Computational Design of Rolling Bearings (eBook)

Dr. Hung Nguyen-Schäfer is a senior technical manager in development of electric machines for hybrid and electric vehicles at EM-motive GmbH, a joint company of Daimler and Bosch in Germany. He has nearly 30 years of experience in automotive industry at Robert Bosch GmbH, Bosch Mahle Turbosystems, and EM- motive. His working areas are gasoline and diesel direct injection systems, fuel supply components, anti-breaking systems, fuel-cell vehicles, automotive turbochargers, hybrid, and electric vehicles.He is also the author of three professional books:Aero and Vibro-acoustics of Automotive Turbochargers. Springer Berlin-Heidelberg (2013)Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers. Springer Berlin-Heidelberg (2014)Rotordynamics of Automotive Turbochargers, Second Edition. Springer Berlin-Heidelberg (2015)

About the Author 8
Preface 10
Contents 12
Chapter 1: Fundamentals of Rolling Element Bearings 16
1.1 Bearing Types 16
1.2 Applications of Bearings 17
1.3 Bearing Geometry 18
1.4 Curvatures of Bearings 25
1.5 Bearing Speeds 31
References 31
Chapter 2: Design of Rolling Bearings 33
2.1 Design Rule of Rolling Bearings 33
2.2 Computing Loads Acting upon Bearings 35
2.2.1 Two-Bearing Rigid Rotors 35
2.2.2 Three-Bearing Flexible Rotors 36
2.3 Basic Static Load Rating 38
2.4 Basic Dynamic Load Rating 41
2.5 Dynamic Equivalent Radial Load on Bearings 42
2.6 Load Distribution on Balls Under Dynamic Equivalent Load 44
2.7 Operating Contact Angle Under Thrust Load 50
2.8 Load Distribution on Balls Under Combined Loads 53
References 60
Chapter 3: Contact Stresses in Rolling Bearings 61
3.1 Hertzian Contact Zone 61
3.2 Procedure of Computing the Hertzian Pressure 62
3.3 Case Study of Computing the Hertzian Pressure 68
3.4 Subsurface Stress in the Hertzian Contact Zone 69
3.5 Influenced Parameters on the Hertzian Pressure 72
References 75
Chapter 4: Oil-Film Thickness in Rolling Bearings 76
4.1 Introduction 76
4.2 Hydrodynamic and Elastohydrodynamic Lubrications 76
4.3 Oil-Film Pressures in the Hertzian Contact Area 80
4.4 Computing the Oil-Film Thickness 84
4.4.1 Governing Equations of the Oil-Film Thickness 88
4.4.2 The Oil-Film Thickness in Ball Bearings 89
4.4.3 The Oil-Film Thickness in Roller Bearings 90
4.4.4 The Oil-Film Pressure Spike in Roller Bearings 91
4.5 Influence of the Oil-Film Thickness on Wear Mechanism 91
4.6 Case Study of Computing the Oil-Film Thickness 93
References 95
Chapter 5: Tribology of Rolling Bearings 96
5.1 Introduction 96
5.2 Characteristics of Lubricating Oils 96
5.3 Grease Lubrication in Rolling Element Bearings 97
5.4 HTHS Viscosity of Lubricating Oils 100
5.5 Viscosity Index of Lubricating Oils 104
5.6 Stribeck Curve 106
5.7 Surface Texture Parameters 109
5.7.1 Surface Height Profile 109
5.7.2 Surface Tribological Parameters 111
5.8 Elastic and Plastic Deformations in the Bearings 119
5.8.1 Normal Stress 120
5.8.2 Shear Stress 121
5.8.3 Friction Force in the Bearings 122
5.8.4 Friction Power in the Bearings 124
5.8.5 Mohr´s Circle Diagram 126
References 128
Chapter 6: Lifetimes of Rolling Bearings 129
6.1 Introduction 129
6.2 Fatigue Lifetime of Rolling Bearings 129
6.2.1 Extended Fatigue Lifetime 129
6.2.2 Fatigue Lifetime at Point Contact of Rolling Elements 141
6.2.3 Fatigue Lifetime at Line Contact of Rolling Elements 142
6.3 Lifetime Factor 144
6.4 Grease Lifetime in Bearings 146
6.5 Bleeding Time of Grease in Bearings 147
6.6 Case Study of Computing Lifetimes of Bearings 148
References 151
Chapter 7: Reliability Using the Weibull Distribution 152
7.1 Introduction 152
7.2 Weibull Distribution 152
7.3 Probability of Survival Samples 155
7.4 Probability Density Function 157
7.5 Time Interval Between Two Failures 159
7.6 Mean Lifetime, Variance, and Median Value 161
7.7 Percentile Lifetime 165
7.8 Estimating the Parameters of beta and eta 168
7.8.1 Weibull Plot (WP) 168
7.8.2 Computational Method of Maximum Likelihood (ML) 171
7.9 Prediction of the System Lifetime 172
7.9.1 Proof of Eq.7.33 173
7.9.2 A Computational Example 174
7.10 Hazard Rate Functions 175
7.11 Weibull Regression 177
7.12 The Monte Carlo Simulation Method 179
References 181
Chapter 8: Bearing Friction and Failure Mechanisms 182
8.1 Friction in Rolling Bearings 182
8.2 Failure Mechanisms in Rolling Bearings 184
8.2.1 Initiated Surface Microcracks 188
8.2.2 Initiated Subsurface Microcracks 190
8.2.3 False Brinelling 192
8.2.4 Surface Distress 194
References 195
Chapter 9: Rotor Balancing and NVH in Rolling Bearings 196
9.1 Reasons for Rotor Balancing 196
9.2 Kinds of Rotor Balancing 196
9.3 Two-Plane Low-Speed Balancing of a Rigid Rotor 197
9.4 Bearing Noises 204
9.4.1 Excitation Frequencies 204
9.4.2 Induced Noises in Bearing Components 208
Induced Noise of the Wavy Inner Raceway 209
Induced Noise of the Wavy Outer Raceway 210
Induced Noise of the Wavy Rolling-Element Surface 211
Induced Noise of the Diameter Deviation of Rolling Elements 211
Induced Noise of the Run-Out Cage 212
9.4.3 Bearing Defect-Related Frequencies 212
9.5 Structure-Borne and Airborne Noise 214
References 216
Appendix A: Normal Probability Density Function and Cumulative Distribution Function 217
Appendix B: Maximum Likelihood Method 220
Appendix C: Simpson´s Rule 223
Computational Results of the Simpson Code 227
Appendix D: Kinematics of Rolling Bearings 231
Appendix E: Least Squares Regression 235
Index 241