the dependency of adhesion and friction on electrostatic attraction b. n. j. persson资料.pdf

该【the dependency of adhesion and friction on electrostatic attraction b. n. j. persson资料 】是由【小舍儿】上传分享，文档一共【8】页，该文档可以免费在线阅读，需要了解更多关于【the dependency of adhesion and friction on electrostatic attraction b. n. j. persson资料 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。:TheJournalofChemicalPhysics148,144701(2018);doi::https:///:http://aip./toc/jcp/148/14PublishedbytheAmericanInstituteofPhysicsTHEJOURNALOFCHEMICALPHYSICS148,144701(2018))PGI-1,FZJulich,¨Julich,¨Germany(Received30January2018;accepted26March2018;publishedonline9April2018)Idevelopageneralmean-?eldtheoryforthein?,namely,,.,the?nger–?,I?ndthatwhentheappliednominalcontactpressureisrelativelysmall,astheappliedvoltageincreases,thereisasharpincreaseinthecontactarea,andhenceinthefriction,:///.,inparticular,attheslidinginterfacewheresurfaceroughness,thecontactbetweenthesolidsisneverper-thesurfacetopography,contamination?lms,?u-?Voveranarrowregionattheinterface,–3However,,inthiscasetoo,onexternalconditionssuchastemperaturesandthehumiditytherewillbeanelectric?eldinthenon-contactregionbetweenandonmechanicalvibrationsandelectric?,.,betweenthe?,anmechanicalcontactstiffness,afundamentalresult?rstderivedappliedelectricvoltagebetweentwosolidsoftenresultinthebyBarber10().Wewillmakeuseofaccumulationofchargesofoppositesignonthesurfacesatthisresultbelowwherethecontactstiffnessandothercon--,denotedelectroadhesion,–17(squeezing-force)andincreasestheareaofcontactandtheslid-Intheliterature,thereisadiscussionaboutthemathemat-,.,icalrelationbetweentheadhesion(andfriction)forceandtheforgrippersforrobotics,-applications,whereoneisinterestedinthefrictionbetweensentedandthereisnogeneralconsensusaboutwhichonea?–,(x,y)thephysicalityoftouchinteractionorforin?uencingshapeisarbitrary,exceptImakethesmall-slopeapproximation,.,|?u|<-slopeapproximationisusuallyThetermelectroadhesionisdrawnfromthe1923workusedin?uiddynamicsatinterfaces,-simpli?cationoftheNavierStokesequations(whichreducesishedlithographicstoneandmetalsurfaces,thistermwasusedtotheReynoldsequationwhen|?u|1).todescribethephysicalphenomenonofconsiderableadhesionanizedasfollows:,whichdevelopedwhenthehighlyresistivestonewasplacedusingthesmall-slopeapproximation,(x,y)dependsontheIdevelopageneralmean-?eldtheoryforthein?uenceattractiveelectrostaticstress,-?eldofelectrostaticattractionbetweentwosolidsonthecontacttreatmentoftheelectroadhesionforce,whereu(x,y)ismod-?rstthelimitingcasewhenanelectrici????,theleakcurrentresultsinnegligiblechargetransfer,:INSULATINGSOLIDSWeconsiderthecontactcon?)URL:ontactinafractionA/A0ofthe0021-9606/2018/148(14)/144701/7/$,144701--,144701(2018)Thenormalstressactingonthesurfacesatthesolid-vacuumponentoftheMaxwellstresstensorwhichgives!2=02=0Vσzz(x)(x)+h0Weareinterestedinthestressaveragedoverthesurfacerough-?(p,u)()sothatonstantsand.Anelectricvolt-1212∞=0V2duP(p,u).(2)zz2separationu=u(x)dependsonthelateralcoordinatex=(x,y).20(u+h0)WecanwritenominalcontactareaA0(inthe?gureA=0).Thenon-contactAregionis?lledwithair,butwecanconsiderthisregionasP(p,u)=δ(u)+P1(p,u),A0onstantofair(air≈)isnearlythesameasthatofvacuum(=1).whereA/A0istherelativecontactareaandwhereP1(p,u)is2normalizedsothatTheelectrostaticpotentialsatis?es?φ=0everywhereexceptatthedifferentinterfaceswherethematerialproper-∞AduP1(p,u)=1?.-0A0nessgivenbythefunctionsh(x)andh(x)beforecontact12Thuswecanwrite(undeformedheightpro?les),wherex=(x,y)denotethe??∞??positionvectorinthexy-02?1A1?hσzzi=V?+duP(p,u)?.(3)heightpro?leh(x)=h?2A1(u+h)2?12?h0000?slopeapproximation|?h|-Thestudyabovecanbeeasilyextendedtothecasewheretact,theinterfacialseparationwillbedenotedbyz=u(x)theappliedvoltageVdependsontime,V=V(t).Ifwede?newhichdifferfromh(x),wecan1approximateV(ω)=dtV(t)eiωt?2φ2π?2φ≈≈0.?z2sothat=?iωtInthiscase,wecanwritetheelectricpotentialas(seeV(t)dωV(ω))Thenthederivationaboveisunchangedandgivesφ=V+bzfor0<z<d,11V(ω)Ez(ω,x)=?,φ=a+b(z?d1)ford1<z<u(x)+d1,u(x)+h0(ω)whereφ=b2(z?u(x)?d1?d2)foru(x)+d1<z<u(x)+d1+(ω)=+,1(ω)2(ω)Notethatφ=Vforz=0andφ=0forz=u(x)+d1+(ω)and(ω)arethedielectricfunctionsofthetwoAtthetwosolid-vacuuminterfacesz=d1andz=u(x)+d1,,ifV(t)=Vcosω,thentheelectricpotentialφandEz(whereEz=?φ/?zisthe00ponentoftheelectric?eld)(ω)=V[δ(ω+ω)+δ(ω?ω)]givestheequations2000anda=V+b1d1,a+bu=?b2d2,V(ω)=??iωt==Ez(t,x)dωeb1b1,b2b2."u(x)+h0(ω)#?iω0tiω0tFromtheseequations,weget1ee=V0+2u(x)+h0(ω0)u(x)+h0(?ω0)V"#b=?.e?iω0tu+d1/1+d2/2=V0Re,u(x)+h0(ω0)Theelectric?eldinthevacuumregion?=?wherewehaveusedthath0(ω)h0(ω).he?φVangleφviaEz=?=?b=.?zu+d/+d/iφ1122u(x)+h0(ω0)=|u(x)+h0(ω0)|e,Wewilldenoteh0=d1/1+d2/2sothatwecanwriteVcos(ω0t+φ)Ez(x)=?.(1)Ez(t,x)=V0.(4)u(x)+h0|u(x)+h0(ω0)|144701-,144701(2018)es"#2!V1e?2iω0tσ(t,x)=00+Rezz2222|u(x)+h0|(u(x)+h0)11+cos(2ωt+2φ)=|u(x)+h0(ω0)|Thenormalstressaveragedoverthesurfaceroughnesses1∞1+cos(2ωt+2φ)hσi=V2duP(p,u)0.(5)zz00240|u+h0(ω0)|,onductivity,?atsurfacesofthetwoblocks,urrentJwill?,:thecurrentisuniforminthexy-planebutclosetotheinterfacehighlynon-CONDUCTINGSOLIDSuniformasthecurrentwill??uroveranarrowregionattheinterface,,ontacttransfercoef?cientαviaJ=α?-quencyrangebyarealdielectricfunction(ω).Howevermostwill?-,oneenoughawayfromthecontactinginterface,thecurrentisuni-ountthatwhenanelectricvolt-forminthexy-plane,butclosetotheinterface,itishighlyageisappliedbetweenthesolids,urrentwill?ownon-uniformasthecurrentwill?owthroughtheareaofrealthroughtheasperitycontactregionsandthevoltagedrop?±δfromtheinterfacewheretheelectricon-currentisapproximatelyuniforminthexy-planeisdeter-ductivitiesκ1andκ2ofthesolidsandonthecontactresistanceminedbytheaverageseparationbetweenthemacroasperity(seebelow).Inthissection,wewillconsiderthisproblemincontactregions,whichdependsontheroll--?V=V2uroverthenarrowregionofwidth～,ontactcon-?eldE=V/dductivityαviaJ=α(V2V1).Sincethevoltage?VistheurrentdensityJ=-quantitywhichdeterminestheCoulombattractionbetweenthetric?eldisduetoasurfacechargedensityneonthesurfacesurfaces,=0,thenE=ne/(urrentrelaxationtime)t=τsothatJτ=?owfromtheupperJ=κ2(V?V2)/d2,J=κ1(V1?0)/().WegetJτ=κEτCombiningtheseequationswithJ=α(V2V1)gives=κneτ/=negivesτ=0/τ,thenwecanneglectαVJ=(6)hargefromtheuppersurface,andin1+α(d1/κ1+d2/κ2)thiscase,,fortimestτ,,we?V=.(7)+α(d1/κ1+d2/κ2)Figure3showstwoelasticblocks,ontactbetweenrandomlyroughsur-conductivity,squeezedtogetherwithanominalcontactpres-faces,ontactconductivity10–?atsurfacesofthetwoblocks,urrentJ2κα=K⊥,(8)E?wheredp0K⊥=?(9)duˉisthemechanicalcontactstiffnessand1?ν21?ν21=12?+(10).(a)onductivityκistheeffectiveYoung’smodulus(E1andν1aretheYoung’sandthe(positive)surfacechargeneonthetopsurface,thechargewill?owmodulusandPoissonratioofsolid1andsimilarforsolid2),towardthebottomsurface.(b)Afteracharacteristictimeoforderτ=0/κ,=1/κ1+1/κ2(11)144701-,144701(2018)onductivity(onduc-whichwecanalsowriteasonductivityofsolid2).2(p?p)/V2=00(18)Substituting(8)into(7)gives∞?2∫0duP(p,u)(u+h0)=VfromwhichwecaneasilycalculateVasafunctionofthe?V?,(12)1+2d0K⊥/()includingonlythesurfacechargeattheinterface,wewhere!=d1d2=κ1d2+κ2d1obtaind0κ+.(13)∞?V2κ1κ2κ1+κ2p=p+0duP(p,u)0212Therelationbetweentheappliednominalcontactpressureacup0andtheaverageinterfacialseparationuˉcanbecalculatedorusing(12),-∞=p+V2duP(p,u),(19)021u2(1+2dK(p)/E?)2whenthenominalcontactpressureisnottoohigh(.,notac0⊥pletecontact)andnotsosmallthat?nitesizewherewehaveindicatedthatthestiffnessK⊥dependsontheeimportant(-contactonlyatafewofthehighestasperities),abilitydistributionP1(p,u)ratherthanP(p,u)=P1(p,u)+[A(p)/A]δ(u)sinceweassumethatthereisnoattrac-p≈βE?exp(?uˉ/u)(14)(19),weget=?uˉ/u0log(βE/p),??22=2(pp0)(1+2d0K⊥(p)/E)/0V∞?.(20)whereu0≈,wherehrmsisthermsroughnessoftheduPpuu2∫ac1(,)(combined)surfaceroughnesspro?,weahaveIn(19),cisacut-,Iuseac=-K⊥=p0/u0tionisverysmall(hereu<uc)formsnarr