APPLICATION OF GREY RELATIONAL ANALYSIS TO MACHINING PARAMETERS DETERMINATION OF WIRE ELECTRICAL DISCHARGE MACHINING

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1 APPLICATION OF GREY RELATIONAL ANALYSIS TO MACHINING PARAMETERS DETERMINATION OF WIRE ELECTRICAL DISCHARGE MACHINING J.T. Huang 1 and Y.S. Liao 1 Department of Automatic Engineering, Kaoyuan Institute of Technology, Lu-Chu, Kaohsiung, 81, Taiwan Fax: tsung@cc.kyit.edu.tw Department of Mechanical Engineering, National Taiwan University, 1, Sec. 4 Roosevelt Rd. Taipei, 106, Taiwan ABSTRACT Grey relational analyses are applied to determine the suitable selection of machining parameters for Wire Electrical Discharge Machining (Wire-EDM) process. The Grey theory can provide a solution of a system in which the model is unsure or the information is incomplete. Besides, it provides an efficient solution to the uncertainty, multi-input and discrete data problem. According to the Taguchi quality design concept, a L18 mixed-orthogonal-array table was chosen for the experiments. With both Grey relational analysis and statistical method, it is found that the table-feedrate has a significant influence on the machining speed, whilst the gap width and the surface roughness are mainly influenced by pulse-on time. Moreover, the optimal machining parameters setting for maximum machining speed and minimum surface roughness (or a desired surface roughness) can be obtained. KEY WORDS: Wire-EDM, Grey relational analysis, Machining parameters setting 1. INTRODUCTION. Wire electrical discharge machining (Wire-EDM) involves a series of complex heating and cooling process. Electrical discharging happens when workpiece (anode) and wire-electrode (cathode) are very close (about µm) with a gap voltage supplied. Good static and dynamic characteristic of machine are necessary to obtain optimal machining performance. In addition, machining parameters, including pulse-on time, pulse-off time, table-feedrate, flushing pressure, wire tension, wire velocity, etc., should be chosen properly. However, 1

2 selection of appropriate machining parameters for Wire-EDM is difficult, and relies heavily on operators experience. The Grey theory can provide a solution of a system in which the model is unsure or the information is incomplete [1]. Besides, it provides an efficient solution to the uncertainty, multi-input and discrete data problem. The relation between machining parameters and performance can be found out with the Grey relational analysis. Also, the Grey relational grade will utilize the discrete measurement method to measure the distance. Some researches related to Wire-EDM machining-parameters setting were conducted. Kravet [] proposed an estimating calculation method for a multi-cut Wire-EDM process. Scott, Boyina and Rajurkar [3] used a factorial design method to determine the optimal combination of control parameters in Wire-EDM. A number of 3 machining settings, which resulted in a better metal removal rate and surface roughness, were determined from 79 experiments. Tarng [4] applied neural network with simulated annealing (SA) algorithm to determine the optimal machining-parameters in Wire-EDM process. However, it can not provide the optimal machining parameters for a desired surface roughness. Liao [5] presented an approach to determine optimal parameters setting based on the Taguchi Quality design method, analysis of variance, regression analysis and feasible direction method. Lin [6] presented the use of Grey relational grade to the machining parameters optimization of the electrical discharge machining (EDM) process. Optimal machining-parameters setting for Wire-EDM still has some difficulty: costly and time-consuming in conducting experiments, many machining parameters, and real mathematical models hard to be derived. The purpose of this paper is to present an efficient method to find the significant parameters affecting machining performance by integrating Grey relational analysis and statistical method. Also, the optimal machining-parameters setting for maximum machining speed and minimum surface roughness can be obtained by applying Grey relational analysis. Furthermore, it is feasible to obtain optimal machining parameters for a desired surface roughness and maximum metal removal rate by the Grey relational analysis.

3 . EXPERIMENTAL METHOD. Experiments were carried out on a Wire-EDM machine with an iso-energy pulse generator, developed by the Industrial Technology Research Institute (ITRI), Taiwan. The workpiece material (anode) is SKD11 alloy steel of 30 mm height. The electrode (cathode) is φ 0.5mm brass wire. The fluid specific resistance is between 10 4 and 10 6 Ω cm. The open voltage and servo reference voltage is set as 95 V and 10 V respectively. According to the Taguchi quality design concept [7], a L18 mixed orthogonal array table was chosen for the experiments as shown in Table 1. Six machining parameters (pulse-on time, pulse-off time, table-feedrate, wire tension, wire velocity and flushing pressure) were chosen for the controlling factors and each parameter was designed to have three levels, denoted by 1,, and 3 as shown in Table. The machining results after Wire-EDM process are evaluated in terms of the following measured machining performance: (1) Metal removal rate (V w, mm 3 /min); () Gap width (D, m); (3) Surface roughness ( R a, m). 3. GREY RELATIONAL ANALYSIS. The Grey theory established by Dr. Deng includes Grey relational analysis, Grey modeling, prediction and decision making of a system in which the model is unsure or the information is incomplete [8]. It provides an efficient solution to the uncertainty, multi-input and discrete data problem. The relation between machining parameters and machining performance can be found out using the Grey relational analysis. And this kind of interaction is mainly through the connection among parameters and some conditions that are already known. Also, it will indicate the relational degree between two sequences with the help of Grey relational analysis. Moreover, the Grey relational grade will utilize the discrete measurement method to measure the distance. When the range of the sequence is too large or the standard value is too enormous, it will cause the influence of some factors to be neglected. Also, in the sequence, if the factors goals and directions are different the relational analysis might also produce incorrect results. Therefore, preprocessing of all the data is necessary. This process is so called as Grey 3

4 relational generating. There are three different types as following: (1) The higher is better x * i(k)= xi min xi [1] max x min x i i () The lower is better x * i(k)= max xi xi [] max x min x i i (3) A desired value X : x * xi x i(k)=1- max x x i [3] where x * i(k) is the generating value of Grey relational analysis; min x i is the minimum value of x i ; max x i is the maximum value of x i The term Grey relational grade, Γ is used to show the relationship among the series. Let (X, Γ ) be a Grey relational space. X stands for the collection of Grey relational factors, and let x i be the compared series, x 0 the reference series: x 0 (k)= ( x 0 (1) x 0 () x 0 (k)) [4] x i (k)=( x i (1) x i () x i (k)) X [5] Where i=1,,m. k=1,,n N The Grey relational grade is calculated as following [9]: 4

5 Γ = oi min ' + + max max [6] where (1) i=1,,m, k=1,,n j i, () x 0 (k):the reference sequence, x i (k): comparative sequences (3) 0i (k)= x 0 (k)- x i (k) (4) = min min min j i k x 0 (k)- x j (k) = j i k x 0 (k)- x j (k) (5) max max max n (6) ' = ( k = 1 ) oi n 4. STATISTICAL ANALYSIS. 4.1 Calculation of S/N Ratio. The characteristic that the higher value represents better machining performance, such as metal removal rate (V w ), is called higher is better, HB. Inversely, LB stands for lower is better, such as surface roughness. The S/N ratio (signal-to-noise ratio, ) is an effective representation to find significant parameters by evaluating minimum variance. For HB and LB, the definition of S/N ratio for machining performance y i of n repeated number (in this case n=3, i=1,,3) are computed as: HB: LB: η= 10 * log(1/ ( ( ))) n y y y 1 η= 10 * log(1/ ( ( y n y y n n ))) [7] [8] 5

6 4. Analysis of Variance and F test. In order to assure significant machining-parameters, analysis of variance (ANOVA) and F test are used to analyze the experimental data with above calculated values as follows: S S m A ( = = η ) 18 η N i Ai, S T S m =, S E i η S = S T m S A [9] Where S is the sum of squares due to total variation; S T m is the sum of squares due to mean; S A is the sum of squares due to factor A (A= f, ti, t o, V wire, F wire, and P); S E is the sum of squares due to error; i is the value of each experiment (i=1--18); Ai is the sum of i level of factor A(i=1, or i=1,,3); N is the Repeating number of each level of factor A. F test is used to determine if variance of significant factor is bigger than the variance of error. F test value is defined as following: S V V A = = f V A, FA0 A A E [10] where f is the degree of freedom of factor A; V A A is the variance of factor A; F AO is the F test value of factor A. The significant factors can be found for the reason that F AO value is bigger than F 0.05,n1,n value. F 0.05,n1,n is the reference value that is larger than 95 % distribution for degree n1 and n. 5. RESULTS AND ANALYSIS. 5.1 Significant Machining Parameters Grey relational analysis The measured data of machining performance including metal removal rate (V w ), surface roughness (R a ) and gap width (D) was shown in Table 3. First, eighteen data of metal removal 6

7 rate (V w ) are set as the reference sequence denoted as X 0 (k). And, the L18-array values of table-feedrate (f), pulse-on time (t i ), pulse-off time (t o ), wire velocity (V wire ), wire tension (F wire ) and flushing pressure (P) were set as six comparative sequence X i (k), i=1,,3,4,5,6 k= In order to satisfy the three characters of Grey relational analysis: normalization, scaling and polarization, the original data of each sequence (f (k), t i (k), t o (k), V wire (k), F wire (k) and P(k)) were calculated by equation 1 under the assumption of all the comparative sequences are the higher is better, HB. Those generated data were shown in Table 4. And, the Grey relational grade of each machining parameter on V w can be obtained by substituting those generating data into equation 6. Also, the Grey relational grade of each machining parameter on R a or D can be found similarly as shown in Table 5. It is found that table-feedrate and pulse-on time have significant influence on metal removal rate, and Gap width and surface roughness are mainly influenced by wire tension Statistical analysis (1) Calculation of S/N ratio The measured data in Table 3 were substituting into equation 7 & 8, and the S/N ratio ( ) were shown in Table 6. In order to obtain the effects of machining parameters on machining performance for each different level, the values of each fixed and level for each machining performance are summed up. From Table 6, taking t i on V w as an example, the values of three levels can be summarized as follows: level 1: on1 = = 77.0 level : on = = level 3: on3 = = Similarly, those values of the other parameters on other machining performance could be evaluated. The total values of the levels of six parameters on metal removal rate (V w ), surface roughness (R a ) and Gap width (D) can be calculated as shown in Table 7. For metal removal rate (V w ), it is found that larger pulse-on time (t i ), table-feedrate (f) and pulse-off time(t o ) are better, and smaller wire velocity (V wire ), wire tension(f wire ) and flushing pressure(p) are better. 7

8 () Analysis of Variance & F test However, it is hard to assure that only this setting will result in maximum V w because of small difference value between different levels, and experimental errors. Hence, analysis of variance (ANOVA) and F test are used to analyze the experimental data to find out the significant machining parameter. The square sum, variance and F test value of machining parameters on V w in Table 8 & 9 were obtained by substituting those data of Table 7 into equation 9 and 10. It is found that the significant factors on V w are f and t i for the reason that both F values are bigger than F AO 0.05,n1,n. Similarly, the significant parameters for each machining performance can be obtained as shown in Table 9. Compared to the result induced by Grey relational analysis in section 5.1.1, it is obvious that the results are different. f and t i have main influence in metal removal rate (V w ), and t i (not wire tension) has significant results in gap width and surface roughness Integration of S/N ratio and Grey relational analysis From the results of S/N ratio analysis in section 5.1., it is found that larger pulse-on time (t i ), table-feedrate (f) and pulse-off time (t o ) are better, and smaller wire velocity (V wire ), wire tension (F wire ) and flushing pressure (P) are better for metal removal rate (V w ). Therefore, the Grey relational generating of sequences of V wire (k), F wire (k) and P(k) in previous section should be calculated by equation as the lower is better, LB. A repeated calculation procedure was conducted as mentioned in section The Grey relational generating value of each sequence is shown in Table 10. Furthermore, the Grey relational grade of each machining parameter on V w, D and R a was shown in Table 11. It is obviously found that f and t i has main influence in metal removal rate (V w ), and t i has significant influence in Gap width and surface roughness, which is the same as shown in Table 9. Hence, it is concluded that the influence of machining parameters on V w, R a and D can not obtained correctly by Grey relational analysis unless the characteristics (HB or LB) of each machining parameter on V w, R a and D are known, which can be obtained by S/N ratio. 8

9 5. Optimal Machining-Parameters Setting Generally speaking, maximum metal removal rate and minimum surface roughness should be considered simultaneously while manufacturing. In order to obtain the optimal machining parameters for multiple quality requests, statistical analysis must integrate some other numerical methods like regression and optimal mathematical theorem. However, it is quite direct and efficient to obtain the optimal machining parameters by Grey relational analysis. A reference sequence X 0 (k)={ V w, R a }= {1,1} is designed. The Grey relational generating data of 18 experiments are taken as sequences X 1 (k), X (k), X 3 (k).x 17 (k), X 18 (k)( k=1(v w ),(R a )) as shown in Table 1. In Grey relational generating process, metal removal rate (V w ) is taken as HB (higher is better) and surface roughness (R a ) is set as LB (Lower is better). Grey relational grade ( Γ ) can be calculated by equation 6. It is found that no. 15 machining parameters oi setting has the highest Grey relational grade from Table 1. Therefore, the no. 15 machining parameters setting is optimal one for maximum V w and minimum R a simultaneously among 18 experiments. For a desired surface roughness and maximum metal removal rate, optimal machining parameters can also obtained by Grey relational analysis. Taking a desired R a = 3 µm (set as the reference sequence X 0 (k)) for example, 18 values of surface roughness were substituted to equation 3 to obtain the Grey relational generating data. After the Grey relational generating and Grey relational grade calculation, the optimal machining parameters setting can be obtained as no. 16. Hence, this approach is feasible to obtain optimal machining parameters for a desired surface roughness and maximum metal removal rate by the Grey relational analysis. 6. CONCLUSION. Based on Taguchi L18 mixed orthogonal table, only eighteen experiments need to be conducted to find the significant machining-parameters. According to the integration of Grey relational analysis and S/N ratio, it is found that table federate and pulse-on time have main influence in metal removal rate, and pulse-on time has significant influence in gap width and surface roughness 9

10 By Grey relational analysis, the optimal machining parameters setting can be obtained for considering maximum metal removal rate and minimum surface roughness simultaneously. Furthermore, this approach is feasible to obtain optimal machining parameters for a desired surface roughness and maximum metal removal rate by Grey relational analysis. 7. REFERENCES. 1. Deng, J.L., "A course on Grey System Theory", HUST Press( in Chinese ), Wuhan, Krvaets, A.T., "Planning of The Wire-EDM Process," Proceedings of the International Symposium for Electro-Machining, (ISEM-10), pp. 18-, Scott, D., Boyina, S. and Rajurkar, K.P., "Analysis and Optimization of Parameter Combination in Wire Electrical Discharge Machining, " Int. J. Prod. Res., Vol.9/11, pp , Tarng, Y.S., Ma, S.C. and Chung, L. K., "Determination of optimal cutting parameters in wire electrical discharge machining, " Int. J. Mach. Tools Manufact., Vol. 35, No. 1, pp , Liao, Y.S., Huang, J.T. and Su, H.C., "A Study on the Machining Parameters Optimization of the Wire Electrical Discharge Machining", Journal of Materials Processing Technology, 71, pp , Lin, J.L. and Tarng, Y.S., "Optimization of the Multi-Response Process by the Taguchi Method with Grey Relational Analysis ", The Journal of Grey System, 4, pp , P. J. Ross, "Taguchi Techniques for Quality Engineering ", McGraw-Hill, New York. 8. Deng, J.L., "Introduction to Grey System ", The Journal of Grey System, Vol.1, pp.1-4, Hsia, K.H. and Wu, J.H., "A Study on the Data Preprocessing in Grey Relation Analysis", Journal of The Chinese Grey System Association, Vol.1, No.1, pp.47-53,

11 Table 1. L18 mixed orthogonal array table (f: feederate, t i : pulse-on time, t o : pulse-off time, V wire : wire velocity, F wire : Wire tension, P: fluid pressure, E 1 &E : error factors) Factors f t i t o V wire F wire P E 1 E Table. Experimental machining-parameter levels Levels Unit Machining parameter Table feedrate mm/min Pulse-on time s 3 Pulse-off time s 4 Wire velocity m/min 5 Wire tension ( ) N 6 Fluid pressure ( ) Pa 11

12 Table 3. The measured data of machining performance V w R a D Table 4. Grey relational value of machining parameters on V w (HB) V w (X 0 ) f t i t o V wire F wire P Table 5. Grey relational grade (all HB) V w R a D f 0.716* t i t o V wire F wire * * P

13 Table 6. The S/N value of machining performance S/N value V w R a D V w R a D Table 7. The S/N value of all levels for V w, R a and D f t i t o V wire F wire P Level * 115.3* Level 1.77* * Level * * Sum Level * -3.87* Level * Level * * -45.7* Sum Level * Level 76.97* * 50.87* * Level * 49.9 Sum Table 8. ANOVA analysis V f A V w R a D f t i t o V wire F wire P Error

14 Table 9. F test value F Vw F Ra F D F 0.05,v1,v f * t i * 7.007* 5.14 t o V wire F wire P Table 10. Grey relational value of machining parameters on metal removal rate (HB for f, t i and t o ) &( LB for V wire, F wire and P) V w f t i t o V wire F wire P Table 11. Grey relational grade V w R a D f 0.716* t i * * t o V wire F wire P

15 Table 1. Grey relational value of machining performance V w R a Γ oi Order * Table 13. Grey relational analysis for V w (HB), R a =3µm V w R a Γ oi Order *