Friction torque

Abstract: : A model is developed for sliding and rolling friction that can be used in simulations of dynamic systems involving mechanical elements that are subject to friction. Sound bases for the model are developed around the hypothesis that the origin of friction is in quasi static contact bonds that are continuously formed and subsequently broken. Sliding friction, including coulomb friction and the so-called 'stiction,' as well as rolling friction are believed to be realistically simulated by the model. The model has been proven to accurately simulate transient torque and rate measurements on ball bearings tested in the laboratory.

Abstract: 1. Introduction.- 2. Friction in Machines.- 2.1. The Contemporary Model of Machine Friction.- 2.2. Boundary Lubricants: a Domain of Many Choices.- 2.3. Relaxation Oscillations.- 2.4. Friction Modeling in the Controls Literature.- 2.5. An Integrated Friction Model.- 3. Experiment Design.- 4. Repeatability.- 5. Break-Away Experiments.- 5.1. Experimental Issues in Measuring Break-Away Torque.- 5.2. Building the Compensation Table.- 6. Friction as a Function of Velocity.- 6.1. Analysis of Variance in the Motion Friction Data.- 6.2. Friction at Low Velocities.- 6.3. Friction During Compliant Motion.- 6.4. The Dahl Effect.- 6.5. The Stribeck Effect.- 6.6. Temporal Effects in the Rise and Decay of Friction.- 6.7. Variance in Friction as Process Noise.- 7. Analysis of Stick-Slip.- 7.1. Dimensional Analysis.- 7.2. Perturbation Analysis.- 7.3. The Impact of Static Friction Rising as a Function of Dwell Time.- 7.4. Integral Control.- 8. Demonstrations of Friction Compensation.- 8.1. Open-Loop Motion of One Joint.- 8.2. Open-Loop Motion of Three Joints.- 8.3. Friction Compensated Force Control.- 9. Suggestions Toward Friction Modeling and Compensation.- 9.1. Suggestions on Experimental Technique.- 9.2. Suggestions on Control.- 9.3. Conclusion.- Appendix A: Small Studies.- A.1 Friction as a Function of Motor Angle.- A.2 Joint 2 Motor Alone and Joint 2 Link Alone.- A.3 Trials with Dither.- A.4 Friction as a Function of Load.- A.5 Creep.- A.6 Effects that were not Observed.

Abstract: Friction force between sliding surfaces arises due to varied and complex mechanisms and can be responsible for undesirable dynamic characteristics in many mechanical systems. Controversies over the theory of friction have been reported in the literature. Friction laws are phenomenological in charcacter since they are based on observable and measurable quantities. The mechanics of contact and friction in metal-metal and elastomer-metal contact surfaces are reviewed. Unfortunately, there is no satisfactory method capable of determining or measuring the area of contact between sliding bodies. Both dry friction and lubricated friction are considered. The modeling of the friction force in mechanical systems depends on several factors. These include the material properties and geometry of the sliding surfaces, surface roughness, surface chemistry, sliding speed, temperature, and normal load. Other factors include the effect of normal and tangential vibrations on the static friction. Here the static friction is considered as a special case of kinetic friction. This background is essential for dynamicists studying friction-induced vibration, chatter, squeal and chaos topics which will be presented in the second part.

Abstract: ROLLING BEARING TYPES AND APPLICATIONS Introduction to Rolling Bearings Ball Bearings Roller Bearings Linear Motion Bearings Bearings for Special Applications Closure References ROLLING BEARING MACROGEOMETRY General Ball Bearings Spherical Roller Bearings Radial Cylindrical Roller Bearings Tapered Roller Bearings Closure References INTERFERENCE FITTING AND CLEARANCE General Industrial, National, and International Standards Effect of Interference Fitting on Clearance Press Force Differential Expansion Effect of Surface Finish Closure References BEARING LOADS AND SPEEDS General Concentrated Radial Loading Concentrated Radial and Moment Loading Shaft Speeds Distributed Load Systems Closure References BALL AND ROLLER LOADS DUE TO BEARING APPLIED LOADING General Ball-Raceway Loading Symmetrical Spherical Roller-Raceway Loading Tapered and Asymmetrical Spherical Roller-Raceway and Roller-Flange Loading Cylindrical Roller-Raceway Loading Closure CONTACT STRESS AND DEFORMATION General Theory of Elasticity Surface Stresses and Deformations Subsurface Stresses Effect of Surface Shear Stress Types of Contacts Roller End-Flange Contact Stress Closure References DISTRIBUTION OF INTERNAL LOADING IN STATICALLY LOADED BEARING General Load-Deflection Relationships Bearings under Radial Load Bearings under Thrust Load Bearings under Combined Radial and Thrust Load Closure References BEARING DEFLECTION AND PRELOADING General Deflections of Bearings with Rigidly Supported Rings Preloading Limiting Ball Bearing Thrust Load Closure References PERMANENT DEFORMATION AND BEARING STATIC CAPACITY General Calculation of Permanent Deformation Static Load Rating of Bearings Static Equivalent Load Fracture of Bearing Components Permissible Static Load Closure References KINEMATIC SPEEDS, FRICTION TORQUE, AND POWER LOSS General Cage Speed Rolling Element Speed Rolling Bearing Friction Rolling Bearing Friction Torque Bearing Power Loss Thermal Speed Ratings Closure References FATIGUE LIFE: BASIC THEORY AND RATING STANDARDS General Rolling Contact Fatigue Fatigue Life Dispersion Weibull Distribution Dynamic Capacity and Life of a Rolling Contact Fatigue Life of a Rolling Bearing Load Rating Standards Effect of Variable Loading on Fatigue Life Fatigue Life of Oscillating Bearings Reliability and Fatigue Life Closure References LUBRICANTS AND LUBRICATION TECHNIQUES General Types of Lubricants Liquid Lubricants Grease Solid Lubricants Lubricant Delivery Systems Seals Closure References STRUCTURAL MATERIALS OF BEARINGS General Rolling Bearing Steels Steel Manufacture Effects of Processing Methods on Steel Components Heat Treatment of Steel Materials for Special Bearings Cage Materials Seal Materials Tribological Coatings for Bearing Components Closure References VIBRATION, NOISE, AND CONDITION MONITORING General Vibration- and Noise-Sensitive Applications The Role of Bearings in Machine Vibration Measurement of Nonroundness and Vibration Detection of Failing Bearings in Machines Condition-Based Maintenance Closure References APPENDIX INDEX