Indian Journal of Engineering & Materials Science Vol. 20, December 2013, pp. 471-475 Taguchi-grey relational based multi response optimization of electrical process parameters in electrical discharge machining T Muthuramalingam a * & B Mohan b a Department of Production Technology, M I T Campus, Anna University, Chennai 600 025, India b Department of Mechanical Engineering, C E G Campus, Anna University, Chennai 600 025, India Received 28 September 2012; accepted 3 May 2013 In modern machining process, optimization technique is used to find the optimal values of input parameters and the effect of those parameters on response variables. If response parameters are more than one, Taguchi method of optimization may give different set of optimal levels for each response. In the present study, Taguchi-grey relational approach based multi response optimization has been used to maximize material removal rate and to minimize surface roughness in electrical discharge machining. Electrical process parameters such as gap voltage, peak current and duty factor have been used as input parameters. It has been found that peak current has most influent nature in electrical discharge machining process. Optimal combination of input parameter to acquire better responses has been found with multi response optimization using Taguchi-grey relational analysis. Keywords: EDM, Taguchi, Current, MRR, Surface roughness Electrical discharge machining (EDM) is a thermal erosion process, in which the material removal from the work piece is obtained by high thermal energy due to the ionization of dielectric medium between tool and electrode. Ho and Newman 1 explained about basic working mechanism involved in thermal erosion process. Figure 1 shows the setup of electrical discharge machining. Since electrical parameters are mainly contributed factor to produce thermal energy, it is needed to find optimal combination of electrical parameters on machinability. Mohan et al. 2 described about the importance of electrical parameters in EDM process. Son et al. 3 explained about need of optimizing the electrical parameters. Fuzhu et al. 4 proved the effects of electrical parameters on machining characteristics in thermal erosion process. Experimental Procedure Since the discharge energy is mainly determined by gap voltage, peak current and duty factor, these factors have been taken as the input parameters. Duty factor is defined as ratio of pulse duration to total pulse cycle. Table 1 shows the process variables used in the present study. 40 V, 60 V and 70 V have been considered as gap voltage variables. 0.4, 0.6 and 0.8 have been chosen as duty factor with the discharge *Corresponding author(e-mail: muthu1060@gmail.com) Process variables Table 1 Selection of the process variables Pulse generator type Work piece Tool Dielectric medium Flushing Depth of cut (mm) Gap voltage (V) Peak current (A) Duty factor Flushing pressure (bar) Description Iso energy pulse AISI 202 Stainless Steel Brass kerosene Normally submerged 5 40, 60,80 9,12,15 0.4,0.6,0.8 1 Fig 1 Electrical discharge machining setup
472 INDIAN J ENG MATER SCI., DECEMBER 2013 current values of 9 A, 12 A and 15 A. AISI 202 stainless steel has been selected as work piece material, whereas brass has been introduced as tool electrode with kerosene as the dielectric medium. Table 2 shows the selected process parameters in EDM process. Lin et al. 5 discussed about Taguchi based optimization of electrical parameters in EDM process. Lin et al. 6 reported about detailed investigation of thermal erosion process to optimize the process variables in EDM process. Meena and Azad 7 explained about grey relational based approach of optimization approach. Siddhi et al. 8 applied Taguchi-grey scale approach for optimizing sintering process parameters to fabricate metal matrix composites. Tsao 9 applied the same approach to optimize the milling parameters of aluminium alloy. Noorul Haq et al. 10 used the Taguchi-grey approach to optimize drilling process parameters. These studies explained about importance and need of multi response optimization on process parameters in EDM process. From the literature, it has been understood that only few attempt has been made to optimize electrical parameters with multi response level approach. Hence in the present study, Taguchi-grey multi level optimization approach has been introduced for obtaining optimal level of response parameters such as material removal rate and surface roughness. Figure 2 shows the surface topography of machined surface in EDM process. Taguchi Method Taguchi method is systematic and efficacy approach to find the optimal combination of input parameters. This method utilizes the orthogonal array of experiments to reduce the number of experiments in any machining process. Since three input parameters have been selected, L9 orthogonal array has been selected for this study. Using the orthogonal array nine experiments have been conducted. Material removal rate has been calculated by weight difference of workpiece before and after the machining process with 0.01 mm high precision balance. The surface roughness has been computed using surfcoder surface roughness tested with 0.8 mm as cutoff length. Table 3 shows the combinations of input factors with their corresponding responses. It is also used to study the effects of input parameters on response variables. This quality analysis tool analyzes the obtained results by using signal-to-noise (S / N) ratio. This ratio is determined by characteristics of the machining process. The categories of this ratio are larger the Factor notation Table 2 Selected process parameters in EDM process. Factor Level 1 Level 2 Level 3 A Gap voltage (V) 40 60 70 B Peak current (A) 9 12 15 C Duty factor 0.4 0.6 0.8 Table 3 Orthogonal L 9 Table for responses A B C A B C Material removal rate (mm 3 /min) Fig. 2 Microstructure topography of machined surface Surface roughness (µm) 1 1 1 1 40 9 0.4 4.74 3.26 2 1 2 2 40 12 0.6 8.6 6.98 3 1 3 3 40 15 0.8 9.51 11.78 4 2 1 2 60 9 0.6 7.46 4.58 5 2 2 3 60 12 0.8 12.8 9.62 6 2 3 1 60 15 0.4 8.384 6.99 7 3 1 3 70 9 0.8 15.51 6.53 8 3 2 1 70 12 0.4 10.9 4.82 9 3 3 2 70 15 0.6 13.36 8.98
MUTHURAMALINGAM & MOHAN: OPTIMIZATION OF PROCESS PRAMETERS IN EDM 473 better, smaller the better and nominal the better. In EDM process, the main aim is to reduce surface roughness and to increase material removal rate. Hence, Larger the better has been applied for material removal rate (MRR) whereas the smaller the better has been applied for surface roughness (SR). For Larger the better, S/N ratio = - 10 log (1/n) Σ ( 1 / Y ij 2 ) (1) For smaller the better, S/N ratio = - 10 log (1/n) Σ ( Y ij 2 ) (2) Where n is the number of replications for each experiment and Y ij is the response values. Table 4 shows the S/N ratio of obtained response from each experiment. Grey Relational Approach In the present study, the multiple performance characteristics have been investigated with grey relational approach. In this method, the multiple performance characteristics can be converted into single grey relational grade. The following stages are done for this approach: Stage 1 The S/N ratios obtained from the Taguchi analysis have to be normalized in the range of 0 to 1. For larger the better, X ij = (Y ij min (Y ij )) / ( max (Y ij ) min (Y ij ) ) (3) For smaller the better, X ij = (max(y ij ) Y ij ) / ( max (Y ij ) min (Y ij ) ) (4) Where X ij is normalized S/N ratio, Y ij is the S/N ratio obtained from the Taguchi analysis, min(y ij ) and max(y ij ) are respectively minimum and maximum values of S/N ratio. Stage 2 Grey relational grade in this analysis indicates the relational degree between every sequences of obtained values. The grey relational coefficient can be calculated as GC ij = ( min + Ψ max ) / ( ij + Ψ max ) (5) Where GC ij is the grey relational grade. Since multi response characteristics consist of both larger the better and smaller the better, Ψ is assumed to 0.5 in this case. min and max are the minimum and maximum absolute difference which is a deviation from target value and can be treated as quality loss. Stage 3 After averaging the grey relational coefficients, grey relational grade (G i ) can be calculated as G i = (1/m) Σ GC ij (6) Where m is the number of response variables. The high value of grey relational grade indicates the stronger relational degree between ideal sequence and present sequence. Ideal sequence is the best response in the machining process. Higher grey grade indicates closer to the optimal response in the process. Results and Discussion Table 4 shows the S/N ratio with its corresponding normalized S/N ratio for material removal rate and surface roughness. These values have been converted Table 4 S/N ratio and normalized S/N ratio for conducted experiments Material removal rate Surface roughness S/N ratio Normalized S/N ratio S/N ratio Normalized S/N ratio 1 13.51557 0-10.2644 1 2 18.68997 0.50253131-16.8771 0.40844403 3 19.56361 0.58737828-21.4229 0 4 17.45478 0.38257092-13.2173 0.73584027 5 22.1442 0.83800194-19.6635 0.15918044 6 18.46903 0.48107353-16.8895 0.40733162 7 23.81224 1-16.2983 0.460226 8 20.74853 0.70245623-13.6609 0.69615416 9 22.51613 0.8741233-19.0655 0.21267373
474 INDIAN J ENG MATER SCI., DECEMBER 2013 MRR (mm 3 /min) Fig. 3 Grey relational grade for multi response into grey scale co-efficients as per stages involved in grey relational analysis. As already indicated, distinguishing coefficient have been taken as 0.5. After getting grey relational coefficients, grey scale grade has been found as illustrated earlier. The rank of each trial has been tabulated based on grey scale grade as shown in Table 5. The higher grey relational grade will have better multi response characteristics. Figure 3 shows the grey relational grade for all experiments. Hence it is proved that experiment 7 has the optimal parameters setting for best multi response characteristics such as material removal rate and surface roughness. The average grey relational grade value for every level of the input parameters is shown in Table 6. These have been calculated by taking the average for each level group Table 5 Grey relational coefficients with grey relational grade Grey relational coefficient R a (µm) Grey relational grade 1 0.333333 1 0.666667 2 2 0.501269 0.458062 0.479665 7 3 0.547872 0.333333 0.440603 9 4 0.447456 0.654313 0.550885 6 5 0.755289 0.372906 0.564098 5 6 0.490713 0.457595 0.474154 8 7 1 0.480874 0.740437 1 8 0.626925 0.62201 0.624467 3 9 0.798879 0.388402 0.593641 4 Input factors Table 6 Response table of the average grey relational grade Average grey relational grade by factor level Level 1 Level 2 Level 3 Rank max-min Gap voltage (V) 0.5290 0.5297 0.6528 0.1238 Discharge current (A) 0.6527 0.5561 0.5028 0.1499 Duty factor 0.5884 0.5414 0.5817 0.0470 Total mean grey relational grade = 0.5705 in all the levels of process parameters. Since it denotes the level of correlation between reference sequence and obtained sequence, the higher value of average grey grade indicates stronger correlation between them. It indicates optimal level of process parameters. The higher max-min value indicates the most important nature on determining response in the process. Hence it is proved that discharge current is most significant factor among electrical input parameters in EDM process. The optimal setting process parameters combination has been obtained from Table 6, i.e., optimal gap voltage level 3; optimal discharge current level 1; optimal duty factor level 1; and the optimal combination of A3 B1 C1. The values of optimum process parameters are gap voltage 70 V, peak current 9 A and duty factor 0.4. Confirmation test After identifying the optimal process parameters, the confirmation test is to be conducted to validate the analysis. In the confirmation test, an experiment has been conducted with optimal process parameters settings. The predicted grey relational analysis using optimal process parameters is given as ϒ = ϒ m + Σ (ϒ n - ϒ m ) (7) Where ϒ m is the total mean grey relational grade; ϒ n is the mean grey relational at optimum level; The predicted value obtained from Eq. (7) is 0.7529. At the optimal setting, the response values from the
MUTHURAMALINGAM & MOHAN: OPTIMIZATION OF PROCESS PRAMETERS IN EDM 475 confirmation experiments are material removal rate is 15.78 and surface roughness is 6.42, and the grey relational grade value is 0.7404. The grey relational grade value of confirmation experiment is improved by 1.7% from the predicted mean value. Conclusions In this study, Taguchi L9 array with grey relational analysis has been used to optimize the multiple performance characteristics such as material removal rate and surface roughness. The largest max-min value has been found from response table. It is found that peak current is most significant factor among process parameters involved in EDM process. The values of optimum process parameters are gap voltage Confirmation test proved that the determined optimum combination has satisfied the real requirement of input process parameters in thermal erosion process. Acknowledgement The authors wish to express their sincere thanks to Department of Production Technology and Centre for Rresearch, Anna University, Chennai, for funding this research. References 1 Ho K H & Newman S T, Int J Mach Tool Manuf, 43 (2003) 1287-1300. 2 Mohan B, Rajadurai A & Satyanarayana K G, J Mater Process Technol, 124 (2002) 297-304. 3 Son S M, Lim H S, Kumar A S & Rahman M, J Mater Process Technol, 190 (2007) 73-76. 4 Fuzhu Han, Li Chen, Dingwen Yu & Xiaoguang Zhou, Int J Adv Manuf Technol, 33 (2007) 474-479. 5 Yan-Cherng Lin, A-Cheng Wang, Der-An Wang & Chih-Cherng Chen, Mater Manuf Process, 24 (2009) 667-674. 6 Yan-Cherng Lin, Chao-Hsu Cheng, Bo-Lin Su & Lih-Ren Hwang, Mater Manuf Process, 21 (2006) 922-929. 7 Meena Vijaya Kumar & Aazad Man Singh, Mater Manuf Process, 27 (2012) 973-977. 8 Siddhi Jailani H, Rajadurai A, Mohan B, Senthil Kumar A & Sornakumar T, Int J Adv Manuf Technol, 45 (2009) 362-369. 9 Tsao C C, Int J Adv Manuf Technol, 40 (2009) 41-48. 10 Noorul Haq A, Marimuthu P & Jeyapaul R, Int J Adv Manuf Technol, 37 (2008) 250-255