Using the orthogonal array with grey relational analysis to(5)

Using the orthogonal array with grey relational analysis to optimize the laser hybrid welding of a 6

Usingtheorthogonalarraywithgreyrelationalanalysis985

Table7Responsetableforthegreyrelationalgrade

Greyrelationalgrade

Factor

A

B

C

D

E

F

G

H

Totalmeanvalueofthegreyrelationalgrade¼

0.7576WeldingparameterWeldingwiretypeShieldinggasLaserpowerLaserfocusTravellingspeedWeldingwirefeedrateRootopeningtoleranceVoltageLevel10.71190.74670.75500.76560.81270.73170.72080.8042Level20.80330.76040.74780.66300.72520.69370.81280.7127Level3–0.76570.76990.84420.73480.84740.73930.7559Max-min0.09140.01890.02210.18110.08750.15370.09200.0915

Fig.3Greyrelationalgradegraph

3.2Analysisofvariance

Theprocessparameterswhichsignificantlyaffectthe

weldingperformancecharacteristicareobtained

throughtheanalysisofvariance(ANOVA)approach

[11,12].TheANOVAapproachseparatesthetotal

variabilityofthegreyrelationalgradesintocontri-

butionsbyeachoftheweldingparametersandits

associatederror.Thetotalvariabilityofthegradeis

computedbythesumofthesquareddeviations

fromthetotalmeanofthegreyrelationalgrade.

ThetotalsumofthesquareddeviationSSTis

calculatedas

SST¼nX

i¼1comparisonsbetweenparameters.Forexample,athree-levelparametercountsfortwodegreesoffreedom.Thecontributionpercentageforeachweldingparameterinthetotalsumofthesquareddeviationsisusedtoevaluatetheimportanceoftheprocessparameter.Inaddition,theF-test[16]statisticallyprovidesadecisionatsomeconfidencelevelastowhethertheseparametershaveanimportanteffectontheperformancecharacteristic.AlargeF-valueindicatesthatthechangeoftheweldingparameterhasmadeasignificantdifferencetotheperformancecharacteristic.FromtheANOVAresultspresentedinTable8,thelargestpercentagecontributionofthethreesignificantweldingparameters,namelythelaserfocus(D),theweldingwirefeedrate(F),andtheweldingwiretype(A),areselectedas29.56percent,22.95percent,and22.44percent,respectively.Fromtheanalysisofcontributiontotheprocess,theabovetwofactorsaresignificantvariablefactorsforimprovingthequalityofhybridwelding.3.3.VerificationanddiscussionTheTaguchiDOE[6,7,17]approachisalsoanopti-mumdesignmethodology.Inthisresearch,theTaguchiDOEapproachiscomparedwiththeoutputofthegreyrelationalanalysis.TheTaguchiDOEapproachhasthesamedefinitionsfordatapre-processingwhicharedependentonthetypeofexperimentalresult.Similartothegreyrelationalgeneratingprocess,ahighvalueofDOEcomputationisconsideredtobeindicativeofagoodcharacteristic

oftheexperimentalresult.Theidenticalvaluesofthe

ultimatetensilestrengths,whichareusedinthegrey

relationalanalysis,arerearrangedasfollows

"#mX11SN¼À10logð6Þmi¼1yiwhereSNisthesignal-to-noise(SN)ratioinunits

ofdecibels.AhighvalueofSNisconsideredto

Proc.IMechEVol.222PartB:J.EngineeringManufactureðgiÀgmÞ2ð5Þwheregmistheaverageofthesumofthegreyrelationalgrade,nisthenumberofexperimentsintheorthogonalarray,andgiisthemeanofthegreyrelationalgradefortheithexperiment.ThetotalsumofthesquareddeviationsSSTisseparatedintotwotypeswhicharethesumofthesquareddeviationoftheweldingprocessparameters(SSP)andthesumofthesquarederror(SSE).ThedegreesoffreedomaredefinedasthenumberofJEM1070ÓIMechE2008