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Application of response surface methodology in the optimization of cutting conditions for surface roughness.pdf
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Journal of Materials Processing Technology 170 (2005) 1116Application of response surface methodology in the optimizationof cutting conditions for surface roughnessH.Oktema, T. Erzurumlub, H. KurtaranbaDepartment of Mechanical Engineering, University of Kocaeli, 41420 Kocaeli, TurkeybDepartment of Design and Manufacturing Engineering, GIT, 41400 Gebze, Kocaeli, TurkeyReceived 16 July 2004; received in revised form 12 March 2005; accepted 12 April 2005AbstractThis paper focuses on the development of an effective methodology to determine the optimum cutting conditions leading to minimumsurface roughness in milling of mold surfaces by coupling response surface methodology (RSM) with a developed genetic algorithm (GA).RSM is utilized to create an efficient analytical model for surface roughness in terms of cutting parameters: feed, cutting speed, axial depthof cut, radial depth of cut and machining tolerance. For this purpose, a number of machining experiments based on statistical three-level fullfactorial design of experiments method are carried out in order to collect surface roughness values. An effective fourth order response surface(RS) model is developed utilizing experimental measurements in the mold cavity. RS model is further interfaced with the GA to optimize thecutting conditions for desired surface roughness. The GA reduces the surface roughness value in the mold cavity from 0.412H9262m to 0.375H9262mcorresponding to about 10% improvement. Optimum cutting condition produced from GA is verified with the experimental measurement. 2005 Elsevier B.V. All rights reserved.Keywords: Milling; Cutting conditions; Surface roughness; Injection molding; Response surface methodology; Genetic algorithm1.tribMillingducingpartsT6aircraftastensileticoffsurffirre0924-0136/$doi:10.1016/j.jmatprotec.2005.04.096IntroductionRecent developments in manufacturing industry have con-uted to the importance of CNC milling operations 1,2.process is required to make mold parts used for pro-plastic products. It is also preferred in machining moldmade of Aluminum 7075-T6 material. Aluminum 7075-material as chosen in this study is commonly utilized inand die/mold industries due to some advantages suchhigh resistance, good transmission, heat treatable and highstrength 3,4.The quality of plastic products manufactured by plas-injection molding process is highly influenced by thatmold surfaces obtained from the milling process. Sur-ace quality of these products is generally associated withace roughness and can be determined by measuring sur-ace roughness 5. Surface roughness is expressed as thegularities of material resulted from various machiningCorresponding author. Tel.: +90 262 742 32 90; fax: +90 262 742 40 91.E-mail address: hoktem.tr (H.Oktem).operations.fsymbol,meticmeananSurftingsuchwditionsmachiningthisditionssuchmodelstoolinbeen718 see front matter 2005 Elsevier B.V. All rights reserved.In quantifying surface roughness, average sur-ace roughness definition, which is often represented with Rais commonly used. Theoretically, Rais the arith-average value of departure of the profile from theline throughout the sampling length 6. Rais alsoimportant factor in controlling machining performance.ace roughness is influenced by tool geometry, feed, cut-conditions and the irregularities of machining operationsas tool wear, chatter, tool deflections, cutting fluid, andorkpiece properties 7,11,16. The effect of cutting con-(feed, cutting speed, axialradial depth of cut andtolerance) on surface roughness is discussed instudy.Several researchers have studied the effect of cutting con-in milling and plastic injection molding processesas in vacuum-sealed molding process 5. Analyticalhave been created to predict surface roughness andlife in terms of cutting speed, feed and axial depth of cutmilling steel material 8,9. An effective approach has alsopresented to optimize surface finish in milling Inconel10.12 Processingforsurfoped.methodologymodeldegeneticleadingisaxialradialdictedepresentture.polynomialnatesGAs.optimizationtions.2.2.1.thementsesideringaxialingcarriedcuttingisbasedMillingconditionsmillingfrom2.2.10TLodesignCuttingFeed,CuttingAxialRadialMachiningFig. 1. Mold part.is PVD AlTiN coated with solid carbide. It has the helixangle of 45and rake angle of 10. Machining experimentsare performed in the mold cavity on aluminum (7075-T6)block with dimensions of 120 mm 120 mm 50 mm. Thechemical composition of workpiece material is given in thefollowing specification (wt.%): 1.6 Cu, 2.5 Mg, 0.23 Cr, 5.40Zn. The hardness of workpiece is measured as 150 BHN.The mechanical properties of aluminum material are: ten-sile strength of 570 MPa, yield strength of 505 MPa, shearstrength of 330 MPa and elongation of 11%.Surface roughness is measured with Surftest 301 pro-H.Oktem et al. / Journal of MaterialsIn this study, a fourth order response surface (RS) modelpredicting surface roughness values in milling the moldaces made of Aluminum (7075-T6) material is devel-In generating the RS model statistical response surface(RSM) is utilized. The accuracy of the RSis verified with the experimental measurement. Theveloped RS model is further coupled with a developedalgorithm (GA) to find the optimum cutting conditionto the least surface roughness value. Cutting conditionrepresented with cutting parameters of feed, cutting speed,depth of cut and machining tolerance. The pre-optimum cutting condition by GA is validated with anxperimental measurement.The RS model and GA developed and utilized in this studyseveral advantages over other methods in the litera-The RS model is a higher order and more sophisticatedmodel with sufficient accuracy. The GA elimi-the difficulty of user-defined parameters of the existingDetails of the RS model generation by RSM and theprocess by GA are given in the following sec-Experimental proceduresPlan of experimentsAn important stage of RS model generation by RSM isplanning of experiments. In this study, cutting experi-are planned using statistical three-level full factorialxperimental design. Cutting experiments are conducted con-five cutting parameters: feed (ft), cutting speed (Vc),depth of cut (aa), radial depth of cut (ar) and machin-tolerance (mt). Overall 35= 243 cutting experiments areout. Lowmiddlehigh level of cutting parameters inspace for three-level full factorial experimental designshown in Table 1. Ranges of cutting parameters are selectedon recommendation of Sandvik Tool Catalogue 12.operations are performed at the determined cuttingon a DECKEL MAHO DMU 60 P five axis CNCmachine. Surface roughness (Ra) values are measuredthe mold surfaces.Tool and materialCutting tool used in experiments has the diameter ofmm flat end mill with four teeth. The material of the toolable 1wmiddlehigh levels of cutting parameters in three-level full factorialof experimentparameters Three- level valuesft(mm/tooth) 0.080.1050.13speed, Vc(m/min) 100200300depth of cut, ar(mm) depth of cut, ar(mm) 11.52tolerance, mt(mm) 0.0010.00550.01filometerpling.mathematicalvastimes.model.2.3.thecations.utilizedpositionandminumOrthoseis2.4.manufgratedCNCfTechnology 170 (2005) 1116at traverse length of 2.5 mm along centerline of sam-Converting the measurement into a numerical value,definition of Rais used. Since this way of con-ersion is common in the literature it is adopted in this studywell 79. Each Rameasurement is repeated at least threeAverage of three Ravalues is saved to establish RSMold partsThe mold part used in this study is utilized to producecomponents of an orthose part in biomechanical appli-It is shown in Fig. 1. Orthose parts are generallyin walking apparatus that holds human legs in stableduring walking. It binds the kneecap region of legis equipped with cylindrical bars that are made of alu-material in diameter of 12 mm and length of 300 mm.part consists of three main components; one of thememployed as the working model in this study.Manufacturing the components of orthose partThree machining processes are implemented in order toacture each component of the orthose part in an inte-manner. Firstly, the selected component is machined inmilling machine. Ravalues are then taken from the sur-aces in the mold cavity. Secondly, plastic product is injectedProcessinginacetalmaterial.sityviscosityFinallyingillustrated3.surfstatisticalniquephase.H.Oktem et al. / Journal of MaterialsFig. 2. The parts obtained from threeFig. 3. The stages taken in creating a response surface model by RSM.plastic injection machine produced by ARBURG. Poly-(POM) C 9021 material is used to inject the polymerThe properties of polymer material has the den-of solution 1.2 g/cm3, the ejected temperature of 165C,of 50 Pa s and melt flow-fill rate of 0.8 cm3/min., net casting process is applied for producing die cast-part. Mold part, plastic product and die casting part arein Fig. 2.Response surface model for surface roughnessRS model, which is an analytical function, in predictingace roughness values is developed using RSM. RSM usesdesign of experiment (experimental design) tech-and least-square fitting method in model generationIt is summarized in Fig. 3. RSM was originally devel-opedandisfwhereoftoMAingAllmodelsgeneratedbecreatingminedfordatatrainingdatalizedvrathersetfroughnesstheFig. 4. Comparison of experimental measurementsTechnology 170 (2005) 1116 13machining process.for the model fitting of physical experiments by BoxDraper 13 and later adopted in other fields. RS modelformulated as following polynomial function:nsummationdisplaynsummationdisplaynsummationdisplay= a0+i=1aixi+i=1 j=1aijxixj+ (1)a0, aiand aijare tuning parameters and n is the numbermodel parameters (i.e. process parameters). In this study,create RS model, a computer program has been written inTLAB programming language.The RS program developed has the capability of creat-RS polynomials up to 10th order if sufficient data exist.cross terms (i.e. interactions between parameters) in thecan be taken into account. RS models can also bein terms of inverse of parameters. That is, xicanreplaced as1xi(i.e. inversely) in RS model if desired, inthe RS models, 243 surface roughness values deter-based on three-level full factorial experimental designfive parameters (ft, Vc, aa, arand mt) are used The 243sets for surface roughness are divided into two parts;data set and the check (i.e. test) data set. Trainingset includes 236 surface roughness values and is uti-in model fitting procedure. Because of large number ofalues and to save space, training data is shown in Fig. 4,than in a table. In Fig. 4, abscissa indicates the datanumber and the ordinate indicates the corresponding sur-ace roughness value. Check data sets include seven surfacevalues and are used in checking the accuracy ofRS model. Check data sets are shown in Table 2. Theywith RS prediction for surface roughness.14 ProcessingTTheSet1234567TTheReciprocalareinchecktoprogram.withTaofRfitsThedata2.05%.accuraccutting4.r4.1.surfpossible.H.Oktem et al. / Journal of Materialsable 2data set used for checking the accuracy of RS modelnumber Cutting conditionsftVcaaarmt0.105 200 0.7 1 0.0010.105 200 0.7 1.5 0.0010.105 200 0.3 1 0.00550.08 200 0.7 1.5 0.00550.08 100 0.7 2 0.00550.08 200 0.3 1.5 0.010.105 200 0.5 2 0.01able 3accuracy error of several RS modelsflag First order Second order Third order Fourth order00000 27 7 4.8 2.700100 25.9 7.28 5.8 2.9500001 52.4 10.9 4.0 2.9911000 27.2 6.63 4.8 2.0501100 25.9 7.0 5.5 2.5500011 54.9 10.5 3.7 2.711100 25.8 7.03 5.7 2.501110 27.5 7.0 5.9 2.811111 53.03 10.5 4.7 2.7selected from 243 data sets to show a good distributionthe cutting parameters space and thereby to have a goodon the accuracy of the RS model.In this study, RS models of varying orders from first orderfourth order are created and tested with the developedSeveral RS model created are demonstrated alongtheir accuracy errors in Table 3. In reciprocal section inable 3, 0 indicates a parameter (xi), 1 indicates the inverse ofparameter (1xi). The full fourth order polynomial functionthe form:a= a0+ a11ft+ a21Vc+ a3aa+ a4ar+ a5mt+ anparenleftbigg1ft1Vcaaarmtparenrightbigg4+am(mt)4(2)best (with minimum fitting error) to the training data set.accuracy of the RS model was checked using the checkset. The maximum accuracy error is found to be aboutThis indicates that RS model generated has sufficienty in predicting surface roughness within the range ofparameters.Optimization of cutting conditions for surfaceoughnessOptimization problem formulationSince it is indicator of surface quality in milling of moldaces, surface roughness value is desired to be as low asLow surface roughness values can be achieved effi-cientlyappropriatemizationinFindMinimizeSubjectedfmizationforcedsearchestheroughnesscuttingon4.2.couplingalgorithmiterati(Darwincedure,rankFig.surfTechnology 170 (2005) 1116Ra(H9262m)Measurement results RSM model Maximum test error (%)0.591 0.5892.050.629 0.6270.781 0.7750.899 0.8950.978 0.9961.674 1.7061.856 1.893by adjusting cutting conditions with the help of annumerical optimization method. For this, mini-of surface roughness problem must be formulatedthe standard mathematical format as below: ft,Vc,aa,ar,mt(3a): Ra(ft,Vc,aa,ar,mt) (3b)to constraints : Ra 0. 412H9262m (3c)Within ranges :0.08 mm ft 0.13 mm100 mm Vc 300 mm0.3mm aa 0.7mm1mm ar 2mm0.001 mm mt 0.01 mm.In Eq. (3), Rais the RS model developed in Section 3.t, Vc, aa, arand mtare the cutting parameters. In the opti-problem definition above, a better solution is alsothrough the constraint definition. Constraint definitiona surface roughness value (Ra), which is less thanlowest value in 243 data set if possible. Minimum surfacevalue in 243 data set is 0.412H9262m. The ranges ofparameters in optimization have been selected basedthe recommendation of Sandvik Tool Catalogue.Optimization problem solutionThe optimization problem expressed in Eq. (3) is solved bythe developed RS model with the developed geneticas shown in Fig. 5.The genetic algorithm 14 solves optimization problemvely based oh biological evolution process in natures theory of survival of the fittest). In the solution pro-a set of parameter values is randomly selected. Set ised bashed on their surface roughness values (i.e. fitness5. Interaction of experimental measurements, RS model and GA duringace roughness optimization.ProcessingTGASubjectPopulationCrossoMutationNumberNumbervleadingcombinationbinationcrossofcannotparameterscalrate,uesselectsletionthetheintofunctionappropriatecientthisdent4.3.the0.375dition.minimumdictedwithvTThePCuttingRFig. 6. Surface roughness measurement.Fig. 6 it is seen that GA result agrees very well with themeasurement.H.Oktem et al. / Journal of Materialsable 4parametersValuessize 50ver rate 1.0rate 0.1of bit 16of generations 540alues in the GA literature). Best combination of parametersto minimum surface roughness is determined. Newof parameters is generated from the best com-by simulating biological mechanisms of offspring,ver and mutation. This process is repeated until sur-ace roughness value with new combination of parametersbe further reduced anymore. The final combination ofis considered as the optimum solution. The criti-parameters in GAs are the size of the population, mutationnumber of iterations (i.e. generations), etc. and their val-are given in Table 4.The GA written in MATLAB programming languagechromosomes based on the objective value and thevel of constraint violation. Fitness values of the popula-are biased towards the minimum objective value andleast infeasible sets in offspring phase. Most of GAs inliterature converts the constrained optimization probleman unconstrained optimization problem through penaltybefore the solution. This brings the difficulty ofselection of problem dependent penalty coeffi-which requires user experience. In the program used instudy, this difficulty is avoided since no problem depen-coefficient is needed 15.Optimization results and discussionBy solving the optimization problem, the GA reducessurface roughness of mold surfaces from 0.412H9262mtoH9262m by about 10% compared to the initial cutting con-The best (optimum) cutting condition leading to thesurface roughness is shown in Table 5. The pre-optimum cutting condition by GA is further validateda physical measurement. Predicted surface roughnessalue is compared with the measurement in Fig. 6. Fromable 5best cutting conditionarameters After optimizationconditionft(m/tooth) 0.083Vc(m/min) 200aa(mm) 0.302ar(mm) 1.002mt(mm) 0.002a(H9262m)Measurement 0.370GA 0.3755.fAluminumingofsurement.(2.05%).aingthewthecuttingsurement.wellthanproposedandmachiningasAcknotionsFehmiatReferTechnology 170 (2005) 1116 15ConclusionsIn this study, a fourth order RS model for predicting sur-ace roughness values in milling mold surfaces made of(7075-T6) material was developed. In generat-the RS model statistical RSM was utilized. The accuracythe RS model was verified with the experimental mea-The accuracy error was found to be insignificantThe developed RS model was further coupled withdeveloped GA to find the optimum cutting condition lead-to the least surface roughness value. Surface roughness ofmold surfaces, which was 0.412H9262m before optimization,as reduced to 0.375H9262m after optimization. GA improvedsurface roughness by about 10%. The predicted optimumcondition was validated with an experimental mea-It was found that GA prediction correlates verywith the experiment. Difference was found to be less1.4%. This indicates that the optimization methodologyin this study by coupling the developed RS modelthe developed GA is effective and can be utilized in otherproblems such as tool life, dimensional errors, etc.well.wledgementsThe authors acknowledge Dr. Mustafa COL for contribu-in making this project at Kocaeli University an
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