Interfacial Mechanics: Theories and Methods for Contact and Lubrication, 1st Edition (Hardback) book cover

Interfacial Mechanics

Theories and Methods for Contact and Lubrication, 1st Edition

By Jane Wang, Dong Zhu

CRC Press

640 pages | 93 Color Illus. | 449 B/W Illus.

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Description

This book discusses "tribological interface" that consists of two solid surfaces in contact with or without fluids in between. This specific type of interface is commonly seen in reality and extremely important in engineering applications. This book is written for engineering researchers and design engineers as well as graduate and senior undergraduate students. Mathematical treatments are tailored to a first degree in engineering often without rigorous descriptions and proofs. It focuses on the basic concepts, mathematic models, numerical solution procedures, major results and their physical meanings, as well as engineering applications.

Table of Contents

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

3.5.6.1. Basic Model

3.5.6.2. Solution for Circular Contacts

3.5.6.3. Solution for Line Contacts

3.5.6.4. General Expressions

3.6. Selected Basic Solutions

3.6.1. Displacements Due to Concentrated Forces

3.6.2. Surface Displacements Induced by Uniform Pressure

3.6.2.1. 2D Plane Strain Problems

3.6.2.2. 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

3.6.5.1. 2D Wavy Surface

3.6.5.2. 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

3.7.2.1. Empirical Formulae by Lee and Ren (1996)

3.7.2.2. 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

3.8.3.1. B Matrix and B Matrix Equation

3.8.3.2. 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. 4.2.2.1. ICs Based on Zero Order Approximation
    6. 4.2.2.2. ICs Based on First Order Approximation
    7. 4.2.2.3. ICs Based on Second Order Approximation
    8. 4.2.3. Influence Coefficients for 3D Half-Space Problems
    9. 4.2.3.1. ICs Based on Zero Order Approximation
    10. 4.2.3.2. ICs Based on Bilinear Approximation

      4.2.3.3. 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. 4.6.3.1. Cyclic Convolution and the DC-FFT Algorithm

      4.6.3.2. DC-FFT Procedure for Point Contacts

      4.6.3.3. Method Comparisons

      4.6.3.4. Numerical Examples

      4.6.4. Continuous Convolution and Fourier Transform (CC-FT)

      4.6.4.1. Description of the CC-FT Approach

      4.6.4.2. Validation and Sample Cases

      4.6.5. DCD-FFT, DCC-FFT, and DCS-FFT Approaches

      4.6.5.1. General Description

      4.6.5.2. DCD-FFT Algorithm

      4.6.5.3. DCC-FFT Algorithm

      4.6.5.4. 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

7.3.7.1. Basic Concept

7.3.7.2. Basic Formulation

7.3.7.3. Discretization of the Pressure Flow Terms

7.3.7.4. Discretization of the Entraining Flow Term

7.3.7.5. Characteristics of the Coefficient Matrix

7.3.7.6. 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

7.3.9.1. General

7.3.9.2. Differential Schemes for Combined Entraining Flow Term

7.3.9.3. Differential Schemes for Separate Entraining Flow Terms

7.3.9.4. Effect of Differential Scheme Arrangement

7.3.9.5. Schemes for Further Separated Entraining Flow Term

7.3.9.6. Differential Schemes for Squeeze Flow Term

7.3.10. Effect of Mesh Density

7.3.10.1. Background

7.3.10.2. Dependence of Film Thickness Solution on Mesh Density

7.3.10.3. Reasonable Mesh Density to be Used in Practice

7.3.10.4. 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

      7.6.2.1. Review of Early Studies

      7.6.2.2. Reexamination of the Empirical Formulae

      7.6.2.3. Application

      7.6.3. Updated Treatment Based on JFO and Elrod

      7.6.3.1. Basic Concept and Formulation

      7.6.3.2. Numerical Solution Method

      7.6.3.3. Typical Sample Solutions

      7.6.3.4. 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

7.7.5.1. Effect of Different Viscosity Models

7.7.5.2. Effect of Lubricant Piezoviscous Property

7.7.5.3. 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

        9.2.2.1. Influence Coefficient Algorithm

        9.2.2.2. Calculation of Influence Coefficients

        9.2.2.3. Three Ways to Carry Out Summation Operations

        9.2.2.4. 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. 9.3.1.1. Basic Equations for Line Contact TEHL Problems

        9.3.1.2. Brief Description of Numerical Method

        9.3.1.3. Typical Line Contact TEHL Results

        9.3.2. Point Contact TEHL Solution

        9.3.2.1. Basic TEHL Equations for Point Contact Problems

        9.3.2.2. Solution Domains and Initial/Boundary Conditions

        9.3.2.3. Numerical Solution Methods

        9.3.2.4. 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

        11.2.1.1. Yield Surface

        11.2.1.2. Yield Criteria

        11.2.2. Strain Hardening and Plastic Flow

        11.2.2.1. Yield Initiation and Strain Hardening

        11.2.2.2. Elastic-Perfectly Plastic (EPP) Behavior

        11.2.2.3. Isotropic Hardening Rule

        11.2.2.4. Kinematic Hardening Rule

        11.2.2.5. Combined Isotropic and Kinematic Hardening Rule

        11.2.2.6. Plastic Strain Increment

        11.3. Elastoplastic Contact Modeling

        11.3.1. FEM Modeling

        11.3.1.1. Elasto-Perfectly Plastic Contact Analysis Through the FEM

        11.3.1.2. FEM Simulations Considering Strain Hardening

        11.3.2. Method by Jacq et al.

        11.3.2.1. General

        11.3.2.2. Description of the Approach

        11.3.2.3. 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

        11.6.4.1. Stresses Due to a Single Inhomogeneity

        11.6.4.2. Surface Coating as an Inhomogeneity

        11.6.4.3. Composites with Distributed Particles

        11.6.4.4. Matrix Material Yield Strength / Hardness

        11.6.4.5. Double Inhomogeneities

        11.6.4.6. 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

12.5.1.1. Basic PEHL Phenomena with a Stationary Asperity

12.5.1.2.Effect of Asperity Height and Radius

12.5.1.3. PEHL Phenomena with a Moving Surface Asperity

12.5.2. PEHL with a Single Surface Dent

12.5.2.1. Basic PEHL Phenomena with a Stationary Dent

12.5.2.2. Effect of Dent Depth and Radius

12.5.2.3. PEHL Phenomena with a Moving Surface Dent

12.5.3. PEHL with Sinusoidal Surfaces

12.5.3.1. Basic PEHL Characteristics and Comparison with EHL Results

12.5.3.2.Effect of Material Hardening Property

12.5.3.3. Effect of Rough Surface Geometric Parameters

12.5.3.4. 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

12.7.3.1. PEHL Results for the First Rolling Cycle

12.7.3.2. PEHL Results for the Second Rolling Cycle

12.7.3.3. Ratcheting and Shakedown

12.7.3.4. PEHL Phenomena in the First Rolling Cycle

12.7.3.5. PEHL Phenomena in the Second Rolling Cycle

12.7.3.6. PEHL Phenomena in the First Five Cycles

12.7.3.7. Effect of Applied Load on the Shakedown or Ratcheting Behavior

12.7.3.8. 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

13.3.2.1. Equations for Lubrication

13.3.2.2. Equations for Surface Displacements and Subsurface Stresses

13.3.2.3. Numerical Solution Procedure

13.3.3. Typical Sample Results

13.3.3.1. EHL with a Bi-Layered Coating

13.3.3.2. EHL with a Multilayered Substrate

13.3.3.3. 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

13.4.2.1. Equations for Point Contact EHL

13.4.2.2. Equations for Surface Displacement Calculation

13.4.2.3. Numerical Procedure

13.4.3. Typical Sample Results and Discussions

13.4.3.1. Selected Cases and Computational Mesh

13.4.3.2. A Single Inhomogeneity

13.4.3.3. Multiple Inhomogeneities

13.4.3.4. 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

14.2.2.1. Gear Geometry and Kinematics

14.2.2.2. Simplified Load Distribution

14.2.2.3. 3D Line Contact Mixed EHL Simulation Model

14.2.2.4. Results for a Sample Gear Set in Mixed EHL

14.2.2.5. Gear Tooth Contact Friction

14.2.2.6. Flash and Bulk Temperatures in Gears

14.2.3. Mixed EHL in Spiral Bevel and Hypoid Gears

14.2.3.1. Background

14.2.3.2. Gearing Geometry and Kinematics

14.2.3.3. Modified Mixed EHL Model

14.2.3.4. Interfacial Friction and Flash Temperature Calculations

14.2.3.5. Sample Results of Calculation

14.2.3.6. 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

14.6.3.1. Problem Description

14.6.3.2. Determinations of Dimple/Groove Depth, Size and Density

14.6.3.3. Texture Distribution Pattern Selection

14.6.3.4. Bottom Shapes of the Dimples and Grooves

14.6.3.5. Basic Results of Comparisons

14.6.3.6. 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

15.2.1.1. Multi-Field Coupling and Fundamental Theories

15.2.1.2. Initial and Boundary Conditions

15.2.1.3. Generalized MEMCT Constitutive Equations

15.2.1.4. Evolution Equations

15.2.2. Generalized MEMCT Theory

15.2.2.1. A Set of Generalized Solutions

15.2.2.2. 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

15.3.3.1. Generalized Gap, Load, and Surface Flux

15.3.3.2. Generalized Contact and Interfacial Conditions for Single-Field Cases

15.3.3.3. Generalized Contact and Interfacial Conditions in Coupled Fields

15.3.3.4. Contact Conditions

15.3.3.5. Interfacial Conditions

15.3.3.6. Other Boundary Conditions

15.4. Examples of Contact subjected to Coupled Fields

15.4.1. Sliding Contact Heat Conduction in Homogeneous Materials

15.4.1.1. Problem Description

15.4.1.2. Solution Scheme

15.4.1.3. Different Modeling Considerations

15.4.1.4. 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

15.4.3.1. Problem Description

15.4.3.2. Analytical Core Solution

15.4.3.3. Contact and Interfacial Conditions

15.4.3.4. Numerical Scheme

15.4.3.5. Disturbed Temperature and Heat Flux Due to Inhomogeneity

15.4.3.6. Effect of Inhomogeneity Size and Location on Disturbed Temperature

15.4.3.7. Effect of Inhomogeneity Distance

15.4.4. Frictional Contact Between Two Multiferroic Materials

15.4.4.1. Problem Description

15.4.4.2. Solution Procedure

15.4.4.3. Indentation of an Smooth MEE Surface

15.4.4.4. Indentation of a Rough MEE Surface

15.4.4.5. Parameter Sensitivity

15.5. Closure

Appendices

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

References

Subject Index

About the Authors

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.

Subject Categories

BISAC Subject Codes/Headings:
TEC009010
TECHNOLOGY & ENGINEERING / Chemical & Biochemical
TEC009070
TECHNOLOGY & ENGINEERING / Mechanical
TEC021000
TECHNOLOGY & ENGINEERING / Material Science