弹性流体动压润滑 : 方法与程序

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 for 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 method and program of 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 for 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 Iteration method 78

4.2.2 Program and example 79

5 Newton–Raphson method and programs to solve EHL problems in line contact 87

5.1 Basic equations 87

5.2 Newton–Raphson iteration method 88

5.2.1 Coefficient matrix 88

5.2.2 Calculation of variables in equations 89

5.3 Numerical method and program of Newton–Raphson method 90

5.3.1 Coefficient treatment in nonlubricated region 90

5.3.2 Determination of ρeHe 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 for isothermal EHL in point contact 99

6.1 Basic equations for isothermal EHL in point contact 99

6.1.1 Basic equations 99

6.1.2 Nondimensional equations 100

6.2 Numerical calculation method and program 101

6.2.1 Differential equations 101

6.2.2 Iteration method 102

6.2.3 Calculation diagram 102

6.2.4 Calculation program 106

6.2.5 Example 111

7 Numerical calculation method and programs of multigrid method for isothermal EHL 113

7.1 Basic principles of multigrid method 113

7.1.1 Grid structure 113

7.1.2 Equation discrete 114

7.1.3 Restriction and extension 114

7.2 Nonlinear full approximation scheme of multigrid method 116

7.2.1 Parameter transformation downwards 116

7.2.2 Correction of lower grid parameters 116

7.2.3 Parameter transformation upwards 118

7.2.4 V and W loops 118

7.3 Key factors to solve EHL problem with multigrid method 119

7.3.1 Iteration methods 119

7.3.2 Relaxation factors selection 121

7.4 Program for EHL in line contact with multigrid method 122

7.4.1 Specification of program 122

7.4.2 Calculation program 123

7.4.3 Example 133

7.5 Program for EHL in point contact with multigrid method 133

7.5.1 Specification of program 133

7.5.2 Calculation program 134

7.5.3 Example 143

8 Numerical calculation method and program for isothermal EHL in ellipse contact 145

8.1 Basic equation 145

8.1.1 Reynolds equation 145

8.1.2 Film thickness equation 146

8.1.3 Viscosity–pressure equation 146

8.1.4 Density–pressure equation 147

8.1.5 Load balancing equation 147

8.2 Calculation program 148

8.2.1 Calculation diagram 148

8.2.2 Calculation program 149

8.2.3 Example 157

9 Numerical calculation method and program for isothermal EHL in elliptical contact with two-dimensional velocities 159

10 Numerical calculation method and program for thermal EHL 173

11 Numerical calculation method and program for grease EHL 217

12 Numerical calculation method and program for EHL considering effect of electric double layer 279

13 Numerical calculation method and program for time-dependent EHL in line contact 295

14 Numerical calculation method and program for isothermal EHL with rough surface 305

15 Numerical calculation method and program for micropolar fluid EHL 329

References 345 Index 347

本书介绍了弹性流体动压润滑（弹流润滑）的数值计算方法和程序。全书共分15章，第1~3章分别是：弹性流体动压润滑基本方程、弹性变形数值计算方法和能量方程数值计算方法，这3章的内容是后面各章的基础；第4~10章包括线接触、点接触、椭圆接触弹流问题的等温解和热解的内容，其中第9章分析了速度方向与主轴方向不一致时的椭圆接触弹流问题，这些章节是弹流润滑计算中最基本、最重要的内容；第11~15章分别介绍了脂润滑、双电层效应、非稳态、粗糙度影响、微极流体的弹流润滑计算，这些计算内容是在对前面程序的简单修改的基础上实现的。本书可以作为机械设计与理论专业研究生及相关专业师生的教材或教学参考书，也可供从事弹流润滑计算分析与研究的工程技术人员参考。

本书是作者与研究生们一起合作出版的《润滑数值计算方法》的姊妹篇。自出版《润滑数值计算方法》以来受到了较广泛的关注和评价，使作者感觉到十分有必要出版本书。本书以弹性流体动压润滑（弹流润滑）数值计算方法和程序为主，详细介绍了弹流计算中的线接触、点接触、椭圆接触的等温解和热解的内容。此外还对特殊工况下的弹流润滑问题，如：不同方向速度、脂润滑、双电层效应、非稳态、粗糙度影响、微极流体等内容进行了简要的介绍。弹流润滑计算是与工程实际联系十分紧密的内容，存在于滚动轴承、齿轮转动等零件中，同时弹流计算又是润滑计算中的难点之一。主要的困难在于必须将Reynolds方程、弹性变形方程、粘压方程，以及能量方程邓联立在一起求解，因此一般需要通过迭代法完成，而这样的求解过程时常会带来计算不收敛。本书尽量采用较为可靠地迭代方法，并对提供的程序和例题进行了验算，确认可以得到满意的结果。