Contents
CHAPTER 1 Properties of gases.......................................................1
1.1 Gas equations .................................................................................1
1.1.1 Ideal gas equations.............................................................. 2
1.1.2 Gas index equation.............................................................. 3
1.1.3 Actual gas equation............................................................. 5
1.1.4 Degree of gas molecular freedom ...................................... 5
1.1.5 Specific heat capacity ......................................................... 7
1.2 Viscosity .........................................................................................7
1.3 Property of wet gas ......................................................................11 1.3.1 Pressure ............................................................................. 12 1.3.2 Humidity............................................................................ 13 1.3.3 Dew point temperature...................................................... 14 References.................................................................................... 14
CHAPTER 2 Gas lubrication equations........................................... 15
2.1 Reynolds equation ........................................................................15
2.1.1 Derivation of Reynolds equation...................................... 16
2.1.2 Reynolds equation in the polar coordinate system .......... 19
2.1.3 Reynolds equation in the cylindrical coordinate system................................................................................ 19
2.1.4 Lubrication parameters ..................................................... 20
2.2 Energy equation............................................................................22
2.2.1 Chang of gas inner energy................................................ 23
2.2.2 External work on gas and energy loss.............................. 24
2.3 Solid heat conduction equation and the interface equation ........26
2.4 Numerical analysis method..........................................................27
2.4.1 Finite difference method................................................... 27
2.4.2 Flow conservation............................................................. 28
2.4.3 Friction force balance ....................................................... 34 References.................................................................................... 35
CHAPTER 3 Isothermal gas lubrication ......................................... 37
3.1 Sliders ...........................................................................................37
3.1.1 Lubrication equation ......................................................... 38
3.1.2 Pressure boundary condition............................................. 40
3.1.3 Lubrication performance parameters................................ 40
VI Contents
3.2
3.3
CHAPTER 4
4.1
4.2
4.3
4.4
3.1.4 Hydrodynamic lubrication characteristics of sliders........ 41
3.1.5 Hydrodynamic lubrication characteristics of divergent sliders ................................................................................ 43
3.1.6 Lubrication characteristics of the magnetic head slider ......................................................................... 45 Journal bearing and radial seal ....................................................51
3.2.1 Lubrication equations........................................................ 52 3.2.2 Boundary conditions ......................................................... 52 3.2.3 Lubrication parameters ..................................................... 53 3.2.4 Lubrication characteristics................................................ 55 Spiral groove thrust bearing.........................................................56 3.3.1 Gas lubrication equations.................................................. 59 3.3.2 Pressure boundary conditions ........................................... 60 3.3.3 Lubrication parameters ..................................................... 60 3.3.4 Lubrication characteristics................................................ 61 3.3.5 Spiral groove face seal...................................................... 64 3.3.6 Lubrication equations........................................................ 65
3.3.7 Pressure boundary conditions ........................................... 65
3.3.8 Seal performance parameters............................................ 66
3.3.9 Lubrication regularity ....................................................... 66 References.................................................................................... 71
Gas thermohydrodynamic lubrication of rigid surfaces....................................................................... 73 Sliders ...........................................................................................73
4.1.1 Gas lubrication equations.................................................. 73
4.1.2 Boundary conditions ......................................................... 75
4.1.3 Thermal lubrication characteristics .................................. 75 Journal bearing and radial seal ....................................................79
4.2.1 Lubrication equations........................................................ 79
4.2.2 Thermal boundary condition............................................. 80
4.2.3 Lubrication property ......................................................... 80 Spiral groove thrust bearing.........................................................83
4.3.1 Lubrication equations........................................................ 83
4.3.2 Boundary conditions ......................................................... 85
4.3.3 Lubrication property ......................................................... 86 Spiral groove face seal.................................................................86
4.4.1 Temperature characteristics of gas film ........................... 91
4.4.2 Lubrication property ......................................................... 94 References.................................................................................... 99
Contents VII
CHAPTER 5 Gas thermoelastohydrodynamic lubrication of face seals ............................................................. 101
5.1 Fundamental equations...............................................................101
5.1.1 Lubrication equations...................................................... 101
5.1.2 Boundary conditions ....................................................... 104
5.2 Choked fluid effect.....................................................................107
5.2.1 Model validation ............................................................. 107
5.2.2 Pressure distribution characteristics ............................... 109
5.3 Characteristics of thermoelastic distortions of seal faces............................................................................................109
5.4 Characteristics of gas thermoelastohydrodynamic lubrication...................................................................................111
5.4.1 Mechanical distortions .................................................... 111
5.4.2 Thermal distortions ......................................................... 115
5.4.3 Thermoelastic distortions................................................ 117 References.................................................................................. 120
CHAPTER 6 Transient thermoelastohydrodynamic gas lubrication of face seals .......................................... 121
6.1 Fundamental equations...............................................................121
6.1.1 Dynamic equations.......................................................... 122
6.1.2 Lubrication equations...................................................... 122
6.1.3 Boundary conditions ....................................................... 123
6.1.4 Dynamic characteristic parameter .................................. 123
6.2 Dynamic characteristics of isothermal gas lubrication .............124
6.2.1 Axial stiffness and damping ........................................... 124
6.2.2 Angular stiffness and damping ....................................... 126
6.2.3 Amplitude-frequency characteristics of gas film ........... 129
6.3 Dynamic characteristics of thermal gas lubrication of rigid surfaces .......................................................................................130
6.3.1 Axial stiffness and damping ........................................... 131
6.3.2 Angular stiffness and damping ....................................... 134
6.3.3 Amplitude-frequency characteristics of gas film ........... 137
6.4 Dynamic characteristics of gas thermoelastohydrodynamic lubrication...................................................................................137
6.4.1 Axial stiffness and damping ........................................... 137
6.4.2 Angular stiffness and damping of gas film .................... 139
6.4.3 Amplitude-frequency characteristics of gas film............................................................................ 140 References.................................................................................. 141
VIII Contents
CHAPTER 7 Vapor-condensed gas lubrication of face seals .......................................................................... 143
7.1 Fundamental equations...............................................................143
7.1.1 Wet gas equations ........................................................... 143
7.1.2 Vapor-condensed parameter ........................................... 145
7.2 Characteristics of vapor condensation in gas lubrication film .............................................................................................145
7.3 Laws of vapor condensation in gas lubrication film.................146
7.3.1 Humidity.......................................................................... 146
7.3.2 Seal clearance.................................................................. 147
7.3.3 Seal pressure ................................................................... 148
7.3.4 Rotational speed.............................................................. 148
7.4 Movement of liquid drops on gas lubrication surfaces.............150
7.4.1 Surface wetting model .................................................... 150
7.4.2 Surface-texture geometry parameters and wettability........................................................................ 152
7.4.3 Droplet motion ................................................................ 158 7.4.4 Drop adsorption on seal surface ..................................... 164 References.................................................................................. 164
CHAPTER 8 Cryogenic gas lubrication of face seals.................. 167
8.1 Fundamental equations...............................................................167
8.1.1 Lubrication equations...................................................... 168
8.1.2 Boundary conditions ....................................................... 171
8.2 Phase change in gas lubrication film.........................................172
8.3 Characteristics of thermoelastic distortions of seal faces .........173
8.4 Characteristics of cryogenic gas lubrication..............................173
8.4.1 Ambient temperature ...................................................... 174
8.4.2 Rotation speed................................................................. 174 References.................................................................................. 177
CHAPTER 9 Surface grooves of gas face seals and testing technology................................................................. 179
9.1 Surface grooves of gas face seals ..............................................179
9.2 Testing technology of gas face seals .........................................185
9.2.1 Experimental setup.......................................................... 185
9.2.2 Face groove machining................................................... 185
9.2.3 Face morphology test...................................................... 187
9.3 Experimental characteristics of gas face seals ..........................188
9.3.1 Seal opening characteristic ............................................. 188
9.3.2 Hydrodynamic characteristics......................................... 190
Contents IX
9.3.3 Surface wear.................................................................... 192 References.................................................................................. 195
CHAPTER 10 Design of gas face seals .......................................... 197
10.1 Force analysis of gas seals.........................................................197
10.1.1 Opening force................................................................ 198
10.1.2 Closing force................................................................. 198
10.1.3 O-ring friction force...................................................... 199
10.2 Geometric parameters of gas face seals ....................................199
10.2.1 Seal clearance................................................................ 199
10.2.2 Seal face width.............................................................. 199
10.2.3 Balance diameter........................................................... 200
10.2.4 Seal face and shaft (shaft sleeve) clearance................. 200
10.3 Performance parameters of gas face seals.................................201
10.3.1 Leakage rate .................................................................. 201
10.3.2 Gas film stiffness .......................................................... 201
10.4 Materials of the seal couple .......................................................202
10.5 Dimension design of seal rings..................................................202
10.5.1 Design of rotor dimension ............................................ 202
10.5.2 Design of stator dimension ........................................... 203
10.5.3 Design of the face groove............................................. 204
10.6 Design of the secondary seal .....................................................205
10.7 Process of seal design and illustration.......................................205
10.7.1 Process of seal design ................................................... 205
10.7.2 Design conditions.......................................................... 206
10.7.3 Design steps .................................................................. 206 References.................................................................................. 218
Index ......................................................................................................................219
