研制、改進(jìn)一臺(tái)齒輪滾刀檢測(cè)裝置

摘要AbstractInindustrializeddevelopmenttoday,endlessvarietyofmechanicalproducts,theaccuracyimproved.Geardriveasamajorcomponentofitsaccuracywilldirectlyaffectthequalityofproducts.Therefore,improvingtheprecisiongeardriveintoimprovingthequalityofproductsofarationaldesign.PrecisionGearmainlybytheleveloftwoaspects:theassemblyofprecision,thegearmanufacturingprecision.Gearmanufacturingprecisionmachiningtoolistobeguaranteed.AndHobprocessinggearisanimportanttool,ArchimedesisparticularlyHobintheprocessingofvariousgeartheprocesstobewidelyused.Therefore,ArchimedesHobaccuracyofdetectionisverynecessary.Thedesignisinthisparticularperiodofbirth,ItsmaintaskistozeroanglebeforetheArchimedesHobprofileerrorwasdetected.KeywordsHobprofileerrorTesterGear第1章緒論1.1課題分析

-頂后面-前刀面-切削刃-側(cè)后刀面圖齒輪滾刀的根本蝸桿圖兩種軸向齒形的比擬圖阿基米德滾刀齒形誤差圖齒形誤差與導(dǎo)程角的關(guān)系圖2-5零前角滾刀刃磨時(shí)砂輪的相對(duì)位置

(取整)取整m=3。取整+絕熱高速切削有限元模型〔3〕AbstractAfiniteelementmodelofatwo-dimensionalorthogonalcuttingprocessisdeveloped.Thesimulationusesstandardfiniteelementsoftwaretogetherwithaspecialmeshgeneratorthatisabletomeshthechipcompletelywithregularquadrilateralelementsandastrongmeshrefinementintheshearzoneforcontinuousandsegmentedchips.Thetechniquesofremeshingandtoensureconvergenceoftheimplicitcalculationisdescribed.Resultsfortheformationofsegmentedchipsarepresentedandthesegmentationprocessisstudied.Ofspecialinterestistheoccurrenceofsplitshearbands.Theinfluenceoftheelasticpropertiesandofthecuttingspeedisalsodiscussed.Keywords:Machining;Finiteelements;Remeshing;Chipsegmentation;AdiabaticshearbandsIntroductionTitaniumalloyslikeTi6Al4Varewidelyusedinaerospaceandotherindustrialapplications.Alargefractionoftheproductioncostsforcomponentsmadeofthesealloysisduetomachining.Thedesignoftitaniumalloyswithbettermachinabilityisthereforeaworthwhileresearchaim.Toachievethis,itisnecessarytoidentifytheimportantmaterialparametersthatcriticallyinfluencethemachinabilityofthematerial.Thiscanbedonebyparameterstudiesusingfiniteelementcomputersimulations.Oncethemostpromisingdesignavenuesaredetermined,theactualalloymodificationcanbedone,whichisthusonlythefinalstepofthematerialdesignprocess.ThisapproachissimilartothestandardCAEproductioncycle,whereonlyafewprototypesarebuilt.*Correspondingauthor.E-mailaddresses:martin.baeker@tu-bs.de(M.Baker),j.roesler@tu-bs.de(J.Rosler),c.siemers@tu-bs.de(C.Siemers).1WorksupportedbyDeutscheForschungsgemeinschaft.Creatingareliablecomputermodelofthemetalcuttingprocessisthefirstandcrucialstepinthisprocess.Inthispaper,wedescribesuchamodelinsomedetail.Itusesstandardfiniteelementsoftwareforthecalculations,thusensuringportabilityandflexibility.Astherequirementsonthemeshingalgorithmarequitestrong,aspecialpreprocessorhasbeendeveloped,whichisprogrammedinCttandisthusalsoportabletodifferentplatforms.Thepaperisorganizedasfollows:afterashortdescriptionoftherequirementsonthemodelinSection2,thedetailsofthefiniteelementmodelaregiveninSection3.SomeresultsproducedwiththemodelareshowninSection4,focussingonthedetailsofthechipformationprocess.Section5summarizestheworkandpointsoutfutureresearchaims.TheproblemInthemetalcuttingprocessmaterialisremovedfromthesurfaceoftheworkpiecebyacuttingtoolandachipisformed.Theprobleminvolveslargeplasticdeformationswhichgenerateaconsiderableamountofheat,asdoesthefrictionbetweentoolandworkpieceandalsobetweentoolandchip.Theseparationofworkpiecematerialinfrontofthetoolalsohastobemodeled.Astheinfluenceofthematerialparametersismoreimportantformaterialdesignconsiderationsthanarethedetailsoftheprocessitself,thecuttingprocesssimulatedhereisthatoforthogonalcutting.Theprocessissimulatedastwo-dimensional,whichstronglyreducesthecomputertimeneededforthecalculation.Afurthersimplificationisdonebyassumingthetooltobeperfectlyrigid.Frictionandheatflowintothetoolhavebeenneglectedsofarinthesimulations,butcaneasilybeincluded.Thereasonforthisomissionisthatitisnecessarytosimplifythecuttingprocessasmuchaspossibletogaininsightsintotheunderlyingmechanismsaswillbeexplainedbelow.Also,thereisnothermalradiationfromthefreesurfaceofthechipandnoheattransferattheboundaryofthematerialisallowed.Rapidmachiningisastronglynon-linearproblemduetotheeffectsdescribedaboveandithastobesimulatedusingafullycoupledthermomechanicalfiniteelementmodel.Itisthereforeaformidabletasktodevelopafiniteelementcodetodealwiththemetalcuttingproblemfromscratch,sothattheuseofcommercialFEsoftwareisanattractivealternative.Modernfiniteelementsoftwarecaninprinciplehandlesuchstronglynon-linearproblems.ForourstudieswehavedecidedtousetheABAQUS/Standardprogramsystem,whichallowsthedefinitionofcomplexcontactconditions,leavesmanypossibilitiestodefinematerialbehaviour,andcanbecustomizedinmanyregardsbyincludinguser-definedsubroutines.WesupposethatmostofthemethodsdescribedbelowwouldworkwithanysimilarlypowerfulFEpackage.Duetotheuseofstandardizedsoftware,theformulationoftheequations(finiteelementformulation,thermomechanicalcoupling,integrationscheme,etc.)canbefoundingreatdetailelsewhere[3].Manyfiniteelementsimulationsofthemetalcuttingprocessareperformedusingtheexplicitmethod(seeforexample[17]),whichisguaranteedtoconverge.(Anoverviewoverfiniteelementsimulationsofthecuttingprocesscanbefoundin[16].)Nevertheless,wehavedecidedtouseanimplicitcode.Hereconvergenceischeckedduringthesimulation,buttheiterativesolutionprocessisnolongerguaranteedtoconverge.OneadvantageofusingtheimplicitcodeABAQUS/Standardisthatthisallowsagreatrangeofflexibleuser-definedsubroutinestobeintroducedinthesimulation.Suchroutinescanbeusedtoimplementcomplicatedmaterialseparationcriteria.Inadditiontothat,theimplicitcodehasabetterscalingbehavioriflocalmeshrefinementisneeded.Ifnarrowshearbandsform,elementsizesoftheorderof1lmorlessarenecessary(seeSection4.2)andtheadvantageinCPUtimeofusinganexplicitalgorithmwillstronglydiminish.Anexplicitmethodisprobablysuperioriffrictionaleffectsarelarge,whichis,however,notthecasehere.Ontheotherhand,explicitmethodsoftenneedtochangesomephysicalparameterslikedensityortoolvelocity,orhavetouseartificialviscosity.Inouropinion,thereisnoreasontoconsideranimplicitsimulationinferiortoanexplicitone,ifconvergencecanbeachieved.Alsodifferentlyfrommanyothersimulations,weusefullyintegratedfirst-orderquadrilateralelements,whichhavebetterconvergencepropertiesthantriangularelements.ThisisdiscussedfurtherinSection3.3.Titaniumalloysformsegmentedchipswhencutorthogonally(seeFig.9).Anydetailedsimulationofthemetalcuttingprocessmustbeabletotakethissegmentationintoaccount.Themechanismsbehindchipsegmentationarestillnotcompletelyunderstood[12,15,25,26].Itisclearthatso-calledadiabaticshearingplaysaprominentroleinthesegmentationprocess:Thermalsofteningofthematerialintheshearzoneleadstoanincreaseddeformationinthiszone,whichproducesheatandleadstofurthersoftening.Thispositivefeedbackbetweensofteninganddeformationcausesanarrowbandofextremelystrongdeformation,whilethesurroundingmaterialisonlyslightlydeformed.Itis,however,notknownwhethertheadiabaticshearbandsarecausedbycracksgrowingintothematerial,asassumedin[25].Ifthisistrue,thestressconcentrationatthecracktipcantheninducetheformationoftheshearband(seee.g.[5]).Forthemodeldescribedhere,weassumethatchipsegmentationiscausedbypureadiabaticshearing,withoutcracksoccurring.Itisquiteclearthattheeffectiveplasticflowcurveofamaterialpointintheshearbandmustshowamaximumforthismechanismtohold.Wehaveusedaflowcurvefieldwhereeventheisothermalflowcurvesshowamaximum.ThisisfurtherdetailedinSection4.1.Ifsegmentedchipsform,theshearconcentrationleadstoa(nearly)discontinuousdeformationofthechip.Measureshavetobetakentoensurethatthefiniteelementmeshisnottoomuchdistortedduetothisdeformation,especiallyinasimulationusingquadrilateralelements.Tosummarize,thesimulationhastomeetthefollowingrequirements:.useofquadrilateralelements,asregularaspossible,avoidingextremelydistortedmeshes;.highmeshdensityintheshearzone;.discontinuousdeformation(segmentation)ofthechip;.convergenceoftheimplicitalgorithm;.useofstandardsoftwareforportabilityandflexibility.Theuseofanalgorithmforautomaticremeshingismandatoryinasimulationofmetalcutting,aselementdistortionsbecomelargeinaLagrangianapproach,2especiallyifsegmentedchipsform.Afrequentremeshingensuresthattheelementsneverbecometoodistorted.Itcanalsobeusedtocreatearefinedmeshintheshearzonethatmoveswiththematerial(seeFig.6).However,standardmeshgeneratorsarenotabletohandlethecomplextasksinvolvedinthisproblemwithoutdifficulties.Thusapreprocessorhasbeenprogrammedthatcanmeshthestronglycurvedregionscreatedbythecuttingprocessusingquadrilaterals.Thepositionoftheshearzoneisautomaticallydeterminedusingageometriccriterionandthemeshisrefinedthere.Thepreprocessorisdescribedinthefollowingsection.Afterwards,detailsofthemeshcreatingprocessandofthemodelingofthesegmentationareexplained.3.Thefiniteelementmodel3.1.PrinciplesofmeshgenerationTheusedpreprocessor(calledPre++)iswritteninCttusingstandardclasslibrariesandisthusportabletodifferentplatforms.Thepreprocessorcanbeusedtocalculateparametrizedgeometrydata,sothatmodelparameterscaneasilybechanged.Itisapplicabletoawiderangeofproblemsintwoand(withsomerestrictions)inthreedimensions.Theeasiestwayofgeneratingquadrilateralelementsistodividethephysicalregiontobemeshedintopartsthatareboundedbyfourlinesandcanbemappedontotheunitsquare.Aregularmeshingoftheunitsquarecanthenbemappedbackontotheregionitselfusingaconformalmap,asdescribedinsomedetailin[23,24].Ifwedefinethecoordinatesinrealspacewith(x;y)andthoseonthesquarewith(n;g),ageneralcurvilinearcoordinatesystemcanbedefinedbysolvingtheLaplaceequation〔1〕〔2〕Herenxxdenotesthepartialderivativeo2n=ox2,etc.Thissystemofequationshasaphysicalinterpretation:thecoordinatescorrespondtotheequipotentiallinesofanelectricfieldontheregionwhentwoopposingsidesareheldonadifferentvoltage.Itisofcoursemucheasiertosolvetheequationusingthecoordinates〔n;g〕asindependentvariables.Inthiscasetheequationhastobeinverted,resultingin〔3〕〔4〕Thisisaquasi-linearellipticsystemofequations,whichcanbesolvedusingstandardmethods.Themeshingalgorithmisusuallyusedtocreateameshonaphysicalregionthatistheresultofafiniteelementcalculation,asitisusedtoautomatizetheremeshingprocess.Therefore,theboundinglinesaredefinedbythenodepositionsofthepreviouscalculationstepandarethusalreadydiscretized.Tosolvetheequations,aregularrectangularmeshisusedwherethegridsizeischosentobesmallerthanthesmallestdistancebetweennodesontheboundingsurfaces,sothatthecontouroftheoldandthenewmeshcloselyagree.Asthenumberofsolutionpointshastobequitelargeforirregularlyshapedregions,itisadvantageoustochoosethesolutionalgorithmwithsomecare.WehavedecidedonafullmultigridalgorithmasintroducedbyBrandt[7].Thisalgorithmhastheadvantagethatitisfast,robust,andthatitalsogivesanestimateofthetruncationerrorinvolvedinthediscretization,sothatthecalculationscanbeperformeduntilthenumericalerroriscomparabletothetruncationerror.Astheequationsarenon-linear,afullapproximationscheme(FAS)methodhastobeused.Themultigridtechniquereliesonthefactthatstandardrelaxationmethods(likeGauss–Seidel)areveryefficientinreducingtheoscillatingpartofthesolutionerror,whereasthesmoother,large-wavelengthpartisnotaffectedverymuch.Thereforeafterafewrelaxationstepsanyequationinvolvingtheerrorcanberepresentedaswellonacoarsergridwithlesspoints.Relaxationonthiscoarsergridagainreducesthesmall-wavelengthcomponents,which,however,nowhavealargerabsolutewavelengthasthegridiscoarser.Therefore,arecursiveschemeisusedwheretheerrorisefficientlyreducedonalllengthscalesinvolved.Thisalgorithmisastandardtoolforthesolutionofellipticequations,sothatthereaderisreferredtotheliteratureforfurtherdetails[20].Itneedsonlyaboutaminuteonastandardworkstationevenwhenthenumberoflatticepointsisabout250000aslongastheboundariesoftheregionarenottoostronglycurved.Fig.1(a)showsthecoordinatelinescreatedwiththedescribedalgorith