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Journal of Materials Processing Technology 170 (2005) 1116 Application of response surface methodology in the optimization of cutting conditions for surface roughness H. Oktem a, , T. Erzurumlu b , H. Kurtaran b a Department of Mechanical Engineering, University of Kocaeli, 41420 Kocaeli, Turkey b Department of Design and Manufacturing Engineering, GIT, 41400 Gebze, Kocaeli, Turkey Received 16 July 2004; received in revised form 12 March 2005; accepted 12 April 2005 Abstract This paper focuses on the development of an effective methodology to determine the optimum cutting conditions leading to minimum surface 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 depth of cut, radial depth of cut and machining tolerance. For this purpose, a number of machining experiments based on statistical three-level full factorial 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 the cutting conditions for desired surface roughness. The GA reduces the surface roughness value in the mold cavity from 0.412H9262m to 0.375H9262m corresponding 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 algorithm 1. trib Milling ducing parts T6 aircraft as tensile tic of f surf f irre 0924-0136/$ doi:10.1016/j.jmatprotec.2005.04.096 Introduction Recent 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 mold made of Aluminum 7075-T6 material. Aluminum 7075- material as chosen in this study is commonly utilized in and die/mold industries due to some advantages such high resistance, good transmission, heat treatable and high strength 3,4. The quality of plastic products manufactured by plas- injection molding process is highly influenced by that mold surfaces obtained from the milling process. Sur- ace quality of these products is generally associated with ace roughness and can be determined by measuring sur- ace roughness 5. Surface roughness is expressed as the gularities of material resulted from various machining Corresponding author. Tel.: +90 262 742 32 90; fax: +90 262 742 40 91. E-mail address: hoktemkou.edu.tr (H. Oktem). operations. f symbol, metic mean an Surf ting such w ditions machining this ditions such models tool in been 718 see front matter 2005 Elsevier B.V. All rights reserved. In quantifying surface roughness, average sur- ace roughness definition, which is often represented with R a is commonly used. Theoretically, R a is the arith- average value of departure of the profile from the line throughout the sampling length 6. R a is also important factor in controlling machining performance. ace roughness is influenced by tool geometry, feed, cut- conditions and the irregularities of machining operations as tool wear, chatter, tool deflections, cutting fluid, and orkpiece properties 7,11,16. The effect of cutting con- (feed, cutting speed, axialradial depth of cut and tolerance) on surface roughness is discussed in study. Several researchers have studied the effect of cutting con- in milling and plastic injection molding processes as in vacuum-sealed molding process 5. Analytical have been created to predict surface roughness and life in terms of cutting speed, feed and axial depth of cut milling steel material 8,9. An effective approach has also presented to optimize surface finish in milling Inconel 10. 12 Processing for surf oped. methodology model de genetic leading is axialradial dicted e present ture. polynomial nates GAs. optimization tions. 2. 2.1. the ments e sidering axial ing carried cutting is based Milling conditions milling from 2.2. 10 T Lo design Cutting Feed, Cutting Axial Radial Machining Fig. 1. Mold part. is PVD AlTiN coated with solid carbide. It has the helix angle of 45 and rake angle of 10 . Machining experiments are performed in the mold cavity on aluminum (7075-T6) block with dimensions of 120 mm 120 mm 50 mm. The chemical composition of workpiece material is given in the following specification (wt.%): 1.6 Cu, 2.5 Mg, 0.23 Cr, 5.40 Zn. 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, shear strength of 330 MPa and elongation of 11%. Surface roughness is measured with Surftest 301 pro- H. Oktem et al. / Journal of Materials In this study, a fourth order response surface (RS) model predicting surface roughness values in milling the mold aces made of Aluminum (7075-T6) material is devel- In generating the RS model statistical response surface (RSM) is utilized. The accuracy of the RS is verified with the experimental measurement. The veloped RS model is further coupled with a developed algorithm (GA) to find the optimum cutting condition to the least surface roughness value. Cutting condition represented with cutting parameters of feed, cutting speed, depth of cut and machining tolerance. The pre- optimum cutting condition by GA is validated with an xperimental measurement. The RS model and GA developed and utilized in this study several advantages over other methods in the litera- The RS model is a higher order and more sophisticated model with sufficient accuracy. The GA elimi- the difficulty of user-defined parameters of the existing Details of the RS model generation by RSM and the process by GA are given in the following sec- Experimental procedures Plan of experiments An important stage of RS model generation by RSM is planning of experiments. In this study, cutting experi- are planned using statistical three-level full factorial xperimental design. Cutting experiments are conducted con- five cutting parameters: feed (f t ), cutting speed (V c ), depth of cut (a a ), radial depth of cut (a r ) and machin- tolerance (m t ). Overall 3 5 = 243 cutting experiments are out. Lowmiddlehigh level of cutting parameters in space for three-level full factorial experimental design shown in Table 1. Ranges of cutting parameters are selected on recommendation of Sandvik Tool Catalogue 12. operations are performed at the determined cutting on a DECKEL MAHO DMU 60 P five axis CNC machine. Surface roughness (R a ) values are measured the mold surfaces. Tool and material Cutting tool used in experiments has the diameter of mm flat end mill with four teeth. The material of the tool able 1 wmiddlehigh levels of cutting parameters in three-level full factorial of experiment parameters Three- level values f t (mm/tooth) 0.080.1050.13 speed, V c (m/min) 100200300 depth of cut, a r (mm) 0.30.50.7 depth of cut, a r (mm) 11.52 tolerance, m t (mm) 0.0010.00550.01 filometer pling. mathematical v as times. model. 2.3. the cations. utilized position and minum Orthose is 2.4. manuf grated CNC f Technology 170 (2005) 1116 at traverse length of 2.5 mm along centerline of sam- Converting the measurement into a numerical value, definition of R a is used. Since this way of con- ersion is common in the literature it is adopted in this study well 79. Each R a measurement is repeated at least three Average of three R a values is saved to establish RS Mold parts The mold part used in this study is utilized to produce components of an orthose part in biomechanical appli- It is shown in Fig. 1. Orthose parts are generally in walking apparatus that holds human legs in stable during walking. It binds the kneecap region of leg is 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 them employed as the working model in this study. Manufacturing the components of orthose part Three machining processes are implemented in order to acture each component of the orthose part in an inte- manner. Firstly, the selected component is machined in milling machine. R a values are then taken from the sur- aces in the mold cavity. Secondly, plastic product is injected Processing in acetal material. sity viscosity Finally ing illustrated 3. surf statistical nique phase. H. Oktem et al. / Journal of Materials Fig. 2. The parts obtained from three Fig. 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 polymer The properties of polymer material has the den- of solution 1.2 g/cm 3 , the ejected temperature of 165 C, of 50 Pa s and melt flow-fill rate of 0.8 cm 3 /min. , net casting process is applied for producing die cast- part. Mold part, plastic product and die casting part are in Fig. 2. Response surface model for surface roughness RS model, which is an analytical function, in predicting ace roughness values is developed using RSM. RSM uses design of experiment (experimental design) tech- and least-square fitting method in model generation It is summarized in Fig. 3. RSM was originally devel- oped and is f where of to MA ing All models generated be creating mined for data training data lized v rather set f roughness the Fig. 4. Comparison of experimental measurements Technology 170 (2005) 1116 13 machining process. for the model fitting of physical experiments by Box Draper 13 and later adopted in other fields. RS model formulated as following polynomial function: n summationdisplay n summationdisplay n summationdisplay = a 0 + i=1 a i x i + i=1 j=1 a ij x i x j + (1) a 0 , a i and a ij are tuning parameters and n is the number model parameters (i.e. process parameters). In this study, create RS model, a computer program has been written in TLAB 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 the can be taken into account. RS models can also be in terms of inverse of parameters. That is, x i can replaced as 1 x i (i.e. inversely) in RS model if desired, in the RS models, 243 surface roughness values deter- based on three-level full factorial experimental design five parameters (f t , V c , a a , a r and m t ) are used The 243 sets for surface roughness are divided into two parts; data set and the check (i.e. test) data set. Training set includes 236 surface roughness values and is uti- in model fitting procedure. Because of large number of alues and to save space, training data is shown in Fig. 4, than in a table. In Fig. 4, abscissa indicates the data number and the ordinate indicates the corresponding sur- ace roughness value. Check data sets include seven surface values and are used in checking the accuracy of RS model. Check data sets are shown in Table 2. They with RS prediction for surface roughness. 14 Processing T The Set 1 2 3 4 5 6 7 T The Reciprocal are in check to program. with T a of R fits The data 2.05%. accurac cutting 4. r 4.1. surf possible. H. Oktem et al. / Journal of Materials able 2 data set used for checking the accuracy of RS model number Cutting conditions f t V c a a a r m t 0.105 200 0.7 1 0.001 0.105 200 0.7 1.5 0.001 0.105 200 0.3 1 0.0055 0.08 200 0.7 1.5 0.0055 0.08 100 0.7 2 0.0055 0.08 200 0.3 1.5 0.01 0.105 200 0.5 2 0.01 able 3 accuracy error of several RS models flag First order Second order Third order Fourth order 00000 27 7 4.8 2.7 00100 25.9 7.28 5.8 2.95 00001 52.4 10.9 4.0 2.99 11000 27.2 6.63 4.8 2.05 01100 25.9 7.0 5.5 2.55 00011 54.9 10.5 3.7 2.7 11100 25.8 7.03 5.7 2.5 01110 27.5 7.0 5.9 2.8 11111 53.03 10.5 4.7 2.7 selected from 243 data sets to show a good distribution the cutting parameters space and thereby to have a good on the accuracy of the RS model. In this study, RS models of varying orders from first order fourth order are created and tested with the developed Several RS model created are demonstrated along their accuracy errors in Table 3. In reciprocal section in able 3, 0 indicates a parameter (x i ), 1 indicates the inverse of parameter ( 1 x i ). The full fourth order polynomial function the form: a = a 0 + a 1 1 f t + a 2 1 V c + a 3 a a + a 4 a r + a 5 m t + + a n parenleftbigg 1 f t 1 V c a a a r m t parenrightbigg 4 +a m (m t ) 4 (2) best (with minimum fitting error) to the training data set. accuracy of the RS model was checked using the check set. The maximum accuracy error is found to be about This indicates that RS model generated has sufficient y in predicting surface roughness within the range of parameters. Optimization of cutting conditions for surface oughness Optimization problem formulation Since it is indicator of surface quality in milling of mold aces, surface roughness value is desired to be as low as Low surface roughness values can be achieved effi- ciently appropriate mization in Find Minimize Subjected f mization forced searches the roughness cutting on 4.2. coupling algorithm iterati (Darwin cedure, rank Fig. surf Technology 170 (2005) 1116 R a (H9262m) Measurement results RSM model Maximum test error (%) 0.591 0.589 2.05 0.629 0.627 0.781 0.775 0.899 0.895 0.978 0.996 1.674 1.706 1.856 1.893 by adjusting cutting conditions with the help of an numerical optimization method. For this, mini- of surface roughness problem must be formulated the standard mathematical format as below: : f t ,V c ,a a ,a r ,m t (3a) : R a (f t ,V c ,a a ,a r ,m t ) (3b) to constraints : R a 0. 412H9262m (3c) Within ranges : 0.08 mm f t 0.13 mm 100 mm V c 300 mm 0.3mm a a 0.7mm 1mm a r 2mm 0.001 mm m t 0.01 mm. In Eq. (3), R a is the RS model developed in Section 3. t , V c , a a , a r and m t are the cutting parameters. In the opti- problem definition above, a better solution is also through the constraint definition. Constraint definition a surface roughness value (R a ), which is less than lowest value in 243 data set if possible. Minimum surface value in 243 data set is 0.412H9262m. The ranges of parameters in optimization have been selected based the recommendation of Sandvik Tool Catalogue. Optimization problem solution The optimization problem expressed in Eq. (3) is solved by the developed RS model with the developed genetic as shown in Fig. 5. The genetic algorithm 14 solves optimization problem vely based oh biological evolution process in nature s theory of survival of the fittest). In the solution pro- a set of parameter values is randomly selected. Set is ed bashed on their surface roughness values (i.e. fitness 5. Interaction of experimental measurements, RS model and GA during ace roughness optimization. Processing T GA Subject Population Crosso Mutation Number Number v leading combination bination crosso f cannot parameters cal rate, ues selects le tion the the into function appropriate cient this dent 4.3. the 0.375 dition. minimum dicted with v T The P Cutting R Fig. 6. Surface roughness measurement. Fig. 6 it is seen that GA result agrees very well with the measurement. H. Oktem et al. / Journal of Materials able 4 parameters Values size 50 ver rate 1.0 rate 0.1 of bit 16 of generations 540 alues in the GA literature). Best combination of parameters to minimum surface roughness is determined. New of 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 parameters be further reduced anymore. The final combination of is considered as the optimum solution. The criti- parameters in GAs are the size of the population, mutation number of iterations (i.e. generations), etc. and their val- are given in Table 4. The GA written in MATLAB programming language chromosomes based on the objective value and the vel of constraint violation. Fitness values of the popula- are biased towards the minimum objective value and least infeasible sets in offspring phase. Most of GAs in literature converts the constrained optimization problem an unconstrained optimization problem through penalty before the solution. This brings the difficulty of selection of problem dependent penalty coeffi- which requires user experience. In the program used in study, this difficulty is avoided since no problem depen- coefficient is needed 15. Optimization results and discussion By solving the optimization problem, the GA reduces surface roughness of mold surfaces from 0.412H9262mto H9262m by about 10% compared to the initial cutting con- The best (optimum) cutting condition leading to the surface roughness is shown in Table 5. The pre- optimum cutting condition by GA is further validated a physical measurement. Predicted surface roughness alue is compared with the measurement in Fig. 6. From able 5 best cutting condition arameters After optimization condition f t (m/tooth) 0.083 V c (m/min) 200 a a (mm) 0.302 a r (mm) 1.002 m t (mm) 0.002 a (H9262m) Measurement 0.370 GA 0.375 5. f Aluminum ing of surement. (2.05%). a ing the w the cutting surement. well than proposed and machining as Ackno tions Fehmi at Refer Technology 170 (2005) 1116 15 Conclusions In 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 accuracy the RS model was verified with the experimental mea- The accuracy error was found to be insignificant The developed RS model was further coupled with developed GA to find the optimum cutting condition lead- to the least surface roughness value. Surface roughness of mold surfaces, which was 0.412H9262m before optimization, as reduced to 0.375H9262m after optimization. GA improved surface roughness by about 10%. The predicted optimum condition was validated with an experimental mea- It was found that GA prediction correlates very with the experiment. Difference was found to be less 1.4%. This indicates that the optimization methodology in this study by coupling the developed RS model the developed GA is effective and can be utilized in other problems such as tool life, dimensional errors, etc. well. wledgements The authors acknowledge Dr. Mustafa COL for contribu- in making this project at Kocaeli University and Dr. ERZINCANLI for supplying a CNC milling machine Gebze Institute of Technology (GIT). ences 1 G. Boothroyd, W.A. Knight, Fundamentals of machining and machine tools, Marcel Dekker Inc., New York, 1989. 16 H. Oktem et al. / Journal of Materials Processing Technology 170 (2005) 1116 2 W.B. Sai, N.B. Salah, J.L. Lebrun, Influence of machining by fin- ishing milling on surface characteristics, Int. J. Mach. Tool Manuf. 41 (2001) 443450. 3 J.E. Hatch, Aluminum: Properties and Physical Metallurgy, American Society for Metals, Ohio, 1999. 4 J.P. Urbanski, P. Koshy, R.C. Dewes, D.K. Aspinwall, High speed machining of mold and dies for net shape manufacture, Mater. 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