Table Of Content(cid:2)
PrinciplesofTribology
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Principles of Tribology
ShizhuWen
TsinghuaUniversity
Beijing,China
PingHuang
SouthChinaUniversityofTechnology
Guangzhou,China
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SecondEdition
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LibraryofCongressCataloging-in-PublicationData
Names:Wen,Shizhu,1932-author.|Huang,Ping,1957-author.
Title:PrinciplesofTribology/WenShizhu,HuangPing.
Description:2ndedition.|Hoboken,NJ:JohnWiley&SonsInc.,2018.|
Includesbibliographicalreferencesandindex.
Identifiers:LCCN2017007236(print)|LCCN2017010423(ebook)|ISBN
9781119214892(cloth)|ISBN9781119214922(AdobePDF)|ISBN
9781119214915(ePub)
Subjects:LCSH:Tribology.
Classification:LCCTJ1075.W432017(print)|LCCTJ1075(ebook)|DDC
621.8/9–dc23
LCrecordavailableathttps://lccn.loc.gov/2017007236
CoverdesignbyWiley
Coverimage:©peepo/Gettyimages
Setin10/12ptWarnockbySPiGlobal,Chennai,India
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v
Contents
AbouttheAuthors xxi
SecondEditionPreface xxiii
Preface xxv
Introduction xxvii
PartI LubricationTheory 1
1 PropertiesofLubricants 3
1.1 LubricationStates 3
1.2 DensityofLubricant 5
(cid:2) 1.3 ViscosityofLubricant 7 (cid:2)
1.3.1 DynamicViscosityandKinematicViscosity 7
1.3.1.1 DynamicViscosity 7
1.3.1.2 KinematicViscosity 8
1.3.2 RelationshipbetweenViscosityandTemperature 9
1.3.2.1 Viscosity–TemperatureEquations 9
1.3.2.2 ASTMViscosity–TemperatureDiagram 9
1.3.2.3 ViscosityIndex 10
1.3.3 RelationshipbetweenViscosityandPressure 10
1.3.3.1 RelationshipsbetweenViscosity,TemperatureandPressure 11
1.4 Non-NewtonianBehaviors 12
1.4.1 Ree–EyringConstitutiveEquation 12
1.4.2 Visco-PlasticConstitutiveEquation 13
1.4.3 CircularConstitutiveEquation 13
1.4.4 Temperature-DependentConstitutiveEquation 13
1.4.5 Visco-ElasticConstitutiveEquation 14
1.4.6 NonlinearVisco-ElasticConstitutiveEquation 14
1.4.7 ASimpleVisco-ElasticConstitutiveEquation 15
1.4.7.1 Pseudoplasticity 16
1.4.7.2 Thixotropy 16
1.5 WettabilityofLubricants 16
1.5.1 WettingandContactAngle 17
1.5.2 SurfaceTension 17
1.6 MeasurementandConversionofViscosity 19
1.6.1 RotaryViscometer 19
1.6.2 Off-BodyViscometer 19
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1.6.3 CapillaryViscometer 19
References 21
2 BasicTheoriesofHydrodynamicLubrication 22
2.1 ReynoldsEquation 22
2.1.1 BasicAssumptions 22
2.1.2 DerivationoftheReynoldsEquation 23
2.1.2.1 ForceBalance 23
2.1.2.2 GeneralReynoldsEquation 25
2.2 HydrodynamicLubrication 26
2.2.1 MechanismofHydrodynamicLubrication 26
2.2.2 BoundaryConditionsandInitialConditionsoftheReynoldsEquation 27
2.2.2.1 BoundaryConditions 27
2.2.2.2 InitialConditions 28
2.2.3 CalculationofHydrodynamicLubrication 28
2.2.3.1 Load-CarryingCapacityW 28
2.2.3.2 FrictionForceF 28
2.2.3.3 LubricantFlowQ 29
2.3 ElasticContactProblems 29
2.3.1 LineContact 29
2.3.1.1 GeometryandElasticitySimulations 29
2.3.1.2 ContactAreaandStress 30
2.3.2 PointContact 31
(cid:2) 2.3.2.1 GeometricRelationship 31 (cid:2)
2.3.2.2 ContactAreaandStress 32
2.4 EntranceAnalysisofEHL 34
2.4.1 ElasticDeformationofLineContacts 35
2.4.2 ReynoldsEquationConsideringtheEffectofPressure-Viscosity 35
2.4.3 Discussion 36
2.4.4 GrubinFilmThicknessFormula 37
2.5 GreaseLubrication 38
References 40
3 NumericalMethodsofLubricationCalculation 41
3.1 NumericalMethodsofLubrication 42
3.1.1 FiniteDifferenceMethod 42
3.1.1.1 HydrostaticLubrication 44
3.1.1.2 HydrodynamicLubrication 44
3.1.2 FiniteElementMethodandBoundaryElementMethod 48
3.1.2.1 FiniteElementMethod(FEM) 48
3.1.2.2 BoundaryElementMethod 49
3.1.3 NumericalTechniques 51
3.1.3.1 ParameterTransformation 51
3.1.3.2 NumericalIntegration 51
3.1.3.3 EmpiricalFormula 53
3.1.3.4 SuddenThicknessChange 53
3.2 NumericalSolutionoftheEnergyEquation 54
3.2.1 ConductionandConvectionofHeat 55
3.2.1.1 ConductionHeatH 55
d
3.2.1.2 ConvectionHeatH 55
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3.2.2 EnergyEquation 56
3.2.3 NumericalSolutionofEnergyEquation 59
3.3 NumericalSolutionofElastohydrodynamicLubrication 60
3.3.1 EHLNumericalSolutionofLineContacts 60
3.3.1.1 BasicEquations 60
3.3.1.2 SolutionoftheReynoldsEquation 62
3.3.1.3 CalculationofElasticDeformation 62
3.3.1.4 Dowson–HigginsonFilmThicknessFormulaofLineContactEHL 64
3.3.2 EHLNumericalSolutionofPointContacts 64
3.3.2.1 TheReynoldsEquation 65
3.3.2.2 ElasticDeformationEquation 66
3.3.2.3 Hamrock–DowsonFilmThicknessFormulaofPointContactEHL 66
3.4 Multi-GridMethodforSolvingEHLProblems 68
3.4.1 BasicPrinciplesofMulti-GridMethod 68
3.4.1.1 GridStructure 68
3.4.1.2 DiscreteEquation 68
3.4.1.3 Transformation 69
3.4.2 NonlinearFullApproximationSchemefortheMulti-GridMethod 69
3.4.3 VandWIterations 71
3.4.4 Multi-GridSolutionofEHLProblems 71
3.4.4.1 IterationMethods 71
3.4.4.2 IterativeDivision 72
3.4.4.3 RelaxationFactors 73
3.4.4.4 NumbersofIterationTimes 73
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3.4.5 Multi-GridIntegrationMethod 73
3.4.5.1 TransferPressureDownwards 74
3.4.5.2 TransferIntegralCoefficientsDownwards 74
3.4.5.3 IntegrationontheCoarserMesh 74
3.4.5.4 TransferBackIntegrationResults 75
3.4.5.5 ModificationontheFinerMesh 75
References 76
4 LubricationDesignofTypicalMechanicalElements 78
4.1 SliderandThrustBearings 78
4.1.1 BasicEquations 78
4.1.1.1 ReynoldsEquation 78
4.1.1.2 BoundaryConditions 78
4.1.1.3 ContinuousConditions 79
4.1.2 SolutionsofSliderLubrication 79
4.2 JournalBearings 81
4.2.1 AxisPositionandClearanceShape 81
4.2.2 InfinitelyNarrowBearings 82
4.2.2.1 Load-CarryingCapacity 83
4.2.2.2 DeviationAngleandAxisTrack 83
4.2.2.3 Flow 84
4.2.2.4 FrictionalForceandFrictionCoefficient 84
4.2.3 InfinitelyWideBearings 85
4.3 HydrostaticBearings 88
4.3.1 HydrostaticThrustPlate 89
4.3.2 HydrostaticJournalBearings 90
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4.3.3 BearingStiffnessandThrottle 90
4.3.3.1 ConstantFlowPump 91
4.3.3.2 CapillaryThrottle 91
4.3.3.3 Thin-WalledOrificeThrottle 92
4.4 SqueezeBearings 92
4.4.1 RectangularPlateSqueeze 93
4.4.2 DiscSqueeze 94
4.4.3 JournalBearingSqueeze 94
4.5 DynamicBearings 96
4.5.1 ReynoldsEquationofDynamicJournalBearings 96
4.5.2 SimpleDynamicBearingCalculation 98
4.5.2.1 ASuddenLoad 98
4.5.2.2 RotatingLoad 99
4.5.3 GeneralDynamicBearings 100
4.5.3.1 InfinitelyNarrowBearings 100
4.5.3.2 SuperimpositionMethodofPressures 101
4.5.3.3 SuperimpositionMethodofCarryingLoads 101
4.6 GasLubricationBearings 102
4.6.1 BasicEquationsofGasLubrication 102
4.6.2 TypesofGasLubricationBearings 103
4.7 RollingContactBearings 106
4.7.1 EquivalentRadiusR 107
4.7.2 AverageVelocityU 107
4.7.3 CarryingLoadPerWidthW/b 107
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4.8 GearLubrication 108
4.8.1 InvoluteGearTransmission 109
4.8.1.1 EquivalentCurvatureRadiusR 110
4.8.1.2 AverageVelocityU 111
4.8.1.3 LoadPerWidthW/b 112
4.8.2 ArcGearTransmissionEHL 112
4.9 CamLubrication 114
References 116
5 SpecialFluidMediumLubrication 118
5.1 MagneticHydrodynamicLubrication 118
5.1.1 CompositionandClassificationofMagneticFluids 118
5.1.2 PropertiesofMagneticFluids 119
5.1.2.1 DensityofMagneticFluids 119
5.1.2.2 ViscosityofMagneticFluids 119
5.1.2.3 MagnetizationStrengthofMagneticFluids 120
5.1.2.4 StabilityofMagneticFluids 120
5.1.3 BasicEquationsofMagneticHydrodynamicLubrication 121
5.1.4 InfluenceFactorsonMagneticEHL 123
5.2 Micro-PolarHydrodynamicLubrication 124
5.2.1 BasicEquationsofMicro-PolarFluidLubrication 124
5.2.1.1 BasicEquationsofMicro-PolarFluidMechanics 124
5.2.1.2 ReynoldsEquationofMicro-PolarFluid 125
5.2.2 InfluenceFactorsonMicro-PolarFluidLubrication 128
5.2.2.1 InfluenceofLoad 128
5.2.2.2 MainInfluenceParametersofMicro-PolarFluid 129
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Contents ix
5.3 LiquidCrystalLubrication 130
5.3.1 TypesofLiquidCrystal 130
5.3.1.1 TribologicalPropertiesofLyotropicLiquidCrystal 131
5.3.1.2 TribologicalPropertiesofThermotropicLiquidCrystal 131
5.3.2 DeformationAnalysisofLiquidCrystalLubrication 132
5.3.3 FrictionMechanismofLiquidCrystalasaLubricantAdditive 136
5.3.3.1 TribologicalMechanismof4-pentyl-4′-cyanobiphenyl 136
5.3.3.2 TribologicalMechanismofCholesterylOleylCarbonate 136
5.4 ElectricDoubleLayerEffectinWaterLubrication 137
5.4.1 ElectricDoubleLayerHydrodynamicLubricationTheory 138
5.4.1.1 ElectricDoubleLayerStructure 138
5.4.1.2 HydrodynamicLubricationTheoryofElectricDoubleLayer 138
5.4.2 InfluenceofElectricDoubleLayeronLubricationProperties 142
5.4.2.1 PressureDistribution 142
5.4.2.2 Load-CarryingCapacity 143
5.4.2.3 FrictionCoefficient 144
5.4.2.4 AnExample 144
References 145
6 LubricationTransformationandNanoscaleThinFilmLubrication 147
6.1 TransformationsofLubricationStates 147
6.1.1 Thickness-RoughnessRatio𝜆 147
6.1.2 TransformationfromHydrodynamicLubricationtoEHL 148
6.1.3 TransformationfromEHLtoThinFilmLubrication 149
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6.2 ThinFilmLubrication 152
6.2.1 PhenomenonofThinFilmLubrication 153
6.2.2 TimeEffectofThinFilmLubrication 154
6.2.3 ShearStrainRateEffectonThinFilmLubrication 157
6.3 AnalysisofThinFilmLubrication 158
6.3.1 DifficultiesinNumericalAnalysisofThinFilmLubrication 158
6.3.2 Tichy’sThinFilmLubricationModels 160
6.3.2.1 DirectionFactorModel 160
6.3.2.2 SurfaceLayerModel 161
6.3.2.3 PorousSurfaceLayerModel 161
6.4 Nano-GasFilmLubrication 161
6.4.1 RarefiedGasEffect 162
6.4.2 BoundarySlip 163
6.4.2.1 SlipFlow 163
6.4.2.2 SlipModels 163
6.4.2.3 BoltzmannEquationforRarefiedGasLubrication 165
6.4.3 ReynoldsEquationConsideringtheRarefiedGasEffect 165
6.4.4 CalculationofMagneticHead/DiskofUltraThinGasLubrication 166
6.4.4.1 LargeBearingNumberProblem 167
6.4.4.2 SuddenStepChangeProblem 167
6.4.4.3 SolutionofUltra-ThinGasLubricationofMulti-TrackMagneticHeads 167
References 169
7 BoundaryLubricationandAdditives 171
7.1 TypesofBoundaryLubrication 171
7.1.1 StribeckCurve 171
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7.1.2 AdsorptionFilmsandTheirLubricationMechanisms 172
7.1.2.1 AdsorptionPhenomenaandAdsorptionFilms 172
7.1.2.2 StructureandPropertyofAdsorptionFilms 174
7.1.3 ChemicalReactionFilmanditsLubricationMechanism 177
7.1.3.1 AdditivesofChemicalReactionFilm 178
7.1.3.2 NotesforApplicationsofExtremePressureAdditives 178
7.1.4 OtherBoundaryFilmsandtheirLubricationMechanisms 179
7.1.4.1 HighViscosityThickFilm 179
7.1.4.2 PolishingThinFilm 179
7.1.4.3 SurfaceSofteningEffect 179
7.2 TheoryofBoundaryLubrication 179
7.2.1 BoundaryLubricationModel 179
7.2.2 FactorsInfluencingPerformanceofBoundaryFilms 181
7.2.2.1 InternalPressureCausedbySurfaceTension 181
7.2.2.2 AdsorptionHeatofBoundaryFilm 182
7.2.2.3 CriticalTemperature 183
7.2.3 StrengthofBoundaryFilm 184
7.3 LubricantAdditives 185
7.3.1 OilyAdditives 185
7.3.2 Tackifier 186
7.3.3 ExtremePressureAdditives(EPAdditives) 187
7.3.4 Anti-WearAdditives 187
7.3.5 OtherAdditives 187
References 189
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8 LubricationFailureandMixedLubrication 190
8.1 RoughnessandViscoelasticMaterialEffectsonLubrication 190
8.1.1 ModificationsofMicro-EHL 190
8.1.2 ViscoelasticModel 191
8.1.3 LubricatedWear 192
8.1.3.1 LubricatedWearCriteria 193
8.1.3.2 LubricatedWearModel 193
8.1.3.3 LubricatedWearExample 193
8.2 InfluenceofLimitShearStressonLubricationFailure 195
8.2.1 Visco-PlasticConstitutiveEquation 195
8.2.2 SlipofFluid–SolidInterface 196
8.2.3 InfluenceofSliponLubricationProperties 196
8.3 InfluenceofTemperatureonLubricationFailure 200
8.3.1 MechanismofLubricationFailureCausedbyTemperature 200
8.3.2 ThermalFluidConstitutiveEquation 201
8.3.3 AnalysisofLubricationFailure 202
8.4 MixedLubrication 203
References 207
PartII FrictionandWear 209
9 SurfaceTopographyandContact 211
9.1 ParametersofSurfaceTopography 211
9.1.1 ArithmeticMeanDeviationR 211
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9.1.2 Root-Mean-SquareDeviation(RMS)𝜎orR 211
q
9.1.3 MaximumHeightR 212
max
9.1.4 Load-CarryingAreaCurve 212
9.1.5 ArithmeticMeanInterceptionLengthofCenterlineS 212
ma
9.1.5.1 Slopeż orż 213
a q
9.1.5.2 PeakCurvatureC orC 213
a q
9.2 StatisticalParametersofSurfaceTopography 213
9.2.1 HeightDistributionFunction 214
9.2.2 DeviationofDistribution 215
9.2.3 AutocorrelationFunctionofSurfaceProfile 216
9.3 StructuresandPropertiesofSurface 217
9.4 RoughSurfaceContact 219
9.4.1 SinglePeakContact 219
9.4.2 IdealRoughnessContact 220
9.4.3 RandomRoughnessContact 221
9.4.4 PlasticityIndex 223
References 223
10 SlidingFrictionanditsApplications 225
10.1 BasicCharacteristicsofFriction 225
10.1.1 InfluenceofStationaryContactTime 226
10.1.2 JerkingMotion 226
10.1.3 Pre-Displacement 227
(cid:2) 10.2 Macro-FrictionTheory 228 (cid:2)
10.2.1 MechanicalEngagementTheory 228
10.2.2 MolecularActionTheory 229
10.2.3 AdhesiveFrictionTheory 229
10.2.3.1 MainPointsofAdhesiveFrictionTheory 230
10.2.3.2 RevisedAdhesionFrictionTheory 232
10.2.4 PlowingEffect 233
10.2.5 DeformationEnergyFrictionTheory 235
10.2.6 BinomialFrictionTheory 236
10.3 Micro-FrictionTheory 238
10.3.1 “Cobblestone”Model 238
10.3.2 OscillatorModels 240
10.3.2.1 IndependentOscillatorModel 240
10.3.2.2 CompositeOscillatorModel 241
10.3.2.3 FKModel 242
10.3.3 PhononFrictionModel 242
10.4 SlidingFriction 243
10.4.1 InfluenceofLoad 243
10.4.2 InfluenceofSlidingVelocity 244
10.4.3 InfluenceofTemperature 245
10.4.4 InfluenceofSurfaceFilm 245
10.5 OtherFrictionProblemsandFrictionControl 246
10.5.1 FrictioninSpecialWorkingConditions 246
10.5.1.1 HighVelocityFriction 246
10.5.1.2 HighTemperatureFriction 246
10.5.1.3 LowTemperatureFriction 247
10.5.1.4 VacuumFriction 247
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