Hydrodynamic Bearings

This Series provides the necessary elements to the development and validation of numerical prediction models for hydrodynamic bearings. This book describes the rheological models and the equations of lubrication. It also presents the numerical approaches used to solve the above equations by finite differences, finite volumes and finite elements methods.

Aurelian FATU, Associate Professor, Prime Institute, University of Poitiers, France.

Dominique SOUCHET, Associate Professor, Prime Institute, University of Poitiers, France.

Foreword by J.F. Booker ix

Foreword by Jean Frêne xiii

Preface xvii

Nomenclature xxiii

Chapter 1 The Lubricant 1

1.1 Description of lubricants 1

1.2 The viscosity 2

1.3 Other lubriciant properties 12

1.4 Lubricant classification and notation 14

1.5 Bibliography 15

Chapter 2 Equations of Hydrodynamic Lubrication 17

2.1 Hypothesis 17

2.2 Equation of generalized viscous thin films 18

2.3 Equations of hydrodynamic for journal and thrust bearings 20

2.4 Film rupture; second form of Reynolds equation 26

2.5 Particular form of the viscous thin film equation in the case of wall slipping 32

2.6 Boundary conditions; lubricant supply 35

2.7 Flow rate computation 43

2.8 Computation of efforts exerted by the pressure field and the shear stress field: journal bearing case 51

2.9 Computation of efforts exerted by the pressure field and the shear stress field: thrust bearing case 54

2.10 Computation of viscous dissipation energy: journal bearing case 57

2.11 Computation of viscous dissipation energy: thrust bearing case 59

2.12 Different flow regimes 59

2.13 Bibliography 61

Chapter 3 Numerical Resolution of the Reynolds Equation 673

3.1 Definition of the problem to be solved 64

3.2 The finite difference method 70

3.3 The finite volume method 82

3.4 The finite element method 90

3.5 Discretization of time derivatives 108

3.6 Comparativ analysis of the different methods 114

3.7 Accounting of film thickness discontinuities 146

3.8 Numerical algorithm for computing bearing axial flow rate 149

3.9 Bibliography 155

Chapter 4 Elastohydrodynamic Lubrication 159

4.1 Bearings with elastic structure 160

4.2 Elasticity accounting: compliance matrices 163

4.3 Accounting of shaft elasticity 178

4.4 Particular case of non-conformal meshes 180

4.5 Bibliography 184

Appendix 185

Index 189

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