The book not only offers scientists and engineers a clear inter-disciplinary introduction and orientation to all major EHL problems and their solutions but, most importantly, it also provides numerical programs on specific application in engineering. * A one-stop reference providing equations and their solutions to all major elastohydrodynamic lubrication (EHL) problems, plus numerical programs on specific applications in engineering * offers engineers and scientists a clear inter-disciplinary introduction and a concise program for practical engineering applications to most important EHL problems and their solutions * brings together a number of case studies in one text, each being solved using solution methods which share common features and methods

This book is a one-stop reference providing equations and solutions to all major elastohydrodynamic lubrication (EHL) problems, in addition to numerical programs on specific applications in engineering. It offers scientists and engineers a clear interdisciplinary introduction and orientation to all major EHL problems and their solutions by first taking them through the basic equations, numerical methods, and calculation programs for Reynolds equation, elastic deformation and energy equation. Readers then progress to problems of isothermal or thermal EHL in line contact, point contact, and ellipse contact. Finally, readers are introduced to the more challenging EHL problems of grease, electric double layer effect, unsteadiness, roughness, and micro-polar fluid.

• Systematic introduction of EHL problems, starting from basic concepts to challenging problems and applications

• Features numerical simulations of the Reynolds equation, elasticity equation of the surfaces, and energy equations

• Offers engineers and scientists a clear interdisciplinary introduction and concise programs for practical engineering applications

• Enhances learning through numerous case studies, with common features and methods in solutions highlighted.

Numerical Calculation of Elastohydrodynamic Lubrication: Methods and Programs is a handy and practical numerical method guide for engineers and technicians. Advanced students in tribology, mechanical engineering and materials science courses will also find it a useful text.

Introduction xi

Preface xiii

Nomenclature xvii

1 Basic equations of elastohydrodynamic lubrication 1

1.1 Basic equations 1

1.1.1 One-dimensional Reynolds equation of elastohydrodynamic lubrication 1

1.1.2 Two-dimensional Reynolds equation of EHL 3

1.1.3 EHL Reynolds equation with two direction velocities 3

1.1.4 Time-dependent EHL Reynolds equation 4

1.2 Film thickness equation without elastic deformation 4

1.2.1 Film thickness equation in line contact 4

1.2.2 Film thickness equation in point contact 5

1.2.3 Film thickness equation in ellipse contact 5

1.3 Surface elastic deformation 6

1.3.1 One-dimensional elastic deformation equation 6

1.3.2 Two-dimensional elastic deformation equation 6

1.4 Viscosity and density equations varying with pressure and temperature 7

1.4.1 Viscosity equations 7

1.4.2 Density equation 9

1.5 Load balancing condition 10

1.5.1 Load balancing equation 10

1.5.2 Numerical calculation of load balancing 11

1.6 Finite difference method of Reynolds equation 15

1.6.1 Discretization of equation 15

1.6.2 Different forms of Reynolds equation 17

1.6.3 Iteration of differential equation 18

1.6.4 Iteration convergence condition 18

2 Numerical calculation method and program of elastic deformation 21

2.1 Numerical method and program of elastic deformation in line contact 21

2.1.1 Equations of elastic deformation 21

2.1.2 Numerical method of elastic deformation 22

2.1.3 Calculation diagram and program 23

2.1.4 Example 25

2.2 Numerical method and program of elastic deformation in point contact 27

2.2.1 Equation of elastic deformation 27

2.2.2 Numerical method for elastic deformation in point contact 28

2.2.3 Calculation diagram 29

2.2.4 Program 30

2.2.5 Example 31

2.3 Numerical calculation method and program for elastic deformation in ellipse contact 33

2.3.1 Contact geometry 33

2.3.2 Contact pressure and contact zone 36

2.3.3 Calculation program 38

2.3.4 Calculation results 44

2.4 Calculation of elastic deformation with multigrid integration technique 44

2.4.1 Principle of multigrid integration 44

2.4.2 Calculation programs and examples 49

3 Numerical calculation method and program for energy equation 61

3.1 Energy equation 61

3.1.1 One-dimensional energy equation 62

3.1.2 Two-dimensional energy equation 62

3.2 Numerical method and program for thermal hydrodynamic lubrication 64

3.2.1 One-dimensional thermal hydrodynamic lubrication 64

3.2.2 Two-dimensional thermal hydrodynamic lubrication 68

4 Numerical calculation method and program of isothermal EHL in line contact 75

4.1 Basic equations and Nondimensional equations 75

4.1.1 Basic equations 75

4.1.2 Nondimensional equations 76

4.1.3 Discrete equations 77

4.2 Numerical calculation method and program 78

4.2.1 Iterative method 78

4.2.2 Program and example 79

5 NewtonRaphson method and programs to solve EHL problems in line contact 87

5.1 Basic equations 87

5.2 NewtonRaphson iterative method 88

5.2.1 Coefficient matrix 88

5.2.2 Calculation of variables in equations 89

5.3 Numerical method and program of NewtonRaphson 90

5.3.1 Coefficient treatment in nonlubricated region 90

5.3.2 Determination of eHe 90

5.3.3 Determination and correction of initial rigid film thickness 91

5.3.4 Calculation Program 91

5.3.5 Example 96

6 Numerical calculation method and program of isothermal EHL in point contact 99

6.1 Basic equations of isothermal EHL in point contact 99

6.1.1 Basic equations 99

6.1.2 Nondimensional equati...