A computer aided tolerancing tool based on kinemat

AComputerAidedTolerancingToolbasedonKine-maticAnalogiesO.W.Salomons,H.J.JongePoerink,F.vanSlooten,F.J.A.M.vanHouten,H.J.J.KalsUniversityofTwente,DepartmentofMechanicalEngineering,LaboratoryofProductionandDesignEngineering,P.O.Box217,7500AEEnschede,TheNetherlands,phone:X–31–53–892532,fax:X–31–53–335612,e–mail:[e-mail]tolerancingtoolispresentedthatassiststhedesignerinfunctionaltolerancespecification.Thetheoreticalconceptsforsubsequenttoleranceanalysisarealsoprovided.Thecomputeraidedtolerancingtoolispartofafeaturebasedobjectoriented(re)–designsupportsys-tem,calledFROOM.FROOM’sassemblymodellingcapabilitiesprovidebasicinformationforfunctionaltolerancespecification.Assemblyconstraintsaresatisfiedbymeansofdegreesoffreedom(DOF)analysis.Thismethodisbasedontheuseofkinematicanalogies.Therotationsandtranslations(macro–DOF’s)thatcomponentsareallowedtohave,areinferredusingthistechnique.ThetolerancerepresentationinFROOMisbasedontheTTRSmethod,byClémentetal.,whichisalsobasedonkinematicanalogies.Inthismethod,thesmalldisplacementsthatareallowedinthetolerancezonecanbedescribedbyatolerancetorsorortransformationmatrix.Usingthetolerancetorsorortransformationmatrix,tolerancesaredescribedasconstraints.Thesmalldisplacementsthatarestillallowedbymeansofthetorsorarereferredtoasmicro–DOF’s.Fortoleranceanalysis,thetorsorapproachoffersamathematicallycorrectdescriptionoftoler-ancezones,althoughalotofequationsaregenerated.Thesearereducedbyapplyingakindofdegreesoffreedomanalysisconsideringboththemacro–DOF’sandthemicroDOF’s(toler-ances).Keywords:tolerancerepresentation,tolerancespecification,toleranceanalysis.1.IntroductionAnintroductionintosomedrawbacksofexistingtolerancingstandardsisprovidedinsection1.1.TheFROOMsystem,whosetolerancingmoduleisthefocusoftheremainderofthispaper,isintroducedinsection1.2.Section1.3providesanoverviewoftheremainderofthepaper.1.1SomedrawbacksofexistingtolerancingstandardsTherearesomeproblemsrelatedtopresenttolerancingstandards.Forinstance,thestandardsdonotprovideforatheoretictolerancingmodelthatisconsistentwithtoday’s3Dgeometrymodels(usuallysolidmodels).Thisisduetothefactthatwhentolerancingstandardsemerged,no3Dsolidmodelsexistedandalotoffreedomwaslefttothehumaninterpretationofthespecifiedtolerances.Therefore,tolerancingstandardsaredrawingoriented,givingrisetoambiguitieswhenhavingtobeprocessedbycomputer.Anotherdrawbackoftoday’stolerancingstandardsisthattheydonotprovideforamethodfortolerancespecification.Preferably,tolerancespecifi-cationshouldbeperformedusingafunctionalpointofviewinthefirstplace:functionaltoleranc-ing.Functionaltolerancingwillpreventredundantorunnecessarytolerancestobespecifiedandwillthereforesupportthedesignofmanufacturableproductsatreasonablecost.Thereasonthatthetolerancingstandardsdonotprovideforamethodforfunctionaltolerancingismainlyduetothestandardsbeingpartorientedandnotassemblyoriented.Itistheassemblywherefunctioningas-pectsare(oftenimplicitly)availableandnotintheindividualparts.Therefore,currenttoleranc-ingstandardscanbecomparedtoalanguagewithalargeandrichsyntaxbutwithnotenoughsemanticsandmethods,atleasttoperformcomputeraidedtolerancing.In[Ballu93a,b],[Kople-wicz93]and[Srinivasan93]moredetailedoverviewsareprovidedregardingtheinsufficienciesincurrenttolerancingstandardsaswellascurrenteffortstoovercomethese.1.2FROOMFROOMisaprototypeofare–designsupportsystem,currentlyunderdevelopment.Thedevel-opmentofFROOMhasbeenmotivatedbythefollowingfacts.First,forre–designtasksnopropercomputersupporttoolsareavailableyet.Second,CADtoolsthatintegratewellwithautomatedprocessplanning(CAPP)systemsareonlyscarcelyavailable.Ifavailable,theyaremostoftennotsuitableinpractice,especiallyinsituationswheredesignandmanufacturingareperformedindifferentcompanies.TheCAPPsystemthatisofparticularinteresttous,isthePARTsystem[Houten91],whichhasbeendevelopedintheauthors’laboratory.FROOMisanacronymforFeatureandRelationbasedObjectOrientedModelling.FROOMisafeaturebasedsystem,allowingthemodellingofbothcomponentsandassemblies.FeaturesintheFROOMcontextcanbedesignformfeatures,manufacturingformfeaturesandevenabstractfeatures.Forareviewoffeature–baseddesign,referto[Salomons93a].FROOMemploysconceptualgraphsforknowledgerepresentation.Theconceptualgraphsallowre–de-signsupporttobeprovidedandfacilitatethelinkwithCAPP[Salomons94a].Thelattersubjectwillnotbeaddressedinthispaper,however.Figure1showsFroom’ssystemarchitecture.End–userInterfaceKernelModellerTuningDatabaseSystemManagerUIInter–Assem–Con–Com–Map–Appli–facecationpingponentmodellingstraintmodel–lingblymodel–lingIODFigure1SystemarchitectureofFROOM;IODmeansinteractiveobjectdefinition.Thear-chitecturedoesnotincludefunctionalityforsupportingcollaborativeengineeringtasks.DatabaseInterfaceFigure1showsthattwodifferentkindsofusersaredistinguished:end–usersandsystemmanagerusers.End–usersarethedesignerswhodesignassemblies,componentsetc.;theyperformtheac-tualdesigntasks.Systemmanagerscustomizethesystemtoacertainapplicationdomain,compa-nyanduser(group).Theydefin