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AssemblyToleranceAnalysisPreparedBy:LouisChangDate:2011-5-16AssemblyToleranceAnalysisAssemblyToleranceAnalysisAssemblyToleranceAnalysisIntroduction

AssemblyToleranceAnalysisExampleAssemblyToleranceAnalysisSummaryAssemblyToleranceIntroductionWorstCaseModelWorstcasemodelisalsocalledas

up-lowerdeviationmodel,limitationmodelandcompleteexchangemodel.Theequationforevaluatingtheconcludinglink

dimensionisasfollowingTheconcludingdimension’stoleranceΔccanbe

foundasfollowingAssemblyToleranceIntroductionStatisticalModelStatisticalmodelisalsocalledasrootsumsquared(RSS)model.Itisassumedalltolerancesarecoincidentwithcertaincurvedistribution.Thedistributionnormalvalueisequaltotolerancezonenormalvalueandthedistributionscopeisthesamewithtolerancescope.Theassemblytoleranceisasfollowing.Instatisticalmethod,theconcludingdimension’stoleranceΔccanbefoundasfollowing:

Sothedeviationoftheconcludinglinkis

AssemblyToleranceIntroductionMonteCarloModel

MonteCarlomodelisakindofnumericalmethodanditsolvesthetolerancewithrandomsamplingsimulation.

Thebasicprincipleisaprobabilityfunctionisdefinedfromallprobabledata.Sotheprobabilityfunctionisaccumulatedtoaccumulativeprobabilityfunctionandthenthemaxvalueforthefunctionisadjustedto1.Thetolerancevalueisgeneratedwithinthescopeofthetolerancewiththehelpofrandomnumbergenerator.Therandomnumberneedmeetcertaindistributionandnormaldistributionisgenerallyapplied.

AssemblyToleranceIntroductionMonteCarloModelGenerallythedistributionisshownwithbetafunction.Fromtheabovefunction,itcanbeconductedasfollowing.Sotheprobabilityfunctioncanbedefinedasbelow.ThreeparameterscanbeadjustedwithMonteCarloModelandtheyareα,βandsimulationtimes.AssemblyToleranceIntroduction6SigmaModel

6Sigmamodelisalsoastatisticalmethod.Itiscloselyconnectedwithpartmanufacturingprocesscapability(Cp,Cpk).Theassemblytoleranceisbasedonmanufacturingprocessstandarddeviation.GenerallyRSSmodelisonly3sigma.

Cp:ItreflectsmanufacturingprocessaccuracyCpk:ComplexProcessCapabilityIndexAssemblyToleranceIntroductionNormalDistributionNormaldistributionisacontinueprobabilitydistributionthathasabell-shapedprobabilitydensityfunction.μ--Meanorexpectationσ--VarianceStandardNormalDistribution:μ=0,

σ2=1AssemblyToleranceIntroductionStandardNormalDistributionBasedon6SigmaAssemblyToleranceIntroductionStandardNormalDistributionBasedon6SigmaLevelPercentageYield(%)PercentageDefective(%)DPMO(PPM)±1σ68.2731.73317300±2σ95.454.5545500±3σ99.730.272700±4σ99.99370.006363±5σ99.9999430.0000570.57±6σ99.99999980.00000020.002AssemblyToleranceIntroductionStandardNormalDistributionwith1.5SigmaShiftAssemblyToleranceIntroductionStandardNormalDistributionwith1.5SigmaShiftLevelPercentageYield(%)PercentageDefective(%)DPMO(PPM)±1σ31.8568.15691462±2σ69.1530.85308538±3σ93.326.6866807±4σ99.380.626210±5σ99.9770.023233±6σ99.999660.000343.4AssemblyToleranceAnalysisExampleAssemblyToleranceAnalysisExampleAssemblyToleranceAnalysisExampleAssemblyToleranceAnalysisExampleΔT=0.003+0.001+0.005+0.008+0.002=0.019a.WorstCaseModelb.RSSModelGAP=0.020±0.010GAP=0.020±0.019c.6SigmaModel(Cpk=1.5)GAP=0.020±0.013AssemblyToleranceAnalysisExampleAssemblyToleranceAnalysisExampleMonteCarloModelBasedonNormalDistributionAssemblyToleranceAnalysisExampleAssemblyToleranceAnalysisExampleStandardNormalDistribution(μ=0)AssemblyToleranceAnalysisExampleAssemblyToleranceAnalysisExampleMeanFrequencyPercentageSigmaLevel0.3505348269.64%±1σ0.3505435287.04%±1.5σ0.3505478695.72%±2σ0.3505494298.84%±2.5σ0.3505499099.80%±3σ0.35055000100.00%±3.5σStandardNormalDistribution(μ=0)AssemblyToleranceAnalysisExampleAssemblyToleranceAnalysisExampleStandardNormalDistribution(μ=1.5σ)AssemblyToleranceAnalysisExampleAssemblyToleranceAnalysisExampleStandardNormalDistribution(μ=1.5σ)MeanFrequencyPercentageSigmaLevel0.3505143528.70%±1σ0.3505338767.74%±2σ0.3505462592.50%±3σ0.3505496999.38%±4σ0.35055000100.00%±5σAssemblyToleranceAnalysisSummaryAssemblyToleranceAnalysisSummaryItneedtobeconvertedintosymmetrytoleranceifthetoleranceisnotsymmetricduringthecourseofassemblytoleranceanalysis.

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