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外文资料--A near-optimal part setup algorithm for 5-axis machining using a parallel.pdf

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外文资料--A near-optimal part setup algorithm for 5-axis machining using a parallel.pdf

DOI101007/S0017000318602ORIGINALARTICLEINTJADVMANUFTECHNOL200525130–139JSONGJMOUANEAROPTIMALPARTSETUPALGORITHMFOR5AXISMACHININGUSINGAPARALLELKINEMATICMACHINERECEIVED19FEBRUARY2003/ACCEPTED4JULY2003/PUBLISHEDONLINE28JULY2004SPRINGERVERLAGLONDONLIMITED2004ABSTRACTANEAROPTIMALPARTSETUPMODELNOPSMISDEVELOPEDTHEPURPOSEOFTHISMODELISTOFINDTHENEAROPTIMALPARTSETUPPOSITIONANDORIENTATIONBASEDONTHEWORKSPACE,STIFFNESSANDACCURACYCAPABILITYOFAPARALLELKINEMATICMACHINETHATCANBEUSEDFOR5AXISMACHININGTOBUILDTHEPROPOSEDNOPSM,THEKNOWLEDGEONTHEHEXAPODKINEMATICS,WORKSPACE,STIFFNESS,STRUCTURALIMPERFECTION,NONUNIFORMTHERMALGRADIENTANDACCURACYISREQUIREDTHUS,ITISACOMPREHENSIVEPERFORMANCECAPABILITYSTUDYFORAPARALLELKINEMATICMACHINETHEPROPOSEDMODELISASOFTWARESOLUTIONCONCEPTTOIMPROVETHEMACHINE’SPERFORMANCEITISVERYCOSTEFFECTIVEANDCANALSOBEMODIFIEDFOROTHER5AXISMACHINETOOLAPPLICATIONSKEYWORDS5AXISMACHININGPARALLELKINEMATICPARTSETUPPERFORMANCEENHANCEMENT1INTRODUCTIONMANYCAD/CAMALGORITHMSCANSIMULATETHEMACHININGPROCESSFORSLANTEDANDFREEFORMSURFACESASWELLASGENERATETHECORRESPONDINGNCCODES;HOWEVER,THETRADITIONALTHREEDEGREEOFFREEDOMCNCMACHINERESTRICTSTHEPOTENCYOFTHESEALGORITHMSONEOFTHEADVANTAGESOFPARALLELKINEMATICHEXAPODMACHINEOVERTHETRADITIONAL3AXISMACHINECENTREISITSDEXTERITYANDFLEXIBILITY1–7THEORETICALLY,THEHEXAPODMACHINEUNDERSTUDYPOSSESSESSIXDEGREESOFFREEDOMACTUALLY,THEPLATFORMORIENTATIONAROUNDTHEZAXISCOINCIDESWITHTHEMACHINESPINDLEROTATION;THUS,THISHEXAPODMACHINEHASFIVEEFFECTIVEDEGREESOFFREEDOMFORMACHININGMANYPARTSTHATHAVESLANTEDORFREEFORMSURFACESCANBEGENERATEDONAHEXAPODMACHINEWITHONESETUPANOTHERADVANTAGEOFTHEHEXAPODMACHINEISITSHIGHERSTIFFNESSCOMPAREDTOTHESERIALLINKEDSTRUCTURALMAJSONGJMOUA117DEPARTMENTOFINDUSTRIALENGINEERING,ARIZONASTATEUNIVERSITY,TEMPE,AZ852875906,USAEMAILJIMOUTSMCCOMCHINESOTHATTHEHIGHSPEEDOPERATIONCANBECARRIEDOUTONTHISMACHINE8,9HOWEVER,ADRAWBACKTHATCOMESWITHTHEDEXTERITYOFTHEHEXAPODMACHINEISITSRELATIVELYSMALLWORKSPACELIKEALLMANUFACTURINGEQUIPMENT,IMPERFECTSTRUCTUREANDNONUNIFORMTHERMALGRADIENTRELATEDERRORSALWAYSEXISTTODEGRADETHEMACHINE’SPERFORMANCEINPRODUCINGQUALITYPRODUCTS10–14DUETOTHEUNIQUECHARACTERISTICSOFPARALLELKINEMATICSTRUCTURES,THEMACHINEINACCURACYDISTRIBUTIONWITHINITSWORKSPACEWILLCHANGEASTHEPLATFORMPOSITIONANDORIENTATIONCHANGEMEANWHILE,ITSSTRUCTURALSTIFFNESSVARIESATDIFFERENTPLATFORMPOSITIONSANDORIENTATIONSTHEREFORE,BASEDONTHEINFORMATIONONTHEHEXAPOD’SNOMINALKINEMATICSTRUCTURE,STRUCTURALERRORS,THERMALERRORS,ANDWORKSPACEANDSTIFFNESSANALYSES,ANEAROPTIMALPARTSETUPMODELNOPSMCOULDBEDEVELOPEDTOSUBOPTIMALLYSETUPAPARTWITHINTHEWORKSPACEOFAHEXAPODMACHINETHECONCEPTOFTHISALGORITHMISGENERICANDCANBEEASILYINTEGRATEDWITHEXISTINGKINEMATICANDTHERMALMODELSOFANYOTHERPARALLELKINEMATICMACHINESWITHSIMPLEMODIFICATIONSTHISAPPROACHCOULDALSOBEEMPLOYEDINTHEAPPLICATIONOFSERIALLYLINKEDROBOTSANDMACHINETOOLSFORNOPSM,THEFIRSTCONSTRAINTISTHATALLSURFACESTOBEMACHINEDNEEDTOBELOCATEDWITHINTHEHEXAPOD’SWORKSPACEONCETHEWORKSPACECONDITIONISSATISFIED,THENEXTCRITERIONAPPLIEDTOFINDTHENEAROPTIMALPARTSETUPISTHEHEXAPODMACHINE’SSTIFFNESSANALYSISTOGENERATEHIGHQUALITYPRODUCT,THEPARTNEEDSTOBEPLACEDATTHEMOSTDESIRABLEPOSITIONSOTHATTHEMACHINECANPOSSESSTHEHIGHESTSTIFFNESSANDACCURACYWHILEGENERATINGTHEPARTTHEALGORITHMSDERIVEDIN15TOFINDTHERELATIONSHIPBETWEENTHEMACHINE’SSTRUCTURAL/THERMALERRORSANDITSACCURACYDISTRIBUTIONBASEDONTHEMACHINE’SSTRUCTURALCHARACTERISTICSANDMACHINE’STEMPERATUREGRADIENTPROFILESAREADOPTEDFORSEARCHINGTHENEAROPTIMALPARTPOSITIONINGANDORIENTATIONINPRACTICE,THEHEXAPODMACHINE’SDYNAMICSANDCONTROLSYSTEMSHOULDALSOBECONSIDEREDFORNEAROPTIMALPARTPOSITIONINGSEARCHESHOWEVER,DUETOTHEPROBLEM’SCOMPLEXITYANDTOLIMITATIONSONTHESCOPEOFTHISRESEARCH,WEWILLNOTDISCUSSTHOSETOPICSHERE1312WORKSPACEANALYSISTHEWORKSPACEISTHEWORKINGVOLUMEOFAMACHINEWITHSPECIFICTOOLSANDFEASIBLESPINDLEPOSITIONANDORIENTATIONINORDERTODETERMINETHEUSABLEWORKSPACEOFTHEHEXAPODMACHINE,ADERIVEDKINEMATICMODEL15CANBEAPPLIEDTODETERMINETHESTRUTLENGTH,THEJOINTROTATIONANGLEANDMOBILEPLATFORMPOSITIONANDORIENTATIONTWOCONSTRAINTSARETAKENINTOACCOUNTINTHISWORKSPACEANALYSISFIRST,THEMACHINE’SSTRUTLENGTHLIMITATIONSMAXIMUMLENGTHDEFINETHELOWERBOUNDOFTHEWORKSPACEFIG1HEXAPODMACHINEWORKSPACEANALYSISFLOWCHARTSECOND,THEMACHINE’SSPHERICALJOINTROTATIONALLIMITATIONSDEFINETHEUPPERBOUNDOFTHEWORKSPACEALTHOUGHTHEMACHINE’SMINIMUMSTRUTLENGTHLIMITATIONSHOULDALSOBETAKENINTOCONSIDERATION,THISCONSTRAINTISOVERRIDDENBYTHESPHERICALJOINTROTATIONALLIMITATIONINDETERMININGTHEMACHINE’SUPPERWORKSPACEANALGORITHMFORTHEDETERMINATIONOFHEXAPODWORKSPACEFORASPECIFICPLATFORMORIENTATIONISSHOWNINFIG1DIFFERENTPLATFORMORIENTATIONSHAVEDIVERSEMACHINEWORKSPACEENVELOPESBYUPDATINGTHEORIENTATIONINFORMATION,THEWORKSPACEENVELOPFORDIFFERENTMACHINEPLATFORMORIENTATIONSCANBEDETERMINEDINFIGS2AND3,THEORIENTATIONSAROUNDTHE132FIG2WORKSPACEENVELOPEWITHSPINDLEORIENTATIONANGLE0˚0˚0˚FIG3WORKSPACEENVELOPEWITHSPINDLEORIENTATIONANGLE−30˚0˚0˚YANDZAXESS,ΒANDΓ,AREKEPTCONSTANT;ONLYTHEORIENTATIONANGLEAROUNDTHEXAXIS,Α,ISCHANGEDASTHEORIENTATIONANGLEAROUNDTHEXAXISINCREASES,THEWORKSPACEISTILTEDANDTHEZDIMENSIONOFTHEWORKSPACEENVELOPEISDECREASEDTHELARGERTHEORIENTATIONANGLE,THEMORESEVERETHEWORKSPACETILTINGTHEWORKSPACEANALYSISRESULTSSHOWTHATASIMILARPHENOMENONOCCURSWHENTHEORIENTATIONANGLEAROUNDTHEYAXIS,Β,ISCHANGED,BUTWITHDIFFERENTTILTINGDIRECTIONSINCETHEPLATFORMORIENTATIONANGLEAROUNDTHEZAXIS,Γ,COINCIDESWITHTHESPINDLEROTATINGDIRECTION,THEEFFECTOFΓISSUPERIMPOSEDONSPINDLEROTATIONANDTHUSNOTTAKENINTOCONSIDERATIONINWORKSPACEENVELOPEANALYSISTHENOPSMADOPTSTHEWORKSPACEANALYSISTODETERMINEWHETHERORNOTTHEMACHININGSURFACESAREWITHINTHEHEXAPODWORKSPACETOENSURETHEEFFICIENCYOFTHEALGORITHM,THEFOLLOWINGTWOCONSTRAINTSARETESTEDFORALLTHESELECTEDPOINTSONTHESURFACETOBEMACHINED1THEHEXAPODMAXIMUMSTRUTLENGTHCONSTRAINT2THEHEXAPODMAXIMUMJOINTANGLEROTATIONCONSTRAINTIFALLTHESELECTEDPOINTSONTHEMACHININGSURFACESSATISFYTHEABOVETWOCONSTRAINTS,STRUCTURALSTIFFNESSANDMACHINEACCURACYWILLTHENBEANALYSEDTOIDENTIFYTHENEAROPTIMALPARTSETUPLOCATIONANDORIENTATION3STIFFNESSANALYSISFORAPARALLELMECHANISM,THEREUSUALLYISACLOSEDFORMSOLUTIONFORTHEINVERSEKINEMATICSTHEINVERSEKINEMATICSFORTHEHEXAPODMACHINECOULDBEUSEDTOCALCULATETHESIXSTRUTLENGTHBASEDONTHEPLATFORMPOSITIONANDORIENTATIONINFORMATION16THISCANBEEXPRESSEDASFOLLOWSLIFIX,Y,Z,Α,Β,Γ1THEAPPLICATIONOFTHECHAINRULEYIELDSDIFFERENTIALSOFLII1,2,,6ASFUNCTIONSOFTHEDIFFERENTIALSOFX,Y,Z,Α,Β,ΓΔLI∂FI∂XΔX∂FI∂YΔY∂FI∂ZΔZ∂FI∂ΑΔΑ∂FI∂ΒΔΒ∂FI∂ΓΔΓ2DIVIDINGBOTHSIDESOFEQ1BYTHEDIFFERENTIALTIMEELEMENTΔTANDEXPRESSINGITINMATRIXFORMATYIELDS˙L1˙L2˙L3˙L4˙L5˙L6∂F1∂X∂F1∂Y∂F1∂Z∂F1∂Α∂F1∂Β∂F1∂Γ∂F2∂X∂F2∂Y∂F2∂Z∂F2∂Α∂F2∂Β∂F2∂Γ∂F6∂X∂F6∂Y∂F6∂Z∂F6∂Α∂F6∂Β∂F6∂Γ˙X˙Y˙Z˙Α˙Β˙Γ3NOTETHESTANDARDJOCOBIANEXPRESSION,˙VJ˙LBYLETTING˙LJ−1˙V,THEINVERSEJOCOBIANMATRIX,J−1,FACILITATESTHEMAPPINGOFTHECARTESIANSPACEVELOCITYVECTORVINTOTHESTRUTDISPLACEMENTRATEVECTORAPPLYINGTHEPRINCIPLEOFVIRTUALWORKTOANARBITRARYMECHANISMALLOWSONETOEQUATEWORKDONEINCARTESIANSPACETERMSTOWORKDONEINCONFIGURATIONSPACETERMSSPECIFICALLY,WORKINCARTESIANTERMSISASSOCIATEDWITHACARTESIANFORCE/TORQUEVECTOR,F,APPLIEDATAMECHANISM’STOOLFRAMEANDACTINGTHROUGHANINFINITESIMALCARTESIANDISPLACEMENT,ΔVWORKINCONFIGURATIONSPACETERMSISASSOCIATEDWITHACONFIGURATIONSPACEFORCE/TORQUEVECTOR,F,APPLIEDATAMECHANISM’SJOINTSANDACTINGTHROUGHINFINITESIMALJOINTDISPLACEMENTS,ΔLTHESTIFFNESSOFTHEHEXAPODCANBEDETERMINEDUSINGMATRIXSTRUCTURALANALYSIS,WHERETHESTRUCTUREISCONSIDEREDTOBEACOMBINATIONOFELEMENTSANDNODESTHEDERIVATIONOFTHEHEXAPODSTIFFNESSMODELISBASEDONTHEFOLLOWINGASSUMPTIONS1THEONLYDEFORMATIONOFTHELINKSISINTHEAXIALDIRECTION2THEREISNOBENDINGORTWISTINGOFTHELINKS3THEREISNODEFORMATIONOFTHEJOINTSWORKISCALCULATEDASTHEDOTPRODUCTOFAFORCE/TORQUEVECTORWITHADISPLACEMENTVECTOR,FTΔVFTΔL,WHEREFTF1,F2,F3,F4,F5,F6ARETHEFORCESEXERTEDONEACHOFTHESIX133STRUTSANDFTFX,FY,FZ,MX,MY,MZARETHEFORCESANDMOMENTSACTINGATTHECENTREOFGRAVITYOFTHEPLATFORMNOTETHATΔVJΔL,SOFTJΔLFTΔL⇒FTJFTTRANSFORMINGBOTHSIDESOFTHEEQUATIONYIELDSFTJTF⇒FJTFONECOULDCONCLUDETHAT‘ACTUATING’AMECHANISMWITHAFORCE/TORQUEVECTOR,F,APPLIEDATTHETOOLISEQUIVALENTTOACTUATINGTHATMECHANISMWITHAFORCE/TORQUEVECTOR,F,APPLIEDATTHEJOINTS,WHENTHESAMEAMOUNTOFVIRTUALWORKISDONEINEITHERCASETHERELATIONSHIPBETWEENANAPPLIEDFORCEFATTHETOOLANDTHERESULTINGAXIALFORCESINTHESTRUTFCANBEDEFINEDASFJ−TFGIVENPUREAXIALLOADING,ΕΔLI/LIΣ/EFI/AE⇒FIAE/LIΔLI,WHEREEISTHEELASTICMODULUSOFTHESTRUTMATERIALANDAISTHECROSSSECTIONALAREAOFTHESTRUTINMATRIXFORMAT,FAE/L1000000AE/L2000000AE/L3000000AE/L4000000AE/L5000000AE/L6ΔL4ORFKSΔL,WHERETHEMATRIXISIDENTICALTOTHESTRUTSPACESTIFFNESSMATRIX,KSNOTETHATΔLJ−1ΔV,SOFKSJ−1ΔVANDFJ−TKSJ−1ΔVLETKCJ−TKSJ−1;THENFKCΔV,WHEREKCISTHECARTESIANSPACESTIFFNESSMATRIXBYSETTINGUPANEIGENVALUEPROBLEM,THEPRINCIPLESTIFFNESSAXES,ΗI,ANDPRINCIPLESTIFFNESS,ΚI,CANBEFOUNDASFOLLOWSFKCΔVΚIΔV5KC−ΚII6ΔV06|KC−ΚII6|07HERE,ΗIISINTHEDIRECTIONOFΔVWHERETHEABOVECONDITIONHOLDSTHEPRINCIPLESTIFFNESSΚIWILLCHANGEASPLATFORMORIENTATIONANDPOSITIONCHANGETHEHIGHERTHEMACHINE’SSTRUCTURALSTIFFNESS,THEBETTERTHEPART’SQUALITYANDACCURACY4STRUCTURALERRORDETECTIONMODELASMENTIONEDEARLIER,THEHEXAPODMACHINESTRUCTUREISNOTPERFECT,ANDSTRUCTURALIMPERFECTIONANDASSEMBLYERRORSEXISTTHESTRUCTURALANDASSEMBLYERRORSARENOTDISTRIBUTEDEVENLYAMONGTHEHEXAPODJOINTSANDSTRUTSTHISUNEVENNESSCAUSESDIVERSEACCURACYLEVELSATDIFFERENTPLATFORMPOSITIONSANDORIENTATIONSAFTERAMACHINEISASSEMBLED,ITISDIFFICULTTOMEASURETHEMACHINESTRUCTURALANDASSEMBLYERRORBYUSINGINSTRUMENTSORSENSORSDIRECTLYHOWEVER,THEMACHINEPLATFORM’SORIENTATIONANDPOSITIONCANBEPRECISELYMEASUREDBYUSINGANEXTERNALINSTRUMENTSUCHASA5DLASERINTERFEROMETERSYSTEMORALASERTRACKERSYSTEMAMODELISTHENNEEDEDTOREVERSEIDENTIFYTHEMACHINESTRUCTURALERRORSBASEDONTHEMEASUREDPLATFORMPOSITIONANDORIENTATIONERRORSTHEHEXAPODNOMINALINVERSEKINEMATICSISDERIVEDAS15ΛTMLMTPTRPPBN−TSM;M1,2,,6;NINTM1/28DIFFERENTIATINGTHEEQUATION,SINCEALLTHEVECTORSAREWITHRESPECTTOTHETABLECOORDINATESYSTEM,THESUPERSCRIPTOFTCANBEOMITTEDΔΛMLMΛMΔLMΔPΔRPPBNRPPΔBN−ΔM9TOSIMPLIFYTHECALCULATION,THEROTATIONERRORMATRIXCANBEWRITTENASΔRPΔ˜ΩRP,WHEREΔΩΔΑ,ΔΒ,ΔΓTISTHEORIENTATIONERRORVECTOR,RPISTHENOMINALORIENTATIONMATRIX,ANDΔ˜ΩISDEFINEDASΔ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