外文翻译在独自领域最佳多功能夹具布置的设计.docx

外文翻译在独自领域最佳多功能夹具布置的设计.docx

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外文翻译在独自领域最佳多功能夹具布置的设计

外文翻译

专业机械设计制造及其自动化

学生姓名

班级

学号

指导教师

MULTI-OBJECTIVEOPTIMALFIXTURELAYOUT

DESIGNINADISCRETEDOMAIN

DianaPelinescuandMichaelYuWang

DepartmentofMechanicalEngineering

UniversityofMaryland

CollegePark,MD20742USA

E-mail:

yuwang@eng.umd.edu

Abstract

Thispaperaddressesamajorissueinfixturelayoutdesign:

toevaluatetheacceptablefixturedesignsbasedonseveralqualitycriteriaandtoselectanoptimalfixtureappropriatewithpracticaldemands.Theperformanceobjectivesconsideredarerelatedtothefundamentalrequirementsofkinematiclocalizationandtotalfixturing（form-closure）andaredefinedastheworkpiecelocalizationaccuracyandthenormanddistributionofthelocatorcontactforces.Anefficientinterchangealgorithmisuaedinamultiple-criteriaoptimizationprocessfordifferentpracticalcases,leadingtopropertrade-offstrategiesforperformingfixturesynthesis.

I.INTRODUCTION

Properfixturedesigniscrucialtoproductqualityintermsofprecisionandaccuracyinpartfabricationandassembly.Fixturingsystems,usuallyconsistingofclampsandlocators,mustbecapabletoassurecertainqualityperformances,besidesofpositioningandholdingtheworkpiecethroughoutallthemachiningoperations.Althoughthereareafewdesignguidelinessuchas3-2-1rule,automatedsystemsfordesigningfixturesbasedonCADmodelshavebeenslowtoevolve.

Thisarticledescribesaresearchapproachtoautomateddesignofaclassoffixturesfor3Dworkpieces.Thepartsconsideredtobefixturedpresentanarbitrarycomplexgeometry,andthedesignedfixturesarelimitedtotheminimumnumberofelementsrequired,i.e.sixlocatorsandaclamp.Furthermore,thefixelsaremodeledasnon-frictionalpointcontactsandarerestrictedtobeappliedwithinagivencollectionofdiscretecandidatelocations.Ingeneral,thesetoffixturelocationsavailableisassumedtobeapotentiallyverylargecollection;forexample,thelocationsmightbegeneratedbydiscretizing

theexteriorsurfacesoftheworkpiece.Thegoalofthefixturedesignistodeterminefirst,fromtheproposeddiscretedomain,thefeasiblefixtureconfigurationsthatsatisfytheform-closureconstraint.Secondly,thesetsofacceptablefixturedesignsareevaluatedonseveralcriteriaandoptimalfixturesareselected.Theperformancemeasuresconsideredinthisworkarethelocalizationaccuracy,andthenormanddistributionofthelocatorcontactforces.Theseobjectivescoverthemostcriticalerrorsourcesencounteredinafixturedesign,thepositionerrorsandtheunwantedstressinthepart-fixtureelementsduetoanoverloadedorunbalancedforcesystem.

Theoptimalfixturedesignapproachisbasedonaconceptofoptimumexperimentdesign.Thealgorithmdevelopedevaluatesefficientlytheadmissibledesignsexploitingtherecursivepropertiesinlocalizationandforceanalysis.Thealgorithmproducestheoptimalfixturedesignthatmeetsasetofmultipleperformancerequirements.

II.RELATEDWORK

Literatureongeneralfixturingtechniquesissubstantial,e.g.,[1].Theessentialrequirementoffixturingisthecentury-oldconceptofformclosure[2],whichhasbeen

extensivelystudiedinthefieldofroboticsinrecentyears[3,4].Thereareseveralformalmethodsforanalyzingperformanceofagivenfixturebasedonthepopularscrewtheory,dealingwithissuessuchaskinematicclosure[5],contacttypesandfrictioneffects[6].Adifferentanalysisapproachbasedonthegeometricperturbationtechniquewasreportedin[7].Anautomaticmodularfixturedesignprocedurebasedonthismethodwasdevelopedin[8]toincludegeometricaccessconstraintsinadditiontokinematicclosure.Theproblemofdesigningmodularfixturesgainedmoreattentionlately[9].Therehasalsobeenextensiveresearchinfixturedesigns,focusingonworkpieceandfixturestructural

rigidity[6],toolaccessibilityandpathclearance[7].Theproblemoffixturesynthesishasbeenlargelystudiedforthecaseofafixednumberoffixtureelements（orfixels）[8,10],particularlyintheapplicationtoroboticmanipulationandgraspingforitsobviouseasons[3,4].Thisarticleaimstobeanextensionoftheresultsonthefixturedesignissuespreviouslyreportedin[14].

III.FIXTUREMODEL

Thefundamentalperformanceofafixtureischaracterizedbythekinematicconstraintsimposedontheworkpiecebeingheldbythefixture.Thekinematicconditionsarewellunderstood[3,4,5,7,12].Forafixtureofnlocators（i=1,2,…,n）,thefixturecanberepresentedby:

y=GTq

where

definesmallperturbationsinthelocatorpositionsandthelocationoftheworkpiecerespectively.Thefixturedesign

isdefinedbythelocatormatrixi

where

andniandridenotethesurfacenormalandpositionattheithcontactpointontheworkpiecesurface.Theproblemoffixturedesignrequiresthesynthesisofafixturingschemetomeetagivensetofperformancerequirements.

IV.QUALITYPERFORMANCECRITERIAFORAFIXTURE

A.AccurateLocalization

Anessentialaspectoffixturequalityistopositionwithprecisiontheworkpieceintothefixturingsystem.Ingeneraltheworkpiecepositionalerrorsareduetothegeometricvariabilityofthepartandthelocatorsset-uperrors.Thispaperwillfocusonlyontheworkpiecepositionalerrorsduetothelocatorpositioningerrors.Asanextensionofthefixturemodelequation（eq.1）,thelocatorpositioningerrorsycanberelatedwiththeworkpiecelocalizationerrorqasfollows:

Clearly,forgivensourceerrorstheworkpiecepositionalaccuracydependsonlyonthelocatorlocationsbeingindependentfromtheclampingsystem,theFisherinformationmatrixM=GGTcharacterizingcompletelythesystemerrors.Ithasbeenshown[12]thatasuitablecriteriontoachievehighlocalizationaccuracyistomaximizethedeterminantoftheinformationmatrix（Doptimality）,i.e.,max（detM）.

B.MinimalLocatorContactForces

Anotherobjectiveinplanningafixturelayoutmightbetominimizeallsupportforcesatthelocatorcontactregionsthroughoutalltheoperationswithcompletekinematicrestraintorforce-closure.Locatorcontactforcesinresponsetotheclampingactionaregivenas:

Normalizingtheseforceswithrespecttotheclampingintensityweobtain:

Theforce-closureconditionrequirestheseforcestobealwayspositiveforeachlocatoriofasetofnlocators:

Computingthenormofthelocatorcontactforces:

leadstoanappropriatedesignobjective,i.e.min

Notethatthisobjectiveindicatesbothlocatorandclamppositionstobedeterminedintheoptimizationprocess.

C.BalancedLocatorContactForces

Anothersignificantissueindesigningafixtureisthatthetotalforceactingontheworkpiecehavetobedistributedasuniformlyaspossibleamongthelocatorcontact

regions.Ifprepresentsthemeanreactiveforceinresponsetotheclampaction,thenwedefinethedispersionofthelocatorcontactforcesas:

Therefore,minimizingthedefineddispersionrepresentsanobjectiveforabalancedforce-closure:

min（d）.

V.OPTIMALFIXTUREDESIGNWITHINTERCHANGEALGORITHMS

Asmentionedearlier,bygeneratingontheexteriorsurfaceoftheworkpiecetobefixturedasetofdiscretelocationsdefinedaspositionandorientation,wecreateapotentialcollectionforthefixtureelements.Forexample,usingtheinformationcontainedinthepartCADmodel,adiscretevectorcollection（unitary,normalvectors）canbegeneratedasuniformlyaspossibleonthosesurfacesaccessibletothefixturecomponents（fig.1）.

Figure1:

PartCADmodelandglobalcollectionofcandidatelocationsforthefixtureelements.

Thefixturedesignlayoutwillselectfromthiscollectionoptimalcandidatesforlocatorsandclampswithrespecttotheperformanceobjectivesandtothekinematicclosurecondition.Dealingwithalargenumberofcandidatelocationsthetaskofselectinganappropriatesetoffixelsisverycomplex.

Asalreadyintroducedin[12,14]aneffectivemethodforfindingthedesiredfixturewithregardtooneofthepreviousqualityobjectivesistheoptimalpursuitmethodwithaninterchangealgorithm.Duetoitsownlimitationsandtothefactthattheobjectivesarefunctionswithmanyextremes,theexchangeproceduremaynotenduptoauniqueoptimizedfixtureconfiguration,buttoseveralimproveddesignsdependingontheinitiallayout.Thereforethesolutionofferedbythemultipleinterchangewithrandominitializationalgorithmisoverwhelmingfavorable,factthatrecommendsthisprocedureoverthesingleinterchangealgorithms.Thealgorithmcanbedescribedasasequenceofthreephases:

Phase1:

Randomgenerationofinitialsetsoflocators.

Thestartinglayoutisgeneratedbyarandomselectionofdistinctsets,eachconsistingfrom6locatorsoutofthelistofNcandidatelocations.Iftheclampispre-determined,a

validselectionisobtainedthroughasimultaneouscheckforallkinematicconstraints.Abiginitialsetofproposedocatorsispreferred,givingtheopportunityoffindingaconvergentoptimalsolution.Howeverfromtheefficiencypointofviewthedesignerhastobalancethealgorithmbetweentheaccuracyofthefinalsolutionandthecomputationtime.

Phase2:

Improvementbyinterchange.

Theinterchangealgorithm'sgoalistopursueforanimprovementoftheinitialsetsoflocatorswithrespecttooneoftheobjectives.Basically,thisisdoneiterativelybyexchangingonebyonetheproposedlocatorswithcandidatelocationsfromtheglobalcollection.Itisalsoessentialtoconsidertheform-closurerestraintduringtheexchangeprocedure.Theprocesswillcontinueaslongasanimprovementoftheobjectivefunctionis