公差分析和尺寸链方法

上汽通用五菱博士后工作站上汽通用五菱—上海交通大学现代车身技术联合研究中心公差分析和车身尺寸链方法ToleranceAnalysis&Auto-bodyDimensionChainMethod车身质量控制系列讲座上汽通用五菱博士后工作站上汽通用五菱—上海交通大学现代车身技术联合研究中心1-DToleranceanalysisAuto-bodyDimensionChainMethodContents•Variationvs.Tolerance•VariationSimulationMethods•AdvantagesandLimitationsofEachMethod•IntegrationofKeyCharacteristicofProduct&Process•AssemblyConstraints•ToleranceandSolvingofDimensionChain上汽通用五菱博士后工作站上汽通用五菱—上海交通大学现代车身技术联合研究中心PartI1-DToleranceanalysis3/49上汽通用五菱博士后工作站上汽通用五菱—上海交通大学现代车身技术联合研究中心CharacterizingtheperformanceofaprocessCentraltendencyormean:SpreadorvariationnxxxxExn...][211)(][12nxxxVarnii-4-3-2-101234-4-3-2-101234Deviation4/49上汽通用五菱博士后工作站上汽通用五菱—上海交通大学现代车身技术联合研究中心Variationvs.ToleranceLSLUSLVariation:•iswhattheprocessgivesus,•maybequitedifferentfromthetolerance.ToleranceorSpecificationis•theallowablelevelofvariation,•basedonfunctionalconsideration,•usedtoestablishapart'sconformabilitytodesign.Butthetechniquesforpredictingvariationortoleranceforanassemblyisthesame.5/49上汽通用五菱博士后工作站上汽通用五菱—上海交通大学现代车身技术联合研究中心VariationSimulation123x±ax±bx±c123y±t123Givenindividualpartdimensionsandtheirdistribution,whataretheassemblydimensions?Butthemethodcanappliedmorewidelythanmechanicalassembly.Thegeneralformis:givenafunctionY=f(x1,x2,…),andthedistributionsofxi,Whatisthedistributionofy?6/49上汽通用五菱博士后工作站上汽通用五菱—上海交通大学现代车身技术联合研究中心DistributionofToleranceWorstCaseStatistical:RootsumsquaresMonteCarloAssemblyModelExplicit:LinearizedSensitivityMechanisticModelNon-linearModelImplicit:VariationSimulationMethodsTwothingsareessentialinordertoperformvariationanalysis.Oneisanassemblymodelorinput-outputmodel.Theotheristhedistributionofvariables.7/49上汽通用五菱博士后工作站上汽通用五菱—上海交通大学现代车身技术联合研究中心CommonlyUsedVariationSimulationMethodsWorstCase:(Conway,1948;ChaseandParkinson,1991)RootSumSquares(RSS):(Spotts,1978,LeeandWoo,1990)MonteCarloSimulation:(Craig,1989)321xxxycbat222cbat123x±ax±bx±c123y±t1238/49上汽通用五菱博士后工作站上汽通用五菱—上海交通大学现代车身技术联合研究中心100+/-0.149.9+/-0.149.9+/-0.1?+/-?(A)(B)(C)SimpleVariationSimulationExampleGivencomponenttolerances,determinethevariationinthemeasureddimension(thegapbetweentheblocksandthebase).上汽通用五菱博士后工作站上汽通用五菱—上海交通大学现代车身技术联合研究中心Inworstcaseanalysis,itisassumedthatthecontributingdimensionsarealwayswithintolerance.Bymakingthisassumptionworstcaselimitscanbefoundwithinwhichthemeasureddimensionmustalwaysfall.WorstCaseAnalysisx(1000.1)(49.90.1)(49.90.1)0.1x(1000.1)(49.90.1)(49.90.1)0.5100+/-0.149.9+/-0.149.9+/-0.1?+/-?(A)(B)(C)上汽通用五菱博士后工作站上汽通用五菱—上海交通大学现代车身技术联合研究中心100+/-0.149.9+/-0.149.9+/-0.1?+/-?(A)(B)(C)RootSumSquaresTheideabehindRSSistotreatatoleranceasanormaldistributionwithcertainprocesscapability,anduserandomassembly.yCABVar(y)Var(C)Var(A)Var(B)173.01.032222BACytoltoltoltol上汽通用五菱博士后工作站上汽通用五菱—上海交通大学现代车身技术联合研究中心Meanandvarianceofsomelinearfunctions][][][2121xbExaEbxaxE]cov[2][][][21221221xxabxVarbxVarabxaxVar12/49上汽通用五菱博士后工作站上汽通用五菱—上海交通大学现代车身技术联合研究中心MonteCarloSimulationTable1DistributionfordimensionADimen.RangeFrequencyCumul.Freq.49.74-49.7830-349.78-49.82204-2349.82-49.869724-12049.86-49.90180121-30049.90-49.94118301-41849.94-49.9877419-49549.98-50.025496-50050.02-50.060N/ATable2DistributionfordimensionBDimen.RangeFrequencyCumul.Freq.49.74-49.7810-149.78-49.8272-849.82-49.86589-6649.86-49.9013467-20049.90-49.94182201-38249.94-49.9890383-47249.98-50.0225473-49750.02-50.063498-50013/49上汽通用五菱博士后工作站上汽通用五菱—上海交通大学现代车身技术联合研究中心Table3DistributionfordimensionCDimen.RangeFrequencyCumul.Freq.99.84-99.8870-799.88-99.92188-2599.92-99.967826-10399.96-100.00147104-250100.00-100.04143251-393100.04-100.0881394-474100.08-100.1225475-499100.12-100.16150014/49上汽通用五菱博士后工作站上汽通用五菱—上海交通大学现代车身技术联合研究中心Table4ResultsofMonteCarloSimulationBuild#(A)A(B)B(C)C(C-A-B)140549.9236249.92485100.100.26210949.8441349.96444100.060.26339949.9237149.92460100.060.22437049.9235649.9219399.980.14534849.9233149.92493100.100.28642649.965249.8416499.980.1872949.849849.88426100.060.34839149.9223849.9211499.980.18917349.889849.88493100.100.341026949.8819149.8819899.980.221140749.9231349.92475100.100.261223849.8823949.928599.940.14135149.8449150.00361100.020.181449449.961749.84328100.020.221523549.8812849.88339100.020.261625749.8834349.92284100.020.22177449.8413149.881999.900.181813849.8826949.92289100.020.221923749.8823249.9212499.980.18206349.8437949.927899.940.1815/49上汽通用五菱博士后工作站上汽通用五菱—上海交通大学现代车身技术联合研究中心LinearizedSensitivityModelAgeneralassemblymodelwillbeafunctionoftheform:Wherexiarethecomponentdimensions,andyistheresultantassemblydimensions.Themeandimensionoftheassemblywillbe:(1)),...,(21nxxxgy)...,,(21nxxxgy16/49上汽通用五菱博士后工作站上汽通用五菱—上海交通大学现代车身技术联合研究中心LinearizedSensitivityModelTocalculatethevariance,weapplyTaylor’sseriesexpansiontoEq.(1),whichwillgive:nnxxgxxgxxgy...2211)(...)()()(2222121nnxVarxgxVarxgxVarxgyVarInthespecialcasewhentheassemblyequationislinear,theexpressionfortheassemblymeanandvarianceareexact.However,fornonlinearassembly,thevarianceestimatemaynotbecorrect.17/49