NASA / CRm2000-210062 Simulating Fatigue Crack Growth in Spiral Bevel Gears Lisa E. Spievak, Paul A. Wawrzynek, and Anthony R. Ingraffea Cornell University, Ithaca, New York ARL-CR-451 May 2000 The NASA STI Program Office in Profile Since its founding, NASA has been dedicated to the advancement of aeronautics and space science. The NASA Scientific and Technical Information (STI) Program Office plays a key part in helping NASA maintain this important role. The NASA STI Program Office is operated by Langley Research Center, the Lead Center for NASA's scientific and technical information. The NASA STI Program Office provides access to the NASA STI Database, the largest collection of aeronautical and space science STI in the world. The Program Office is also NASA's institutional mechanism for disseminating the results of its research and development activities. 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I wish to thank Dr. David Lewicki and Dr. Robert Handschuh of the U.S. Army Research Laborato D" at NASA Glenn Research Center. Much of this thesis" work is a direct result of their advice and expertise. Lehigh University professor Dr. Eric Kaufmann's time and technical knowledge were instrumental with the scanning electron microscope observations contained in this thesis. In addition, Dr. Richard N. White at Cornell University volunteered his time and skills to photograph the tested spiral bevel pinion. Many of his photographs are contained in this volume. NASA Center for Aerospace Information 7121 Standard Drive Hanover, MD 21076 Price Code: A06 Available from National Technical Information SelaTice 5285 Port Royal Road Springfield, VA 22100 Price Code: A06 ! TABLE OF CONTENTS CHAPTER ONE: INTRODUCTION 1 1.1 Background 1 1.2 Numerical Analyses of Gears 3 1.3 Overview of Chapters 5 CHAPTER TWO: GEAR GEOMETRY AND LOADING 7 2.1 2.2 2.3 2.4 2.5 2.6 Introduction 7 Basics of Spiral Bevel Gear Geometry 7 Teeth Contact and Loading of a Gear Tooth 11 Gear Materials 16 Motivation to Model Gear Failures 16 2.5.1 Gear Failures 18 2.5.2 OH-58 Spiral Bevel Gear Design Objectives 19 Chapter Summary 19 CHAPTER THREE: COMPUTATIONAL FRACTURE MECHANICS 21 3.1 Introduction 21 3.2 Fracture Mechanics and Fatigue 21 3.2.1 Fatigue 23 3.2.2 Example: Two dimensional, mode I dominant fatigue crack growth simulation with static, proportional loading 27 3.2.3 Example: Three dimensional, mode I dominant fatigue crack growth simulation with static, proportional loading 31 3.3 Fracture Mechanics Software 33 3.4 Chapter Summary 34 CHAPTER FOUR: FATIGUE CRACK GROWTH RATES 35 4.1 4.2 4.3 4.4 4.6 Introduction 35 Fatigue Crack Closure Concept 35 Application of Newman' s Model to AISI 9310 Steel 40 Sensitivity of Growth Rate to Low R 44 Chapter Summary 46 CHAPTER FIVE: PREDICTING FATIGUE CRACK GROWTH TRAJECTORIES IN THREE DIMENSIONS UNDER MOVING, NON- PROPORTIONAL LOADS 47 5.1 Introduction 47 5.2 BEM Model 47 5.2.1 Loading Simplifications 49 5.2.2 Influence of Model Size on SIF Accuracy 51 5.3 Initial SIF History Under Moving Load 54 NAS A/CR 2000-210062 v 5.4 5.5 5.6 Methodfor ThreeDimensionalFatigueCrackGrowthPredictionsUnderNon- ProportionalLoading 58 5.4.1 LiteratureReview 58 5.4.2 ProposedMethod 59 5.4.3 Approximationsof Method 63 SimulationResults 64 ChapterSummary 67 CHAPTER SIX: EXPERIMENTAL RESULTS 69 6.1 Introduction 69 6.2 Test Results 69 6.3 Fractography 71 6.3.1 Overview 71 6.3.2 Results 73 6.4 Chapter Summary 79 CHAPTER SEVEN: DISCUSSION AND SENSITIVITY STUDIES 81 7.1 Introduction 81 7.2 Comparisons of Crack Growth Results 81 7.3 Sensitivity Studies 85 7.3.1 Fatigue Crack Growth Rate Model Parameters 86 7.3.2 Crack Closure Model Parameters 87 7.3.3 Loading Assumptions 89 7.4 Highest Point of Single Tooth Contact (HPSTC) Analysis 96 7.5 Chapter Summary , 99 CHAPTER EIG_: CONCLUDING REMARKS 10! 8.1 Accomplishments and Significance of Thesis 101 8.2 Recommendations for Future Research 103 APPENDIX A 104 APPENDIX B 106 APPENDIX C 108 REFERENCES 110 NASA/CR 2000-210062 vi LIST OF ABBREVIATIONS AGMA BEM EDM FEM FRANC3D HPSTC LEFM NASA/GRC OSM RC SEM SIF American Gear Manufacturers Association Boundary element method Electro-discharge machined Finite element method FRacture ANalysis Code - 3D Highest point of single tooth contact Linear elastic fracture mechanics National Aeronautics and Space Administration - Glenn Research Center Object Solid Modeler Rockwell C Scanning electron microscope Stress intensity factor NAS A/CR 2000-210062 vii . Failures 18 2.5.2 OH-58 Spiral Bevel Gear Design Objectives 19 Chapter Summary 19 CHAPTER THREE: COMPUTATIONAL FRACTURE MECHANICS 21 3 .1 Introduction 21 3.2 Fracture Mechanics and Fatigue 21 3.2 .1 Fatigue. CONCLUDING REMARKS 10 ! 8 .1 Accomplishments and Significance of Thesis 10 1 8.2 Recommendations for Future Research 10 3 APPENDIX A 10 4 APPENDIX B 10 6 APPENDIX C 10 8 REFERENCES 11 0 NASA/CR 2000- 210 062. LOADING 7 2 .1 2.2 2.3 2.4 2.5 2.6 Introduction 7 Basics of Spiral Bevel Gear Geometry 7 Teeth Contact and Loading of a Gear Tooth 11 Gear Materials 16 Motivation to Model Gear Failures 16 2.5.1