数学方法来分析和优化设计的夹具定位方案

DOI10.1007/s00170-005-2509-0ORIGINALARTICLEIntJAdvManufTechnol(2006)29:349–359G.H.Qin·W.H.Zhang·M.WanAmathematicalapproachtoanalysisandoptimaldesignofafixturelocatingschemeReceived:23June2004/Accepted:3December2004/Publishedonline:23November2005©Springer-VerlagLondonLimited2005AbstractInmanufacturingengineering,localizationaccuracyisakeyconcerninthedesignofafixturetospecifyalocatingschemeandtoleranceallocation.Thispaperpresentsageneralanalysismethodologythatisabletocharacterizetheeffectsoflo-calizationsourceerrorsbasedonthepositionandorientationoftheworkpiece.Fromthismethodology,afixturemodelisformu-latedbytakingintoaccounttheoverallerrorsamongthesystemconsistingoftheworkpieceandthefixtureinthedesignofthefixturelocatingscheme.Withthismodel,thelocatingprincipleandacriterionoftherobustoptimaldesignarethenproposedtoimprovethelocalizationqualityofthefixture.Someexam-plesareprovidedandallowforadetaileddiscussionabouthowtocarryouttheoptimaldesignofthelocatingscheme.Acom-parativestudyisalsomadebetweentheoptimalsolutionandtheempiricalone.Finally,anexperimentismadetovalidatethefix-turelocatingschemeforacylindricalworkpiece.Weconcludethatthisrobustdesignmethodeffectivelyachievesstablema-chiningprecisioninworkpieces.KeywordsLocatingprinciple·Locatingscheme·Localizationsourceerror·Optimaldesign·Workpiecepositionerror1IntroductionTraditionally,fixturedesignhasbeenperformedmanually.Afterexhaustivestudyandpractice,expertsandskilledworkersac-cumulatedasignificantamountofexperienceinfixturedesign,G.H.Qin·W.H.Zhang(
)·M.WanSino-FrenchLaboratoryofConcurrentEngineering,DepartmentofAircraftManufacturingEngineering,NorthwesternPolytechnicalUniversity,P.O.Box552,710072Xi’an,Shannxi,ChinaE-mail:[e-mail].:[phone]Fax:[phone]G.H.QinDepartmentofMechanicalEngineering,NanchangInstituteofAeronauticalTechnology,P.O.Box61,330034Nanchang,Jiangxi,Chinaandestablishedsomeempiricalprinciples[1].Adrawingoffix-turedesignisoftenpreparedbasedontheoperationplanandworkpieceinformation.Sincethe1980’s,computeraidedfixturedesign(CAFD)techniqueshavebeenextensivelydeveloped.Theperiodoffixturedesignisshortenedandsomeburdensometaskssuchasconsultinghandbooksofjigandfixturedesign,drawingallassemblyviewsandcompilingatechnicaldocumentationbe-comegreatlysimplified[2].Moreover,thequalityandefficiencyoffixturedesignareimprovedtoacertainextent.However,thefixturespecificationformachiningisstronglydependentuponthedesigner’sexperienceandknowledge;assuch,optimumso-lutionoffixturedesignisgenerallydifficulttoobtain[3].Forthisreason,considerableresearchefforthasbeenmadeinthisfield.Severalmethodsexistforfixtureanalysisanddesign.Chouetal.[4]usedthescrewtheorytoinvestigatethefixturedesignconcerningdeterministiclocating,selectionofclampingpointsfromasetofinitialpoints,stableclampingandtotalre-straint.AsadaandBy[5]firstdevelopedakinematicmodelthatcanbeusedtoanalyzethefixturelayout,deterministiclocating,accessibilityanddetachability,bilateralrestrainingandtotalre-straint.AsimilarstudywasconductedbyHong[6].Caietal.[7]investigatedfixturedesignqualityusingavariationalmethod.Thefixturemodelisformulatedwiththeworkpiecepositionerrorresultingfromworkpiecesurfaceerrorandlocatorsetuperror.Basedonsuchamodel,thelayoutofcontactpointswasopti-mized.Wang[8–10]attemptedtominimizetheworkpiecepos-itionerrorbymeansofsequentialoptimizationtechniques.Here,itwasassumedtheworkpiecepositionerrorwasmainlyinducedbytheinappropriatepositioningandperturbedshapesofthelo-cator,andthegeometricvariationoftheworkpiece.Todeterminelocatorsandclamps,sixcontactpointsandoneormoreclamp-ingpointsareselectedfromasetofcandidatepointsdiscretizingthe3-Dworkpiecesurface.Kang[11,12]consideredthecaseofalocatingfromaflatsurfacetomodelthegeometricrelationbe-tweenworkpiecedisplacementandlocatordisplacement.Itwasassumedtheworkpiecepositionerrorresultedfrommanufactur-ingandsetuperrorsoflocators.Thelocatorlayoutisfinallyob-tainedbyoptimizingauser-definedlocatingperformanceindex.Inadditiontothis,Menassa,KashyapandDeVries[13,14]used350thefiniteelementanalysis(FEA)methodtodeterminepositionsofthefixturesupportingpointsinordertominimizenormaldefor-mationsoftheworkpieceattheprimarylocatingsurface.However,alloftheaboveworksweremainlyrestrictedtothelayoutdesignofcontactpoints.Thedesignoflocators’dimen-sionsandlocationsarenotsimultaneouslyinvolvedinthemodel.AlthoughGuoetal.[15]presentedbasicconceptsofthero-bustnessoffixturepositioningschemestostudytheinfluenceoflocators’dimensions,rulefunctionandrestraintconditions,therelationshipbetweenthelocalizationerroranditscauseswasstillunderdevelopedandthusneedstobeprofoundlyinvestigated.Inthispaper,asyntheticanalysisismadetoinvestigatetheworkpiecepositionerrorinfixturelocatingschemes.Ageneralformulationoffixturemodelingisproposedtoestablishthere-lationshipbetweentheworkpiecepositionerroranditssourceerrors.First,mathematicalformulationsofalocatingprincipleareestablishedsystemically,andsixcriteriaareproposedquanti-tativelyforthevalidationoffixturedesign.Second,animprovedrobustdesignmethodisdevelopedtoperfo