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

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

981

Usingtheorthogonalarraywithgreyrelationalanalysistooptimizethelaserhybridweldingofa6061-T6Alalloysheet

HRKimandKYLee*

SchoolofMechanicalEngineering,YonseiUniversity,Seoul,RepublicofKorea

Themanuscriptwasreceivedon27November2007andwasacceptedafterrevisionforpublicationon24April2008.DOI:10.1243/09544054JEM1070

Abstract:Amethodologyfordeterminingtheoptimumprocessconditionsassociatedwith

Nd:YAGlaser–gasmetalarchybridweldingof6061-T6Alalloysheetispresented.Theweld-

abilityisdependentonvariousprocessparameterswhichincludetheweldingwiretype,shield-

inggas,laserpower,laserfocus,travellingspeed,weldingwirefeedrate,rootopening

tolerance,andvoltage.Experimentsareperformedwithdesignatedweldingconditions

obtainedusinganL18orthogonalarray.Fortheevaluationofweldability,comparingtheresult

oftheultimatetensilestrengthontheweldzoneisessential.Inordertodeterminetheopti-

mumweldingconditions,agreyrelationalanalysisiscarriedoutthroughtheresultoftheulti-

matetensilestrengthforeachweldingexperiment.Basedontheresultsofthegreyrelational

analysis,ingtheanalysisofvariance

approachthesignificantweldingparametersarefound.Theresultsshowthattheoptimum

weldingconditionsdeterminedusinggreyrelationalanalysisaremuchbetterthantheoriginal

preliminarysetofexperimentalconditions.

Keywords:laserhybridwelding,aluminiumalloy,orthogonalarray,greyrelationalanalysis,

variance

1INTRODUCTION

Aluminiumhasalowspecificdensityandagoodcor-

rosionresistancewhenintheatmosphere,water,oil,

andmanychemicalsthatisduetotheexistenceofa

thinoxidefilmonthesurfaceofthemetal.The

6061-T6aluminiumalloyisextensivelyusedin

applicationsthathavemediumtohigh-strength

requirementsandgoodtoughnesscharacteristics.

However,thepresenceofthesurfaceoxide(thatis

stableuptotemperaturesof2000 C)meansthat

porosityeffectscanbecreatedintheweldzone.

Thus,anappropriateweldingtechniqueisrequired.

Alloy6061-T6iseasilyweldedandjoinedbyusing

variousweldingtechniques.Hybridweldinghas

attractedconsiderableattentionintheliterature

[1–5].Thisisduetoitsmanyadvantagessuchas

increasedjoinpenetration,improvedrootopening

*Correspondingauthor:SchoolofMechanicalEngineering,

YonseiUniversity,134Sinchon-dong,Seodaemum-gu,Seoul

120-749,RepublicofKorea.email:KYL2813@yonsei.ac.k

JEM1070ÓIMechE2008tolerance,misalignmenttolerance,increasedweldingspeed,andenhancedprocessstability.Taguchi[6]andRoss[7]proposedtheuseoforthogonalarraystoeffectareductioninthenumberofexperimentsevenwhenconsideringalldesignatedparameters.ThegreysystemtheoryproposedbyDeng[8–10]dealswithasystemwhichhasincompleteanduncer-taininformation.Greyrelationalanalysisisbasedonthegreysystemtheoryandcanbeusedtoanalysecomplicatedperformancecharacteristics[11–13].Theuseofgreyrelationalanalysisleadstothecrea-tionofanoptimumvalueofasinglegreyrelationalgradewithqualitativeindicesofaperformancechar-acteristic.Theuseofthistechniquereducestheamountoftimerequiredtoverifyproductquality.Themainfocusofthisstudyistoexplorethepos-sibilityofusinggreyrelationalanalysistooptimizetheweldingparametersforNd:YAGlaser–gasmetalarchybridweldingof6061-T6aluminiumalloy.Basedontheresultsofthegreyrelationalanalysis,asetofoptimumweldingparametersisobtained.Adesignofexperiment(DOE)approachisthenProc.IMechEVol.222PartB:J.EngineeringManufacture

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

982HRKimandKYLee

usedtoverifytheanalysisresults.Finally,usingan

analysisofvarianceapproachsignificantprocess

parametersforthehybridweldingareinvestigated.

2EXPERIMENTALPROCEDURE

Thebasemetalusedinthisstudyisa6061-T6alumi-

niumalloyandeachplateisofsize150·300·2mm

andusedforsquaregrooveweldingofabuttjoint.

Thechemicalcompositionofthealloyisgivenin

Table1andthemechanicalandthermalproperties

arelistedinTable2.Aschematicdiagramofthe

hybridweldingsystemisshowninFig.1andthe

experimentalset-upisshowninFig.2.Inthisstudy,

aNd:YAGdiodepumpedlaser(withamaximum

powerP0¼4.4kW)andagasmetalarcweldingmachine(withamaximumcurrentI0¼400A)intheDCarcmodeareused.

Basedontheorthogonalarrayapproachproposed

byTaguchi,18experimentswereperformedand

thengreyrelationalanalysiswasappliedtoinvesti-

gatetheperformancecharacteristicsofthehybrid

weldingapproach.

2.1Weldingparameterselection

Inordertoselecttheweldingparameters,theweld-

ingcodesforaluminiumrecommendedbythe

AmericanWeldingSociety[14,15]andthemanuals

forthelaserandgasmetalarcweldingequipment

wereconsulted.Eightweldingparameterswere

selected:theweldingwiretype,theshieldinggas,

Table1thelaserpower,thelaserfocus,thetravellingspeed,theweldingwirefeedrate,therootopeningtoler-ance,andthevoltage.Theseparametersdecidethequalityoftheweld-ing.ApreliminaryexperimentalweldingparameterwasdeterminedbyfollowingthestructuralweldingcodesobtainedfromtheAmericanWeldingSocietyandtheweldingequipmentmanuals.Afternumeroustrialexperiments,apreliminarysettingfortheweld-ingconditionswasobtainedwithouttheuseofgreyrelationalanalysis.ThepreliminarysettingsandweldtestresultsarelistedinTable3.However,theseresultssuggestthatitispossibletoobtainahigherweldqualityifanalternativeapproachsuchasgreyrelationalanalysisandDOEapproachareused.Thelevelofeachprocessparameterwaschosentobewithintheavailablerange.Theweldingexperi-mentswereperformedbysettingER5356orER4043solidweldingwire,withargonorheliumorwithoutashieldinggas,withthelaserpowerintherangefrom3to4kW,thelaserfocusintherangefrom0toÀ1mm,thetravellingspeedintherangefrom80to160mm/s,theweldingwirefeedrateintherangefrom4.5to6.5m/min,therootopeningtoleranceintherangefrom0to0.5mm,andthevoltageintherangefrom10to15V.Theselectedweldingpara-metersforeachlevelarelistedinTable4.2.2TheorthogonalarrayAfterselectionoftheeightparameters,theexperi-mentorderwasmadebycombiningweldingChemicalcompositionof6061-T6aluminiumalloy

Chemicalcomposition(wt%)

Si

0.40–0.8Fe0.7Cu0.15–0.40Mn0.15Mg0.8–1.2Cr0.04–0.35Zn0.25Ti0.15Alremainder

Table2Mechanicalandthermalpropertiesof6061-T6

aluminiumalloy

Mechanicalproperties

Density(·1000kg/m3)

Poisson’sratio

Elasticmodulus(GPa)

Tensilestrength(MPa)

Yieldstrength(MPa)

Elongation(%)

Hardness(Brinell)

Hardness(RockwellA)

Hardness(RockwellB)

Fatiguestrength(MPa)

Thermalproperties

Meltingpoint( C)

Thermalconductivity(W/mK)

5821672.70.3368.92902401695406096.5Fig.1Schematicdiagramofthehybridweldingsystem

JEM1070ÓIMechE2008Proc.IMechEVol.222PartB:J.EngineeringManufacture

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

Usingtheorthogonalarraywithgreyrelationalanalysis983

Table3

Factor

A

B

C

D

E

F

G

H

WeldtestresultPreliminarysettingandweldtestresultWeldingparameterWeldingwiretypeShieldinggasLaserpower(kW)Laserfocus(mm)Travellingspeed(mm/s)Weldingwirefeedrate(m/min)Rootopeningtolerance(mm)Voltage(V)PreliminarysettingER4043He3.50805.7012.6

Fig.2Experimentalweldingset-up(a)laserhead,(b)

GMAWtorch,(c)weldjigUltimatetensilestrength(MPa)231.86–1.77

Table4

Factor

A

B

C

D

E

F

G

HParametersWeldingparametersandtheirlevelsLevel1ER5356None30804.5010Level2ER4043Ar3.5À0.51205.70.212.6Level3–He4À11606.50.515WeldingwireShieldinggasLaserpower(kW)Laserfocus(mm)Travelingspeed(mm/s)Weldingwirefeedrate(m/min)Rootopeningtolerance(mm)Voltage(V)

Table5

Group

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18FactorA111111111222222222FactorB111222333111222333ExperimentallayoutusingL18orthogonalarrayFactorC123123123123123123FactorD123123231312231312FactorE123231123312312231FactorF123231312231123312FactorG123312231231312123FactorH123312312123231231

parametersusingTaguchi’sorthogonalarray

approach.Interactionsbetweenweldingparameters

wereneglectedinthisstudy.AnL18(21·37)orthogo-

nalarraytablewasconsultedaboutwhichexperi-

mentstoconduct.Eachexperimentwasrepeated

threetimestoensureanaccurateresult.Theexperi-

mentallayoutadoptedusingtheL18orthogonalarray

isshowninTable5.

JEM1070ÓIMechE20083DETERMINATIONOFTHEOPTIMUMWELDINGPARAMETERS3.1GreyrelationalanalysisTheexperimentaldataarenormalizedbeforegreyrelationalanalysisisperformed.Thethreeexperi-mentalresultsfortheultimatetensilestrength

wereProc.IMechEVol.222PartB:J.EngineeringManufacture

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

984HRKimandKYLee

convertedintotherangebetweenzeroandoneby

usingalinearnormalizationprocedureandthispro-

cessiscalledgreyrelationalgenerating.Inthispro-

cessthedataaredescribedusingoneofthree

possibledescriptions:‘thelargerthebetter’,‘the

smallerthebetter’,and‘thenominalthebetter’.In

thisstudy,theultimatetensilestrengthisrelatedto

theform‘the-larger-the-better’followingitscharac-

teristic.Intheseexperimentsthenormalizedexperi-

mentalresultsoftheultimatetensilestrengthwere

expressedas

ÃxiðkÞ¼xðkÞÀminxðkÞ

maxxiið1Þ

wherexiðkÞisthekthexperimentalresultintheithÃexperiment,xiðkÞisthenormalizedresultxiðkÞafterthedatapre-processingstep,maxxiðkÞisthelargestvalueofxiðkÞ,andminxiðkÞimpliesthesmallestvalueofxiðkÞ.Alargevalueofthenormalizedresultimpliesagoodperformance.

Then,thegreyrelationalgrade[8–13]isdefinedas

followsÀÃÃÁDminþDmaxgx0;xiwi¼Gi¼ð2Þ0imax

n1XÃDðkÞð3ÞD0i¼nk¼10iÀÃÃÁð4Þ;xiwi610<gx0

whereD0iðkÞisthedeviationofthereferencevalueÃx0ðkÞ.ThecomparabilityvaluexiÃwiðkÞandweightingfactorwiforeachtensilestrengthareassignedtobe

equalwithvaluesof0.34,0.33,and0.33underthe

conditionthatthesumoftheweightingfactorsisone.

ThegreyrelationalgradeGirepresentsthelevelof

correlationbetweenthereferencevalueandthe

Table6specificvaluewithwhichitiscompared.Theevalu-atedgradeisbetweenzeroandoneandisequaltooneifthetwosequencesareexactlyidentical.BecausethegradeGiisestimatedthroughintegratedconsiderationoftherequirement,thehighestgradeamongall18groupsexactlyrepresentstheoptimizedcombinationforlaser-archybridwelding.Ahighergradealsoimpliesagreaterdominanceofthespecificvalueoverothervalues.Therefore,greyrelationalanalysisinvolvesaseriesofcalculationsthatincludemeasurementofthedifferencebetweenoriginaldatasequences.Table6showstheexperimentalresult,thenormalizeddata,andacomputedgradeforthe18groups.Experiment15hasthebestperfor-mancecharacteristicamongthe18experimentsbecauseithasthehighestgreyrelationalgrade.Thus,theperformancecharacteristicisstatisticallyconvertedintoasinglegreyrelationalgrade.Sincetheorthogonalarrayisusedfortheexperi-mentaldesign,itispossibletoseparateouttheeffectofeachweldingparameteronthegreyrelationalgradeatdifferentlevels.Forexample,themeanofthegreyrelationalgradefortheweldingwiretypeatlevels1and2canbecomputedbyaveragingthegreyrelationalgradeforexperiments1to9and10to18,respectively(Table5).ThemeanofthegreyrelationalgradeforeachleveloftheotherweldingoperationparameterscanbecalculatedinasimilarwayanditissummarizedinTable7.Figure3showsthegreyrelationalgradegraphandthedashedlineisthevalueofthetotalmeanofthegreyrelationalgrade.Basically,thelargerthegreyrelationalgrade,thebettertheperformancequality.Asaresult,thelevelofthelaserfocusshowsthelargestdifferencewhiletheeffectoftheshieldinggastypeshowslittledifference.Theexperimentalresult,itsnormalizeddataandgradefor18groups

Greyrelationalcoefficient

1

0.6532

0.0000

0.7784

0.2896

0.4936

0.7232

0.7094

0.7212

0.2877

0.9094

0.8680

0.3547

0.4257

0.9557

1.0000

0.8198

0.8493

0.634620.63930.00000.83020.30190.53430.81850.87830.71280.34510.85320.85480.37250.31460.71061.00000.81760.60870.593030.63110.00000.81450.27680.48390.87230.83800.73740.25870.88620.85210.39030.31340.78951.00000.82650.74610.6317Grade0.73980.50500.84120.58940.67270.83870.84130.78690.59200.89730.87810.61900.61150.85001.00000.85090.79430.7285Ultimatetensilestrength(MPa)Group1234567891011121314151617181216.81141.68231.20174.99198.45224.85223.27224.63174.77246.27241.51182.47190.64251.59256.69235.96239.36214.662217.62143.72239.69178.62205.48238.34245.25226.12183.61242.35242.53186.78180.09225.87259.32238.23214.09212.273216.52151.06235.54179.77201.25241.54237.98227.54177.89242.98239.44191.54183.57232.95254.78236.78228.45216.58

Proc.IMechEVol.222PartB:J.EngineeringManufactureJEM1070ÓIMechE2008

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

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

986HRKimandKYLee

Table8

Weldingparameter

[A]Weldingwiretype

[B]Shieldinggas

[C]Laserpower

[D]Laserfocus

[E]Travellingspeed

[F]Weldingwirefeedrate

[G]Rootopeningtolerance

[H]Voltage

Error

TotalSumofsquare0.03760.00110.00150.09900.02770.07690.02840.02520.00390.3012ResultsoftheanalysisofvarianceDegreeoffreedom12222222Meansquare0.03760.00060.00080.04950.01380.03840.01420.0126F9.71780.14810.196612.79873.57449.93603.67323.2514Contribution(%)22.440.340.4529.568.2622.958.487.51100

Table10

Table9

Group

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

181216.81141.68231.20174.99198.45224.85223.27224.63174.77246.27241.51182.47190.64251.59256.69235.96239.36214.66TheSNratiooftheTaguchi’sDOE2217.62143.72239.69178.62205.48238.34245.25226.12183.61242.35242.53186.78180.09225.87259.32238.23214.09212.273216.52151.06235.54179.77201.25241.54237.98227.54177.89242.98239.44191.54183.57232.95254.78236.78228.45216.58SNratio(dB)46.7343.2547.4445.0046.0947.4147.4247.0945.0447.7447.6545.4345.3347.4648.2047.4947.1046.63Group12345678910111213141516

17

18ComparisonrankorderbetweengreyrelationalgradeandTaguchiSNratioRankorder1Greyrelationalanalysis111871713861016231415514912Rankorder2SNratioofTaguchiDOE111861713871016231415514912

Table11

Factor

A

B

C

D

E

F

G

HAcomparisonoftheresultsofthepreliminaryandoptimumprocessparametersWeldingparameterWeldingwiretypeShieldinggasLaserpower(kW)Laserfocus(mm)Travellingspeed(mm/s)Weldingwirefeedrate(m/min)Rootopeningtolerance(mm)Voltage(V)PreliminarysettingER4043He3.50805.7012.6

231.86–1.77OptimumsettingER4043Ar401206.50.210257.05–2.27Ultimatetensilestrength(MPa)

reflectagoodcharacteristicoftheoptimumhybrid

weldability.Similartotheresultofthegrey

relationalanalysis,experiment15hasthebest

performancecharacteristicamongthe18experi-

mentsusingtheTaguchiDOEapproach(Table9).

TheSNratiooftheTaguchidesignofexperimentis

alsolistedinTable9.Theoverallresultofthe

gradingorderisingoodagreementwitha

comparisonofbothrankingordersasshownin

Table10.

Proc.IMechEVol.222PartB:J.EngineeringManufactureFromtheabove,thefollowingoptimumprocessparametersweredeterminedfromtheL18orthogonalarray–theweldingwiretypeatlevel2,theshieldinggasatlevel2,thelaserpoweratlevel3,thelaserfocusatlevel1,thetravellingspeedatlevel2,theweldingwirefeedrateatlevel3,therootopeningtoleranceatlevel2,paringtheresultslistedinTable11,theweldingperformancecharacter-isticsoftheoptimumsettingarefoundtobemuchhigherthanthepreliminarysettingslistedinTable3.JEM1070ÓIMechE2008

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

Usingtheorthogonalarraywithgreyrelationalanalysis987

4CONCLUSIONS

ANd:YAGlaser–gasmetalarchybridwelding

experimentwasperformedwiththeexperimental

directionsdictatedbyanL18orthogonalarrayas

suggestedbyTaguchi.Theultimatetensilestrength

wasmeasuredinordertoevaluatetheweldability.

Agreyrelationalanalysisapproachwasadoptedto

optimizethehybridweldingperformancecharacter-

isticsintoasingleperformancecharacteristic,called

thegreyrelationalgrade.Thistechniquesimplifies

theoptimizationofcomplicatedperformancechar-

acteristics.Theanalyticalresultofthegreyrelational

analysisshowsanexcellentagreementwiththe

TaguchiDOEapproachandthemostsignificant

hybridweldingparametersarethelaserfocus,the

weldingwirefeedrate,andtheweldingwiretype.

Theexperimentalresultfortheoptimumsetting

givesmuchbetterweldingconditionsthanthe

preliminarysetting.

ACKNOWLEDGEMENT

Thisworkwassupportedbygrant10024116-2007-13

fromtheKoreaInstituteofIndustrialTechnology

EvaluationandPlanning(ITEP).

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JEM1070ÓIMechE2008Proc.IMechEVol.222PartB:J.EngineeringManufacture

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

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