电接触的原理应用和技术教材electrical contacts fundamentals,applications and technology chapter 3 tribology电气工程电力工程教材教程

电接触的原理应用和技术教材ElectricalContactsFundamentals,ApplicationsAndTechnologyChapter3Tribology电气工程电力工程教材教程 3Tribology3.1FRICTIONFrictionisthemostwidespreadphenomenonindailylife.StudiesoffrictiondatebacktothetimesofAristotleandLeonardo.25Frictionaccompaniesnotonlyanymotion,butalsotendencyfordisplacement.Althoughtheterm“friction”iswell-known,fewpeoplerealizewhatitreallymeansbecauseofthehighlyintricatenatureofthisphenomenon.Primarily,internalfriction,asresistancetorelativedisplacementofthecomponentsofoneandsamebody,shouldbediscriminatedfromtheexternalfrictionofsolidsorjustfrictionthatistreatedbelow.Frictioncanbeconsideredasaformationofrealcontactareaundernormalloadandshearingofthecontactinterface.Theenvironmentisanadditionalimportantfactorinfluencingtheprocess.Thiscombinationresultsinnumeroussurfaceeffectsandavarietyoffrictionmechanisms.Slidingfrictionoccursbetweentworelativelymovingbodiesincontact,inwhichtheirsurfacevelocitiesinthecontactareaaredifferentwithrespecttomagnitudeand/ordirection.Itisgovernedbytheprocessesthatoccurinthinsurfacelayers.Therearetwomainnoninteractingmechanismsoffriction:adhesionanddeformation.23,24Thisideaisessentialforthetwo-termmodeloffriction,althoughtheindependenceofthesemechanismsisamatterofconvention.3.1.1LAWSOFFRICTIONWhentwobodiesareincontact,atangentialforcemustbeappliedtoproducetheirrelativedisplacement.Whenthisforceincreasesfromzerotoafinitevalue,microdisplacementdoccursinthecontactzone,thoughthebodiesthemselvesremainmotionlessasawholeuntilthetangentialforcesreachessomelimitingvaluetermedthestaticfrictionforce,Fs(Figure3.1).TheintermediatevaluesoftheappliedtangentialforceFintaretermedthepartialstaticfrictionforce.Apparently,thereisaforcethatimpedesthebreakofrelativestateatrestandincipientmotion.Theforceisalwaysnonzeroandpossessesafinitevalue.Thisprincipalfactshouldbetreatedasthefundamentallawoffrictionthatcanbeformulatedasfollows:astaticfrictionexistswhentwosolidsformacontact.Toretainthenumberingofthelaws,asisacceptedinthetribologicalliterature,thislawshouldbetermedthezerolaw.Notwithstandingitssimpleformulation,thislawisofgreatsignificance.Itisexactlythefrictionatrestthatisatypicalfeatureofexternalfrictiondistinguishingitfromtheinternalfrictioninducedbyanyinfinitesimaltangentialdisplacement.Moreover,withoutstaticfrictiontheworldwouldbequeerandeerie,ifitwouldexistatall.Humanswouldnotbeabletowalkintheircustomaryshoes.Abookplacedonadeskwouldgraduallyslipoffasifitwasslidingdownaslope.Thetiresofanyvehiclewouldslide.ReferringtoFigure3.1,afterthebodybeginstomove,theresistancetoitsmotiondecreasesbutitnevervanishescompletelybecauseitremainsapproximatelyconstantiftheconditionsformotionremainunchanged.Thisresistancetomotionistermedkineticfrictionandtheresistanceforceistermedthekineticfrictionforce,Fk.35q2006byTaylor&FrancisGroup,LLCTherelationbetweenthefrictionforce(staticorkinetic)andnormalloadiscommonlytermedthecoefficientoffriction(staticorkinetic,respectively).LeonardodaVinci(1452–1519)believedthatthecoefficientoffrictionofsmoothsurfaceswasconstantandequalto0.25.Thisviewpointpersistedinscienceforaverylongtime.GuilliomAmontons(1663–1705)assumedthatthefrictioncoefficientofiron,leather,lead,andwoodwasequalto1/3.Inreality,thecoefficientoffrictionmayvaryoverawiderange,fromapproximately0.001inrollingbearingsunderlightloadstotensofunitsbetweenthoroughlycleanedsurfaceslikemetalscontactinginvacuum.Asarule,undernormalconditionsoffrictioninair,thecoefficientoffrictionchangeswithinacomparativelynarrowrangefrom0.1to1.Itisnotthemagnitudeofthefrictioncoefficientbutratheritsconstancythat,infact,istheessentialimplicationofthefirstlawoffriction,frequentlycalledtheAmontons’law.Figure3.2showsasimpleexperimentaldesignillustratingthislaw.Ifabody(forinstance,abook)liesontheplaneandhastheweightP,theforceneededtomovethisbodyisequaltoF.Tomoveapileofnbooks(nZ2inthefigure),thetangentialforceshouldbentimeslarger.Therefore,thefirstlawoffrictionisformulatedinthefollowingmanner:thefrictionforceisdirectlyproportionaltothenormalload.Whenmdesignatesthecoefficientoffrictionthat,fromtheaboveformulation,isconstantandindependentofthenormalload,thefirstlawoffrictionstatesthat:FZmP:(3.1)XFFkFsdFintFIGURE3.1Transitionfromstaticfrictiontokineticfriction.W2WF1F2FIGURE3.2Thefrictionforceincreasespracticallyproportionallytotheappliednormalload(firstlawoffriction.)ElectricalContacts:Fundamentals,ApplicationsandTechnology36q2006byTaylor&FrancisGroup,LLC’statementreceivedacoolwelcomebytheFrenchRoyalAcademyofSciences,whichinstructedsenioracademicianDelaHiretoverifyAmontons’experiments.Additionaltests(1699–1700)corroboratedbothofAmontons’lawsandhisformulationofthesecondlawforestalledmodernideasthatsolidsareindiscretecontact.Expresseditinmodernterms,Amontons’paradoxarisesbecausesolidsareincontactbyindividualspotsbecausetheirrealsurfacesareroughandtheyareunabletocontactovertheirentirenominalsurfaces.Thetotalareaofthespots(realcontactareawhichistreatedmorethoroughlyinsubsequentchapters)isverysmallcomparedwiththeapparentarea.Ifthelatterisspecified,experienceshowsthattherealareaincreaseslinearlyasafunctionofload.Thefrictionforce,inturn,isproportionaltotherealcontactarea.Differentfacesofthespecimencanbearrangedsothattheareaoftherealcontactismaintainedanddependsonlyontheload.Consequently,itisclearwhyfrictiondoesnotdependontheapparentcontactarea.Thethirdlaw,oftenattributedtoCoulomb(1736–1806),isaddedtotheabovetwo:thefrictionforcedoesnotdependontheslidingvelocity.Thislawwaslesssubstantiatedthantheothers.Incidentally,Coulombobservedinhisexperimentsthatthefrictionforceincreasesordecreasesasafunctionofvelocity.Nevertheless,thislawcanbetruewithinareasonablerangeofvelocities,providedthatthecontacttemperatureinfrictionvariesinsignificantlyandthefeaturesofthecontactzoneremainpracticallyunchanged.nAm<AnF1F2F1=F2FIGURE3.3FragmentofLeonardodaVinci’sdrawingillustratingthesecondlawoffriction.Tribology37q2006byTaylor&FrancisGroup,LLCInconclusion,itshouldbenotedthatthelawsoffrictionaregoodempiricalrulesallowingtacklingthetribologicalsituationsemerginginvariousapplications.3.1.2REALCONTACTAREAWhentwosurfacesapproacheachother,theiropposingasperitieswithmaximumheightcomeintocontact.Astheloadisincreased,newpairsofasperitieswithsmallerheightscomeintocontact,formingindividualspots.Theoverallareaofthesespotsisknownastherealcontactarea(seeChapter2).Therealcontactareadependsbothonthemechanicalbehaviorofthesurfacelayersandtheirroughness.Thelattermayvaryundercompressionandfrictionconditions.Whentherealcontactareaisbuiltup,partsofthesurfaceasperitieselasticallydeform;othersundergoplasticstrain.Inthegeneralcase,thedeformationiselastoplasticwithhardening.Therealcontactareavariesindirectproportionwithloadtothepowerindexintherangefrom2/3to1.Aloadindexveryclosetounityisnotanindicationofthecontactplasticdeformationbecausethecontactbehaviorisalsogovernedbystatisticalgeometryofroughsurfacesincontact.Themeandiameterofasinglecontactspotisscarcelyaffectedbytheappliedload.Therateofthespotareagrowthisaboutanorderofmagnitudelessthanthatoftherealcontactarea.Therealcontactareaincreaseswithincreasingcurvatureradiusofasperityanddecreaseswhenyieldpoint,elasticitymodulus,andmaterialhardeningincrease.3.1.3INTERFACIALBONDS(ADHESIONCOMPONENTOFFRICTION)Iftwocleansurfacesarebroughtintocontact,theforcesofattractionatinteratomicdistancesarethesameasinthebulk.Severaltypesoftheseforcescanbedifferentiated(Figure3.4).10Theionicbondoccursbetweenanionsandcationsheldtogetherbyelectrostaticforces.Theionicsolidshavehighstrength;suchisthecaseofaluminumoxide.Thecovalent(homopolar)bondbetweenneutralatomsisgeneratedbyoverlapoftheirelectronfieldsthatresultsinverystrongbondingforcesincrystallinesolidssuchasdiamond.ThevanderWaalsbondmayoccurbetweenanyatomsandmoleculesduetodipole–dipoleinteraction(theatomsaretreatedasmomentarydipolesbecausethecentersofpositiveandnegativechargesareinequitableatanytime).Itisresponsibleforphysicaladsorptionofenvironmentalspeciesbyasolidsurface.Themetallicbondisfoundinallmetalsandisrealizedbyfreeelectronsfreelymovinginioniclattice.Thebondingisgeneratedbetweentherubbingsurfacesonlywhenthesurfacefilmsareabsent(e.g.,whenslidinginhighvacuumorwhenwearrateofthefilmexceedstherateoffilmformation).Eachindividualatominthebulkofamaterialinteractswithitsnearestneighborsthroughtheseforces.Aspecificamountofenergyassociatedwiththeinteractionisreferredtoasthecohesiveenergythatplaysanimportantpartintribology.Anatominthefreesurfaceisunderdifferentconditionsbecausethenumberofneighborshasbeenreducedand,asaresult,thereisnobondingoutsidethesolid(Figure3.5).Forthisreason,thesurfaceexhibitsanexcessenergyknownasthesurfaceenergy.Thisenergycontrolsthecapacityofsurfacestoformtheadhesivejunctions.IonicCovalentVanderWaalsMetallicFIGURE3.4Maintypesofbondingforces.ElectricalContacts:Fundamentals,ApplicationsandTechnology38q2006byTaylor&FrancisGroup,LLCAdhesionreferstoanatomicbondingprocessthatoccursbetweencontactingpointsonopposingsurfaces.Thejunctionsmayformatbothstaticcontactandfriction.BowdenandTaborhaveproposedthesimplemodeloftheadhesivejunctionformation.23Itisamatterofgeneralexperiencethatcleanironsurfacesseizeinvacuumduetoformationofstrongadhesivebonds.Thisisnotalwaysthecasewhenthesurfacescomeintocontactatnormalconditions.Thejunctionsmayappearonlybetweenverysmoothsurfacesunderhighloadand,inthiscase,amutualmicroslipofthematingsurfacesisdesirable.Thisisduetothepresenceoftheabsorbedfilms(includingnaturaloxides),moisture,andothersubstancesonthesolidsurface.Thesecontami-nantslowerthesurfaceenergy,therebyreducingthepossibilityofstrongjunctionformation.Initially,whentworoughsurfacesareapproachingoneanother,atleasttwoasperitiescomeintocontact.Becausethecontactareaissmall,thepressureisveryhigh,evenunderaverysmallload.Thematerialofthesofterasperityundergoesplasticflow;thesurfacescontinuetoapproach,bringingmoreandmoreasperitiesintocontact.Theprocesscontinuesuntiltheareaofcontactbecomessufficienttowithstandtheload.Theareaofanindividualcontactspot,An,isproportionaltotheload,Pn,andinverselyproportionaltotheyieldpointofthesoftermaterial,pm:AnZPnpm:(3.2)ThissimpleexplanationisthebasisofthemodelofslidingfrictiondevelopedbyBowdenandTabor.23Theyassumedthatthe“weldingbridges”(adhesivebonds)appearoneachcontactspotwiththeshearstrengthequaltos.Thesebondsfail(undergoshear)duringrelativeslidingofthesurfaces;hence,thefrictionforceisequaltothisshearingforce.Analytically,thefrictionforcecanbewrittenasFZArs;(3.3)whereAristhetotalrealcontactareaequaltoSAn.SubstitutingthisvalueinsteadofAryieldsFZPspm;(3.4)wherePZSPn.Phase1Phase2Interfaceγsγ2γ1FIGURE3.5SurfaceenergygS(shadedregion)asanexcessenergyofphases1and2thatarebroughtintocontact.Tribology39q2006byTaylor&FrancisGroup,LLCFromthissimpleequation,itfollowsthatthefrictionforceisproportionaltotheloadandindependentoftheapparentcontactarea;thisisinagreementwiththefirsttwolawsoffriction.Itisworthwhiletonotethattheshearstrength,s,ofthemajorityofmetalsisontheorderof0.2pm.Thecoefficientoffriction,mZF/P,then,isequaltos/pmZ0.2.ThisvalueisclosetothatproposedbyLeonardodaVinci,butstillnotsufficientwithrespecttorealfrictionvalues.Thefactisthattheexplanationinquestionisextremelysimplifiedandignoresalargenumberoffactors.Forexample,itwasassumedthatplasticflowduringcompressionofamaterialandtheshearingofadhesivebondsevolvedindependently.Thisisnotquitetrueifthecontactingrubbingmaterialsarehardenedand/oradhesivebonds(junctions)growunderthecombinedeffectofnormalandtangentialforces.Inreality,inaccordancewiththeyieldcriterion,arelationshipbetweennormal,p,andtangential,s,stressesaffectingthebondingshouldexistasp2Cas2Zp2m:(3.5)Here,pmistheyieldpointofamaterialduringuniaxialcompression,wherepZP/ArandF/Ar.Whenasurfaceasperityundergoescompletetransformationintotheplasticstateundernormalloading,thensZ0andpZpm.Generallyspeaking,theyieldcriterionbreaksdownwhenatangentialloadisapplied.Toretainitsvalidity,thenormalstressesshouldbereduced.ThisoccurswhenthecontactareaincreasestoacertainvalueAwhensurfacescomeintoamoreintimatecontact.Substitutionofpandsshowsthatthecontactspotareaincreasesinthefollowingmanner:Aw1CaeF=PT2??1=2:(3.6)Itmightseemthatthecontactspotareawouldexpandunrestrictedasthetangentialloadincreases.However,duetoanumberoffactors,includingthelimitedshearstrengthsaofadhesivebonds,thebondsfailandslidingbeginsatadefinitevalueofFZsaA.ItfollowsfromtheprecedingequationsthatthefrictioncoefficientisequaltomZsapZaes=saT2K1????K1=2(3.7)Hence,itisapparentthatiftheshearingstrengthofadhesivebondsisclosetotheshearingstrengthofthemetal,thecoefficientoffrictionmaytakeanyarbitrarilylargevalue.Yet,itdropssharplywhensadecreases,forexample,whensaZ0.7(ataZ10)oftheshearstrengthofthemetal,thecontactspotareaincreases1.4timesandthecoefficientoffrictionmZ0.31.Asimilarsituationoccurswhenthecontactingsurfacesmoverelativetoeachother(kineticfriction).However,rubbingmayfacilitatepenetrationofprotectivesurfacefilms,allowingastrongjunctiontoform.Therefore,thenatureofadhesivejunctionsformingatfrictionmaybeverydifferent:fromthestrongmetallicbondsbetweenvirginportionsofthecontactingsurfacestotheweakvanderWaalsbondsbetweentheabsorbedfilmsprotectingtherubbingbodies.Thejunctionswillhavetobeshearedundertheappliedtangentialforce.Thisisthefrictionalforce.Thatis,theworkcompletedbythefrictionalforceisextendedfordamagetotheinterfacialbonds.Frictionisthereforetreatedasaprocessofcontinuousformationandfractureofadhesivebonds.Thisworkcompletedbythefrictionalforceisextendedfordamagetotheinterfacialisessenceofadhesion(molecular)componentoffriction.Whentangentialloadisapplied,thebondsaresheared.Theirshearingstrengthisdeterminedby:tnZt0Cbpr(3.8)ElectricalContacts:Fundamentals,ApplicationsandTechnology40q2006byTaylor&FrancisGroup,LLCwheret0andbareempiricalconstantsdependingoncharacterofsurfaceinteraction;prispressureonasinglecontactspot.ThisrelationshipwasfirstobtainedbyBridgmaninhisstudyofhighpressures.Thesitewherefractureoccursdependsontherelativestrengthofthejunctionandtherubbingmaterials(Figure3.6).Iftheinterfacialbondingisstrongerthanthecohesivestrengthoftheweakermaterial,thenthismaterialisfracturedandthematerialtransfertakesplace.Otherwise,fractureoccursattheinterface.Ingeneral,theinterfacialjunctions(theirformation,growthandfracture)areinfluencedbythenatureandchemistryofthesurfaceandthestressstateofsurfacelayers(theloadingconditions).Theinterfacialjunctions,togetherwithproductsoftheirfractureandthehighlydeformedlayerswheresheardeformationislocalized,havebeennamedbyKragelskiiasathirdbody.24Thistermimpliesthatthematerialentrappedinthefrictionprocessmaypossesspropertiesthatdifferdras-ticallyfromthoseoftherubbingmaterials.3.1.4DEFORMATIONATFRICTIONAnothersourcefromwhichthefrictionalforcearisesisattributedtodeformationoccurringwhentheasperitiesoftwoslidingsurfacescomeintocontactwitheachother.Thisdeformationisaccompaniedbydissipationofmechanicalenergymechanismsthatmaybehighlydiversified,dependingondeformationmode,slidingconditions,rubbingmaterials,environment,andotherfactors.IntheBowden–Tabormodelforslidingfriction,theasperitiesofthehardersurfaceareassumedtoploughthroughthesoftercounterpart.Theploughingresistancecausesaforcecontributingtothefrictionalforce.Thiscontributionisreferredtoastheploughingcomponentoffriction,i.e.,thedeformationterm.AssumethatundertheloadPasinglecone-shapedasperitywiththeopeningangle2w(Figure3.7)penetratestoadepthhintotheplasticmaterialwiththehardnessH.UndertheactionofthetangentialforceF,theconeploughsagrooveintothesoftermaterial.Thisgrooveisatriangleinthecrosssectionwithheighthandbase2a.Astheconemoves,thenormalloadisapparentlysustainedbythesemicirclewiththeradiusa,i.e.,thefollowingrelationshouldexistbetweentheloadPandthedepthhtowhichtheirregularitypenetrates:PZ0:5ph2Htan2w;(3.9)wherelaZhtanw.Ontheotherhand,thetangentialforce(dragforce)equaltothefrictionforceshouldovercometheresistanceofthematerialaheadoftheindenter,i.e.,itactsonthecrosssectionofthegroovewiththeareaequaltoahZh2tanw,thenAdhesivefractureCohesivefractureCounterbodyCounterbodyCounterbody(a)(b)(c)MixedfractureAsperityAsperityAsperityFIGURE3.6Fracturetypesofadhesionjunctionsformingatfriction:(a)adhesivefracture;(b)cohesivefracture;(c)mixedfracture.Tribology41q2006byTaylor&FrancisGroup,LLCPZHh2cotw:(3.10)Hence,thecoefficientoffrictionduetotheploughing(deformation)isrecordedasmdZ2pcotw:(3.11)Asarule,theasperitiesonarealsurfacehaveaslopeontheorderof5–108,i.e.,theangle2wis80–858.Substitutionofthisvalueintothelastformulayieldsadeformation(ploughing)componentofthecoefficientoffrictionwithintherange0.07–0.14.Usually,thesetwocomponents(bothadhesionanddeformation)arejustaddedarithmetically,assumingthattheseareadditive.Inreality,thisisnotquitetruebecausedeformation,whileenlargingthecontactarea,enhancesadhesionandthestrongeradhesionincreasestheseverityofdeformationduringfriction.Never-theless,becausetheareasoverwhichthesetwoprocessesevolvechangeinsignificantly,theassumptionthatthesetwocomponentsareadditiveiscorrect.Moreover,thisisadvantageousforgainingmoreinsightintothenatureoffriction.Notethat,almostwithoutexception,ploughing(Figure3.8a)isaccompaniedbyadhesion(Figure3.8b)and,undercertainconditions,theploughingmayresultinmicrocutting(Figure3.8c),i.e.,additionalworkiscompletedandthefrictionisincreased.Duringdeformation,thereareothermechanismsofenergydissipation.Hence,whenapolymerwithviscoelasticbehaviorslidesagainstahard,roughsurface,dissipationofenergyoccurswithhighhysteresislosses.Thisdeformationcomponentisknownasanelastichysteresisfriction.Theenergymayalsobecarriedawayalongotherchannelsofdissipation.Forinstance,duetonucleationanddevelopmentofmicrocracksontheslidingsurfaceandinthebulkofthematerial,theelasticwavesaregeneratedattheinterfacewithatendencytowardsinfinity.3.1.5FRICTIONASAFUNCTIONOFOPERATINGCONDITIONSDependingupontherubbingmaterials,theroughness,theoperatingconditions(load,slidingvelocity,temperature)andtheenvironment,therelativecontributionofadhesionanddeformationcomponentstofrictioncanvaryoverawiderange.Thisismostnoticeableintheloaddependenceofthefrictioncoefficient(Figure3.9).AccordingtoKragelsciisuchdependencehasaminimumFqqA2A1GrooveGrooveμ=F/W=A1/A2=(2p)ctgqq=85?μ=0.07q=80?μ=0.14FIGURE3.7Deformationalcomponentoffrictionappearingwhenplasticmaterialisploughedwithcone-shapedirregularity.ElectricalContacts:Fundamentals,ApplicationsandTechnology42q2006byTaylor&FrancisGroup,LLCthatisconnecteddirectlywiththetransitionfromelastictoplastic(increasedload)contactandtheassociatedchangeintherelativecontributionsfromthefrictioncomponents.Asdiscussedearlier,therealareaofelasticcontactisproportionaltoloadwithpowerlessthan1,i.e.,theadhesioncomponentandthereforethefrictioncoefficientwilldecreasewithloadduetonegligiblecontributionfromthedeformationcomponent.Whencontactbecomesplastic,therealcontactareaandtheadhesioncomponentbecomeload-independent.Atthesametime,penetrationoftheasperitiesintothecounterbodyincreaseswithloadand,asaresult,sodoesthedeformationcomponent(theploughingterm).Thetotalcoefficientoffrictionincreases.Thistransitionfromadescendingtoanascendingbranchofthecurvedefinestheminimum.Itspositiondependsuponaratioofadhesionanddeformationcomponentsandisshiftedtowardslowervaluesoffrictionwithincreasingma/md.Itshouldbeemphasizedthattheminimuminthisrelationshipisnotverypronounced.Theexperimentalevidenceindicatesthatduetonumerousfactorsexertinganadditionalinfluenceonfriction,alargenumberoftheserelationships,fromadescending(orascending)curvetoaload-independentrelation,exists.Itisinterestingtonotethatsimilarbehaviorisobservedinthedepen-denceofthefrictioncoefficientontheroughness,i.e.,thesmallertheheightofasperities,thegreaterContactload,PCoefficientoffirction,mElasticcontactPlasticcontactFIGURE3.9Thedependenceoffrictioncoefficientonload.PloughingPloughingwithadhesionCutting(a)(b)(c)FIGURE3.8Deformationcomponentoffriction.Tribology43q2006byTaylor&FrancisGroup,LLCistherealcontactareaandthereforetheadhesioncomponent.Ontheotherhand,thehighertheasperitiesandthesmallerthecurvatureradiusattheirtips,thegreaterthedeformationcomponent.Itisinterestingthatthedependenceofthefrictioncoefficientonroughnesshassimilarcharacter:thelowertheasperityheight,thegreatertherealcontactareaandtheadhesioncomponent.Ontheotherhand,thehighertheasperitiesandthesmallertheradiiofpeakcurvature,thegreateristhedeformationcomponent.However,itshouldberememberedthatroughnessitselfvariesduringfriction:averysmoothsurfacebecomesrougher,whereasaveryroughsurfacemaybesmoothed.Thereisaconceptofequilibriumroughnessthatisindependentofinitialroughness;dependingonthewearconditions,itmaybeeitherlessthanorgreaterthantheinitialroughness(Figure3.10).Dependenceoffrictiononslidingvelocityisacomplexissuebecausetheeffectofvelocityisoftenindistinguishablefromthetemperatureeffect.Nonetheless,itisevidentthatwhenslidingisinitiated,reductionofthefrictioncoefficientmaybeobserved(thezerolawoffriction).Alternatively,thefrictionbecomesindependentoftheslidingspeed(thethirdlawoffriction)whenaperfectlyelasticbodyisrubbedundertheconditionswherebythecontacttemperatureremainsalmostunchanged.Inpractice,morecomplicateddependencesmaybeobservedbecauseincreasingtheslidingspeedincreasesthestrainrateandthecontacttemperature.Thesefactorsaffectthemechanicalbehavioroftherubbingmaterialsand,consequently,theadhesionanddeformationcomponentsoffriction.Therefore,becausetheplasticdeformationislocalizedinathinnersurfacelayer,thefrictionforcedecreases.Forimperfectlyelasticmaterials,thefrictionisassociatedwiththespeedandisthereforealsoassociatedwithgenerationofthehysteresislosses.Ingeneral,thespeed-dependentfrictionpassesthroughamaximumthatmaybereducedbycertainconditions,resultinginadescendingtendencyoffriction.Theeffectofcontacttemperaturemustbeemphasizedbecauseincreasingtemperatureweakensthestrengthofadhesivebondsandthecontactbecomesmoreplastic;this,inturn,enlargestherealcontactarea.Thesetoftheseeffectsmaygivewide-rangingeffectsofthefrictiontemperaturedependence.3.1.6THEPRELIMINARYDISPLACEMENTThekineticfrictionisprecededbyaprocesscalledpreliminarydisplacement.Theprocessinvolvesrelativemicrodisplacementsofthecontactingbodies,originallyatrestundernormalloadW,FIGURE3.10Changeinroughnessduringrunning-in:(a)increasingtheroughnesswhentheinitialroughnessislessthantheequilibriumone;(b)decreasingtheroughnesswhentheinitialroughnessisgreaterthantheequilibriumone.ElectricalContacts:Fundamentals,ApplicationsandTechnology44q2006byTaylor&FrancisGroup,LLCbyapplyingandincreasingthetangentialloadFfromzerotosomecriticalvalueFs(staticfrictionforce)responsibleforgrosssliding.Thisphenomenonexertsprimarycontroloverwearandserviceabilityofsuchprecisionengin-eeringdevicesaselectronicswitches,magnetichead–disccontactsincomputer,andsoon.Numerousexperimentshaverevealedthatmicrodisplacementincreasesmonotonicallywithincreasingtangentialforceonlyduringtheinitialstageoftheprocess.Thismicrodisplacementcomprisesreversibleandirreversiblecomponentsandissmallerthanthejunctionsize(thediameterofacontactspot).Underthepreliminarydisplacement,energydissipationoccursjointlywithstoringofthemechanicalenergy.Themechanismofpreliminarydisplacementcanbeconvenientlyexplainedusingasphere-on-flat-contactconfiguration(Figure3.11).LetthespherebeloadedbyaconstantforceW.Thecontactisassumedtobeelastic.ThenormalpressureisaHer