Rolling Bearing Analysis FIFTH EDITION Essential Concepts of Bearing Technology Tedric A. Harris Michael N. Kotzalas ( C\ Taylor & Francis \0t*' ) Taylors«.Francis Group Boca Raton London New York CRC is an imprint of the Taylor & Francis Group, an informa business
Table of Contents Chapter 1 Rolling Bearing Types and Applications 1 1.1 Introduction to Rolling Bearings 1 1.2 Ball Bearings 10 1.2.1 Radial Ball Bearings 10 1.2.1.1 Single-Row Deep-Groove Conrad-Assembly Ball Bearing 10 1.2.1.2 Single-Row Deep-Groove Filling-Slot Assembly Ball Bearings 14 1.2.1.3 Double-Row Deep-Groove Ball Bearings 15 1.2.1.4 Instrument Ball Bearings 15 1.2.2 Angular-Contact Ball Bearings 17 1.2.2.1 Single-Row Angular-Contact Ball Bearings 17 1.2.2.2 Double-Row Angular-Contact Ball Bearings 17 1.2.2.3 Self-Aligning Double-Row Ball Bearings 18 1.2.2.4 Split Inner-Ring Ball Bearings 21 1.2.3 Thrust Ball Bearings 22 1.3 Roller Bearings 22 1.3.1 General 22 1.3.2 Radial Roller Bearings 23 1.3.2.1 Cylindrical Roller Bearings 23 1.3.2.2 Needle Roller Bearings 23 1.3.3 Tapered Roller Bearings 25 1.3.4 Spherical Roller Bearings 28 1.3.5 Thrust Roller Bearings 32 1.3.5.1 Spherical Roller Thrust Bearings 32 1.3.5.2 Cylindrical Roller Thrust Bearings 32 1.3.5.3 Tapered Roller Thrust Bearings 32 1.3.5.4 Needle Roller Thrust Bearings 33 1.4 Linear Motion Bearings 34 1.5 Bearings for Special Applications 35 1.5.1 Automotive Wheel Bearings 35 1.5.2 Cam Follower Bearings 38 1.5.3 Aircraft Gas Turbine Engine and Power Transmission Bearings 39 1.6 Closure 40 References 40 Chapter 2 Rolling Bearing Macrogeometry 43 2.1 General 44 2.2 Ball Bearings 44 2.2.1 Osculation 45 2.2.2 Contact Angle and Endplay 45 2.2.3 Free Angle of Misalignment 49 2.2.4 Curvature and Relative Curvature 50
2.3 Spherical Roller Bearings 53 2.3.1 Pitch Diameter and Diametral Play 53 2.3.2 Contact Angle and Free Endplay 53 2.3.3 Osculation 54 2.3.4 Curvature 54 2.4 Radial Cylindrical Roller Bearings 55 2.4.1 Pitch Diameter, Diametral Clearance, and Endplay 55 2.4.2 Curvature 56 2.5 Tapered Roller Bearings 56 2.5.1 Pitch Diameter 56 2.5.2 Endplay 57 2.5.3 Curvature 58 2.6 Closure 58 References 59 Chapter 3 Interference Fitting and Clearance 61 3.1 General 62 3.2 Industrial, National, and International Standards 62 3.2.1 Method of Establishment and Scope 62 3.2.2 Tolerances for Press-Fitting of Bearing Rings on Shafts and in Housings 62 3.3 Effect of Interference Fitting on Clearance 65 3.4 Press Force 69 3.5 Differential Expansion 69 3.6 Effect of Surface Finish 70 3.7 Closure 70 References 71 Chapter 4 Bearing Loads and Speeds 73 4.1 General 74 4.2 Concentrated Radial Loading 74 4.2.1 Bearing Loads 74 4.2.2 Gear Loads 76 4.2.3 Belt-and-Pulley and Chain Drive Loads 77 4.2.4 Friction Wheel Drives 78 4.2.5 Dynamic Loading Due to an Eccentric Rotor 78 4.2.6 Dynamic Loading Due to a Crank-Reciprocating Load Mechanism 79 4.3 Concentrated Radial and Moment Loading 81 4.3.1 Helical Gear Loads 82 4.3.2 Bevel Gear Loads 82 4.3.3 HypoidGear 86 4.3.4 WormGear 87 4.4 Shaft Speeds 88 4.5 Distributed Load Systems 90 4.6 Closure 91 References 91 Chapter 5 Ball and Roller Loads Due to Bearing Applied Loading 93 5.1 General 93 5.2 Ball-Raceway Loading 94
5.3 Symmetrical Spherical Roller-Raceway Loading 94 5.4 Tapered and Asymmetrical Spherical Roller-Raceway and Roller-Flange Loading 95 5.5 Cylindrical Roller-Raceway Loading 96 5.5.1 Radial Loading 96 5.5.2 Roller Skewing Moment 98 5.6 Closure 99 Chapter 6 Contact Stress and Deformation 101 6.1 General 102 6.2 Theory of Elasticity 102 6.3 Surface Stresses and Deformations 106 6.4 Subsurface Stresses 114 6.5 Effect of Surface Shear Stress 120 6.6 Types of Contacts 123 6.7 Roller End-Flange Contact Stress 130 6.8 Closure 133 References 133 Chapter 7 Distributions of Internal Loading in Statically Loaded Bearing 135 7.1 General 136 7.2 Load-Deflection Relationships 136 7.3 Bearings under Radial Load 137 7.4 Bearings under Thrust Load 141 7.4.1 Centric Thrust Load 141 7.4.2 Angular-Contact Ball Bearings 141 7.4.3 Eccentric Thrust Load 144 7.4.3.1 Single-Direction Bearings 144 7.4.3.2 Double-Direction Bearings 146 7.5 Bearings under Combined Radial and Thrust Load 148 7.5.1 Single-Row Bearings 148 7.5.2 Double-Row Bearings 153 7.6 Closure 156 References 157 Chapter 8 Bearing Deflection and Preloading 159 8.1 General 160 8.2 Deflections of Bearings with Rigidly Supported Rings 160 8.3 Preloading 161 8.3.1 Axial Preloading 161 8.3.2 Radial Preloading 165 8.3.3 Preloading to Achieve Isoelasticity 165 8.4 Limiting Ball Bearing Thrust Load 166 8.4.1 General Considerations 166 8.4.2 Thrust Load Causing Ball to Override Land 167 8.4.3 Thrust Load Causing Excessive Contact Stress 170
8.5 Closure 170 References 170 Chapter 9 Permanent Deformation and Bearing Static Capacity 171 9.1 General 172 9.2 Calculation of Permanent Deformation 172 9.3 Static Load Rating of Bearings 174 9.4 Static Equivalent Load 176 9.5 Fracture of Bearing Components 177 9.6 Permissible Static Load 178 9.7 Closure 179 References 179 Chapter 10 Kinematic Speeds, Friction Torque, and Power Loss 181 10.1 General 182 10.2 Cage Speed 182 10.3 Rolling Element Speed 183 10.4 Rolling Bearing Friction 184 10.5 Rolling Bearing Friction Torque 185 10.5.1 Ball Bearings 185 10.5.1.1 Torque Due to Applied Load 185 10.5.1.2 Torque Due to Lubricant Viscous Friction 186 10.5.1.3 Total Friction Torque 186 10.5.2 Cylindrical Roller Bearings 187 10.5.2.1 Torque Due to Applied Load 187 10.5.2.2 Torque Due to Lubricant Viscous Friction 187 10.5.2.3 Torque Due to Roller End-Ring Flange Sliding Friction 187 10.5.2.4 Total Friction Torque 188 10.5.3 Spherical Roller Bearings 188 10.5.3.1 Torque Due to Applied Load 188 10.5.3.2 Torque Due to Lubricant Viscous Friction 189 10.5.3.3 Total Friction Torque 189 10.5.4 Needle Roller Bearings 189 10.5.5 Tapered Roller Bearings 190 10.5.6 High-Speed Effects 192 10.6 Bearing Power Loss 192 10.7 Thermal Speed Ratings 192 10.8 Closure 193 References 193 Chapter 11 Fatigue Life: Basic Theory and Rating Standards 195 11.1 General 197 11.2 Rolling Contact Fatigue 197 11.2.1 Material Microstructure before Bearing Operation 197 11.2.2 Alteration of the Microstructure Caused by Over-Rolling 197 11.2.3 Fatigue Cracking and Raceway Spalling Caused by Over-Rolling 200 11.2.4 Fatigue Failure-Initiating Stress and Depth 201
11.3 Fatigue Life Dispersion 201 11.4 Weibull Distribution 204 11.5 Dynamic Capacity and Life of a Rolling Contact 208 11.5.1 Line Contact 214 11.6 Fatigue Life of a Rolling Bearing 215 11.6.1 Point-Contact Radial Bearings 215 11.6.2 Point-Contact Thrust Bearings 224 11.6.3 Line-Contact Radial Bearings 229 11.6.4 Line-Contact Thrust Bearings 233 11.6.5 Radial Roller Bearings with Point and Line Contact 234 11.6.6 Thrust Roller Bearing with Point and Line Contact 237 11.7 Load Rating Standards 238 11.8 Effect of Variable Loading on Fatigue Life 240 11.9 Fatigue Life of Oscillating Bearings 243 11.10 Reliability and Fatigue Life 248 11.11 Closure 251 References 252 Chapter 12 Lubricants and Lubrication Techniques 255 12.1 General 255 12.2 Types of Lubricants 255 12.2.1 Selection of Lubricant Type 255 12.2.2 Liquid Lubricants 256 12.2.3 Greases 256 12.2.4 Polymerie Lubricants 256 12.2.5 Solid Lubricants 256 12.3 Liquid Lubricants 256 12.3.1 Types of Liquid Lubricants 256 12.3.1.1 Mineral Oil 256 12.3.1.2 Synthetic Oils 257 12.3.1.3 Environmental^ Acceptable Oils 257 12.3.2 Base Stock Lubricant 259 12.3.3 Properties of Base Liquid Lubricants 259 12.3.3.1 Viscosity 259 12.3.3.2 Viscosity Index 259 12.3.3.3 Pour Point 260 12.3.3.4 Flash Point 260 12.3.3.5 Evaporation Loss 260 12.3.4 Lubricant Additive 260 12.3.4.1 Purpose 260 12.3.4.2 VI Improvers 261 12.3.4.3 Extreme Pressure/Antiwear 261 12.3.4.4 Other Additives 262 12.4 Grease 262 12.4.1 How Grease Lubrication Functions 262 12.4.2 Advantages of Grease Lubrication 262 12.4.3 Types of Greases 262 12.4.3.1 General 262 12.4.3.2 Lithium Soap Greases 263
12.4.3.3 Calcium Soap Greases 263 12.4.3.4 Sodium Soap Greases 263 12.4.3.5 Aluminum Complex Greases 263 12.4.3.6 Nonsoap-Base Greases 264 12.4.3.7 Inorganic Thickeners for Grease 264 12.4.3.8 Combining Greases 264 12.4.4 Grease Properties 264 12.4.4.1 Properties of Retained Oil 264 12.4.4.2 Dropping Point 264 12.4.4.3 Low-Temperature Torque 264 12.4.4.4 Oil Separation 265 12.4.4.5 Penetration 265 12.5 Solid Lubricants 265 12.6 Lubricant Delivery Systems 266 12.6.1 Oil Bath/Splash Oil 266 12.6.2 Circulating Oil 267 12.6.3 Air-Oil/Oil Mist 268 12.6.4 Grease 268 12.6.5 Polymerie Lubricant 269 12.7 Seals 270 12.7.1 Function of Seals 270 12.7.2 Types of Seals 271 12.7.2.1 Labyrinth Seals 271 12.7.2.2 Shields 272 12.7.2.3 Elastomeric Lip Seals 272 12.7.2.4 Garter Seals 274 12.8 Closure 275 References 276 Chapter 13 Structural Materials of Bearings 277 13.1 General 277 13.2 Rolling Bearing Steels 277 13.2.1 Types of Steels for Rolling Components 277 13.2.2 Through-Hardening Steels 277 13.2.3 Case-Hardening Steels 278 13.2.4 Steels for Special Bearings 278 13.3 Steel Manufacture 280 13.3.1 Melting Methods 280 13.3.2 Raw Materials 280 13.3.3 Basic Electric Furnace Process 281 13.3.4 Vacuum Degassing of Steel 281 13.3.5 Ladle Furnace 281 13.3.6 Methods for Producing Ultraliigh-Purity Steel 282 13.3.6.1 Vacuum Induction Melting 282 13.3.6.2 Vacuum Are Remelting 283 13.3.6.3 Electroslag Refining 283 13.3.7 Steel Products 284 13.3.8 Steel Metallurgical Characteristics 284
13.3.8.1 Cleanliness 284 13.3.8.2 Segregation 286 13.3.8.3 Structure 287 13.4 Effects of Processing Methods on Steel Components 287 13.5 Heat Treatment of Steel 288 13.5.1 Basic Principles 288 13.5.2 Time-Temperature Transformation Curve 290 13.5.3 Continuous Cooling Transformation Curves 290 13.5.4 Hardenability 291 13.5.5 Hardening Methods 293 13.5.6 Through-Hardening, High-Carbon-Chromium Bearing Steels 294 13.5.6.1 General Heat Treatment 294 13.5.6.2 Martensite 294 13.5.6.3 Marquenching 294 13.5.6.4 Bainite 294 13.5.7 Surface Hardening 295 13.5.7.1 Methods 295 13.5.7.2 Carburizing 295 13.5.7.3 Carbonitriding 296 13.5.7.4 Induction Heating 297 13.5.7.5 Flame-Hardening 298 13.5.8 Thermal Treatment for Structural Stability 298 13.5.9 Mechanical Properties Affected by Heat Treatment 300 13.5.9.1 Elasticity 300 13.5.9.2 Ultimate Strength 300 13.5.9.3 Fatigue Strength 300 13.5.9.4 Toughness 301 13.5.9.5 Hardness 301 13.5.9.6 Residual Stress 302 13.6 Materials for Special Bearings 303 13.7 Cage Materials 306 13.7.1 Material Types 306 13.7.2 Low-Carbon Steel 307 13.7.3 Brass 307 13.7.4 Bronze 307 13.7.5 Polymerie Cage Materials 307 13.7.5.1 Advantages and Disadvantages 307 13.7.5.2 Rolling Bearing Polymer Cages 308 13.7.6 High-Temperature Polymers 312 13.8 Seal Materials 313 13.8.1 Function, Description, and Illustration 313 13.8.2 Elastomeric Seal Materials 313 13.9 Tribological Coatings for Bearing Components 317 13.9.1 Coatings in General 317 13.9.2 Coating Deposition Processes 317 13.9.2.1 General 317 13.9.2.2 Chemical Conversion Coatings 317 13.9.2.3 Electroplating and Electroless Plating 318 13.9.2.4 Chemical Vapor Deposition 318 13.9.2.5 Physical Vapor Deposition 318
13.9.3 Surface Treatments for Mitigation of Damage Mechanisms Associated with Severe Operating Conditions 319 13.9.3.1 General 319 13.9.3.2 Interruption or Lack of Lubricant Supply to the Bearing 319 13.9.3.3 False Brinelling 320 13.9.3.4 Indentations Caused by Hard Particle Contaminants 321 13.9.3.5 Severe Wear (Galling or Smearing) 321 13.9.3.6 Surface-Initiated Fatigue 323 13.10 Closure 325 References 326 Chapter 14 Vibration, Noise, and Condition Monitoring 329 14.1 General 329 14.2 Vibration- and Noise-Sensitive Applications 330 14.2.1 Significance of Vibration and Noise 330 14.2.2 Noise-Sensitive Applications 330 14.2.3 Vibration-Sensitive Applications 331 14.3 The Role of Bearings in Machine Vibration 332 14.3.1 Bearing Effects on Machine Vibration 332 14.3.2 Structural Elements 333 14.3.3 Variable Elastic Compliance 333 14.3.4 Geometrie Imperfections 334 14.3.4.1 General 334 14.3.4.2 Microscale 335 14.3.4.3 Waviness and Other Form Errors 335 14.3.5 Waviness Model 337 14.4 Measurement of Nonroundness and Vibration 340 14.4.1 Waviness Testing 340 14.4.2 Vibration Testing 341 14.4.3 Bearing Pass Frequencies 341 14.4.4 Relation of Vibration and Waviness or Other Defects 343 14.5 Detection of Failing Bearings in Machines 344 14.6 Condition-Based Maintenance 348 14.7 Closure 353 References 354 Appendix 355 Index 359