公差累积分析PPT幻灯片

17-1,DesignAnalysis,DesignanalysisisusedinplaceoftestandinspectiontofindtheexpectedpartperformanceItbasicallymeanswearelookingforthemeanandsigmaofthedistributionbeforewebuildthepartsTechniquesusedfordesignanalysisinclude:1.WorstCaseAnalysis2.SensitivityAnalysisa)MonteCarloSimulationb)TaylorSeriesExpansionc)DesignofExperiments,17-2,1.WorstCaseAnalysis,WorstcaseisusedtodeterminewhathappenswhenalltheparametersareattheirlimitsSeteveryparametertoitsspeclimitMeasuretheresponseThisisthesameasaddingtolerancesIfalltheparametersrepresent3sigmalimitsthenThenumberofpartsbadforoneparameteris0.0026Fourparameters(0.0026)4=0.00000000000286(3inatrillion)For20parametersweget2outof1058bad!Analysisshouldlimitprobabilitiesto6sigmaThisisabout3parametersallattheirlimits,17-3,ToleranceStackUp,Whatisthetolerancestackupfromthetoptobottom?Willtheylineup?,17-4,WorstCaseAnalysisTough!,Shaft1+-0.002Hole1+.003,-.001Shaft2+-0.002Hole2+-.003-.001Shaft3+-.002Hole3+-.003-.001TotalWorstcaseis.002+.003+.002+.003+.002+.003=+0.015,-.009TheSHAFTWONTFITINTHELASTHOLEUNLESSITS.009SMALLER!,17-5,WorstCase,Forthefirstshaftandholetheshaftcanbe+-.002andthehole+.003,-.001.Iftheholeissmallthen-.001andtheshaftislargethen+.002.Thedifferencebetweenthetwomustbe0.003tomakesureitfits.Addanothersetandtheworstcasesaysthesecondholeandshaftmustbe0.006differentinsizeAthirdsetwouldhaveto0.009etc.Theproblemwiththisisitmakesforatooconservativedesignwhenyoustackuptolerances,Perfect,Worstcase,17-6,2.SensitivityAnalysis,a)MonteCarloSimulationSimulatevariationintheresultsb)TaylorSeriesExpansionMathematicalevaluationofvariationsc)DesignofExperimentsCarefulexperimentation(testing)approach,17-7,2a)MonteCarloAnalysis,MonteCarloisthenameofagamblingcityontheMediterraneanSea.WithMCanalysisyou“rollthedice”andestimatetheoutcomemany,manytimesIfyourandomizetheresultoftenenoughyougetagoodideaoftheoutcomeofasystemYouneedtoknowthefollowingAnequationforwhatyouaresimulatingThedistributionoftheparameterssotheycanvaryovertime,17-8,CircuitExample,MeanStdDevV=voltage1005r=resistance101f=capacitance505L=inductance.004.0008,Theequationforthecurrentthroughthecircuitisshown.Thevoltageofthepowersupplyisusuallyat100Voltsbutitvaries+-5Volts1sigma1Sigmameans68%ofthetime,2Sigmais95%and3Sigmais99%,sothevoltagecouldbe100-3*5=85Voltssometimes.Ifthepackagesaysa1%toleranceon10Ohmresistors,thatmeanstheresistorscanbebetween9or11ohms99%ofthetime(or3sigma).,17-9,MonteCarloAnalysisCircuitExample,MeanStdDevV=voltage1005r=resistance101f=capacitance505L=inductance.004.0008(1)V=5*Z+100(2)R=1*Z+10(3)f=5*Z+50(4)L=0.0008*Z+.004(5)CalculateIandplotZisarandomnumber(6)Repeat1000softimesNormallydistributed,17-10,2b)TaylorSeriesExpansion,TheTaylorSeriescalculatesthesystemvariancebasedonthederivativesofthefunctionwithrespecttoeachparameterGivetheequationg(x1,x2,x3)then,17-11,SensitivityAnalysis,Thesensitivityoftheoutputtochangesintheinputcanbecalculatedfromthederivatives.ThesensitivityofItochangesinVThismeansthatwhenVincreasesfromitsmeanby1sigma,Iincreasesby0.5,17-12,TaylorSeriesExample,17-13,Example,EvaluatetheexpressionforIusingthemeanandstandarddeviations,17-14,RootSumSquared(RSS),RootSumSquaredissimplytheTaylorSeriesexpansionforalinearsystemg=x1+x2+x3Thisonlyworkforlinearsystem(mechanicaltolerances)ThisisVERYpopularinindustry!,17-15,RevisitingToleranceStackup,Shaft1+-0.002impliesthatalltheunitsvarybythismuch.So3Sigmais0.002andSigma=0.00067Hole1+.003,-.001impliesthe3Sigmais.001/3=.00033RSSfor2partsisSQRT(0.000672+.000332)=0.00075for1Sigmaofthesystem.3Sigmaofthesystemisthen.00225not0.003.For6partsinthesystemyougetSQRT(0.000672+.000332+0.000672+.000332+0.000672+.000332)=.00129for1Sigma.So3Sigmais0.004not0.009shownbyworstcase.,17-16,2c)DesignOfExperiments,DOEisastatisticaltoolthatallowsthemostinformationtobeextractedfromanexperimentNormalexperimentsholdeveryvariableconstantandchangeone.InthepreviousexampleholdallfixedexceptR.ChangeittoitslimitsandseehowthenetworkrespondsDOE(alsocalledTaguchimethods)allowmorethanonevariabletochangesothatmultipleinteractionscanbemeasuredWhathappensifRislowandfishigh?,17-17,D.O.E.Process,Firstdeterminethenumberoffactors(controllablevariables)youwanttochange.Callitn.Thenumberofexperimentsnecessarytotesteverythingatthehighandlowlimitsofeachvariableis2nTheminimumnumbe