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Parametric optimization of powder mixed electrical discharge machining by response surface methodology
Journal of Materials Processing Technology 169 (2005) 427–436
Parametric optimization of powder mixed electrical discharge machining by response surface methodology H.K. Kansal a,∗ , Sehijpal Singh a,b , P. Kumar a,c b
a Department of Mechanical Engineering, SLIET Longowal, 148106 Punjab, India Department of Mechanical and Production Engineering, G.N.D.E.C Ludhiana, 147001 Punjab, India c Department of Mechanical and Industrial Engineering, I.I.T. Roorkee, 247667 Uttaranchal, India
Received 21 May 2004; received in revised form 21 May 2004; accepted 24 March 2005
Abstract In the present work, a study has been made to optimize the process parameters of powder mixed electrical discharge machining (PMEDM). Response surface methodology has been used to plan and analyze the experiments. Pulse on time, duty cycle, peak current and concentration of the silicon powder added into the dielectric fluid of EDM were chosen as variables to study the process performance in terms of material removal rate and surface roughness. Experiments are performed on a newly designed experimental setup developed in the laboratory. The results identify the most important parameters to maximize material removal rate and minimize surface roughness. The recommended optimal process conditions have been verified by conducting confirmation experiments. © 2005 Elsevier B.V. All rights reserved. Keywords: Powder mixed EDM; Surface roughness; Material removal rate; Process optimization
1. Introduction Electrical discharge machining (EDM) is a common nonconventional material removal process. This technique has been widely used in modern metal working industry for producing complex cavities in dies and moulds, which are otherwise difficult to create by conventional machining [1]. The process also has the advantage of being able to machine hardened tool steels. However, its low machining efficiency and poor surface finish restricted its further applications [2]. To address these problems, one relatively new technique used to improve the efficiency and surface finish is EDM in the presence of powder suspended in the dielectric fluid [2–13]. This new hybrid material removal process is called powder mixed EDM (PMEDM). In this technique, fine abrasive powder are mixed into the dielectric fluid of EDM. The added powder significantly affects the performance of EDM process. The electrically conductive powder reduces the insu∗ Corresponding author. Tel.: +91 1672 284962 (O)/280038 (R); fax: +91 1672 284860/280057. E-mail address: [email protected] (H.K. Kansal).
0924-0136/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2005.03.028
lating strength of the dielectric fluid and increases the spark gap between the tool and workpiece [2,4,7–10,14–17]. As a result, the process becomes more stable thereby improving material removal rate (MRR) and surface finish. The effect of impurities (copper, aluminum, iron and carbon) in dielectric fluid of EDM was first studied by Erden and Bilgin [10]. It was reported that the machining rate increased with increase the concentration of the powder due to decrease the time lag. Thereafter, Jeswani [11] investigated that by addition of 4 g/l graphite powder into kerosene oil, MRR is improved around 60% and wear ratio is reduced by 15%. Mohri et al. [6,12,18] studied the effects of silicon powder addition on machining rate and surface roughness (SR) in EDM. The fine and corrosion resistant surfaces having roughness of the order of 2 m were produced. However, this performance could only be achieved at controlled machining conditions (even distribution of additives into dielectric, short discharge time, etc.). The use of silicon powder was also reported in [19–21]. It was further reported that under specific working conditions, aluminum and graphite powders exhibit more improvement in surface finish than caused by silicon powder. The glossy and smooth surface finish can be achieved
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by mixing the different additives (silicon, graphite, molybdenum, aluminum and silicon carbide) into the dielectric fluid of EDM [14]. The presence of powder increases the gap distance as compared to traditional EDM by at least a factor of two [14]. The enlarged and widened discharge channel lowers the break down strength of the dielectric fluid and reduces the electrical density on the machining spot and thus generates shallow craters [20]. Ming and He [15] observed that a bridging effect is created with the addition of powder, which facilitates the dispersion of discharge into several increments. As a result, several discharge trajectories are formed within a single input impulse and several discharge spots are created and hence MRR and surface finish improves [16]. The non-conductive materials like glass and Si3 N4 ceramics can be finely machined by PMEDM [22]. The PMEDM process improved the wear and corrosion resistance of the work surfaces by depositing a hard layer on its outer surface [23,24]. Tzeng and Chen [8] applied the optimization strategy in order to reduce the functional variability of EDM process. The literature reveals that PMEDM finds many applications to improve the surface finish, but very little effort is reported on the use of powder mixed EDM in rough machining phase. Further, PMEDM involves a large number of parameters, which affect the quality of the product. Due to this large number of parameters and their complex nature, it is difficult to relate them in a single analytical model. Extensive experimental work is therefore needed to analyze and optimize the process parameters to understand their effect on the product quality. Response surface methodology (RSM) of experimental design is one emerging technique, which helps in carrying out the analysis of experiments with the least experimental effort [25]. In the present paper, an attempt has been made to obtain an optimal setting of process parameters, which may yield optimum MRR and surface finish on the components processed by PMEDM process. Response surface methodology has been used to plan and analyze the experiments.
2. Powder mixed EDM Process The schematic diagram of an experimental setup developed for PMEDM is shown in Fig. 1. To avoid the wastage of kerosene oil, a small dielectric circulating system is designed. A stirring system is incorporated to avoid the particle settling. The modified circulation and stirring system is designed in such a way that, it can be employed at the commercial level (refer to Fig. 1). In this system, a micro pump is installed for better circulation of the powder mixed dielectric fluid. The pump and the stirrer are employed in the same tank in which machining is performed. For constant reuse of powder mixed dielectric fluid, magnetic forces are used to separate the powder particles from the debris produced due to machining (refer to Fig. 1). PMEDM has a different machining mechanism from the conventional EDM [2]. In this process, a suitable material in the powder form is mixed into the dielectric fluid of EDM. When a voltage of 80–320 V is applied to both the electrodes, an electric field in the range 105 –107 V/m is created. The spark gap is filled up with additive particles and the gap distance setup between tool and the workpiece increased from 25–50 to 50–150 m [7]. The powder particles get energized and behave in a zigzag fashion (refer to Fig. 2). The grains come close to each other under the sparking area and gather in clusters. The interlocking between the different powder particles takes place due to variation in their shape and size. They arrange themselves in the form of chain at different places under the sparking area. The chain formation helps in bridging the gap between both the electrodes. Due to bridging effect, the gap voltage and insulating strength of the dielectric fluid decreases. The easy short circuit takes place, which causes early explosion in the gap. As a result, the ‘series discharge’ starts under the electrode area. Due to increase in frequency of discharging, the faster sparking within a discharge takes place which causes faster erosion from the work piece surface. At the
Fig. 1. Schematic diagram of experimental setup.
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4. Process parameters of powder mixed EDM In order to identify the process parameters that affect the quality of component processes by PMEDM, an Ishikawa cause–effect diagram was constructed as shown in Fig. 3. The parameters can be classified as follows:
Fig. 2. Principle of powder mixed EDM.
same time, the added powder modifies the plasma channel. The plasma channel becomes enlarged and widened [2]. The electric density decreases; hence sparking is uniformly distributed among the powder particles. As a result, even and more uniform distribution of the discharge takes place, which causes uniform erosion (shallow craters) on the workpiece. This results in improvement in surface finish.
3. Experimental detail Experiments was conducted on a EZNC fuzzy logic Die Sinking EDM machine manufactured by Electronica Machine Tools Ltd., India. Silicon powder is suspended into the commercial available kerosene oil. The powder particle size is in the range of order 20–30 m. Each trial run is performed for duration of 60 min. The experiment has been performed with positive polarity as recommended in [2]. In this study, EN-31 (comparable to AISI 52100) tool steel is selected as the work material. The chemical composition of the workpiece material is given as: C = 0.9–1.2%, Si = 0.1–0.3%, Mn = 0.3–0.7%, Cr = 1–1.6%, S and P each 0.025% (max.) and balance is ferrous. Copper electrode with diameter 25 mm has been used to machine the EN-31 tool steel.
1. Electrical parameters: peak current, pulse on time, pulse off time and supply voltage. 2. Non-electrical parameters: electrode lift time, working time, gain and nozzle flushing. 3. Powder based parameters: powder type, its concentration and other properties such as shape, size, conductivity, etc. 4. Electrode based parameters: material and size of electrode. The following four independent parameters were chosen for the study: 1. 2. 3. 4.
Pulse on time, A; Duty cycle, B; Peak current, C; Concentration of the added silicon powder, D.
The ranges of these parameters were selected on the basis of preliminary experiments conducted by using one variable at a time approach. Table 1 gives the levels of various parameters and their designation. The response parameter in the present study was MRR and surface roughness (SR). In each test, the MRR was calculated by the weight loss method. The SR was measured in terms of arithmetic mean roughness of
Table 1 Design scheme of process parameters and their levels Factor symbol
A B C D
Fig. 3. Cause and effect diagram.
Parameter
Pulse on time, TON (s) Duty cycle, DC Peak current, Ip (A) Concentration, Conc. (g/l)
Levels Low (−1)
High (+1)
50 0.7 3 0
150 0.9 12 2
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the evaluated roughness profile (Ra in m) by using a Surfcoder SE1200 surface testing analyzer.
5. Response surface methodology Response surface methodology (RSM) is a collection of mathematical and statistical techniques that are useful for the modelling and analysis of problems in which a response of interest is influenced by several variables and the objective is to optimize this response [25,26]. It is a sequential experimentation strategy for empirical model building and optimization. By conducting experiments and applying regression analysis, a model of the response to some independent input variables can be obtained. Based on the model of the response, a near optimal point can then be deduced. RSM is often applied in the characterization and optimization of processes. In RSM, it is possible to represent independent process parameters in quantitative form as: Y = f (X1 , X2 , X3 , . . . Xn ) ± ε
(1)
where, Y is the response (yield), f is the response function, ε is the experimental error, and X1 , X2 , X3 , . . ., Xn are independent parameters. By plotting the expected response of Y, a surface, known as the response surface is obtained. The form of f is unknown and may be very complicated. Thus, RSM aims at approximating f by a suitable lower ordered polynomial in some region of the independent process variables. If the response can be well modeled by a linear function of the independent variables, the function (Equation (1)) can be written as: Y = C0 + C1 X1 + C2 X2 + . . . + Cn Xn ± ε
(2)
However, if a curvature appears in the system, then a higher order polynomial such as the quadratic model (Equation (3)) may be used: Y = C0 +
n i=1
Ci Xn +
n
di Xi2 ± ε
(3)
Fig. 4. Procedure of response surface methodology.
with a standard RSM design called central composite design (CCD) [27]. In this investigation, total 30 experiments were conducted at the stipulated conditions based on the procedure mentioned already. In this design, the factorial design is full factorial design with all combinations of the factors at the two levels, the eight star points at the face of the cube portion on the design and six central points. The star points corresponds to an α value of 1 and this type of design is commonly called face centered CCD. The ‘Design Expert 6.0’ software was used for regression and graphical analysis of the data obtained [28]. The optimum values of the selected variables were obtained by solving the regression equation and by analyzing the response surface contour plots [29].
i=1
The objective of using RSM is not only to investigate the response over the entire factor space, but also to locate the region of interest where the response reaches its optimum or near optimal value. By studying carefully the response surface model, the combination of factors, which gives the best response, can then be established. The response surface method is a sequential process and its procedure can be summarized as shown in Fig. 4.
6. Machining conditions and experimental plan As already mentioned, and accordance with the literature consulted, as well as drawing from personal experience [13], four factors are being studied and their low and high levels are given in Table 1. The PMEDM process was studied
7. Results and discussions The 30 experiments were conducted in duplicate and the average values of MRR and SR along with design matrix were tabulated in Table 2. For analysis the data, the checking of goodness of fit of the model is very much required. The model adequacy checking includes test for significance of the regression model, test for significance on model coefficients and test for lack of fit [29]. For this purpose, analysis of variance (ANOVA) is performed. 7.1. Analysis of material removal rate The fit summary recommended that the quadratic model is statistically significant for analysis of MRR. The results
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Table 2 Design of Experimental matrix and results for the PMEDM performance characteristics Exp. no.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Process parameters
Observed values
Pulse on time, TON , A
Duty cycle, DC, B
50 150 50 150 50 150 50 150 50 150 50 150 50 150 50 150 50 150 100 100 100 100 100 100 100 100 100 100 100 100
0.7 0.7 0.9 0.9 0.7 0.7 0.9 0.9 0.7 0.7 0.9 0.9 0.7 0.7 0.9 0.9 0.8 0.8 0.7 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8
Peak current, Ip , C
3 3 3 3 12 12 12 12 3 3 3 3 12 12 12 12 7.5 7.5 7.5 7.5 3 12 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5
of the quadratic model for MRR in the form of ANOVA are given in Table 3. The value of R2 and adjusted R2 is over 99%. This means that regression model provides an excellent explanation of the relationship between the independent variables (factors) and the response (MRR). The associated p-value for the model is lower than 0.05 (i.e. α = 0.05, or 95% confidence) indicates that the model is considered to be statistically significant [29]. The lack-of-fit term is non significant as it is desired. Further, factor A (pulse on time), factor C (peak current), factor D (concentration of silicon powder), interaction effect of A (pulse on time) with factor C (peak current), interaction effect of factor C (peak current) with factor D (concentration) and second order term of factor C (peak current) have significant effect. These significant effects, in descending order, are factor C (peak current), the quadratic effect of factor C (peak current), factor D (concentration), the interaction of factor C (peak current) with factor D (concentration), factor A (pulse on time) and finally, the interaction of factor A (pulse on time) with factor C (peak current). The result proves that the powder added into the dielectric fluid enhances the MRR [2,5,11]. The other model terms are said to be nonsignificant.
Concentration, Conc., D 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 1 1 1 1 1 1 0 2 1 1 1 1 1 1
MRR (mm3 /min)
SR (m)
I
II
Average
I
II
Average
1.84 1.98 2.19 2.88 22.30 23.41 21.65 24.21 3.17 3.30 3.16 3.19 26.98 28.38 26.00 28.21 4.75 8.20 7.19 7.43 2.10 25.50 5.20 6.94 6.18 6.70 6.22 7.93 6.61 7.58
2.22 2.84 2.00 1.94 23.10 24.20 23.70 25.20 3.17 3.47 3.24 3.56 25.21 29.44 26.39 29.20 4.63 6.19 5.20 7.14 1.95 24.52 7.19 7.65 6.21 7.28 8.09 6.59 7.15 6.82
2.03 2.41 2.10 2.41 22.70 23.81 22.68 24.71 3.17 3.38 3.20 3.38 26.10 28.91 26.19 28.71 4.69 7.19 6.21 7.29 2.03 25.01 6.21 7.29 6.19 6.99 7.15 7.26 6.88 7.20
2.48 1.98 2.30 2.41 7.21 6.14 6.50 6.36 2.11 1.21 4.68 1.31 5.5 6.19 6.40 5.00 3.55 7.39 6.00 7.32 1.71 6.91 7.55 4.20 7.32 6.30 6.51 6.30 6.75 5.11
1.96 2.30 2.33 1.88 6.42 9.36 8.91 7.13 2.34 1.48 3.54 1.37 5.48 4.05 3.84 5.23 7.81 6.51 6.02 5.48 1.89 5.06 6.07 5.36 5.47 7.30 7.09 6.09 5.55 6.85
2.22 2.14 2.32 2.14 6.82 7.75 7.70 6.75 2.22 1.34 4.11 1.34 5.50 5.12 5.12 5.12 5.68 6.95 6.01 6.40 1.80 5.99 6.81 4.78 6.39 6.80 6.80 6.19 6.15 5.98
To fit the quadratic model for MRR appropriate, the nonsignificant terms are eliminated by backward elimination process. The ANOVA Table for the reduced quadratic model for MRR is shown in Table 4. The reduced model results indicate that the model is significant (R2 and adjusted R2 are 99.77% and 99.71%, respectively), lack of fit is non significant (p-value is less than 0.05). Fig. 5 displays the normal probability plot of the residuals for MRR. Notice that the residuals are falling on a straight line, which means that the errors are normally distributed. Further, each observed value is compared with the predicted value calculated from the model in Fig. 6. It can be seen that the regression model is fairly well fitted with the observed values. After eliminating the non-significant terms, the final response equation for MRR is given as follows: (In coded terms) MRR = 6.71 + 0.67A + 11.37C + 1.18D +7.34C2 + 0.46AC + 0.74CD
(4)
(In actual factors) MRR = 8.39 − 1.99TON − 3.27IP − 0.05Conc. + 0.36Ip2 +2.05TON IP + 0.16IP Conc.
(5)
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Table 3 ANOVA table for MRR (before elimination) Source
Sum of squares
Degrees of freedom
Mean square
f-Value
Prob > f
Model A B C D A2 B2 C2 D2 AB AC AD BC BD CD Residual Lack of fit Pure error Cor. total
2762.72 8.11 0.22 2328.12 25.16 0.51 0.35 131.73 0.35 0.016 3.42 0.22 0.029 0.068 8.73 4.69 3.91 0.78 2767.41
14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15 10 5 29
197.34 8.11 0.22 2328.12 25.16 0.51 0.35 131.73 0.35 0.016 3.42 0.22 0.029 0.068 8.73 0.31 0.39 0.16
630.55 25.90 0.70 7439.08 80.39 1.64 1.11 420.91 1.11 0.050 10.94 0.71 0.092 0.22 27.90
<0.0001 (significant) 0.0001 0.4172 <0.0001 <0.0001 0.2202 0.3098 <0.0001 0.3098 0.8262 0.0048 0.4140 0.7654 0.6488 <0.0001
Standard deviation = 0.56 Mean = 11.11 Coefficient of variation = 5.03 Predicted residual error of sum of squares (PRESS) = 18.94
Fig. 7 shows the estimated response surface for MRR in relation to the design parameters of peak current and pulse on time. As can be seen from this figure, the MRR tends to increase, considerably with increase in peak current for any value of pulse on time. Hence, maximum MRR is obtained at high peak current (12 A) and high pulse on time (150 s). This is due to their dominant control over the input energy. However, at low range of peak current (3–5 A), maximum MRR is obtained at 100 s pulse on time. The effect of concentration and peak current on MRR is shown in Fig. 8. This figure displays that the value of MRR increases with increase in peak current. The reason is same as stated earlier. The effect of concentration on MRR can be also seen from this figure. The powder added into the dielec-
2.50
0.1619 (not significant)
R2 = 0.9983 R2 adjusted = 0.9967 Predicted R2 = 0.9932 Adequate precision = 67.427
tric fluid enhances the MRR. With increase in concentration of the powder, the MRR tends to increase. This is because the added additive causes bridging effect between both the electrodes, facilitates the dispersion of discharge into several increments and hence increases the MRR. The maximum MRR is obtained at highest level of concentration of added silicon powder (2 g/l) and peak current (12 A). 7.2. Analysis of surface roughness For surface roughness, the fit summary recommended that the quadratic model is statistically significant for analysis. Table 5 presents the ANOVA table for a quadratic model for SR.
Table 4 ANOVA table for MRR (after backward elimination) Source
Sum of squares
Degrees of freedom
Mean square
f-Value
Prob > f
Model A C D C2 AC CD Residual Lack of fit Pure error Cor. total
2761.12 8.11 2328.12 25.16 387.58 3.42 8.73 6.29 5.51 0.78 2767.41
6 1 1 1 1 1 1 23 18 5 29
460.19 8.11 2328.12 25.16 387.58 3.42 8.73 0.27 0.31 0.16
1681.08 29.63 8509.29 91.95 1416.61 12.51 31.92
<0.0001 (significant) <0.0001 <0.0001 <0.0001 <0.0001 0.0018 <0.0001
Standard deviation = 0.52 Mean = 11.11 Coefficient of variation = 4.71 Predicted residual error of sum of squares (PRESS) = 9.47
1.96
R2 = 0.9977 R2 adjusted = 0.9971 Predicted R2 = 0.9966 Adequate precision = 104.693
0.2358 (not significant)
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Fig. 7. Effect of peak current and pulse on time on MRR. Fig. 5. Normal probability plot residuals for MRR.
R2
R2
The value of and adjusted are 96% and 92.32%, respectively. This means that regression model provides an excellent explanation of the relationship between the independent variables (factors) and the response (SR). The associated p-value for the model is lower than 0.05 (i.e. α = 0.05, or 95% confidence) indicates that the model is considered statistically significant. The lack-of-fit term is non significant as it is desired. Further, factor C (peak current), factor D (concentration of silicon powder), interaction effect of factor C (peak current) with factor D (concentration) and second order term of factor C (peak current) have significant effect. These significant effects, in descending order, are factor C (peak current), the quadratic effect of factor C (peak current), factor D (concentration) and finally, the interaction of factor C (peak current) with factor D (concentration). The result proves that the powder added into the dielectric fluid enhances the surface finish [6,14]. The other model terms are said to be non-significant. To fit the quadratic model for SR appropriate, the nonsignificant terms are eliminated by backward elimination
Fig. 6. Plot of actual vs. predicted response of MRR data.
process. The ANOVA Table for the reduced quadratic model for MRR is shown in Table 6. The reduced model results indicate that the model is significant (R2 and adjusted R2 are 92.75% and 91.60%, respectively), lack of fit is non significant (p-value is less than 0.05). Fig. 9 displays the normal probability plot of the residuals for SR. Notice that the residuals are falling on a straight line, which means that the errors are normally distributed. Further, each observed value is compared with the predicted value calculated from the model in Fig. 10. It can be seen that the regression model is fairly well fitted with the observed values. After eliminating the non-significant terms, the final response equation for SR is given as follows: (In coded terms) SR = 6.25 + 2.01C − 0.56D − 2.05C2 − 0.52CD
(6)
(In actual factors) SR = −3.12 + 2.08IP + 0.31Conc. − 0.10IP2 −0.11IP Conc.
Fig. 8. Effect of peak current and concentration on MRR.
(7)
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Table 5 ANOVA table for SR (before elimination) Source
Sum of squares
Degrees of freedom
Mean square
f-Value
Prob > f
Model A B C D A2 B2 C2 D2 AB AC AD BC BD CD Residual Lack of fit Pure error Cor. total
117.18 0.51 0.20 72.88 5.58 0.17 0.058 12.09 0.18 0.75 0.77 0.89 0.38 0.15 4.38 4.85 4.25 0.60 122.03
14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15 10 5 29
8.37 0.51 0.20 72.88 5.58 0.17 0.058 12.09 0.18 0.75 0.77 0.89 0.38 0.15 4.38 0.32 0.42 0.12
25.88 1.57 0.61 225.39 17.25 0.54 0.18 37.39 0.54 2.33 2.38 2.75 1.18 0.48 13.54
<0.0001 (significant) 0.2298 0.4480 <0.0001 0.0008 0.4737 0.6779 <0.0001 0.4725 0.1479 0.1436 0.1182 0.2947 0.5006 0.0022
3.53
0.0882 (not significant)
R2 = 0.9603 R2 adjusted = 0.9232 Predicted R2 = 0.7828 Adequate precision = 16.297
Standard deviation = 0.57 Mean = 5.01 Coefficient of variation = 11.34 Predicted residual error of sum of squares (PRESS) = 26.51 Table 6 ANOVA table for SR (after backward elimination) Source
Sum of squares
Degrees of freedom
Mean square
f-Value
Prob > f
Model C D C2 CD Residual Lack of fit Pure error Cor. total
113.18 72.88 5.58 30.34 4.38 8.85 8.25 0.60 122.03
4 1 1 1 1 25 20 5 29
28.29 72.88 5.58 30.34 4.38 0.35 0.41 0.12
79.96 205.95 15.76 85.74 12.37
<0.0001 (significant) <0.0001 0.0005 <0.0001 0.0017
3.43
0.0882 (not significant)
R2 = 0.9275 R2 adjusted = 0.9159 Predicted R2 = 0.8875 Adequate precision = 21.156
Standard deviation = 0.59 Mean = 5.01 Coefficient of variation = 11.87 Predicted residual error of sum of squares (PRESS) = 13.73
Fig. 11 shows the estimated response surface for SR in relation to the design parameters of peak current and pulse on time. As can be seen from this figure, the SR tends to increase, considerably up to the 10 A peak current. Beyond 10 A peak current, the SR again starts decreasing for any value of the pulse on time. The SR also increases with increase in pulse on time. This is due to their dominant control over the input
energy. It is clear from Fig. 11 that the best surface finish is obtainable at the lower level of peak current (3 A) and pulse on time (50 s). The effect of concentration and peak current on SR is shown in Fig. 12. This figure displays that the value of SR increases with increase in peak current at least up to its maximum level, after which it tends to decrease for high value
Table 7 Confirmation tests and their comparison with the results Exp. no.
1 2 3
MRR (mm3 /min)
Machining conditions
SR (m)
Pulse on time, A (s)
Duty cycle, B
Peak current, C (A)
Conc., D (g/l)
Exp.
Predicted
Error (%)
Exp
Predicted
Error (%)
50 100 150
0.7 0.8 0.9
3 7.5 12
2 1 0
3.17 6.20 24.71
2.91 6.71 24.63
7.91 −8.03 0.32
2.22 6.39 6.75
2.15 6.25 7.28
3.15 2.19 −7.85
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Fig. 11. Effect of peak current and pulse on time on SR. Fig. 9. Normal probability plot residuals for SR.
of concentration of the added powder. In this way, in order to obtain a good surface finish, low values of peak current (3 A) and high level of concentration of added powder (2 g/l) should be used. On other side, the low levels of the SR can be also obtained at high values of peak current and concentration of the added powder into the dielectric fluid of EDM. In both ways, the low value of SR is obtained at high level of concentration of the added powder. This proves that the added additive plays a significant role to modify the plasma channel. The plasma channel becomes enlarged and widened [2]. The electric density decreases; hence sparking is uniformly distributed among the powder particles. As a result, even and uniform surfaces are produced.
8. Confirmation experiments Since the response surface equations were derived from quadratic regression fit, confirmation tests must be performed
Fig. 12. Effect of peak current and concentration on SR.
to verify their validity. Of course, the independent variable values selected for the confirmation test must lie within the ranges for which the formulas were derived. The three conformation experiments were performed for MRR and SR. The data from the confirmation runs and their comparisons with the predicted designed for MRR and SR are listed in Table 7. From the analysis of Table 7, it can be observed that the calculated error is small. The error between experimental and predicted values for MRR and SR are lie within ±8% and −7.85% to 3.15%, respectively. Obviously, this confirms excellent reproducibility of the experimental conclusions.
9. Conclusions
Fig. 10. Plot of actual vs. predicted response of SR data.
Silicon powder was suspended into the dielectric fluid of EDM and an enhanced rate of material removal and surface finish has been achieved. Empirical modelling with the help
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of response surface methodology has led to the following conclusions about the variation of response parameters in terms of independent parameters within the specified range. The silicon powder suspended in the dielectric fluid of EDM affects both MRR and SR. The slope of the curve indicates that the MRR increases with the increase in the concentration of the silicon powder. Therefore, more improvement in MRR is expected at still higher concentration level of silicon powder. There is discernible improvement in surface roughness of the work surfaces after suspending the silicon powder into the dielectric fluid of EDM. However, more improvement in SR is still expected at higher concentration level of silicon powder. The analysis of variance revealed that the factor C (peak current) and factor D (concentration) are the most influential parameters on MRR and SR. The quadratic term of factor C (peak current) also have significant effect. Factor C (peak current) and factor D (concentration) interact with each other. The combination of high peak current and high concentration yields more MRR and smaller SR. The confirmation tests showed that the error between experimental and predicted values of MRR and SR are within ±8% and −7.85% to 3.15%, respectively.
Acknowledgements The authors would like to acknowledge the support of department of mechanical engineering, SLIET, Longowal, India and M/S Electronica Machine Tools Ltd., Pune, India. We are thankful to Mr. Kulwinder Singh, department of mechanical engineering, SLIET, Longowal. We are also grateful to Prof. P.L. Bali, LIET, Jalandhar and Er. Baljit Singh, PSEB for their guidance and expert comments in response to our queries and problems.
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[7] K. Furutani, A. Saneto, H. Takezawa, N. Mohri, H. Miyake, Accertation of titanium carbide by electrical discharge machining with powder suspended in working fluid, Prec. Eng. 25 (2001) 138– 144. [8] F.Y. Tzeng, Fu Chen, A simple approach for robust design of highspeed electrical-discharge machining technology, Int. J. Mach. Tool Manuf. 43 (2003) 217–227. [9] M. Kunieda, K. Yanatori, Study on debris movement in EDM gap, Int. J. Electr. Mach. 2 (1997) 43–49. [10] A. Erden, S. Bilgin, Role of impurities in electric discharge machining, in: Proceedings of the 21st International Machine Tool Design and Research Conference, Macmillan, London, 1980, pp. 345– 350. [11] M.L. Jeswani, Effects of the addition of graphite powder to kerosene used as the dielectric fluid in electrical discharge machining, Wear 70 (1981) 133–139. [12] N. Mohri, et al., Mirror-like finishing by EDM, in: Proceedings of the 25th International Symposium on Machine Tool Design and Research, UK, 1985, pp. 329–336. [13] H. Kansal, S. Singh, P. Kumar, State of the art concerning powder mixed EDM, in: Proceedings of the International Conference on Emerging Technology (ICET-2003) KIIT, Bhubansewar, India, 2003. [14] Y.S. Wong, L.C. Lim, I. Rahuman, W.M. Tee, Near-mirror-finish phenomenon in EDM using powder-mixed dielectric, Int. J. Adv. Manuf. Technol. 79 (1998) 30–40. [15] Q.Y. Ming, L.Y. He, Powder-suspension dielectric fluid for EDM, J. Mater. Process. Technol. 52 (1995) 44–54. [16] H.M. Chow, B.H. Yan, F.Y. Huang, J.C. Hung, Study of added powder in kerosene for the micro-slit machining of titanium alloy using electro-discharge machining, J. Mater. Process. Technol. 101 (2000) 95–103. [17] B.M. Schumacher, About the role of debris in the gap during electrical discharge machining, Ann. CIRP 39 (1) (1990) 197–199. [18] N. Mohri, et al., Surface modification by EDM—an innovation in EDM with semi-conductive electrodes, in: Proceedings of the Winter Annual Meeting of ASME, vol. 34, 1988, pp. 21–30. [19] B.H. Yan, S.L. Chen, Characteristics of SKD11 by complex process of electric discharge machining using liquid suspended with aluminum powder, J. Jpn. Inst. Light Met. 58 (9) (1994) 1067–1072. [20] Y. Uno, A. Okada, Surface generation mechanism in electrical discharge machining with silicon powder mixed fluid, Int. J. Electro Mach. 2 (1997) 13–18. [21] P. Pecas, E.A. Henriques, Emerging technologies in penetration EDM, O Molde 55 (2002) 26–36. [22] T. Tani, F. Fukuzawa, N. Mohri, M. Okada, Machining phenomena in EDM of insulating ceramics using powder suspended working oil, in: Proceedings of the 12th ISEM, Bilbao, 2001. [23] Y. Uno, A. Okada, Y. Hayashi, Y. Tabuchi, Surface integrity in EDM of aluminum bronze with nickel powder mixed fluid, J. Jpn. Soc. Electr. Mach. Eng. 32 (70) (1998) 24–31 (in Japanese). [24] A. Okada, Y. Uno, K. Hirao, Formation of hard layer by EDM with carbon powder mixed fluid using titanium electrode, in: Proceedings of the 5th International Conference on Progress of Machining Technology, 2000, pp. 464–469. [25] D.C. Montgomery, Design and Analysis of Experiments, fourth ed., Wiley, New York, 1997. [26] G. Cochran, G.M. Cox, Experimental Design, Asia Publishing House, New Delhi, 1962. [27] C.F. Jeff Wu, Experiments Planning, Analysis and Parameter Design Optimization, Wiley, New York, 2002. [28] Design Expert Software, Version 6, Users Guide, Technical manual, Stat-Ease Inc., Minneapolis, MN, 2004. [29] D.C. Montgomery, E.A. Peck, G.G. Vining, Introduction to Linear Regression Analysis, third ed., Wiley, New York, 2003.
Parametric optimization of powder mixed electrical discharge machining by response surface methodology H.K. Kansal a,∗ , Sehijpal Singh a,b , P. Kumar a,c b
a Department of Mechanical Engineering, SLIET Longowal, 148106 Punjab, India Department of Mechanical and Production Engineering, G.N.D.E.C Ludhiana, 147001 Punjab, India c Department of Mechanical and Industrial Engineering, I.I.T. Roorkee, 247667 Uttaranchal, India
Received 21 May 2004; received in revised form 21 May 2004; accepted 24 March 2005
Abstract In the present work, a study has been made to optimize the process parameters of powder mixed electrical discharge machining (PMEDM). Response surface methodology has been used to plan and analyze the experiments. Pulse on time, duty cycle, peak current and concentration of the silicon powder added into the dielectric fluid of EDM were chosen as variables to study the process performance in terms of material removal rate and surface roughness. Experiments are performed on a newly designed experimental setup developed in the laboratory. The results identify the most important parameters to maximize material removal rate and minimize surface roughness. The recommended optimal process conditions have been verified by conducting confirmation experiments. © 2005 Elsevier B.V. All rights reserved. Keywords: Powder mixed EDM; Surface roughness; Material removal rate; Process optimization
1. Introduction Electrical discharge machining (EDM) is a common nonconventional material removal process. This technique has been widely used in modern metal working industry for producing complex cavities in dies and moulds, which are otherwise difficult to create by conventional machining [1]. The process also has the advantage of being able to machine hardened tool steels. However, its low machining efficiency and poor surface finish restricted its further applications [2]. To address these problems, one relatively new technique used to improve the efficiency and surface finish is EDM in the presence of powder suspended in the dielectric fluid [2–13]. This new hybrid material removal process is called powder mixed EDM (PMEDM). In this technique, fine abrasive powder are mixed into the dielectric fluid of EDM. The added powder significantly affects the performance of EDM process. The electrically conductive powder reduces the insu∗ Corresponding author. Tel.: +91 1672 284962 (O)/280038 (R); fax: +91 1672 284860/280057. E-mail address: [email protected] (H.K. Kansal).
0924-0136/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2005.03.028
lating strength of the dielectric fluid and increases the spark gap between the tool and workpiece [2,4,7–10,14–17]. As a result, the process becomes more stable thereby improving material removal rate (MRR) and surface finish. The effect of impurities (copper, aluminum, iron and carbon) in dielectric fluid of EDM was first studied by Erden and Bilgin [10]. It was reported that the machining rate increased with increase the concentration of the powder due to decrease the time lag. Thereafter, Jeswani [11] investigated that by addition of 4 g/l graphite powder into kerosene oil, MRR is improved around 60% and wear ratio is reduced by 15%. Mohri et al. [6,12,18] studied the effects of silicon powder addition on machining rate and surface roughness (SR) in EDM. The fine and corrosion resistant surfaces having roughness of the order of 2 m were produced. However, this performance could only be achieved at controlled machining conditions (even distribution of additives into dielectric, short discharge time, etc.). The use of silicon powder was also reported in [19–21]. It was further reported that under specific working conditions, aluminum and graphite powders exhibit more improvement in surface finish than caused by silicon powder. The glossy and smooth surface finish can be achieved
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by mixing the different additives (silicon, graphite, molybdenum, aluminum and silicon carbide) into the dielectric fluid of EDM [14]. The presence of powder increases the gap distance as compared to traditional EDM by at least a factor of two [14]. The enlarged and widened discharge channel lowers the break down strength of the dielectric fluid and reduces the electrical density on the machining spot and thus generates shallow craters [20]. Ming and He [15] observed that a bridging effect is created with the addition of powder, which facilitates the dispersion of discharge into several increments. As a result, several discharge trajectories are formed within a single input impulse and several discharge spots are created and hence MRR and surface finish improves [16]. The non-conductive materials like glass and Si3 N4 ceramics can be finely machined by PMEDM [22]. The PMEDM process improved the wear and corrosion resistance of the work surfaces by depositing a hard layer on its outer surface [23,24]. Tzeng and Chen [8] applied the optimization strategy in order to reduce the functional variability of EDM process. The literature reveals that PMEDM finds many applications to improve the surface finish, but very little effort is reported on the use of powder mixed EDM in rough machining phase. Further, PMEDM involves a large number of parameters, which affect the quality of the product. Due to this large number of parameters and their complex nature, it is difficult to relate them in a single analytical model. Extensive experimental work is therefore needed to analyze and optimize the process parameters to understand their effect on the product quality. Response surface methodology (RSM) of experimental design is one emerging technique, which helps in carrying out the analysis of experiments with the least experimental effort [25]. In the present paper, an attempt has been made to obtain an optimal setting of process parameters, which may yield optimum MRR and surface finish on the components processed by PMEDM process. Response surface methodology has been used to plan and analyze the experiments.
2. Powder mixed EDM Process The schematic diagram of an experimental setup developed for PMEDM is shown in Fig. 1. To avoid the wastage of kerosene oil, a small dielectric circulating system is designed. A stirring system is incorporated to avoid the particle settling. The modified circulation and stirring system is designed in such a way that, it can be employed at the commercial level (refer to Fig. 1). In this system, a micro pump is installed for better circulation of the powder mixed dielectric fluid. The pump and the stirrer are employed in the same tank in which machining is performed. For constant reuse of powder mixed dielectric fluid, magnetic forces are used to separate the powder particles from the debris produced due to machining (refer to Fig. 1). PMEDM has a different machining mechanism from the conventional EDM [2]. In this process, a suitable material in the powder form is mixed into the dielectric fluid of EDM. When a voltage of 80–320 V is applied to both the electrodes, an electric field in the range 105 –107 V/m is created. The spark gap is filled up with additive particles and the gap distance setup between tool and the workpiece increased from 25–50 to 50–150 m [7]. The powder particles get energized and behave in a zigzag fashion (refer to Fig. 2). The grains come close to each other under the sparking area and gather in clusters. The interlocking between the different powder particles takes place due to variation in their shape and size. They arrange themselves in the form of chain at different places under the sparking area. The chain formation helps in bridging the gap between both the electrodes. Due to bridging effect, the gap voltage and insulating strength of the dielectric fluid decreases. The easy short circuit takes place, which causes early explosion in the gap. As a result, the ‘series discharge’ starts under the electrode area. Due to increase in frequency of discharging, the faster sparking within a discharge takes place which causes faster erosion from the work piece surface. At the
Fig. 1. Schematic diagram of experimental setup.
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4. Process parameters of powder mixed EDM In order to identify the process parameters that affect the quality of component processes by PMEDM, an Ishikawa cause–effect diagram was constructed as shown in Fig. 3. The parameters can be classified as follows:
Fig. 2. Principle of powder mixed EDM.
same time, the added powder modifies the plasma channel. The plasma channel becomes enlarged and widened [2]. The electric density decreases; hence sparking is uniformly distributed among the powder particles. As a result, even and more uniform distribution of the discharge takes place, which causes uniform erosion (shallow craters) on the workpiece. This results in improvement in surface finish.
3. Experimental detail Experiments was conducted on a EZNC fuzzy logic Die Sinking EDM machine manufactured by Electronica Machine Tools Ltd., India. Silicon powder is suspended into the commercial available kerosene oil. The powder particle size is in the range of order 20–30 m. Each trial run is performed for duration of 60 min. The experiment has been performed with positive polarity as recommended in [2]. In this study, EN-31 (comparable to AISI 52100) tool steel is selected as the work material. The chemical composition of the workpiece material is given as: C = 0.9–1.2%, Si = 0.1–0.3%, Mn = 0.3–0.7%, Cr = 1–1.6%, S and P each 0.025% (max.) and balance is ferrous. Copper electrode with diameter 25 mm has been used to machine the EN-31 tool steel.
1. Electrical parameters: peak current, pulse on time, pulse off time and supply voltage. 2. Non-electrical parameters: electrode lift time, working time, gain and nozzle flushing. 3. Powder based parameters: powder type, its concentration and other properties such as shape, size, conductivity, etc. 4. Electrode based parameters: material and size of electrode. The following four independent parameters were chosen for the study: 1. 2. 3. 4.
Pulse on time, A; Duty cycle, B; Peak current, C; Concentration of the added silicon powder, D.
The ranges of these parameters were selected on the basis of preliminary experiments conducted by using one variable at a time approach. Table 1 gives the levels of various parameters and their designation. The response parameter in the present study was MRR and surface roughness (SR). In each test, the MRR was calculated by the weight loss method. The SR was measured in terms of arithmetic mean roughness of
Table 1 Design scheme of process parameters and their levels Factor symbol
A B C D
Fig. 3. Cause and effect diagram.
Parameter
Pulse on time, TON (s) Duty cycle, DC Peak current, Ip (A) Concentration, Conc. (g/l)
Levels Low (−1)
High (+1)
50 0.7 3 0
150 0.9 12 2
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the evaluated roughness profile (Ra in m) by using a Surfcoder SE1200 surface testing analyzer.
5. Response surface methodology Response surface methodology (RSM) is a collection of mathematical and statistical techniques that are useful for the modelling and analysis of problems in which a response of interest is influenced by several variables and the objective is to optimize this response [25,26]. It is a sequential experimentation strategy for empirical model building and optimization. By conducting experiments and applying regression analysis, a model of the response to some independent input variables can be obtained. Based on the model of the response, a near optimal point can then be deduced. RSM is often applied in the characterization and optimization of processes. In RSM, it is possible to represent independent process parameters in quantitative form as: Y = f (X1 , X2 , X3 , . . . Xn ) ± ε
(1)
where, Y is the response (yield), f is the response function, ε is the experimental error, and X1 , X2 , X3 , . . ., Xn are independent parameters. By plotting the expected response of Y, a surface, known as the response surface is obtained. The form of f is unknown and may be very complicated. Thus, RSM aims at approximating f by a suitable lower ordered polynomial in some region of the independent process variables. If the response can be well modeled by a linear function of the independent variables, the function (Equation (1)) can be written as: Y = C0 + C1 X1 + C2 X2 + . . . + Cn Xn ± ε
(2)
However, if a curvature appears in the system, then a higher order polynomial such as the quadratic model (Equation (3)) may be used: Y = C0 +
n i=1
Ci Xn +
n
di Xi2 ± ε
(3)
Fig. 4. Procedure of response surface methodology.
with a standard RSM design called central composite design (CCD) [27]. In this investigation, total 30 experiments were conducted at the stipulated conditions based on the procedure mentioned already. In this design, the factorial design is full factorial design with all combinations of the factors at the two levels, the eight star points at the face of the cube portion on the design and six central points. The star points corresponds to an α value of 1 and this type of design is commonly called face centered CCD. The ‘Design Expert 6.0’ software was used for regression and graphical analysis of the data obtained [28]. The optimum values of the selected variables were obtained by solving the regression equation and by analyzing the response surface contour plots [29].
i=1
The objective of using RSM is not only to investigate the response over the entire factor space, but also to locate the region of interest where the response reaches its optimum or near optimal value. By studying carefully the response surface model, the combination of factors, which gives the best response, can then be established. The response surface method is a sequential process and its procedure can be summarized as shown in Fig. 4.
6. Machining conditions and experimental plan As already mentioned, and accordance with the literature consulted, as well as drawing from personal experience [13], four factors are being studied and their low and high levels are given in Table 1. The PMEDM process was studied
7. Results and discussions The 30 experiments were conducted in duplicate and the average values of MRR and SR along with design matrix were tabulated in Table 2. For analysis the data, the checking of goodness of fit of the model is very much required. The model adequacy checking includes test for significance of the regression model, test for significance on model coefficients and test for lack of fit [29]. For this purpose, analysis of variance (ANOVA) is performed. 7.1. Analysis of material removal rate The fit summary recommended that the quadratic model is statistically significant for analysis of MRR. The results
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Table 2 Design of Experimental matrix and results for the PMEDM performance characteristics Exp. no.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Process parameters
Observed values
Pulse on time, TON , A
Duty cycle, DC, B
50 150 50 150 50 150 50 150 50 150 50 150 50 150 50 150 50 150 100 100 100 100 100 100 100 100 100 100 100 100
0.7 0.7 0.9 0.9 0.7 0.7 0.9 0.9 0.7 0.7 0.9 0.9 0.7 0.7 0.9 0.9 0.8 0.8 0.7 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8
Peak current, Ip , C
3 3 3 3 12 12 12 12 3 3 3 3 12 12 12 12 7.5 7.5 7.5 7.5 3 12 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5
of the quadratic model for MRR in the form of ANOVA are given in Table 3. The value of R2 and adjusted R2 is over 99%. This means that regression model provides an excellent explanation of the relationship between the independent variables (factors) and the response (MRR). The associated p-value for the model is lower than 0.05 (i.e. α = 0.05, or 95% confidence) indicates that the model is considered to be statistically significant [29]. The lack-of-fit term is non significant as it is desired. Further, factor A (pulse on time), factor C (peak current), factor D (concentration of silicon powder), interaction effect of A (pulse on time) with factor C (peak current), interaction effect of factor C (peak current) with factor D (concentration) and second order term of factor C (peak current) have significant effect. These significant effects, in descending order, are factor C (peak current), the quadratic effect of factor C (peak current), factor D (concentration), the interaction of factor C (peak current) with factor D (concentration), factor A (pulse on time) and finally, the interaction of factor A (pulse on time) with factor C (peak current). The result proves that the powder added into the dielectric fluid enhances the MRR [2,5,11]. The other model terms are said to be nonsignificant.
Concentration, Conc., D 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 1 1 1 1 1 1 0 2 1 1 1 1 1 1
MRR (mm3 /min)
SR (m)
I
II
Average
I
II
Average
1.84 1.98 2.19 2.88 22.30 23.41 21.65 24.21 3.17 3.30 3.16 3.19 26.98 28.38 26.00 28.21 4.75 8.20 7.19 7.43 2.10 25.50 5.20 6.94 6.18 6.70 6.22 7.93 6.61 7.58
2.22 2.84 2.00 1.94 23.10 24.20 23.70 25.20 3.17 3.47 3.24 3.56 25.21 29.44 26.39 29.20 4.63 6.19 5.20 7.14 1.95 24.52 7.19 7.65 6.21 7.28 8.09 6.59 7.15 6.82
2.03 2.41 2.10 2.41 22.70 23.81 22.68 24.71 3.17 3.38 3.20 3.38 26.10 28.91 26.19 28.71 4.69 7.19 6.21 7.29 2.03 25.01 6.21 7.29 6.19 6.99 7.15 7.26 6.88 7.20
2.48 1.98 2.30 2.41 7.21 6.14 6.50 6.36 2.11 1.21 4.68 1.31 5.5 6.19 6.40 5.00 3.55 7.39 6.00 7.32 1.71 6.91 7.55 4.20 7.32 6.30 6.51 6.30 6.75 5.11
1.96 2.30 2.33 1.88 6.42 9.36 8.91 7.13 2.34 1.48 3.54 1.37 5.48 4.05 3.84 5.23 7.81 6.51 6.02 5.48 1.89 5.06 6.07 5.36 5.47 7.30 7.09 6.09 5.55 6.85
2.22 2.14 2.32 2.14 6.82 7.75 7.70 6.75 2.22 1.34 4.11 1.34 5.50 5.12 5.12 5.12 5.68 6.95 6.01 6.40 1.80 5.99 6.81 4.78 6.39 6.80 6.80 6.19 6.15 5.98
To fit the quadratic model for MRR appropriate, the nonsignificant terms are eliminated by backward elimination process. The ANOVA Table for the reduced quadratic model for MRR is shown in Table 4. The reduced model results indicate that the model is significant (R2 and adjusted R2 are 99.77% and 99.71%, respectively), lack of fit is non significant (p-value is less than 0.05). Fig. 5 displays the normal probability plot of the residuals for MRR. Notice that the residuals are falling on a straight line, which means that the errors are normally distributed. Further, each observed value is compared with the predicted value calculated from the model in Fig. 6. It can be seen that the regression model is fairly well fitted with the observed values. After eliminating the non-significant terms, the final response equation for MRR is given as follows: (In coded terms) MRR = 6.71 + 0.67A + 11.37C + 1.18D +7.34C2 + 0.46AC + 0.74CD
(4)
(In actual factors) MRR = 8.39 − 1.99TON − 3.27IP − 0.05Conc. + 0.36Ip2 +2.05TON IP + 0.16IP Conc.
(5)
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Table 3 ANOVA table for MRR (before elimination) Source
Sum of squares
Degrees of freedom
Mean square
f-Value
Prob > f
Model A B C D A2 B2 C2 D2 AB AC AD BC BD CD Residual Lack of fit Pure error Cor. total
2762.72 8.11 0.22 2328.12 25.16 0.51 0.35 131.73 0.35 0.016 3.42 0.22 0.029 0.068 8.73 4.69 3.91 0.78 2767.41
14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15 10 5 29
197.34 8.11 0.22 2328.12 25.16 0.51 0.35 131.73 0.35 0.016 3.42 0.22 0.029 0.068 8.73 0.31 0.39 0.16
630.55 25.90 0.70 7439.08 80.39 1.64 1.11 420.91 1.11 0.050 10.94 0.71 0.092 0.22 27.90
<0.0001 (significant) 0.0001 0.4172 <0.0001 <0.0001 0.2202 0.3098 <0.0001 0.3098 0.8262 0.0048 0.4140 0.7654 0.6488 <0.0001
Standard deviation = 0.56 Mean = 11.11 Coefficient of variation = 5.03 Predicted residual error of sum of squares (PRESS) = 18.94
Fig. 7 shows the estimated response surface for MRR in relation to the design parameters of peak current and pulse on time. As can be seen from this figure, the MRR tends to increase, considerably with increase in peak current for any value of pulse on time. Hence, maximum MRR is obtained at high peak current (12 A) and high pulse on time (150 s). This is due to their dominant control over the input energy. However, at low range of peak current (3–5 A), maximum MRR is obtained at 100 s pulse on time. The effect of concentration and peak current on MRR is shown in Fig. 8. This figure displays that the value of MRR increases with increase in peak current. The reason is same as stated earlier. The effect of concentration on MRR can be also seen from this figure. The powder added into the dielec-
2.50
0.1619 (not significant)
R2 = 0.9983 R2 adjusted = 0.9967 Predicted R2 = 0.9932 Adequate precision = 67.427
tric fluid enhances the MRR. With increase in concentration of the powder, the MRR tends to increase. This is because the added additive causes bridging effect between both the electrodes, facilitates the dispersion of discharge into several increments and hence increases the MRR. The maximum MRR is obtained at highest level of concentration of added silicon powder (2 g/l) and peak current (12 A). 7.2. Analysis of surface roughness For surface roughness, the fit summary recommended that the quadratic model is statistically significant for analysis. Table 5 presents the ANOVA table for a quadratic model for SR.
Table 4 ANOVA table for MRR (after backward elimination) Source
Sum of squares
Degrees of freedom
Mean square
f-Value
Prob > f
Model A C D C2 AC CD Residual Lack of fit Pure error Cor. total
2761.12 8.11 2328.12 25.16 387.58 3.42 8.73 6.29 5.51 0.78 2767.41
6 1 1 1 1 1 1 23 18 5 29
460.19 8.11 2328.12 25.16 387.58 3.42 8.73 0.27 0.31 0.16
1681.08 29.63 8509.29 91.95 1416.61 12.51 31.92
<0.0001 (significant) <0.0001 <0.0001 <0.0001 <0.0001 0.0018 <0.0001
Standard deviation = 0.52 Mean = 11.11 Coefficient of variation = 4.71 Predicted residual error of sum of squares (PRESS) = 9.47
1.96
R2 = 0.9977 R2 adjusted = 0.9971 Predicted R2 = 0.9966 Adequate precision = 104.693
0.2358 (not significant)
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Fig. 7. Effect of peak current and pulse on time on MRR. Fig. 5. Normal probability plot residuals for MRR.
R2
R2
The value of and adjusted are 96% and 92.32%, respectively. This means that regression model provides an excellent explanation of the relationship between the independent variables (factors) and the response (SR). The associated p-value for the model is lower than 0.05 (i.e. α = 0.05, or 95% confidence) indicates that the model is considered statistically significant. The lack-of-fit term is non significant as it is desired. Further, factor C (peak current), factor D (concentration of silicon powder), interaction effect of factor C (peak current) with factor D (concentration) and second order term of factor C (peak current) have significant effect. These significant effects, in descending order, are factor C (peak current), the quadratic effect of factor C (peak current), factor D (concentration) and finally, the interaction of factor C (peak current) with factor D (concentration). The result proves that the powder added into the dielectric fluid enhances the surface finish [6,14]. The other model terms are said to be non-significant. To fit the quadratic model for SR appropriate, the nonsignificant terms are eliminated by backward elimination
Fig. 6. Plot of actual vs. predicted response of MRR data.
process. The ANOVA Table for the reduced quadratic model for MRR is shown in Table 6. The reduced model results indicate that the model is significant (R2 and adjusted R2 are 92.75% and 91.60%, respectively), lack of fit is non significant (p-value is less than 0.05). Fig. 9 displays the normal probability plot of the residuals for SR. Notice that the residuals are falling on a straight line, which means that the errors are normally distributed. Further, each observed value is compared with the predicted value calculated from the model in Fig. 10. It can be seen that the regression model is fairly well fitted with the observed values. After eliminating the non-significant terms, the final response equation for SR is given as follows: (In coded terms) SR = 6.25 + 2.01C − 0.56D − 2.05C2 − 0.52CD
(6)
(In actual factors) SR = −3.12 + 2.08IP + 0.31Conc. − 0.10IP2 −0.11IP Conc.
Fig. 8. Effect of peak current and concentration on MRR.
(7)
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Table 5 ANOVA table for SR (before elimination) Source
Sum of squares
Degrees of freedom
Mean square
f-Value
Prob > f
Model A B C D A2 B2 C2 D2 AB AC AD BC BD CD Residual Lack of fit Pure error Cor. total
117.18 0.51 0.20 72.88 5.58 0.17 0.058 12.09 0.18 0.75 0.77 0.89 0.38 0.15 4.38 4.85 4.25 0.60 122.03
14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15 10 5 29
8.37 0.51 0.20 72.88 5.58 0.17 0.058 12.09 0.18 0.75 0.77 0.89 0.38 0.15 4.38 0.32 0.42 0.12
25.88 1.57 0.61 225.39 17.25 0.54 0.18 37.39 0.54 2.33 2.38 2.75 1.18 0.48 13.54
<0.0001 (significant) 0.2298 0.4480 <0.0001 0.0008 0.4737 0.6779 <0.0001 0.4725 0.1479 0.1436 0.1182 0.2947 0.5006 0.0022
3.53
0.0882 (not significant)
R2 = 0.9603 R2 adjusted = 0.9232 Predicted R2 = 0.7828 Adequate precision = 16.297
Standard deviation = 0.57 Mean = 5.01 Coefficient of variation = 11.34 Predicted residual error of sum of squares (PRESS) = 26.51 Table 6 ANOVA table for SR (after backward elimination) Source
Sum of squares
Degrees of freedom
Mean square
f-Value
Prob > f
Model C D C2 CD Residual Lack of fit Pure error Cor. total
113.18 72.88 5.58 30.34 4.38 8.85 8.25 0.60 122.03
4 1 1 1 1 25 20 5 29
28.29 72.88 5.58 30.34 4.38 0.35 0.41 0.12
79.96 205.95 15.76 85.74 12.37
<0.0001 (significant) <0.0001 0.0005 <0.0001 0.0017
3.43
0.0882 (not significant)
R2 = 0.9275 R2 adjusted = 0.9159 Predicted R2 = 0.8875 Adequate precision = 21.156
Standard deviation = 0.59 Mean = 5.01 Coefficient of variation = 11.87 Predicted residual error of sum of squares (PRESS) = 13.73
Fig. 11 shows the estimated response surface for SR in relation to the design parameters of peak current and pulse on time. As can be seen from this figure, the SR tends to increase, considerably up to the 10 A peak current. Beyond 10 A peak current, the SR again starts decreasing for any value of the pulse on time. The SR also increases with increase in pulse on time. This is due to their dominant control over the input
energy. It is clear from Fig. 11 that the best surface finish is obtainable at the lower level of peak current (3 A) and pulse on time (50 s). The effect of concentration and peak current on SR is shown in Fig. 12. This figure displays that the value of SR increases with increase in peak current at least up to its maximum level, after which it tends to decrease for high value
Table 7 Confirmation tests and their comparison with the results Exp. no.
1 2 3
MRR (mm3 /min)
Machining conditions
SR (m)
Pulse on time, A (s)
Duty cycle, B
Peak current, C (A)
Conc., D (g/l)
Exp.
Predicted
Error (%)
Exp
Predicted
Error (%)
50 100 150
0.7 0.8 0.9
3 7.5 12
2 1 0
3.17 6.20 24.71
2.91 6.71 24.63
7.91 −8.03 0.32
2.22 6.39 6.75
2.15 6.25 7.28
3.15 2.19 −7.85
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Fig. 11. Effect of peak current and pulse on time on SR. Fig. 9. Normal probability plot residuals for SR.
of concentration of the added powder. In this way, in order to obtain a good surface finish, low values of peak current (3 A) and high level of concentration of added powder (2 g/l) should be used. On other side, the low levels of the SR can be also obtained at high values of peak current and concentration of the added powder into the dielectric fluid of EDM. In both ways, the low value of SR is obtained at high level of concentration of the added powder. This proves that the added additive plays a significant role to modify the plasma channel. The plasma channel becomes enlarged and widened [2]. The electric density decreases; hence sparking is uniformly distributed among the powder particles. As a result, even and uniform surfaces are produced.
8. Confirmation experiments Since the response surface equations were derived from quadratic regression fit, confirmation tests must be performed
Fig. 12. Effect of peak current and concentration on SR.
to verify their validity. Of course, the independent variable values selected for the confirmation test must lie within the ranges for which the formulas were derived. The three conformation experiments were performed for MRR and SR. The data from the confirmation runs and their comparisons with the predicted designed for MRR and SR are listed in Table 7. From the analysis of Table 7, it can be observed that the calculated error is small. The error between experimental and predicted values for MRR and SR are lie within ±8% and −7.85% to 3.15%, respectively. Obviously, this confirms excellent reproducibility of the experimental conclusions.
9. Conclusions
Fig. 10. Plot of actual vs. predicted response of SR data.
Silicon powder was suspended into the dielectric fluid of EDM and an enhanced rate of material removal and surface finish has been achieved. Empirical modelling with the help
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of response surface methodology has led to the following conclusions about the variation of response parameters in terms of independent parameters within the specified range. The silicon powder suspended in the dielectric fluid of EDM affects both MRR and SR. The slope of the curve indicates that the MRR increases with the increase in the concentration of the silicon powder. Therefore, more improvement in MRR is expected at still higher concentration level of silicon powder. There is discernible improvement in surface roughness of the work surfaces after suspending the silicon powder into the dielectric fluid of EDM. However, more improvement in SR is still expected at higher concentration level of silicon powder. The analysis of variance revealed that the factor C (peak current) and factor D (concentration) are the most influential parameters on MRR and SR. The quadratic term of factor C (peak current) also have significant effect. Factor C (peak current) and factor D (concentration) interact with each other. The combination of high peak current and high concentration yields more MRR and smaller SR. The confirmation tests showed that the error between experimental and predicted values of MRR and SR are within ±8% and −7.85% to 3.15%, respectively.
Acknowledgements The authors would like to acknowledge the support of department of mechanical engineering, SLIET, Longowal, India and M/S Electronica Machine Tools Ltd., Pune, India. We are thankful to Mr. Kulwinder Singh, department of mechanical engineering, SLIET, Longowal. We are also grateful to Prof. P.L. Bali, LIET, Jalandhar and Er. Baljit Singh, PSEB for their guidance and expert comments in response to our queries and problems.
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