STABILITY AND CONTROL ISSUES ASSOCIATED WITH LIGHTLY LOADED ROTORS AUTOROTATING IN HIGH ADVANCE RATIO FLIGHT A Dissertation Presented to The Academic Faculty by James Michael Rigsby In Partial Fulfillment Of the Requirements for the Degree Doctor of Philosophy in the School of Aerospace Engineering Georgia Institute of Technology December 2008 STABILITY AND CONTROL ISSUES ASSOCIATED WITH LIGHTLY LOADED ROTORS AUTOROTATING IN HIGH ADVANCE RATIO FLIGHT Approved by: Professor J.V.R. Prasad, Advisor Professor Dewey H. Hodges School of Aerospace School of Aerospace Engineering Engineering Georgia Institute of Technology Georgia Institute of Technology Professor Daniel P. Schrage Professor L.N. Sankar School of Aerospace School of Aerospace Engineering Engineering Georgia Institute of Technology Georgia Institute of Technology Professor David A. Peters Date Approved: October 14, 2008 Department of Mechanical, Aerospace and Structural Engineering Washington University, St. Louis ACKNOWLEDGEMENTS I would like to acknowledge my sincerest appreciation to Professor J.V.R. Prasad for his mentorship, incredible patience, and guidance during my time at the Georgia Institute of Technology. I would also like to thank Professor Daniel Schrage and Professor Lakshmi Sankar as well. It was within this circle of influence that I developed my appreciation for rotorcraft engineering, undoubtedly one of the most interesting, challenging, and multidisciplinary fields in all of aerospace engineering. In addition, I thank Professor Dewey Hodges and Professor David Peters for their guidance and participation in the review and evaluation of this work. I also thank the students who were finishing as I was just beginning: Chen Chang, Geoffrey Jeram, Suraj Unnikrishnan, Illkay Yavrucuk, and many others. Special thanks to Manuj Dhingra, whose friendship, assistance, and patience opened my eyes to the wider world of computing and who was always there to resolve my major computing crises with a few magical lines of code. I thank all of my friends at Georgia Tech for their help and support. Those friends include, but are not limited to: Mandy Goltsch, B.Y. Min, Alex Moodie, Kyle Collins, Troy Schank, and Jongki Moon, Ersel Olcer, and Suresh Kannon. Also, I offer a special thanks to Dr. Hong Xin, for friendship and fantastic software support. Finally, I thank my family, without whose love and support, none of this would have been possible. My wife Xiaohong, my parents, my sister and brother-in-law, all encouraged me and provided steadfast support. I dedicate this work to them. iii TABLE OF CONTENTS ACKNOWLEDGEMENTS ............................................................................................. iii LIST OF TABLES ..........................................................................................................vi LIST OF FIGURES........................................................................................................vii LIST OF SYMBOLS AND ABBREVIATIONS .............................................................. xii SUMMARY....................................................................................................................xv CHAPTER 1: INTRODUCTION...................................................................................... 1 1.1 Overview .............................................................................................................. 1 1.2 Literature Review.................................................................................................. 2 1.2.1 The Fairey Rotodyne.................................................................................... 3 1.2.2 The McDonnell Aircraft XV-1 Convertiplane ................................................. 5 1.2.3 High Advance Ratio Wind-Tunnel Experiments ............................................ 6 1.2.4 Analytical Investigations ............................................................................... 9 1.2.5 Autogyros....................................................................................................11 1.2.6 Compound Helicopters................................................................................12 1.2.7 Additional Works .........................................................................................14 1.3 Present Work.......................................................................................................14 1.4 Organization of Dissertation.................................................................................18 CHAPTER 2: MODELING AND SIMULATION ENVIRONMENT ..................................21 2.1 Rotor Model Formulation .....................................................................................21 2.2 Rotor Speed Degree of Freedom Model ..............................................................29 2.3 Airframe Model ....................................................................................................31 2.4 Operational Envelope and Test Conditions..........................................................32 2.5 Analysis Selection and Methodology Overview....................................................33 iv CHAPTER 3: ISOLATED ROTOR ANALYSIS .............................................................37 3.1 Autorotating Rotor Trim and Performance Trends................................................37 3.2 Rotor Stability ......................................................................................................50 3.3 Steady-State Control Hub Moments and Cross-Coupling ....................................60 3.4 Rotor Steady-State Gust Sensitivity.....................................................................75 3.5 Rotor Transient Response and Slowed-Rotor Dynamics .....................................78 3.6 Rotor Speed Response to Swashplate Controls ..................................................87 3.7 Cruise Condition Rotor Performance and Multiple Trim Solutions........................91 3.8 Source of Rotor Speed Non-linear Response to Control Inputs ...........................96 3.9 Preferred Rotor Operating Point Selection Criteria.............................................103 3.10 Effect of Blade Twist at the Cruise Condition ...................................................107 3.11 Rotor Performance Out of Moment Trim ..........................................................110 3.12 Chapter Summary............................................................................................112 CHAPTER 4: COUPLED ROTOR-AIRFRAME ANALYSIS ........................................114 4.1 Rotor Control in Quasi-Steady Maneuvers.........................................................115 4.1.1 Commanded Rotor Speed Transition Maneuver........................................115 4.1.2 Flight Path Transition Maneuver................................................................123 4.3 Coupled Rotor and Airframe Flight Dynamics Characteristics............................125 4.4 Rotor Speed and Longitudinal Mode Coupling...................................................133 4.5 Chapter Summary..............................................................................................135 CHAPTER 5: CONCLUSIONS AND RECOMMENDATIONS .....................................136 5.1 Conclusions.......................................................................................................136 5.2 Recommendations for Future Work ...................................................................142 APPENDIX..................................................................................................................145 REFERENCES............................................................................................................146 v LIST OF TABLES Page Table 1: Fixed Baseline Rotor Parameters ....................................................................26 Table 2: Rotor Mass Properties for Parametric Analysis................................................26 Table 3: Parametric Baseline Rotor Properties ..............................................................29 Table 4: Airframe Model Properties ...............................................................................31 Table 5: Eigenvalues from 13-State Linear Model – Longitudinal Modes.....................126 Table 6: System ID and Linear Analysis Results – Coupled Pitch Motion ....................129 Table 7: Eigenvalues from 13-State Linear Model – Lateral / Directional Modes .........131 Table 8: System ID and Linear Analysis Results – Coupled Roll Motion......................132 vi LIST OF FIGURES Page Figure 1: The Fairey Rotodyne, from ref [4] ................................................................... 4 Figure 2: The McDonnell Aircraft XV-1 Convertiplane, from reference [5]....................... 5 Figure 3: Center Spring Approximation Rotor Model from Ref. [52] ...............................24 Figure 4: Articulated Rotor Model Hinge Sequence from Ref. [54].................................25 Figure 5: Fan Plots for Parametric Rotor Models ...........................................................28 Figure 6: Flap Frequencies at Reduced Rotor Speed....................................................28 Figure 7: Rotor Drivetrain Response at Sea Level Hover...............................................30 Figure 8: Test Conditions Envelope...............................................................................32 Figure 9: Baseline Rotor Thrust Coefficient vs. Advance Ratio......................................38