Tolerance_stack-up[17P][290KB]

17-1DesignAnalysis•Designanalysisisusedinplaceoftestandinspectiontofindtheexpectedpartperformance•Itbasicallymeanswearelookingforthemeanandsigmaofthedistributionbeforewebuildtheparts•Techniquesusedfordesignanalysisinclude:1.WorstCaseAnalysis2.SensitivityAnalysisa)MonteCarloSimulationb)TaylorSeriesExpansionc)DesignofExperiments17-21.WorstCaseAnalysis•Worstcaseisusedtodeterminewhathappenswhenalltheparametersareattheirlimits–Seteveryparametertoitsspeclimit–Measuretheresponse–Thisisthesameasaddingtolerances•Ifalltheparametersrepresent3sigmalimitsthen–Thenumberofpartsbadforoneparameteris0.0026–Fourparameters(0.0026)4=0.00000000000286(3inatrillion)–For20parametersweget2outof1058bad!•Analysisshouldlimitprobabilitiesto6sigma–Thisisabout3parametersallattheirlimits17-3ToleranceStackUp•Whatisthetolerancestackupfromthetoptobottom?•Willtheylineup??17-4WorstCaseAnalysisTough!•Shaft1+-0.002•Hole1+.003,-.001•Shaft2+-0.002•Hole2+-.003-.001•Shaft3+-.002•Hole3+-.003-.001•TotalWorstcaseis–.002+.003+.002+.003+.002+.003=+0.015,-.009TheSHAFTWON’TFITINTHELASTHOLEUNLESSITS.009SMALLER!17-5WorstCase•Forthefirstshaftandholetheshaftcanbe+-.002andthehole+.003,-.001.–Iftheholeissmallthen-.001andtheshaftislargethen+.002.Thedifferencebetweenthetwomustbe0.003tomakesureitfits.–Addanothersetandtheworstcasesaysthesecondholeandshaftmustbe0.006differentinsize–Athirdsetwouldhaveto0.009etc.•TheproblemwiththisisitmakesforatooconservativedesignwhenyoustackuptolerancesPerfectWorstcase17-62.SensitivityAnalysisa)MonteCarloSimulation•Simulatevariationintheresultsb)TaylorSeriesExpansion•Mathematicalevaluationofvariationsc)DesignofExperiments•Carefulexperimentation(testing)approach17-72a)MonteCarloAnalysis•MonteCarloisthenameofagamblingcityontheMediterraneanSea.•WithMCanalysisyou“rollthedice”andestimatetheoutcomemany,manytimes•Ifyourandomizetheresultoftenenoughyougetagoodideaoftheoutcomeofasystem•Youneedtoknowthefollowing–Anequationforwhatyouaresimulating–Thedistributionoftheparameterssotheycanvaryovertime17-8CircuitExampleIVRfL222()MeanStdDevV=voltage1005r=resistance101f=capacitance505L=inductance.004.0008•Theequationforthecurrentthroughthecircuitisshown.•Thevoltageofthepowersupplyisusuallyat100Voltsbutitvaries+-5Volts1sigma•1Sigmameans68%ofthetime,2Sigmais95%and3Sigmais99%,sothevoltagecouldbe100-3*5=85Voltssometimes.•Ifthepackagesaysa1%toleranceon10Ohmresistors,thatmeanstheresistorscanbebetween9or11ohms99%ofthetime(or3sigma).17-9MonteCarloAnalysisCircuitExampleMeanStdDevV=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)Repeat1000’softimesNormallydistributedIVRfL222()17-102b)TaylorSeriesExpansion•TheTaylorSeriescalculatesthesystemvariancebasedonthederivativesofthefunctionwithrespecttoeachparameter•Givetheequationg(x1,x2,x3)thenggxxgxxgxx211222233217-11SensitivityAnalysis•Thesensitivityoftheoutputtochangesintheinputcanbecalculatedfromthederivatives.•ThesensitivityofItochangesinV•ThismeansthatwhenVincreasesfromit’smeanby1sigma,Iincreasesby0.5IVV05.17-12TaylorSeriesExampleIVRfL222()IVRfL22122()IRVRfLR05222232.()IfVRfLL05242232.()ILVRfLf05242232.()17-13Example•EvaluatetheexpressionforIusingthemeanandstandarddeviationsIV01.IR10.If00005.IL313.I212506.I110.IVRfLIVIRIfIL2222217-14RootSumSquared(RSS)•RootSumSquaredissimplytheTaylorSeriesexpansionforalinearsystemg=x1+x2+x3•Thisonlyworkforlinearsystem(mechanicaltolerances)•ThisisVERYpopularinindustry!2322212321xxxgxgxgxg2322212xxxg17-15RevisitingToleranceStackupShaft1+-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.17-162c)DesignOfExperiments•DOEisastatisticaltoolthatallowsthemostinformationtobeextractedfromanexperiment•Normalexperimentsholdeveryvariableconstantandchangeone.–InthepreviousexampleholdallfixedexceptR.Changeittoitslimitsandseehowthenetworkresponds•DOE(alsocalledTaguchimethods)allowmorethanonevariabletochangesothatmultipleinteractionscanbemeasured–WhathappensifRislowandfishigh?17-17D.O.E.Process•Firstdeterminethenumberoffactors(controllablevariables)youwanttochange.Callitn.•Thenumberofexperimentsnecessarytotesteverythingatthehighandlowlimitsofeachvariableis2n•Theminimumnumberofexperimentsisthelargerofnand2x•Ifwehave5variablesweneed25or32experiments•WithDOEweneed23or8experiments•Themathissimple(Excelspreadsheet)butittakessomeknowledgetosetthisupanduseit.•Thisispopularforexpensivetestinginindustry.