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Active and Passive Techniques for Tiltrotor Aeroelastic Stability Augmentation

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Active and Passive Techniques for Tiltrotor Aeroelastic Stability Augmentation The Pennsylvania State University The Graduate School College of Engineering ACTIVE AND PASSIVE TECHNIQUES FOR TILTROTOR AEROELASTIC STABILITY AUGMENTATION A Thesis in Aerospace Engineering by Eric L. Hathaway c 2005 Eric L. Hathaway Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2005 The thesis of Eric L. Hathawaywas reviewed and approved* by the following: Farhan Gandhi Associate Professor of Aerospace Engineering Thesis Adviser Chair of Committee Edward C. Smith Professor of Aerospace Engineering Joseph F.Horn Assistant Professor of Aerospace Engineering Christopher D. Rahn Professor of Mechanical Engineering George A. Lesieutre Professor of Aerospace Engineering Head of the Department of Aerospace Engineering *Signatures are on file in the Graduate School. Abstract Tiltrotors are susceptible to whirl flutter, an aeroelastic instability characterized by a coupling of rotor-generated aerodynamic forces and elastic wing modes in high speed airplane-mode flight. The conventional approach to ensuring adequate whirl flutter stability will not scale easily to larger tiltrotor designs. This study constitutes an investigation of sev- eral alternatives for improving tiltrotor aerolastic stability. A whirl flutter stability analysis is developed that does not rely on more complex models to determine the variations in cru- cial input parameters with flight condition. Variation of blade flap and lag frequency, and pitch-flap, pitch-lag, and flap-lag couplings, are calculated from physical parameters, such as blade structural flap and lag stiffness distribution (inboard or outboard of pitch bearing), collective pitch, and precone. The analysis is used to perform a study of the influence of various design parameters on whirl flutter stability. While previous studies have investi- gated the individual influence of various design parameters, the present investigation uses formal optimization techniques to determine a unique combination of parameters that max- imizes whirl flutter stability. The optimal designs require only modest changes in the key rotor and wing design parameters to significantly increase flutter speed. When constraints on design parameters are relaxed, optimized configurations are obtained that allow large values of kinematic pitch-flap (δ3) coupling without degrading aeroelastic stability. Larger values of δ3 may be desirable for advanced tiltrotor configurations. An investigation of active control of wing flaperons for stability augmentation is also conducted. Both stiff- and soft-inplane tiltrotor configurations are examined. Control systems that increase flutter iii speed and wing mode sub-critical damping are designed while observing realistic limits on flaperon deflection. The flaperon is shown to be particularly effective for increasing wing vertical bending mode damping. Controller designs considered include gain scheduled full- state feedback optimal control, constant gain full-state controllers derived from the optimal controllers, and single-state feedback systems. The dominant feedback parameters in the optimal control systems are identified and examined to gain insight into the most important feedback paths that could be exploited by simpler reduced-order controllers. iv Contents List of Figures ix List of Tables xviii List of Symbols xix Dedication xxi Acknowledgments xxii 1 Introduction 1 1.1 Overview of tiltrotor aeroelastic and aeromechanical stability research . 3 1.2 Influence of passive design parameters on tiltrotor stability . .............................. 11 1.3 Application of active control to tiltrotor aircraft . ............ 14 1.4 Summary . .............................. 17 2 Objectives of Present Research 35 2.1 Development of simple tiltrotor stability analysis . ............ 35 2.2 Optimization of passive design parameters . ................ 37 2.3 Active control of wing flaperons for stability augmentation . .............................. 38 v 3 Description of Present Analysis 40 3.1 Overview of formulation . ....................... 40 3.1.1 Aerodynamics . ....................... 42 3.1.2 Assembling rotor/wing equations . ................ 44 3.2 Validation . .............................. 45 3.2.1 XV-15 . .............................. 45 3.2.2 Boeing Model 222 . ....................... 46 3.2.3 1/5-scale V-22 aeroelastic model . ................ 46 3.2.4 WRATS model . ....................... 47 3.2.5 WRATS Semi-Articulated, Soft-Inplane rotor model . ..... 48 3.3 Influence of unique model features . ................ 50 3.3.1 Structural flap-lag coupling . ................ 50 3.3.2 Gimbal/Blade flapping degrees of freedom . ............ 54 3.3.3 Modeling blade pitch-flap and pitch-lag coupling . ..... 56 3.4 Summary . .............................. 63 4 Optimization of Rotor and Wing Design Parameters 86 4.1 Wing model . .............................. 87 4.2 Parametric study . .............................. 88 4.2.1 Influence of individual rotor design parameters . ..... 88 4.2.2 Influence of individual wing design parameters . ..... 93 4.3 Parametric optimization . ....................... 95 4.3.1 Selection of objective function . ................ 96 4.3.2 Optimization of rotor parameters . ................ 99 4.3.3 Optimization of wing parameters . ................102 4.3.4 Concurrent wing/rotor optimization . ................105 vi 5 Active Control of Wing Flaperons for Stability Augmentation 127 5.1 Flaperon active control formulation . ................128 5.1.1 Limits on control gains . .......................130 5.1.2 Wing unsteady aerodynamic modeling ................131 5.2 Optimal Control Results . .......................135 5.2.1 XV-15 . ..............................136 5.2.2 Model 222 ..............................137 5.3 Influence of Unsteady Aerodynamics . ................138 5.4 Full-State Constant Gain Controller . ................141 5.5 Effect of Rotor Speed on Flaperon Control . ................142 5.6 Investigation of Key Feedback Parameters . ................143 6 Conclusions 162 6.1 Optimization of rotor and wing design parameters . ............163 6.2 Active control of wing flaperons .......................165 6.3 Recommendations for future work . ................167 6.3.1 Model Correlation . .......................167 6.3.2 Passive Design Optimization . ................168 6.3.3 Active Control . .......................168 6.3.4 Active–Passive Hybrid Optimization . ................170 Bibliography 171 Appendix A. Analytical Model 179 A.1 Degrees of Freedom ..............................179 A.2 Acceleration of a Point on the Blade . ................180 A.3 Rotor Equations of Motion . .......................182 A.3.1 Blade flapping equations .......................182 A.3.2 Blade lead-lag equations .......................184 vii A.4 Blade Root Loads – Inertial Contribution . ................186 A.5 Rotor Hub Loads – Inertial Components . ................187 A.6 Rotor Aerodynamics . .......................189 A.6.1 Introduction ..............................189 A.6.2 Section aerodynamic forces . ................189 A.6.3 Rotor aerodynamic forces and moments . ............191 A.7 Gimbal/Rotor Speed Degrees of Freedom . ................197 A.8 Rotor Equations of Motion . .......................198 A.9 Wing Models . ..............................211 A.9.1 FEM wing structural model . ................211 A.9.2 FEM wing aerodynamics .......................218 A.9.3 FEM Wing assembly and pylon inertial contribution . .....224 A.9.4 Modal wing representation . ................225 A.10 Wing/Rotor Coupling . .......................227 Appendix B. Wing Unsteady Aerodynamic Model 229 B.1 Generating RFA model from frequency-domain data ............229 B.1.1 Optimal pole placement to improve fit ................233 B.1.2 Results of RFA fitting process . ................234 B.2 Integration of RFA aero model with FEM wing . ............234 B.2.1 Conversion to time domain . ................235 B.2.2 Numerical integration across span of wing elements . .....236 viii List of Figures 1.1 The Bell/Boeing V-22 Osprey tiltrotor aircraft ................ 19 1.2 The Bell Eagle Eye tiltrotor UAV ....................... 20 1.3 The Bell/Agusta BA-609 civilian tiltrotor . ................ 21 1.4 Effect of Lag Frequency on Hub Loads (from Ref. 4) ............ 22 1.5 The Lockheed Electra turboprop airliner . ................ 22 1.6 Simple propeller model used to validate analysis of Ref. 8 . ..... 23 1.7 Pitch and Yaw Stiffness Required for Neutral Whirl Flutter Stability (from Ref. 7) ..................................... 24 1.8 Transcendental Model 1-G (from Ref. 10) . ................ 25 1.9 Transcendental Model 2 (from Ref. 10) . ................ 25 1.10 First flight of Bell XV-3 tiltrotor research aircraft, August 11, 1955 (from Ref. 10) . .............................. 26 1.11 Later configuration of XV-3 in airplane mode flight (from Ref. 10) ..... 27 1.12 XV-3 in the NASA Ames Research Center 40- by 80- ft. wind tunnel (from Ref. 10) . .............................. 28 1.13 Proprotor Whirl Flutter: Origin of destabilizing aerodynamic force (from Ref. 11) . .............................. 29 1.14 Bell Model 300 rotor in the Ames 40- by 80-ft wind tunnel (from Ref. 10) . 30 1.15 Boeing Model 222 rotor in the Ames 40- by 80-ft wind tunnel (from Ref. 10) 31 1.16 XV-15 Tiltrotor Research Aircraft in hover . ................ 32 ix 1.17 WRATS wind tunnel model in NASA Langley TDT (from Ref. 39) ..... 33 1.18 Bell semi-articulated soft-inplane rotor installed on WRATS model (from Ref.
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