Journal of Scientific & Industrial Research 606
J SCI IND RES VOL 69 AUGUST 2010
Vol. 69, August 2010, pp. 606-612
Optimization of multiple-machining characteristics in wire electrical discharge machining of punching die using Grey relational analysis Kamal Jangra1*, Ajai Jain2 and Sandeep Grover1 1
Department of Mechanical Engineering, YMCA University of Science and Technology, Faridabad 121 006, India 2
Department of Mechanical Engineering, National Institute of Technology, Kurukshetra 136 119, India Received 29 March 2010; revised 13 May 2010; accepted 18 May 2010
This study presents optimization of performance characteristics in wire electrical discharge machining (WEDM) using Taguchi method and Grey relational analysis. Performance characteristics (cutting speed, surface roughness and dimensional lag) were investigated during rough cutting operation. Process parameters (peak current, pulse-on, pulse-off, wire speed and wire tension) were investigated using mixed L18 orthogonal array. Keywords: Grey relational analysis, Multiple performance characteristics, Taguchi method, WEDM
Introduction Wire electrical discharge machining (WEDM) is an extremely potential electro-thermal process for machining of hard metal alloys and metal matrix composites without making any mechanical contact. In order to reduce machining cost during die manufacturing, high discharge energy is used across workpiece and wire electrode during roughening operation resulting in higher material removal rate. High discharge energy due to improper selection of process variables may cause poor surface finish, dimensional overcut and deep recast layer1-3 on work surface. Scott et al4 constructed a mathematical model to predict material removal rate and surface finish at different machining conditions. Kahng et al5 studied surface characteristic behaviour of eroded surface in electrical discharge machining. Puri & Bhattacharyya6 studied geometrical inaccuracy caused due to wire lag phenomenon using Taguchi method involving 13 control factors with three levels for an orthogonal array L27(313). Tosun et al7 investigated wire wear in WEDM and observed that increase in pulse duration and open circuit voltage increase wire wear ratio, whereas increasing wire speed decreases wear ratio. Tosun et al8 optimized machining parameters on kerf and material removal rate (MRR) in WEDM using *Author for correspondence E-mail:
[email protected]
Taguchi’s design of experiment. Sarkar et al9 studied wire electrical discharge machining of ?-titanium aluminide using artificial neural network. Mahapatra & Patnaik10 investigated process parameters of WEDM for material removal rate, surface roughness and kerf using Taguchi approach. Taguchi method11,12 is a systematic application of design and analysis of experiments for designing and improving of product quality. However, original Taguchi method was designed to optimize single performance characteristic and for multiple performance characteristics it requires further research13,14. Grey relational analysis (GRA) 15 is useful for multiple performance characteristics in machining process. Grey system theory16 measures degree of approximation among sequence using a gray relational grade. GRA based on grey system theory can be used to solve complicated interrelationships among multiple performance characteristics effectively17-22. This study presents optimization of performance characteristics [cutting speed (CS), surface roughness (SR) and dimensional lag (Dlag)] during rough cutting operation in WEDM of D3 die steel using GRA in order to reduce total machining cost during die manufacturing. Experimental Section Punching die was used for making square blanks in thin sheets. Experiments were performed on 5-axis sprint cut (ELPLUS-40) wire electrical discharge machine manufactured by Electronica Machine Tool Ltd, India.
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Table 1—Process variables and their levels Symbol A B C D E
Process parameters Peak current Pulse-on time Pulse-off time Wire speed Wire tension
Level 1
Level 2
Level 3
Level 4
Level 5
Level 6
40 105 20 6 7
70 115 30 7 8
100 125 40 8 9
130 ... ... ... ...
160 ... ... ... ...
190 ... ... ... ...
tolerances, a rough cut (first cut) followed by 1 or 2 trim cuts were considered as a probable solution. Trim cutting operation improves surface finish and reduces inaccuracies produced by minor job deformations after first cut. Trim cut improves die life by reducing thickness of thermally affected formed layer. In rough cut (Fig. 1), Point 0 and 1 shows starting and finishing point of programmed path. It was expected that finish cuts with a wire offset value less than 0.140 mm with low pulse energy would results in die width of 9.52 mm with good surface finish. Fig. 1—Programmed path for rough cut
Zinc coated brass wire (diam, 0.25 mm) was used as electrode. Fixed parameters used were as follows: wire type, zinc coated brass; angle of cut, vertical; work thickness, 20 mm; wire off-set, 0.14 mm; work piece hardness, 56 HRC; corner cutting factor, 5; dielectric flow, 12 LPM; dielectric conductivity, 17 S; difference between work surface and upper wire guide, 1 mm. Variable parameters used were as follows: peak current, 10-230 amp.; pulse-on time, 100-131; pulse-off time, 0-63; wire speed, 1-15 m/min; wire tension, 1-15 N. A block of D3 tool steel (250 mm×100 mm×20 mm) was used for experiments. As die is for punching thin sheets, D3 tool steel is a suitable material because of high hardness and easy heat treatment. In order to reduce wear rate and to eliminate other internal defects, die material was heat treated and hardened to 56 HRC. Chemical composition of die material is as follows: C, 2.1; Cr, 12; V, 0.6; Si, 0.3; Mo, 1; Mn, 0.4; and Fe, 83.6 %. EDAX test performed for this composition was ±3%. Die Geometry
Process variables/control parameters [peak current (A), pulse-on (B), pulse-off (C), wire speed (D) and wire tension (E)] were selected as input variables. CS, SR and Dlag were measured as performance characteristics. In order to produce a die with desired dimensional
Design of experiments using Taguchi Approach
Orthogonal array (OA) was used to conduct experimental results. Control parameters A, B and C are most important parameters in WEDM. For maximum utilisation of wire without breakage, D was selected as a variable. E affects dimensional accuracies and also included. In order to study effect of complete range of peak current (10-230 Amp) on machining objectives, six levels of equal intervals of 30 Amp were selected. Rest of four parameters were selected with three levels each (Table 1). Total degree of freedom (DOF) associated with five parameters is equal to 13 (5×1+2×4). Therefore, a mixed OA having DOF greater than 13 should be selected. A standard mixed L18(61×36) OA having DOF equal to 17 was chosen from MINITAB15 to conduct experiments. In Taguchi method, a loss function is defined to calculate deviation between experimental value and desired value. Loss function value is further converted into signal-to-noise (S/N) ratio. HB for cutting speed, LB for surface roughness and dimensional lag was selected for obtaining optimal machining performance. Minimizing quality loss is equivalent to maximizing S/N ratios as S/N ratio for cutting speed and dimensional lag =
− 10 log{
1 n 1 ∑ } n i =1 y i2
…(1)
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A
B
C
D
E
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 2 3 1 3 1 2 2 3 1 3 1 2
1 2 3 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1
1 2 3 2 3 1 3 1 2 2 3 1 1 2 3 3 1 2
Level no’s
Ra, µm
Exp. No.
mm/min
Table 2—Orthogonal array for L18
Level no’s
n
Results and Discussion In this study, L18 OA was selected to conduct experimental runs. Experiments were performed randomly for each parameter setting (Table 2). Each experiment was repeated three times. In each trial, for every replication, CS, SR and Dlag were measured. In experiment number 18, due to higher values of A and B, higher discharge energy was produced across workpiece and wire electrode, and it caused unstable machining and wire breakage occurred frequently. SR (µm) was measured in terms of mean absolute deviation (Ra) using digital surface tester Mitutoyo 201P (made in Japan). Difference between target die width (9.5 mm) and actual experimental value is taken as Dlag. Table 3 shows mean values and S/N ratios of CS, SR and Dlag. Fig. 2 shows relative effect of each factor level of five process parameters on performance characteristics (CS, SR and Dlag). Multiple Performance Characteristics Optimization
In order to optimize three machining characteristics simultaneously, GRA was utilized. After selecting process parameters and their ranges, experimental results were obtained using Taguchi’s design of experiment method. For multiple performance characteristics
Dimensional lag, mm
S/N ratio for surface roughness= − 10 log{ 1 ∑ y 2} n i =1 i …(2)
Level no’s Fig. 2—Effect of levels of process parameters on: a) cutting speed; b) surface roughness); c) dimensional lag
optimization using GRA, following steps were followed: i) Conduction of experiments at different settings of parameters based on OA; ii) Normalization of S/N ratio of experimental results for all performance characteristics; iii) Performance of grey relational generating and calculation of grey relational coefficient (GRC); iv) Calculation of grey relational grade (GRG) using weighing factor for performance characteristics; v) Analysis of experimental results using GRG and statistical analysis of variance (ANOVA); vi) Selection of optimal levels of process parameters; and vii) Conducting confirmation experiment to verify optimal process parameter settings.
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Table 3—Mean and S/N ratio of experimental results Exp. No.
CS
S/N ratio
SR
S/N ratio
Dlag
S/N ratio
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Average
0.69 2.37 1.89 0.94 2.86 2.42 1.62 2.98 3.87 0.98 3.13 3.73 1.51 2.58 4.85 1.27 3.46 3.86 2.50
-3.223 7.4949 5.5292 -0.537 9.1273 7.676 4.1903 9.4843 11.754 -0.1754 9.9108 11.4341 3.5795 8.232 13.715 2.076 10.781 11.7317 6.82115
0.92 1.773 1.986 1.116 2.96 3.146 1.58 2.81 3.956 1.243 3.06 4.083 1.493 2.916 5.11 1.443 3.13 3.673 2.578
0.724 -4.974 -5.9595 -0.9532 -9.4258 -9.9551 -3.9731 -8.9741 -11.9451 -1.8894 -9.714 -12.219 -3.4812 -9.2957 -14.1786 -3.1853 -9.9108 11.3004 -7.256127
0.028 0.048 0.058 0.034 0.014 0.025 0.018 0.008 0.011 0.013 0.013 0.026 0.023 0.003 0.025 0.017 0.016 0.028 0.023
31.0568 26.37517 24.7314 29.3702 37.0774 32.0412 34.8945 41.9382 39.1721 37.7211 37.7211 31.7005 32.7654 50.4575 32.0412 35.391 35.9176 31.0568 34.5238
CS, cutting speed; SR, surface roughness; Dlag, dimensional lag
Table 4—Data preprocessing of S/N ratios of experimental result for each performance characteristics Exp. No.
CS
SR
Dlag
Reference sequence Comparability sequence 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
1.000
1.000
1.000
0 0.63272 0.5167 0.1585 0.72915 0.64346 0.4376 0.75022 0.8842 0.1799 0.7754 0.8653 0.4016 0.6763 1.00 0.3128 0.8267 0.8829
1.00 0.6176 0.5495 0.8874 0.3189 0.2834 0.6848 0.3492 0.1498 0.8246 0.2995 0.1315 0.7178 0.3276 0.00 0.7376 0.2863 0.19313
0.2458 0.6389 0.000 0.1803 0.4799 0.28413 0.39505 0.6688 0.56132 0.5049 0.5049 0.27089 0.31228 1.00 0.2841 0.41435 0.4348 0.2458
CS, cutting speed; SR, surface roughness; Dlag, dimensional lag Grey Relational Analysis (GRA) for Experimental Results
Grey data processing must be performed before calculation of GRCs. In this study, a linear normalization of S/N ratios for CS, SR and Dlag were performed in the range of 0 and 1 (Table 4). A linear data preprocessing method for S/N ratio can be expressed as
…(3) where xi*(k), sequence after data processing; xio(k), original sequence of S/N ratio, where i = 1, 2, 3…., m
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Table 5—Grey relational coefficient and grey relational grade for 18 comparability sequences No. CS Comparability sequence 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Grey relational coefficient SR
0.3333 0.5765 0.50849 0.3727 0.6486 0.5837 0.4706 0.6669 0.8119 0.3787 0.69 0.7877 0.4552 0.607 1.00 0.42115 0.7426 0.81024
1.000 0.5666 0.526 0.8162 0.4233 0.41098 0.6133 0.4344 0.3703 0.7403 0.4165 0.3653 0.6392 0.4264 0.3333 0.6558 0.4119 0.382
Grey relational grade Dlag 0.3986 0.3481 0.3788 0.3788 0.4901 0.4112 0.4525 0.6015 0.5326 0.5024 0.5024 0.4068 0.42098 1.00 0.4112 0.46057 0.4693 0.39868
0.57551 0.49557 0.45470 0.52113 0.52036 0.46805 0.51153 0.56794 0.57121 0.54008 0.53596 0.51880 0.50428 0.68102 0.57979 0.51198 0.54054 0.52899
CS, cutting speed; SR, surface roughness; Dlag, dimensional lag
and k =1, 2,…., n; max , largest value of ; min , smallest value of . GRC (Table 5), calculated with preprocessed sequence, is defined as
…(4) where is deviation sequence of reference sequence and comparability sequence , i.e. = is absolute value of difference between and . min. min. , max. max. . ζ is is set as 0.5. distinguishing coefficients, Defining this coefficient shows relational degree between reference sequences and comparability 18 , where i = 1, 2, …, m and k =1, 2, .., n sequences with m =18 and n =3. GRG is a weighting-sum of GRCs. Using GRG, performance characteristics are evaluated as
…(5)
where βk represents weighting value of kth performance characteristics and
= 1.
Weighting factors for CS and SR were taken as 0.33 and for D lag as 0.34. As present study deals with roughening operation, therefore, target die dimensions at higher CS and good SR are desired. Therefore, little higher weight is given to Dlag. Optimization of multiple performance characteristics can be converted into optimization of single GRG. It is clear that experiment no. 14 have larger value of grade. Therefore, it provides best combination for multiple performance characteristics. But at this setting, CS was low. In order to separate out effect of each process variable on GRG at different levels, using Taguchi methodology, GRG graph was plotted (Fig. 5). Mean value of GRA is 0.53486. Basically, the larger GRG, the better is the multiple performance characteristics. Combination of A5 B2 C1 D1 and E2 showed larger value of GRG for factors A, B, C, D and E respectively. Therefore, A5B2C1D1E2 was optimal parameter combination for three performance characteristics. However, significant contribution of process parameters was still need to be known to predict optimal values of performance characteristics.
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Table 6--ANOVA for grey relational grade Source
DF
Sum of square
Mean square
F
p-value
% contribution
A
5
0.014586
0.002917
1.01
0.511
34.21
B
2
0.004526
0.002263
0.78
0.517
10.61
C
2
0.005039
0.002520
0.87
0.485
11.81
D
2
0.002454
0.001227
0.42
0.681
5.75
E
2
0.004458
0.002229
0.77
0.521
10.45
Error
4
0.011573
0.002893
Total
17
0.042636
27.14
DF, degree of freedom Table 7—Predicted and experimental value at optimal setting Performance characteristics
Optimal combination
CS, mm/min SR, µm Dlag, mm
A5B2C1D1E2
Predicted grey relational grade
Predicted mean 3.63 3.54 0.009
0.64772
Experimental value 3.80 3.65 0.008
CS, cutting speed; SR, surface roughness; Dlag, dimensional lag
Analysis of Variance (ANOVA)
To investigate significant contribution of process parameters in performance characteristics, ANOVA was used on GRG (Table 6). It showed that factor A contributed maximum; B, C and E had nearly equal contribution, and D contributed least and it can be neglected.
Predicting Optimal Values
Estimated GRG (ηopt.) can be calculated as Fig. 3—Graph of grey relational grade
…(6) , total mean of GRG; , mean GRG at where optimum level; and q, number of process parameters having significant contribution in multiple performance characteristics. Using Eq. (6) and response graphs (Fig. 2), optimal values were predicted similar to GRG. Predicted values for multiple performance characteristics at optimal setting of process parameters are confirmed through experimental results (Table 7).
Conclusions GRA was applied to determine optimal process parameters for optimization of multiple performance characteristics (CS, SR and Dlag), which were investigated during rough cutting operation in D3 tool steel. Using GRA, optimal setting of process parameters for multiple performance characteristics was set with A5 B2 C1 D1 E2. Corresponding predicted values were confirmed experimentally. Cutting speed (3.80 mm/min) was achieved with a dimensional lag of 0.008 mm, which is
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quite acceptable for rough cut. But surface roughness was poor and can be improved by assigning high weightage in grey relational grade.
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