ORIGINALARTICLEOnthefiniteelementmodellingofhighspeedhardturningA.G.Mamalis&J.Kundrk&A.Markopoulos&D.E.ManolakosReceived:7November2006/Accepted:25May2007/Publishedonline:14August2007#Springer-VerlagLondonLimited2007AbstractTheresultsreportedinthispaperpertaintothesimulationofhighspeedhardturningwhenusingthefiniteelementmethod.Inrecentyearshighspeedhardturninghasemergedasaveryadvantageousmachiningprocessforcuttinghardenedsteels.Amongtheadvantagesofthismodernturningoperationarefinalproductquality,reducedmachiningtime,lowercostandenvironmentallyfriendlycharacteristics.Forthefiniteelementmodellingacommer-cialprogramme,namelytheThirdWaveSystemsAdvant-Edge,wasused.Thisprogrammeisspeciallydesignedforsimulatingcuttingoperations,offeringtotheusermanydesigningandanalysistools.Inthepresentanalysisorthogonalcuttingmodelsareproposed,takingseveralprocessingparametersintoaccount；themodelsarevalidat-edwithexperimentalresultsfromtherelevantliteratureanddiscussed.Additionally,obliquecuttingmodelsofhighspeedhardturningareconstructedanddiscussed.Fromthereportedresultsusefulconclusionsmaybedrawnanditcanbestatedthattheproposedmodelscanbeusedforindustrialapplication.KeywordsMachining.Finiteelementmethod.Hardturning1IntroductionHardturning,amachiningoperationusedfortheprocess-ingofhardmaterialssuchashardenedsteels,hasbeenbroughtintotheforefrontofmodernmetalcuttingoperationswiththeincreasingdemandformanufacturinghighqualitycomponents,e.g.,gears,shafts,bearings,diesandtools,fromthesekindsofmaterials.Cuttingtoolsemployedinhardturningaremadeofspecializedtoolmaterials,suchascubicboronnitrite(CBN),thatareabletoovercometheproblemsexperiencedduringtheprocess1.Thesecuttingtoolsareidealformachiningiron-basedmaterialsattheseverecuttingconditionsassociatedwithhardturning；theypossessexquisiteproperties,evenatelevatedtemperatures,allowingfortheirapplicationathighcuttingspeedsandwithouttheuseofanycuttingfluids2；bydrycuttingnotonlyenvironmentally-friendlycharacter-isticsareattributedtotheprocess,butalsocostreductioncanbeattainedbyomittingbuyinganddisposalcostsofthecuttingfluids35.Inadditionthecombinationofhardturningandhighspeedmachiningisprovedtobeveryadvantageoussinceagreatreductioninprocessingtimecanbeachieved1.Hardturningisveryadvantageousforawidespectrumofapplicationsandisalsoconsideredasanalternativeforavarietyofprocesses,sincethesingle-stepsuperfinishhardturningcanreplacetheabrasiveprocesses,traditionallyusedasfinishingoperations,ornon-traditionalprocesses,suchaselectricaldischargemachining(EDM),inmachin-inghardparts,offeringaccuracyequaltoorbetterthanthatprovidedsofar,flexibilityandconsiderablemachiningtimeandcostreduction47.Note,however,thathardturninghasnotbeenintroducedintomodernindustryasmuchasitshouldbe,mainlybecauseofphenomenasuchasrapidtoolwearorcrackingIntJAdvManufTechnol(2008)38:441446DOI10.1007/s00170-007-1114-9A.G.Mamalis(*):A.Markopoulos:D.E.ManolakosManufacturingTechnologyDivision,NationalTechnicalUniversityofAthens,Athens,Greecee-mail:mamaliscentral.ntua.grJ.KundrkDepartmentofProductionEngineering,UniversityofMiskolc,Miskolc,Hungaryandchippingofthecuttingedgeduetoextremepressureandtemperatureimposedonthecuttingtool,whichleadtopoormachiningresults8.Furthermore,asanovelmachiningprocess,itneedstobefurtherstudiedsothatitmaybeoptimized.Mostresearchworkislimitedtoexperimentalresults,but,also,themodellingofhardturningcanprovideusefuldatatobetterunderstandingtheprocess.Numericalmodellingand,especially,thefiniteelementmethod(FEM)havebeenwidelyusedinthepastfortheanalysisandthepredictionofthecuttingperfor-manceinmachiningoperations.FEMhasbeenaverypowerfultoolinthecuttingtechnologyandcanbeappliedtohighspeedhardturningaswell.InthepresentpaperFEMisemployedinordertosimulatedryhighspeedhardturning,investigatingtheinfluenceofthecuttingspeedontheperformanceofthecuttingoperationandpredictingthecrucialprocessingparameters,someofthembeingsometimesverydifficulttobemeasuredorcalculatedotherwise,e.g.,temperaturefieldswithintheworkpieceandthetoolduringtheprocess.However,hardturningisarathercomplexprocess,withcuttingconditionsthataredifferentfromconventionalturningand,thereforeitisdesirabletotakeintoaccountsomespecialcharacteristics；forthispurpose,theFEMprogrammeThirdWaveAdvantEdge,whichisspeciallydesignedtosimulatecuttingoperations,isused.Forthesimulationofhardturningbothanorthogonalandanobliquecuttingmodelareproposed.2FiniteelementmodellingSimulationsofvariousmachiningoperationsusingthefiniteelementmethodhavebeenreportedoverthelastthreedecades；inReferences9,10acollectionofsuchpaperscanbefound.Thefirstmodelsthatappearedinthe1970susedtheEulerianformulationformodellingorthogonalcutting.Inthisapproachthefiniteelementmeshisspatiallyfixedandthematerialflowsthroughit,inordertosimulatethechipformation.Thecomputationaltimeinsuchmodelsisreduced,duetothefewelementsrequiredformodellingtheworkpieceandthechip,anditismainlyusedforsimulatingthesteadystateconditionofthecuttingprocess.Theelementsdonotundergoseveredistortion,sincethemeshisaprioriknown,butthisformulationrequirescomplexprogramming.Furthermore,experimentaldatamustbeonhandpriortotheconstructionofthemodelinordertodeterminethechipgeometry.Althoughthisformulationisstillutilizedbysomeresearchers,theupdatedLagrangianformulationhasbeenproposedandismorewidelyusedtoday.Inthisapproach,theelementsareattachedtothematerialandtheunde-formedtoolisadvancedtowardstheworkpiece.Fortheformationofthechip,achipseparationcriterioninfrontofthetooledgeisapplied.Therearemanycriteriaproposedsofarwhichcanbegeometricorphysicalandmayinvolveforexampleacriticaldistancebetweenthetoolandtheworkpiece；whenthetoolreachesthiscriticaldistancefromtheworkpiecetheelementsaheadofthetooledgearedividedandthusthechipisformed.Otherseparationcriteriapertaintocriticalvaluesofe.g.,stressorstraininordertoinitiatethechipformationandevencrackpropagationcriteriahavebeenreportedforthisprocedure.Adisadvantageofthismethodisconnectedtothelargemeshdeformationobservedduringthesimulation；duetotheattachmentofthemeshonthework-piecematerial,themeshisdistortedbecauseoftheplasticdeformationinthecuttingzone.Inordertoovercomethisdisadvantagecontinuousremeshingandadaptivemeshingareusuallyapplied,increasingconsiderablytherequiredcalcula-tiontime.Nevertheless,theadvancesincomputershavemadeitpossibletoreducethetimeneededforsuchananalysistoacceptablelevels.NotethatanarbitraryLagrangian-Eulerianformulation(ALE)hasalsobeenproposedwiththeaimofcombiningtheadvantagesofthetwomethods,butitisnotaswidelyused.Mostofthemodellingworkpublishedsofarpertainsto2Dmodelsoforthogonalcutting,while3Dmodelsareratherrareintherelevantliterature.Thatismainlybecause,eventhough3Dcuttingismorerealistic,sincecuttingis3Dinnature,itrequiresamuchmorecomplexconsiderationofworkpieceandcuttingtoolgeometry,contactpropertiesand,ofcourseadditionalcomputationaltime.Inparticular,theworkdedicatedtohardturningisevenmorelimited1115.ThemodelsprovidedbelowaredevelopedemployingtheThirdWaveAdvantEdgesoftware,whichintegratesspecialfeaturesappropriateformachiningsimulation.Theprogrammemenusaredesignedinsuchawaythattheyallowtheusertominimizethemodelpreparationtime.Furthermore,itincludesawidedatabaseofworkpieceandtoolmaterialscommonlyusedincuttingoperations,offeringalltherequireddataforeffectivematerialmodelling.TheAdvantEdgecodeisaLagrangian,explicit,dynamiccode,whichcanperformcoupledthermo-mechanicaltransientanalysis.TheprogramappliesadaptivemeshingandFig.1Orthogonalcuttingmodelschematicdiagram442IntJAdvManufTechnol(2008)38:441446continuousremeshingforchipandworkpiece,allowingforaccurateresults.Forananalyticaldiscussiononthenumericaltechniquesusedintheprogrammeandacompre-hensivepresentationofitsfunctionsseeReference16.3Resultsanddiscussion3.1OrthogonalcuttingmodelsTheorthogonalcuttingschematicdiagramusedintheprogrammeisshowninFig.1.Thedepthofcutisperpen-diculartotheplaneshowninthefigureandintheplanestraincase,itisconsideredtobelargeincomparisontothefeed.InthepresentanalysistheworkpiecematerialistheAISIH-13hotworktoolsteelanditslengthistakenequaltol=3mm.ThetoolmaterialisCBNandthemodellingoftool-chipinterfacefrictionisbasedonCoulombsfrictionlaw,withfrictioncoefficientsetconstantatthevalue=0.5.Acuttingtool,with5rakeangle,5clearanceangleand0.02mmcuttingedgeradius,isusedfortheanalysis.Furthermore,thefeedistakenequaltof=0.05mm/rev,whilethreedifferentcuttingspeeds,namelyvc=200,250and300m/min,areconsidered.InFig.2(a)and(b)theinitialmeshandatypicalmeshcreatedafterthetoolhascuthalfoftheworkpiecelength(l=1.5mmfortimet=3104s),forvc=300m/minrespectively,areshown.Inthisfigure,thecontinuousmeshingandtheadaptiveremeshingprocedurescanbeobserved.Note,that,inFig.2(a)themeshisdensernearthetooltip,wheredeformationisabouttotakeplace,whileinFig.2(b)newelementsarecreatedintheshearzonewherethestrainrateisexpectedtobehigh.Note,also,thatthemeshdensityinthechip,especiallyinitsinnerandoutersurfaces,isalsohighbecauseofthedeformationofthematerialinthisarea；finermeshcanfollowthecurveofthecurlingmaterialmorecloselyand,furthermore,providemoreaccurateresults.Forthevalidationoftheproposedhardturningmodelexperimentalresultsfromtherelevantliteratureareused,wherethehighspeedturningofhardsteeltubes(55HRC),inordertoachieveorthogonalcuttingconditions,isperformed17.InFig.3theexperimentalvaluesofthethrustforceFtandthecuttingforceFcarecomparedtotheonespredictedfromthemodels.Fromthisfigureitcanbeseenthattheexperimentalandthenumericalresultsareinaverygoodagreementand,generally,theyfollowthesametrends；thrustforce,whichisthelargestforcecomponent,decreasesforincreasingcuttingspeed,whilecuttingforceincreasesslightly.Nevertheless,inalmostallthecases,theFig.2(a)Initialmeshand(b)meshatl=1.5mmFig.3NumericalandexperimentalresultsofthrustandcuttingforcesforthreedifferentcuttingspeedsIntJAdvManufTechnol(2008)38:441446443numericalvaluesseemtooverestimatetheexperimentaloneswhilethediscrepanciesarelargerforhighercuttingspeeds；thismaybeattributedtothelargestrain-ratesdevelopedduringtheprocessthataltersthematerialbehaviourinsuchawaythattheycannotbetakenintoaccountbythemodelortoinadequatefrictionmodelling,whichmeansthatamoreadvancedfrictiontheoryneedstobemodelled.Note,also,thatitispossible,besidesthecuttingandthrustforces,toextractfromtheproposedmodelpredic-tionsforvaluesthatitwouldbeverylaboriousorevenimpossibletoobtainotherwise.Examplesofsuchcasesare:thetemperaturedistributionintheworkpieceandtoolintheformofisothermalbandsandthevonMisesstressesdevelopedduringcutting.InFig.4(a)and(b)thetemperaturefieldsandthevonMisesstresses,respectively,forcuttingwithvc=300m/min,areshown.Thesefiguresdemonstratethemodelatastepoftheanalysis,specificallyforlengthofcutl=1.5mm,wherecuttingiswellintothesteady-stateregion.Theformoftheresultsissimilarforallconditions,exceptofcoursethemagnitude.Fromtheresultsobtained,itmaybeconcludedthatthemaximumtemperatureincreaseswithincreasingcuttingspeed,being620C,690Cand730Cforthethreedifferentcuttingspeedsconsidered.Thismayexplainthatthethrustforcedecreasesforhighercuttingspeed,sincesofteningofth