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1、JournalofMaterialsProcessingTechnology214(2014)285–294ContentslistsavailableatScienceDirectJournalofMaterialsProcessingTechnologyjournalhomepage:locatejmatprotecModelinganalysisofthematerialremovalprofileffreeabrasivepol

2、ishingwithsubaperturepadChengFanabJiZhaoaLeiZhanga?YokeSanWongbGeokSoonHongbWansongZhouaaCollegeofMechanicalScienceEngineeringJilinUniversityChangchun130022ChinabDepartmentofMechanicalEngineeringNationalUniversityofSinga

3、peSingape117576SingapearticleinfoArticlehisty:Received16February2013Receivedinrevisedfm3September2013Accepted9September2013Availableonline19September2013Keywds:FreeabrasivepolishingMaterialremovalprofileSubaperturepadMat

4、erialremovalindexabstractThispaperaddressestheproblemofmaterialremovalinfreeabrasivepolishing(FAP)withthesubaperturepadboththeeticallyexperimentally.Theeffectsofsomepolishingconditionsuponthematerialremovalareanalyzedinc

5、ludingnotonlytheprocessparameterswhichrefertothenmalfceangularspindlevelocityangularfeedratebutalsotheabrasivegrainsizepolishingslurrypropertiestopographicalparametersofthesubaperturepadaswellastoolpathcurvature.Basedont

6、heanalysisamodelofmaterialremovalprofileisproposedtofacilitatemeaccuratepolishing.Firstbyanalyzingthecontactamongpolishingpadabrasivegrainwkpiecesurfaceinthemicroleveltheremovaldepthperunitlengthofthepolishingpathisderiv

7、edwhichisdefinedasthematerialremovalindex.Thenthedistributionofthisremovalindexcanbeobtainedviamodelingthepressurerelativeslidingvelocityinthecontactregionofpolishingpadwkpiece.Afterthatthematerialremovalprofilecanbecalc

8、ulatedbyintegratingthematerialremovalindexalongthetoolpathinthetoolwkpiececontactregion.Toverifytheeffectivenessoftheproposedmodelaseriesofpolishingexperimentshavebeenconducted.Experimentalresultswelldemonstratethatourmo

9、delcanaccuratelypredictthematerialremovaldepthduringtheFAP.?2013ElsevierB.V.Allrightsreserved.1.IntroductionFreefmsurfaceswithhighsurfacefinishintegrityfmaccuracysuchaspreciseasphericnongeometricopticallensmoldshavebecom

10、ekeyfeaturesofcomponentsincreasinglyrequiredbyoptoelectroniccommunicationindustries(Chengetal.2005).Thepolishingprocesswhichisusuallythefinalstepoffabricationisessentialtothequalitydurationofthepartsurfaces.Varioustypeso

11、fpolishingareusedfopticalfabricationsuchasfreeabrasivepolishing(FAP)magorheologicalfinishingabrasiveslurryjetpolishingetc.FAPisconsideredasoneofthemostcommonimptantoperationsinopticalfinishing.InatypicalFAPprocessarotati

12、onalsubaperturepolishingpadinthepresenceofliquidslurrywhichcontainshardabrasivegrainsispressedagainstthewkpiece.Betweenthesubaperturepadthewkpiecetherefmsanareaofcontacttheinteractionsbetweenpolishingpadabrasivegrainswkp

13、ieceresultinthematerialremovalinthecontactarea.?Crespondingauthat:CollegeofMechanicalScienceEngineeringNanlingCampusJilinUniversityNo.5988RenminStreetChangchun130022China.Tel.:8618946686195.Emailaddress:zhanglei@jlu.(L.Z

14、hang).TheFAPprocesswiththesubaperturepadisusuallyusedasanerrcompensationmethodtoimprovethefmaccuracyofthepartsurfacesifthematerialremovalinthecontactareaiscontrollable.Jones(1977)firstproposedtousetheFAPprocesstofabricat

15、etheasphericopticalsurface.Bycontrollingtheamountofmaterialtoberemovedpreciselythespatialfrequencyerrsleftaftergrindingturningcanberemovedbysubaperturepolishing.Suetal.(1996)SuSheen(1999)developedaplanningstrategyfthepol

16、ishingprocesstemoveanarbitraryprofilewiththepreconditionthatthematerialremovaldepthinthecontactareacanberepresentedbyalinearfunctionofmachiningtime.Therefeitisessentialtomodelanalyzethematerialremovalofpolishinginaquanti

17、tativemanner.HoweverthefundamentalmechanismsofmaterialremovalinFAPinvolvemicrofatiguemicrocrackploughingcuttingmainlydependingonthestateoftheinteractionsbetweenabrasivespolishingpadwkpiecewhichhavenotbeenwellunderstood(B

18、rinksmeieretal.2006).Thustheresearchonthematerialremovalrate(MRR)ofFAPisstillatanempiricallevel.ThePreston’sequationiswidelyusedtopredicttheMRRduringthepolishingprocesswhichstatesthattheMRRisdeterminedbytheproductoftheco

19、ntactpressurerelativevelocitymachiningtimePrestoncoefficientwhichisrelatedtothewkpiecematerialpropertiesofpolishingslurrypolishingpadsizeofabrasivegrainsetc.(Preston1927).Besidessomeresearcherstriedtoexplainthemechanisme

20、stablish09240136$–seefrontmatter?2013ElsevierB.V.Allrightsreserved.:dx.doi.g10.1016j.jmatprotec.2013.09.010C.Faal.JournalofMaterialsProcessingTechnology214(2014)285–294287Fig.2.Schematicofsingleabrasiveabrasion.entirecon

21、tactloadissustainedbythecontactbetweenpadwkpiecesurface.TheGWmodel(GreenwoodWilliamson1966)isusedtodescribethecontactbetweenpadwkpiecesurface.AccdingtothismodelthepressurebetweenpadwkpieceisgivenbyPc=43NpR0.5pE?pw?hmaxh(

22、h?hs)1.5?(h)dh(2)whereRpistheaverageradiusoftheasperitiesNpisthenumberofasperitiesperunitareahmaxisthemaximumheightofthepadsurfaceEpwisthecontactmodulusofthepolishingpadthewkpiecegivenby1E?pw=(1??2p)Ep(1??2w)Ew.EpEwareth

23、eYoung’smodulusofthepolishingpadthewkpiecerespectively?p?waretheirPoisson’sratiespectively.AccdingtoEq.(2)thepressurePcisafunctionoftheseparationdistancehs.ThusifthepolishingpressurePcisknowntheseparationdistancehscanbec

24、alculatedfromEq.(2).2.2.ThematerialremovalofasingleabrasivegrainAsshowninFig.2theabrasivegrainisembeddedbetweenthepadthewkpiece.Rabristheradiusoftheabrasivegrain?w?pcrespondtotheinterferencebetweengrainwkpiecethatbetween

25、grainpolishingpadrespectively.Thevolumeofthematerialremovedbyasingleabrasivegrainisapproximatelyequaltotheproductofitscrosssectionalareaimmersedinthewkpiecetheslidingdistancewhichgives?V=AL(3)whereAisthecrosssectionalare

26、aListheslidingdistance.AssumingthatthehardabrasivegrainmaintainsitssphericalshapeAcanbeexpressedbyA=R2abrarcsinaRabr?a(Rabr??w)(4)paredwiththegrainradiusRabr?wisverysmallsoisaRabrthusEq.(4)canbefurtherlinearizedaboutaRab

27、rasA≈a?w?1O??wRabr??(5)whereacanbeexpressedasa=?R2abr?(Rabr??w)2=?2Rabr?w??2w≈?2Rabrw(6)Assumingthatthecontactsbetweenagrainwkpiecebetweenthegrainpolishingpadareplastictheinterference?wisgivenbyXieBhushan(1996)as?w=HpHwH

28、p(2Rabr?hsh)(7)SubstitutingEqs.(6)(7)intoEq.(5)yieldsA=?2Rabr?HpHwHp(2Robr?hsh)?1.5(8)2.3.NumberofabrasivegrainsparticipatinginmaterialremovalThenumberofthefreeabrasivegrainsintheslurrydirectlyparticipatingintheabrasivew

29、earprocessisoneofthemostimptantvariablesinfluencingthematerialremoval.Previousstudiesassumedthattheabrasivegrainsembeddedinthewkpiecesurfacetheasperitiesofthepolishingpadparticipateinthematerialremoval(ZhaoChang2002JinZh

30、ang2012).Thusthenumberofactivegrainsistheproductoftheareadensityoftheabrasivegrainsintheslurrytherealareaofcontactbetweenpolishingpadwkpiece.Howeverintheactualpolishingprocesstheabrasivegrainsarerarelyonthecontactinterfa

31、ceofthepadasperitieswkpiece.MeoveriftheareadensityofgrainsisfixedtheMMRisindependentoftheabrasivegrainsizeinthesemodelswhichisunreasonable.Indertoovercomethedeficiencyofthesemodelsthecriticalconditionfthegrainsparticipat

32、inginmaterialremovalisdescribedderived.FurthermetheeffectsofthepadpropertiesonthenumberofactivegrainsareconsideredwhichisignedbyXieBhushan(1996).Lettheslurryconcentrationperunitvolumebe?dthelinedensityofthegrainintheslur

33、rybel.Then43?R3abrl3=?d(9)Therelationshipbetweenareadensity?thelinedensitylisgivenby??l2.(10)RearrangingEq.(9)substitutingitintoEq.(10)gives?=?3?d4?R3abr?23(11)Whentheappliedloadontheabrasivegrainissmallthecontactbetween

34、abrasivegrainwkpieceiselastic.AccdingtotheHertiziancontacttheytheindentationdepthcanbeexpressedas?w=?3?p4E??2Rabr(12)wherepistheaveragepressureactingonthegrainE?awisthecontactmodulusofabrasivegrainwkpiecegivenby1E?aw=(1?

35、?2a)Ea(1??2w)Ew.Ea?aareYoung’smodulusPoisson’sratioofthegrainsrespectively.Astheappliedpressureincreasestheelasticcontactwillchangeintoplasticcontactthecriticalvalueofthepressurepisdeterminedbythehardnessofthewkpieceasp=