英文原文CaseStudyTheoreticalandpracticalaspectsofthewearofvanepumpsPartA.AdaptationofamodelforpredictivewearcalculationAbstractTheaimofthisinvestigationisthedevelopmentofamathematicaltoolforpredictingthewearbehaviourofvanepumpsuscdinthestandardmethodforindicatingthewcarcharactcristicsofhydraulicfluidsaccordingtoASTMD2882/DIN51389.Thederivationofthecorrespondingmathematicalalgorithmisbasedonthedescriptionofthecombinedabrasiveandadhesivewearphenomenaoccurringontheringandvanesofthepumpbytheshearenergyhypothesis,inconnectionwithstochasticmodellingofthecontactingroughsurfacesastwo-dimensionalisotropicrandomfields.Startingfromacomprehensiveanalysisofthedecisivering-vanetribocontact,whichsuppliesessentialinputdataforthewearcalculation,thecomputationalmethodisadaptedtotheconcretegeometrical,motionalandloadingconditionsofthetribosystemvanepumpandextendedbyinclusionofpartialelastohydrodynamiclubricationinthemathematicalmodej.Forcomparisonofthecalculatedwearbehaviourwithexpenmentalresults,atestseriesonarigdescribedinPartBwascarriedout.Amineraloil-basedlubricantwithoutanyadditiveswasusedtoexcludetheinfluenceofadditiveswhichcannotbedescribedinthemathematicalmodel.Agoodqualitativecorrespondencebetweencalculationandexperimentregardingthetemporalwearprogressandtheamountofcalculatedwearmasswasachieved.Keywords:Mathematicalmodelling；Simulationofwearmechanisms；Weartestingdevices；Hydraulicvanepumps；Elastohydrodynamiclubrication；Surfaceroughness1.IntroductionInthisstudy,thepreliminaryresultsofanewmethodologicalapproachtothedevelopmentoftribo-metersforcomplicatedtribosysLemsarepresented.Thebasicconceptinvolvesthederivationofamathematicalalgofithmforwearcalculationinaninteractiveprocesswithexperiments,whichcanbeusedmodelofthetribosystemtobesimulated.Inthisway,anadditionaldesigntooltoachievethecorrelationofthewearratesofthemodelandoriginalsystemiscreated.TheinvestigationsareperformedfortheVickersvanepumpV104CusedinthestandardmethodforindicatingthewearcharacteristicsofhydraulicfluidsaccordingtoASTMD2882/DIN51389.Inafirststep,amathematicaltheorybasedonthedescriptionofabrasiveandadhesivewearphenomenabytheshearenergyhypothesis,andincludingstochasticmodellingofthecontactingroughsurfaces,isadaptedtothetribologicalrealityofthevanepump,extendedbyaspectsofpartialelastohydrodynamiclubricationandverifiedbycorrespondingexperiments.PartAofthisstudyisdevotedtothemathematicalmodellingofthewearbehaviourofthevanepumpandtotheverificationoftheresultingalgorithm；experimentalwearinvestigationsrepresentthefocalpointofPartB,andthesearecomparedwiththeresultsofthecomputationalmethodderivedinPartA.2.AnalysisofthetribocontactTheVickersvanepumpV104Cisconstructedasapumpforconstantvolumeflowperrevolution.Thesystempressureisledtothebottomsideofthe12vanesintherotorslotstosealthecellsformedbyeachpairofvanes,thering,therotorandthebushingsinthetribologicallyinterestinglinecontactofthevaneandinnercurvatureofthering(Fig.1).Simultaneously,allothervanesidesarestressedwithdifferentandperiodicallyalternatingpressuresofthefiuid.Acomprehensivestructureandstressanalysisbasedonquasistaticmodellingofallinertialforcesactingonthepump,andconsideringtheinnercurvatureofthering,theswivelmotionofthevanesinrelationtothetangentofcurvatureandtheloadingassumptions,isdescribedinRefs.1-3.Thereby,acharacteristicgraphforthecontactforceFeasafunctionoftheturnanglecanbeobtained,whichdependsonthegeometryofthevanesusedineachrunandthesystempressure.Fromthis,theinnercurvatureoftheringcanbedividedintofourzonesofdifferentloadingconditionsinvane-ringtribocontact(Fig.2),whichisingoodagreementwiththewearmeasurementsontherings:intheareaofmaximumcontactforce(zonen),thehighestlinearwearcouldbefound2,3(seealsoPartB).3.Mathematicalmodelling3.1.BasicrelationsforwearcalculationThevaneandringshowcombinedabrasiveandadhesivewearphenomena(Fig.3).ThebasicconceptsofthetheoryforthepredictivecalculationofsuchwearphenomenaaredescribedinRefs.4-6.Startingfromtheassumptionthatweariscausedbysheareffectsinthesurfaceregionsofcontactingbodiesinrelativemotion,thefundamentalequation(1)forthelinearwearintensityIhinthestationarywearstatecanbederived,whichcontainsthespecificshearenergydensityes/ro,interpretableasamaterialconstant,andtherealareaArsoftheasperitycontactsundergoingshear.Todeterminethisrealcontactarea,thede-scriptionofthecontactingroughsurfacesastwo-dimensionalisotropicgaussianfieldsaccordingtoRef.7isincludedinthemodelling.Thustheimplicitfunctionalrelationwiththeweightfunction(2)isfound,whichcanbeusedtocalculatethesurfaceratioinEq.(1)forunlubricatedcontactsfromthehertzianpressurePaactingintheinvestigatedtribocontactbyacomplicatediterativeprocessdescribedinRefs.6,8.TheconcretestructureofthefunctionsFandcdependsontherelativemotionofthecontactingbodies(sliding,rolling).Theparametera-（m0m4）/m22representsthepropertiesoftheroughsurfacebyitsspectralmoments,whichcanbedeter-minedstatisticallyfromsurfaceprofilometry,andtheplasticityindex妒=(mOm4)y4(E/H)isameasureoftheratioofelasticandplasticmicrocontacts.3.2.ExtensiontolubricatedcontactsThealgorithmresultingfromthebasicrelationsforwearcalculationwasappliedsuccessfullytounlubricatedtribosystems8.ThefirstconceptsforinvolvinglubricationinthemathematicalmodelaredevelopedinRef.8.Theyarebasedontheapplicationoftheclassicaltheoryofelastohydrodynamiclubrication(EHL)tothemicrocontactsoftheasperities,neglectingthefactthatthereisalsoamacrolubricationfilmwhichseparatesthecontactingbodiesandisinterruptedinthecaseofpartiallubricationbytheasperitymicrocontacts.There