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【机械类毕业论文中英文对照文献翻译】响应曲面法在最优化切削条件下获得最小表面粗糙度的应用
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机械类毕业论文中英文对照文献翻译
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【机械类毕业论文中英文对照文献翻译】响应曲面法在最优化切削条件下获得最小表面粗糙度的应用,机械类毕业论文中英文对照文献翻译,机械类,毕业论文,中英文,对照,文献,翻译,响应,曲面,优化,切削,条件下,获得,最小,表面,粗糙,应用
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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 0.412?m to 0.375?mcorresponding 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. IntroductionRecentdevelopmentsinmanufacturingindustryhavecon-tributed to the importance of CNC milling operations 1,2.Milling process is required to make mold parts used for pro-ducingplasticproducts.ItisalsopreferredinmachiningmoldpartsmadeofAluminum7075-T6material.Aluminum7075-T6 material as chosen in this study is commonly utilized inaircraft and die/mold industries due to some advantages suchashighresistance,goodtransmission,heattreatableandhightensile strength 3,4.The quality of plastic products manufactured by plas-tic injection molding process is highly influenced by thatof mold surfaces obtained from the milling process. Sur-face quality of these products is generally associated withsurface roughness and can be determined by measuring sur-face roughness 5. Surface roughness is expressed as theirregularities of material resulted from various machiningCorresponding author. Tel.: +90 262 742 32 90; fax: +90 262 742 40 91.E-mail address: .tr (H.Oktem).operations. In quantifying surface roughness, average sur-face roughness definition, which is often represented with Rasymbol, is commonly used. Theoretically, Rais the arith-metic average value of departure of the profile from themean line throughout the sampling length 6. Rais alsoan important factor in controlling machining performance.Surface roughness is influenced by tool geometry, feed, cut-tingconditionsandtheirregularitiesofmachiningoperationssuch as tool wear, chatter, tool deflections, cutting fluid, andworkpiece properties 7,11,16. The effect of cutting con-ditions (feed, cutting speed, axialradial depth of cut andmachining tolerance) on surface roughness is discussed inthis study.Several researchers have studied the effect of cutting con-ditions in milling and plastic injection molding processessuch as in vacuum-sealed molding process 5. Analyticalmodels have been created to predict surface roughness andtool life in terms of cutting speed, feed and axial depth of cutinmillingsteelmaterial8,9.Aneffectiveapproachhasalsobeen presented to optimize surface finish in milling Inconel718 10.0924-0136/$ see front matter 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.jmatprotec.2005.04.09612H.Oktem et al. / Journal of Materials Processing Technology 170 (2005) 1116In this study, a fourth order response surface (RS) modelfor predicting surface roughness values in milling the moldsurfaces made of Aluminum (7075-T6) material is devel-oped. In generating the RS model statistical response surfacemethodology (RSM) is utilized. The accuracy of the RSmodel is verified with the experimental measurement. Thedeveloped RS model is further coupled with a developedgeneticalgorithm(GA)tofindtheoptimumcuttingconditionleadingtotheleastsurfaceroughnessvalue.Cuttingconditionis represented with cutting parameters of feed, cutting speed,axialradial depth of cut and machining tolerance. The pre-dicted optimum cutting condition by GA is validated with anexperimental measurement.TheRSmodelandGAdevelopedandutilizedinthisstudypresent several advantages over other methods in the litera-ture. The RS model is a higher order and more sophisticatedpolynomial model with sufficient accuracy. The GA elimi-nates the difficulty of user-defined parameters of the existingGAs. Details of the RS model generation by RSM and theoptimization process by GA are given in the following sec-tions.2. Experimental procedures2.1. Plan of experimentsAn important stage of RS model generation by RSM isthe planning of experiments. In this study, cutting experi-ments are planned using statistical three-level full factorialexperimentaldesign.Cuttingexperimentsareconductedcon-sidering five cutting parameters: feed (ft), cutting speed (Vc),axial depth of cut (aa), radial depth of cut (ar) and machin-ing tolerance (mt). Overall 35=243 cutting experiments arecarried out. Lowmiddlehigh level of cutting parameters incuttingspaceforthree-levelfullfactorialexperimentaldesignisshowninTable1.Rangesofcuttingparametersareselectedbased on recommendation of Sandvik Tool Catalogue 12.Milling operations are performed at the determined cuttingconditions on a DECKEL MAHO DMU 60 P five axis CNCmillingmachine.Surfaceroughness(Ra)valuesaremeasuredfrom the mold surfaces.2.2. Tool and materialCutting tool used in experiments has the diameter of10mm flat end mill with four teeth. The material of the toolTable 1Lowmiddlehigh levels of cutting parameters in three-level full factorialdesign of experimentCutting parametersThree- level valuesFeed, ft(mm/tooth)0.080.1050.13Cutting speed, Vc(m/min)100200300Axial depth of cut, ar(mm)Radial depth of cut, ar(mm)11.52Machining tolerance, mt(mm)0.0010.00550.01Fig. 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 120mm120mm50mm. Thechemical composition of workpiece material is given in thefollowingspecification(wt.%):1.6Cu,2.5Mg,0.23Cr,5.40Zn. The hardness of workpiece is measured as 150BHN.The mechanical properties of aluminum material are: ten-sile strength of 570MPa, yield strength of 505MPa, shearstrength of 330MPa and elongation of 11%.Surface roughness is measured with Surftest 301 pro-filometerattraverselengthof2.5mmalongcenterlineofsam-pling. Converting the measurement into a numerical value,mathematical definition of Rais used. Since this way of con-version is common in the literature it is adopted in this studyas well 79. Each Rameasurement is repeated at least threetimes. Average of three Ravalues is saved to establish RSmodel.2.3. Mold partsThe mold part used in this study is utilized to producethe components of an orthose part in biomechanical appli-cations. It is shown in Fig. 1. Orthose parts are generallyutilized in walking apparatus that holds human legs in stableposition during walking. It binds the kneecap region of legand is equipped with cylindrical bars that are made of alu-minum material in diameter of 12mm and length of 300mm.Orthose part consists of three main components; one of themis employed as the working model in this study.2.4. Manufacturing the components of orthose partThree machining processes are implemented in order tomanufacture each component of the orthose part in an inte-gratedmanner.Firstly,theselectedcomponentismachinedinCNC milling machine. Ravalues are then taken from the sur-faces in the mold cavity. Secondly, plastic product is injectedH.Oktem et al. / Journal of Materials Processing Technology 170 (2005) 111613Fig. 2. The parts obtained from three machining process.Fig. 3. The stages taken in creating a response surface model by RSM.in plastic injection machine produced by ARBURG. Poly-acetal (POM) C 9021 material is used to inject the polymermaterial. The properties of polymer material has the den-sity of solution 1.2g/cm3, the ejected temperature of 165C,viscosity of 50Pas and melt flow-fill rate of 0.8cm3/min.Finally, net casting process is applied for producing die cast-ing part. Mold part, plastic product and die casting part areillustrated in Fig. 2.3. Response surface model for surface roughnessRS model, which is an analytical function, in predictingsurfaceroughnessvaluesisdevelopedusingRSM.RSMusesstatistical design of experiment (experimental design) tech-nique and least-square fitting method in model generationphase. It is summarized in Fig. 3. RSM was originally devel-oped for the model fitting of physical experiments by Boxand Draper 13 and later adopted in other fields. RS modelis formulated as following polynomial function:f = a0+n?i=1aixi+n?i=1n?j=1aijxixj+ (1)wherea0,aiandaijaretuningparametersandnisthenumberof model parameters (i.e. process parameters). In this study,to create RS model, a computer program has been written inMATLAB programming language.The RS program developed has the capability of creat-ing RS polynomials up to 10th order if sufficient data exist.All cross terms (i.e. interactions between parameters) in themodels can be taken into account. RS models can also begenerated in terms of inverse of parameters. That is, xicanbe replaced as1xi(i.e. inversely) in RS model if desired, increating the RS models, 243 surface roughness values deter-mined based on three-level full factorial experimental designfor five parameters (ft, Vc, aa, arand mt) are used The 243data sets for surface roughness are divided into two parts;training data set and the check (i.e. test) data set. Trainingdata set includes 236 surface roughness values and is uti-lized in model fitting procedure. Because of large number ofvalues and to save space, training data is shown in Fig. 4,rather than in a table. In Fig. 4, abscissa indicates the dataset number and the ordinate indicates the corresponding sur-face roughness value. Check data sets include seven surfaceroughness values and are used in checking the accuracy ofthe RS model. Check data sets are shown in Table 2. TheyFig. 4. Comparison of experimental measurements with RS prediction for surface roughness.14H.Oktem et al. / Journal of Materials Processing Technology 170 (2005) 1116Table 2The data set used for checking the accuracy of RS modelSet numberCutting conditionsRa(?m)ftVcaaarmtMeasurement resultsRSM modelMaximum test error (%)10.1052000.710.0010.5910.5892.0520.105200010.6290.62730.1052000.310.00550.7810.77540.082000550.8990.89550.081000.720.00550.9780.99660.0820011.6741.70670.1052000.520.011.8561.893Table 3The accuracy error of several RS modelsReciprocal flagFirst orderSecond orderThird orderFourth order000002774.82.70010025.97.285.82.950000152.410.94.02.991100027.26.634.82.050110025.97.05.52.550001154.91110025.87.035.72.50111027.57.05.92.81111153.03are selected from 243 data sets to show a good distributionin the cutting parameters space and thereby to have a goodcheck on the accuracy of the RS model.In this study, RS models of varying orders from first orderto fourth order are created and tested with the developedprogram. Several RS model created are demonstrated alongwith their accuracy errors in Table 3. In reciprocal section inTable3,0indicatesaparameter(xi),1indicatestheinverseofa parameter (1xi). The full fourth order polynomial functionof the form:Ra= a0+ a11ft+ a21Vc+ a3aa+ a4ar+ a5mt+ +an?1ft1Vcaaarmt?4+ + am(mt)4(2)fits best (with minimum fitting error) to the training data set.The accuracy of the RS model was checked using the checkdata set. The maximum accuracy error is found to be about2.05%. This indicates that RS model generated has sufficientaccuracy in predicting surface roughness within the range ofcutting parameters.4. Optimization of cutting conditions for surfaceroughness4.1. Optimization problem formulationSince it is indicator of surface quality in milling of moldsurfaces, surface roughness value is desired to be as low aspossible. Low surface roughness values can be achieved effi-ciently by adjusting cutting conditions with the help of anappropriate numerical optimization method. For this, mini-mization of surface roughness problem must be formulatedin the standard mathematical format as below:Find : ft,Vc,aa,ar,mt(3a)Minimize : Ra(ft,Vc,aa,ar,mt)(3b)Subjected to constraints : Ra 0.412?m(3c)Within ranges :0.08mm ft 0.13mm100mm Vc 300mm0.3mm aa 0.7mm1mm ar 2mm0.001mm mt 0.01mm.In Eq. (3), Rais the RS model developed in Section 3.ft, Vc, aa, arand mtare the cutting parameters. In the opti-mization problem definition above, a better solution is alsoforcedthroughtheconstraintdefinition.Constraintdefinitionsearches a surface roughness value (Ra), which is less thanthelowestvaluein243datasetifpossible.Minimumsurfaceroughness value in 243 data set is 0.412?m. The ranges ofcutting parameters in optimization have been selected basedon the recommendation of Sandvik Tool Catalogue.4.2. Optimization problem solutionTheoptimizationproblemexpressedinEq.(3)issolvedbycouplingthedevelopedRSmodelwiththedevelopedgeneticalgorithm as shown in Fig. 5.The genetic algorithm 14 solves optimization problemiteratively based oh biological evolution process in nature(Darwinstheoryofsurvivalofthefittest).Inthesolutionpro-cedure, a set of parameter values is randomly selected. Set isranked bashed on their surface roughness values (i.e. fitnessFig.5. Interactionofexperimentalmeasurements,RSmodelandGAduringsurface roughness optimization.H.Oktem et al. / Journal of Materials Processing Technology 170 (2005) 111615Table 4GA parametersSubjectValuesPopulation size50Crossover rate1.0Mutation rate0.1Number of bit16Number of generations540values in the GA literature). Best combination of parametersleading to minimum surface roughness is determined. Newcombination of parameters is generated from the best com-bination by simulating biological mechanisms of offspring,crossover and mutation. This process is repeated until sur-face roughness value with new combination of parameterscannot be further reduced anymore. The final combination ofparameters is considered as the optimum solution. The criti-calparametersinGAsarethesizeofthepopulation,mutationrate,numberofiterations(i.e.generations),etc.andtheirval-ues are given in Table 4.The GA written in MATLAB programming languageselects chromosomes based on the objective value and thelevel of constraint violation. Fitness values of the popula-tion are biased towards the minimum objective value andthe least infeasible sets in offspring phase. Most of GAs inthe literature converts the constrained optimization probleminto an unconstrained optimization problem through penaltyfunction before the solution. This brings the difficulty ofappropriate selection of problem dependent penalty coeffi-cient which requires user experience. In the program used inthis study, this difficulty is avoided since no problem depen-dent coefficient is needed 15.4.3. Optimization results and discussionBy solving the optimization problem, the GA reducesthe surface roughness of mold surfaces from 0.412?m to0.375?m by about 10% compared to the initial cutting con-dition. The best (optimum) cutting condition leading to theminimum surface roughness is shown in Table 5. The pre-dicted optimum cutting condition by GA is further validatedwith a physical measurement. Predicted surface roughnessvalue is compared with the measurement in Fig. 6. FromTable 5The best cutting conditionParametersAfter optimizationCutting conditionft(m/tooth)0.083Vc(m/min)200aa(mm)0.302ar(mm)1.002mt(mm)0.002Ra(?m)Measurement0.370GA0.375Fig. 6. Surface roughness measurement.Fig. 6 it is seen that GA result agrees very well with themeasurement.5. ConclusionsIn this study, a fourth order RS model for predicting sur-face roughness values in milling mold surfaces made ofAluminum (7075-T6) material was developed. In generat-ing the RS model statistical RSM was utilized. The accuracyof the RS model was verified with the experimental mea-surement. The accuracy error was found to be insignificant(2.05%). The developed RS model was further coupled witha developed GA to find the optimum cutting condition lead-ingtotheleastsurfaceroughnessvalue.Surfaceroughnessofthe mold surfaces, which was 0.412?m before optimization,was reduced to 0.375?m after optimization. GA improvedthe surface roughness by about 10%. The predicted optimumcutting condition was validated with an experimental mea-surement. It was found that GA prediction correlates verywell with the experiment. Difference was found to be lessthan 1.4%. This indicates that the optimization methodologyproposed in this study by coupling the developed RS modelandthedevelopedGAiseffectiveandcanbeutilizedinothermachiningproblemssuchastoollife,dimensionalerrors,etc.as well.AcknowledgementsThe authors acknowledge Dr. Mustafa COL for contribu-tions in making this project at Kocaeli University and Dr.Fehmi ERZINCANLI for supplying a CNC milling machineat Gebze Institute of Technology (GIT).References1 G. Boothroyd, W.A. Knight, Fundamentals of machining andmachine tools, Marcel Dekker Inc., New York, 1989.16H.Oktem et al. / Journal of Materials Processing Technology 170 (2005) 11162 W.B. Sai, N.B. Salah, J.L. Lebrun,
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