
19 T = 1/f; % sampling interval
20 t = 0:T:n*T; % time array
21 zeta_ini = 0.01; % simulated damping ratio: 1% of critical damping
22 omega1 = 2*pi*5; % 5 Hz natural frequency to rad/s
23
24 % Damped Signal
25 s = A*exp(-zeta_ini(1)*omega1*t).*sin(sqrt(1-zeta_ini(1)?2)*omega1*t
?? );
26
27 %% Add noise - simplified MATLAB function awgn()
28 SNR = 1.5; % ratio of signal to noise
29 sigPower = sum(abs(s).?2)/numel(s);
30 noisePower = sigPower/SNR;
31 noise = sqrt(noisePower)*randn(size(s)); % white noise signal
32 s = s+noise; % final signal plus noise
33
34 %% Plot Damped Signal
35 figure
9
36 c = plot(t,s?);
37 ylim([-25 20])
38 xlabel(?Time, sec?)
39 ylabel(?Strain, m\epsilon?)
40 set(c,?linewidth?,2);
41 set(gca,?fontweight?,?bold?,?fontsize?,12);
42
43 %% Step 1a: Set the index for looking at the damped signal (
?? simulated signal is easy to start at sample 1)
44
45 % Look at signal FFT resolution
46 sig_start = 1; % signal starts at sample 1
47
48 % Calculate the frequency in Hz
49 [sig,ftemp] = dataFFT(s?,f); % uncorrected amplitude and energy
50 figure
51 b = plot(ftemp,sig);
52 xlim([0 20])
53 set(b,?linewidth?,2)
54 set(gca,?fontweight?,?bold?,?fontsize?,12)
55 xlabel(?Frequency, Hz?)
56 ylabel(?Amplitude (m\epsilon)?)
10
57
58 %% Step 1b finding the frequencies of interest
59 lowerfreq = 4; % lower bound when searching for frequency peak
60 upperfreq = 6; % upper bound when searching for frequency peak
61 l1b = find(ftemp>lowerfreq,1); % find the indices of the frequency
?? bands, lower 1st freq bound
62 u1b = find(ftemp>upperfreq,1); % upper 1st frequency bound
63 [pks1,locs1] = findpeaks(sig(l1b:u1b),?SortStr?,?descend?); % sort
?? by descending order, largest peak first
64 locs1 = l1b+locs1; % the lower bound index + the location index of
?? the largest peak within the lower and upper bounds gives the
?? actual location index
65
66 % These frequencies will be used to calculate damping ratio at the
?? end
67 harmonics = [ftemp(locs1(1)) ftemp(locs1(1)) ftemp(locs1(1))]; %
?? Multiple elements allows for looping, can be changed to have
?? different frequencies when signal has multiple modes.
68
69 %% Step 2 Creating Blocks of the Signal
70 % The size of the block or window is mostly a trial and error
?? exercise
11
71 window_size = [2?9 2?10 2?11]; % block sizes per harmonic for f=1000
?? sample rate
72
73 % For each frequency, calculate the damping ratio. For this example
?? there is only 1 harmonic and 3 block sizes so the damping
?? ratio is calculated for each block size.
74 for ind = 1:length(harmonics)
75 num_windows = length(s)-window_size(ind)-1; % Maximum number of
?? sample shifts that can be made in the full signal.
76 time(ind).windowsize = 0:T:(num_windows-1)*T; % time array to
?? match the number of shifts
77
78 % Initialize
79 ini_index = sig_start;
80 amplitude = zeros(1,num_windows);
81
82 % Loop through the moving blocks and record the amplitudes of
?? the interested frequencies
83 for i = 1:num_windows
84 % Creating a block
85 StrainWindow = s(ini_index:ini_index+window_size(ind)-1);
86 [fftstrain, freq] = dataFFT(StrainWindow,f);
12
87
88 % % Take a look at the FFT of the first block
89 % if i==1
90 % figure(3)
91 % b = plot(freq,fftstrain);
92 % xlim([0 20])
93 % set(b,?linewidth?,2)
94 % set(gca,?fontweight?,?bold?,?fontsize?,12)
95 % xlabel(?Frequency, Hz?)
96 % ylabel(?Amplitude (m\epsilon)?)
97 % hold on
98 % end
99
100 %% Step 3 Storing the Amplitudes of the Frequencies from FFT
101 % Search algorithm to get the frequency band of interest,
?? and find
102 % max peak in that range, can be used for multiple
?? frequencies
103
104 % if ind == 1
105 l1b = find(freq>lowerfreq,1); %find the indices of the
?? frequency bands, lower 1st freq bound
13
106 u1b = find(freq>upperfreq,1); %upper 1st frequency bound
107 [pks,locs] = findpeaks(fftstrain(l1b:u1b),?SortStr?,?descend?
?? );
108 locs = l1b+locs-1;
109 % elseif ind == 2
110 % l2b = find(freq>8,1); %lower 2nd frequency bound
111 % u2b = find(freq>11,1); %upper 2nd freq bound
112 % [pks,locs] = findpeaks(fftstrain(l2b:u2b),?SortStr?,?
?? descend?);
113 % locs = l2b+locs-1;
114 % elseif ind == 3
115 % l3b = find(freq>16,1); %lower 3rd freq bound
116 % u3b = find(freq>20,1); %upper 3rd freq bound
117 % [pks,locs] = findpeaks(fftstrain(l3b:u3b),?SortStr?,?
?? descend?);
118 % locs = l3b+locs-1;
119 % end
120 amplitude(i) = pks(1); %Store frequency peak value
121
122 %% Step 4 Move block a sample down
123 ini_index = ini_index+1; %Next sample
124
14
125 end
126
127 %% Step 5 Take the log of the final amplitudes array and plot it
128 log_amp(ind).windowsize = log(amplitude);
129 figure(4)
130 e = plot(time(ind).windowsize,log_amp(ind).windowsize);%,time,
?? log_amp0)
131 xlabel(?Time, sec?)
132 ylabel(?Log of Amplitude?)
133 set(gca,?FontSize?,12,?FontWeight?,?Bold?);
134 set(e,?Linewidth?,2);
135 hold on
136
137 %% Step 6a Plot the fitted line through the log of amplitude
?? line
138 % Fit a linear line through the result and the slope will allow
?? you to
139 % calculate the damping ratio
140 P = polyfit(time(ind).windowsize,log_amp(ind).windowsize,1);
141 yfit = P(1)*time(ind).windowsize+P(2);
142 hold on;
143 plot(time(ind).windowsize,yfit,?r-.?)%,time,yfit0,?b-.?);
15
144
145 %% Step 6b Calculate the Damping Ratio
146 zeta_movingblock(ind) = -P(1)/(harmonics(ind)*2*pi);
147
148 end
149
150 %% Test fits with lesser time
151 % In some cases, the oscillating line has a higher slope (more
?? damping) in the initial second than the rest of the signal
?? and so this section investigates the damping ratio of shorter
?? signals by performing a linear fit over a shorter duration.
?? This example takes the time used in the largest block size.
152 P1 = polyfit(time(1).windowsize(1:length(time(3).windowsize)),
?? log_amp(1).windowsize(1:length(time(3).windowsize)),1);
153 %yfit1 = P1(1)*time(1).windowsize(1:2000)+P1(2);
154 P2 = polyfit(time(2).windowsize(1:length(time(3).windowsize)),
?? log_amp(2).windowsize(1:length(time(3).windowsize)),1);
155 %yfit2 = P2(1)*time(2).windowsize(1:2000)+P2(2);
156 P3 = polyfit(time(3).windowsize,log_amp(3).windowsize,1);
157 %yfit3 = P3(1)*time(3).windowsize(1:2000)+P3(2);
158 zeta1 = -P1(1)/(harmonics(ind)*2*pi)
159 zeta2 = -P2(1)/(harmonics(ind)*2*pi)
16
160 zeta3 = -P3(1)/(harmonics(ind)*2*pi)
161
162 %% FFT function
163 %Calculates the FFT of a signal
164 %Inputs: raw_data = signal array of data
165 %sampling_frequency = scalar denoted in samples/sec
166
167 function [data, freq] = dataFFT(raw_data,sampling_frequency)
168 L = length(raw_data);
169 NFFT = 2?6*L;%2?nextpow2(L); % Zero-padding to get higher
?? resolution in FFT
170 freq = sampling_frequency/2*linspace(0,1,floor(NFFT/2)+1);
171 data = fft(raw_data,NFFT)/L;
172 data = 2*abs(data(1:floor(NFFT/2)+1));
173
174 %% Original FFT function, no zero padding of fft
175 % Y=fft(raw_data);
176 % P2 = abs(Y/L);
177 % data = P2(1:L/2+1);
178 % data(2:end-1) = 2*data(2:end-1);
179 % freq = sampling_frequency*(0:(L/2))/L;
180 end
17
MTR Pin Connections
The wire connection sheet documents the wires and pin connections from the
MTR instruments to the DAQ. Follow each of the columns starting from the left to
the right of the page. Under System column, PL denotes pitch link. Under Screw
Terminal column, the screw terminals at the nose of the rotor are labeled with J#.
For example, J5-21 means the pitch link wires connect to the J5-J21 terminals. J5 is
the inner terminal that connects to the slip ring wires, and J21 is the outer terminal
that connects to the pitch link wires. The pins on terminal J5 and J21 are connected
through the printed circuit board directly, so J5 pin 1 is electrically connected to
J21 pin 1. Slip Ring Wire # column denotes the slip ring wire which is synonymous
with the pins on the slip ring. There are four slip ring cables that run from the slip
ring to the DAQ, with 16 wires inside each cable. These wires are also numbered and
colored which are documented in columns ?Slip Ring Cable End Pin #? and ?Slip
Ring Cable Wire Color?. The slip ring cable wires have 8 colored wires paired with
white wires for each color. So to denote the white wires, they are described with the
color they are twisted to. For example, ?Red? is the fully red wire, and ?Red-W? is
the fully white wire that is twisted with the red wire. These wires are pinned into
connectors, the majority of which are Molex. The connectors have labels on the
housing that denote the pin numbers. The last 4 columns show the destination on
the DAQ. ?Destination on Module? column shows two 4331 modules with (5) and
(7) appended; this identifies the modules in slot 5 or slot 7 on the DAQ. ?6365-0?
and ?6365-2? denotes the 6365 module and the slot that the sensors are connected
to. There are three slots on the 6365: slot 0, 1 and 2, and only slots 0 and 2 are
used. Note it is important to reference the pinout diagram for the 6365 module as
1
the pins are NOT the same between each slot. Slot 0 has AI/AO and DI/DO pins
while slots 1 and 2 are AI pins ONLY. The pitch encoders were separated from other
sensors and placed in the cDAQ module because they caused significant noise in the
other sensors during pitching motions.
2
Slip Ring Slip Ring Destinati
Screw Slip Ring Connect Destination 
System Cable System Wire Function Wire Color Pin # Cable End Cable Wire Connector on Pin Pin Label
Terminal Wire # or Pin # Function
Pin # Color Module
PL 1 5V Red 1 53 1 Red 1 DAQ 4331 (7) CH 0 EX+
PL 1 GND Black J 5-21 2 25 9 Red-W 9 DAQ 4331 (7) CH 0 EX-
PL 1 Signal- Green 3 61 2 Orange 2 DAQ 4331 (7) CH 0 AI-
PL 1 Signal+ White 4 8 10 Orange-W 10 DAQ 4331 (7) CH 0 AI+
PL 2 5V Red 1 4 3 Brown 3 DAQ 4331 (7) CH 1 EX+
PL 2 GND Black J 10-26 2 42 11 Brown-W 11 DAQ 4331 (7) CH 1 EX-
PL 2 Signal- Green 3 10 4 Purple 4 DAQ 4331 (7) CH 1 AI-
16-channel Slip Ring Cable PL 2 Signal+ White 4 49 12 Purple-W Molex 16-pin 12 DAQ 4331 (7) CH 1 AI+
SR1 PL 3 5V Red 1 18 5 Yellow 5 DAQ 4331 (7) CH 2 EX+
PL 3 GND Black J 8-24 2 12 13 Yellow-W 13 DAQ 4331 (7) CH 2 EX-
PL 3 Signal- Green 3 17 6 Black 6 DAQ 4331 (7) CH 2 AI-
PL 3 Signal+ White 4 27 14 Black-W 14 DAQ 4331 (7) CH 2 AI+
Shaft 5V Red 1 32 7 Green 7 DAQ 4331 (7) CH 3 EX+
Shaft GND Black J 1-17 2 14 15 Green-W 15 DAQ 4331 (7) CH 3 EX-
Shaft Signal- Green 3 5 8 Blue 8 DAQ 4331 (7) CH 3 AI-
Shaft Signal+ White 4 24 16 Blue-W 16 DAQ 4331 (7) CH 3 AI+
Blade 3 Bend 5V Red 1 51 1 Red 1 DAQ 4331 (7) CH 4 EX+
GND Black J 3-19 2 50 9 Red-W 9 DAQ 4331 (7) CH 4 EX-
Signal- Green 3 40 2 Orange 2 DAQ 4331 (7) CH 4 AI-
Signal+ White 4 33 10 Orange-W 10 DAQ 4331 (7) CH 4 AI+
Blade 1 Tor 5V Red 1 47 3 Brown 3 DAQ 4331 (7) CH 5 EX+
GND Black J 11-27 2 59 11 Brown-W 11 DAQ 4331 (7) CH 5 EX-
Signal- Green 3 13 4 Purple 4 DAQ 4331 (7) CH 5 AI-
16-channel Slip Ring Cable Signal+ White 4 44 12 Purple-W Molex 16-pin 12 DAQ 4331 (7) CH 5 AI+
SR2 Blade 1 Bend 5V Red 1 48 5 Yellow 5 DAQ 4331 (7) CH 6 EX+
GND Black J 13-29 2 15 13 Yellow-W 13 DAQ 4331 (7) CH 6 EX-
Signal- Green 3 35 6 Black 6 DAQ 4331 (7) CH 6 AI-
Signal+ White 4 30 14 Black-W 14 DAQ 4331 (7) CH 6 AI+
Blade 3 Tor 5V Red 1 38 7 Green 7 DAQ 4331 (7) CH 7 EX+
GND Black J 14-30 2 9 15 Green-W 15 DAQ 4331 (7) CH 7 EX-
Signal- Green 3 34 8 Blue 8 DAQ 4331 (7) CH 7 AI-
Signal+ White 4 11 16 Blue-W 16 DAQ 4331 (7) CH 7 AI+
Pitch Encoder 1 GND White J 4-20 1 1 1 Black 1 PWR 5V Neg
Pitch Encoder 2+3 GND White J 9-25 1 7 9 Black-W Molex 4-pin 2 PWR 5V Neg
Pitch Encoder 1 5V Brown J 12-28 1 26 2 Red 3 PWR 5V Pos
Pitch Encoder 2+3 5V Brown J 2-18 1 16 10 Red-W 4 PWR 5V Pos
Pitch Encoder 1 A- Yellow J 12-28 2 29 11 Brown-W 7 cDAQMod2 9401 1 COM
Pitch Encoder 3 B Blue J 4-20 4 63 16 Purple-W 9 cDAQMod1 9401 20 PFI4 (ctr3)
Pitch Encoder 3 B- Red J 4-20 2 3 5 Purple 3 cDAQMod1 9401 1 COM
Pitch Encoder 1 B Green J 12-28 3 23 3 Brown 1 cDAQMod2 9401 14 PFI0 (ctr0)
note: A and B were 
swapped in VI 
Pitch Encoder 1 A Blue J 12-28 4 45 4 Blue 2 cDAQMod2 9401 17 PFI2 (ctr0) because angles 
16-channel Slip Ring Cable were moving 
SR3 wrong directions
Pitch Encoder 1 B- Red J 4-20 3 64 12 Blue-W Molex 12-pin 8 cDAQMod2 9401 1 COM
Pitch Encoder 2 A- Yellow J 2-18 2 2 14 Green-W 10 cDAQMod2 9401 7 COM
Pitch Encoder 3 A Green J 9-25 2 43 16 Orange-W 12 cDAQMod1 9401 25 PFI7 (ctr3)
Pitch Encoder 3 A- Yellow J 9-25 4 58 8 Orange 6 cDAQMod1 9401 1 COM
Pitch Encoder 2 B Green J 2-18 3 21 6 Green 4 cDAQMod2 9401 16 PFI1 (ctr1)
note: A and B were 
swapped in VI 
Pitch Encoder 2 A Blue J 2-18 4 22 7 Yellow 5 cDAQMod2 9401 19 PFI3 (ctr1) because angles 
were moving 
wrong directions
Pitch Encoder 2 B- Red J9-25 3 60 15 Yellow-W 11 cDAQMod2 9401 7 COM
J 7-23 2 41 9 Brown-W 1 PWR 5V Neg
J 15-31 1 46 1 Brown 4 PWR 5V Pos
Hall 1 5V Red J 6-22 1 36 2 Red Molex 6-pin 2 PWR 5V Pos
Hall 1 GND Black J 6-22 2 20 3 Black 3 PWR, DAQ 5V Neg
Hall 2 5V Green J 16-32 1 57 10 Red-W 5 PWR 5V Pos
Hall 2 GND Black J 16-32 2 52 11 Black-W 6 PWR, DAQ 5V Neg
J 15-31 2 54 12 Orange-W 7
NC - Broken terminal J 7-23 1 28 14 Green-W 9
16-channel Slip Ring Cable J 7-23 4 6 6 Green 3
SR4 J 15-31 3 62 4 Orange 1
J 15-31 4 37 5 Yellow 2
J 7-23 3 19 13 Yellow-W Molex 12-pin 8
Hall 1 GND Black J 6-22 2 20 3 Black 10 PWR, DAQ 6365-0 58 AI 6-
Hall 1 Signal White J 6-22 3 31 7 Blue 4 DAQ 6365-0 25 AI 6+
Hall 2 Signal White J 16-32 3 56 15 Blue-W 5 DAQ 6365-0 57 AI 7+
Hall 2 GND Black J 16-32 2 52 11 Black-W 11 PWR, DAQ 6365-0 23 AI 7-
J 6-22 4 55 8 Purple 6 DAQ 6365-0 56 GND
NC - Broken terminal J 16-32 4 39 16 Purple-W 12 DAQ 6365-0 56 GND
Load Cell SG0 Output Brown 9 1 DAQ 6365-0 68 AI 0+
Load Cell SG0 Reference Brown/White 18 9 DAQ 6365-0 34 AI 0-
Load Cell SG1 Output Yellow 8 2 DAQ 6365-0 33 AI 1+
Load Cell SG1 Reference Yellow/White 17 10 DAQ 6365-0 66 AI 1-
Load Cell SG2 Output Green 7 3 DAQ 6365-0 65 AI 2+
Load Cell SG2 Reference Green/White 16 11 DAQ 6365-0 31 AI 2-
Load Cell SG3 Output Blue 6 Molex 16-pin 4 DAQ 6365-0 30 AI 3+
Load Cell Cable Load Cell SG3 Reference Blue/White 15 12 DAQ 6365-0 6 AI 3-
Load Cell SG4 Output Violet 5 5 DAQ 6365-0 28 AI 4+
Load Cell SG4 Reference Violet/White 14 13 DAQ 6365-0 61 AI 4-
Load Cell SG5 Output Grey 4 6 DAQ 6365-0 60 AI 5+
Load Cell SG5 Reference Grey/White 13 14 DAQ 6365-0 26 AI 5-
Load Cell AI GND Black 22 16 DAQ 6365-0 27 AI GND
Load Cell 5V Red 2 Molex 2-pin NC - 5V supplied from alternate source
Load Cell 0V Red/White 11
Motor Brake Input 1 1 DAQ 4322 AO 0+
Motor Reverse 4 3 DAQ 4322 AO 2+
Motor Throttle Input 6 Molex 12-pin 2 DAQ 4322 AO 1+
Motor Impulse Input 8 4 DAQ 4322 NC 
Motor Motor 5V 9 5 DAQ 4322 AO 3+
Motor GND 5 7 DAQ 4322 AO 0-4 (-)
Motor GND 5 5 DAQ 8430
Motor RxD 2 DB-9 3 DAQ 8430 Port 4
Motor TxD 3 2 DAQ 8430
Actuator 1 ANV Red DAQ 4322 AO 5+
Actuator 1 GND Black DAQ 4322 AO 5-
Actuator 2 ANV Red Molex 6 pin DAQ 4322 AO 6+
3
 
Molex 6-pin
Actuator 2 GND Black DAQ 4322 AO 6-
Actuator 3 ANV Red DAQ 4322 AO 7+
Actuator 3 GND Black DAQ 4322 AO 7-
Actuator 1 GND Brown L 5 DAQ 8430
Actuator Control Actuator 1 RxD Yellow M DB-9 3 DAQ 8430 Port 1
Actuator 1 TxD Green K 2 DAQ 8430
Actuator 2 GND Brown L 5 DAQ 8430
Actuator 2 RxD Yellow M DB-9 3 DAQ 8430 Port 2
Actuator 2 TxD Green K 2 DAQ 8430
Actuator 3 GND Brown L 5 DAQ 8430
Actuator 3 RxD Yellow M DB-9 3 DAQ 8430 Port 3
Actuator 3 TxD Green K 2 DAQ 8430
5V Red DAQ 6365-0 14 5V
GND Black DAQ 6365-0 29 AI GND
Throttle White DAQ 6365-2 65
Control Box Collective White Bare Leads DAQ 6365-2 68
Lat Cyc White DAQ 6365-2 33
Long Cyc White DAQ 6365-2 32
E-Stop Red DAQ 6365-2 64 AI 92
E-Stop Black DAQ 6365-0 8 5V
Shaft Hall 5V Red DAQ 6365-0 14 5V
Shaft Hall GND Black DAQ 6365-2 9 D GND
Shaft Hall Signal White DAQ 6365-2 52
Triax Accel BNC DAQ 4492 AI0
Wing Beam 5V Red DAQ 4331 (5) CH 4 EX+
Wing Beam GND Black Bare Leads DAQ 4331 (5) CH 4 EX-
Wing Beam Signal- Green DAQ 4331 (5) CH 4 AI-
Wing Beam
Nonrotating Instruments Signal+ White DAQ 4331 (5) CH 4 AI+
Wing Chord 5V Red DAQ 4331 (5) CH 1 EX+
Wing Chord GND Black Bare Leads DAQ 4331 (5) CH 1 EX-
Wing Chord Signal- Green DAQ 4331 (5) CH 1 AI-
Wing Chord Signal+ White DAQ 4331 (5) CH 1 AI+
Wing Torsion 5V Red DAQ 4331 (5) CH 2 EX+
Wing Torsion GND Black Bare Leads DAQ 4331 (5) CH 2 EX-
Wing Torsion Signal- Green DAQ 4331 (5) CH 2 AI-
Wing Torsion Signal+ White DAQ 4331 (5) CH 2 AI+
4
LabVIEW Block Diagram
This appendix is a manual for the LabVIEW block diagram and front panel.
Pin connections should be deferred to the pin connection sheet as that is the most
up to date, however, the layout and overall programming of the block diagrams
are correct. This document can be found on the MTR DAQ computer in the MTR
folder. Any changes made to the block diagram should be updated in this document.
1
Maryland Tiltrotor Rig 
LabVIEW Documentation 
January 21, 2021 
Objectives:  
? Act as a basic user manual the Maryland Tiltrotor Rig (MTR) VI 
? Describe common functions and important parameters  
? Detail how major code blocks function 
Overview 
Figure 1 shows a snapshot of the VI block diagram is a VI Snippet. There is no way to zoom out to view the entire block 
diagram, so the best solution is to select all of the diagram by pressing Ctrl+A and create a VI Snippet by selecting 
?Create VI Snippet from Selection? in the Edit dropdown menu. This document will highlight how sensor datatypes are 
acquired and what manipulations are performed on the data. 
 
Figure 1 VI snippet of MTR block diagram 
 2
The front panel of the VI looks like Figure 2. The separate VI on the far right is for reading the motor serial 
communication. 
 
Figure 2 MTR front panel 
Using DAQmx 
The MTR VI uses DAQmx in LabVIEW, meaning the functions and nodes used are a lower level than the common Express 
VIs using DAQassistant.  
Navigate to the DAQmx palette by right clicking the block diagram, scroll cursor to the Measurement I/O dropdown and 
select DAQmx ? Data Acquisition folder in the upper left. Shown in Figure 3. These are the function nodes that are used 
to acquire and write data. Only the nodes that are used in the MTR VI will be explained in this document. 
 
Figure 3 Navigating to DAQmx Palette 
 3
Data Acquisition Chassis 
Two chassis are used: NI PXIe-1082 and NI CompactDAQ-9174 (cDAQ-9174). 
PXIe-1082 Modules:   
? PXIe-8840 Quad Core Embedded Controller 
? PXIe-4331 8-Ch Bridge Analog Input (x2) 
? PXIe-4492 Sound and Vibration  
? PXIe-4322 8-Ch Analog Output 
? PXIe-6365 Multifunction I/O  
cDAQ-9174 Modules: 
? NI-9401 Digital I/O Input (x2) 
For a list of the sensors and pin connections to the modules, refer to the Wire Connections.xlsx worksheet. 
Sensor Datatypes 
The MTR uses: 
? Analog Voltage Inputs ? Hall effect sensors, load cell 
? Analog Voltage Outputs ? Actuator controls 
? Strain Gage Inputs ? Wing and blade strain gages 
? Counter Inputs ? Pitch encoders 
? Serial Communication Inputs ? Motor data (separate VI, not in main MTR VI) 
Each type of input/output datatype is acquired on the same task. 
The counter inputs are exceptions. Each counter-type sensor is on a separate task. 
Synchronizing Tasks 
MTR VI uses a Flat Sequence Structure to start the tasks. This is so all tasks start at the same time and therefore have the 
same timestamps during data acquisition. However, due to having a second chassis in the cDAQ-9174, the start task for 
the cDAQ and the PXIe do not start at exactly the same time. 
Each chassis? timebase is separate so they are not synchronized. The only way to bypass this is to import the PXIe 10MHz 
Timebase available on the backplane into the cDAQ. An attempt was made to do this; however, any signal connection 
between the PXIe and cDAQ significantly increased the signal noise in the gimbal hall effect sensors. This was deemed 
unacceptable. 
By placing the cDAQ tasks in the same VI as the PXIe tasks, the timestamps from the PXIe tasks can be used for the cDAQ 
tasks. Since data is acquired at a 10kHz sample rate, the real-time difference between the cDAQ datapoints and 
corresponding PXIe datapoints is small enough to assume data between the two chassis occurs at the same timestamp. 
Setting Up Tasks 
The first step in acquiring data is using DAQmx Create Virtual Channel node to declare the type of signal. This section will 
go through each datatype?s setup. 
Analog Input Voltages 
From the DAQmx palette, place the Create Virtual Channel node into the block diagram. The dropdown menu below the 
node allows the user to choose the kind of data to be acquired; this node is Analog Input > Voltage. This can be seen in 
Figure 4. 
 4
 
Figure 4 Analog input voltage node 
The channel pins are input as a constant, seen as PXI1Slot4/ai0:7, PXI1Slot4/ai39, PXI1Slot4/ai16:19, meaning these are 
the default pins that the VI will see when the program starts. However, a control is branched off, labeled as ?physical 
channels?, and that allows the user to modify the channels on the front panel. The scalar values 10 and -10 above the 
block are max and min values for voltage signals. Choosing to make constants, controls, or indicators can be done by 
right-clicking the terminal of interest and selecting the desired option. 
The virtual channel node creates a task and that task terminal, at the upper right corner of the node, must be drawn to 
the next node, which is the timing function shown on the right side of Figure 4. 
Analog Output Voltages 
From the DAQmx palette, place the Create Virtual Channel node into the block diagram. The dropdown menu below the 
node allows the user to choose the kind of data to be acquired; this node is Analog Output > Voltage. This can be seen in 
Figure 5Figure 4. 
 
Figure 5 Analog output voltage node 
The channels are input as a constant here, but like the Analog Input Voltage Node, another branch for control can be 
connected to the same terminal. 
The virtual channel node creates a task and that task terminal, at the upper right corner of the node, must be drawn to 
the next node, which is the timing function shown on the right side of Figure 5Figure 4. 
This node is used as a means to control the MTR, so the voltages must be written to the module and the physical pins on 
the module are connected to the electric actuators and the motor controller on the rig. For further explanation jump to 
the Write Task section. 
 5
Strain Gage Inputs 
From the DAQmx palette, place the Create Virtual Channel node into the block diagram. The dropdown menu below the 
node allows the user to choose the kind of data to be acquired; this node is Analog Input > Strain > Strain Gage. This can 
be seen in Figure 5Figure 4. 
 
Figure 6 Strain gage input node 
The channel pins are input as a constant here, but like the Analog Input Voltage Node, another branch for control can be 
connected to the same terminal. 
The virtual channel node creates a task and that task terminal, at the upper right corner of the node, must be drawn to 
the next node, which is the timing function shown on the right side of Figure 6Figure 5Figure 4. 
Counter Inputs 
From the DAQmx palette, place the Create Virtual Channel node into the block diagram. The dropdown menu below the 
node allows the user to choose the kind of data to be acquired; this node is Counter Input > Position > Angular Encoder. 
This can be seen in Figure 7Figure 5Figure 4. 
 
Figure 7 Counter input for pitch encoders 
 6
The counter channels are input as constants to the Virtual Channel node, and are using counters from the cDAQ. Other 
significant terminals on the node are: units specified as degrees, and pulses per revolution is 31232 as specified by the 
encoder manual. An Initial Blade Pitch control is connected to the initial angle terminal on the bottom of the Virtual 
Channel node. This is so the user can set the blade angles and the encoders will measure angles relative to that initial 
angle. 
The virtual channel node creates a task and that task terminal, at the upper right corner of the node, must be drawn to 
the next node, which is a channel property node, then into a control task node, and finally the timing function all shown 
in Figure 7Figure 6Figure 5Figure 4. These nodes are explained in the next sections. 
Counter Outputs 
To acquire the encoder signals, a counter (ctr) channel must be specified. 
The NI-9401 module has four counters (ctr0, ctr1, ctr2, ctr3) accessed by nibbles on the module. Nibbles refer to the 
package of digital lines (PFI lines 0:3 and PFI lines 4:7). Two encoders are placed on one NI-9401 module, taking up ctr0 
and ctr1, using an input nibble with PFI0:3. The third encoder is on a separate NI-9401 module using ctr0 of the chassis 
and an input nibble PFI0:3 on that module. Note: ctr0 and ctr1 does not have to be PFI0:3, it can be user-defined which 
counters go to which PFI lines, as long as PFI0:3 are the same kind of direction (input or output). 
The second nibble (PFI4:7) on the first 9401 module is used as a counter output task shown in Figure 8. This node is 
created by selecting Counter Output > Pulse Generation > Frequency from the dropdown menu. 
 
Figure 8 Counter output task to use as sample clock 
Counter tasks require an external clock to time continuous acquisitions. Since there is no external clock, an internal 
signal is generated by this counter output task to be used as an internal clock. If the PXIe chassis clock was imported to 
the cDAQ, then this counter output task would not have been needed.  
It can be seen the counter channel is using cDAQ2/_ctr3 with an underscore before the counter, this is the internal 
counter of the chassis. This is different from cDAQ2Mod2/ctr3 which is the counter available on the module. 
Channel Property Node 
The channel property node is found in the DAQmx folder, shown in Figure 9 which is outlined in blue. Once placed and 
the task line from the virtual channel node is connected, the user can declare properties by selecting the field, which is 
itself a dropdown menu. 
If the small arrows in the field are on the left side, it means it is in write mode, so the user can change the properties. 
The user can change this to read mode by right-clicking the field and navigating to Change To > Read, which would shift 
 7
the small arrows to the right side of the box, meaning the node is reading the desired property and not changing 
anything. 
 
Figure 9 Channel property node 
Use the channel property node to define the terminal the signals will go through either as inputs or outputs. 
For the counter output task, a terminal is defined for pulse generation, however it is physically unused on the module, it 
is only declared so no wire will be placed in that terminal. 
Control Task Node 
The control task is used to reserve the resource, or task. Supposedly this is to avoid using conflicts in using resources. NI 
has a forum suggestion on how to avoid this here, where all tasks are reserved except one, and that one unreserved task 
is started first. However, for the MTR VI, all tasks were reserved and that seemed to work just fine. 
The control task node can be found by going to the DAQmx palette and navigating to the Advanced Task Options folder 
shown in Figure 10. 
 8
 
Figure 10 Control Task node 
Timing Node 
The Timing node is used to get tasks aligned and synchronized for data acquisition. The Timing node can be found in the 
DAQmx palette shown in Figure 11. 
When using one DAQ, for example the PXIe chassis, the user can specify the ?Sample Clock? on the Timing node for all 
tasks and that is all that is needed.  
However, with the cDAQ chassis, the clock being used is the generated pulse signal made by the module. This requires 
some timing manipulation which is explained in the next section. 
 9
  
Figure 11 Timing node 
Importing a Generated Clock 
Refer to Figure 8 to see the Timing node is using ?Implicit (Counter)? as the selected option because the task is not using 
the chassis? sample clock, but using its implicit counter as the clock. 
The source of the clock generated by the cDAQ is ?/cDAQ2/_ctr3InternalOutput?. This string must be concatenated by 
the Concatenate Strings function shown in Figure 12. 
This string must be passed to the other counter input Timing nodes so those counter input tasks recognize the new 
clock. The line coming from the concatenated string function is pink and must be connected to the source terminal on 
the Timing nodes of the counter input tasks, shown in Figure 7. 
Two constants that are connected to the counter output task are frequency and duty cycle. Duty cycle is the ratio of 
time that the signal is on vs off and by default is 0.5. For timing purposes, the duty cycle is arbitrary. The frequency is set 
to be 10kHz, the same frequency as the other tasks being acquired. 
 10
 
Figure 12 Concatenate strings function 
Starting Tasks 
This was briefly touched upon in the Overview subsection Synchronizing Tasks, the MTR VI uses a Flat Sequence 
Structure to have the tasks start at the same time. 
Flat Sequence Structure 
The Flat Sequence Structure acts like a rollfilm, where each frame is executed sequentially. Frames in a Flat Sequence 
structure execute from left to right and when all data values wired to a frame are available. This is helpful in executing 
tasks at the same time. 
In Figure 13, there are six start task nodes. The four in the first frame correspond to counter input task 1 from 
cDAQMod2, counter input task 2 from cDAQMod2, counter input task 3 from cDAQMod1, and analog input strain gage 
from PXIe from top to bottom. The two start tasks in the second frame correspond to the counter output task from 
cDAQ and analog input voltage task from PXIe chassis. Notice there is no bottom of the frame structure shown in Figure 
13; there is another start task in the first frame that continues further down which is the analog output task from the 
PXIe. 
What this does is all the tasks in the first frame are queued and ready to execute in the first frame, but do not start until 
the second frame tasks are executed. 
Since the cDAQ and PXIe are separate chassis, their corresponding tasks are independent from the other chassis tasks, 
which is why there are two start tasks in the second frame. Should there only be a PXIe chassis, all tasks would be 
queued up in the first frame, waiting for a single start task in the second frame to initialize the tasks all together. 
 11
Notice the start tasks in the second frame have another small 
flat sequence structure connected to the error wires of the 
tasks. This is monitoring the start times of those two start 
tasks using ?Get Date/Time in Seconds? and ?Format 
Date/Time String? functions found in the Timing Palette. The 
user can observe or save these values if need be. 
Reading Data 
The MTR VI reads data from all tasks except the analog output 
voltage task, which writes data. 
Have all read and write tasks and data manipulation logic 
within a While Loop Structure, otherwise the program will not 
run continuously. Read, denoted with spectacles,  and write 
tasks, denoted with a pencil, can be found in the DAQmx 
palette, shown in Figure 14. For all Read and Write nodes, the 
task and error lines should go directly to the border of the 
While Loop structure and then connect to Clear Task nodes. 
 
Figure 14 Read and Write Tasks in DAQmx palette 
All Analog Input Data 
All analog input voltage data includes: 
1. Load Cell Fx 
2. Load Cell Fy 
3. Load Cell Fz 
4. Load Cell Mx 
5. Load Cell My 
6. Load Cell Mz 
7. Gimbal Hall 1 
8. Gimbal Hall 2 
9. Azimuth Hall 
10. Collective 
11. Lateral Cyclic 
12. Longitudinal Cyclic 
13. Throttle 
 12
Figure 13 Flat Sequence Structure to start tasks 
Load Cell Data 
The load cell is an ATI Omega 160 load cell rated for: 
? Fx, Fy: 600 lb 
? Fz: 1500 lb 
? Mx, My, Mz: 3600 lbf-in 
The output signal from the load cell is a 6x1 array of voltages. This array is multiplied with a calibration matrix to get the 
final loads and moments. 
The Read node obtains waveforms of all the analog input voltages in separate rows of the array. From the dropdown 
menu below the node select Analog > Multiple Channels > Multiple Samples > 1D Waveform (Samples). The number of 
samples terminal is connected to a constant of 5000 samples. To separate each row the entire analog input array to 
manipulate the load cell data, the Index Array function is used. This is shown in Figure 15. Index Array function takes the 
waveform and splits the row out from it based on the specified index number connected to the index terminal. Since the 
load cell data consist of the first 6 data rows in the analog input task, the indices range from 0-5. These are then 
recombined using Merge Signals functions and written to a raw voltage file. In addition, the recombined signals are 
manipulated to output the actual forces and moments in the front view. 
 
Figure 15 Load cell raw data read 
The manipulation portion of the load cell data, shown in Figure 16, includes obtaining the actual loads and moments and 
calculating the CG offset based on the in-plane forces. These sections will be detailed in the following sections. 
B 
A 
D 
C 
 
Figure 16 Load cell data manipulation: (A) Zeroing Data, (B) Calibration matrix, (C) Displaying Loads, (D) Calculating CG Offset 
 13
A. Zeroing Data 
Zeroing the load cell data uses a Case Structure with a Boolean button connected to the frame shown in Figure 17. 
When the Boolean is True, the current load cell data is stored in an array, F/T Zeros, and subtracted from the original 
signal. This will always give an output of zero because whatever data is being read is being subtracted at the same time, 
as long as the case structure stays True. When the case is False, whatever the last stored array for F/T Zeros was, stays 
stored, and will continually be subtracted from the streaming data. In the False case, the local variable of F/T Zeros is 
referenced. Local variables are created by right-clicking on the object in the front panel, in this case, the F/T Zeros array, 
and selecting Create > Local variable. 
     
Figure 17 Zeroing data: True stores the data array (left), False pauses storage and subtracts the last stored array from the original signal (right) 
B. Calibration Matrix 
The calibration matrix is a 6x6 matrix that was determined from calibration tests. Use the Linear Algebra palette to 
obtain the ?A x B? function for matrix multiplication. The calibration matrix is A, and the voltage array is B. The output 
from the multiplication will be loads and moments in respective rows. The MTR VI displays these in columns by using a 
Transpose Matrix function found in the Matrix folder within the Linear Algebra palette. These are shown in Figure 18. 
 
Figure 18 Calibration matrix and final loads and moments 
 14
C. Displaying Loads and Moments 
When performing the calculation of the loads and moments, the time data of the waveforms gets stripped away. So to 
properly display the new loads and moments with correct timing, they must be rebuilt into waveforms, shown in Figure 
19. Using the raw voltage signal waveform (prior to zeroing or calibration), the waveform is split into its components 
using ?Get Waveform Components? found in the Waveform palette. The components are initial start time t0, time 
increment dt, and signal values Y. By porting the t0 and dt of the raw voltage signal to the new calibrated loads and 
moments Y values using the ?Build Waveform? function, the new loads and moments can be displayed with the correct 
timestamps. 
With the waveforms rebuilt, the signals can be combined using Merge Signals and shown using graph indicators. The 
Force In-Plane graph indicator shows Fx and Fy (indices 0 and 1) loads, Moment In-Place graph indicator shows Mx and 
My (indices 3 and 4) moments, Thrust graph indicator shows Fz (index 2) load, and Torque graph indicator shows Mz 
(index 5) as well as torque strain gage signal. 
 
Figure 19 Displaying loads and moments with rebuilt waveforms 
D. CG Offset Calculation 
The in-plane center of gravity offset is a concern because a large offset will cause a large 1/rev oscillation in the hub 
which can potentially be damaging to the rig. It is an important task to be able to measure this offset and reduce it by 
adding weight to the opposing side of the offset. 
 15
 
Figure 20 CG Offset Calculation 
Following along in Figure 20 from left to right and top to bottom, first the in-plane force resultant is calculated by taking 
the square root of ?2? + ?
2
? . This is shown in a graphical indicator on the front panel. The resultant will always be 
positive, but the ideal observation as the rotor is spinning is a zero resultant. If the Observing a large resultant indicates 
a large CG offset. 
The next step is to find out where the CG offset is in relation to the azimuthal position of the shaft. A simple running 
mean is established for Fx, Fy, and the Azimuth angle signals to reduce the variance in a 10kHz sampling rate. This is 
done by using ?Reshape Array? on the 5000 sample array, changing it to an array of 1000 rows and 5 columns and then 
using ?Mean? function for each row in a For Loop structure. This reduced the data from 5000 samples, to 1000 samples. 
The outputs of Fx and Fy are fed into ?Inverse Tangent (2 Input)? function found in Trigonometric Functions palette, 
which gives the angles of the signals from (??: ?). Radians is converted to degrees using an ?Expression Node? found in 
the Numeric palette. To get the range from (-180:180) to (0:360) degrees, the output is fed into the ?Quotient and 
Remainder? function as X. Y is the desired range of 360 degrees. This function is otherwise known as the modulo 
operation and also found in the Numeric palette. 
A local variable of the Shaft Azimuth position is created and also put through a running mean operation. 
Subtracting the angle of the shaft azimuth from the angle of the CG offset, the location of the CG offset with respect to 
the shaft azimuth is obtained. Note the running mean of the shaft will contain a handful of values that are not helpful in 
this calculation during the jump between 360 degrees and 0 degrees. 
The means are taken in this way because the data is a 5000 sample array updated each iteration, and not a continuous 
stream of data. Some functions work differently on arrays vs. continuous data. 
 16
Hall Effect Sensors 
Components that use hall effect sensors are the gimbal hub angles and the shaft angle. 
Gimbal Hub Angles 
ADD AN OFFSET FOR AZIMUTH BETWEEN GIMBALS AND HUB FRAME. There are two hall effect signals for the universal 
joint in the MTR gimballed hub. This section describes how to get from the hall effect sensor voltages to the B1s vs B1c 
chart used to trim the rotor to zero flapping. It is assumed the user has performed sensor calibrations to find the 
relationship between voltage and the position. The two important parameters that are user-inputs are the slope of the 
line for degrees/voltage, and the zero angle voltage. The LabVIEW code is block diagram of this is shown in Figure 21. 
 
Figure 21 Gimbal hub angles conversion to B1s and B1c chart 
Hall sensor 1 is index 6 and hall sensor 2 is index 7 in the list of analog input voltages being read. Following hall sensor 1 
wires, the Hall 1 Offset (V) value of 2.42 is the zero angle voltage of that hall effect sensor. That is subtracted from the 
raw signal, then multiplied by the slope of the degrees/voltage line found from prior calibration tests of -108.5 degrees 
to get the final gimbal angle in degrees. This is in the rotating frame and must be converted into the fixed frame. 
B1s, or lateral flap, is along the Y axis of the rotor. B1c, longitudinal flap, is in the direction of the X axis of the rotor. To 
calculate B1s and B1c: 
?1? = ??????1 ? cos(?) ? ??????2 ? sin(?) 
?1? =  ???????1 ? sin(?) ? ??????2 ? cos(?) 
Where ? is the rotor azimuth. ? is determined by the rotor azimuth, called as a local variable, plus (-46.25) degrees 
because the hall effect sensors are rotated by that amount about the shaft?s zero azimuth point. The rest of the block 
diagram consists of trig functions found in the Trigonometric Functions palette and arithmetic operators found in the 
Numeric palette. As with the any manipulation of signals, the waveform time data must be ported to the final 
reconstructed signals which is done by splitting the raw signal with the Get Waveform Components function and 
rebuilding the new signal with Build Waveform function. 
The final signals are put together using the Bundle function found in the Cluster, Class, and Variant palette. The Bundle 
function creates clusters and this is wired to display on the front panel through an XY graph indicator. 
  
NOTE: Hall 2 Offset toggles between 0.985 and 3.31 Volts. This phenomenon has been difficult to reproduce so if the 
user noticed the B1s vs B1c plot is off the chart, most likely the Hall 2 Offset needs to be set to the other value. 
 17
Exact values for the zero degree angle voltages are given below for a power supply voltage of 5.002 V: 
Gimbal 1: 2.4206638192 
Gimbal 2: 0.98507670708 or 3.316209105 
Shaft Azimuth and Frequency 
The shaft hall sensor is index 8 in the analog input voltage read task. 
The signal is used to track the azimuth of the shaft as well as to calculate the rotor speed in Hz and RPM shown in Figure 
22. 
 
Figure 22 Block diagram for shaft hall sensor data 
The raw waveform is split with Get Waveform Components so time data can be ported to the new signal and the Y value 
component can be manipulated. The minimum and maximum voltage output by the shaft hall sensor are logged and set 
as the threshold for where the shaft angle jumps from 360 degrees to 0 degrees. The logic is shown below: 
(??? ??????? ? min ???????)/(max ??????? ? min ???????) ? 360 = ? (???????) 
There is an addition operator after the azimuth is converted to degrees to allow for a new shaft position, if desired, i.e. 
getting the shaft to be zero azimuth at the X-axis. The output is fed into the ?Quotient and Remainder? function to 
ensure the azimuth stays between 0 and 360 degrees. This is connected to an indicator so the scalar value of the 
azimuth can be observed, then the waveform is reconstructed with the raw time data and wired to a graph indicator. 
To calculate the RPM, the discontinuities in the signal from 360 to 0 degrees is first identified by locating the differences 
in voltage of 2.5 volts. 
Using the For Loop structure to iterate through each point in the 5000 sample array, every time a difference in voltage 
greater than 2.5 volts is detected, a 1 is output, and the shift registers on the border of the For Loop structure stores this 
value so it is retained as the loop iterates. All the 1 values are added throughout the for loop until the total is 
determined. This scalar is divided by ? a second to get frequency in revolutions/second because 5000 samples in a 
10kHz sample rate signal is ? a second. This value is then multiplied by 60 to obtain the frequency in revolutions per 
minute or RPM. 
Controller Voltage Inputs 
Collective, Lat Cyclic, Long Cyclic, and Throttle are voltage signals manipulated by the physical controls of the pilot. 
These get written to the analog voltage output task which control the actuator voltages. 
Longitudinal and Lateral Cyclics 
The block diagram for cyclic controls are shown in Figure 23. The lateral and longitudinal cyclic signals are indexed as 10 
and 11 respectively in the analog voltage data stream. 
 18
 
Figure 23 Section of block diagram for longitudinal and lateral cyclics 
First step for both these signals is account for a voltage offset by subtracting 2.55V from longitudinal and 2.48V from 
lateral cyclic data. 
Next, the signals are fed into a For Loop structure that sets a deadband range, where any values between -0.25V and 
0.25V from the set voltage returns the same set voltage. 
The long and lat signals continue into a Case structure for Level Swashplate. This structure, when true, sets the long and 
lat cyclic feedback signals to zero, seen in Figure 24. 
 
Figure 24 Set Long and Lat signals to zero if Level Swashplate is true. 
An array of 5000 zeroes is created outside the While Loop structure using Initialize Array function and fed into the Level 
Swashplate true case. The signal splits into two, becoming the proxy for the longitudinal and lateral cyclic data signals. 
The last value of the arrays from the Level Swashplate are stored by using Array Size, Decrement, and Index Array 
functions. A Feedback Node function, found in the Structures palette, is used to send the value back to the For Loop 
structure. The Feedback Node is essentially a shift register, storing the previous iteration?s values. 
When false, the signal is unchanged from the deadband output shown in Figure 25. 
 19
 
Figure 25 Level Swashplate set to false, signals are unchanged from deadband output. 
The next portion is a Case structure for the perturbing the long and lat signals by adding an oscillating signal, which is 
covered in the Perturbation System section. When false, the perturbation system is bypassed and the signals go into a 
series of comparisons to determine if they are reached a maximum tilt limit. Then these signals are passed to more 
mathematical manipulation to determine the actuator voltage that to be written to the actuators, shown in Figure 26. 
Using ?In Range and Coerce? functions, found in Comparisons palette, the signals are compared to an upper limit of 
0.087266389 V and lower limit of -0.087266389 V. If the signals were to exceed the limits, the signals are coerced to stay 
at that limit. The output labeled ??? is a Boolean array of true if the values are within the range, and false if the values 
exceed the range. These Boolean arrays are fed into ?AND Array Elements? functions which returns true if all elements 
in the array are true or empty, otherwise it returns false. So if the limit is exceeded by just 1 element within the 5000 
sample array, the AND Array Elements function will return a false.  
The signals are scalar Booleans at this point and fed into a standard AND function, so if both are true (or both are within 
range), it returns true, otherwise it is false. This is wired to a NOT function, because the desired output is to flag all the 
times the Booleans are false to indicate an exceedance in swashplate tilt. This is displayed as a green light indicator on 
the front panel, lighting when there is an exceedance. 
 20
 
Figure 26 Long and lateral signals manipulations to obtain required actuator voltages. 
With the swashplate tilt limits set, the coerced signals are wired to a Tangent function then multiplied by Actuator 
locations in the body fixed frame, converted to the rotating frame using sines and cosines functions. 
 
Collective 
 
Figure 27 Overlapped at the bottom of the previous figure, collective signal is used to in conjunction with longitudinal and lateral cyclics 
 21
Throttle 
 
Figure 28 Throttle logic 
Perturbation System 
 
Figure 29 Perturbation logic 
 
 22
Strain Gage Data 
Strain gage signals are read from the same task. The type of data is determined from the dropdown menu by selecting 
Analog > Multiple Channels > Multiple Samples > 1D Waveform (Samples) shown in Figure 30. The signal is immediately 
multiplied by 1e6 because the raw data is recorded in strains but the data values are on the order of microstrains. 
Multiplying by 1e6 removes all the leading zeroes ahead of the first significant digits. This is important for writing to 
measurement files because writing to files allots a set amount of characters to be written. If characters being written are 
leading zeroes, then they reduce the resolution that can be used for significant digits. 
A Case structure is used to zero all the strain gages. When True, the raw data is input into a Basic Averaged DC-RMS 
subVI found in the Waveform Measurements palette. This subVI takes all 5000 samples in each waveform of strain data 
and outputs a 1D array representing the average value for each waveform. When False, the last stored array is used to 
zero the raw signals. The output is also drawn to the While Loop border and connected to a Shift Register to retain the 
array for each loop iteration. This is a different from the load cell zeroing method, which does not take an average value, 
but an instantaneous value. 
 
Figure 30 Strain gage Read node 
The first 3 signals from the strain gage task are pitch link strains, followed by the shaft torque strain gage, 4 channels for 
blade strains, 3 wing strains, and 5 open strain channels. 
Pitch Link Strains 
The pitch link strains are indexed as 0, 1, and 2 in the data stream. These are separated by using the Index Array function 
and setting the index. The individual pitch link signals are zeroed by subtracting the DC value of each pitch link signal. 
 23
This is done by using Index Array function on the Basic Averaged DC-RMS subVI output and setting the respective index 
of the pitch link signals. 
The zeroed pitch link signals are then multiplied by a calibration factor found from calibration tests to obtain the pitch 
link loads in lbf. These signals are finally compiled together using Merge Signals, plotted on the front panel using a graph 
indicator, and stored in the measurement file. 
Pitch Link 3 
Pitch link 3 has a butterworth filter applied to it because there is a large amount of noise in the signal. This was applied 
through a DFD Filtering node found in the Processing palette and a DFD Butterworth Design subVI found in Advanced IIR 
Filter Design palette shown in Figure 31. 
 
Figure 31 Butterworth filter for pitch link 3 
The Filtering node takes the pitch link 3 raw data as input, the butterworth filter as the filter type, and outputs the 
filtered signal. The datatype is selected from the dropdown menu of the node: Single Channel > Multiple Samples > 
Waveform. 
The Butterworth filter is placed outside of the While Loop structure and then connected to the Filtering node. This is 
done due to the array form of the data. If the data was a continuous stream of points, the butterworth filter can be 
placed inside the while loop. 
Notice the order is a Lowpass filter and the low cutoff frequency is 0.002*(sampling frequency) which in the MTR?s case 
is 20 Hz. 
Shaft Torque Strain 
The shaft torque strain is index 3 in the strain gage data and follows the same manipulation as the pitch link 3, including 
a butterworth filter because the raw signal is noisy. 
The shaft strain is recorded to measurement file before the filter is applied. The filtered signal is shown in graph 
indicator just to have a second measurement to compare to the load cell Mz component. From Figure 30, the strain gage 
output is seen to continue off to the right. Figure 32 shows the continuation of the shaft strain gage signal. 
 24
 
Figure 32 Shaft strain gage continuation 
The signal is input into a DFD Filter node and a different butterworth filter is connected to this shown in Figure 33. This 
butterworth filter subVI is also placed outside the while loop. The filtered signal is multiplied by 161.5, which is a 
calibration factor from previous calibration tests to obtain the torque in units of in-lb. The result is shown on the same 
graph indicator as Mz component of the load cell. 
 
Figure 33 Butterworth filter for shaft strain gage, the pink wire connects to the filter terminal in the Filter node. 
The strain gage filter is a lowpass filter with a low cutoff frequency of 0.001*(sampling frequency) or 10Hz. 
Wing Strains 
The wing strains are indexed as 8, 9 and 10 in the strain gage data, shown in Figure 34. After zeroing the signals, they are 
all wired to individual graph indicators.  The amplitudes are calculated from the signals by using Array Max & Min 
functions from the Array palette and subtracting the min from the max values. These amplitudes are shown in numeric 
indicators and the units are in microstrains. 
 25
 
Figure 34 Wing strain data block 
The amplitudes are for observation on the front panel, only the zeroed wing strain signals are written to file. 
Pitch Encoder Counter Data 
The pitch encoders are connected to the cDAQ chassis through the NI 9401 modules and are each on their separate 
Read nodes shown in Figure 35. These datatypes are selected from the dropdown menu on the node as Counter > Single 
Channel > Multiple Samples > 1D DBL. Number of samples per channel is 5000. 
 
Figure 35 Pitch encoder Read nodes 
Because the data is being read from the cDAQ, the time stamps are different from the PXIe timestamps. Therefore, the 
time data is taken from the Analog Input Voltage Read node and the pitch encoder signals are rebuilt with the PXIe 
timestamps. This is done using Get Waveform Components function on the analog input data, taking the t0 and dt data 
and rebuilding the pitch encoder signals using Build Waveform functions. The reconstructed signals are combined using 
a Merge Signal function and stored in the measurement file. In actuality, the stored data is the blade root pitch angle. 
The pitch at 75% span of the radius is 18.013 degrees more than the blade root pitch. For observational purposes, the 
0.75*R pitch angle is displayed in a graph indicator. 
Counter Output Data Task 
The cDAQ counter output task line and error lines go directly through the While Loop structure, and out the other side 
to the Clear Task node. There are no other actions to take with this as it is only used to start the counter inputs at the 
same time. 
 26
Write Task 
The data used with a DAQmx Write node are the voltages to the three actuators and the voltages for the motor brake, 
throttle, reverse/forward direction, and accessories. Once those voltages are acquired and manipulated from the 
handheld controller, the voltages are written to the Analog Output module on the PXIe. That is why the Write task is 
simply at the end of all the manipulations for those parameters shown in Figure 36. 
The datatype is selected from the dropdown menu through Analog > Multiple Channels > Multiple Samples > 1D 
Waveform. 
This means that the write task is writing 5000 samples to the module every loop which occurs every half second. So the 
response from the rig is about a half second delayed from when the input is given. 
 
Figure 36 Write node for actuators and motor voltages 
The Write node task and errors lines go directly to the While Loop structure and out to Clear Task nodes. 
 27
Writing Data to File 
Writing the data to file uses the Write Delimited Spreadsheet node found in the File I/O palette and shown in Figure 37. 
The node takes a file path as a control. The format terminal determines how many digits to include in the data, ?%.6f? 
means 6 digits after the decimal place and the numbers are floats (meaning they have decimal places). The data being 
written is 2D meaning there are multiple columns and multiple rows. The two Boolean terminals are ?append to file??, 
and ?transpose??. If append to file is TRUE then each time the node is called, it will append data to the existing file path 
unless the file path is changed and if transpose is TRUE then the 2D data rows and columns will be flipped like a matrix 
transpose. The MTR VI has set both to TRUE. At bottom of the node is a terminal for the delimiter which is set to a 
comma. 
The MTR VI does not continually record data. There is a Case structure with a Boolean trigger to determine when the 
data should be saved. There is also a Case structure for timing the action which allows the user to see the duration of 
the data is being saved. 
All the signals from the Read node and including the Write nodes are saved into the measurement file by using Merge 
Signal function. The very first signal is a timestamp from one of the analog input voltage signals, and that sets the first 
column of data to be timestamps. 
 
Figure 37 Writing to measurement file using a Write Delimited Spreadsheet node in the upper right hand corner 
The list of signals are listed below in order: 
1) Time 13) Azimuth 25) Strain 3 Open 
 28
2) Pitch Encoder 1 14) Pitch Link 1 26) Strain 4 Open 
3) Pitch Encoder 2 15) Pitch Link 2 27) Strain 5 Open 
4) Pitch Encoder 3 16) Pitch Link 3 28) Strain 6 Open 
5) Load Cell Fx 17) Shaft Torque 29) Strain 7 Open 
6) Load Cell Fy 18) Blade Strain 1 30) Actuator 1 Voltage  
7) Load Cell Fz 19) Blade Strain 2 31) Actuator 2 Voltage 
8) Load Cell Mx 20) Blade Strain 3 32) Actuator 3 Voltage 
9) Load Cell My 21) Blade Strain 4 33) Brake Voltage 
10) Load Cell Mz 22) Wing Bending 34) Throttle Voltage 
11) Gimbal Hall Voltage 1 23) Wing Chord 35) Forward/Reverse Voltage 
12) Gimbal Hall Voltage 2 24) Wing Torsion 36) Accessories Voltage 
  
 
Clearing Tasks and Error Handling 
As a matter of standard practice, all task and error wires exiting the While Loop structure should connect to a Clear Task 
node. The error wires from the Clear Task nodes should be combined using the Merge Errors function found in the 
Dialog & User Interface palette. 
The combined errors go into the Simple Error Handler node which is set to ?OK message + warnings? for the type of 
dialog if an error occurs. 
 
Figure 38 Clear task and collecting errors 
 29
Derivations
This appendix covers derivations for beam mode frequencies and moving block
method.
1
Derivations?for?uncoupled?Wing?Beam,?Chord,?and?Torsion?Frequencies??
1) Cantilever?Beam?w/?distributed?load?
?  
?
Equation?of?motion:??
?? ? ??? ? ? ?
?? ??????????? ???? ? 0 ???? ?? ? ??? ? 0?
Boundary?Conditions:?
@? 0, ? 0,? 0?
@? ?, ????? ????? ??? 0?
??? ??????? ?????? ??? 0?
2) Cantilever?beam?w/?tip?load?
F(t) 
?
Same?equation?of?motion?as?1?without?distributed?load.?
Boundary?Conditions:?
@? 0, ? 0,? 0?
@? ?, ??? ? ? ? ?
??? 0?
Signs?by?convention?to?the?right??>>>?
2
3) Cantilever?Beam?w/?tip?load?and?tip?mass?
F(t) 
?  
?
Same?EOM?as?1?without?distributed?load?
? ? ? 
Boundary?conditions:?
@? 0, ? 0,? 0?
@? ?, ??? ? ? ? ? ? ? ?
??? ? 0?
Assumed?Solution?
? ?? ????? ? ????? ?????????
Then?
@? 0, ?? 0,??? 0?
@? ?, ??? ? ? ? ? ? ? ? ? ?
??? ? ? 0?
Sub?? ???into?EOM,?and?since?it?s?an?approximation,?you?get?some?error??:?
??? ??? ? ??
Assume?error?also?follows?shape?function?and?integrate?along?the?beam:?
? ??? ??? ? ???
? ??? ??? ?  ?? ?? ???
Set?the?error?to?zero?since?that?is?the?goal:?
3
? ??? ??? ?  ?? 0?
Then:?
???? ?? ? ??? ? ?? 0 ?
Simplify:?
? ??  ?? ? ? ???  ?? 0?
For?2nd?term?in?expression,?use?changing?variables?rule:?
? ? ? ? ?? ? ? ? ? ? ? ? ? ???
So?then:??
? ? ???  ?? ? ? ??? ? ?? ??? ????
Use?changing?variables?rule?again?for?the?highlighted?term?on?right?side:?
? ? ??? ?? ? ? ??? ? ??? ?? ?
Combined?expression:?
? ??  ??  ? ? ??? ? ? ??? ? ??? ?? 0?
The?2nd?term?becomes:?
? ? ??? ? ? ? ? ? ? ? ?
The?3rd?term?in?this?equation?is?zero?due?to?the?boundary?condition:?
??? ? 0?
Then:?
? ??  ??  ? ? ? ? ? ? ? ? ? ??? ?? 0?
Simplify?into?Lagrangian?form:?
??  ??  ? ? ? ? ? ??? ?? ? ?? ? ?
4
? ??  ??  ? ? ? ?
? ? ??? ?? ?
Assume?solution?q?is?of?form:?
? ? ????? ? ??????
? ?? ????? ?? ??????
? ? ? ????? ? ? ????? ? ??
Then:?
?? ?? ?? ? ?
? ? ? ?? ?? ? ?
Characteristic?equation:?
? ? ? ? ?? ? ?
Deflection?solution:?
? ?? ?? ? ? ?
Natural?frequency:?
? ? ? ??? ??? ??  ??  ? ? ? ?
For?a?shape?function:?
? ?? ?
? 2?? ?
? 2? ?
? ? 1?
Then:?
? ?? ? ?? 4? ? ?
4??
? ?
5
? ??  ??  ? ? ? ??3 ? ?
? 4??? ? ??
? ?
3 ?
4) Cantilever?beam?with?tip?mass?and?mass?moment?of?inertia:?
? ,  ?  
?
Equation?of?motion,?same?as?the?flap?EOM,?but?using?v?for?deflection?instead?of?w.?
?? ? ??? ? 0?
Assumed?solution:?? ???
Boundary?conditions:?
@? 0, ? 0, ?? 0?
@? ?, ??? ? ? ? ? ?? ? ??
??? ? ? ? ? ? ? ? ?,
???? ?? ???????? ??? ?? ?????????? ?? ?? ??????? ?????? ????? ?? ????????.?
Then?going?through?the?same?calculus?as?flap,?starting?with?equation?of?motion:?
? ??  ?? ? ? ???  ?? 0?
For?2nd?term?in?expression,?use?changing?variables?rule:?
? ? ? ? ?? ? ? ? ? ? ? ? ? ???
So?then:??
? ? ???  ?? ? ? ??? ? ?? ??? ????
Use?changing?variables?rule?again?for?the?highlighted?term?on?right?side:?
? ? ??? ?? ? ? ??? ? ??? ?? ?
6
Combined?expression:?
? ??  ??  ? ? ??? ? ? ??? ? ? ??? ?? 0?
2nd?term?becomes:?
? ? ? ??
3rd?term?becomes:?
? ? ? ??
Then:?
? ??  ??  ? ? ? ? ? ? ? ? ? ? ??? ?? 0?
??  ??  ? ? ? ? ? ? ? ? ??? ?? ? 0?
? ? ??? ?? ?
? ??  ??  ? ? ? ? ? ? ?
For?a?shape?function:?
? ?? ?
? 2?? ?
? 2? ?
? ? 1?
? ? 2??
Then:?
? 4??? ?
? ??3 ?
4
? ? ?
Natural?frequency:?
7
4??
? ?? ? 4 ?
3 ? ? ?
5) Consider?a?cantilever?beam?under?torsion.?
? ,  ?  
y?
With?an?applied?tip?torque?? .?
Equation?of?motion:?
? ? ??? 0?
? ???
Boundary?conditions:?
@? 0, ? 0,?? 0?
@? ?, ??? ??? ? ? ? ? ? ? ? ? ? ? ??
Equation?of?motion:?
? ?? ??? ? 0?
? ? ?  ?? ? ? ???  ?? 0?
Changing?variables?rule?on?2nd?term:?
? ? ???  ?? ? ???? ? ? ??? ???
Combined?equation:?
? ? ?  ?? ? ???? ? ? ??? ?? 0?
From?B.C,?the?2nd?term?becomes:?
8
? ???? ? ? ? ? ? ? ? ?
Then:?
? ? ?  ?? ? ? ? ? ? ? ??? ?? ? ? ? ?
Lagrangian?form:?
? ?  ?? ? ? ? ? ? ??? ??  ? ? ? ? ?
? ? ??? ???
? ? ?  ?? ? ? ? ?
Torsion?frequency:?
? ? ??? ??? ? ?  ?? ? ? ? ?
? ???
? 1??
? ? 1?
? ?? 1 ?? ??? ? ?
? ? ? ? ?? ?? ? 3 ? ?
? ??? ? ? ?
? ?
3 ?
????? ? ??? ?  ??? ? ? mass 112 length ? ??
? ? ?? ? ?? ??? ? 12 12 ?
?
9
1 
 
Moving Block Method Derivation 
Reference: Hammond, C.E. ?Determination of Subcritical Damping by Moving-Block/RandomDec Applications? 
Starting with a damped sinusoidal signal: 
 ?(?) = ??????? sin(?? + ?) (1) 
Where, 
? = ????????? ?? ?????? 
? = ??????? ????? 
?? = ???????? ??????? ????????? 
? = ???1 ? ?
2 = ?????? ??????? ????????? 
Take a Fourier Transform of the signal: 
?+?
?(?) = ? ?(?)??????? 
?
?+?
?(?) = ? ??????? sin(?? + ?) ??????? 
?
Combine terms: 
 ?+?
?(?) = ? ???(???+??)? sin(?? + ?) ?? (2) 
?
Integration by parts, part 1: 
? ??? = ?? ? ? ??? 
Set: 
? = ??(???+??)?  
??
= sin(?? + ?) 
??
Then: 
?? = ?(??? + ??)?
?(???+??)? 
1
? = ? cos (?? + ?) 
?
Apply to Eq. (2): 
 ? ? + ? ? ?+?
?(?) = ? ??(???+??)? cos(?? + ?) ?  ? (?? + ??) ? ??(???+??)?? cos(?? + ?) ?? (3) ? ?
? ?
Integration by parts on red highlighted term: 
? = ??(???+??)?  
??
= cos(?? + ?) 
??
Then: 
?? = ?(?? + ??1)?0?(???+??)??  
2 
 
1
? = sin (?? + ?) 
?
Apply to Eq. (3): 
 ? ? + ? ? ? + ?
?(?) = ? ??(???+??)? cos(?? + ?) ?  ? (??? + ??)?
?(???+??)? sin(?? + ?) ?  
? ?2
? ? (4) 
1 ?+?
? (?? + ??)2 ? ???(???+??)?? sin(?? + ?) ?? ?2 ?
Red highlighted expression is the same expression as Eq. (2), therefore bring to left side, and expand right side: 
 1
?(?) [1 + (??? + ??)
2]
?2
? ? + ?
= ? ??(???+??)? cos(?? + ?) ?  
?  
?
? ? + ?
? (?? + ??)??(???+??)?? sin(?? + ?) ?  ?2
 
?
Simplify LHS and expand RHS: 
 ?? 2? 2???
?(?) [( ) + ? ]
? ?
? ?
= ? ??(???+??)(?+?) cos(?(? + ?) + ?) + ??(???+??)? cos(?? + ?)
? ?  
?
? (?? + ??)??(???+??)(?+?)? sin(?(? + ?) + ?)?2
?
+ (?? + ??)??(???+??)?? sin(?? + ?) ?2
?? 2? 2??Divide through by [( ) + ? ?] and collect ? terms and ? + ? terms: 
? ?
 ?
?(?) = (??? + ??)?
?(???+??)? sin(?? + ?)
?? 2 2??
?2 [( ?) + ? ?]
? ?
?
+ ??(???+??)? cos(?? + ?)
?? 2? 2??? [( ) + ? ?]
? ?
?  
? (??? + ??)?
?(???+??)(?+?) sin(?(? + ?) + ?)
2 ??
2
? 2??? [( ) + ? ?]
? ?
?
? ??(???+??)(?+?) cos(?(? + ?) + ?) 
?? 2 2??
? [( ?) + ? ?]
? ?
Simplified: 
11
3 
 
 ?
?(?) = (?? + ??)??(???+??)?? sin(?? + ?)???[??? + ?2?]
??
+ ??(???+??)? cos(?? + ?)
???[??? + ?2?]
?  
? (??? + ??)?
?(???+??)(?+?) sin(?(? + ?) + ?)
???[??? + ?2?]
??
? ??(???+??)(?+?) cos(?(? + ?) + ?) 
???[??? + ?2?]
Simplify further: 
 ?
?(?) = [??(???+??)?[(??? + ??) sin(?? + ?) + ? cos(?? + ?)]???(??? + ?2?) (5) 
? ??(???+??)(?+?)[(??? + ??) sin(?(? + ?) + ?) + ? cos(?(? + ?) + ?)]] 
Fourier transform has form: 
?(?) = ? + ?? 
And amplitude of transform is: 
|?(?)| = ??2 + ?2 
Split Eq. (5) into its real and imaginary components, assuming ? ? 1, ? ? ??: 
 ?
?(?) = [??(???+???)?[(??? + ???) sin(??? + ?) + ?? cos(??? + ?)]???(??? + ?2??) (5.1) 
? ??(???+???)(?+?)[(??? + ???) sin(??(? + ?) + ?) + ?? cos(??(? + ?) + ?)]] 
Starting with green: 
? ? (? ? 2?) ?(? ? 2?) ?? ?2?
=  ? = = ?  
???(??? + ?2??) ??
2
?(? + ?2) (? ? 2?) ??
2(?2? + 4) ??
2
?(?
2 + 4) ??2(?2? + 4)
For red and blue, use exponential identity ??+?? = ??(cos ? + ? sin ?): 
??????????? = ??????(cos(???? + ?) + ? sin(???? + ?)) = ?
?????(cos(??? + ?) ? ? sin(??? + ?)) 
?????(?+?)????(?+?) = ?????(?+?)(cos(???(? + ?) + ?) + ? sin(???(? + ?) + ?)
= ?????(?+?)(cos(??(? + ?) + ?) ? ? sin(??(? + ?) + ?)) 
Substitute into Eq. (5.1): 
 ??
?(?) = (
??2?(?
2 + 4)
?2?
? ) [[??????(2 cos(??? + ?) ? ? sin(??? + ?))][(??? + ???) sin(??? + ?)?? (?2? + 4) (6) 
+ ?? cos(??? + ?)]
? [?????(?+?)(cos(??(? + ?) + ?) ? ? sin(??(? + ?) + ?))][(??? + ???) sin(??(? + ?) + ?)
+ ?? cos(??(? + ?) + ?)]] 
Working within the large brackets containing the red and blue terms, expand and simplify: 
[[??????(cos(??? + ?) ? ? sin(??? + ?))][(??? + ???) sin(??? + ?) + ?? cos(??? + ?)]
? [?????(?+?)(cos(??(? + ?) + ?) ? ? sin(??(? + ?) + ?))][(??? + ???) sin(??(? + ?) + ?)
+ ?? cos(??(? + ?) + ?)]] 12
4 
 
[[(?????? cos(? ? + ?) ? ???????? sin(??? + ?))][(??? + ???) sin(??? + ?) + ?? cos(??? + ?)]
? [(?????(?+?) cos(? (? + ?) + ?) ? ??????(?+?)? sin(??(? + ?) + ?))][(???
+ ???) sin(??(? + ?) + ?) + ?? cos(??(? + ?) + ?)]] 
First half of bracket, multiplying red-bracketed terms: 
(?? + ?? )??????? ? sin(??? + ?) cos(??? + ?) + ???
????? cos2(??? + ?) ? (?? + ?? )??
?????
? ? sin
2(??? + ?)
? ?? ??????? sin(??? + ?) cos(??? + ?) 
Expand: 
????
????? sin(??? + ?) cos(? ? + ?) + ?? ?
?????
? ? sin(?
????? 2
?? + ?) cos(??? + ?) + ??? cos (??? + ?)
? ??? ??????? sin
2(??? + ?) + ? ?
????? sin2(? ? + ?) ? ?? ??????? ? ? sin(??? + ?) cos(??? + ?) 
Simplify, cos2(?) + sin2(?) = 1, and purple cancels out: 
?? ?????? sin(? ? + ?) cos(? ? + ?) + ? ??????? ? ? ? ? ???
?????
?? sin
2(??? + ?) 
1 1 1
Half angle formula, sin2(?) = ? cos(2?); double angle formula, sin(?) cos(?) = sin(2?): 
2 2 2
 ?? ?????? ??? ?????? ??? ???????
sin(2? ? + ?) + ? ????
? ?
??
? ? ? + cos(2??? + ?) (6.1) 2 2 2
Second half of bracket, multiplying blue-bracketed terms: 
(?? + ?? )?????(?+?)? ? cos(??(? + ?) + ?) sin(??(? + ?) + ?) + ? ?
????(?+?)
? cos
2(??(? + ?) + ?)
? (??? + ??
????(?+?)
?)?? sin
2(??(? + ?) + ?)
? ? ??????(?+?)? sin(??(? + ?) + ?) cos(??(? + ?) + ?) 
Expand: 
?? ?????(?+?)? cos(??(? + ?) + ?) sin(? (? + ?) + ?) + ?? ?
????(?+?)
? ? cos(??(? + ?) + ?) sin(??(? + ?) + ?)
+ ? ?????(?+?) cos2? (??(? + ?) + ?) ? ?? ??
????(?+?)
? sin
2(??(? + ?) + ?)
? ?2? ?????(?+?)? sin
2(??(? + ?) + ?) ? ?? ?
????(?+?)
? sin(??(? + ?) + ?) cos(??(? + ?) + ?) 
Simplify, cos2(?) + sin2(?) = 1, purple cancels out: 
?? ?????(?+?)? sin(??(? + ?) + ?) cos(??(? + ?) + ?) + ? ?
????(?+?)
? ? ??? ?
????(?+?)
? sin
2(??(? + ?) + ?) 
1 1 1
Half angle formula, sin2(?) = ? cos(2?); double angle formula, sin(?) cos(?) = sin(2?): 
2 2 2
?? ??????? ?????
????(?+?) ??? ?????(?+?)
sin(2? ????(?+?)
?
?(? + ?) + ?) + ??? ? + cos(2??(? + ?) + ?) (6.2) 2 2 2
Combine Eq. (6.1) and (6.2) into Eq. (6), remember to subtract Eq. (6.2): 
 ?? ?2? ?? ?????? ??? ??????? ?
?(?) = ( 2 ? 2 ) ( sin(2? ? + ?) + ? ?
????? ?
???(?
2 + 4) ?? (?2 + 4) 2 ? ?? 2
?????
????? ?? ???????
+ cos(2??? + ?) ? sin(2? (? + ?) + ?) ? ? ?
????(?+?) (7) 
2 2 ? ?
?????
????(?+?) ??? ?????(?+?)?
+ ? cos(2??(? + ?) + ?)) 2 2
Expand Eq. (7): 
13
5 
 
? ????
????? ??? ?????? ??? ??????? ?
(
2 ? ? 2?) ( sin(2??? + ?) + ? ?
?????
? ? + cos(2??? + ?)?? (?2? + 4) 2 2 2
?? ????? ????(?+?)?? ?????
? sin(2??(? + ?) + ?) ? ? ?
????(?+?) +
2 ? 2
??? ?????(?+?)?
? cos(2??(? + ?) + ?)) 2
? ?2? ?????? ??2? ?????? ??2? ??????? ??? ? ? ?( sin(2 2??? + ?) + ????
? ? + cos(2??? + ?)?? (?2? + 4) 2 2 2
?2? ????? 2 ????(?+?)?? ?? ? ?
? sin(2? (? + ?) + ?) ? ?? ?????(?+?)
?
? ? +2 2
??2? ?????(?+?)?
? cos(2??(? + ?) + ?) ? ??? ?
?????
? sin(2??? + ?) ? ?2? ?
?????
? ? ?? ?
?????
2 ?
+ ?? ??????? cos(2??? + ?) + ??? ?
?????
? sin(2??(? + ?) + ?) + ?2???
????(?+?)
+ ?? ?????(?+?) ? ?? ?????(?+?)? ? cos(2??(? + ?) + ?)) 
Neglect ?2 terms assuming they are small, red terms denote imaginary component: 
? ?2? ?????? ??2? ?????? ??2? ??????? ? ?
( sin(2? ?????2 ?? + ?) + ???? ? + cos(2??? + ?)?? 2?(? + 4) 2 2 2
?2? ??????? ??
2? ?????(?+?)?
? sin(2??(? + ?) + ?) ? ?? ?
????(?+?) +
2 ? 2
??2? ?????(?+?)?
? cos(2??(? + ?) + ?) ? ??? ?
?????
? sin(2??? + ?) ? ?2? ?
????? ? ?? ??????
2 ? ?
+ ?? ??????? cos(2??? + ?) + ??? ?
?????
? sin(2??(? + ?) + ?) + ?2? ?
????(?+?)
?
+ ?? ?????(?+?) ? ?? ?????(?+?)? ? cos(2??(? + ?) + ?)) 
Simplify: 
?
(?? ?????? ? ?? ?????(?+?) ? ??? ??????? ? ? sin(2??? + ?) ? ?2? ?
????? ? ?? ?????
(2? )2? ? ?
?
?
+ ????
????? cos(2??? + ?) + ??? ?
?????
? sin(2?
????(?+?)
?(? + ?) + ?) + ?2???
+ ?? ?????(?+?)? ? ?? ?
????(?+?)
? cos(2??(? + ?) + ?)) 
Collect real and imaginary terms: 
Real:  
?
(?????? cos(2? ? + ?) ? ?????(?+?)? cos(2??(? + ?) + ?)) 4??
Imag: 
?? 2 2
(??????? sin(2? ? + ?) ? ?????? + ??????? sin(2? (? + ?) + ?) + ?
????(?+?)) 
4?? ?
? ?
Substitute into amplitude formula: 
|?(?)| = ??2 + ?2 
14
6 
 
2
?
|?(?)| = (( (?????? cos(2? ? + ?) ? ?????(?+?)? cos(2??(? + ?) + ?)))4??
1
2 2
? 2 2
+ ( (??????? sin(2??? + ?) ? ?
????? + ?????? sin(2? ????(?+?)
4? ? ?
(? + ?) + ?) + ? )) )   
? ?
?
|?(?)| = (??2???? cos2(2? ? + ?) ? 2??2?????????? cos(2??? + ?) cos(2??(? + ?) + ?)4??
2
+ ??2???(?+?) cos2(2??(? + ?) + ?) + ?
?2???? sin2(2? ?2?????? + ?) + ? sin(2?? ?
? + ?)
2
? ??2???? sin(2??? + ?) sin(2??(? + ?) + ?) ? ?
?2????????? sin(2? ? + ?)
? ?
2 4 2 4
+ ??2???? sin(2? ? + ?) + ??2???? ? ??2????? sin(2?
?2?????????
? ?2 ? ?
(? + ?) + ?) ? ?
?2
2
? ??2???? sin(2??? + ?) sin(2? (? + ?) + ?) ? ?
?2????
? sin(2??(? + ?) + ?)?
2
+ ??2???? sin2(2? (? + ?) + ?) + ??2?????????? sin(2??(? + ?) + ?)?
2 4 2
? ??2????????? sin(2? ? + ?) ? ??2????????? + ??2?????????? sin(2??(? + ?) + ?)? ?2 ?
1
4 2
+ ??2???(?+?))  
?2
4
Factor out 2 from the square root: ?
? 2 ?2 ?2
|?(?)| = ( ) ( ??2???? cos2(2? ? + ?) ? ??2?????????? cos(2??? + ?) cos(2??(? + ?) + ?)4?? ? 4 2
?2 ?2 ?
+ ??2???(?+?) cos2(2? (? + ?) + ?) + ??2???? sin2(2? ? + ?) + ??2????? ? sin(2??? + ?)4 4 2
?2 ?
? ??2???? sin(2??? + ?) sin(2??(? + ?) + ?) ? ?
?2????????? sin(2??? + ?)4 2
? ?
+ ??2???? sin(2? ? + ?) + ??2???? ? ??2????? sin(2??(? + ?) + ?) ? ?
?2?????????
2 2
?2 ?
? ??2???? sin(2? ? + ?) sin(2? (? + ?) + ?) ? ??2????? ? sin(2??(? + ?) + ?)4 2
?2 ?
+ ??2???? sin2(2? (? + ?) + ?) + ??2?????????? sin(2??(? + ?) + ?)4 2
? ?
? ??2????????? sin(2? ? + ?) ? ??2????????? + ??2?????????? sin(2??(? + ?) + ?)2 2
1
2
+ ??2???(?+?))  
Eliminate ?2 terms: 
15
7 
 
? ?2 ?2
|?(?)| = ( ??2???? cos2(2??? + ?) ? ?
?2????????? cos(2??? + ?) cos(2??(? + ?) + ?)2??? 4 2
?2 ?2 ?
+ ??2???(?+?) cos2(2??(? + ?) + ?) + ?
?2???? sin2(2? ? + ?) + ??2????? sin(2??? + ?)4 4 2
?2 ?
? ??2???? sin(2? ? + ?) sin(2? (? + ?) + ?) ? ??2?????????? ? sin(2?4 2 ?
? + ?)
? ?
+ ??2???? sin(2??? + ?) + ?
?2???? ? ??2???? sin(2? (? + ?) + ?) ? ??2?????????
2 2 ?
?2 ?
? ??2???? sin(2??? + ?) sin(2?
?2????
4 ?
(? + ?) + ?) ? ? sin(2??(? + ?) + ?)2
?2 ?
+ ??2???? sin2(2??(? + ?) + ?) + ?
?2????????? sin(2??(? + ?) + ?)4 2
? ?
? ??2????????? sin(2? ? + ?) ? ??2????????? + ??2?????????? sin(2?2 2 ?
(? + ?) + ?)
1
2
+ ??2???(?+?))  
Resulting in: 
? ? ? ?
|?(?)| = ( ??2???? sin(2? ? + ?) ? ??2?????????? sin(2? ? + ?) + ?
?2???? sin(2? ? + ?) + ??2????
2??? 2 2
? 2 ?
? ?
? ??2???? sin(2? (? + ?) + ?) ? ??2????????? ? ??2????? sin(2??(? + ?) + ?)2 2
? ?
+ ??2????????? sin(2? (? + ?) + ?) ? ??2?????????? sin(2?
?2?????????
2 2 ?
? + ?) ? ?
1
? 2
+ ??2????????? sin(2??(? + ?) + ?) + ?
?2???(?+?))  
2
Combine like terms, color-coded: 
?
|?(?)| = (???2???? sin(2? ? + ?) ? ???2????????? sin(2? ? + ?) + ??2????
2?? ? ??
? ???2???? sin(2? (? + ?) + ?) ? 2??2????????? + ???2?????????? sin(2??(? + ?) + ?)
1
+ ??2???(?+?))2 
Rearranging by ? + ?, or ? terms: 
?
|?(?)| = (??2???? + ??2???(?+?) ? 2??2????????? + (??2???? ? ??2?????????)? sin(2??? + ?)2???
1
+ (??2????????? ? ??2????)? sin(2??(? + ?) + ?))
2 
Factor out ??2????: 
 ???????
|?(?)| = (1 + ??2???? ? 2?????? + (1 ? ??????)? sin(2??? + ?)2???
1 (8) 
? (1 ? ??????)? sin(2? (? + ?) + ?))2?  
The reference by Hammond gives: 
16
8 
 
???????
|?(?)| = (1 + ??2???? ? 2?????? + (1 ? ??????)? sin(2??? + ?)2???
1
? ??????(1 ? ??????)? sin(2??(? + ?) + ?))
2 
An extra ?????? factor is present, but this is not evident in this derivation. Further work to evaluate this discrepancy is 
needed. Perhaps the initial cancellation of ?2 caused terms to be missed. 
For convenience, write Eq. (8) as: 
 
??????? 1 + ?(?)
|?(?)| = ?  (9) 
2? ?2?
Where, 
?(?) = ??2???? ? 2?????? + (1 ? ??????)? sin(2??? + ?) ? (1 ? ?
?????)? sin(2??(? + ?) + ?) 
Take the natural log of Eq. (9): 
 ? 1 1 + ?(?)
ln|?(?)| = ????? + ln ( ) + ln ( ) (10) 2?? 2 ?
2
Last term can be expanded in a Maclaurin series, which is a Taylor series centered about zero: 
???(0) ????(0) ??(0)
?(?) = ?(0) + ??(0)? + ?2 + ?3 + ? + ?? + ? 
2! 3! ?!
1 1 + ?(?)
?(?) = ln ( ) 
2 ?2
1 1 + ?(0) 0
?(0) = ln ( ) =  
2 0 0
Use L?hopital?s rule? 
??(?)
lim(? ? ?) = 0 
2?
First derivation: 
??(?) = ?2? ???2???? + 2? ???????? ? + sin(2??? + ?) ? ?
????? sin(2??? + ?) + ?? ??
?????
? sin(2??? + ?)
? sin(2? (? + ?) + ?) + ??????? sin(2??(? + ?) + ?) ? ?? ??
?????
? sin(2??(? + ?) + ?) 
??(0) = ?2??? + 2??? + sin(2??? + ?) ? sin(2??? + ?) ? sin(2??(? + ?) + ?) + sin(2??(? + ?) + ?) = 0 
Second derivative: 
???(?) = 4(? ?)2??2????? ? 2(???)
2?????? + ? ???????? sin(2? ? + ?) ? ?
?????
? sin(2??? + ?)
+ ?????
????? sin(2??? + ?) ? ????
????? sin(2??(? + ?) + ?)
? ? ???????? sin(2??(? + ?) + ?) + ?(???)
2?????? sin(2??(? + ?) + ?) 
???(0) = 4(???)
2 ? 2(???)
2 + ??? sin(2??? + ?) ? sin(2??? + ?) ? ??? sin(2??(? + ?) + ?)
? ??? sin(2??(? + ?) + ?) 
???(0) = 2(???)
2 + (??? ? 1) sin(2??? + ?) ? 2??? sin(2??(? + ?) + ?) 
Third derivative: 
17
9 
 
????(?) = ?8(? ?)3??2????? + 2(???)
3?????? ? (? 2 ????? ???????) ? sin(2??? + ?) + ???? sin(2??? + ?)
+ ? ???????? sin(2??? + ?) ? ?(? ?)
2??????? sin(2??? + ?)
+ (? ?)2??????? sin(2??(? + ?) + ?) + (?
2 ?????
??) ? sin(2??(? + ?) + ?)
+ (???)
2?????? sin(2??(? + ?) + ?) ? ?(? ?)
3??????? sin(2??(? + ?) + ?) 
????(0) = ?8(???)
3 + 2(???)
3 ? (? ?)2? sin(2??? + ?) + ??? sin(2??? + ?) + ??? sin(2??? + ?)
+ (? ?)2? sin(2??(? + ?) + ?) + (???)
2 sin(2??(? + ?) + ?) + (???)
2 sin(2??(? + ?) + ?) 
????(0) = ?6(???)
3 + (2??? ? (???)
2) sin(2??? + ?) + 3(?
2
??) sin(2??(? + ?) + ?) 
Substitute into Maclaurin series: 
???(0) ????(0)
?(?) = ?(0) + ??(0)? + ?2 + ?3 + ? 
2! 3!
?(0) = ?1 
??(0) = 0 
???(0) = 2(???)
2 + (??? ? 1) sin(2??? + ?) ? 2??? sin(2??(? + ?) + ?) 
????(0) = ?6(? ?)3? + (2??? ? (? ?)
2
? ) sin(2??? + ?) + 3(?
2
??) sin(2??(? + ?) + ?) 
??? ? 1
?(?) = ?1 + ((? 2??) + sin(2??? + ?) ? ??? sin(2??(? + ?) + ?)) ?
2
2
2??? ? (???)
2 (???)
2
+ (?(? 3??) + sin(2??? + ?) + sin(2??(? + ?) + ?)) ?
3 
6 2
Substitute back into amplitude equation: 
?
ln|?(?)| = ????? + ln ( )2??
1 ??? ? 1
+ ln ((???)
2 + sin(2??? + ?) ? ??? sin(2??(? + ?) + ?)2 2
2? ? ? (? ?)2? ? (? ?)
2
?
+ ? (?(? 3??) + sin(2??? + ?) + sin(2??(? + ?) + ?))) 6 2
 ?
ln|?(?)| = ????? + ln ( )2??
1 ??? ? 1
+ ln ((? 2??) + sin(2??? + ?) ? ??? sin(2??(? + ?) + ?) (11) 2 2
2 ? ??? ???
? ???? ((???)
2 ? ( ) sin(2??? + ?) ? sin(2??(? + ?) + ?))) 6 2
Third term in Hammond?s reference, assuming it is the first 4 terms of the series: 
1
? + ln ((? 2??) + ???(sin(2??? + ?) ? sin(2??(? + ?) + ?))2
? 2??? + sin(2??? + ?) ? 3 sin(2??(? + ?) + ?
? ? ? ( )) 
4 ? ??? + sin(2??? + ?) ? sin(2??(? + ?) + ?)
Assuming T is an integral multiple of the basic period of oscillation: 
2??
? = , ??? ? = 1, 2, 3, ? 
??
18
10 
 
Eq. (11) becomes: 
?
ln|?(?)| = ????? + ln ( )2??
1 2? ? 1
+ ln ((2?)2 + sin(2??? + ?) ? 2? sin(2??(?) + ?)2 2
2 ? 2? 2?
? ?2? ((2?)2 ? ( ) sin(2??? + ?) ? sin(2??(?) + ?))) 6 2
?
ln|?(?)| = ????? + ln ( )2??
1 2? ? 1
+ ln ((2?)2 + sin(2? ? + ?) ? 2? sin(2? ? + ?)
2 2 ? ?
2 ? 2? 2?
? ?2? ((2?)2 ? ( ) sin(2??? + ?) ? sin(2??? + ?))) 6 2
2?(25) 50?
So if we were to calculate the Fourier amplitude of ? = 10, ? = 0.01, ?? = 5, ? = 0, ? = 50, ? = =  ?? ??
??????? 1 + ?(?)
|?(?)| = ?  
2? ?2?
?(?) = ??2???? ? 2?????? + (1 ? ??????)? sin(2? ? + ?) ? (1 ? ??????? )? sin(2??(? + ?) + ?) 
? ?
?(0.01) = ??? ? 2??2 ? (1 ? ??2) 0.01 sin(100?)
= ?0.37254523443775156731949350249822952879202757345290613316. .. 
10 1 + ?(0.01)
|?(?)| = ? = 79.212 
10 0.0001
2?
So if we were to calculate the Fourier amplitude of ? = 10, ? = 0.01, ?? = 5, ? = 0, ? = 1, ? =  ??
??????? 1 + ?(?)
|?(?)| = ?  
2? 2? ?
?(?) = ??2???? ? 2?????? + (1 ? ??????)? sin(2? ? + ?) ? (1 ? ??????? )? sin(2??(? + ?) + ?) 
?(0.01) = ??400? ? 2??200? ? (1 ? ??200?)0.01 sin(4?) 
10 1 + ?(0.01)
|?(?)| = ? ? 100 
10 0.0001
  
19
11 
 
Windowing; Multiplication 
Multiplying a sine wave by a Hanning Window gives a new signal that contracts at the ends. What is the new equation of 
the signal? 
Sine wave signal: 
? ? sin ?? 
???
? = 10, ? = 5 ?? ?? 10?  
?
From ? = 0: 1.9 ? 
Hanning Window signal: 
?
sin2 ( ?) 
1.9
Multiply: 
?
10 sin(10??) sin2 ( ?) 
1.9
Trig identity: 
1
sin(?) ? sin(?) = (cos(? ? ?) ? cos(? + ?)) 
2
1
sin(?) ? cos(?) = (sin(? ? ?) + sin(? + ?)) 
2
 
Then 
? ?
10 sin(10??) ??? ( ?) ??? ( ?) 
1.9 1.9
1 2?
10 sin(10??) (1 ? cos ( ?)) 
2 1.9
2?
5 (sin(10??) ? sin(10??) cos ( ?)) 
1.9
1 2? 2?
5 (sin(10??) ? (sin (10?? ? ?) + sin (10?? + ?))) 
2 1.9 1.9
5 2? 2?
? (?2 sin(10??) + sin (10?? ? ?) + sin (10?? + ?)) 
2 1.9 1.9
5 170? 210?
? (sin ( ?)  ?  2 sin(10??)  + sin ( ?)) 
2 19 19
170? 210?
New frequencies  and  are generated. An FFT initially gives you amplitude and phase through 
19 19
complex numbers, which will display these new frequencies in question as zeroes. However, once an absolute value is 
taken on the FFT values to get magnitude of displacement, these new frequencies are not apparent. 
20
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