ThermalExpansionintoCAD-Based3-DimensionalAssemblyVariationAnalysis IncorporatingThermalExpansionIntoCAD-Based3-DimensionalVariationAnalysis Contents Abstract___________________________________________________________________________________________________
1Background_______________________________________________________________________________________________
1HowtoCreateanurateAssemblyVariationModel________________________________________________3Integration&CADFunctionality________________________________________________________________________5IncorporatingThermalExpansion______________________________________________________________________5Conclusion________________________________________________________________________________________________

6 IncorporatingThermalExpansionIntoCAD-Based3-DimensionalVariationAnalysis Abstract Properintegrationofthirdparty,add-onsoftwaresolutionsbringsgreatpowerandspeedtoproductdevelopment.ThesoftwarearchitecturebehindCETOL6σToleranceAnalysisSoftwareprovidesanefficientprocesstoanalyzeassemblybehavioratanyoperatingtemperatureincludingassemblieswithdiversematerialproperties.ThispaperdescribestheintegrationofCETOL6σtechnologywithCADtechnology,howtocreateanurateassemblyvariationmodel,andhowtointroducethermalexpansionintotheCAD/CETOL6σsysteminordertoanalyzethefitandfunctionofassembliesoperatingatanyfeasibleoperatingtemperature. Background Forpanies,assemblyvariationanalysisisdoneutilizingsimplifyingassumptionsinordertoeasilycreatecalculationsinspreadsheets.plexassembliesusinga1dimensional,“stack-up”approachrequirestheusertoignore2Dand3Daffectsthatwouldotherwiseintroduceleverageintothedesign.Thisleverage,alsoknownassensitivity,cansignificantlyalterthelocationofpartswithrespecttoeachotherresultinginreducedfunctionalityandimpactingtheabilitytoassembletheproduct. Insteadofignoringthe2D&3Dbehaviors,spreadsheetscanbeprogrammedtoprojectthe2Deffectsintothe1Ddirectionusingtrigonometrybutthisaddstoplexityofthespreadsheetandisoftenavoided.Further,anychangestotheCADgeometrycancausetheformulasfor2Dand3Dstackstobeout-of-syncandthereforeerroneous.Avoidancecanbeduetoanumberofreasonsincluding,1)themathematicalnatureoftheproblem2)lackofstandardizedprogramstopletethetolerancestacks,3)timeandconfidencerequiredtoprogramaspreadsheet,and4)schedulepressurewhichultimatelyforcesthedesignertousethesimplifiedapproachinorderpletethetask. Solutionstothechallengeofcreatingplexanalyseshavebeenaroundforwellover20years.Withtheintroductionof3DsolidmodelingpackageslikePTCCreo,SOLIDWORKS,CATIA,etc.,thesoftwaredevelopmentteambehindCETOL6σhasbeenabletotakeadvantageof3dimensionalsurfaceinformationtocreateproperlyconstrainedassembliesbasedonthe Page1 IncorporatingThermalExpansionIntoCAD-Based3-DimensionalVariationAnalysis kinematicconstraintdefinitionderivedfromfunctionalassemblyinterfaces.Kinematicconstraintdefinitionreferstothenaturaldegreeoffreedomconditionthatresultswhentwofeatures,“featurepairs”,areplacedincontact.Forexample,acylindricalsurface(feature)ononepartcontactingaplanarsurfaceonanotherpartwouldresultinlinecontact.Thiscontactbydefaultconstrainstwodegreesoffreedom(DOFs)betweenthetwoparts,onetranslationalDOFandonerotationalDOF.Seeimagebelow. CouplingpartcontactbehaviorwiththeCADgeometry,amathematicalmodelcanbeconstructedbythesoftwaretounderstandhowsurfacevariationwillaffectotherkeypartrelationshipsintheassembly.Thesekeyrelationships,representedby“measurements”inCETOL6σ,arethe“fitandfunction”requirementsfortheassemblyandareusuallyderivedoutofsomeformoffailuremodeanalysis,i.e.DFMEA,DesignFailureModeandEffectAnalysis.Thevariationofsurfacesiscontrolledbydimensionschemeswithassignedtolerances.Forstatisticalanalysis,theexpectedvariationfromthemanufacturingprocessforthesurfaceisfactoredinbasedonaCporCpkvalue.Expectedvariationisthenreplacedwithmeasuredvariationasthedesignapproachesproductreleaseandinspectionprocessvalidatesuppliercapabilities.Followingisanexamplethatgoesintomoredetailonfeaturepairs,kinematicconstraints,DOFs,andmeasurements. Page2 IncorporatingThermalExpansionIntoCAD-Based3-DimensionalVariationAnalysis HowtoCreateanurateAssemblyVariationModel Studyingassemblyvariationinvolvesthreebasicdatasourcesincluding:1)functionalassemblyinterfaces,2)functionalassemblyrequirements,and3)partdimensionschemes. ThediagramontheleftshowstheCETOL6σmodelingprocessbutthiscanbegeneralizedintosimpleassemblyengineeringthinking.First,defineprecisely,usingactualCADsurfaces,thetruephysicalassemblyconditions.CADassemblymodelsaretypicallyanidealizedrepresentation.CETOL6σenablesapreciserepresentationoftheactualassemblyconstraints.Secondly,whatdidtheDFMEAsayaboutwhatthisproductissupposedtodo?
CreaterelationshipsbetweenpartsthatrepresentstherequirementsoftheDFMEA.Finally,definetherelationshipsbetweenfeatureswithinapartwitheitherstandarddimensionorgeometrictolerances,GD&
T. Takeforexamplethepump-motorassemblyshownontheright.Theassemblymodelingrequiredmustrepresentthephysicalconditions.Thepumphousingsitsofthreemountingfeaturesandlocatesusingpins.Thepinsareinsertedintoonetightfittingholeandatightfittingslotwiththelengthoftheslot“pointing’towardsthehole.Thefirstassemblyinterfaceisthecontactwiththethreemountingpadsonthemotor.Thefeaturesusedarethesmallplanarsurfacesatthethreelocations.Whilethiscouldbemodeledwithasingleplanarfeature,therealityisthatmanufacturingvariation,especiallyinthepumphousing,assumedtobemolded,resultsindifferentdegreesofvariationateachofthepumphousing“legs”.Therefore,theproperanalysissetupwouldbetoincludeallthreelegsindependentlywiththeirownvariation.Thiscanbedoneusingthreepointsofcontact. Thenextmostcontrollinginterfaceisthepininthetight-fittinghole.Thefeaturepairinthiscaseisanexternalcylinderinsideaninternalcylinder.Thesefeaturesconstrainthetwoin-planetranslations,2DOFs,effectivelyleavingthepumphousingfreetospinabouttheaxisofthispin.That’swheretheesin.Thethirdinterfacebetweenthepinandtheslotcontrolstheclockingofthepumphousingwithrespecttothemotor. Page3 IncorporatingThermalExpansionIntoCAD-Based3-DimensionalVariationAnalysis Theresultingkinematicdegreesoffreedomatthese(5)interfaceswouldbe:(3)pointcontact,one“concentricatpoint”contactcontrollingthetwoin-planetranslations,andonepointcontactattheslotinthedirectionoftheminorwidth.Bydefiningthephysicalbehaviorusingdegreesoffreedom,thelocationandorientationofthepumphousingwithrespecttothemotorwillupdatebasedonthedimensionschemesappliedatthemountingpads,thetwopins,thehole,andtheslot.Forexample,asthelocationoftheslotvarieswithrespecttotheholeinthemotor,thepumphousingmustmovetomodatethevariation.pleteness,theclearancebetweenthepin-holeandpin-slotinterfacesmustalsobeconsideredtobeafloatingconditionorbiasedwherethepinsaretangentintheholeandslotduetosomeexternalforce. Theobjectiveforthisexampleanalysisistopreventleakagebetweentheshaftandthepumphousing.Iftheshaftdecentersbymorethan0.25mm,thepossibilityofleakageexists.Ameasurementiscreatedbetweentheshaftandthecenterholeinthepumphousing.Partandassemblyprocessvariationwillaffectthecenteringoftheshaft. Variationisintroducedbythetoleranceassignedtothefeatureto-featurerelationshipswithinapartotherwiseknownasthedimensionscheme.Forexample,theshaftonthemotorcouldbelocatedrelativetothesidesofthemotorhousingwithsimplelineardimensionsandatolerance.Alternatively,apositionalgeometricconstraintcouldbeappliedtotheshaftrelativetothemountingfeatures(DatumFeatureA),hole(DatumFeatureB),andslot(DatumFeatureC). Regardlessofthedimensionschemeapproach,atolerance,orpermissiblevariationmustbedeterminedtoensurethatleakagewillnotur.Afterall,itisagiventhattheshaftwillnotalwaysbeperfectlylocatedwithrespecttotheotherfeaturesonthemotor. Page4 IncorporatingThermalExpansionIntoCAD-Based3-DimensionalVariationAnalysis Integration&CADFunctionality Thekeytoeasilyincorporatingthermalexpansionintoa3DassemblyvariationmodelistheuniqueCADfeatureidentifier.AllfeaturesusedinaCETOL6σanalysisaretiedtoauniquegeometryIDsinCADpartmodels.Thegeometricrelationshipsrequiredforavariationanalysisarederivedbasedonthecurrentstateofthemodel,i.e.thelocationandorientationofthefunctionalfeaturesusedtoconstructassemblyconstraints,measurements,anddimensionschemes.ModificationoftheserelationshipsdoesnotchangethegeometryIDs.Therefore,aCETOL6σanalysisupdatesautomaticallywithpartgeometrychanges.Whatwouldyoulikeyourreaderstounderstand?
Addnotesonkeytakeawayshere. IncorporatingThermalExpansion Thermalexpansionisthetendencyofmattertochangeinvolumeinresponsetoachangeintemperature.Thedegreeofexpansiondividedbythechangeintemperatureisreferredtoasthematerial'scoefficientofthermalexpansion. Thecoefficientofthermalexpansiondescribeshowthesizeofanobjectchangeswithachangeintemperature.Specifically,itmeasuresthefractionalchangeinsizeperdegreechangeintemperatureataconstantpressure.Commonengineeringsolidsusuallyhavecoefficientsofthermalexpansionthatdonotvarysignificantlyovertherangeoftemperatureswheretheyaredesignedtobeused,sowhereextremelyhighuracyisnotrequired,practicalcalculationscanbebasedonaconstant,average,valueofthecoefficientofexpansion. TheexpansionisountedforbyscalingthegeometryinCADmodel.Thescalefactoriscontrolledbythefollowingequation: DS=CTE(T1-T0) where,DSCTET0T1 =Changeinscalefactor(S=1+DS)=Coefficientofthermalexpansion=Referencetemperature=Newtemperature Page5 IncorporatingThermalExpansionIntoCAD-Based3-DimensionalVariationAnalysis Procedure:
1.DevelopaCETOL6σmodelfortheassemblyyouwishtoanalyze.2.Foreachpartinthemodelforwhichyouwanttoincludetheeffectsofthermalexpansion,scalethemodelusingavailableCADfunctionality(themethodvariesbasedonyourCADsystem).Youcancalculatethescalefactorusingthefollowingequation:S=1+CTE(T1-T0)
3.Toanalyzeatadifferenttemperature,applyadifferentscalefactortoeachpartasdescribedinstep2.(Togetbacktotheoriginaldimensions,scalethepartsbythereciprocalofthepreviousscalefactor.)
4.UpdatetheassemblymodelusingCADfunctionality,i.e.regenerate,rebuild,etc.5.InCETOL6σ,reconnectwithassemblymodelandrecalculateanswer(s). Itisworthmentioningthatthismethodhasasimplifyingassumptiontonotscalethetolerancesbythelinearcoefficientofexpansion.Thisintroducesasmallamountoferrorreducingtheuracyprimarilyforworst-caseresults.Whenmultipledimensionsareinvolvedintheloopwith1:1sensitivity,obviouslythelossofuracygrowsandshouldbeconsideredinverytightapplicationssuchpressorsorengines.Sincetheerrorisproportionaltothemagnitudeofthetolerance,ifthetolerancesarerelativelysmall,errorislow.Theimpacttostatisticalresultsismostlyinsignificantgiventheerrorwouldaffectthetailsofthedistributionforagivendimension. Conclusion Gainingefficienciesinthedevelopmentofproductspaniestogettothemarketaheadofpetition.Inmostproductdevelopmentefforts,timeisthemostvaluedresource.Forthedesignengineer,havingsoftwaretoolsthatareintegratedcloselywiththeCADmodelresultsindesignreuseandincreasestheagilityofthedevelopmentteamtoaddressallaspectsoftheproductinashorterperiodoftime.Standardizingontherightproductdevelopmentsoftwaretoolsnotonlyleadstohigherqualityproductsandgreatermarketshare,butalsobuildsconfidencewithinpany’smunity. Page6