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Ò»±¾²»´íµÄÈ󻬷ÖÎöµÄÊé¼®£¬ÔÚ¹úÍâÉÏѧʱͼÊé¹Ýϵģ¬ÖªÊ¶µã·ÖÎöµÄÂùϸµÄ¡£1 Friction, Wear, and Lubrication ................................. 1
1.1 Friction,Wear,andLubrication¡ªTribology ................... 1
1.2 VariousFormsofLubrication ................................ 2
1.2.1 SolidFriction ....................................... 4
1.2.2 HydrodynamicLubrication ............................ 6
1.3 MeaningsofTribology ...................................... 7 References..................................................... 8
2 Foundations of Hydrodynamic Lubrication ....................... 9
2.1 Tower¡¯sExperiment ........................................ 9
2.2 Reynolds¡¯TheoryofHydrodynamicLubrication ................ 11
2.2.1 InterpretationofReynolds¡¯Equation.................... 18
References..................................................... 22
3 Fundamentals of Journal Bearings ............................... 23
3.1 CircularJournalBearings.................................... 25
3.1.1 CrossSectionofaBearing ............................ 25
3.1.2 ShapeoftheOilFilm................................. 26
3.1.3 BearingLength(BearingWidth) ....................... 27
3.1.4 BoundaryConditionsfortheOilFilm ................... 27
3.2 InfinitelyLongBearings..................................... 29
3.2.1 OilFilmPressure .................................... 29
3.2.2 Infinitely Long Bearing Under Sommerfeld¡¯s Condition . . . . 31
3.2.3 Infinitely Long Bearing Under Gu ̈mbel¡¯s Condition . . . . . . . 37
3.3 ShortBearings............................................. 41
3.3.1 OilFilmPressure .................................... 41
3.3.2 Characteristics of a Short Bearing Under Gu ̈mbel¡¯s Condition 42
3.4 FiniteLengthBearings ...................................... 43
References..................................................... 46
VIII Contents
4 Fundamentals of Thrust Bearings................................ 47
4.1 InfinitelyLongPlanePadBearings............................ 48
4.1.1 BasicFormulae...................................... 49
4.1.2 BasicCharacteristics ................................. 49
4.2 FiniteLengthPlanePadBearings ............................. 54
4.3 SectorPadBearings ........................................ 55
4.3.1 Reynolds¡¯ Equation in Cylindrical Coordinates . . . . . . . . . . . 55
4.3.2 NumericalSolutionofaSectorPad ..................... 57
4.4 AdditionalTopics .......................................... 58
4.4.1 InfluenceofDeformationofthePad .................... 58
4.4.2 MagneticDiskMemoryStorage........................ 59
References..................................................... 60
5 Stability of a Rotating Shaft ¡ª Oil Whip ......................... 63
5.1 OilWhip.................................................. 64
5.2 OilWhipTheory ........................................... 67
5.2.1 OilFilmPressure .................................... 68
5.2.2 OilFilmForce ...................................... 71
5.2.3 LinearizationoftheOilFilmForce ..................... 72
5.2.4 EquationsofMotion.................................. 75
5.2.5 StabilityLimit....................................... 76
5.2.6 OccurrenceofOilWhip¡ªHysteresis................... 84
5.2.7 CoordinateAxes..................................... 88
5.3 StabilityofMultibearingSystems............................. 89
5.4 InfluenceofEarthquakesonOilWhip ......................... 92
5.4.1 BasicEquations ..................................... 94
5.4.2 ExamplesofSimulation............................... 95
5.5 LimitCycleinanUnstableDomain ........................... 98
5.5.1 Approximate Nonlinear Analysis of Journal Bearing Characteristics ...................................... 98
5.5.2 ResultsofAnalysis................................... 101
5.6 FloatingBushBearings ..................................... 102
5.7 ThreeCircularArcBearings ................................. 106
5.8 PorousBearings............................................ 109
5.8.1 GoverningEquations ................................. 109
5.8.2 StabilityofaShaftSystem ............................ 110
5.9 ChaosinRotor¨CBearingSystems ............................. 111
5.10 PreventionofOilWhip...................................... 113
References..................................................... 114
6 FoilBearings .................................................. 119
6.1 BasicEquations............................................ 121
6.2 FiniteElementSolutionoftheBasicEquations.................. 122
6.2.1 Reynolds¡¯ Equation .................................. 122
6.2.2 EquationofBalancefortheFoil........................ 125
6.2.3 SolutionProcedure................................... 126
6.3 CharacteristicsofFoilBearings............................... 126
6.3.1 SingleCylinderHeads................................ 127
6.3.2 DoubleCylinderHeads ............................... 128
6.3.3 ComparisonwithExperiments ......................... 130
6.4 AdditionalTopics .......................................... 130
6.4.1 MagneticTapeMemoryStorage........................ 130
6.4.2 FoilDisk ........................................... 131
References..................................................... 136
7 SqueezeFilm .................................................. 137
7.1 BasicEquations............................................ 138
7.2 SqueezeBetweenRigidSurfaces ............................. 141
7.2.1 SqueezeWithoutFluidInertia.......................... 141
7.2.2 SqueezewithFluidInertia............................. 142
7.2.3 SinusoidalSqueezeMotion............................ 144
7.3 Sinusoidal Squeeze by a Rigid Surface (Experiments) . . . . . . . . . . . . 145
7.3.1 MildSinusoidalSqueeze.............................. 145
7.3.2 IntenseSinusoidalSqueeze¡ªCavitation ................ 146
7.4 SinusoidalSqueezewithaSoftSurface ........................ 149
7.4.1 Low-FrequencySqueeze .............................. 150
7.4.2 High-FrequencySqueeze.............................. 153
7.4.3 ResultsofExperimentandCalculation .................. 154
References..................................................... 159
8 Heat Generation and Temperature Rise........................... 161
8.1 Basic Equations for Thermohydrodynamic Lubrication . . . . . . . . . . . 162
8.2 GeneralizedReynolds¡¯Equation.............................. 163
8.2.1 BalanceofForces.................................... 163
8.2.2 FlowVelocity ....................................... 164 8.2.3 ContinuityEquation.................................. 164
8.2.4 GeneralizedReynolds¡¯Equation ....................... 165
8.3 EnergyEquation ........................................... 166
8.3.1 GeneralEnergyEquation.............................. 166
8.3.2 EnergyEquation..................................... 168
8.3.3 TransformationoftheEnergyEquation.................. 170
8.4 TemperatureDistributioninBearings.......................... 171
8.5 Temperature Analyses of Tilting Pad Thrust Bearings ¡ª Sector Pads 172
8.5.1 BasicEquations ..................................... 173
8.5.2 BoundaryConditions................................. 175
8.5.3 NumericalAnalyses.................................. 175
8.5.4 Examples of Three-Dimensional Analyses of Temperature Distribution......................................... 177
8.5.5 Comparisons of Three-Dimensional, Two-Dimensional, andIsoviscousAnalyses .............................. 178
Contents IX
X
Contents
9
8.5.6 AnalysisConsideringInertiaForces..................... 180
8.5.7 Comparison of Calculated Results and Experiments . . . . . . . 184
8.6 TemperatureAnalysesofCircularJournalBearings.............. 185
8.6.1 BasicEquations ..................................... 187
8.6.2 BoundaryConditions................................. 187
8.6.3 Comparison of Calculated Results and Experiments . . . . . . . 189
References..................................................... 193
Turbulent Lubrication .......................................... 197
9.1 Time-Average Equation of Motion and the Reynolds¡¯ Stress . . . . . . . 198
9.2 TurbulentFlowModel ...................................... 201
9.2.1 MixingLengthModel ................................ 201
9.2.2 k-¦ÅModel .......................................... 203
9.3 Turbulent Lubrication Theory Using the Mixing Length Model . . . . 204
9.3.1 ModifiedMixingLength .............................. 204
9.3.2 Turbulent Velocity Distribution Between Two Surfaces . . . . . 206
9.3.3 TurbulentReynolds¡¯Equation ......................... 208
9.3.4 TurbulentCoefficientsofFluidFilmSeals ............... 209
9.4 Comparison of Analyses Using the Mixing Length Model with Experiments............................................... 211
9.4.1 Turbulent Static Characteristics of Fluid Film Seals . . . . . . . . 211
9.4.2 Turbulent Dynamic Characteristics of Fluid Film Seals . . . . . 213
9.5 TurbulentLubricationTheoryUsingthek-¦ÅModel .............. 214
9.5.1 Applicationofthek-¦ÅModeltoanOilFilm.............. 215
9.5.2 TurbulentReynolds¡¯Equation ......................... 216
9.6 Comparison of Analyses Using the k-¦Å Model with Experiments . . . 218
9.7 Reduction of Friction in a Turbulent Bearing by Toms¡¯ Effect . . . . . . 222
9.8 TaylorVorticesinaJournalBearing ........................... 224
References..................................................... 226
Index ............................................................. 229
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