Habchi, Wassim - Finite element modeling of elastohydrodynamic lubrication problems-John Wiley & Sons (2018).pdf
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Habchi, Wassim - Finite element modeling of elastohydrodynamic lubrication problems-John Wiley & Sons (2018).pdf
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FiniteElementModelingofElastohydrodynamicLubricationProblemsFiniteElementModelingofElastohydrodynamicLubricationProblemsWassimHabchiLebaneseAmericanUniversityLebanonThiseditionfirstpublished20182018JohnWiley&SonsLtdAllrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,exceptaspermittedbylaw.Adviceonhowtoobtainpermissiontoreusematerialfromthistitleisavailableathttp:
/rightofWassimHabchitobeidentifiedastheauthorofthisworkhasbeenassertedinaccordancewithlaw.RegisteredOffice(s)JohnWiley&Sons,Inc.,111RiverStreet,Hoboken,NJ07030,USAJohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UKEditorialOfficeTheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UKFordetailsofourglobaleditorialoffices,customerservices,andmoreinformationaboutWileyproductsvisitusat.Wileyalsopublishesitsbooksinavarietyofelectronicformatsandbyprint-on-demand.Somecontentthatappearsinstandardprintversionsofthisbookmaynotbeavailableinotherformats.LimitofLiability/DisclaimerofWarrantyWhilethepublisherandauthorshaveusedtheirbesteffortsinpreparingthiswork,theymakenorepresentationsorwarrantieswithrespecttotheaccuracyorcompletenessofthecontentsofthisworkandspecificallydisclaimallwarranties,includingwithoutlimitationanyimpliedwarrantiesofmerchantabilityorfitnessforaparticularpurpose.Nowarrantymaybecreatedorextendedbysalesrepresentatives,writtensalesmaterialsorpromotionalstatementsforthiswork.Thefactthatanorganization,website,orproductisreferredtointhisworkasacitationand/orpotentialsourceoffurtherinformationdoesnotmeanthatthepublisherandauthorsendorsetheinformationorservicestheorganization,website,orproductmayprovideorrecommendationsitmaymake.Thisworkissoldwiththeunderstandingthatthepublisherisnotengagedinrenderingprofessionalservices.Theadviceandstrategiescontainedhereinmaynotbesuitableforyoursituation.Youshouldconsultwithaspecialistwhereappropriate.Further,readersshouldbeawarethatwebsiteslistedinthisworkmayhavechangedordisappearedbetweenwhenthisworkwaswrittenandwhenitisread.Neitherthepublishernorauthorsshallbeliableforanylossofprofitoranyothercommercialdamages,includingbutnotlimitedtospecial,incidental,consequential,orotherdamages.LibraryofCongressCataloging-in-PublicationDataNames:
Habchi,Wassim,1982-author.Title:
Finiteelementmodelingofelastohydrodynamiclubricationproblems/byWassimHabchi.Description:
Hoboken,NJ:
JohnWiley&Sons,2018.|Includesbibliographicalreferencesandindex.|Identifiers:
LCCN2017050348(print)|LCCN2018000724(ebook)|ISBN9781119225157(pdf)|ISBN9781119225140(epub)|ISBN9781119225126(cloth)Subjects:
LCSH:
Elastohydrodynamiclubrication.|Finiteelementmethod.Classification:
LCCTJ1077.5.E43(ebook)|LCCTJ1077.5.E43H332018(print)|DDC621.8/9dc23LCrecordavailableathttps:
/lccn.loc.gov/2017050348CoverDesign:
WileyCoverImages:
Frontcoverbackgroundmalija/iStockphoto;LeftImagescanrail/iStockphoto;RightImageandbackcover:
courtesyofWassimHabchiSetin10/12ptWarnockProbySPiGlobal,Chennai,IndiaPrintedandboundbyCPIGroup(UK)Ltd,Croydon,CR04YY10987654321vContentsPrefacexiiiNomenclaturexviiAbouttheCompanionWebsitexxvPartIIntroduction11ElastohydrodynamicLubrication(EHL)31.1EHLRegime31.2GoverningEquationsinDimensionalForm71.2.1GeneralizedReynoldsEquation91.2.2FilmThicknessEquation151.2.3LinearElasticityEquations181.2.4LoadBalanceEquation241.2.5EnergyEquations241.2.6ShearStressEquations281.3GoverningEquationsinDimensionlessForm281.3.1DimensionlessParameters291.3.2GeneralizedReynoldsEquation311.3.3FilmThicknessEquation321.3.4LinearElasticityEquations331.3.5LoadBalanceEquation341.3.6EnergyEquations341.3.7ShearStressEquations361.4LubricantConstitutiveBehavior361.4.1PressureandTemperatureDependence371.4.1.1Density371.4.1.2Viscosity391.4.1.3ThermalConductivityandHeatCapacity411.4.2ShearDependenceofViscosity411.4.3LimitingShearStress(LSS)431.5DimensionlessGroups441.6ReviewofEHLNumericalModelingTechniques461.7Conclusion52References52viContents2FiniteElementMethod(FEM)592.1FEM:
TheBasicIdea592.2ModelPartialDifferentialEquation(PDE)612.3Steady-StateLinearFEMAnalysis632.3.1ElementaryIntegralFormulations642.3.1.1Weighted-ResidualForm642.3.1.2WeakForm652.3.2SolutionApproximation662.3.2.1MeshingandDiscretization672.3.2.2LagrangeLinearElements692.3.2.3LagrangeQuadraticElements732.3.3GalerkinFormulation752.3.4IntegralEvaluations:
MappingbetweenReferenceandActualElements782.3.5ConnectivityofElements852.3.6AssemblyProcessandTreatmentofBoundaryConditions862.3.7ResolutionProcess902.3.8Post-ProcessingoftheSolution912.3.9One-DimensionalExample922.4Steady-StateNonlinearFEMAnalysis992.4.1NewtonMethodsforNonlinearSystemsofEquations992.4.1.1NewtonMethod1002.4.1.2Damped-NewtonMethod1022.4.2NonlinearFEMFormulation1052.5TransientFEMAnalysis1092.5.1Space-TimeDiscretization1102.5.2Time-DependentFEMFormulation1112.6Multi-PhysicalFEMAnalysis1122.6.1Multi-PhysicalFEMFormulation1132.6.2AssemblyProcess1152.6.3CouplingStrategies1162.6.3.1WeakCoupling1172.6.3.2Full/StrongCoupling1172.7StabilizedFEMFormulations1182.7.1IsotropicDiffusion(ID)1202.7.2StreamlineUpwindPetrovGalerkin(SUPG)1212.7.3GalerkinLeastSquares(GLS)1212.8Conclusion123References123PartIIFiniteElementModelingTechniques1253Steady-StateIsothermalNewtonianLineContacts1273.1ContactConfiguration1273.2Geometry,ComputationalDomains,andMeshing1283.2.1Geometry1283.2.2ComputationalDomains128Contentsvii3.2.3MeshingandDiscretization1303.3GoverningEquationsandBoundaryConditions1323.3.1ReynoldsEquation1333.3.2LinearElasticityEquations1363.3.3LoadBalanceEquation1383.4FEMModel1383.4.1ConnectivityofElements1393.4.2WeakFormFormulation1393.4.3ElementaryMatrixFormulations1413.4.3.1ElasticPart1423.4.3.2HydrodynamicPart1443.4.3.3LoadBalancePart1453.4.4StabilizedFormulations1463.5OverallSolutionProcedure1503.6ModelCalibrationandPreliminaryResults1533.6.1MeshSensitivityAnalysis1533.6.2PenaltyTermTuning1533.6.3SolidDomainSizeCalibration1563.6.4PreliminaryResults1573.7Conclusion161References1614Steady-StateIsothermalNewtonianPointContacts1654.1ContactConfiguration1654.2Geometry,ComputationalDomains,andMeshing1664.2.1Geometry1664.2.2ComputationalDomains1664.2.3MeshingandDiscretization1694.3GoverningEquationsandBoundaryConditions1704.3.1ReynoldsEquation1714.3.2LinearElasticityEquations1734.3.3LoadBalanceEquation1744.4FEMModel1754.4.1ConnectivityofElements1754.4.2WeakFormFormulation1764.4.3ElementaryMatrixFormulations1774.4.3.1ElasticPart1784.4.3.2HydrodynamicPart1804.4.3.3LoadBalancePart1824.4.4StabilizedFormulations1834.5OverallSolutionProcedure1874.6ModelCalibrationandPreliminaryResults1904.6.1MeshSensitivityAnalysis1904.6.2PenaltyTermTuning1914.6.3PreliminaryResults1924.7Conclusion196References196viiiContents5Steady-StateThermalNon-NewtonianLineContacts1995.1ContactConfiguration1995.2Geometry,ComputationalDomains,andMeshing2005.2.1Geometry2005.2.2ComputationalDomains2005.2.3MeshingandDiscretization2015.3GoverningEquationsandBoundaryConditions2035.3.1GeneralizedReynoldsEquation2045.3.2LinearElasticityEquations2055.3.3LoadBalanceEquation2055.3.4EnergyEquations2055.3.5ShearStressEquation2075.4FEMModel2085.4.1ConnectivityofElements2085.4.2WeakFormFormulation2105.4.3ElementaryMatrixFormulations2135.4.3.1ElasticPart2155.4.3.2HydrodynamicPart2155.4.3.3LoadBalancePart2185.4.3.4ThermalPart2195.4.3.5ShearStressPart2245.4.4StabilizedFormulations2255.5OverallSolutionProcedure2275.6ModelCalibrationandPreliminaryResults2285.6.1MeshSensitivityAnalysis2305.6.2FullversusWeakCoupling2305.6.3PreliminaryResults2395.7Conclusion240References2416Steady-StateThermalNon-NewtonianPointContacts2436.1ContactConfiguration2436.2Geometry,ComputationalDomains,andMeshing2446.2.1Geometry2446.2.2ComputationalDomains2446.2.3MeshingandDiscretization2456.3GoverningEquationsandBoundaryConditions2476.3.1GeneralizedReynoldsEquation2486.3.2LinearElasticityEquations2496.3.3LoadBalanceEquation2496.3.4EnergyEquations2496.3.5ShearStressEquations2526.4FEMModel2526.4.1ConnectivityofElements2536.4.2WeakFormFormulation255Contentsix6.4.3ElementaryMatrixFormulations2586.4.3.1ElasticPart2606.4.3.2HydrodynamicPart2616.4.3.3LoadBalancePart2646.4.3.4ThermalPart2646.4.3.5ShearStressPart2706.4.4StabilizedFormulations2736.5OverallSolutionProcedure2746.6ModelCalibrationandPreliminaryResults2756.6.1MeshSensitivityAnalysis2766.6.2PreliminaryResults2766.7Conclusion280References2807TransientEffects2817.1ContactConfiguration2817.2Geometry,ComputationalDomains,andMeshing2817.3GoverningEquations,Boundary,andInitialConditions2827.3.1ReynoldsEquation2827.3.2LinearElasticityEquations2847.3.3LoadBalanceEquation2847.4FEMModel2847.4.1ConnectivityofElements2857.4.2WeakFormFormulation2857.4.3ElementaryMatrixFormulations2867.4.3.1ElasticPart2887.4.3.2HydrodynamicPart2887.4.3.3LoadBalancePart2897.5OverallSolutionProcedure2897.6PreliminaryResults2917.7Conclusion295References2958ModelOrderReduction(MOR)Techniques2978.1Introduction2978.2ReducedSolutionSpaceTechniques2998.2.1ModalReduction3028.2.2Ritz-Vector-LikeMethod3038.2.3EHL-BasisTechnique3048.2.3.1TypicalTestCaseResults3068.2.3.2PerformanceAnalysis:
ReducedversusFullModel3108.3StaticCondensationwithSplitting(SCS)3138.3.1StaticCondensation3158.3.2Splitting3168.3.3OverallNumericalProcedure316xContents8.3.4ResultsandDiscussion32
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