ThreeandfiveaxesmillingofsculpturedsurfacesR.Baptistaa,*,1,J.F.AntuneSimoesb,2aInstitutoSuperiorTecnico,TechnicalUniversityofLisboa,Libson,PortugalbEscolaSuperiordeTecnologia/Inst.PolitecnicodeSetubal,SchoolofTechnology/PolytechnicInstituteofSetubal,Setubal,PortugalAccepted17December1999AbstractTheaimofthisworkistheanalysisoftheinfluenceofthemillingparametersonthesurfacefinish.Thisworkisofinteresttobothscienceandindustry.Ononehand,ittriestoreducethemanualpolishingtime,whichrepresentsahighpercentageoftheproductiontimeofmoulds.Ontheotherhand,whiletheliteraturemainlyreferstosteelmoulds,thisworkwascarriedoutonaluminiumbecauseofitsadvantagesformachininganditssuitabilityformoulds.Insmallbatchproductionthemanufacturersareinterestedintheproductionofaluminiummoulds.A5axisCNCmillingmachinewasusedforthesurfacefinishingofseveralparts,previously3axismachined,withinequalcuttingconditions.Differentmachiningconditionson3and5axesfinishingoperationsweretested.Thecomparisonoftheresultsallowstoconcludethatabettersurfacefinishisachievedwith5axismillingusinganendmillinclinedinthefeedinsteadofthetraditional3axismillingwithaballnosecutter.TheapplicationoftheDesignofExperimentstechniquetogetherwithmultiplelinearregressionenablestheestablishmentofamathematicalmodeloftheprocessthatgivestheprocessparametervaluesthatleadtotheminimummachiningtimeinordertoachieveacertainroughness.Keywords:Threeandfiveaxesmilling；Tooltypeandorientation；Surfacefinishandmachiningtime1.IntroductionThedevelopmentoftheaeronauticandautomobileindus-triesbroughtnewtechnologicalchallenges,relatedtothegrowingcomplexityoftheproductsandthenewgeometriesmodelledinCADsystems.Thesemorecomplexgeometriesimposenewchallengingmanufacturingsituationsforthemillingofmouldsandstampingtools.Thisisanimportantreasonforthedevelopmentofnewmillingtechnology,namely5axismilling.Thestudyofthesenewmillingtechniqueisveryimpor-tantinordertoidentifyinwhatconditionseachoneofthesetechniquescangivethebestresult.Manualpolishingofsculpturedsurfacesisalmostneces-sarytoobtainthedesiredsurfaceroughness.Thiskindofoperationisaconsequenceoftheinabilityofthemillingprocesstoachieveeconomicallytherequiredsurfacequalityandinourdaysismoreandmoreaffectedbythedecreasingnumberofqualifiedworkers.The5axismillingis,now,oneofthetechniquesthatcangiveenormousadvantagesinmachiningoperations,potentialforsignificantreductionoftherequiredmanualfinish.Inthispaper,theroughness(Ra)ofthemachiningsurfaceisrelatedtotheoperatingparameters,appealingtoamath-ematical-statisticmodel.Thepartgeometrywasselectedinordertorepresent,inablockofsmalldimensions,allthedifferentgeometriesthatcanbefoundinmouldsandstampingtools.Theequationsrelatingtheroughnessleveltothemachin-ingconditions(feedpertoothandstepover),onparticularpartarea,weredetermined.Asexpected,thedevelopedmathematicalmodelexpressesadequatelytheexperimentalresultsandenablestheutilisationofanoptimisationcriter-ion,machiningtimeinthiscase.Thisfactemphasisestheimportanceofthemathematicalmodelstoestablishthemachiningparametersaimingtheoptimaluseoftheresources.TheexperimentalworkplanningandtheanalysisoftheresultsweredoneaccordingtotheDesignofExperimentsmethod.2.ExperimentalworkThisworktargetsaspecificindustrialproblemthefinishingofsculpturedsurfacebymillingoperation.TheJournalofMaterialsProcessingTechnology103(2000)398403*Correspondingauthor.1M.S.O.,AssistantProfessoroftheIST.2C.P.,AssistantoftheEST.workcarriedoutconsistedonthecomparisonoftheper-formanceof5axismillingcomparativetothe3axismillingofsculpturedsurfaces.Alloftheprocessvariableshavebeenidentifiedandthemostrelevantoneswereselectedforstudy.Thefinalobjectiveistoquantifytheirvaluesinordertoobtaintheminimummachiningtimeforafixedroughness.2.1.IdentificationandselectionofprocessvariablesTheprocessparametersselectedfortheexperimentalworkwerethestepover,thefeedpertooth,thefeeddirectionandthe3andthe5axesmillingtechnology.Asthemillingmachinehadalowrotationlimitof4.200rpm,andthetoolcouldworkinhigherspeed,itwasdecidedtokeepthecuttingspeedconstant.Also,thetooldiameterwaskeptconstantandasmalldiameterof10and12mm,suchasoccurswithindustrialpractice,werechoseninordertoavoidgeometricalinterferencebetweenthetoolandthepart.Thecuttingdepthwasalsomaintainedconstantnotonlytoreducethenumberofvariablesbutalsobecauseinfinishingoperationsthedepthisalwayssmall.2.2.EquipmentThemillingoperationswereperformedona5axisCNCmillingmachine(HermleUWF1202H)equippedwithanHeidenhainTNC425CNCcontroller.MasterCamversion5.54wasusedtocreatetheCNCpartprograms.Multisurfmodulefor3axisandFlowlinemodulefor5axis,wereused.3.Experimentalset-upTheexperimentalworkwasdividedintotwophases.Thefirstphasewasthe3axismillinganalysis,withaballnosemill.Thesecondphasewasthe5axismilling,withtwokindsoftools,aballnoseandanendmill.Thecontrolparametersconsideredwerethesurfaceroughness,dimensionalaccuracyandshapeofthepartgeometry,andmachiningtime.Thepartsgeometryhasfourdifferentshapes:aconvexshape,aconcaveshape,anhorizontalplaneshapeandaninclinedplaneshape(Fig.1).Althoughthisstudyisabout5axismilling,theparthadacurvatureonlyinonedirection(thedoublecurvaturewillbringonlymorecomplexity,andthismodelcanalsobeappliedinthatcase).So,itwasdecidedtoinvolveonlyonerotationaxis(AaxisrotationoverthelinearXaxis).Thepartsmaterialwasanaluminiumalloyofthe7.000series,usedinthemanufacturingofplasticsinjectionmouldsforsmallandmediumseriesproduction.3.1.ThreeaxismillingInitially,theimportanceofthestepoverandthefeedpertoothparametersonfinishingoperationswereinvestigatedbythreeaxismilling.Afterthisinitialstudy,thefeeddirectionimportancewasanalysed.Thisparameterwasstudiedconsideringthreedifferentdirections:(a)thedirectionof08；(b)thedirectionof458；(c)thedirectionof908(contouring)(Fig.2).Asthenextpictureprintsout,oneofthecharacteristicsin3axismillingoperationsisthatthelead/lagangleisnotconstant.Thisangleisdefinedbetweenthetoolaxisandthesurfacenormal.On3axismillingoperationsitispossibletoidentifythreedifferentcuttingtypes:thedownwardcutting,theplanecutting,andtheupwardcutting,Fig.31.Thecuttingspeedisnotconstantalongthemachiningpath.Fig.3alsoshowsthatthecuttingspeeddistributioninthetooledgeisdifferentforeachoneofthethreecuttingtypes.3.2.FiveaxismillingOnthefinishingoperationsby5axismillingthelead(bf0)/lag(bf0)(Thetoolshasthesamediameterandstepover.)Fig.6.(a)Inclinationoftheballnosemill(bf158)；(b)inclinationoftheendmill(bf48).400R.Baptista,J.F.AntuneSimoes/JournalofMaterialsProcessingTechnology103(2000)398403therearedifferentvaluesofstepoverandfeedpertoothleadingtothesameroughnessvalue,butwithdifferentmachiningtime；forthestepoverandfeedpertoothparameters,thereisalowerlimitwhereadramaticaggravationonthemachin-ingtimebegins.Processmodel.Withthelastresultsfortheinclinedplaneshapeaprocessmodelwasdeveloped.RoughnessRa0:7810:4676logStepover1:2436logFeedpertooth(1)Eq.(1)relatestheroughnesswiththestepoverandthefeedpertooth.Thisequationwasobtainedbyamultiplelinearregression(thelogarithmicapproachdisplayedthebestresults).Machiningtime921:94=Stepover74:98Feedpertooth310:8(2)Eq.(2)relatesthemachiningtimetothestepoverandfeedpertooth.Itisanapplicationoftheuniformmovementequation.Afterthedefinitionoftherequiredroughnessva