Optimization of Surface Roughness in End Milling of Medium Carbon Steel by Coupled Statistical Approach with Genetic Algorithm

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1 Optimization of Surface Roughness in End Milling of Medium Carbon Steel by Coupled Statistical Approach with Genetic Algorithm Md. Anayet Ullah Patwari Islamic University of Technology (IUT) Department of Mechanical & Chemical Engineering Board Bazaar, Gazipur-1704, Dhaka, Bangladesh Corresponding Author s aupatwari@hotmail.com A. K. M. Nurul Amin International Islamic University Malaysia (IIUM) Department of Manufacturing & Materials Engineering P.O. Box 10, Kuala Lumpur, Malaysia Muammer D. Arif Islamic University of Technology (IUT) Department of Mechanical & Chemical Engineering Board Bazaar, Gazipur-1704, Dhaka, Bangladesh Abstract- This paper describes mathematically the effect of cutting parameters on surface roughness in end milling of Medium Carbon Steel. The mathematical model for the surface roughness has been developed, in terms of cutting speed, feed rate, and axial depth of cut. The effect of these cutting parameters on the surface roughness has been carried out using design of experiments and response surface methodology (RSM). Cutting at high speed, depth of cut, and feed, of course, will increase the production rate; however, it will sacrifice the machining quality, such as surface roughness values. This paper presents an approach to predicting the surface finish in end milling of Medium Carbon Steel using coated TiN insert under dry conditions with full immersion and its optimization by coupling the prediction model with genetic algorithm. Central composite design was employed in developing the surface roughness models in relation to primary cutting parameters. The experimental results indicate that the proposed mathematical models suggested could adequately describe the performance indicators within the limits of the factors that are being investigated. Keywords- Coated Titanium Nitride, Model, Response Surface Methodology, Surface Roughness. I. INTRODUCTION The use of advanced computer-based systems for the selection of optimum conditions of mechanical components during process planning becomes essential for today s complex products. Computer aided manufacturing (CAM) has widely been implemented to obtain more accurate machining data and to ensure that optimum production is achieved. Machinability of a material provides an indication of its adaptability to be manufactured by a machining process. In general, machinability can be defined as an optimal combination of factors such as low cutting force, high material removal rate, good surface integrity, accurate and consistent work-piece geometrical characteristics, low tool wear rate, and good curl or breakdown of chips. 41.1

2 Md. Anayet Ullah Patwari, A. K. M. Nurul Amin, and Muammer D. Arif In machinability studies investigations, statistical design of experiments is used quite extensively. Statistical design of experiments refers to the process of planning the experiment so that the appropriate data can be analyzed by statistical methods, resulting in valid and objective conclusions [1]. Design and methods such as factorial design, response surface methodology (RSM) and Taguchi methods are now widely used in place of one-factor-at-a-time experimental approach which is time consuming and exorbitant in cost. A machinability model may be defined as a functional relationship between the input of independent cutting variables (speed, feed, depth of cut) and the output known as responses (tool life, surface roughness, cutting force, etc.) of a machining process [2]. Response surface methodology (RSM) is a combination of experimental and regression analysis, and statistical inference. RSM is a dynamic and foremost important tool of design of experiment (DOE), wherein the relationship between response(s) of a process with its input decision variables is mapped to achieve the objective of maximization or minimization of the response properties [3]. Many machining researchers have used response surface methodology to design their experiments and assess results. Kaye et al. [4] used response surface methodology in predicting tool flank wear using spindle speed change. A unique model has been developed which predicts tool flank wear, based on the spindle speed change, provided the initial flank wear at the beginning of the normal cutting stage is known. An empirical equation has also been derived for calculating the initial flank wear; given the speed, feed rate, depth of cut, and work-piece hardness. Alauddin et al. [5] applied response surface methodology to optimize the surface finish in end milling of Inconel 718 under dry condition. They developed contours to select a combination of cutting speed and feed without increasing the surface In order to establish an adequate functional relationship between the responses (such as surface roughness, cutting force, tool life/wear) and the cutting parameters (cutting speed, feed, and depth of cut), a large number of tests are needed for each and every combination of cutting tool and work-piece materials. This increases the total number of tests and as a result the experimentation cost also increases. Response Surface Methodology (RSM), as a group of mathematical and statistical techniques, is useful for modelling the relationship between the input parameters (cutting conditions) and the output variables. RSM saves cost and time by reducing the number of experiments required. In this paper, the technique is used to develop a mathematical model that utilizes the response surface methodology and method of experiments to predict the surface roughness when milling Medium carbon steel S45C using TiN coated carbide inserts. The predicted surface roughness results are presented in terms of mean values with 95% confidence interval. The developed model was coupled with genetic algorithm for the optimization of the minimum surface II. EXPERIMENTAL DETAILS A. Experimental Setup Cutting tests were conducted mainly on Vertical Machining Center (VMC ZPS, Model: 1060) powered by a 30 KW motor with a maximum spindle speed of 8000 rpm. Fig.1 shows the experimental set up cutting test conditions on end milling for machining of Medium carbon steel with TiN inserts. Surface measuring instrument (SURFTEST) SV-500 was used to measure the surface Fig. 1 Experimental set up for end milling Special Issue of the International Journal of the Computer, the Internet and Management, Vol. 19 No. SP1, June,

3 Optimization of Surface Roughness in End Milling of Medium Carbon Steel by Coupled Statistical Approach with Genetic Algorithm B. Coding of the Independent Variables The independent variables were coded taking into consideration the limitations and capacities of the cutting tools. Levels of independent and coding identification are presented in Table I, for experiment using Coated TiN inserts, respectively. TABLE I CODING IDENTIFICATION FOR END MILLING USING COATED TIN CARBIDE INSERT TABLE II SURFACE ROUGHNESS RESULTS & CUTTING CONDITIONS IN CODED FACTORS The transforming equations for each of the independent variables are: C. Experimental Design The design of the experiments [6] has an effect on the number of experiments required. Therefore, it is important to have a well-designed experiment to minimize the number of experiments which often are carried out randomly. Cutting conditions in coded factors and the surface roughness values obtained using TiN coated cemented carbide inserts are presented in Table II. In the experiment, small central composite design was employed to develop the surface roughness model. The analyses of the mathematical models were carried out using Design-expert package. The Fit and summary test, indicates that the quadratic CCD model was more significant than the linear model and it also proved that the linear model has a significant lack of fit (LOF). Therefore, the quadratic model was chosen in order to develop the CCD model. The second order surface roughness model is given as: The quadratic CCD model (above equation) shows that feed has the most significant effect on surface roughness, followed by axial depth of cut and cutting speed. The interaction effect between cutting speed and 41.3

4 Md. Anayet Ullah Patwari, A. K. M. Nurul Amin, and Muammer D. Arif feed will also have a significant effect on surface roughness values. III. GENETIC ALGORITHMS OPTIMIZATION Genetic algorithms are a family of computational models inspired by evolution. These algorithms encode a potential solution to a specific problem on a simple chromosome like data structure and apply recombination operators to these structures so as to preserve critical information. Genetic algorithms are often viewed as function optimizers, although the range of problems to which genetic algorithms have been applied is quite broad. The objective of the optimization is to achieve minimum average surface roughness by adjusting the cutting conditions with the help of numerical optimization technique. Genetic algorithms are search algorithms for optimization, based on the mechanics of natural selection and genetics. The optimization problem in this study will be solved by coupling the RSM surface roughness model with the GA algorithm. In the solutions of the optimization techniques GA will begin with a set of chromosomes (bit strings) which will be randomly generated or selected. The entire set of these chromosomes will comprise a population. The chromosomes will evolve several iterations or generations and will make new generations called offsprings using crossover and mutation techniques. The chromosomes will be evaluated using fitness criteria and the best one will be kept and the others will be discarded. The optimization will be formulated in the standard mathematical format: language, selects chromosomes based on objective value and level of constraint violation. The genetic parameters are shown in Table III (following section). IV. OPTIMIZATION RESULTS By solving the optimization problem, GA predicted the optimum roughness as μm for the machining of Medium Carbon steel S45C in the selected cutting condition range. The optimum conditions leading to minimum surface roughness are shown in Table IV. The GA-predicted optimum conditions were further validated with physical measurements. The performance of fitness value with every generation and the best individual performances are shown in Fig. 2 in coded form. The experimental results of surface roughness with the optimum cutting parameters (as predicted by GA) show good agreement. TABLE III GA PARAMETERS In this work, MATLAB 7.0 Toolbox GA was used to develop the GA program. The GA, written in MATLAB programming Special Issue of the International Journal of the Computer, the Internet and Management, Vol. 19 No. SP1, June,

5 Optimization of Surface Roughness in End Milling of Medium Carbon Steel by Coupled Statistical Approach with Genetic Algorithm TABLE IV BEST CUTTING CONDITION FOUND IN GA The quadratic CCD model indicates that the feed was the most significant influence on surface roughness, followed by depth of cut and cutting speed An increase in either the feed or the axial depth of cut increases the surface roughness, whilst an increase in the cutting speed decreases the surface Contours of surface outputs are constructed in planes containing two of the independent variables. These contours were further developed to enable the selection on the proper combination of cutting speed and feed to increase the metal removal rate without sacrificing the quality of the surface finish produced. The CCD model developed by RSM using Design Expert package is able to provide accurately the predicted values of surface roughness close to actual values found in the experiments. The equations are checked for their adequacy with a confidence level of 95%. Fig. 2 The performance of fitness value with generation and the best individual performances of variables in coded form V. CONCLUSIONS This research paper discussed the development of a theoretical and experimental model for improving the efficiency of end milling of Medium carbon steel (S45C) using coated TiN inserts. The general conclusions can be summarized as follows: The two-stage effort, obtaining a surface roughness model by surface response methodology and optimization of this model by Genetic Algorithms, has resulted in a fairly useful method of obtaining process parameters in order to attain the required surface quality. REFERENCES [1] D. C. Montgomery, Design and Analysis of Experiments, 6th ed., Wiley, New York, [2] I. A. Choudhury, and M. A. El-Baradie, Machinability assessment of Inconel 718 by factorial design of experiment coupled with response surface methodology, in Journal of Material Processing and Technology, 1999, paper 95, pp [3] G. E. P. Box, and K. B. Wilson, On the experimental attainment of optimal conditions, Journal of the Royal Statistical Society, B 13, pp. 1-45, [4] J. E. Kaye, D. H. Yan, N. Popplewell, and S. Balakrishnan, Predicting tool flank wear using spindle speed change, in Int. J. Mach. Tools Manufacture, 1995, Vol. 35, No. 9, pp [5] M. Alauddin, M. A. El-Baradie, and M. S. J. Hashmi, Optimization of surface finish in end milling Inconel 718, in Journal of Material Processing and Technology, 1996, 56, pp [6] Design-Expert Software (Version 6.0.8), User s Guide, Technical Manual, Stat-Ease Inc., Minneapolis, MN,