Advanced Dynamics of Rolling Elements

1. Introduction.- 1.1 Rolling Bearing Elements and Basic Interactions.- 1.2 Types of Analytical Models.- 1.2.1 Quasi-Static Model.- 1.2.2 Dynamic Model.- 1.3 Nomenclature.- 1.3.1 Coordinate Frames.- 1.3.2 Vector Transformations.- 1.3.3 List of Symbols.- 1.4 Summary.- 2. Equations of Motion and Coordinate Transformations.- 2.1 Coordinate Frames and Transformations.- 2.2 Equations of Motion.- 2.2.1 Mass Center Motion.- 2.2.2 Rotational Motion.- 2.3 Moving Coordinate Frames.- 2.4 General Motion Simulation.- 2.5 Summary.- 3. Geometric Interactions in Rolling Bearings.- 3.1 Rolling Element/Race Interactions.- 3.1.1 Ball/Race Interactions.- 3.1.2 Roller/Race Interactions.- 3.1.3 Roller/Race-Flange Interactions.- 3.2 Rolling Element/Cage Interactions.- 3.2.1 Geometric and Kinematic Considerations.- 3.2.2 Hydrodynamic Models.- 3.2.3 Dry Contact Models.- 3.3 Race/Cage Interactions.- 3.3.1 Geometric and Kinematic Considerations.- 3.3.2 Hydrodynamic Models.- 3.3.3 Dry Contact Models.- 3.4 Interactions Between Rolling Elements.- 3.4.1 Ball Bearings.- 3.4.2 Roller Bearings.- 3.5 External System Interactions and Constraints.- 3.5.l Equilibrium Constraint for Ball Bearings.- 3.5.2 Equilibrium Constraint for Roller Bearings.- 3.6 Summary.- 4. Elastohydrodynamic Lubrication.- 4.1 General Consideration in Lubricant Traction Modeling.- 4.1.1 Rolling Element/Race Contact Zone.- 4.1.2 Lubricant Rheology.- 4.1.3 Typical Traction-Slip Behavior.- 4.2 An E1astohydrodynamic Traction Model.- 4.2.1 Film Thickness Computation.- 4.2.2 Computation of Traction.- 4.2.3 Estimation of Lubricant Constitutive Equation.- 4.3 Traction Behavior of Some Lubricants.- 4.3.1 U.S. Specification MIL-L-23699.- 4.3.2 U.S. Specification MIL-L-7808.- 4.3.3 Traction Fluid Santotrac 30.- 4.3.4 Polyphenyl Ether.- 4.3.5 SAE-30-Type Oil.- 4.4 Summary.- 5. Churning and Drag Losses.- 5.l Estimation of Drag Forces.- 5.2 Estimation of Churning Moments.- 5.2.1 Loss on the Cylindrical Surface.- 5.2.2 Loss on the End Surface.- 5.3 Effective Lubricant Viscosity and Density.- 5.4 Summary.- 6. Numerical Integration of the Equations of Motion.- 6.1 Dimensional Organization.- 6.2 Explicit Algorithms.- 6.2.1 Step-Changing Criterion.- 6.3 Implicit Algorithms.- 6.3.1 Predictor Formula.- 6.3.2 Corrector Formula.- 6.3.3 Step-Changing Criterion.- 6.3.4 Change of Order.- 6.3.5 Computational Considerations.- 6.4 Selection of a Method.- 6.5 External Constraints.- 6.5.1 Equilibrium Constraints.- 6.5.2 Fictitious Damping.- 6.6 Summary.- 7. The Computer Program ADORE.- 7.1 Program Overview.- 7.2 Structure of ADORE.- 7.3 ADORE Capabilities.- 7.3.1 Bearing Types.- 7.3.2 Types of Cages.- 7.3.3 Operating Conditions.- 7.3.4 External Constraints.- 7.3.5 Radial Preloads.- 7.3.6 Material Properties.- 7.3.7 Lubricant Traction.- 7.3.8 Churning and Drag.- 7.3.9 Roller Skew.- 7.3.10 Rolling Element Skid.- 7.3.11 Cage Instability.- 7.3.12 Bearing Power Loss.- 7.3.13 Wear.- 7.3.14 Geometric Imperfections.- 7.3.15 Bearing Noise.- 7.3.16 Bearing Life for Arbitrary Load and Speed Cycles.- 7.3.17 Flexibility in Units.- 7.3.18 Graphic Output.- 7.3.19 Integrating Algorithms.- 7.3.20 Restart Capabilities.- 7.4 Input/Output Data.- 7.4.1 Input Data.- 7.4.2 Print Output.- 7.4.3 Plot Output.- 7.4.4 User-Programmable Subroutines.- 7.4.5 Data Management in ADORE.- 7.5 Computer Resource Requirement.- 7.6 Summary.- 8. Some Dynamic Performance Simulations.- 8.1 Numerical Considerations.- 8.2 Vibrational Characteristics.- 8.2.1 Cylindrical Roller Bearings.- 8.2.2 Ball Bearings.- 8.3 General Ball Motion and Skid.- 8.4 Cage Stability.- 8.5 Roller and Cage Motion in Cylindrical Roller Bearings.- 8.5.1 Roller Misalignment and Skew.- 8.5.2 Time-Varying Loads and Speeds.- 8.6 Summary.- 9. Experimental Validation of ADORE.- 9.1 Ball Motion and Skid.- 9.2 Cage Motion.- 9.2.1 Cage Mass Center Orbit.- 9.2.2 Whirl Velocities.- 9.2.3 Coning Motion of Cage.- 9.3 Summary.- 10. Guidelines for Rolling Bearing Design.- 10.1 System Overview.- 10.2 Rotor-Bearing System Interaction.- 10.3 ADORE: A Design and Performance Diagnosis Tool.- 10.4 Summary.- Appendix I: Hertz Point-Contact Solutions.- Appendix II: Shrink Fit and Thermal Expansion of Races.- Appendix III: Fatigue Life Computation.- Appendix IV: Source Listing of ADORE.- Appendix V: Typical Example.- References.- Author Index.