Finite Element Modeling of Elastohydrodynamic Lubrication Problems

Covers the latest developments in modeling elastohydrodynamic lubrication (EHL) problems using the finite element method (FEM)

This comprehensive guide introduces readers to a powerful technology being used today in the modeling of elastohydrodynamic lubrication (EHL) problems. It provides a general framework based on the finite element method (FEM) for dealing with multi-physical problems of complex nature (such as the EHL problem) and is accompanied by a website hosting a user-friendly FEM software for the treatment of EHL problems, based on the methodology described in the book. Finite Element Modeling of Elastohydrodynamic Lubrication Problems begins with an introduction to both the EHL and FEM fields. It then covers Standard FEM modeling of EHL problems, before going over more advanced techniques that employ model order reduction to allow significant savings in computational overhead. Finally, the book looks at applications that show how the developed modeling framework could be used to accurately predict the performance of EHL contacts in terms of lubricant film thickness, pressure build-up and friction coefficients under different configurations.

Finite Element Modeling of Elastohydrodynamic Lubrication Problems offers in-depth chapter coverage of Elastohydrodynamic Lubrication and its FEM Modeling, under Isothermal Newtonian and Generalized-Newtonian conditions with the inclusion of Thermal Effects; Standard FEM Modeling; Advanced FEM Modeling, including Model Order Reduction techniques; and Applications, including Pressure, Film Thickness and Friction Predictions, and Coated EHL.

This book:

• Comprehensively covers the latest technology in modeling EHL problems

• Focuses on the FEM modeling of EHL problems

• Incorporates advanced techniques based on model order reduction

• Covers applications of the method to complex EHL problems

• Accompanied by a website hosting a user-friendly FEM-based EHL software

Finite Element Modeling of Elastohydrodynamic Lubrication Problems is an ideal book for researchers and graduate students in the field of Tribology.

Autorentext

WASSIM HABCHI, PHD, is an Associate Professor of Mechanical Engineering in the Department of Industrial and Mechanical Engineering at the Lebanese American University, Lebanon. His main area of expertise is in the finite element modeling of elastohydrodynamic lubrication problems. He is a leading authority in this field, and has published in numerous tribology journals.

Inhalt
Preface xiii

Nomenclature xvii

About the CompanionWebsite xxv

Part I Introduction 1

1 Elastohydrodynamic Lubrication (EHL) 3

1.1 EHL Regime 3

1.2 Governing Equations in Dimensional Form 7

1.2.1 Generalized Reynolds Equation 9

1.2.2 FilmThickness Equation 15

1.2.3 Linear Elasticity Equations 18

1.2.4 Load Balance Equation 24

1.2.5 Energy Equations 24

1.2.6 Shear Stress Equations 28

1.3 Governing Equations in Dimensionless Form 28

1.3.1 Dimensionless Parameters 29

1.3.2 Generalized Reynolds Equation 31

1.3.3 FilmThickness Equation 32

1.3.4 Linear Elasticity Equations 33

1.3.5 Load Balance Equation 34

1.3.6 Energy Equations 34

1.3.7 Shear Stress Equations 36

1.4 Lubricant Constitutive Behavior 36

1.4.1 Pressure and Temperature Dependence 37

1.4.1.1 Density 37

1.4.1.2 Viscosity 39

1.4.1.3 Thermal Conductivity and Heat Capacity 41

1.4.2 Shear Dependence of Viscosity 41

1.4.3 Limiting Shear Stress 43

1.5 Dimensionless Groups 44

1.6 Review of EHL Numerical Modeling Techniques 46

1.7 Conclusion 52

References 52

2 Finite ElementMethod (FEM) 59

2.1 FEM:The Basic Idea 59

2.2 Model PDE 61

2.3 Steady-State Linear FEM Analysis 63

2.3.1 Elementary Integral Formulations 64

2.3.1.1 Weighted-Residual Form 64

2.3.1.2 Weak Form 65

2.3.2 Solution Approximation 66

2.3.2.1 Meshing and Discretization 67

2.3.2.2 Lagrange Linear Elements 69

2.3.2.3 Lagrange Quadratic Elements 73

2.3.3 Galerkin Formulation 75

2.3.4 Integral Evaluations: Mapping between Reference and Actual Elements 78

2.3.5 Connectivity of Elements 85

2.3.6 Assembly Process and Treatment of B.C.'s 86

2.3.7 Resolution Process 90

2.3.8 Post-Processing of the Solution 91

2.3.9 One-Dimensional Example 92

2.4 Steady-State Nonlinear FEM Analysis 99

2.4.1 Newton Methods for Nonlinear Systems of Equations 99

2.4.1.1 Newton Method 100

2.4.1.2 Damped-NewtonMethod 102

2.4.2 Nonlinear FEM Formulation 105

2.5 Transient FEM Analysis 109

2.5.1 Space-Time Discretization 110

2.5.2 Time-Dependent FEM Formulation 111

2.6 Multi-Physical FEM Analysis 112

2.6.1 Multi-Physical FEM Formulation 113

2.6.2 Assembly Process 115

2.6.3 Coupling Strategies 116

2.6.3.1 Weak Coupling 117

2.6.3.2 Full/Strong Coupling 117

2.7 Stabilized FEM Formulations 118

2.7.1 Isotropic Diffusion 120

2.7.2 Streamline Upwind PetrovGalerkin 121

2.7.3 Galerkin Least Squares 121

2.8 Conclusion 123

References 123

Part II Finite ElementModeling Techniques 125

3 Steady-State Isothermal Newtonian Line Contacts 127

3.1 Contact Configuration 127

3.2 Geometry, Computational Domains, and Meshing 128

3.2.1 Geometry 128

3.2.2 Computational Domains 128

3.2.3 Meshing and Discretization 130

3.3 Governing Equations and Boundary Conditions 132

3.3.1 Reynolds Equation 133

3.3.2 Linear Elasticity Equations 136

3.3.3 Load Balance Equation 138

3.4 FEM Model 138

3.4.1 Connectivity of Elements 139

3.4.2 Weak Form Formulation 139

3.4.3 Elementary Matrix Formulations 141

3.4.3.1 Elastic Part 142

3.4.3.2 Hydrodynamic Part 144

3.4.3.3 Load Balance Part 145

3.4.4 Stabilized Formulations 146

3.5 Overall Solution Procedure 150

3.6 Model Calibration and Preliminary Results 153

3.6.1 Mesh Sensitivity Analysis 153 3.6.2 Penalty T...