Theory and Practice of Gearing and Transmissions (eBook)

Preface 6
Contents 7
1 Prof. Faydor L. Litvin: A Life Dedicated to the Development of the Modern Theory of Gearing 10
Abstract 10
1 Introduction 11
2 Teaching, Research, and Awards 11
3 The Gear Research Center at UIC 13
4 The Gallery of Fame 14
5 Final Remarks 15
Appendix 15
References 26
2 Prof. F.L. Litvin: Contribution to the Formation of the Russian School of the Theory of Gearing 27
Abstract 27
1 Introduction 27
2 A Little Prehistory. Principles of Generation of Spatial Gearing 28
3 Kinematic Method for Investigation of Spatial Gearing 29
4 Matrix Method of Coordinate Transformation in the Theory of Gearing 31
5 General Problems of the Theory of Spatial Gearing 31
6 Geometry of Gearing for Specific Types of Gears 32
7 Investigations Made in the 1970s 33
8 Conclusion 34
Appendix 34
References 43
3 Considerations on History of Mechanism and Machine Science with an IFToMM Role for Future Developments 45
Abstract 45
1 Introduction 45
2 A Short History of MS 46
3 Challenges in MMS 49
4 IFToMM and Its Role in MMS 53
5 Conclusions 60
References 60
4 Development of the Theory and Practice of Spiroid Gears 63
Abstract 63
1 Introduction 63
2 Development of the Theory and Practice of Spiroid Gearbox Design 65
3 Mastering the Production of Spiroid Gears and Gearboxes 70
4 Conclusion 72
References 72
5 Cause of Failure Beyond Conjugate Theory of Gear Meshing 75
Abstract 75
1 Introduction 75
2 Examples of Failure 76
3 Contact of Tooth Tip Edge and Stress Distribution Over Tooth Form 78
4 Increase of Rotational Delay Due to Lead Crowning and Tooth Form Correction 82
5 Trochoidal Interference and Mal-Effect on Surface Durability 83
6 Contact of Tooth Side Edge 85
7 Merging of Subsurface Cracks from Side and Root 93
8 Crush of Wear Debris 94
9 Positive Feedback System of Failure Development 101
10 Conclusions 103
Appendix 103
References 104
6 Several Issues of Tooth Generating Process by Two-Parametric Families of Generating Lines 105
Abstract 105
1 Introduction 105
1.1 Formation of Spiroid Gearwheel Teeth by a Generating Line---Cutting Edge of the Fly Cutter 106
1.2 Formation of Spiroid Gearwheel Teeth by a Generating Line---Cutting Edge of the Cutter of the Flat Cutter Head 108
1.3 Formation of Multithread Worms by a Generating Line---Cutting Edge of the Face Cutter Head 110
1.4 Practical Implementation and Prospects 111
1.5 Choice of Generating Parameters 113
1.6 Pairs of Remarkable Straight Lines 116
1.7 Are Parameters Independent While Tooth Machining? Can the Relation Between Them Be Changed Arbitrarily in Real Tooth Cutting? 119
1.8 Is It Possible to Generate Teeth by Means of the Family of Generating Lines with a Number of Independent Parameters Greater Than 2? 121
1.9 About Terminology 122
2 Conclusion 123
References 123
7 Direct Gear Design for Asymmetric Tooth Gears 125
Abstract 125
1 Introduction 125
2 Geometry of Asymmetric Tooth Gears 127
3 Gear Mesh Characteristics 131
4 Asymmetric Tooth Gearing Limits 134
5 Tooth Geometry Optimization 137
5.1 Asymmetry Factor K Selection for Reversible Asymmetric Tooth Gears 137
5.2 Root Fillet Optimization 139
6 Analytical and Experimental Comparison Symmetric and Asymmetric Tooth Gears 141
7 Implementation of Asymmetric Tooth Gears 146
References 150
8 Analogs of Axes of Meshing in General Type Worm Gearing 152
Abstract 152
1 General Type Worm Gears 152
2 Axes of Meshing and Their Analogs in General Type Worm Gears 155
3 Modified Double-Enveloping Worm Gears 158
4 Gears with Bevel Worms 161
5 Gears with Face Worms 162
6 Gears with Cylindrical Worms 163
7 Conclusion 164
References 164
9 Development of Kinematic Method of Theory of Gearing to Determine Areas of Tooth Flanks Produced by Jogs of Generating Solids 166
Abstract 166
1 Problem Analysis and Investigation Tasks 166
1.1 Problem Analysis 166
1.2 Possible Ways of Solving the Problem 168
1.3 Proposed Solution 170
2 Equations of Generating According to the Classical Theory of Gearing 170
3 Types of Jog and Geometrical Images Produced by Them 173
4 Peculiarities of Developing Mathematical Models When Generating by Jogs 175
5 Generation of Lines by Jogs of Profiles in Planar Gearing 177
5.1 Theory of Generation by Plane Jog 177
5.2 Examples of Investigating Planar Gearing 180
5.2.1 Example 1. Generation of the Cylindrical Gearwheel Root 180
5.2.2 Example 2. Cutting the Involute Gearwheels with Internal Teeth 180
6 Generation of Surfaces by Edge Jogs of Solids 185
7 Generation of Surfaces by Vertex Jogs of Solids 189
8 Summary 193
References 194
10 Damage Types, Load Capacity and Efficiency of Crossed Helical Gears with Wheels from Sintered Steel 196
Abstract 196
1 Introduction 197
2 Characteristics of Materials 199
2.1 Chemical Composition of Sintered Steel and Material Variants 199
2.2 Material Tests 199
2.2.1 Density of Test Gears 199
2.2.2 Hardness Test 201
2.2.3 E--Module 203
2.2.4 Poisson'S Ratio 204
2.2.5 Tensile Test 204
3 Test Conditions 206
4 Microstructure of the Tested Materials 207
4.1 Additional Hardening 207
4.2 Microstructure 210
5 Lubrication 212
5.1 Synthetic Oil 212
5.2 Mineral Oil 213
5.3 Grease 214
6 Hertzian Contact Stress 215
7 Damage Types and Load Capacity 217
7.1 Wear 217
7.2 Pitting 222
7.3 Scuffing 224
7.4 Scoring 225
7.5 Load Capacity 227
8 Experimental and Theoretical Research of Efficiency 227
8.1 Overall Efficiency 227
8.2 Influence of Temperature 230
8.3 Prediction of Wheel Tooth Mass Temperature by FEA 231
9 Summary 233
References 238
11 Modern Methods of Calculation and Increasing the Load-Carrying Capacity of Surface-Hardened Gears of Transmissions and Drives 240
Abstract 240
1 Contact Strength of Parts with Hardened Surface Layer or Wear-Resistant Coating 240
1.1 Model of Depth Contact Failure of Loaded Parts with Structurally Non-uniform Hardened Surface Layer 240
1.2 Principles of Hardness Change in Surface Layer After Surface Hardening 245
1.3 Conditions of Plastic Deformation Appearance and Calculation of Load-Carrying Capacity at Maximum Load 248
2 Methods of Analysis of Surface-Hardened Involute Gearwheels for Depth Contact Strength 258
2.1 Methods of Analysis of Case-Hardened, Nitro-Carburized and Laser-Hardened Teeth for Depth Contact Strength at Static Loads (Overloads) 258
2.2 Method of Depth Contact Strength Analysis at Cyclic Loads 261
2.3 Application Area of Depth Contact Strength Analysis 264
References 268
12 Kinematical and Efficiency Analysis of Planetary Gear Trains by Means of Various Graph-Based Approaches 269
Abstract 269
1 Introduction 269
2 Related Work 271
3 Graph-Based Models of Planetary Gears 272
3.1 Mixed Graphs 273
3.2 Contour Graphs 274
3.3 Bond Graphs 275
4 Exemplary Gear and Assigned Graph-Based Models 277
4.1 Graph-Based Models of the Gear (Drive DE2) 279
4.2 Willis Method for Drive DE2 285
4.3 Graph-Based Models of the Gear (Reversed Drive) 285
5 Efficiency of Meshing for the Selected Drives 287
5.1 Efficiency of Meshing for the Second Economic Drive DE2 287
5.2 Efficiency of Meshing for the Reverse Drive 289
6 Conclusion 289
References 290
13 Rational Designs of Planetary Transmissions, Geometry of Gearing and Strength Parameters 291
Abstract 291
1 Introduction 291
2 Rational Design of Planetary Transmissions with Internal Engagement 292
3 Geometry of Internal Engagement of Gearwheels with Non-standard (Modified) Basic Rack Profile 294
4 Evaluation of Gearwheel Tooth Strength and Gear Load-Carrying Capacity 300
5 Experimental Investigation of Planetary Transmissions with Internal Gearing 303
6 Conclusion 305
References 305
14 Compensation of Errors of Alignment Caused by Shaft Deflections in Spiral Bevel Gear Drives 307
Abstract 307
1 Introduction 307
2 Development of the Finite Element Model of a Complete Spiral Bevel Gear Drive 309
3 Analytical Determination of Relative Errors of Alignment in Spiral Bevel Gear Drives 312
3.1 Definition and Computation of Reference Points 313
3.2 Computation of Relative Alignment Errors 316
4 Brief Description of Computational Procedure for Compensation of Errors of Alignment 317
5 Numerical Example 317
6 Conclusions 324
Acknowledgments 324
References 325
15 Ease-Off and Application in Tooth Contact Analysis for Face-Milled and Face-Hobbed Spiral Bevel and Hypoid Gears 326
Abstract 326
1 Introduction 326
2 Face Milling and Face Hobbing 327
3 Definition of Ease-Off 328
4 Ease-Off Topography 331
5 Tooth Contact Analyses Using Ease-Off Concept 332
6 Numerical Examples 340
7 Conclusions 343
References 344
16 Methods and Results of Composite Gears Design 345
Abstract 345
1 Introduction 345
2 Calculation Methods for Composite Gears 346
2.1 Simplified Description of the Stress-Strain Properties of Composite Materials 346
2.2 Detailed Description of the Stress-Strain Properties of Composite Materials 350
2.3 Determination of Wear Resistance of the Gears Made of Composite Materials by Calculations 352
2.4 Three-Level Method of Designing Gears Made of Disperse-Reinforced Composites 356
3 Consideration of Specific Features of Polymer Materials in Assessing Deformability of Gears 360
3.1 Analysis of the Influence of a Material's Poisson's Ratio on Gear Deformability 360
3.2 Analysis of the Influence of a Material's Viscoelasticity on Composite Gear Deformability 365
3.3 Example of Calculation of the Composite Gears on Wear Resistance 368
4 Conclusions 371
References 371
17 Selection of Overlap Ratios in Helical Gear with Low Vibration Excitation 373
Abstract 373
References 384
18 Terminology and Design of Asymmetrical Gears for Aircraft 385
Abstract 385
1 Introduction 385
2 Terminology 386
2.1 Design Terminology 386
2.2 Manufacturing Terminology 386
3 Key Rule of Asymmetrical Teeth Designing 386
4 Selection of Optimal Geometry 387
5 The Factor YFS Considering the Teeth Form and Stress Concentration at a Root Fillet of Teeth 387
6 Specific Stiffness C2032 388
7 Example of Calculation of a Gear with Asymmetrical Teeth 389
8 Example of Calculation of a Gear with HCR Teeth 394
9 Summary 394
References 396
19 Quality Control of Spur Gears on the Basis of Simulating Their Production Processes 397
Abstract 397
1 Introduction 397
2 Experimental Investigations of Spur Gear Production Processes 398
3 Theoretical Principles of Modeling the Production Process for Spur Gears 398
4 Main Results of Production Process Analysis for Spur Gears 402
5 Design Techniques for the Manufacture of Spur Gears that Provide Their Quality 403
6 Summary 407
References 407
20 New Concept of the Process of Designing Gearboxes and Gear Systems 408
Abstract 408
1 Introduction 408
2 Classical Approach to the Design of Gearboxes 409
3 New Approach to the Process of Gearbox Design 411
4 Conclusions 424
References 425
21 Design of Shaping Machine and Tooling Systems for Gear Manufacturing 427
Abstract 427
1 Introduction 428
2 Mathematical Model of the Kinematic Scheme 429
3 Classification of Kinematic Schemes 433
4 Synthesis of the Machine Tool Layout 435
5 Optimized Synthesis Layouts Shaping Machine Tools 437
6 Determining Possible Configurations of a Machine Tool's Structure 439
7 Structural Extraction of a Subset of Configurations 442
8 Conclusion and Prospect 450
References 451