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NASA Simulating in Spiral Lisa E. Spievak, Cornell May ARL-CR-451 / CRm2000-210062 University, 2000 Fatigue Bevel Paul Growth Gears A. Wawrzynek, Ithaca, Crack New York and Anthony R. Ingraffea The NASA STI Program Since its founding, NASA has been dedicated the advancement of aeronautics and space science. The NASA Scientific and Technical Information (STI) Program in helping NASA maintain Office... CONFERENCE to Office plays a key part this important role. SPECIAL technical, the following report MEMORANDUM. extensive CONTRACTOR TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientific and technical material pertinent to NASA's mission. Specialized sen, ices that complement the STI Program Office's diverse offerings include creating custom thesauri, building customized data bases, organizing and publishing research results.., even providing videos. For more information Program analysis. REPORT. 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The Series, which in Profile Home via the Intemet Page to and Write to: NASA Access Help Desk NASA Center for AeroSpace 7121 Standard Drive Hanover, Information MD 21076 i NASA/CRm2000-210062 ARL-CR-451 U,S. ARMY RESEARCH Simulating Fatigue in Spiral Lisa Bevel E. Spievak, Cornell Prepared National LABORATORY Paul University, under Grant Aeronautics Space Administration Glenn Research May 2000 Center New NAG3-1993 and Growth Gears A. Wawrzynek, Ithaca, Crack York and Anthony R. Ingraffea Acknowledgments The research contained in this thesis was conducted under grant NAG3-1993 between Cornell NASA Glenn Research Center. I wish to thank Dr. David Lewicki and Dr. Robert Handschuh University and 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. Available NASA Center 7121 Standard for Aerospace Drive Hanover, MD 21076 Price Code: A06 Information from National Technical Information SelaTice 5285 Port Royal Road Springfield, VA 22100 Price Code: A06 ! TABLE CHAPTER ONE: INTRODUCTION 1.1 Background 1.2 Numerical Analyses 1.3 Overview of Chapters CHAPTER Introduction 2.2 Basics 2.3 2.4 Teeth Contact Gear Materials 2.5 Motivation 1 ............................................................................ GEOMETRY AND LOADING Bevel Gear Geometry Gear Failures Failures OH-58 Spiral Summary Fracture Mechanics 3.2.1 Fatigue 3.2.2 Example: 3.3 Fracture Example: simulation Mechanics 3.4 Chapter Summary CHAPTER FOUR: 4.1 Introduction 4.2 Fatigue 4.3 Application 4.4 Sensitivity 4.6 Chapter CHAPTER 7 11 16 ................................................................. 16 .................................................................................... 18 Bevel 19 Gear Design Objectives ................................... ............................................................................................ 19 and Fatigue ........... ...................................................................... Two dimensional, with static, mode I dominant proportional loading fatigue 23 crack growth ...................................... ............................................................................................ FATIGUE CRACK Closure Concept of Newman' of Growth Summary FIVE: TRAJECTORIES PROPORTIONAL 27 Three dimensional, mode I dominant fatigue crack growth with static, proportional loading ...................................... 31 Software .......................................................................... 33 GROWTH RATES ............................... ..................................................................................................... Crack 21 21 21 .............................................................................................. simulation 7 7 ............................................................ and Loading of a Gear Tooth ................................................... ................................................................................................. Gear 3.2.3 5 .................................. CHAPTER THREE: COMPUTATIONAL FRACTURE MECHANICS 3.1 Introduction ..................................................................................................... 3.2 3 ........................................................................................ to Model 2.5.2 1 ..................................................................................................... of Spiral Chapter of Gears GEAR 2.1 2.6 ........................................................................ ........................................................................................................ TWO: 2.5.1 OF CONTENTS ....................................................................... s Model to AISI 9310 Steel ..................................... Rate to Low R .............................................................. ............................................................................................ PREDICTING FATIGUE CRACK 34 35 35 35 40 44 46 GROWTH IN THREE DIMENSIONS UNDER MOVING, NONLOADS ...................................................................................... 47 5.1 Introduction ..................................................................................................... 47 5.2 BEM Model ..................................................................................................... 47 5.2.1 5.2.2 5.3 Loading Simplifications ................................................................... Influence of Model Size on SIF Accuracy ....................................... Initial SIF History NAS A/CR--2000-210062 Under Moving Load .......................................................... v 49 51 54 5.4 5.5 5.6 Methodfor ThreeDimensionalFatigueCrackGrowth PredictionsUnder NonProportionalLoading....................................................................................... 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 .................................................... 6.1 Introduction ..................................................................................................... 69 69 6.2 Test Results 69 6.3 Fractography .................................................................................................... 6.3.1 Overview .......................................................................................... 71 71 6.3.2 .............................................................................................. 73 ............................................................................................ 79 6.4 Results Chapter CHAPTER Summary SEVEN: 7.1 Introduction 7.2 Comparisons 7.3 ..................................................................................................... Sensitivity DISCUSSION of Crack Studies STUDIES .................. 7.3.3 Loading Highest Point of Single Chapter Summary EIG_: Results ........................................................... ....................................................................... Tooth Contact .................... CONCLUDING 81 81 81 85 Growth Rate Model Parameters ................................ Model Parameters ..................................................... Assumptions 7.5 Accomplishments Recommendations Growth ........................... Fatigue Crack Crack Closure 7.4 8.1 8.2 SENSITIVITY ..................................................................................................... 7.3.1 7.3.2 CHAPTER AND (HPSTC) Analysis ............................. ,........... .... ..... ................................................. REMARKS 86 87 89 96 99 .............................................. 10! and Significance of Thesis ............................................... for Future Research ......................................................... 101 103 APPENDIX A ........................................................................................................ 104 APPENDIX B ........................................................................................................ 106 APPENDIX C ........................................................................................................ 108 ........................................................................................................ 110 REFERENCES NASA/CR--2000-210062 vi LIST OF ABBREVIATIONS AGMA American Gear Manufacturers BEM Boundary element EDM Electro-discharge FEM Finite FRANC3D FRacture HPSTC Highest LEFM Linear NASA/GRC National Center OSM Object RC Rockwell C SEM Scanning electron SIF Stress NAS A/CR--2000-210062 element method machined method ANalysis point elastic Association Code of single fracture Aeronautics - 3D tooth contact mechanics and Space Solid Modeler intensity microscope factor vii Administration - Glenn Research CHAPTER ONE: INTRODUCTION 1.1 Background A desirable weight. objective A lighter system is one transmission gears. gears aircraft example system Because using in the design operates where utilizes more design various methods of gears, been is to minimize A helicopter's focused is relatively has components efficiently. is types spur gear geometry numerical of aircraft on weight transmission minimization. optimizing researched the design significantly. addition, However, fatigue removing cracks material can sacrifice in gears are a design concern on a gear tooth. Research shows that the size tooth height determines the crack trajectories knowledge is critical because geometry. Two common failure fracture, shown of the aircraft fracture often affected in Figure detected 1985]. prior by design modes fracture to catastrophic changes 1988], is important hand, failure. to predict Figure failure modes to its This based on Rim and lead to the loss mode how In loading and tooth fracture. 1.2 is an example failure Knowing with respect 1 the amount of the gear. of the cyclical can be catastrophic is the benign ..T, NASA/CR--2000-210062 because of a gear are rim fracture On the other Tooth strength the has focused of a spur gear's rim with respect [Lewicki et al. 1997a, 1997b]. the designer 1.1 [Albrecht and lives. [Alban it allows the bevel of these However, geometry of spiral bevel gears is much more complex, and less research on using numerical methods to evaluate their design and safety. One obvious method to minimize the weight of a gear is to reduce of material. A such as spur gears and spiral simple, the because crack of a tooth it is most trajectories to these two failure modes. are Figure In general, 1.2: Spiral gears bevel in rotorcrafl gear tooth failure [Alban 1985]. applications are designed for gears are designed to prevent any type of failure damage tolerant design approach could reduce cost gear. Lewicki trajectories et al.'s work is a good on determining example of how the effect damage examples 1984] [Rudd train rails of damage 1984] [Jeong structure design et al. 1999], the rim thickness can be on crack applied to gears. mode allows a designer to select failure mode would be benign. can be found helicopter life; rotor in aircraft heads structures [Irving [Swift et al. 1999], and et al. 1997]. Damage the tolerant [Miller of gear tolerance Knowing how the gear's geometry affects the failure a geometry Such that, if a crack were tO develop,:ihe Other infinite from occurring. Developing a and increase effectiveness of the tolerance [Rudd involves 1984]. designing The initial under design the then assumption focuses that flaws on making the exist in structure sufficiently tolerant to the flaws such that the structural integrity is not lost. Damage tolerant design ailows for multiple load paths to prevent the structure from failing within a specified for the benign catastrophic. time after one element failure Current mode, American tables and indices The finite element tooth Gear fails. failure, In this regard, as opposed Manufacturers to approximate method (_M) gears would to rim failure, Association be designed which (AGMA) could standards related Limited This is most three spur dimensional gears, can dimensions to modeling work likely gears has focused because requires a crack simpler geometry allows NASAJCR--2000-210062 bevel crack gear's trajectories geometry to also be introduce model modeled unique consists for a two dimensional 2 in in spiral is complex Structures with uncomplicated in two dimensions. Modeling dimensional crack representations modeling in two dimensions. A three dimensional crack for this recent numerically. on predicting a spiral representation. be modeled use the Strength characteristics of gears [AGMA 1996]. and boundary element method (BEM) are becoming more useful and common approaches to study gear designs. A primary reason is the tremendous increase in computing power. Section 1.2 summarizes research be three challenges bevel and gears. requires geometries, an object dimensions. Three that do not arise of a continuous crack simplification, a crack front. front a such as in three when When is now a