ORIGINAL ARTICLE
Evaluation of the characteristics of the microelectrical
discharge machining process using response surface
methodology based on the central composite design
Y. C. Lin&C. C. Tsao&C. Y. Hsu&S. K. Hung&D. C. Wen
Received: 17 August 2011 / Accepted: 3 November 2011 / Published online: 17 November 2011 # Springer-Verlag London Limited 2011
Abstract Evaluation of the characteristics of a micro-electrical discharge machining (Micro-EDM) process is challenging, because it involves complex, interrelated relationships so a proper modeling approach is necessary to clearly identify the crucial machining variables and their interrelationships in order to initiate more effective strate-gies to improve Micro-EDM qualities (electrode wear (EW), material removal rate (MRR) and overcut). This paper uses a response surface method (RSM) based on the central composite design (CCD) for Micro-EDM problems with four EDM variables (peak current, pulse on-time, pulse off-time and electrode rotation speed). Experimental results indicate that peak current is the EDM variable that most affects the Micro-EDM qualities for SK3 carbon tool steel while pulse off-time had a significant interaction with that. The results show that RSM based on the CCD could efficiently be applied for the modeling of Micro-EDM
qualities (EW, MRR, and overcut), and it is an economical way to obtain the performance characteristics of Micro-EDM process parameters with the fewest experimental data. Keywords Response surface method . Central composite design . Electrode wear . Material removal rate . Overcut . Microelectrical discharge machining
1 Introduction
EDM is a complex process characterized by the use of electric-thermal energy to remove material from the machined areas, regardless of material hardness. Micro-EDM uses EDM for micro manufacturing. Micro-EDM using small energy levels (<100 μJ) has been the focus of intensive research in recent years in order to improve the quality of the finish, because it is an effective machining operation for the production of microholes and microslots in the production of mold inserts for microstructures. The supplied energy in Micro-EDM depends on the discharge voltage, the peak current and the pulse duration in Micro-EDM [1]. However, machining defects, such as electrode wear (EW) and overcut, occur during the Micro-EDM process leading to a lack of machining accuracy in the geometry of workpiece. SK3 carbon tool steel is widely used in the dies and molds, machine parts and cutting tools because of its high toughness and excellent wear resistance. Son et al. [1] reported that a shorter EDM pulse makes a precision part more efficiently with a higher MRR. Han et al. [2] showed that shortening the pulse on-time is more efficient than reducing the peak current in achieving a high quality machined surface. Egashira et al. [3] found that EDM with ultralow discharge energy (voltages <40 V) has the advantage of a low wear ratio, as well as a high machining accuracy. Liu et al. [4] Y. C. Lin
:
S. K. HungDepartment of Mechanical Engineering, National Chiao Tung University, Taiwan, Republic of China C. C. Tsao
Department of Mechatronic Engineering, Tahua Institute of Technology,
Taiwan, Republic of China C. Y. Hsu
Department of Mechanical Engineering, Lunghwa University of Science and Technology, Taiwan, Republic of China
D. C. Wen (*)
Department of Mechanical Engineering, China University of Science and Technology, Taiwan, Republic of China
pointed out that small input energy pulses and high precision systems are the two major requirements on Micro-EDM. Peng et al. [5] combined Micro-EDM deposition with a microreversible EDM selective removal process to fabricate micrometal structures. Pham et al. [6] pointed out that errors from different sources such as the accuracy and repeatability of positioning of the machine, electrode dressing, jigs and fixtures, and electrode wear directly affect the accuracy of the Micro-EDM process. Wong et al. [7] reported that the volume and size of microcraters using single RC-pulse discharges are more consistent for lower-energy than for higher-energy discharges. Aligiri et al. [8] proposed a new tool wear compensation method to solve the problem of geometrical inaccuracy of machined hole depth in Micro-EDM.
Response surface methodology (RSM) is an effective technique for developing, improving, and optimizing processes, which is often used to combine several indepen-dent variables and assess how their complex interactions affect desired responses [9,10]. RSM uses statistical design of experiment techniques, such as the central composite design (CCD) and least-squares fit in the model generation phase. The performance of the proposed model is then demonstrated using checking tests provided by analysis of variance. Response surface plots can be used to investigate the surfaces and locate the optimum condition. A number of researchers have used RSM to evaluate the results and efficiency of manufacturing operations [11–15].
In this study, a method using a relatively small number of experimental trials was used to investigate Micro-EDM process characteristics (EW, MRR, and overcut). Using concepts from design of experiment, a CCD approach is proposed to determine the required number of experimental trials and the locations of the Micro-EDM process characteristics. The experimental trials are performed in the MINITAB (Minitab Inc.) Release 14.0 statistical software. Regression analysis is used to build the statistical models with the variable of interest and the Micro-EDM process characteristics. These models are also used as objective functions for the optimization problems.
2 Experimental design and central composite design An effective alternative to the factorial design is the CCD, originally developed by Box and Wilson [16], and improved upon by Box and Hunter [17]. The CCD gives almost as much information as a three-level factorial, requires much fewer tests than the full factorial and has been shown to be sufficient to describe the majority of steady-state process responses [18, 19]. For four variables (n=4), the central
composite design can be represented by points on a cube, each axis corresponding to a factor represents thirty
experi-ments, consisting of 2n (24=16) factor points, 2n (2×4=8) axial points and six center points (six replications). The codes are calculated as functions of the range of interest of each variable based on the preliminary experiments, as shown in Table1.
When the response data are obtained from the test, a regression analysis is performed to determine the coeffi-cients of the response model and their standard errors and significance. In general, a second-order polynomial re-sponse surface mathematical model is used to analyze the parametric influences of the parameters on the various response criteria. The second-order model demonstrates the second-order effect of each variable, separately, and the two-way interaction between combinations of these varia-bles. This second-order mathematical model can be represented as follows: Y ¼ boþ Xn i¼1 biXiþ Xn i¼1 biiXii2þ X i<j bijXiXjþ " ð1Þ where Y is the corresponding response, Xi is the input variables, Xii2 and XiXj are the squares and interaction terms of these input variables,bo,bi,bij, andbiiare the regression coefficients of the parameters, andε is the experimental error. All 30 experimental runs for the CCD were performed as shown in Table2. Table2 shows that the central composite design composes four independent variables;X (peak current (X1), pulse on-time (X2), pulse off-time (X3) and electrode
rotation speed (X4)), and the response,Y (electrode wear (Y1),
material removal rate (Y2) and overcut (Y3)).
3 Experimental procedures
The workpiece material used for the experiments was SK3 carbon tool steel (3 mm in thickness), which was ground with a diamond-grain resin-bond grinding wheel to produce parallel faces. The tool electrode material was tungsten carbide. Tungsten carbide tools were dressed from 0.3 to 0.2 mm diameter using a very accurate CNC grinding machine. A series of experiments on a microgroove of 0.5 mm length and 0.02 mm depth were carried out on an EDM machine (OCT 200-MA, Ocean Technologies) that used an iso-frequent pulse generator, with a maximum operating discharge current of 3A and the capability to set open-circuit voltage at 10 V. The maximum travel of the machine was 200 mm (X)×150 mm (Y)×150 mm (Z) with a positional resolution of 0.1μm, in the X, Y, and Z directions and a fully closed feedback control to ensure sub-micron accuracy. The overcut was measured using an automatic vision inspector (MTCRO.VU InSpec).
During the Micro-EDM process, the electrode diam-eter was maintained at a constant value. Therefore, the
Table 2 Experimental results
for EW, MRR and overcut Std Actual factors Response variables
X1 X2 X3 X4 Y1(mm) Y2×10−5(mm3/min) Y3(mm)
Observed Predicted Observed Predicted Observed Predicted
1 0.3 6 3 100 0.039 0.038 1.721 2.094 0.0098 0.0090 2 1 6 3 100 0.060 0.054 5.319 5.506 0.0174 0.0190 3 0.3 25 3 100 0.039 0.044 1.879 1.792 0.0081 0.0069 4 1 25 3 100 0.083 0.064 4.681 5.366 0.0245 0.0229 5 0.3 6 13 100 0.046 0.039 1.483 1.939 0.0141 0.0138 6 1 6 13 100 0.213 0.197 2.410 2.575 0.0142 0.0147 7 0.3 25 13 100 0.043 0.018 1.659 2.417 0.0121 0.0147 8 1 25 13 100 0.150 0.179 4.104 3.216 0.0217 0.0217 9 0.3 6 3 500 0.039 0.022 3.451 4.254 0.0107 0.0116 10 1 6 3 500 0.045 0.059 9.414 8.348 0.0257 0.0230 11 0.3 25 3 500 0.045 0.055 5.752 5.229 0.0117 0.0103 12 1 25 3 500 0.085 0.095 9.697 9.487 0.0254 0.0278 13 0.3 6 13 500 0.041 0.048 2.815 1.891 0.0080 0.0100 14 1 6 13 500 0.226 0.226 2.782 3.209 0.0104 0.0123 15 0.3 25 13 500 0.042 0.053 3.697 3.646 0.0119 0.0118 16 1 25 13 500 0.254 0.234 5.010 5.128 0.0207 0.0202 17 0.3 13 6 300 0.041 0.055 2.994 2.188 0.0139 0.0123 18 1 13 6 300 0.125 0.126 4.592 5.169 0.0241 0.0225 19 0.5 6 6 300 0.109 0.129 3.339 2.918 0.0130 0.0099 20 0.5 25 6 300 0.146 0.141 3.342 3.535 0.0110 0.0109 21 0.5 13 3 300 0.134 0.133 4.562 4.397 0.0063 0.0091 22 0.5 13 13 300 0.160 0.176 2.697 2.633 0.0152 0.0092 23 0.5 13 6 100 0.104 0.139 3.980 2.327 0.0087 0.0079 24 0.5 13 6 500 0.166 0.146 3.067 4.491 0.0117 0.0093 25 0.5 13 6 300 0.149 0.146 3.263 3.201 0.0085 0.0099 26 0.5 13 6 300 0.171 0.146 2.695 3.201 0.0073 0.0099 27 0.5 13 6 300 0.152 0.146 3.045 3.201 0.0081 0.0099 28 0.5 13 6 300 0.146 0.146 2.953 3.201 0.0090 0.0099 29 0.5 13 6 300 0.163 0.146 3.347 3.201 0.0084 0.0099 30 0.5 13 6 300 0.149 0.146 3.222 3.201 0.0084 0.0099
Table 1 Parameters and levels for Micro-EDM
Workpiece SK3 carbon tool steel thickness =3 mm
Electrode Tungsten carbide diameter=0.2 mm
Dielectric fluid Kerosene
Polarity Electrode negative
Workpiece positive
Symbol Factors Levels
−1 0 +1
X1 Peak current (mA) 0.3 0.5 1.0
X2 Pulse on-time (μs) 6 13 25
X3 Pulse off-time (μs) 3 6 13
EW and MRR for the Micro-EDM operation were calculated using Eqs. 2 and 3, respectively, which are shown below:
EW¼ ASΔL ð2Þ
MRR¼ ASFO ð3Þ
where ΔL is the distance between an ideal blind hole and machined blind hole in micrometers, AS is the area of
electrode in square micrometers andFO is the cutting feed
in micrometers per minute for Micro-EDM. Table 3 Analysis of variance for EW
Source Sum of squares Degree of freedom Mean square F value p value>F
Model 0.1099 14 0.0078 17.158 < 0.0001 Significant X1 0.0443 1 0.0443 96.850 < 0.0001 Significant X2 0.0002 1 0.0002 0.497 0.4916 X3 0.0221 1 0.0221 48.419 < 0.0001 Significant X4 0.0017 1 0.0017 3.847 0.0687 X12 0.0126 1 0.0126 27.703 < 0.0001 Significant X22 0.0004 1 0.0004 0.927 0.3507 X32 7.02E−07 1 7.02E−07 0.001 0.9693 X42 3.73E−05 1 3.73E−05 0.081 0.7789 X1X2 8.68E−06 1 8.68E−06 0.018 0.8923 X1X3 0.0207 1 0.0207 45.270 < 0.0001 Significant X1X4 0.0004 1 0.0004 0.903 0.3568 X2X3 0.0007 1 0.0007 1.683 0.2141 X2X4 0.0006 1 0.0006 1.476 0.2431 X3X4 0.0005 1 0.0005 1.283 0.2750 Residual 0.0068 15 0.0004 Lack of fit 0.0063 10 0.0006 6.62 0.0250 Pure error 0.0004 5 0.00009 Correlation total 0.1168 29
Table 4 Analysis of variance for MRR
Source Sum of squares Degree of freedom Mean square F value p value>F
Model 9.24E−09 14 6.60E−10 8.42 < 0.0001 Significant
X1 2.69E−09 1 2.69E−09 34.25 < 0.0001 Significant
X2 2.93E−10 1 2.93E−10 3.73 0.0724
X3 2.28E−09 1 2.28E−09 29.13 < 0.0001 Significant
X4 1.86E−09 1 1.86E−09 23.66 0.0002 Significant
X12 6.56E−12 1 6.56E−12 0.084 0.7764
X22 8.13E−13 1 8.13E−13 0.010 0.9203
X32 1.12E−10 1 1.12E−10 1.43 0.2499
X42 1.12E−11 1 1.12E−11 0.14 0.7110
X1X2 2.73E−12 1 2.73E−12 0.035 0.8544
X1X3 8.00E−10 1 8.00E−10 10.20 0.0060 Significant
X1X4 4.76E−11 1 4.76E−11 0.61 0.4483
X2X3 6.25E−11 1 6.25E−11 0.80 0.3862
X2X4 1.65E−10 1 1.65E−10 2.10 0.1681
X3X4 4.96E−10 1 5.00E−10 6.33 0.0238
Residual 1.18E−09 15 7.84E−11
Lack of fit 1.15E−09 10 1.15E−10 19.77 0.0021
Pure error 2.90E−11 5 5.80E−12
4 Results and discussion
4.1 Analysis of variance and fitted regression models A series of experiments was performed using a CCD, as shown in Table2. Various statistical data (standard error of estimate, sum of squares of the errors, F statistics, and p
value) for EW, MRR, and overcut in Micro-EDM were examined. Using 5% and 1% significance levels, a model was considered significant if the p value (significance probability value) was less than 0.05 and 0.001, respec-tively. From thesep values for EW, presented in Table3, it can be seen that the effects ofX1,X3, X12and X1X3 were
statistically significant. From thep values for MRR, shown Table 5 Analysis of variance for overcut
Source Sum of squares Degree of freedom Mean square F value p value>F
Model 0.00088 14 6.34E−05 7.89 0.0001 Significant
X1 3.79E−04 1 3.79E−04 47.22 < 0.0001 Significant
X2 3.65E−05 1 3.65E−05 4.54 0.0499
X3 9.12E−06 1 9.12E−06 1.13 0.3036
X4 1.24E−06 1 1.24E−06 0.15 0.6999
X12
7.02E−05 1 7.02E−05 8.74 0.0098 Significant
X22 3.06E−07 1 3.06E−07 0.03 0.8479 X32 1.62E−06 1 1.62E−06 0.20 0.6597 X42 4.57E−06 1 4.57E−06 0.56 0.4623 X1X2 3.79E−05 1 3.79E−05 4.71 0.0463
X1X3 8.46E−05 1 8.46E−05 10.53 0.0054 Significant
X1X4 1.93E−06 1 1.93E−06 0.24 0.6309
X2X3 9.41E−06 1 9.41E−06 1.17 0.2962
X2X4 8.04E−07 1 8.04E−07 0.10 0.7560
X3X4 4.11E−05 1 4.11E−05 5.12 0.0389
Residual 1.20E−04 15 8.03E−06
Lack of fit 0.00011 10 1.18E−05 37.46 0.0004
Pure error 1.58E−06 5 3.17E−07
Correlation total 0.00100 29
Fig. 1 Relationship between experimental and predicted electrode wear for Micro-EDM using Eq.4
Fig. 2 Relationship between experimental and predicted material removal rate for Micro-EDM using Eq.5
in Table4, it can be seen that the effects ofX1,X3, andX4
were statistically significant. From thep values for overcut, reported in Table5, it can be seen that the effect ofX1was
statistically significant. However, of these four variables, peak current (X1) was the major factor affecting the
Micro-EDM qualities of SK3 carbon tool steel while pulse off-time (X3) had a significant interaction.
From the experimental design and the results in Table2, the second-order response functions representing electrode wear (Y1), material removal rate (Y2) and overcut (Y3) of
SK3 carbon tool steel can be expressed as a function of four operating parameters for the Micro-EDM, namely peak current (X1), pulse on-time (X2), pulse off-time (X3), and
electrode rotation speed (X4). The relationship between the
responses (EW, MRR, and overcut of SK3 carbon tool steel) and operating parameters were obtained for a coded unit as follows: EW model equation: Y1¼ 0:188 þ 0:878X1þ 5:117 103X2 5:252 103X3 4:104 105X4 0:710X12 1:533 104X22 2:510 105X32 9:501 108X42 þ2:185 104X 1X2þ 2:018 102X1X3þ 7:193 105X1X4 1:443 104X 2X3þ 3:408 106X2X4þ 6:008 106X3X4 ðmmÞ ð4Þ MRR model equation: Y2¼ 8:946 106þ 7:844 105X1 2:793 107X2 3:74 106X3þ 2:2 108X4 1:614 105X 12 6:707 109X22þ 3:175 107X32þ 5:194 1011X42 þ1:226 107X 1X2 3:965 106X1X3þ 2:438 108X1X4 þ4:108 108X 2X3þ 1:681 109X2X4 5:521 109X3X4 ðmm3= minÞ ð5Þ
Overcut model equation:
Y3¼ 1:636 102 5:378 102X1 4:371 104X2þ 1:536 103X3þ 2:896 105X4 þ5:284 102X 12þ 4:117 106X22 3:816 105X32 3:323 108X42 þ4:568 104X 1X2 1:29 103X1X3þ 4:918 106X1X4 þ1:595 105X 2X3þ 1:176 107X2X4 1:59 106X3X4 ðmmÞ ð6Þ
The response factors for any regime within the interval of the selected experimental design can be calculated from Eqs. 4 to 6. The predicted values obtained using model equations (Eqs.4,5, and6) are shown in Figs.1,2, and3,
respectively. It is clear that the predicted values match the experimental values reasonably well with R2of 0.939 for EW,R2of 0.876 for MRR, andR2of 0.867 for overcut of SK3 carbon tool steel for Micro-EDM.
Fig. 3 Relationship between experimental and predicted overcut for Micro-EDM using Eq.6
4.2 Effect of the Micro-EDM variables on EW
The response surface plots, shown in Fig. 4, demonstrate the effect of different Micro-EDM variables on EW. The figures show the relationship between two Micro-EDM
variables and electrode wear at the middle level of the other two variables. Figure4ashows the effect of pulse off-time and peak current on EW. A lower pulse off-time and a lower peak current have a minor effect on EW, but it is worth noting that larger EW occurs for the center level of Fig. 4 Response surface plots showing the effect of two variables on
the EW of Micro-EDM. The other two variables are maintained at the middle level. a Pulse off-time and peak current; b pulse on-time and
peak current; c electrode rotation speed and peak current; d pulse off-time and pulse on-off-time; e electrode rotation speed and pulse on-off-time and f electrode rotation speed and pulse off-time
the peak current. Figure 4b shows the effect of pulse on-time and peak current on EW. It can be seen that EW depends more on the peak current than on pulse on-time. It is also worth noting that lower EW occurs for a lower peak current. Figure 4c shows the effect of electrode rotation
speed and peak current on EW. The general form of the three-dimensional (3D) relationship is similar to that of the previous figure. Figure 4d shows the effect of pulse off-time and pulse on-off-time on EW. A minor EW occurs for minimum level pulse off-time and pulse on-time. Figure4e
Fig. 5 Response surface plots showing the effect of two variables on the MRR of Micro-EDM. The other two variables are maintained at the middle level. a Pulse off-time and peak current; b pulse on-time
and peak current; c electrode rotation speed and peak current; d pulse off-time and pulse time; e electrode rotation speed and pulse on-time and f electrode rotation speed and pulse off-on-time
shows the effect of electrode rotation speed and pulse on-time on EW. The general form of the 3D relationships is similar to that shown in Fig.4a–c. EW depends more on the pulse on-time than on electrode rotation speed. It is clear that lower EW occurs for a lower pulse on-time and lower
electrode rotation speed. Figure 4f shows the effect of electrode rotation speed and pulse off-time on EW. A minor EW occurs for the minimum level of electrode rotation speed and pulse off-time. It can be seen that EW depends more on the pulse off-time than on electrode rotation speed. Fig. 6 Response surface plots showing the effect of two variables on
the overcut of Micro-EDM. The other two variables are maintained at the middle level. a Pulse off-time and peak current; b pulse on-time
and peak current; c electrode rotation speed and peak current; d pulse off-time and pulse time; e electrode rotation speed and pulse on-time and f electrode rotation speed and pulse off-on-time
4.3 Effect of Micro-EDM variables on MRR
Figure5 shows the response surface plots for two Micro-EDM variables and MRR at the middle level for the other two variables. Figure5ashows the effect of pulse off-time and peak current on MRR. It can be seen that maximum MRR occurs for a minimum level pulse off-time, but a maximum peak current level. Peak current has a significant effect on MRR whilst pulse off-time has a trivial effect. Figure 5b reports the effect of pulse on-time and peak current on MRR. It can be seen that maximum MRR occurs for a maximum level pulse on-time and maximum peak current level, but the effect of the peak current is more powerful than that of the pulse on-time. Figure5c shows the effect of electrode rotation speed and peak current on MRR. The general form of the 3D relationship is similar to that of the previous figure. Figure 5d shows the effect of pulse off-time and pulse on-time on MRR. Both variables have the same effect on MRR. As the pulse off-time or on-time is increased, MRR is increased. Figure5e shows the effect of electrode rotation speed and pulse on-time on MRR. It is clear that, as the electrode rotation speed increases, MRR increases steadily. It can be seen that MRR depends more on the electrode rotation speed rather than on pulse on-time. Figure 5f shows the effect of electrode rotation speed and pulse off-time on MRR. It is of note that the general form of the 3D relationship is similar to that of the previous figure. Namely, as the electrode rotation speed is increased, MRR is increased and when the pulse off-time is increased, MRR is increased progressively.
4.4 Effect of Micro-EDM variables on overcut
The response surface plots, as shown in Fig.6, demonstrate the effect of different Micro-EDM variables on overcut. Figure 6a shows the effect of pulse off-time and peak current on overcut. Minimum overcut occurs for a minimum level pulse off-time and a middle level of peak current. It is clear from Fig.6athat the middle level of peak current is best for lower overcut. Figure6bshows the effect of pulse on-time and peak current on overcut. It can be seen that minimum overcut occurs for a minimum level pulse on-time and middle level of peak current, but the effect of peak current is greater than that of pulse on-time. Figure6c
shows the effect of electrode rotation speed and peak current on overcut. The general form of the 3D relationship is similar to that of the previous figure. Figure6dshows the effect of pulse off-time and pulse on-time on overcut. Both variables have a non-liner effect on overcut. As the pulse off-time is increased, overcut is increased, as it is for an increase in pulse on-time. Figure 6epresents the effect of electrode rotation speed and pulse on-time on overcut. An increased pulse on-time does not cause a lower overcut at
the center level of electrode rotation speed. Figure6fshows the effect of electrode rotation speed and pulse off-time on overcut. It is clear that as the pulse off-time is decreased, overcut is decreased progressively, and that the middle level of electrode rotation speed is not a good condition for lower overcut but the extreme levels are good.
5 Summary and conclusion
The use of RSM and CCD for modeling the influence of four machining variables (namely, peak current, pulse on-time, pulse off-on-time, and electrode rotation speed) on the performance of the Micro-EDM machined SK3 carbon tool steel was evaluated. The predicted values match the experimental values reasonably well with R2of 0.939 for EW, R2 of 0.876 for MRR, and R2 of 0.867 for overcut. This study demonstrates that CCD and RSM can be successfully used to model some machining parameters of the Micro-EDM process for SK3 carbon tool steel using the fewest possible number of experiments. Findings from this study, however, indicate that peak current (X1) is the
significant factor of the four machining variables that affects Micro-EDM qualities for SK3 carbon tool steel. Lower peak current minimizes the EW and overcut, and maximizes the MRR, but decreased pulse on-time and increased electrode rotation speed, considerably, which is necessary to induce more discharge energy for lower EW, higher MRR and lower overcut.
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