OPTIMIZATION OF MULTIPLE PERFORMANCE CHARACTERISTICS IN EDM PROCESS OF HPM 38 TOOL STEEL USING RESPONSE SURFACE METHODOLOGY AND NON-LINEAR PROGRAMMING

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1 VOL., NO., JANUARY ISSN Asian Research Publishing Network (ARPN). All rights reserved. OPTIMIZATION OF MULTIPLE PERFORMANCE CHARACTERISTICS IN EDM PROCESS OF HPM 38 TOOL STEEL USING RESPONSE SURFACE METHODOLOGY AND NON-LINEAR PROGRAMMING Amirul Akbar, Bobby O. P. Soepangkat and Arif Wahjudi Manufacturing Process Lab., Department of Mechanical Engineering, Faculty of Industrial Technology, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia Design and Development Product Lab., Department of Mechanical Engineering, Faculty of Industrial Technology, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia amirul.yakusa@yahoo.com ABSTRACT The application of response surface methodology and non-linear programming for optimizing multiple performance characteristic in electro discharge machine (EDM) sinking process of HPM 38 steel was investigated. In this research, the main objective was to minimize surface roughness with electrode wear rate and material removal rate as constraints. The experiments were conducted based on Box-Behnken design (BBD) consisting 7 numbers of experiments. Quadratic model regression of response surface methodology was developed as efficient approaches to determine the optimal machining parameters in EDM process. Analysis of variance was applied to investigate the influence of process parameters (pulse current, gap width, on time and off time) and their interactions on surface roughness, electrode wear rate and material removal rate. A confirmation test was carried out to check the deviation of the predicted (optimum value) with experimental results. Keywords: EDM sinking, surface roughness, electrode wear rate, material removal rate, response surface methodology, non-linear programming. INTRODUCTION Electro discharge machine (EDM) is one of the non-conventional machining processes which is more efficient than conventional machining processes due to the ease of machining materials with complex geometry and burr-free []. EDM is used for machining of hard and high strength conductive materials which are hard enough to cut by conventional processes. In the process, there is no physical contact between the electrode and work piece that can eliminate mechanical stresses, chatter and vibration problems during machining. Hence, precision machining can be achieved by EDM []. It thus plays a major role in the machining of dies, tools, etc., made of tungsten carbides, stellites or hard steels [3]. In EDM, the removal of material is based upon the electro discharge erosion effect of electric sparks occurring between the electrode and work piece that are separated by a dielectric fluid. Material removal takes place as a result of the generation of extremely high temperatures (thermal energy) generated by the highintensity discharge that melt and evaporate the electrode and work piece [4]. The function of dielectrid fluid in EDM process is to flush out the eroded particle from the machining gap, provide insulation between the electrode and work piece and cooling the section that was heated by the discharge effect []. Performance characteristic of EDM machining process generally determined by surface roughness (SR), electrode wear rate (EWR) and material removal rate (MRR). The EDM parameters which affect the performance characteristics are polarity, on time, off time, working voltage, working current, flushing pressure and spark gap [, 8]. Electrode wear and material removal produced during EDM process can also affect the surface roughness significantly. A high quality of surface roughness in EDM machining process can be obtained with a low rate of removal material, but the slow process will affect the completion time of products and will increase the cost of production. This research takes HPM 38 steel as work piece and investigates three performance characteristics, i.e., surface roughness, material removal rate and electrode wear rate. Experiments were carried out using a fourvariable Box-Behnken design. The performance characteristics of surface roughness and electrode wear rate are smaller the better and material removal rate is higher the better. Response surface methodology was employed to develop experimental models. Non-linear programming was applied to minimize the surface roughness with electrode wear rate and material removal rate as contraints. EXPERIMENTAL DESIGN Machining Parameter Selection An EDM machine H. Walter Exeron 4 E was used as experimental machines. Copper with size of mm (length) x mm (width) x mm (thickness) was used for an electrode (as a negative polar) to erode a work piece of HPM 38 tool steel with size of mm (length) x mm (width) x mm (thickness). The electrode and

2 VOL., NO., JANUARY ISSN Asian Research Publishing Network (ARPN). All rights reserved. work piece were separated by kerosene dielectric using side flushing. An area with mm (length) x mm (width) and mm (depth) the work piece EDMachined. Machining experiments for determining the optimal machining parameters were carried out by setting pulse current (PC), gap width (GW), on time (On) and off time (Off). The total number of levels which provided in EDM machine for pulse current is levels, gap width is 9 levels, on time is 9 levels and of time is l9 evels. One level of pulse current, gap width, on time and off time are equal to 3 amperes, m, 84. s and 84. s respectively. In this research, the experiments were conducted based on Box-Behnken design (BBD) consisting 7 number of experiments. Machining parameters and their levels using Box- Behnken design are shown in Table-. In Box-Behnken design of response surface methodology, each parameter has 3 levels (low, medium and high) and the natural value of each machining parameter must be transformed to code units (X i ). The machining parameters are usually coded to - as a low level, as a medium level and as a high level. The machining parameter transformed model is [9]: X i = X real (X max + X min )/ (X max X min )/ The Box-Behnken design matrix of the experiment shown in Table-. Table-. Machining parameters and their levels. Machining Parameters Pulse current (X ) Unit Low level Medium level () High level Ampere 4 8 Gap width (X ) µm (X 3 ) µs 7 Off time (X 4 ) µs Run Ord. Table-. Matrix of experiment design. Code Parameters PC GW On Off Machining Performance Evaluation The measurements of surface roughness were performed by using a Mitutoyo surftest 4 with a cut off length ( s ) of 8 µm, sampling length ( c ) of. mm and the number of sampling length is times. The arithmetic mean surface roughness (R a ) was used for measuring the value of surface roughness. The material removal rate (MRR) is the ratio of material removal volume (V m ) and machining time in minute (t). The electrode wear rate (EWR) is the ratio of electrode removal volume (V e ) and machining time in minute (t). The formulas of MRR and EWR are: MRR = V m (mm 3 ) t (minute) () 7

3 VOL., NO., JANUARY ISSN Asian Research Publishing Network (ARPN). All rights reserved. EWR = V e (mm 3 ) t (minute) Design of Experiments The experiments were designed based on the Box-Behnken design (BBD) of response surface methodology (RSM). The Box-Behnken design is an independent quadratic design in that it does not contain an embedded factorial or fractional factorial design [9]. The advantages of Box-Behnken design are rotatable design; rotatable means that the model would possess a reasonably stable distribution of scaled prediction variance throughout the experimental design region []. Experimental Results RSM is a collection of mathematical and statistical technique useful for the modeling and analysis of problems in which a response of interest is influenced (3) by several variables and the objective is optimized the responses (multiple performance characteristics) []. To find a suitable approximation for the true functional relationship between the independent variables (machining parameters) and the response, the second order model is utilized in RSM [9]. Table-3 shows the experimental result of multi performance characteristics. The experimental results are used for developing of an empirical model using RSM. Model Adequacy Checking and Significance Test Experimental results were used to develop the second order (quadratic) regression model using Minitab software. Regression analysis and analysis of variance (ANOVA) were employed to check model adequacy and significance of machining parameters []. Tables 4 and show the results of regression analysis and ANOVA. Table-3. The experimental results of performance characteristics based on Box-Behnken design. Parameters SR EWR MRR X X X 3 X 4 µm mm 3 /mi n mm 3 /mi n Run Ord. Parameters SR EWR MRR X X X 3 X 4 µm mm 3 /min mm 3 /min Reg. Anlys. Term Coef Table-4. Regression analysis. Surface Roughness Electrode Wear Rate Material Removal Rate SE Coef T p value Coef SE Coef T p value Coef Constant X SE Coef X T -.47 X X p value 8

4 VOL., NO., JANUARY ISSN Asian Research Publishing Network (ARPN). All rights reserved. X X X 3 X X * X X * X X * X X * X X * X X 3 * X S =.943 PRESS =.4 R-Sq = 99.7% R-Sq(pred) = 97.8% S = PRESS =.8339 R-Sq = 99.8% R-Sq(pred) = 97.3% S =.9 PRESS = 4.83 R-Sq = 98.8% R-Sq(pred) = 94.% Table-. Analysis of variance (ANOVA). Surface Roughness Electrode Wear Rate Source D Adj D Adj Seq SS Adj SS F p F MS value Seq SS Adj SS F MS Regressio n 9 Linear Square Interaction Residual Error Lack-of Fit 9 9 Pure Error Total F p value Table-. Analysis of variance (ANOVA). Material removal rate Source DF Seq SS Adj SS Adj MS F p value Regression Linear Square Interaction Residual Error Lack-of-Fit Pure Error Total 7.9 9

5 VOL., NO., JANUARY ISSN Asian Research Publishing Network (ARPN). All rights reserved. Based on the regression analysis and ANOVA, all the quadratic models were adequate and machining parameters (linear, interactions and quadratic terms) were significant. The quadratic models of SR, EWR and MRR are: Surface roughness Y SR = (.8 * PC) - (.747 * GW) + (.9 * ON) - (.4 * OFF) + (.479 * PC ) + (.9979 * GW ) + (.7 * ON ) + (.47 * OFF ) - (. * (PC * GW)) + (.487 * (PC * ON)) + (.3 * (PC * OFF)) - (.4 * (GW * ON)) + (.337 * (GW * OFF)) - (.4 * (ON * OFF)) (4) Electrode wear rate Y EWR = (.38 * PC) - (.38 * GW) - (.97 * ON) - (.873 * OFF) + (.748 * PC ) + (.988 * GW ) + (.449 * ON ) + (.73 * OFF ) - (.9 * (PC * ON)) - (.7 * (PC * OFF)) - (.8388 * (GW * ON)) - (.94 * (GW * OFF)) + (.94 * (ON * OFF)) () Material removal rate Y MRR =.3 + (4.3 * PC) - (4.38 * GW) + (.9 * ON) - (.99 * OFF) + (3.33 * PC ) + (.33 * GW ) + (.7 * ON ) + (.93 * OFF ) - (.4 * (PC * GW)) + (3.3 * (PC * ON)) - (.3 * (PC * OFF)) - (.77 * (GW * ON)) - (.38 * (GW * OFF)) () Response Surface and Contour Plots In order to investigate the influence of machining parameters on the surface roughness, electrode wear rate and material removal rate, response surface plots and contour plots are drawn in Figures, and 3. Response surface plots and contour plots are drwned based on the quadratic model to evaluate the variation of response and also give assessment of the correlation between the machining parameters and responses []. In all these figures, two of the four machining parameters are held in constant level. As can be seen in Figure-, related to pulse current, surface roughness decreases considerably with decrease in pulse current. The minimum value of surface roughness is obtained under a lower on time. Figure- shows that the increase of pulse current would affect electrode wear rate considerably compared to the increase of on time. As can be deduced from Figure-3, material removal rate increases considerably with increase in both pulse current and on time. Gap width Off time, 7 9 Gap width Off time, 8 SR , -, -, -, 4 -,,,, (a) (b) Figure-. (a) Response surface and (b) contour plots of surface roughness. Gap width Off time,,7, Gap width Off time, EWR,,,,, -, - -, -, -, -,,,,,,, (a) (b) Figure-. (a) Response surface and (b) contour plots of electrode wear rate. 7

6 VOL., NO., JANUARY ISSN Asian Research Publishing Network (ARPN). All rights reserved. Gap width Off time, Gap width Off time, MRR 3 pulse current, - - pulse curre -, -, -, -,,,, (a) (b) Figure-3. (a) Response surface and (b) contour plots of material removal rate. Optimization and Confirmation Tests In this study, non-linear programming with Lingo software is used to optimize the multiple performance characteristics. The optimization of multiple performance characteristics aimed to obtain the minimum value of the SR with EWR and MRR as constraints and machining levels parameters as boundaries. From this step, the levels of the machining parameters which would yield minimum SR could be obtained. The first step is to minimize EWR and to maximize MRR for obtaining the constraint values that would be used in minimizing SR. This optimization was conducted by using Lingo software and the resulted minimum value of EWR was.388 mm 3 /minute and the maximum value of MRR was 3.44 mm 3 /minute. The next step is to minimize SR using the following optimization model: Target: minimize surface roughness = Y SR Y SR = (.8 * PC) - (.747 * GW) + (.9 * ON) - (.4 * OFF) + (.479 * PC ) + (.9979 * GW ) + (.7 * ON ) + (.47 * OFF ) - (. * (PC * GW)) + (.487 * (PC * ON)) + (.3 * (PC * OFF)) - (.4 * (GW * ON)) + (.337 * (GW * OFF)) - (.4 * (ON * OFF)) Constraints: EWR and MRR Electrode wear rate Y EWR = (.38 * PC) - (.38 * GW) - (.97 * ON) - (.873 * OFF) + (.748 * PC ) + (.988 * GW ) + (.449 * ON ) + (.73 * OFF ) - (.9 * (PC * ON)) - (.7 * (PC * OFF)) - (.8388 * (GW * ON)) - (.94 * (GW * OFF)) + (.λ4 * (ON * OFF)).388 Material removal rate Y MRR =.3 + (4.3 * PC) - (4.38 * GW) + (.9 * ON) - (.99 * OFF) + (3.33 * PC ) + (.33 * GW ) + (.7 * ON ) + (.93 * OFF ) - (.4 * (PC * GW)) + (3.3 * (PC * ON)) - (.3 * (PC * OFF)) - (.77 * (GW * ON)) - (.38 * (GW * OFF)) 3.44 Boundaries: - pulse current (PC) - gap width (GW) - on time (ON) - off time (OFF) The minimum value of SR was m and the combination levels of the machining parameters which would yield minimum SR are: Parameters [code unit] Pulse current Gap width.3474 Off time.777 These coded levels of the optimum machining parameters should be adjusted to the available levels of the machining parameters in EDM machine H. W. Exeron 4 E, for obtaining the real optimum value of SR, EWR and MRR. The available levels in EDM machine are: Parameters [code unit] [machine unit] Pulse current 8 (4 A) Gap width m 7 (89 µs) Off time. 7 (89 µs) The optimum value of the EDM multiple performance characteristics are: SR : 3.447λ78 m 3.4 µm EWR : mm 3 /minutet.3 mm 3 /minute MRR : mm 3 /menit λ.3 mm 3 /minute The final step is conducting confirmation test. The results of the confirmation test are shown in Table-. By using statistical test, it could be proved that there are no significant differences between the surface roughness, electrode wear rate and material removal rate resulted from non-linear programming optimization and confirmation test. 7

7 VOL., NO., JANUARY ISSN Asian Research Publishing Network (ARPN). All rights reserved. Table-7. Confirmation test. Optimum Experiments 3 SR (µm) EWR (mm 3 /min) MRR (mm 3 /min) CONCLUSIONS In this research, the application of response surface methodology and non-linear programming for optimizing multiple performance characteristics in electro discharge machine (EDM) sinking process of HPM 38 steel was investigated. Quadratic model regression of response surface methodology is developed to determine the optimal machining parameters in EDM process. Analysis of variance was applied to investigate the influence of machining parameters (pulse current, gap width, on time and off time) on surface roughness, electrode wear rate and material removal rate. Confirmation test was carried out to check the deviation of the predicted. The conclusions of this research are as follows: Pulse current followed by on time, off time and gap width are statistically significant in affecting surface roughness. The order of machining parameters that statistically and significantly affect electrode wear rate are pulse current, gap width, off time and on time respectively The two main significant machining parameters that affect the material removal rate are pulse current and on time. The setting of machining parameters to minimize surface roughness with electrode wear rate and material removal rate as constraints, are pulse current, gap width, on time and off time at 8 (4 A), 44 m, 7 (89 µs) and 7 (89 µs) respectively. The minimum value of surface roughness with electrode wear rate and material removal rate as constraints is 3.4 µm. The minimum value of electrode wear rate is.3 mm 3 /minute. The maximum value of material removal rate is 9.3 mm 3 /minute. REFERENCES [] B. O. P. Soepangkat and B. Pramujati. 3. Optimization of Surface Roughness and Recast Layer Thickness in the Wire-EDM Pocess of AISI D Tool Steel Using Taguchi-Grey-Fuzy. Applied Mechanics and Materials. 393: -8. [3] P. C. Pandey and H. S. Shan. 98. Modern Machining Process. Tata McGraw-Hill Publishing Company Limited, New Delhi. [4] H. A. G. El-Hofy.. Advanced Machining Processes. McGraw Hill Companies, New York. [] C. Sommer.. Complete EDM Handbook. Advanced Publishing Inc., Houston. [] R. Rajesh and M. D. Anand.. The Optimization of the Electro-Discharge Machining Process Using Response Surface Methodology. International Conference on Modeling. Optimization and Computing. 38: [7] T. Vaani and M. Hameedullah.. Optimization Control Parameter in Electric Discharge Machining of Hardened Steel with Copper Electroplated Aluminum Electrode. Proceeding of the International Conference on Recent Advance in Mechanical and Material Engineering, Malaysia. [8] M. R. Shabgard, M. Seyedzavvar, S. N. B. Oliael.. Influence of Input Parameters on the Characteristics of the EDM Process. Journal of Mechanical Engineering. 7: [9] K. Yang and B. El-Haik. 3. Design for Six Sigma, McGraw Hill, New York. [] D. C. Montgomery. 9. Design and Analysis of Experiment. 7 th edition. John Wiley and Sons Inc, New York. [] K. T. Chiang. 8. Modelling and analysis of the effects of machining parameters on the performance characteristics in EDM process of Al O 3 + TiC mixed ceramic. Int. J. Adv. Manuf. Technology. 47: [] A. Shashikant, K. Roy and K. Kumar. 4. Effect and optimization of various machine process parameters on the surface roughness in EDM for an EN 9 material using response surface methodology. International of Conference on Advances in Manufacturing and Materials Engineering. : [] E. B. Guitrau The EDM Handbook. Hanser Gardner Publications, Cincinnati. 7