外文资料--Developing a Postprocessor for Three Types of Five-Axis Machine Tools.pdf

IntJAdvManufTechnol(1997)13:658-665©1997Springer-VerlagLondonLimitedTheInternationalJournalofRdvancedmanufacturinglechnologgDevelopingaPostprocessorforThreeTypesofFive-AxisMachineToolsR.-S.LeeandC.-H.SheDepartmentofMechanicalEngineering,NationalChengKungUniversity,Tainan,Taiwan,RepublicofChinaThispaperpresentsapostprocessorcapableofconvertingcutterlocation(CL)damtomachinecontroldataforthreetypicalfive-axismachinetoolstoestablishaninterfacebetweencomputer-aidedmanufacturing(CAM)systemsandnumericallycontrolled(NC)machines,TheanalyticalequationsforNCdataareobtainedusingthehomogeneouscoordinatetrans-formationmatrixandinversekinematics.Inaddition,thedevelopedpostprocessormethodisimplemenwdthroughatrial-cutonafive-axismachineandverifiedonthecoordinatemeasurementmachine.Experimentalresultsconfirmedtheeffectivenessoftheproposedpostprocessormethodwhichcanbeusedtointegratethevariousfive-axismachinetoolsemployedinmanufacturingsystems.Keywords:Coordinatetransformationmatrix；Cutterlocationdata；Five-axismachines；NCprogramming；Postprocessor1.IntroductionFreeformsurfaces(orsculpturedsurfaces)havefoundextensiveindustrialapplications,suchasinautomobilebodies,shiphullsandaerospaceparts.Themouldorstampingdieusedtocreatesuchapartisusuallymachinedusingnumericallycontrolled(NC)machinetools.Theconventionalwayofmachiningfree-formsurfacesisbyusingathree-axismachinetoolwithaballend-mill.Three-axismachinetoolscannotchangethetoolorientation,soafive-axismachinetoolisintroducedtosetthecuttingtoolinanappropriateorientationforefficientmachin-ing.Withtherapidlyadvancingcomputertechnology,commer-cialCAD/CAMsystemscandesignfreeformsurfacesandgenerateeitherthethree-axisorfive-axistoolpath.Thecutterlocation(CL)data,composedofcuttertippositionandthetoolorientation,canthenbedirectlyobtainedfromaCADmodelofaproductdesigncreatedintheCAD/CAMsystems.However,difficultyfrequentlyarisesincommunicationbetweentheCAMsystemsandtheNCmachinetools,especiallywhenCorrespondenceandoffprintrequeststo:ProfessorRong-SheanLee,DepartmentofMechanicalEngineering,NationalChengKungUniver-sity,Tainan,Taiwan70101,RepublicofChina.variousmachinetoolsareemployed.TheinterfacethatlinkstheCAMsystemsandNCmachinesiscalledthepostprocessoranditconvertsCLdatatomachinecode.Essentially,differentcombinationsofmachinetoolandcontrolunitrequiredifferentpostprocessors.Consequently,amanufacturingsystemwithavarietyofmachinetoolsrequiresseveralpostprocessors.Variousstudieshaveaddressedtheissueofdevelopingpostprocessorsformachinetools.BediandVickers1developedapostprocessorprogramforFANUC6MBmachinetool.Balaji2presentedthedevelopmentandimplementationofapostprocessorbyconvertingAPTsourcecodestoamachinecodeformat.LinandChu3derivedtheNCdataformachinetoolstomanufacturecamswithfiat-facefollowersusingamodifiedDenavit-Hartenberg(D-H)notation.However,theaboveworksareonlyrelatedtothree-axismachining.Inaddition,sincethetoolaxisorientationisfixedforathree-axismachinetool,thetransformationfromCLdatatoNCdataisstraightforwardandnoadditionalcoordinatetransformationtechniqueisnecessaU.Tofulfiltheindustrialdemandforgeometricvarietyandhighprecision,theuseofmulti-axismachininghasincreased,especiallyformachiningsculpturedsurfaces.SuhandLee4developedafour-axisCAMsystemincludingCLdatagenerationandpostprocessing.Vickersetal.5usedaG-surfmethodtodefineandmachinecompoundcurvaturesurfacesonthree-,four-andfive-axismachinetool.TakeuchiandWatanabe6proposedafive-axiscontrolcollision-freetoolpathandpostprocessormethodfortwotypesofmachineconfiguration.SakamotoandInasaki7classifiedtheconfigurationoffive-axismachinetoolsintothreetypes.However,theanalyticalNCdataexpressionisnotavailableintheaboveworks.LinandTsai8recentlyusedtheD-HnotationtogenerateanNCdataequationformachiningaspatialcamonafour-axismachinetool.Furthermore,Warkentinetal.9presentedatechniqueformachiningsphericalsurfaces.Intheirwork,thedesiredNCdataisderivedforonlyoneconfigurationoffive-axismachine.Meanwhile,Raoetal.10developedtheprincipal-axismethodtomachinecomplexsurfacesontwoconfigurationsoffive-axismachines.Nevertheless,onlyrotationalmovementsweredetermined.Translationalmove-mentsforthemachinetoolwerenotinvestigated.Sincetheremaybeaconsiderablenumberofcombinationsoffive-axisDevelopingaPostprocessorfi)rFive-AxisMachineTools659machinetoolconfiguration,thepostprocessorwillinevitablybedevelopedindividually6.However,accordingtotheclassificationproposedbySakamotoandInasaki7,thestructureofthefive-axismachinetoolcanbedividedintothreebasictypes.NoneoftheabovestudieshasderivedthecompleteanalyticalequationsforNCdatawhichcontainthreelinearmotionsandtworotarymotions.Thisworkaimstodevelopapostprocessorforthreekindsoffive-axismachinetools,basedonthehomogeneouscoordinatetransformationmatrix.TheanalyticalequationsforNCdatacanbeobtainedbyequatingtheform-shapingfunctionmatrixandtheknownCLdataandsolvingthesimultaneousalgebraicequations.Moreover,themachinetoolsettingprocedureandthecharacteristicsfordifferentconfigurationsarediscussed.Toverifythevalidityandeffectivenessofthedevelopedpostprocessor,adesignedBeziersurfaceismachinedwithmodelmaterialonatypicalfive-axismachiningcentreandthenmeasuredonthecoordinatemeasurementmachine(CMM).2.KinematicsModelMachinetoolsarearticulatedopenchainsofseriallyconnectedlinkswithjoints.Thejointsmayeitherberevoluteorprismatic.Actuationofarevolutejointrotatesthelinkaboutthejointaxis,whileactuationofaprismaticjointtranslatesthelinkalongthejointaxis.Toadequatelycontrolthepositionandorientationofthecuttingtoolandthemachinetool,akinemat-icsmodelestablishingthemathematicaldescriptionofthegeometryandmotionofamachinetoolisrequired.DenavitandHartenberg11firstintroducedthespatialtransformationbetweentwosuccessivelinkcoordinatesystemsusinga4x4homogeneouscoordinatetransformationmatrix,whichwaslateradoptedbyPaul12.Itisaconventionalmodellingtechniqueusedformechanisms,robotics,erroranalysisandcomputervisions.Inthispaper,fourfundamentaltransformationmatricesusingPaulsnotationareintroduced.Theycanbeexpressedasfollows:Trans(a,b,c)=ii10Rot(X,0)=000Rot(Y,0)=-SO0SORot(Z,O)=°°i110010000CO-SOSOCO00OSO0l000CO0001-SO00CO00010001(1)(2)(3)(4)Trans(a,b,c)impliesatranslationgivenbythevectorai+bj+ck,andRot(X,0),Rot(Y,0),Rot(Z,0)implyrotationsof0abouttheX,YandZcoordinateaxis,respectively；and"C"and"S"refertocosineandsinefunctions,respectively.Thespatialtransformationfromonecoordinatesystemtoanothercoordinatesystemcanthereforebedecomposedbycombiningthefundamentaltransformationmatrices.3.DefinitionofCLDataforFive-AxisMachiningThecutterlocationdataforfive-axismillingconsistsofthepositionandorientationofthecutterwithrespecttotheworkpiececoordinatesystem,asshowninFig.1.Inthispaper,thepointvectoriswrittenasQQyQ1T,andvectorsoftheformKxK,KzOTareusedtorepresentdirectionsforhomogeneouscoordinatenotation；thesuperscript"T"denotesthetransposedmatrix.Itisworthmentioningthatthesignificantcutterpositionisdefinedasthecuttercentretipandnotthecuttercontactpoint.Foragivenparametricdesignsurfacetobemachinedusingfive-axismillingwithageneralisedcuttingtooldefinedaccordingtoDIN66215whereanypointofthecuttingtoolcanbedefinedasthecontactpoint,theappropriateCLdatacanbedetermined13bydifferentialgeometryandthehomogeneouscoordinatetransformationmatrix.4.PostprocessorforFive-AxisMachiningTheCLfile,onceobtained,shouldbetransformedintofivereferenceinputs(i.e.threelinearmotionsplustworotationalmotions)usingtheinversekinematicstransformationforcon-trollersofthefive-axismachine.ThistranslationisknownaspostprocessingandthetranslatingsoftwareiscalledtheZwThetoolaxisvectorKKyKzogTheworkpiecesurfaceThecuttertipcentreQxeyQz1TowFig.1.GeometricdefinitionofCLdata.Yw660R.-S.LeeandC.-H.She(xIxFig.2.Configurationforthreekindsoffive-axismachiningcentres.(a)Table-tiltingtype.(b)Spindle-tiltingtype.(c)Table/spindle-tiltingtype.postprocessor.Theinversekinematicstransformationdependsonthegeometricstructureofthefive-axismachinetoolused.Theoretically,therearenumerouscombinationstoyieldthefive-axismachinetoolconfiguration.However,inpractice,theconfigurationcanbeclassifiedintothreebasictypesaccordingtothedistributionofthetworotationalmovementunits6,7:1.Table-tiltingwithtworotationsonthetable.2.Spindle-tiltingwithtworotationsonthespindle.3.Table/spindle-tiltingwithonerotationeachonthetableandspindle.Thepostprocessorforfive-axismachiningpresentedinthispaperisappliedtotheabovethreetypes.Moreover,thekinematicstructuresinFigs2(a)to2(c),areselectedtodemon-stratethederivationprocedure.Inaddition,thetworotaryaxesareassumedtobecontinuouslyintersectedwitheachotherfortable-tiltingtypeandspindle-tiltingtypeofconfigurationstosimplifytheformulations.Generallyspeaking,tomachineaworkpieceonaCNCmachineaccordingtoapartprogram,acoordinatesystemandanaxisdesignationsystemmustfirstbeestablished.Inadditiontothreelinearperpendicularaxes(X,Y,Z),CNCmachinetoolsmayinvolverotarymotionaroundtherotationalaxes,whicharedesignatedbythecharactersA,B,andCtoindicatetherotarymotionsaroundtheX,Y,andZaxes,respectively.Therefore,thefive-axismachinetoolconfigurationinFigs2(a)to2(c)canbecharacterisedby(X,Y,Z,A,C)and(X,Y,Z,A,B).Allthemovementsshouldbereferredtotheprogramcoordinatesystem,e.g.theG54-G59codeisusedtodefinetheprogramcoordinatesystemintheFANUCcontroller.Inmostcases,theprogramcoordinatesystemiscoincidentwiththeworkpiececoordinatesystemandisthusappliedinthispaper.4.1Table-TiltingTypeRegardingthetable-tiltingtype,Fig,3depictsrelevantcoordi-natesytems.CoordinatesystemsOwXwYwZwandOtXtY,Z,areattachedtotheworkpieceandthecuttingtool,repsectively.DevelopingaPostprocessorforFive-AxisMachine7bols661CuttingtooltOtiZwWorkpieceAOffsetvector-/L°:se.v:；:Lzkq,pivotont,Fig.3.Coordinatesystemsoftable-tiltingtypeconfiguration.ThepivotpointRistheintersectionofthetworotaryaxes.TheoffsetvectorLxi+Lj+LkasdeterminedfromoriginOwtopointRisrequiredforthecoordinatetransformation.Sincethestructuralelementsofthemachinetoolconsistofarotarytable,lineartable,machinebed,spindleandthecuttingtool,thegeneratingmotionofthemachinetool,whichdeterminesthedesignedcharacteristicsformachinetoolandisreferredtoastheform-shapingfunction14,canbecharacterisedsequen-tiallystartingfromtheworkpieceandendingatthecuttingtool.ForthemachinetoolconfigurationshowninFig.2(a),theconsecutivestructuralelementscanbedescribedaccordingtoFig.4.Consequently,therelativeorientationandpositionofthecuttingtoolwithrespecttotheworkpiececoordinatesystemcanbedeterminedbymultiplyingthecorrespondingfundamen-taltransformationmatricesinseries,andshouldbeequaltotheknownCLdata,KKyKz0TandQxQyQz1T,respect-ively.Themathematicalexpressionisdescribedasfollows:K:KyKz0T=Trans(Lx,Ly,Lz)Rot(Z,-+c)Rot(X,-(A)Trans(P,p.,P)o01oT(5)QxQyQz1T=Trans(Lx,Le,L0Rot(Z,-+c)Rot(X,-+A)Trans(P,P)0001T(6)wheredpaand4caretherotationanglesabouttheX,andZaxes,respectively,andpositiverotationisinthedirectiontoadvancearight-handscrewinthe+Xand+Zaxisdirections.P,Py,ParetherelativetranslationdistancesoftheX,Y,andZtables,respectively.Multiplyingequations(5)and(6),yields:StructuralelementsWorkpieceIPrimaryrotationonfixturetable(C-axis)IISecondaryrotationonfixturetable(A-axis)XtableZtableIIMachinebedIIIIoogtooIFig.4.Relationshipofstructuralelementsoftable-tiltingtypecon-figuration.ixILxexClcl-PyC(t)AS(bcqyezS+AS(c-ilLz-PySqb；+PzCd)A=ILy-Pxsqbc+PrcqbACqbc+PzSSAC+c(8)Fromtheaboveequations,therotationangles(+a,+c)andtherelativetranslationdistances(Px,Py,Pz)canbesolved.Ontheotherhand,theX,Y,ZvaluesoftheNCdatainprogram-mingareobtainedusingequation(6)underthecondition+A=qbc=0,andQxQyQz1T=XYZ1Tsincetheprogramcoordinatesystemiscoincidentwiththeworkpiececoordinatesystem.Thisleadsto:XYZlT=Lx+P,LA-PyLz+P1T(9)Thus,thedesiredequationsforNCdataofthisconfigurationcanbeexpressedasfollows:a=(ba=arccos(Ks)(0-<qbA-<70(10)C=6c=arctan2(Kx,Ky)(-w<-qbc<-r)(11)X=Lx+P.=(Qx-L.)Cqbc-(Qy-Ly)Sd)c+Lx(12)