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Modelling of laser processing cut quality by an adaptive network-based fuzzy inference system

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Proceedings of the Institution of MechanicalEngineers, Part C: Journal of Mechanical

Engineering Sciencehttp://pic.sagepub.com/

Sivarao Subramonian, P Brevern, N S M El-Tayeb and V C Vengkatesh

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 2009 223:

2369

DOI: 10.1243/09544062JMES1319

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2369

Modellingoflaserprocessingcutqualitybyanadaptivenetwork-basedfuzzyinferencesystem

SivaraoSubramonian1∗,PBrevern2,NSMEl-Tayeb2,andVCVengkatesh21

ManufacturingEngineeringFaculty,TechnicalUniversityofMalaysia,Malaka,AyerKeroh,Melaka,Malaysia2

FacultyofEngineeringandTechnology,MultimediaUniversity(MMU),Malaysia

Themanuscriptwasreceivedon10August2008andwasacceptedafterrevisionforpublicationon21April2009.DOI:10.1243/09544062JMES1319

Abstract:Real-worldproblemsinprecisionmachiningnowrequireintelligentsystemsthatintegrateknowledge,techniques,andmethodologies.Intelligentsystemspossesshuman-likeexpertisewithinaspeciﬁcdomaintoadaptthemselvesandtolearntodobetterinmakingdeci-sionsforanintelligentmanufacturingsystem.Anintelligenttoolcalledadaptivenetwork-basedfuzzyinferencesystem(ANFIS)wasusedtomodelandpredictthelasercutqualityofa2.5mmmanganese–molybdenum(Mn–Mo)alloypressurevesselplateinthisarticle.A3kWCO2lasermachinewithsevenselecteddesignparameterswasusedtocarryout128experimentsbasedon2kfactorialdesignwithsinglereplication.Becausesurfaceroughness(Ra)wastheresponseparameter,itwastargetedtobe<15µmtomeettherequirementandbenchmarkofthepressurevesselmanufacturerwhosponsoredthisproject.TheDIN2310-5Germanlasercuttingofmetal-licmaterialsstandardandprocedurewasreferredtoforevaluatingsurfaceroughness,whereexperimentallyobtainedresultswereusedforRapredictivemodelling.Predictionsofnon-linearlaserprocessingbyANFISwerefoundtobeextremelypromisinginsupplyingthedesiredoutput,whereRawaspredictedtoanexcellentdegreeofaccuracy,reachingalmost70percentwiththeexperimentalpureerrorbelow30percent.

Keywords:adaptivenetwork-basedfuzzyinferencesystem,lasermachining,surfaceroughness,cutquality,hybridmodelling

1INTRODUCTION

Thecontrolofmachiningparametersplaysanimpor-tantroleindeterminingthequalityofthemachinedpart,particularlyinprecisionmachining.Machin-ingparametersarebecomingmorecomplex,espe-ciallyinsophisticatednon-traditionalmachinetools[1,2].Anadaptivenetwork-basedfuzzyinferencesys-tem(ANFIS)isanartiﬁcialintelligencetoolthatiswidelyusedinmodelling,monitoring,andcontrol-ling.Thisarticlepresentsaprojectthatinvolvesthreestages:experimental,modelling,andpredictionoflaserprocessing,whereamanganese–molybdenum(Mn–Mo)alloypressurevesselplatewithathickness

∗Correspondingauthor:ManufacturingEngineeringFaculty,Tech-

nicalUniversityofMalaysia,Malaka,AyerKeroh,Melaka75450,Malaysia.

email:sivarao@utem.edu.my;kpe_siva@yahoo.com

JMES1319©IMechE2009

of2.5mmwasusedastheworkmaterial.Atotalof128experimentswerecarriedoutbasedon2kfactorialdesign,where2isthelevelnumberandkindicatesthenumberofusedfactors.SurfaceroughnessandcutqualitywereobservedbasedontheDIN2310-5standardtogetherwiththeDINENISO9013:2000standardforsurfacequalityanddimensionaltoler-anceevaluation.Allexperimentswerecarriedoutusinga3kWCO2lasercuttingmachinewitha4󰀋×8󰀋sacriﬁcialtable.Usingtheentireexperimentaldatasets,asurfaceroughness(Ra)predictivemodelwasdevelopedusingANFIS,andcomparativeinvestiga-tionsweremadebetweentheexperimentallyobservedandmodelledvalues.Thepredictionaccuracyyieldsabout70percent,provingthepowerofANFISinmodellingthenon-linearbehaviouroflaserpro-cessing.TheentireresearchprojectwassponsoredandfundedbyKaraPowerPte.Ltd(M),theleadingboilerandpressurevesselmanufacturingindustryinMalaysia.

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2370SivaraoSubramonian,PBrevern,NSMEl-Tayeb,andVCVengkatesh

2LITERATUREREVIEW

Variouspredictivemodelshavebeendevelopedandutilizedinmetalmachiningandprocessing;ANFISpredictionandmonitoring[3]andtoolwearcon-ditioningwithestimatedcuttingforceprovedtheexcellenceofANFISinempiricalmodelling[4,5].Theresultsproducedbythefuzzymodelwereusedefﬁ-cientlytooptimizeCNCdownmillingofAlumic-79forbettersurfaceroughness[6].ANFISpredictionsofsur-faceroughnessinthegrindingprocessproducedverysatisfactoryresults[7].Ananalyticalmodelwasdevel-opedtoevaluatemeltgeometryinthelasercuttingofsteels[8].Lasercuttingofthickceramicsubstrateswasinvestigatedtorelatelaserparameters,cutgeom-etry,andstresslevelbythepredictivemodel[9].Theformationofstriationinthelasercuttingofmetallicmaterialsledtoamathematicalmodeldevelopmentforthelasercuttingprocess[10].Thecapabilityof60Wlow-powerCO2laserprocessingwasstudiedbydevelopingatheoreticalmodeltoestimatedepthofcutintermsofmaterialpropertiesandcuttingspeed[11].Alumpedparametermodelwasdevelopedtostudythecutdepthofalaser[12].CO2lasercuttingparameterswereinvestigatedtostudytherelation-shipbetweengasandcuttingparametersrelatingtoitscutquality[13].Amodeloflaserprocessingwasdevelopedtoinvestigatecuttingspeedandlaserpowerintensity[14].Thermalmodellingoflasercuttingbyaccommodatingtheboundarylayereffectsofassist-inggas[15],andmodellingforkerfsizepredictionconcludingtheeffectoflaserpower,spotsize,andcut-tingspeedinﬂuence[16]werecarriedout.Kerfwidthwasmodelledusingalumpedparameteranalysistotheimprovemachinabilityofcompactedgraphiteiron[17].Numericalandexperimentalinvestigationsofgas-assistedlasermachiningofthickmetalswascar-riedouttoinvestigateappropriatepenetrationspeed[18].Theshapeofthecuttingsectionstronglydependsoncuttingspeed,laserpower,andfocalposition;however,assistinggaspressurehadaslighteffectoncutgeometry[19].Lasercuttingofinconelalloyandcutqualityassessmentwereinvestigatedwithlaserpulsingfrequency[20].Thestudyoflaserprocessingparametersoncutgeometrywasinvestigated[21].TheeffectofCO2laserpowerandfeedratewasinvestigatedinresponsetokerfwidthandsurfaceroughnessfor400seriesstainlesssteel[22].3

EXPERIMENTALSET-UPANDPROCEDURE

anindustrialexpert’sadviceandone-factor-at-a-time(OFAT)techniquewasemployedtoidentifysigniﬁ-cantparameters.Fromtheanalysis,thelastsevenparameters(italic)werefoundtobesigniﬁcantandwereselectedasdesignparameterstocarryouttheexperimentsbasedon2kfactorialdesign.Therefore,27=128experimentsweredesignedandarrangedasperthedesignmatrixinTable1.Alltheexperimentswerereplicatedoncewithdifferentstockmaterialstostudythevariance.TheRavaluesoftheorigi-nalandreplicatedrunswereaveragedandtakenasabsoluteobservedvaluesforANFISmodellingpur-poses.AlltheexperimentswereextensivelyplannedandcarefullycarriedoutaspertheprocessplanningshowninFig.1.Alltheobserveddatasetswerecrit-icallyanalysedbeforetheywereusedforANFIS-Ramodelling.3.1

Lasermachining

Lasermachiningisnormallyusedinprecisionindus-triesbecauseithastheabilitytocutintricateproﬁlesfeaturingextraordinaryshapes,corners,slots,andholeswithahighdegreeofrepeatabilityandasmallregionoftheheat-affectedzone[14].Inlasermachin-ing,surfaceroughnessisoneofthemainqualityevaluationfactorsbesideskerfwidthandstraightness.TheschematicoflasermachiningandkerfformationisshowninFig.2.Sevensigniﬁcantdesignparameterswereﬁnallyselectedandcontrolledinthisinvestiga-tion:SOD,FD,gaspressure(Pg),power(P),cuttingspeed(Sc),frequency(Freq),anddutycycle(Cd).Anozzlewithadiameterof0.5mmwasusedwithafocusedbeamof0.25mm.3.23.2.1

Experimentalparameters,machines,andequipments

Controlledsigniﬁcantparameters

Level

Variables

Power(watt)

Cuttingspeed(mm/min)Frequency(Hz)SOD(mm)FD(mm)

Pressure(0.1)(bar)Dutycycle(%)

Low16001800150010575

High2300250018001.50.5885

TherewereafewcontrollableprocessparametersontheselectedCO2lasermachine:gasjet,lenstype,gastype,nozzletype,gaspressure,focaldistance(FD),stand-offdistance(SOD),power,dutycycle,fre-quency,andcuttingspeed.Itwillbeveryuneconom-icaltocontrolallofthemsimultaneously;therefore,

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3.2.2Lasermachine

1.Model:HeliusHybrid2514CO2lasercuttingmachine.

2.Controller:FANUCSeries160i−L.3.Maximumcapacity:3kW.

4.Laserbeamwavelength:10.6µm.

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Modellingoflaserprocessingcutqualitybyanadaptivenetwork-basedfuzzyinferencesystem2371

Table1

GasCutDuty1stRun,Replicated,AveragePure

RunSODFDpressurePowerspeedFrequencycycleRaRaRaerrorno.(mm)(mm)(0.1B)(W)(mm/min)(Hz)(%)(micron)(micron)(micron)(%)1234567101112131415161718192021222324252627282930313233343536373839404142434445474849505152535455565758596061626365

1.51.51.5111.51.51.511.51.51.5111.511.51.511.5111.511.51.51.511.51.5111.5111.511.5111.51.51111.511.51111.511.51.51.51111.51.51.51.51.51

0.500.5000000.50.50.50.5000.500.500.5000.50.500.5000.500.500.50.50.50.500.50.5000.5000.50.500000.500.50.5000.500000.500.50.50

55858558885855585585888555585885555855885588555885885888858558555

23001600230016001600230023002300160016002300230023002300160016002300230016001600160023001600160023002300230016002300160023002300160023001600230023001600160016001600160023002300160016002300230016002300160023002300230016002300230016002300160016001600230016002300

18002500250018001800180025001800250025001800250018001800250025002500250025001800180018001800250025002500180018002500180025002500180025002500250025002500250018001800250018002500250018002500180025001800180025001800180025001800180025002500180018002500250025001800

18001800150018001500180015001800150015001500180018001800150015001500180018001500180015001800150015001500150018001800150018001800150015001800180018001800180018001500150015001800150015001500150018001500150015001500150015001500180015001500180018001800180015001500

8575858575758585757585758575758575758585858585758575858585757575757585858575857585857575757575757575857585857575858585858575858585

1.766.352.3.025.752.055.029.308.127.165.544.983.205.672.516.582.692.541.167.5212.6513.026.992.051.692.226.012.192.687.952.352.985.344.324.551.2.404.003.028.353.698.919.386.807.197.002.382.952.522.996.462.197.834.8.984.014.3.003.012.942.2.304.096.366.90

1.745.073.472.6.092.274.3611.208.928.884.725.123.045.452.856.402.432.301.468.2010.399.168.071.972.392.184.292.672.486.491.933.145.0.365.452.171.863.662.787.373.6510.819.266.429.036.062.542.253.003.336.861.979.633.466.263.575.852.702.853.082.922.544.476.067.50

1.755.713.182.844.922.1.6910.258.528.025.135.053.125.562.686.492.562.421.317.8611.5211.097.532.012.042.205.152.432.587.222.143.065.204.345.002.032.133.832.907.863.679.869.326.618.116.532.462.602.763.166.662.088.734.165.623.795.372.852.933.012.782.424.286.217.20

1.1420.1620.0711.9228.8710.7313.1520.439.8524.0214.802.815.003.8813.552.749.679.4525.869.0417.8729.6515.453.9041.421.8028.6221.927.4618.3617.875.375.240.9319.7814.8122.508.507.9511.741.0821.321.285.5925.5913.436.7223.7319.0511.376.1910.0522.9928.8125.7010.9719.6310.005.324.7610.6110.439.294.728.70

ANFISComparativepredictederror(%)1.826.023.242.585.072.324.7410.496.067.5.094.252.995.692.836.502.783.011.9.0410.1110.598.321.982.001.995.242.282.316.272.553.045.205.015.571.962.563.722.817.693.4210.0510.267.027.986.052.322.803.024.037.012.549.055.343.992.774.732.083.252.992.793.115.005.877.01

4.005.431.9.153.057.411.072.3428.875.7420.2715.844.172.345.600.158.5924.3825.1915.0112.244.5110.491.491.969.551.756.1710.4713.1619.160.650.0015.4411.403.4520.192.873.102.166.811.9310.096.201.607.355.697.699.4227.535.2622.123.6728.3729.0026.9111.9227.0210.920.660.3628.5116.825.482.(Continued)

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2372SivaraoSubramonian,PBrevern,NSMEl-Tayeb,andVCVengkatesh

Table1Continued

ANFISComparativepredictederror(%)

12.6110.4717.8121.8611.087.2319.3812.458.6612.440.3314.411.9315.671.355.192.6712.296.2214.1627.2716.0315.9326.882.728.3313.6614.0213.310.833.334.0713.6621.7516.4329.3915.711.919.5618.357.8713.7010.6920.6020.008.956.0610.180.145.637.259.224.1013.070.331.9815.4312.2723.5313.332.370.8520.60

GasCutDuty1stRun,Replicated,AveragePure

RunSODFDpressurePowerspeedFrequencycycleRaRaRaerrorno.(mm)(mm)(0.1B)(W)(mm/min)(Hz)(%)(micron)(micron)(micron)(%)66676869707172737475767778798081828384858687809192939495969799100101102103104105106107108109110111112113114115116117118119120121122123124125126127128

1.51.511.511111.51.51.51.51.511.511.51.5111.511.51111.511.511.51111.51.51111.51.51.51.511.51.5111.511.511111.5111.5111.51

0.50.50.500.5000.50000.500.50.50.5000.500.500.50.5000.5000.50.500.50.500.50.500000.50.50.500.50.50.500.50.50.5000.500.50.50.50000.5

888558858885858858558588555585885858885585885588858858588555588

160016001600160023002300230016002300230016002300160023002300230016001600160016002300160023001600230023001600160023001600160016001600230016001600160023002300230016002300230023002300160023002300230016001600160023002300160016002300230023001600160016001600

180025001800250018001800180018001800250018002500180025002500250018001800180018001800180018002500250025001800250025001800250025001800180025002500250025002500180025001800180018001800250018002500250025001800180018002500250025002500180018001800250018001800

180018001800150018001500180018001800150015001800180015001800150018001800150015001800150015001500180015001800180015001500180015001800150018001500180015001800150015001800180018001800180018001500180018001500150015001800150018001800180015001800180015001500

757575758585757575758575858585757575757585858585858575758585857585758585757575758575757585858585757585857585858585757575857575

7.826.667.242.992.3.083.3310.027.117.286.122.502.313.9.014.552.502.216.033.922.012.5510.092.012.353.392.006.878.355.555.396.252.383.504.503.502.668.054.023.504.116.345.402.262.226.558.951.566.992.658.222.758.301.676.557.992.012.771.762.651.826.991.85

8.846.528.261.953.613.563.079.907.218.805.941.941.834.0610.255.092.742.515.874.841.732.199.751.712.793.332.107.258.336.535.436.032.163.125.242.762.567.633.722.823.776.365.262.401.886.6310.851.787.193.039.162.8.281.395.718.171.752.611.2.751.567.052.13

8.336.597.752.473.253.323.209.967.168.046.032.222.074.029.634.822.622.365.954.381.872.379.921.862.573.362.057.068.346.045.416.142.273.314.873.132.617.843.873.163.946.355.332.332.056.599.901.677.092.848.692.828.291.536.138.081.882.691.702.701.697.021.99

13.047.282.105.9014.096.3734.783.0124.912.15.583.087.812.581.2011.201.416.5420.8.042.946.0522.402.5420.782.112.014.6513.769.5011.875.079.602.5513.572.652.656.3223.475.0013.932.3814.121.993.378.3414.932.3618.722.501.773.085.002.335.538.050.247.2317.665.990.745.233.525.9.242.5810.8.0316.445.6721.144.053.763.025.227.997.463.5019.432.588.274.250.327.222.594.766.191.8515.321.1.226.0021.2310.5014.101.502.867.0814.343.0011.449.325.093.080.247.9516.771.3312.826.112.257.9212.941.595.783.026.822.103.772.3414.291.730.866.9615.141.58

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Modellingoflaserprocessingcutqualitybyanadaptivenetwork-basedfuzzyinferencesystem2373

CO2 Laser Machining Quality Investigation & Modeling 5.ThelasersourceusedtocreatealaserbeamisCO2gas.TheactualingredientismixtureofN2(55percent),He(40percent),andCO2(5percent)withpurityof99.995percent.6.Pressure:maximum2bar.3.2.3Workmaterials1.2.3.4.

DIN17155HIIstandard.2.5mmMn–Mo.Grade:B.

Tensilestrength:550–690MPa.

Process Parameters IdentificationMaterial Identification and Final Selection One Factor at a Time (OFAT) and Expert Advice 3.2.4Proﬁlometer

Design Parameters Identification Full Factorial analysis 1.MitutoyoproﬁlometerSJ301.2.Samplinglengthrange(0.8–8).3.2.5Scanningelectronmicroscope1.EVO50XVP.2.Englandmade.

3.2.6Datacollectionandinterpretations

1.Alltheexperimentalmaterials,procedures,datacollections,analysis,andsoonareconductedasperthestandardrecommendationsof‘lasercuttingofmetallicmaterials’Germanstandard,DIN2310-5.2.TheDINENISO9013:2000standardwasreferredtoforevaluatingthequalityofcuttingsurfaces,qualityclassiﬁcations,anddimensionaltolerances.3.3

Experimentalobservation

Experimentation and Ra Observation Based on DIN Laser Germany Metal Cutting Standard Visual Analysis/Observation ANFIS ModelingComparative Analysis and Model ValidationModel Recommendation to the Sponsored IndustryFig.1Investigationprocessplanning

3.3.1Surfaceroughnessmeasurement

Thesurfaceroughnessofanymachinedpartsaysagreatdealabouthowlongtheseitemswilllast.Ithasamarkedinﬂuenceonthefunctionalpropertiesofthemachinedpartandlargemicro-geometricaldeviations,whichcouldcausenon-uniformwearatdifferentsectionsofthesurface.Surfaceroughnesswasmeasuredatone-thirdfromthetoptransversely.TheobserveddatasetswiththeirrespectiveresponsesaretabulatedinTable1.

3.3.2Micro-qualityvisualization(SEM)

Ascanningelectronmicroscopewasusedtomicro-graphthecommondefectsoflasermachining.Figure3showscompletesectionviewofthecutfacewithmicro-defects:striation,dross,recast,andmicro-crack.Figure4showsthemagniﬁedtophalfofthecutpart,wherethecommonstriationanddrossexistencearevisible,whereas,Fig.5showsthebottomhalfofthesamespecimenexaminedinFig.4,wheretherecastphenomenonisseen.Figure6showsthepresenceofdrosspitsandhairlinecracks,whicharealmost

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Fig.2Schematicoflasermachiningandkerfformation

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2374SivaraoSubramonian,PBrevern,NSMEl-Tayeb,andVCVengkatesh

Fig.3Fullviewofthecutfacewithmajordefects

Fig.5Inclusions,striation,andrecastphenomenon

Fig.6

Fig.4

Magniﬁedstriationanddross

Evidenceofmicro-cracks

perpendiculartothegasjetejectionlines.Figure7showsseveredrossformationatthebottomsideofthepart.Thisnormallyhappensbecauseofthere-solidiﬁcationofmoltenmetalbeforeitcouldbefullyblowndownbytheejectinggaspressurewhilecut-ting.Allthementioneddefectsarequitecommoninlasercutting,butcanbeminimizedbyﬁnetuningtheprocessparameters.4

ANALYSISOFVARIANCEANALYSISFORDESIGNPARAMETERS

Analysisofvariancewascarriedouttoinvestigatethesigniﬁcanceofdesignparameters.Theyweresta-tisticallyanalysedandevaluatedbyprobabilityplot,Paretochart,maineffectplot,andresiduals,asshowninFigs8to11,respectively.AnalysisbythestatisticaltoolMinitab14provedthatalltheparametersbasedonanindustrialexpert’sadviceandOFATexperimen-tationshaveasigniﬁcanteffectonsurfaceroughness.

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Fig.7Severedrossformation

Figure8showsthesigniﬁcantparameterswiththeirrespectivemainandinteractioneffectfortargetedresponseparameterRa.TheParetochartinFig.9clearlyindicatestheselectedparameterswiththeirpossibleinteractions,withthelimitsetto1.98and

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Modellingoflaserprocessingcutqualitybyanadaptivenetwork-basedfuzzyinferencesystem2375

Fig.8Normalprobabilityofanalyseddatasets

Fig.9Paretoplotwitnessingsigniﬁcantparameters

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2376SivaraoSubramonian,PBrevern,NSMEl-Tayeb,andVCVengkatesh

Fig.10Maineffectinteractionofdesignparameters

Fig.11

Replicateddatasetsanalysedforresidualinves-tigation

automaticallytoacquiredesiredmembershipfunc-tionsofthefuzzyif–thenrulestoachievegoals.Itcanbetrainedtodevelopif–thenfuzzyrulesanddeterminemembershipfunctionsforinputandout-putvariablesofthesystem.ExpertknowledgecanbeeasilyincorporatedintothestructureofANFIS,wheretheconnectioniststructureavoidsfuzzyinferenceandentailssubstantialcomputationalburden.TodescribeANFISarchitectureinbrief,considertwofuzzyif–thenrulesthatwerebasedontheﬁrst-orderSugenomodel:

(a)rule1:if(xisA1)and(yisB1)then(f1=p1x+

q1y+r1);

(b)rule2:if(xisA2)and(yisB2)then(f2=p2x+

q2y+r2);xandyareinputs,AiandBiareappropriatefuzzysets,p1,q1,andr1arecertainparameters,andf1andf2contributetotheoutputofthesystem.ThepossibleANFISarchitectureforimplementingtheserulesisshowninFig.12.Ithasaﬁve-layerarchitec-ture;acircleandasquareindicateﬁxednodesandadaptivenodes,respectively,whoseparametersarechangedduringadaptationortraining.ThetaskofthelearningalgorithmofthisarchitectureistotuneallthemodiﬁableparameterstomatchANFISoutputwiththetrainingdata.Therefore,thehybridlearningalgorithmusesboththeleast-squaresmethodandthe

JMES1319©IMechE2009

5percentofthealphavalue.Figure10showsthesig-niﬁcanceoftheselectedparameterswiththeirlowandhighlevelvalues,whereasFig.11showstheresidu-alsandﬁtanalysiscarriedoutfortheexperimentaldatasets.

ADAPTIVENETWORK-BASEDFUZZYINFERENCESYSTEM

ANFISisafuzzyTakagi–Sugenomodel,whichisputtogetherintheframeworkofadaptivesystemstofacilitatelearningandadaptation.Suchaframeworkmakesthemodelsystematicandlessdependentonexpertknowledge.TheANFIScontrollercanevolve

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Layer5:aﬁxednodewithafunctionofsummation

󰀁

¯ifiw(5)O5,1=overalloutput=

Thisisthebasicprincipleofhowtheinputvectorisfed

throughthenetworklayerbylayertogenerateANFIS.6

Fig.12

FundamentalANFISarchitecture

ANFISMODELLING

back-propagationalgorithmtoidentifyoptimalvaluesfortheparameterspi,qi,andri,wherethedetailsofthealgorithmformulationareasfollowsLayer1:adaptivenodesO1,i=µAi(x),O1,i=µBi−2(x),

i=1,2i=3,4

µAi(x)andµBi(x):anyappropriateparameterizedmembershipfunctionsµAi(x)=

1+[(x−ci)2/ai2]bi

(1)

{ai,bi,ci}→premiseparameters

Layer2:ﬁxednodeswithafunctionofmultiplicationO2,i=wi=µAi(x)×µBi(x),i=1,2(ﬁringstrengthofarule)

(2)

Layer3:ﬁxednodeswithafunctionofnormalization¯i=O3,i=w

w1+w2

i=1,2(normalizedﬁringstrength)

(3)

Layer4:adaptivenodes

¯ifi=w¯i(pix+qiy+ri)O4,i=w

{pi,qi,ti}→consequentparameters

(4)

ThecommerciallyavailableMATLAB2006ahasbeen

utilizedasatooltomodel,train,analyse,andtestsur-faceroughnesspredictions.Alltheexpertrulesandconnectionswereprogrammedandinterconnectedaccordingtotheinputandoutputdatasetsofthemodellingenvironment.SomeoftheANFISnetworkvariableswerefedbytrialanderrorinconjunctionwithﬁnetuninginanticipationofgoodmodeldevel-opment.Partoftheautoprogrammedfuzzyexpertrules,fuzzy-basedtoolbox,andANFISmembershipfunctionsareillustratedinthisarticlethroughFigs13to15.PartofthedevelopedfuzzyexpertrulesinthismodellingtechniqueisshowninFig.13,andtheserulesareintegratedbasedonnetworkconnec-tionsassignedtothesystem.Figure14showspartofthefuzzytoolbox-basedANFISmodellingforsurfaceroughnessprediction,wherethetoolboxwascriti-callyanalysedtoobservetheinteractionsofalltheincorporateddesignparameters.

Theﬁnalmembershipfunctionofeachmachiningvariableusedinmodellingenabledsmoothandcon-cisenotationbell-shapedmembershipasshowninFig.15,wheremembershipfunctionsplayamajorroleindevelopingagoodpredictivemodel.Three-dimensionalsurfacemodelsweredevelopedtostudytheinteractionsbetweendesignparametersandtheirbehaviourovertheirrespectiveobjectivefunction.Figures16to21aretheANFISsurfacemodelsshow-ingtheireffectsandsigniﬁcances,whereasFig.16showstheinteractionofcuttingspeedandSODdistanceforRa.Surfaceroughnessesbelow5µmwereachievedbyoptimallysettingcuttingspeedto2400mm/minandSODto1.2mm.Ontheother

Fig.13

JMES1319©IMechE2009

PartofANFISgeneratedrules

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2378SivaraoSubramonian,PBrevern,NSMEl-Tayeb,andVCVengkatesh

Fig.14PartoftheruleviewerofthefuzzytoolboxinANFISplatform

Fig.15Finalmembershipfunctionsforeachmachiningparameter

hand,Fig.17showsthatthebestsurfacerough-nesscouldbeobtainedifSODandfrequencyweresetathigherlevelswithintherangeofexperimentalvalues.

Figure18showsthatlowerlevelsofSODandhigherlevelsdutycyclewithinexperimentalvaluescouldpro-ducegoodsurfaceroughness.Figure19showstheeffectofFDonSOD,wheresurfaceroughnesswasfoundtobealmostproportionaltoSODbutinverselyproportionaltothereductionofFD.Figure20shows

Proc.IMechEVol.223PartC:J.MechanicalEngineeringScience

theeffectonsurfaceroughnesswhengaspressureandSODarecontrolled,wherealowerlevelofgaspres-surewithahigherlevelSODresultedinbettersurfaceroughness.ItisalsoclearthatFDvariationdoesnothaveasigniﬁcanteffectonRaascomparedtogaspres-sure,whichisverysensitivetoitsresponse.Figure21showstheinteractionofpowerandSODoverRawhereRawasfoundtobebetteratahigherlevelofSODcom-binedwithalowerlevelofpowerwithintherangeofexperimentalvalues.

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Modellingoflaserprocessingcutqualitybyanadaptivenetwork-basedfuzzyinferencesystem2379

Fig.16

SurfacemodelofcuttingspeedandSODforsurfaceroughness

Fig.19

SurfacemodelofFDandSODforsurfacerough-ness

Fig.17

SurfacemodeloffrequencyandSODforsurfaceroughness

Fig.20

SurfacemodelofgaspressureandSODforsurfaceroughness

Fig.18

SurfacemodelofdutycycleandSODforsurfaceroughness

Fig.21

SurfacemodelofpowerandSODforsurfaceroughness

7RESULTSANDDISCUSSION

ExperimentallyobservedandANFISpredictionswerecomparedinFig.22.Ingeneral,theexperimentallyobservedsurfaceroughnessvaluesforlasermachining

ofthespeciﬁedworkmaterialfallwithintherangeoftheDINstandard[23],whichare10to15µmformetalthicknessesof1–6mm.Thus,theycanbeconsideredasexcellentexperimentaloutput,whichprovesthatthelasermachiningexperimenthasbeenconducted

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2380SivaraoSubramonian,PBrevern,NSMEl-Tayeb,andVCVengkatesh

2.3.

Fig.22

ComparativeanalysisofsurfaceroughnessforexperimentallyobservedandpredictedANFIS

inproperstepsasperthedesignoftheexperiment.ThisalsoprovesthatOFATscreeningandanindustrialexpert’sadviceinidentifyingsigniﬁcantparameterswerehighlysuccessful.Fromtheobservation,experi-mentnumbers5and27witnessedhighestpureerrorreachingalmost30percent,andexperimentnum-bers34and94witnessedleastpureerrorofabout1percent.Ontheotherhand,thehighestobservedRavaluewasslightly>11percent,inwhichitisabout20percentbetterthantheexpectedvaluesbytheDINandTRIUMPFstandards,thusprovingthattheexperimentsweredesignedandconductedexcellently.Fromthecomparativeanalysis,itisclearthatANFISmodellingwithonadequateamountofexperimentaldatasets,precisefuzzyexpertrules,excellentinferencesystem,andgoodnetworkselectionwithpropercon-nectionshasenabledagoodmodelwitherrornotexceeding29percent.TheexcellenceoftheANFISpredictivemodelandtheprecisionoftraineddatahavebeenwellacceptedlaserprocessingwork,whereerrorsarewithintheacceptablerangeofmodellingtechniquesandmatchwellthestatementsofpreviousresearchersthattheANFISmodelpossessesanexcel-lentabilityofrules,training,andinferencesystemgeneralizationtopredictnon-linearconditions.Asforthefuturework,themodelistobeexperimentallyvalidatedtoitsbestinterpolationandextrapolationlimits.

trainingcapability,whichhasenableddevelop-mentofagoodmodelwithpredictionerrorsbelow30percent.

AlltheexperimentallyobservedvalueswerewithintherangeofthereferredDINstandardbenchmark-ingtheresearchmethodology.

Satisfactorysurfaceroughnesswasobtainedwiththeinteractioneffectof(SODˆ:frequencyˆ),(SODv:dutycycleˆ),(FDˆ:SODv),(powerv:SODˆ),(cuttingspeedˆ:SODv)withintherangeofexper-imentalvalueswherevandˆdenotelowerandhigherlevels,respectively.Ontheotherhand,fre-quencyandSODdonothaveasigniﬁcanteffectonRawhentheyaretreatedasindependent/mainfactors.

Thisarticlehasdemonstratedthefeasibilityoftak-ingadvantageoftheANFISmodeltopredictthesurfaceroughnessusingMATLABasthetoolandplatformtosolveprecisionmachiningproblemsformetalcuttingindustries.

Experimentalvalidationsaretobeconductedinfuturetovalidatethemodelextremeranges.

ACKNOWLEDGEMENTS

TheauthorsthankDrKhorWongGhee,EngrVijayan,andEngrSegaran,fortheirsincereguidance,advice,andexpertknowledgesharinginconductingthislasermodellingresearchproject.TheauthorsalsothankthetoplevelmanagementofKaraPowerPte.Ltdforsponsoringandmakingtheresearchprojectsuccessful.REFERENCES

1Yilbas,B.S.Lasercuttingqualityassessmentandther-malefﬁciencyanalysis.J.Mater.Process.Technol.,2004,155–156,2106–2115.

2HajraChoudhry,K.,HajraChoudhry,A.K.,andRoy,N.Elementsofworkshoptechnology,11thedition,vol.1,2000(ManufacturingProcesses,MediaPromoters&PublishersPrivateLtd,Mumbai,India).

3Li,X.,Dong,S.,andVenuvinod,P.K.Hybridlearningfortoolwearmonitoring.Int.J.Adv.Technol.,2000,16,303–307.

4Kothamasu,R.,Huang,S.H.,andMarinescu,I.Intelli-genttoolwearestimationforhardturning:neural-fuzzymodelingandmodelevaluation.InProceedingsofthe2002InternationalCIRPDesignSeminar,HongKong,16–18May2002,pp.56–.5Li,X.,Li,H.-X.,Guan,X.-P.,andDu,R.Fuzzyestimationoffeedcuttingforcefromcurrentmeasurement–acasestudyonintelligenttoolwearconditionmonitoring.IEEETrans.Syst.ManCybern.C,Appl.Rev.,2004,34,4.

6Dweiri,F.,Al-Jarrah,M.,andAl-Wedyan,H.FuzzysurfaceroughnessmodelingofCNCdownmillingofAlumic-79.Int.J.Mater.Process.Technol.,2003,133,266–275.

8CONCLUSIONS

Thepurposeofthisresearcharticlewastoinvesti-gatethecapabilityofdevelopingasurfaceroughnesspredictivemodelbyANFISforlaserprocessingusingselecteddesignparameters.Thefollowingconclusionscanbedrawn.

1.ANFISwasfoundtohaveanexcellentcapabil-ityforcombiningfuzzyexpertruleswithnetwork

Proc.IMechEVol.223PartC:J.MechanicalEngineeringScience

Downloaded from pic.sagepub.com at Shanghai Jiaotong University on March 29, 2012

Modellingoflaserprocessingcutqualitybyanadaptivenetwork-basedfuzzyinferencesystem2381

7Samhouri,M.S.andSurgenor,B.W.Surfaceroughnessingrinding:on-linepredictionwithadaptiveneuro-fuzzyinferencesystem.Trans.NAMRI/SME,2005,33,14–23.

8Campana,G.,Tani,G.,andTomesani,L.Predictionofmeltgeometryinlasercutting.Appl.Surf.Sci.,2003,208–209,142–147.

9Tsai,C.andChen,H.Lasercuttingofthickceramicsubstratesbycontrolledfracturetechnique.I.J.Mater.Process.Technol.,2003,136,166–173.

10Wee,L.M.andLi,L.Ananalyticalmodelforstriation

formationinlasercutting.Appl.Surf.Sci.,2005,247,277–284.

11Mahdavian,S.M.andZhou,B.H.Experimentalandthe-oreticalanalysisofcuttingnonmetallicmaterialsbylowpowerCO2laser.J.Mater.Process.Technol.,2004,146,188–192.

12Li,Y.G.,Latham,W.P.,andKar,A.Lumpedparame-termodelformultimodelasercutting.Opt.LasersEng.,2001,35,371–386.

13Yilbas,B.S.ExperimentalinvestigationintoCO2laser

cuttingparameters.J.Mater.Process.Technol.,1996,58,323–330.

14Yilbas,B.S.Effectofprocessparametersonthekerf

widthduringthelasercuttingprocess.Proc.IMechE,PartB:J.EngineeringManufacturing,2001,215(B10),1357–1365.DOI:10.1243/0954411519132.

15Yilbas,B.S.andSahin,A.Z.Oxygenassistedlasercutting

mechanics–alaminarboundaryapproachincluding

thecombustionprocess.Opt.LaserTechnol.,1995,27,175–184.

Alﬁlle,J.P.,Pilot,G.,andDePrunele,D.NewpulsedYAGlaserperformancesincuttingthickmetallicmaterialsfornuclearapplications.Int.Soc.Opt.Eng.,1996,27,134–144.

Skvarenina,S.andShin,Y.C.Laser-assistedmachiningofcompactedgraphiteiron.Int.J.Mach.ToolsManuf.,2006,46,7–17.

Makashev,N.K.,Buzykin,O.G.,andAsmolov,E.S.Computationalandexperimentalinvestigationofgas-assistedlasercuttingofthickmetal.Proc.SPIE-Int.Soc.Opt.Eng.,1996,2713,248–252.

Duan,J.,Man,H.A.,andYue,T.M.ModellingthelaserfusioncuttingprocessIII.Effectsofvariousprocessparametersoncutkerfquality.J.Phys.D,Appl.Phys.,2001,34,2143–2150.

Yilbas,Z.Classiﬁcationofstriationpatternsusinganeu-ralnetworkinCO2lasercutting.LaserEng.,1998,7,25–37.

Sundar,J.K.S.,Thawari,G.,Sundararajan,G.,andJoshi,S.V.InﬂuenceofprocessparametersduringpulsedNd:YAGlasercuttingofnickel-basesuperalloys.J.Mater.Process.Technol.,2005,170,229–239.

Cheraghi,S.H.,Rajaram,N.,andSheikh-Ahmad,J.CO2lasercutqualityof4130steel.Int.J.Mach.ToolsManuf.,2003,43,351–358.

DIN2310-5andTRIUMPF,lasercuttingqualityevalua-tionstandard,2000,1–45.

Downloaded from pic.sagepub.com at Shanghai Jiaotong University on March 29, 2012

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