1st Edition

Interfacial Mechanics Theories and Methods for Contact and Lubrication

By Jane Wang, Dong Zhu Copyright 2020
    662 Pages 93 Color & 449 B/W Illustrations
    by CRC Press

    662 Pages 93 Color & 449 B/W Illustrations
    by CRC Press

    Understanding the characteristics of material contact and lubrication at tribological interfaces is of great importance to engineering researchers and machine designers. Traditionally, contact and lubrication are separately studied due to technical difficulties, although they often coexist in reality and they are actually on the same physical ground. Fast research advancements in recent years have enabled the development and application of unified models and numerical approaches to simulate contact and lubrication, merging their studies into the domain of Interfacial Mechanics.

    This book provides updated information based on recent research progresses in related areas, which includes new concepts, theories, methods, and results for contact and lubrication problems involving elastic or inelastic materials, homogeneous or inhomogeneous contacting bodies, using stochastic or deterministic models for dealing with rough surfaces. It also contains unified models and numerical methods for mixed lubrication studies, analyses of interfacial frictional and thermal behaviors, as well as theories for studying the effects of multiple fields on interfacial characteristics. The book intends to reflect the recent trends of research by focusing on numerical simulation and problem solving techniques for practical interfaces of engineered surfaces and materials.

    This book is written primarily for graduate and senior undergraduate students, engineers, and researchers in the fields of tribology, lubrication, surface engineering, materials science and engineering, and mechanical engineering.

    Chapter 1 Introduction

      1. 1.1. Significance of the Topics
      2. 1.2. Tribological Interface Systems

        1. Interface Systems Defined Based on Geometry
        2. Interface Systems Defined Based on Relative Motion
        3. Interface Systems Defined Based on Lubricating Media
        4. Interface Systems Defined Based on Lubrication Status

      1. 1.3. Brief Historic Review
      2. 1.3.1. Empirical Knowledge Accumulated in Early Years
      3. 1.3.2. Pioneering Studies
      4. 1.3.3. Establishment of Contact Mechanics and Lubrication Theory
      5. 1.3.4. Rapid Development Assisted by Digital Computers
      6. 1.3.5. Recent Advancements
      7. 1.3.6. Conclusion Remarks
      8. 1.4. Interfacial Mechanics
      9. 1.5. Coverage of This Book

    Chapter 2 Properties of Engineering Materials and Surfaces

      1. Mechanical Properties of Typical Solid Materials
      2. Topographic Properties of Engineering Surfaces
        1. Engineering Surfaces
        2. Surface Characterization by Statistic Parameters
        3. Surface Characterization by Direct Digitization
        4. Rough Surfaces Generated by Computer

      3. Lubricant Properties
        1. Viscosity
        2. Effect of Temperature on Viscosity
        3. Effect of Pressure on Viscosity
        4. Density
        5. Non-Newtonian Behaviors
        6. Additives in Lubricants

    Chapter 3 Fundamentals of Contact Mechanics

            1. 3.1. Introduction

        1. 3.2. Basic Half-Space Elasticity Theories
        2. 3.2.1. Potential Equations

          3.2.2. Displacements Due to Normal Loading

          3.2.3. Displacements Due to Tangential Traction

          3.2.4. General Equations for Surface Displacements

          3.2.5. Subsurface Stresses

        3. 3.3. Line Contact Hertzian Theory
        4. 3.3.1. Basic Model
        5. 3.3.2. Contact Pressure and Surface Deformation
        6. 3.3.3. Subsurface Stresses
        7. 3.4. Point Contact Hertzian Theory
        8. 3.4.1. Basic Model
        9. 3.4.2. Contact Pressure and Surface Deformation
        10. 3.4.3. Subsurface Stresses

      1. Contact Strength Analysis Based on the Subsurface Stress Field
        1. Theories for Yield Criteria

    3.5.2. Subsurface Stress Field and Yield Pressure in Line Contacts

    3.5.3. Subsurface Stress Field and Yield Pressure in Circular Contacts

    3.5.4. Subsurface Stress Field in Elliptical Contacts

    3.5.5. Effect of Friction on the Subsurface Stresses

    3.5.6. Contact Yield Initiation in a Case Hardened Solid Basic Model Solution for Circular Contacts Solution for Line Contacts General Expressions

    3.6. Selected Basic Solutions

    3.6.1. Displacements Due to Concentrated Forces

    3.6.2. Surface Displacements Induced by Uniform Pressure 2D Plane Strain Problems 3D Half-Space Problems

    3.6.3. Indentation by a Rigid Punch

    3.6.4. Frictionless Indentation by a Blunt Wedge or Cone

    3.6.5. A Sinusoidal Wavy Surface in Contact with a Flat 2D Wavy Surface 3D Wavy Surface

    3.7. Contact with Rough Surfaces

    3.7.1. A Stochastic Model for Rough Surface Contacts

    3.7.2. Empirical Formulae Based on Numerical Solutions for Rough Surface Contacts Empirical Formulae by Lee and Ren (1996) Empirical Formulae by Chen et al. (2007)

    3.8. Contact of Multilayer Materials

    3.8.1. Problem Description

    3.8.2. Fourier Transforms of the Governing and Boundary/Interfacial Equations

    3.8.3. Structures of B and AC Matrices B Matrix and B Matrix Equation AC Matrix and AC Matrix Equation

    3.8.4. Solutions of Matrix Equations

    3.8.5. Typical Sample Cases

    3.8.6. Solution for Problems with a Single Layer Coating

    3.8.7. Extended Hertzian Theories

    3.9. Closure

    Chapter 4 Numerical Methods for Solving Contact Problems

      1. 4.1. Introduction
            1. 4.1.1. Background

        1. 4.1.2. FEM Approach
        2. 4.1.3. Stochastic Models
        3. 4.1.4. IC Matrix Approach
        4. 4.1.5. Quadratic Programming Approach and CGM
        5. 4.1.6. Fast Fourier Transform (FFT) Approaches
        6. 4.1.7. Discrete Convolution and Fast Fourier Transform (DC-FFT) Approach
        7. 4.1.8. Contact Problems with Inelastic and Inhomogeneous Materials

      2. 4.2. Discretization with Influence Coefficients
      3. 4.2.1. Basic Concept
      4. 4.2.2. Influence Coefficients for 2D Half-Plane Problems
      5. ICs Based on Zero Order Approximation
      6. ICs Based on First Order Approximation
      7. ICs Based on Second Order Approximation
      8. 4.2.3. Influence Coefficients for 3D Half-Space Problems
      9. ICs Based on Zero Order Approximation
      10. ICs Based on Bilinear Approximation ICs Based on Biquadratic Approximation

        4.3. Comparative Cases for Deformation Calculation

        4.3.1. Deformation Due to Indentation by a Rigid Punch

        4.3.2. Deformation Due to Cylindrical Contact Hertzian Pressure

        4.3.3. Deformation Due to Point Contact Hertzian Pressure

        4.4. Solution for Contact Pressure Distribution

        4.4.1. Problem Description

        4.4.2. Conjugate Gradient Method for Solving Contact Problems

        4.5. Numerical Examples

      11. 4.6. FFT-Based Methods for Efficient Surface Deformation Calculation
      12. 4.6.1. Background
      13. 4.6.2. Three Types of Convolution
      14. 4.6.3. DC-FFT Algorithm for Non-Periodic Contact Problems
      15. Cyclic Convolution and the DC-FFT Algorithm DC-FFT Procedure for Point Contacts Method Comparisons Numerical Examples

        4.6.4. Continuous Convolution and Fourier Transform (CC-FT) Description of the CC-FT Approach Validation and Sample Cases

        4.6.5. DCD-FFT, DCC-FFT, and DCS-FFT Approaches General Description DCD-FFT Algorithm DCC-FFT Algorithm DCS-FFT Algorithm

        4.7. Calculation of Subsurface Stresses

        4.7.1. General Equations

        4.7.2. Influence Coefficients

        4.7.3. DC-FFT Approach for Stress Calculation

        4.7.4. Additional Numerical Examples

        4.8. Closure

        1. Chapter 5 Fundamentals of Hydrodynamic Lubrication

      16. 5.1. Introduction
      17. 5.2. Reynolds Equation
        1. 5.2.1. Derivation of Generalized Reynolds Equation
        2. 5.2.2. Simplified Reynolds Equations
        3. 5.2.3. Boundary Conditions for the Reynolds Equation
        4. 5.2.4. Reynolds Equation for Non-Newtonian Lubricants
        5. 5.2.5. Average Reynolds Equation
        6. 5.3. Energy Equations

          5.3.1. Energy Equation for the Lubricant Film

          5.3.2. Heat Transfer Equations for Contacting Bodies

          5.3.3. Surface Temperature Equations

          5.4 Analytical Solutions for Simplified Bearing Problems

        7. 5.4.1. General Description
        8. 5.4.2. Infinitely Long Journal Bearings
        9. 5.4.3. Infinitely Short Journal Bearings
        10. 5.4.4. Infinitely Long Thrust Bearings
        11. 5.5 Closure

          Chapter 6 Numerical Methods for Hydrodynamic Lubrication

          6.1. Finite Length Journal Bearings

        12. 6.1.1. Finite Difference Method (FDM)
        13. 6.1.2. Finite Element Method (FEM)
        14. 6.2. Mixed Thermal Elastohydrodynamic Lubrication (TEHL) Analyses for Journal Bearings

          6.2.1. Background

        15. 6.2.2. Hydrodynamic Lubrication Model Considering Roughness Effect
        16. 6.2.3. Asperity Contact Models
        17. 6.2.4. Evaluation of Body Deformations

    6.2.5. Thermal Analysis

        1. Numerical Procedure
        2. Typical Sample Results

      1. Piston Skirts in Mixed Lubrication
      2. 6.3.1. Equation of Motion

        6.3.2. Average Reynolds Equation

        6.3.3. Wavy Surface Contact Pressure

        6.3.4. Deformations of Piston Skirts and Cylinder Bore

        6.3.5. Numerical Procedure

        6.3.6. Typical Sample Results

      3. Closure

    Chapter 7 Lubrication in Counterformal Contacts – Elastohydrodynamic Lubrication (EHL)

      1. 7.1. Introduction
      2. 7.2. Background and Early Studies
        1. 7.2.1. Martin’s Theory (Isoviscous - Rigid)
        2. 7.2.2. Blok’s Theory (Piezoviscous - Rigid)
        3. 7.2.3. Herrebrugh’s Solution (Isoviscous - Elastic)
        4. 7.2.4. Grubin’s Inlet Analysis (Piezoviscous - Elastic)
        5. 7.2.5. First Full EHL Solution in Line Contacts by Petrusevich (1951)
        6. 7.2.6. Full EHL Solution in Line Contacts by Dowson-Higginson (1959)
        7. 7.2.7. First Full EHL Solution in Point Contacts by Ranger et al. (1975)
        8. 7.2.8. Full EHL Solution in Point Contacts by Hamrock & Dowson (1976-77)
        9. 7.2.9. Dimensionless Parameter Groups
        10. 7.2.10. Maps of Lubrication Regimes
        11. 7.3. EHL Numerical Solution Methods

        12. 7.3.1. Nonlinearity of EHL Equation Systems
        13. 7.3.2. Straightforward Iterative Method

    7.3.3. Inverse Solution

    7.3.4. System Analysis through the Newton-Raphson Procedure

    7.3.5. Multi-Grid Method

    7.3.6. Coupled Differential Deflection Method

    7.3.7. Semi-System Approach Basic Concept Basic Formulation Discretization of the Pressure Flow Terms Discretization of the Entraining Flow Term Characteristics of the Coefficient Matrix Sample Mixed EHL Solutions from the Semi-System Approach

    7.3.8. Simulation of Contact by Using EHL Equation System

    7.3.9. Effect of Differential Schemes General Differential Schemes for Combined Entraining Flow Term Differential Schemes for Separate Entraining Flow Terms Effect of Differential Scheme Arrangement Schemes for Further Separated Entraining Flow Term Differential Schemes for Squeeze Flow Term

    7.3.10. Effect of Mesh Density Background Dependence of Film Thickness Solution on Mesh Density Reasonable Mesh Density to be Used in Practice Limitations of the MG Approach

    7.3.11. Progressive Mesh Densification (PMD) Method

      1. Experimental Validation of Numerical Solution
      2. EHL with Arbitrary Entrainment Angle
      3. 7.5.1. Background

        7.5.2. Formulation and Numerical Method

        7.5.3. Typical Results for Validating the Model and Showing Basic Characteristics

        7.5.4. Curve-Fitting Formula

        7.5.5 Transition of Lubrication Condition with Roughness Considered

      4. Treatments for Starvation and Cavitation
      5. 7.6.1. Background

        7.6.2. Conventional Treatment Review of Early Studies Reexamination of the Empirical Formulae Application

        7.6.3. Updated Treatment Based on JFO and Elrod Basic Concept and Formulation Numerical Solution Method Typical Sample Solutions Comparison with Conventional Treatment

      6. Isothermal EHL Behaviors with Smooth Surfaces
        1. Background
        2. Entraining Speed Effect
        3. Load Effect
        4. Effect of Contact Ellipticity
        5. Effect of Materials Properties Effect of Different Viscosity Models Effect of Lubricant Piezoviscous Property Effect of Elastic Property of Solids

    7.8. Closure

    Chapter 8 Mixed Lubrication with Rough Surfaces

    8.1. Introduction

        1. 8.1.1. Background
        2. 8.1.2. Review of Stochastic Models

          8.1.3. Review of Deterministic Models

          8.1.4. Review of Combined Stochastic-Deterministic Approach

          8.1.5. Terminology

          8.2. Stochastic Approach

          8.3. Deterministic Approach for Artificial Roughness

        3. 8.3.1. General
        4. 8.3.2. Calculation Methods for Derivatives ∂H/∂X and ∂H/∂T
        5. 8.3.3. Error Analysis
        6. 8.3.4. Sample Validation Cases
        7. 8.4. Deterministic Approach for Machined Roughness

        8. 8.4.1. Problem Description
        9. 8.4.2. Two Ways to Calculate ∂S/∂X and ∂S/∂T
        10. 8.4.3. Accuracy Comparison Between Methods I+D and D+I
        11. 8.4.4. Sample Rough Surface EHL Solutions
        12. 8.5. Stability of Transient Solution

          8.5.1. Contribution to Coefficient Matrix by Squeeze Flow Term

          8.5.2. Initial Value Problem

          8.5.3. Effect of Time Step Length Employed

          8.5.4. Effect of Convergence Accuracy Requirement

        13. 8.6. 3D Infinitely Long Line Contact Mixed EHL Solution
        14. 8.6.1. Background
        15. 8.6.2. Model Description

        16. 8.6.3. Sample Cases with Smooth Surfaces for Model Verification
        17. 8.6.4. Sample Cases with Machined Surface Roughness
        18. 8.7. 3D Finite Roller Contact Mixed EHL Solution
        19. 8.7.1. Introduction
        20. 8.7.2. Roller Contact Geometry
        21. 8.7.3. Typical Sample Cases
        22. 8.7.4. Simulation of Lubrication Transition with Roughness
        23. 8.8. Basic Mixed EHL Characteristics
        24. 8.8.1. Background
        25. 8.8.2. Limitations of Stochastic Mixed Lubrication Models

        26. 8.8.3. Rough Surface Mixed EHL Model Validation
        27. 8.8.4. Transition Characterized by l Ratio
        28. 8.8.5. Effect of Roughness Height on the Mixed EHL Behaviors
        29. 8.9. Effect of Roughness Orientation on Film Thickness
        30. 8.9.1. Background
        31. 8.9.2. Case Study with Machined Roughness
        32. 8.9.3. Case Study with Sinusoidal Wavy Surfaces
        33. 8.10. Clouse
        34. Chapter 9 Thermal Behaviors at Counterformal Contact Interfaces

          9.1. Introduction

          9.2. Flash Temperature Calculation

        35. 9.2.1. Three Methods
        36. 9.2.2. Point Heat Source Integration Method

 Influence Coefficient Algorithm

 Calculation of Influence Coefficients

 Three Ways to Carry Out Summation Operations

 Comparative Study via. Numerical Examples

          9.2.3. Simplified Approach for Cases at High Peclet Numbers

          9.3. Full TEHL Solution with Smooth Surfaces

        37. 9.3.1 Line Contact TEHL Solutions
        38. Basic Equations for Line Contact TEHL Problems

 Brief Description of Numerical Method

 Typical Line Contact TEHL Results

          9.3.2. Point Contact TEHL Solution

 Basic TEHL Equations for Point Contact Problems

 Solution Domains and Initial/Boundary Conditions

 Numerical Solution Methods

 Sample Results and Discussions

          9.4. Full Solution of Mixed TEHL with Rough Surfaces

        39. 9.4.1. Mixed TEHL Model Description
        40. 9.4.2. Numerical Methods
        41. 9.4.3. Model Validation
        42. 9.4.4. Basic TEHL Characteristics
        43. 9.4.5. TEHL with Surface Roughness
        44. 9.4.6. Transition from Boundary and Mixed to Full-Film Lubrication
        45. 9.4.7. Effect of Lubricant Non-Newtonian Behaviors
        46. 9.5. Thermal Reduction of EHL Film Thickness

          9.6. Bulk Temperature

          9.7. Closure

          Chapter 10 Behaviors of Interfacial Friction

          10.1. Introduction

          10.1.1. Importance of the Topic

          10.1.2. Brief Review of Early Studies

          10.1.3. Friction in Full-Film EHL

          10.1.4. Friction in Mixed Lubrication

          10.1.5. Development of the Stribeck Curves

          10.2. Dry Contact Friction

          10.2.1. Basic Model

          10.2.2. Classic Laws of Friction

          10.2.3. Mechanisms of Friction

          10.2.4. Summary to Classic Friction Theories

          10.3. Boundary Lubrication Friction

          10.3.1. General Description

          10.3.2. Formation of Adsorption Film

          10.3.3. Effect of Boundary Additives on Lubrication Performance

          10.4. Rolling Friction

          10.5. Friction in Lubricated Conformal Contacts

          10.6. Friction in Lubricated Counterformal Contacts (EHL Friction)

          10.6.1. Background

          10.6.2. Basic Characteristics of EHL Friction

          10.6.3. Rheological Models

          10.6.4. Calculation of EHL Friction

          10.6.5. Sample Calculation Results

          10.7. Friction in Mixed Lubrication

          10.7.1. Basic Concept

          10.7.2. Mixed Lubrication Friction in Conformal Contacts

          10.7.3. Mixed Lubrication Friction in Counterformal Contacts

          10.7.4. Friction Reduction in Mixed Lubrication

          10.8. The Stribeck Curve

          10.8.1. Calculation of the Stribeck Curves

          10.8.2. Test Apparatus for the Stribeck Curve Measurements

          10.8.3. Sample Stribeck Curves Measured

          10.8.4. Comparison Between Measured and Calculated Stribeck Curves

          10.9. More Friction Reduction Technologies

          10.10 Closure

          Chapter 11 Contact of Elastoplastic and Inhomogeneous Materials

          11.1. Introduction

          11.2. Fundamentals of Plasticity Theory

          11.2.1. Plasticity of Materials

 Yield Surface

 Yield Criteria

          11.2.2. Strain Hardening and Plastic Flow

 Yield Initiation and Strain Hardening

 Elastic-Perfectly Plastic (EPP) Behavior

 Isotropic Hardening Rule

 Kinematic Hardening Rule

 Combined Isotropic and Kinematic Hardening Rule

 Plastic Strain Increment

          11.3. Elastoplastic Contact Modeling

          11.3.1. FEM Modeling

 Elasto-Perfectly Plastic Contact Analysis Through the FEM

 FEM Simulations Considering Strain Hardening

          11.3.2. Method by Jacq et al.


 Description of the Approach

 Typical Examples for a Repeated Rolling/Sliding Contact

          11.4. Inclusion and Equivalent Inclusion Method (EIM)

          11.4.1. Inclusion and Eigenstrain

          11.4.2. Inhomogeneity and EIM

          11.4.3. Elastic Fields Caused by Eigenstrains

          11.5. Core Solutions to Eigenstrain-Induced Elastic Fields

          11.5.1. Background

          11.5.2. General Description

          11.5.3. Displacements

          11.5.4. Stress Field Outside 

          11.5.5. Stress Field Inside 

          11.5.6. Surface Displacement 

          11.5.7. Uniform Unit Eigenstrain in a Cuboid and Related Influence Coefficients

          11.5.8. Discrete Correlation and Fast Fourier Transform (DCR-FFT)

          11.6. SAM by Numerical EIM

          11.6.1. General Formulation and Numerical Procedure for Contact Problems

          11.6.2. Traction Cancellation Method (TCM)

          11.6.3. Other Enhancement Methods

          11.6.4. Numerical Examples

 Stresses Due to a Single Inhomogeneity

 Surface Coating as an Inhomogeneity

 Composites with Distributed Particles

 Matrix Material Yield Strength / Hardness

 Double Inhomogeneities

 Rolling Contact Fatigue of Composite Materials

          11.7. Unified Contact Modeling and Advantages of the SAM

          11.7.1. Unified Framework for Contact Modeling

          11.7.2. SAM with Numerical EIM

          11.8. Closure

          Chapter 12 Plasto-Elastohydrodynamic Lubrication (PEHL)

          12.1. Introduction

          12.1.1. Importance of the Topic

          12.1.2. Brief Review of the Available Studies

          12.2. PEHL Formulation

          12.2.1. Problem Description

          12.2.2. Basic Mixed PEHL Equations

          12.3. Numerical Procedure for Solving the PEHL Problems

          12.4. Smooth Surface PEHL Simulations

          12.4.1. PEHL Model Validation

          12.4.2. Preliminary Sample Cases

          12.4.3. Smooth Surface PEHL Under an Increasing Load

          12.4.4. Effect of Work Hardening Property

          12.5. Rough Surface PEHL Simulations

        47. 12.5.1. PEHL with a Single Surface Asperity Basic PEHL Phenomena with a Stationary Asperity Effect of Asperity Height and Radius PEHL Phenomena with a Moving Surface Asperity

    12.5.2. PEHL with a Single Surface Dent Basic PEHL Phenomena with a Stationary Dent Effect of Dent Depth and Radius PEHL Phenomena with a Moving Surface Dent

    12.5.3. PEHL with Sinusoidal Surfaces Basic PEHL Characteristics and Comparison with EHL Results Effect of Material Hardening Property Effect of Rough Surface Geometric Parameters Effect of Operating Conditions

    12.5.4. PEHL with Real Machined Rough Surfaces

    12.6. PEHL in Line Contacts of Both Infinite and Finite Lengths

    12.6.1. Background

    12.6.2. Smooth Surface PEHL Solutions

    12.6.3. Rough Surface Mixed PEHL Solutions

    12.7. PEHL in a Rolling Contact

    12.7.1. Basic Model for PEHL in a Rolling Contact

    12.7.2. Numerical Procedure

    12.7.3. Results and Discussions PEHL Results for the First Rolling Cycle PEHL Results for the Second Rolling Cycle Ratcheting and Shakedown PEHL Phenomena in the First Rolling Cycle PEHL Phenomena in the Second Rolling Cycle PEHL Phenomena in the First Five Cycles Effect of Applied Load on the Shakedown or Ratcheting Behavior Effect of Material Hardening Law on the Shakedown or Ratcheting Behavior

    12.8. Closure

    Chapter 13 EHL of Inhomogeneous Materials

    13.1. Introduction

    13.2. EHL with a Single Layered Coating

    13.2.1. Background

    13.2.2. Model for Point Contact EHL with Single Layered Coating

    13.2.3. Model Verification

    13.2.4. Influences of Coating Properties on Point Contact EHL

    13.2.5. Influences of Speed, Load and Lubricant Properties

    13.2.6. Curve-Fitting Formulae for Stiff Coating EHL

    13.3. EHL with a Multilayered Coating

    13.3.1. Background

    13.3.2. Theory and Model Description Equations for Lubrication Equations for Surface Displacements and Subsurface Stresses Numerical Solution Procedure

    13.3.3. Typical Sample Results EHL with a Bi-Layered Coating EHL with a Multilayered Substrate EHL with a Functionally Graded Coating

    13.3.4. Remarks

    13.4. EHL with General Inhomogeneities

    13.4.1. Background

    13.4.2. Theory and Model Description Equations for Point Contact EHL Equations for Surface Displacement Calculation Numerical Procedure

    13.4.3. Typical Sample Results and Discussions Selected Cases and Computational Mesh A Single Inhomogeneity Multiple Inhomogeneities Functionally Graded Coatings

    13.4.4. Computational Efficiency

    13.4.5. Remarks

    13.5. Closure

    Chapter 14 Application Topics

    14.1. Introduction

    14.2. Mixed EHL in Gears

    14.2.1. Background

    14.2.2. Mixed EHL in Spur and Helical Gears Gear Geometry and Kinematics Simplified Load Distribution 3D Line Contact Mixed EHL Simulation Model Results for a Sample Gear Set in Mixed EHL Gear Tooth Contact Friction Flash and Bulk Temperatures in Gears

    14.2.3. Mixed EHL in Spiral Bevel and Hypoid Gears Background Gearing Geometry and Kinematics Modified Mixed EHL Model Interfacial Friction and Flash Temperature Calculations Sample Results of Calculation Summary

    14.3. Pitting Life Prediction for Gears

    14.3.1. Problem Description

    14.3.2. Pitting Life Prediction Model

    14.3.3. Gear Pitting Life Prediction Procedure

    14.3.4. Life Prediction Results and Their Comparisons with Testing Data

    14.3.5. Effect of Surface Finish on Predicted Pitting Life

    14.4. Fatigue Life in Rolling-Sliding Contacts

    14.4.1. Problem Description

    14.4.2. Asperity Stress Cycle Counting

    14.4.3. Life Prediction Procedure

    14.4.4. Influence of Relative Sliding on Peak Pressure

    14.4.5. Subsurface Stress Variation Due to Sliding

    14.4.6. Influence of Sliding on Fatigue Life

    14.5. Simulation of Sliding Wear in Mixed Lubrication

    14.5.1. Problem Description

    14.5.2. Brief Review of Available Wear Models

    14.5.3. Wear Simulation Procedure

    14.5.4. A Numerical Example

    14.5.5. Phases of Wear

    14.5.6. Wear Coefficient Calibration

    14.6. Surface Design Through Virtual Texturing

    14.6.1. Importance of Surface Texture Design and Optimization

    14.6.2. Virtual Texturing and Its Procedure

    14.6.3. An Application Example Problem Description Determinations of Dimple/Groove Depth, Size and Density Texture Distribution Pattern Selection Bottom Shapes of the Dimples and Grooves Basic Results of Comparisons Practical Concerns

    14.6.4. Summary

    14.7. EHL with Emulsion Lubricants

    14.7.1. Background

    14.7.2. Test Apparatus

    14.7.3. Emulsion Lubricants Tested

    14.7.4. Oil Pool Formation and Disappearance

    14.7.5. Results of Measured Film Thickness

    14.7.6. Friction Measurements

    14.7.7. Summary

    14.8. Closure

    Chapter 15 Multifield Interfacial Issues and Generalized Contact Modeling

    15.1. Introduction

    15.1.1. Background

    15.1.2. Brief Review of Related Multifield Studies

    15.2. Coupled Mechanical-Electrical-Magnetic-Chemical-Thermal (MEMCT) Theory for Material Systems

    15.2.1. Fundamental Theories and the MEMCT Framework Multi-Field Coupling and Fundamental Theories Initial and Boundary Conditions Generalized MEMCT Constitutive Equations Evolution Equations

    15.2.2. Generalized MEMCT Theory A Set of Generalized Solutions Strategy

    15.3. Generalized Contact Model

    15.3.1. Contact Model Considerations

    15.3.2. Linearized Constitutive Equations and Generalized Boundary Conditions

    15.3.3. Generalized Contact and Interfacial Conditions Generalized Gap, Load, and Surface Flux Generalized Contact and Interfacial Conditions for Single-Field Cases Generalized Contact and Interfacial Conditions in Coupled Fields Contact Conditions Interfacial Conditions Other Boundary Conditions

    15.4. Examples of Contact subjected to Coupled Fields

    15.4.1. Sliding Contact Heat Conduction in Homogeneous Materials Problem Description Solution Scheme Different Modeling Considerations Stress and Temperature Affected by Sliding Velocity

    15.4.2. Contact Heat Conduction with Surface Heat Convection

    15.4.3. Contact Heat Conduction in an Inhomogeneous Half-Space Problem Description Analytical Core Solution Contact and Interfacial Conditions Numerical Scheme Disturbed Temperature and Heat Flux Due to Inhomogeneity Effect of Inhomogeneity Size and Location on Disturbed Temperature Effect of Inhomogeneity Distance

    15.4.4. Frictional Contact Between Two Multiferroic Materials Problem Description Solution Procedure Indentation of an Smooth MEE Surface Indentation of a Rough MEE Surface Parameter Sensitivity

    15.5. Closure


    Appendix A: Basic Expressions in Linear Elasticity

    Appendix B: Fourier Series, Fourier Transform, Convolution and Correlation

    Appendix C: Solutions of the FRFs for Multilayered Materials

    Under Normal and Shear Loadings

    Appendix D: Reference Source Code in FORTRAN for Discrete Convolution

    and Fast Fourier Transform (DC-FFT)

    Appendix E: Basic Equations and Their Discretization Schemes for

    Numerical Solution of Mixed EHL

    Appendix F: Potential Functions, Derivatives and Equations Used in Chapter 11

    Appendix G: Stresses and Surface Displacement Caused by a Cuboidal

    Inclusion with Uniformly Distributed Eigenstrain

    Appendix H: Solutions of the FRFs for Multilayered Materials Under Normal and Shear Loadings

    Appendix I: Frequency Response Functions for Temperature


    Subject Index


    Q. Jane Wang received her Ph. D. in mechanical engineering from Northwestern University, IL, USA, in 1993. She taught for five years at Florida International University, Miami, FL, USA, and is now a Professor in the Mechanical Engineering Department at Northwestern University, USA. She was elected Fellow of the American Society of Mechanical Engineers (ASME) in 2009 and Society of Tribologists and Lubrication Engineers (STLE) in 2007. Her research interests are mainly in the areas of contact and interfacial mechanics and tribology of advanced materials and novel lubricants.

    Dong Zhu received his Ph. D. in mechanical engineering from Tsinghua University of China in April of 1984. He started to work at the Center for Engineering Tribology, Northwestern University, USA, as a Research Fellow in January of 1986. He joined the Technical Center of Aluminum Company of America in the beginning of 1991 then Eaton Innovation Center in 1994, doing tribology and surface engineering related research and product development. After his retirement from Eaton, he was appointed to a Professor position at Sichuan University of China and Adjunct Professor at Tsinghua University. He is now an Adjunct Professor at Harbin Engineering University. He was elected Fellow of the American Society of Mechanical Engineers (ASME) in 2007 and Society of Tribologists and Lubrication Engineers (STLE) in 2006. His research interests mainly include elastohydrodynamic lubrication (EHL), mixed lubrication, surface engineering and tribological testing.