Numerical Simulation and Analysis for Metal Cutting Processes Based on FEM and SPH.pdf

NumericalSimulationandAnalysisforMetalCuttingProcessesBasedonFEMandSPH*AbstractByusingthecouplingmethodofFEMandSPH,constitutivebehaviorofmaterialinthemetalcuttingprocesswassimulatedandcuttingmechanismswereanalyzed.Thesimulationresultsshowthatthecuttingprocessisaplasticdeformationprocessinwhichcuttinglayermaterialproducesshearingslipduetotheextrusionofcuttingtool;theextrusionandfrictionfromcuttingedgeresultincoldplasticdeformationofmaterialinformedsurfacelayer,andformresidualstress;thecuttingforceincreasesrapidlyandthendecreases,eventuallyvariesinacertainrange;themaximaleffectivestressvariesatacertaindistancetothecuttingedgeinstablecuttingstage.Keywords:metalcutting;numericalsimulation;finiteelementmethod;SPHmethodI.INTRODUCTIONMetalcuttingprocessisacomplexmachiningtechnology.Itnotonlyrelatestoelasticity,plasticityandfracturemechanicsbutalsoinvolvestribologyandthermodynamics.Cuttingqualityisinfluencedbymanyfactors,suchastheshapeoftool,cuttingparameters,cuttingheat,cutting-toolwearandsoon1.Itisverydifferenttoquantificationallyanalyzeandresearchcuttingmechanismbyanalyticmethod.Itwastesman-hourandincreasesproductioncostsbytrialanderrormethod.Asanewresearchmethodformetalcuttingmechanism,computersimulationmethodisconvenientandefficient.Amongthem,finiteelementmethodismostwidelyusedinthesimulationofmetalcutting,andhasgotsomesignificantachievements2,3.Finiteelementmethodisameshmethod.Separationcriterionandfracturecriterionofchiphavetobeartificiallysetinthesimulationofmetalcuttingprocess,orthemeshesinthecuttingdeformationareawillbedistorted.Itisnotexactlyinagreementwithactualconditions.Thedevelopmentofmeshlessmethodprovidesaneffectivesolutionfortheproblem.Smoothparticlehydrodynamics(SPH)isakindofmaturemeshlessmethod.SimulationmodelisbuiltwithdiscreteparticlesinSPH,sobigdeformationinmetalcuttingprocesscanbeeffectivelysolved4-6.Inthesimulationofmechanicaldeformationofcontinuummedium,FEMismoreefficientthanSPH,butitisinferiortoSPHinthesimulationrelatestobigdeformationanddiscontinuousmedium.SothepapersimulatesmetalcuttingprocessbythecouplingmethodofFEMandSPHbasedonLS-DYNAsoftware.Itcomplementstheshortcomingsofsinglemethod.II.BASICPRINCIPLESOFTHESPHMETHODInSPH,simulationmodelisbuiltwithdiscreteparticles.Themassofparticleisfixedinitscoordinatesystem.ThereforeSPHmethodissimilartoLagrangemethod.Itsbasicequationsarealsoenergyconservationequationandconstructiveequationofsolidmaterial.PhysicalflowfieldinSPHisdescribedwithasetofflowingparticleswhichhasacertainvelocity.Eachparticleisaninterpolationpointwithcharacteristicsofflowfield.Thewholesolutioncanbegotbytheinterpolationfunctionoftheseparticles7,8.ThebasisofSPHisinterpolationprinciple9.Anymacrovariable(suchasdensity,press,temperatureetc)canbegotbyintegralinterpolationofasetofdisorderedparticles.Interactionsofparticlesareexpressedbyinterpolationfunction.Approximatefunctionofparticlesis,(1)=yh,yxWyfxfh)d()()(whereWisthekernelfunction(interpolationkernel),itisexpressedbelow:)()(1)(xxhh,xWd=,(2)wheredisthespacedimension,histhesmoothinglength.Assistantfunctionis+=2021)2(2501750511)(332uuu.uu.u.Cu,(3)whereCisanormalizationconstant.Thesmoothinglengthhisanimportantinfluencefactorofcomputationefficiencyandprecision.Inordertoavoidnegativeinfluenceduetomaterialcompressionandexpansion,varyingsmoothinglengthisproposedbyW.Benz.Smoothinglengthhdynamicallyvarieswiththevariationoftimeandspace.Itincreaseswiththeincreaseofdistancebetweenparticles.Itdecreaseswiththedecreaseofdistancebetweenparticles.ItsvariationrangeisHMINh0hHMAXh0,(4)whereh0istheinitialsmoothinglength.InfluencerangeofSPHparticleisasphericalregion,whoseradiusish.Ineverytimestep,itmustbeknownthatwhichparticlesareintheregion.Thereforesearchmustbeimplemented.BucketclassificationmethodofcontactsearchingalgorithmisusedforthesearchinSPH.AsshowninFig.1,firstly,thewholeregionisdividedintosomesub-regions,andthentheregionofeachparticleandits*ThisworkissupportedbythescientificresearchkeyprojectfundoftheMinistryofEducationofChina#20060145017SPHparticlesneighborregionsaresearched.Byusingthesearchingmethod,III.MODELINGANDcomputationisgreatlyreduced.SIMULATIONA.CouplingmareaofworkpieceisparticlesandLagrangemeshes.ItsleftpartisSPHparticles.odelofFEMandSPHInthispaper,bigdeformationmodeledwithSPHparticles,andsmalldeformationareaofworkpieceandcuttingtoolaremodeledwithLagrangemeshes.Fig.2showsthecouplingschematicillustrationofSPHItsrightpartisLagrangemeshes.SPHparticlesandLagrangemeshesarecoupledbyusingnode-surfacecontacttypeinLS-DYNA.Failurecriterionofcouplingcontact10is121snmmfffails,failn,+ff,(5)wherefn,fs,fn,fai,fs,failarethenormalstress,shearstress,lissimpaterialis45steel.Materialmodelisnormalfailurestressandshearfailurestress.m1,m2areexponentsofnormalstressandshearstress,respectively.Inordertoreducecomputingtime,simulationmodelified,asshowninFig.3.Workpieceisacuboidof6mm(length)4mm(height)0.2mm(width).Thesizeoffiniteelementmeshis0.1mm.CuttingdeformationareaismodeledwithSPHparticlesof0.33mm(radius).Toolrakeangle0is10andreliefangle0is6.B.MaterialmodelWorkpiecempiecewiselinearisotropicplasticitywithanarbitrarystressversusstraincurve.Itissuitableforsteels.StrainrateisaccountedforusingtheCowper-Symondsmodel.Therelationbetweenstrainrateandyieldstress10is()()PeffnP1YfC+=01,(6)wheristhestrainrate,CandParethestrainrateparameters,T5).Itshardnessandstrene0istheinitialyieldstressand)(peffnfisthehardeningfunctionwitheffectiveplasticstrain.Toolmaterialishardalloy(Ygtharemuchhigherthanworkpiece.Itisconsideredaselasticbody.Table1listssomematerialcharacteristicsofcuttingtoolandworkpiece,where16arecorrespondingyieldstressvaluestoeffectiveplasticstrainvalues16.TABLEIMATERIALCHARACTERISTICSOFCUTTINGTOOLANDWORKPIECEUNITSYSTEMS:kg-mm-ms123456Elasticratio(E)PoissonratioDensity()Strainrateparameters(C)Strainrateparameters(P)1234560.360.380.420.500.560.60workpiece2000.307.810-64050.0150.0250.050.0750.10.15Cuttingtool6000.151.310-5C.BoundaryconditionsCuttingtoolmovesalongthenegativedirectionofthex-axis,thereforey,ztranslationsandallrotationsareconstrained.Alltranslationsandrotationsofthebottomoffiniteelementmodelareconstrained.ForSPHpart,symmetricplanesmustbeestablishedbyvirtualparticles.Theseparticlesareactuallymirrorparticlesofsolidparticlesnearbytheboundaryof2h0(h0isinitialsmoothinglength),asshowninFig.4.Physicalquantitiesofvirtualparticlesandsolidparticlesaresymmetricaboutthefixedboundaryplane.Thereforevirtualparticlescanproduceconstrainttosolidparticles.ItmakesthevelocityofsolidparticleskeepintheFig.33DsimulationmodelofmetalcuttinghFiniteelementmeshFig.1BucketclassificationandlocalsearchFig.2CouplingschematicillustrationofSPHparticlesandLagrangemeshes.valueofzero,andsolidparticlescannotpenetrateboundary.IV.ANALYSISOFSIMULATIONRESULTSA.ChipformationInthispaper,theprocessesofcuttingdeformationandchipformationof45steelaresimulated.Cuttingvelocityvsis10m/s.Cuttingdepthapis0.5mm.FromFig.5(a)itcanbeseenthatthereexistsbiggishcontactstressatthecontactzonebetweentooledgeandcuttinglayermaterial.Itishighupto658.6MPa.Thevalueishigherthanyieldstrengthof45steel.Thereforethematerialatthecontactzoneproducesirreversibledeformation;thematerialofotherzonesisstillinelasticstate.Withthecontinuousmovingoftool,thecontactareabetweentooledgeandcuttinglayerincreasesgradually.Thecuttinglayermaterialhappenstopileupontherakeface.Innerstressofthematerialincreasesgradually.AsshowninFig.5(b),theeffectivestressinprimarydeformationzoneismuchhigherthanyieldstrength.Thereforethematerialinprimarydeformationzoneisinplasticstate.Undertheextrusionofcuttingtoolandsubsequentflowingmaterial,thematerialinplasticstatemovesupwardalongrakeface.Thematerialformschipafterflowingoutprimarydeformationzone,asshowninFig.5(c).FromFig.5(d)itcanbeseenthatinternalstructureofformedsurfacelayermaterialhappenstochange,andexistresidualstressintheformedsurfacelayer.Thesimulationprocessshowsthattheextrusionandfrictionfromcuttingedgeresultincoldplasticdeformationofmaterialinformedsurfacelayer,andformresidualstress.Fig.6showsvariationcurveofmaximumeffectivestressofworkpieceinmetalcuttingprocess.Itcanbeseenthatmaximumeffectivestresssharplyincreasesinthestartingphase.Thevalueishighupto1.4GPaat0.11ms,andthendecreases.Chipformsgraduallyatthistime.Themaximumeffectivestresseventuallyvariesattherangeof1.21.4GPa.B.AnalysisofcuttingforceFromFig.7itcanbeseenthatthecuttingforceincreasessharplyandthendecreases,eventuallyvariesinacertainrange.Inthemetalcuttingprocess,withtheincreaseofcontactareabetweencuttingtoolandcuttinglayermaterial,cuttingforceandinnerstressofthematerialatcontactzoneincreasegradually.Whentheinnerstressisuptoyieldstrength,thematerialproducesshearingslipandflowsoutfromprimarydeformationzone.Itmakescuttingforcedecreasealittle.Materialyieldingandchipformationcontinuouslyhappen,thereforecuttingforcewavesinacertainrange.C.AnalysisofstressandstrainofcuttingtoolFromdynamicsimulationprocessitcanbeseenthatthereexistsbiggishcontactstressatcuttingedgeinthebeginningofcutting.Withtheproceedingofcutting,thematerialdeformedmovesupwardalongrakefaceandextrudesrakeface.Themaximumcontactstressatrakefacemovesupwardtoo.Aftertheformationofchip,themaximumeffectivestresswavesatacertaindistancetothecuttingedge(asshowninFig.8).Thereforecutting-toolwearissevereintheposition.Stressdistributioncurveofrakefaceat0.2msisshowninFig.9.Itcanbeseenthatcontactstressatcuttingedgeisbiggish.Itisuptomaximumvalueat0.4mmtocuttingedge,Fig.6VariationcurveofmaximumeffectivestressTime(ms)Maximumeffectivestress(GPa)Fig.4SymmetricplaneofSPHmodel2h0hhh0SolidparticleVirtualparticleSmoothinglengthInitialsmoothinglengthFig.5Deformationprocessofthecuttinglayermaterial(a)t=0.02ms(b)t=0.06ms(c)t=0.14ms(d)t=0.35msFig.7VariationcurveofcuttingforceResultantforce(kN)Time(ms)andthendecreasesgradually.curvesofmaximumeffectiveV.CONCLUSION1)ThecouplingmethodofFEMandSPHcomplementstheshortcomingsofsinglemethod.Thesimulationresultsshowthatitiseffectiveinthesimulationofmetalcuttingprocess.2)Thecuttingprocessisaplasticdeformationprocessinwhichcuttinglayermaterialproducesshearingslipduetotheextrusionofcuttingtool.3)Theextrusionandfrictionfromcuttingedgeresultincoldplasticdeformationofmaterialinformedsurfacelayer,andeventuallyformresidualstress.uidance.Withouthisconsisttruction,thispapercoul1J.-Z.Lu,J.-N.Sun,TheTheoryofMetalCuttingandCuttingTool,Beijing:MechanicalIndustryPublishingHouse,2001.2S.-JChen,Q.-LPangandK.Cheng,“Finiteelementsimulationoftheorthogonalmetalcuttingprocess”,MaterialsScienceForum,no.471-472,pp.582-586,2004.3A.-G.Mamalis,M.Horvath,A.-S.Branis,etal,“FiniteElementSimulationofChipFormationinOrthogonalMetalCutting”,JournalofMaterialsProcessingTechnology,vol.110,no.5,pp.19-27,Mar,2001.4R.Vignjevic,J.-R.Reveles,“SPHinatotallagrangianformalism”CMES-ComputerModelinginEngineeringandSciences,vol.14,no.3,pp.181-198,2006.5W.Benz,E.Asphaug,“SimulationofBrittleSolidsUsingSmoothParticleHydrodynamics”,ComputerPhysicsCommunications,vol.87,no.1-2,pp.253-265,1995.6C.Antoci,M.GallatiandSibilla,S,“Numericalsimulationof.7fcirculartubeusingSPHmethod”,KeyEngineering8ang,R.-R.Long,“SPHsimulationofhypervelocity9“SPHmethodappliedtohigh10poration.Livermore,California,1998Fig.9Stressdistributioncurveofrakefaceat0.2msFig.10showsvariationstressandstrainatcuttingtoolsurface.Withoutconsideringtheabnormallocaljumpinthecurves,itcanbeseenthatthemaximumeffectivestresssharplyincreasesto0.28GPa,andeventuallykeepwavingat0.35GPa.Themaximumeffectivestrainkeepswavingat0.03%.Elasticdeformationofcuttingtoolisverysmall4)Aftertheformationofch