Contents
AbouttheAuthorsxvii
SecondEditionPrefacexix
Prefacexxi
Introductionxxiii
PartILubricationTheory1
1PropertiesofLubricants3
1.1LubricationStates3
1.2DensityofLubricant5
1.3ViscosityofLubricant7
1.3.1DynamicViscosityandKinematicViscosity7
1.3.1.1DynamicViscosity7
1.3.1.2KinematicViscosity8
1.3.2RelationshipbetweenViscosityandTemperature9
1.3.2.1Viscosity–TemperatureEquations9
1.3.2.2ASTMViscosity–TemperatureDiagram9
1.3.2.3ViscosityIndex10
1.3.3RelationshipbetweenViscosityandPressure10
1.3.3.1RelationshipsbetweenViscosity,TemperatureandPressure11
1.4Non-NewtonianBehaviors12
1.4.1Ree–EyringConstitutiveEquation12
1.4.2Visco-PlasticConstitutiveEquation13
1.4.3CircularConstitutiveEquation13
1.4.4Temperature-DependentConstitutiveEquation13
1.4.5Visco-ElasticConstitutiveEquation14
1.4.6NonlinearVisco-ElasticConstitutiveEquation14
1.4.7ASimpleVisco-ElasticConstitutiveEquation15
1.4.7.1Pseudoplasticity16
1.4.7.2Thixotropy16
1.5WettabilityofLubricants16
1.5.1WettingandContactAngle17
1.5.2SurfaceTension17
1.6MeasurementandConversionofViscosity19
1.6.1RotaryViscometer19
1.6.2Off-BodyViscometer19
1.6.3CapillaryViscometer19
References21
2BasicTheoriesofHydrodynamicLubrication22
2.1ReynoldsEquation22
2.1.1BasicAssumptions22
2.1.2DerivationoftheReynoldsEquation23
2.1.2.1ForceBalance23
2.1.2.2GeneralReynoldsEquation25
2.2HydrodynamicLubrication26
2.2.1MechanismofHydrodynamicLubrication26
2.2.2BoundaryConditionsandInitialConditionsoftheReynoldsEquation27
2.2.2.1BoundaryConditions27
2.2.2.2InitialConditions28
2.2.3CalculationofHydrodynamicLubrication28
2.2.3.1Load-CarryingCapacityW28
2.2.3.2FrictionForceF28
2.2.3.3LubricantFlowQ29
2.3ElasticContactProblems29
2.3.1LineContact29
2.3.1.1GeometryandElasticitySimulations29
2.3.1.2ContactAreaandStress30
2.3.2PointContact31
2.3.2.1GeometricRelationship31
2.3.2.2ContactAreaandStress32
2.4EntranceAnalysisofEHL34
2.4.1ElasticDeformationofLineContacts35
2.4.2ReynoldsEquationConsideringtheEffectofPressure-Viscosity35
2.4.3Discussion36
2.4.4GrubinFilmThicknessFormula37
2.5GreaseLubrication38
References40
3NumericalMethodsofLubricationCalculation41
3.1NumericalMethodsofLubrication42
3.1.1FiniteDifferenceMethod42
3.1.1.1HydrostaticLubrication44
3.1.1.2HydrodynamicLubrication44
3.1.2FiniteElementMethodandBoundaryElementMethod48
3.1.2.1FiniteElementMethod(FEM)48
3.1.2.2BoundaryElementMethod49
3.1.3NumericalTechniques51
3.1.3.1ParameterTransformation51
3.1.3.2NumericalIntegration51
3.1.3.3EmpiricalFormula53
3.1.3.4SuddenThicknessChange53
3.2NumericalSolutionoftheEnergyEquation54
3.2.1ConductionandConvectionofHeat55
3.2.1.1ConductionHeatHd55
3.2.1.2ConvectionHeatHv55
3.2.2EnergyEquation56
3.2.3NumericalSolutionofEnergyEquation59
3.3NumericalSolutionofElastohydrodynamicLubrication60
3.3.1EHLNumericalSolutionofLineContacts60
3.3.1.1BasicEquations60
3.3.1.2SolutionoftheReynoldsEquation62
3.3.1.3CalculationofElasticDeformation62
3.3.1.4Dowson–HigginsonFilmThicknessFormulaofLineContactEHL64
3.3.2EHLNumericalSolutionofPointContacts64
3.3.2.1TheReynoldsEquation65
3.3.2.2ElasticDeformationEquation66
3.3.2.3Hamrock–DowsonFilmThicknessFormulaofPointContactEHL66
3.4Multi-GridMethodforSolvingEHLProblems68
3.4.1BasicPrinciplesofMulti-GridMethod68
3.4.1.1GridStructure68
3.4.1.2DiscreteEquation68
3.4.1.3Transformation69
3.4.2NonlinearFullApproximationSchemefortheMulti-GridMethod69
3.4.3VandWIterations71
3.4.4Multi-GridSolutionofEHLProblems71
3.4.4.1IterationMethods71
3.4.4.2IterativeDivision72
3.4.4.3RelaxationFactors73
3.4.4.4NumbersofIterationTimes73
3.4.5Multi-GridIntegrationMethod73
3.4.5.1TransferPressureDownwards74
3.4.5.2TransferIntegralCoefficientsDownwards74
3.4.5.3IntegrationontheCoarserMesh74
3.4.5.4TransferBackIntegrationResults75
3.4.5.5ModificationontheFinerMesh75
References76
4LubricationDesignofTypicalMechanicalElements78
4.1SliderandThrustBearings78
4.1.1BasicEquations78
4.1.1.1ReynoldsEquation78
4.1.1.2BoundaryConditions78
4.1.1.3ContinuousConditions79
4.1.2SolutionsofSliderLubrication79
4.2JournalBearings81
4.2.1AxisPositionandClearanceShape81
4.2.2InfinitelyNarrowBearings82
4.2.2.1Load-CarryingCapacity83
4.2.2.2DeviationAngleandAxisTrack83
4.2.2.3Flow84
4.2.2.4FrictionalForceandFrictionCoefficient84
4.2.3InfinitelyWideBearings85
4.3HydrostaticBearings88
4.3.1HydrostaticThrustPlate89
4.3.2HydrostaticJournalBearings90
4.3.3BearingStiffnessandThrottle90
4.3.3.1ConstantFlowPump91
4.3.3.2CapillaryThrottle91
4.3.3.3Thin-WalledOrificeThrottle92
4.4SqueezeBearings92
4.4.1RectangularPlateSqueeze93
4.4.2DiscSqueeze94
4.4.3JournalBearingSqueeze94
4.5DynamicBearings96
4.5.1ReynoldsEquationofDynamicJournalBearings96
4.5.2SimpleDynamicBearingCalculation98
4.5.2.1ASuddenLoad98
4.5.2.2RotatingLoad99
4.5.3GeneralDynamicBearings100
4.5.3.1InfinitelyNarrowBearings100
4.5.3.2SuperimpositionMethodofPressures101
4.5.3.3SuperimpositionMethodofCarryingLoads101
4.6GasLubricationBearings102
4.6.1BasicEquationsofGasLubrication102
4.6.2TypesofGasLubricationBearings103
4.7RollingContactBearings106
4.7.1EquivalentRadiusR107
4.7.2AverageVelocityU107
4.7.3CarryingLoadPerWidthW/b107
4.8GearLubrication108
4.8.1InvoluteGearTransmission109
4.8.1.1EquivalentCurvatureRadiusR110
4.8.1.2AverageVelocityU111
4.8.1.3LoadPerWidthW/b112
4.8.2ArcGearTransmissionEHL112
4.9CamLubrication114
References116
5SpecialFluidMediumLubrication118
5.1MagneticHydrodynamicLubrication118
5.1.1CompositionandClassificationofMagneticFluids118
5.1.2PropertiesofMagneticFluids119
5.1.2.1DensityofMagneticFluids119
5.1.2.2ViscosityofMagneticFluids119
5.1.2.3MagnetizationStrengthofMagneticFluids120
5.1.2.4StabilityofMagneticFluids120
5.1.3BasicEquationsofMagneticHydrodynamicLubrication121
5.1.4InfluenceFactorsonMagneticEHL123
5.2Micro-PolarHydrodynamicLubrication124
5.2.1BasicEquationsofMicro-PolarFluidLubrication124
5.2.1.1BasicEquationsofMicro-PolarFluidMechanics124
5.2.1.2ReynoldsEquationofMicro-PolarFluid125
5.2.2InfluenceFactorsonMicro-PolarFluidLubrication128
5.2.2.1InfluenceofLoad128
5.2.2.2MainInfluenceParametersofMicro-PolarFluid129
5.3LiquidCrystalLubrication130
5.3.1TypesofLiquidCrystal130
5.3.1.1TribologicalPropertiesofLyotropicLiquidCrystal131
5.3.1.2TribologicalPropertiesofThermotropicLiquidCrystal131
5.3.2DeformationAnalysisofLiquidCrystalLubrication132
5.3.3FrictionMechanismofLiquidCrystalasaLubricantAdditive136
5.3.3.1TribologicalMechanismof4-pentyl-4′-cyanobiphenyl136
5.3.3.2TribologicalMechanismofCholesterylOleylCarbonate136
5.4ElectricDoubleLayerEffectinWaterLubrication137
5.4.1ElectricDoubleLayerHydrodynamicLubricationTheory138
5.4.1.1ElectricDoubleLayerStructure138
5.4.1.2HydrodynamicLubricationTheoryofElectricDoubleLayer138
5.4.2InfluenceofElectricDoubleLayeronLubricationProperties142
5.4.2.1PressureDistribution142
5.4.2.2Load-CarryingCapacity143
5.4.2.3FrictionCoefficient144
5.4.2.4AnExample144
References145
6LubricationTransformationandNanoscaleThinFilmLubrication147
6.1TransformationsofLubricationStates147
6.1.1Thickness-RoughnessRatio??147
6.1.2TransformationfromHydrodynamicLubricationtoEHL148
6.1.3TransformationfromEHLtoThinFilmLubrication149
6.2ThinFilmLubrication152
6.2.1PhenomenonofThinFilmLubrication153
6.2.2TimeEffectofThinFilmLubrication154
6.2.3ShearStrainRateEffectonThinFilmLubrication157
6.3AnalysisofThinFilmLubrication158
6.3.1DifficultiesinNumericalAnalysisofThinFilmLubrication158
6.3.2Tichy’sThinFilmLubricationModels160
6.3.2.1DirectionFactorModel160
6.3.2.2SurfaceLayerModel161
6.3.2.3PorousSurfaceLayerModel161
6.4Nano-GasFilmLubrication161
6.4.1RarefiedGasEffect162
6.4.2BoundarySlip163
6.4.2.1SlipFlow163
6.4.2.2SlipModels163
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