Journal of Materials Processing Technology 187–188 (2007) 711–714<br />
<br />
Statistical analysis on electrode wear in EDM of tool steel<br />
DIN 1.2714 used in forging dies<br />
H. Zarepour a,∗ , A. Fadaei Tehrani b , D. Karimi c , S. Amini a<br />
a<br />
<br />
Department of Manufacturing Engineering, School of Engineering (2),<br />
Islamic Azad University, Najafabad Branch, Isfahan, Iran<br />
b Department of Mechanical Engineering, Isfahan University of Techology, Isfahan, Iran<br />
c Department of Mechanical Engineering, Tarbiat Modarres University, Tehran, Iran<br />
<br />
Abstract<br />
Electrical discharge machining (EDM) is a widespread process which works very effectively in machining of difﬁcult-to-cut materials and alloys<br />
in die and aerospace industries with high dimensional accuracies. However, this capability could be deteriorated due to electrode wear leading to<br />
decrease of process productivity. In this study, the effect of machining parameters of EDM process including on-time, current, voltage, the engaging<br />
time between workpiece and electrode, and pre-EDM roughing on electrode wear were experimentally investigated. Main effects of factors and<br />
interactions were considered in this paper and regression equation was derived. A L50 (21 × 511 ) Taguchi’s standard orthogonal array was employed<br />
as experimental design. Copper was used as electrode to machine the hot work tool steel 1.2714, which is widely used to make forging dies and<br />
mandrels.<br />
© 2007 Elsevier B.V. All rights reserved.<br />
Keywords: EDM; Electrode wear; Orthogonal array; Statistical analyses<br />
<br />
1. Introduction<br />
Among the non-traditional methods of material removal processes, electrical discharge machining (EDM) has drawn a great<br />
a deal of researchers’ attention because of its broad industrial<br />
applications. This process is well suited for machining of casting<br />
and forging dies, powder metallurgy and injection molds, and<br />
aerospace parts.<br />
The process is a spark erosion method, eroding the workpiece by high frequency spark discharges [1]. EDM has a high<br />
capability of machining the accurate cavities of dies and molds.<br />
Nevertheless, electrode wear occurs during EDM process leading to a lack of machining accuracy in the geometry of workpiece<br />
[2]. Furthermore, electrode wear imposes high costs on manufacturers to substitute the eroded complicated electrodes by<br />
new ones for die making. In order to increase the machining<br />
efﬁciency, erosion of the workpiece must be maximized and<br />
that of the electrode minimized in EDM process [1]. Therefore,<br />
<br />
∗<br />
<br />
Corresponding author. Tel.: +98 312 37 58930; fax: +98 312 37 56900.<br />
E-mail address: h-zare@iaun.ac.ir (H. Zarepour).<br />
<br />
0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved.<br />
doi:10.1016/j.jmatprotec.2006.11.202<br />
<br />
studying the electrode wear and related signiﬁcant factors would<br />
be effective to enhance the machining productivity and process<br />
reliability.<br />
A series of investigations have been conducted on electrode<br />
wear in EDM process. Soni and Chakraverti [3,4] studied the surface quality, material removal rate, wear ratio, and dimensional<br />
accuracy in EDM of alloy steels. Singh et al. investigated the<br />
effect of machining parameters on electrode wear in die-sinking<br />
EDM of En-31 tool steel with different electrode materials [5].<br />
Also, Luis et al. have carried out a study on electrode wear<br />
in EDM of silicon carbide using the technique of design of<br />
experiments [6].<br />
In this research, an experimental study is conducted to investigate on electrode wear in die-sinking EDM of DIN 1.2714 hot<br />
work tool steel. The selection of this material was made taking into account its wide range of applications in die and mold<br />
industries such as hammer and hydraulic forging dies. The aim<br />
of this study is to ﬁnd out from which process parameters (factors) electrode wear is affected and to which factor interactions it<br />
is related. This is usually done by means of analysis of variance<br />
(ANOVA). Furthermore, regression analysis is used to establish the correlation between factors and response (tool wear).<br />
The appropriate degree of the polynomial regression equation is<br />
<br />
712<br />
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H. Zarepour et al. / Journal of Materials Processing Technology 187–188 (2007) 711–714<br />
<br />
found which is thought to be useful assessment of the predictive<br />
equation [7,8]. Finally, the optimal factor levels are obtained.<br />
2. Experimentation<br />
2.1. Experimental design<br />
During EDM experiments, the input parameters (factors)<br />
were on-time (pulse-on duration), peak current, pulsed voltage,<br />
engaging time, and pre-EDM roughing accuracy. The pulse-off<br />
duration was kept constant which could effectively control the<br />
ﬂushing of the debris from the gap, giving machining stability. Therefore, the effect of the pulse-off duration on machining<br />
process was not considered in the present work. Table 1 shows<br />
factors and factor levels assessed in this study.<br />
The design of experiments was performed through Taguchi<br />
approach of experimental design. Accordingly, a L50 standard<br />
orthogonal array was employed. All the main effects of factors<br />
and two-order interactions were desired to be considered in this<br />
study.<br />
2.2. Experimental equipment and setup<br />
Fifty DIN 1.2714 steel specimens were machined for 50<br />
experimental runs in this work. The holes were created in the<br />
workpieces in ﬁve groups of dimensions as roughed cavities<br />
before EDM process. The allowances left for EDM die-sinking<br />
were considered equal to 0.25, 0.5, 0.75, 1, and 1.25 mm (preEDM rouging accuracy) for each group of dimensions. These<br />
dimensions are referred as 1, 2, 3, 4, and 5, respectively, in<br />
Table 1 and analyses. Hardness of the specimens was increased<br />
up to 48–50 HRC, nearly the same as the hardness of forging<br />
dies.<br />
Cylindrical copper rods with 99% purity and 8.98 g/cm3<br />
density were machined with good surface ﬁnish and exact<br />
dimensions as tool electrodes. Fig. 1 illustrates a sample of copper electrodes. Both electrodes and workpieces were deburred<br />
carefully providing stable conditions in EDM process. The specimens were machined on a “Pishtazan-Pulse Generator 120”<br />
die-sinking EDM machine which has an iso-pulse generator with<br />
a maximum 120 A current intensity.<br />
The experiments were carried out in petroleum-Behran oil 42<br />
dielectric (10:1, v/v) covering the workpiece by 10 mm. Final<br />
dimensions of machined holes in workpieces were exactly the<br />
same for all experimental runs. The electrode was negative polarity and the specimen was positive polarity during the EDM<br />
process. Weight of electrodes was measured after experiments<br />
<br />
Fig. 1. A sample of copper electrodes and related dimensions.<br />
<br />
using an accurate digital balance and the percentage of electrodes<br />
weight reduction was calculated as tool wear (wt.%).<br />
3. Data analysis<br />
3.1. Effect of factors and interactions on electrode wear<br />
Fig. 2 depicts the plot of main effects for electrode wear. Note<br />
that this plot illustrates data means versus factor levels. Based<br />
on this plot, the effect of each factor can be graphically assessed.<br />
Fig. 2a shows that pre-EDM roughing factor has a signiﬁcant<br />
effect on electrode wear. It can also be seen from this ﬁgure that<br />
the effect of this factor is directly proportional to electrode wear.<br />
Also, it can be stated that by increasing the pre-EDM roughing<br />
factor electrode wear increases signiﬁcantly. Fig. 2b portraits the<br />
effect of current on electrode wear. This ﬁgure presents that electrode wear is almost constant when current is increased from 5 to<br />
10 A. By increasing the current form 10 to 20 A, electrode wear<br />
increases dramatically. Finally, one can interpret that current<br />
has a signiﬁcant direct impact on electrode wear. Further experiments are needed to consider effect of current on electrode wear<br />
when current ﬂuctuates between 5 and 15 A. Fig. 2c indicates<br />
the effect of on-time on electrode wear. This ﬁgure shows that<br />
on-time is reciprocally proportional to electrode wear. Fig. 2d<br />
suggests that voltage has a subtle effect on electrode wear. It<br />
is obvious from this ﬁgure that by changing voltage during this<br />
process electrode wear ﬂuctuates insigniﬁcantly between 0.3 and<br />
0.4%. So, it is concluded that the effect of voltage on electrode<br />
wear is almost negligible. Eventually, Fig. 2e shows the effect<br />
<br />
Table 1<br />
Factors and factor levels<br />
Factor<br />
<br />
Level 1<br />
<br />
Level 2<br />
<br />
Level 3<br />
<br />
Level 4<br />
<br />
Level 5<br />
<br />
On-time, A (s)<br />
Current, B (A)<br />
Voltage, C (V)<br />
Engaging time, D (s)<br />
Pre-EDM roughing, E<br />
<br />
200<br />
5<br />
35<br />
1<br />
1<br />
<br />
500<br />
10<br />
40<br />
2<br />
2<br />
<br />
–<br />
15<br />
50<br />
3<br />
3<br />
<br />
–<br />
20<br />
55<br />
4<br />
4<br />
<br />
–<br />
–<br />
–<br />
–<br />
5<br />
Fig. 2. (a–e) Plot of main effects on electrode wear.<br />
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H. Zarepour et al. / Journal of Materials Processing Technology 187–188 (2007) 711–714<br />
<br />
713<br />
<br />
Table 2<br />
Values of estimated effects<br />
Term<br />
<br />
Effect<br />
<br />
Term<br />
<br />
Effect<br />
<br />
A<br />
B<br />
C<br />
D<br />
E<br />
A×B<br />
A×C<br />
A×D<br />
<br />
−0.1359<br />
0.4351<br />
0.0188<br />
−0.0909<br />
0.2910<br />
−0.2059<br />
0.0333<br />
−0.0610<br />
<br />
A×E<br />
B×C<br />
B×D<br />
B×E<br />
C×D<br />
C×E<br />
D×E<br />
<br />
−0.1710<br />
−0.0945<br />
0.0440<br />
0.2674<br />
0.0582<br />
−0.0032<br />
0.0018<br />
<br />
of engaging time between electrode and workpiece on electrode<br />
wear. This ﬁgure shows that the engaging time exhibits little<br />
effect on electrode wear. But unlike voltage, by increasing the<br />
engaging time electrode wear ﬁrst increases and then stalls off<br />
insigniﬁcantly.<br />
Factor effects are calculated here to consider effect of factors<br />
on electrode wear more accurately than graphical assessment.<br />
Table 2 shows the magnitude of factor effects. Using this table<br />
one can sort factors in order of their signiﬁcance. Also, this table<br />
illustrates the proportionality of factor effects to the response<br />
(electrode wear). Positive values of factor effects indicate direct<br />
proportionality of the respective factors, while negative values demonstrate that the corresponding factor is reciprocally<br />
proportional to the response.<br />
Note that two-way interactions are also included in Table 2.<br />
It can be seen from this table that current (B) has the most significant effect on electrode wear and is directly proportional to it.<br />
The interaction between engaging time and pre-EDM roughing<br />
(D × E) has the least effect on electrode wear and is directly proportional to it. One shortcoming to Table 2 is that the inferences<br />
made based on this table are only comparatively valid. To cope<br />
with the problem analysis of variance (ANOVA) is numerously<br />
used by experimenters. But ANOVA is not employed here since<br />
error normality and error independency assumptions are not satisﬁed. For more information on ANOVA assumptions consult<br />
reference [7].<br />
Normal probability plot of standardized effects is used here<br />
as an alternative to ANOVA approach. Although electrode wear<br />
does not follow the normal distribution, estimated effects can be<br />
assumed to exhibit normal distribution [9].<br />
Normal probability plot of standardized effects is shown in<br />
Fig. 3 to separate signiﬁcant factors from insigniﬁcant factors.<br />
Factors and interactions which have departed considerably from<br />
the straight line have signiﬁcant impact on electrode wear.<br />
3.2. Regression analysis<br />
A quadratic polynomial regression equation, in terms of factors (Table 1), is obtained to ﬁt experimental data. Least square<br />
method is used in regression analysis to ﬁnd the coefﬁcients of<br />
the equation. It is shown as Eq. (1).<br />
Wear (%) = 0.4895 + 0.0007A + 0.0068B − 0.0268C<br />
+ 0.08049D − 0.1185E + 0.0016B2 + 0.0003C2<br />
<br />
Fig. 3. Normal probability plot of effects.<br />
<br />
+ 0.0026D2 − 0.0037E2 − 0.0001AB<br />
− 0.0000004AC − 0.0002AD + 0.00007AE<br />
− 0.00013BC + 0.0072BD − 0.0022BE<br />
− 0.00072CD + 0.0030CE − 0.0056DE<br />
<br />
(1)<br />
<br />
Note that A2 has been removed from the equation since it is<br />
highly correlated with other variables.<br />
Regression statistics R2 and R2 are obtained equal to 98.7<br />
Adj<br />
and 97.8%, respectively. The R2 value indicates that the predictors explain 98.7% of variance in electrode wear. The R2 value<br />
Adj<br />
accounts for the number of predictors in the model. Both values indicate that the presented model ﬁts the data very well.<br />
The analysis of variance for regression analysis is shown in<br />
Table 3. The p-value shows that the model is signiﬁcant at α-level<br />
of 0.05.<br />
Model adequacy is checked by means of plot of residuals<br />
versus ﬁts, plot of residuals versus order of the data, and normal<br />
plot of residuals. Fig. 4 shows the plot of residuals versus ﬁts.<br />
It is clearly observed from this plot that residuals have constant<br />
variance. Plot of residuals versus order of the data is illustrated<br />
in Fig. 5. This ﬁgure indicates that residuals are independent of<br />
one another.<br />
Also, normal plot of residuals is shown in Fig. 6.<br />
Anderson–Darling statistic (AD) and the p-value calculated<br />
based on it, are shown in this ﬁgure. It is easily found out<br />
that residuals are normally distributed. The presented discussion<br />
implies that the predictive model is adequate.<br />
<br />
Table 3<br />
ANOVA table for regression analysis<br />
Source<br />
<br />
DF<br />
<br />
SS<br />
<br />
MS<br />
<br />
F<br />
<br />
p<br />
<br />
Regression<br />
Residual error<br />
<br />
19<br />
28<br />
<br />
4.21979<br />
0.05659<br />
<br />
0.22209<br />
0.00202<br />
<br />
109.90<br />
<br />
0.000<br />
<br />
Total<br />
<br />
47<br />
<br />
4.27638<br />
<br />
DF: degrees of freedom, SS: sum of Squares, MS: mean squares, F: F-value, p:<br />
p-value.<br />
<br />
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H. Zarepour et al. / Journal of Materials Processing Technology 187–188 (2007) 711–714<br />
<br />
of all compared with effects of noises (uncontrollable factors).<br />
S/N ratio statistic (η) can be obtained by Eq. (2):<br />
η = −10 log10<br />
<br />
1<br />
n<br />
<br />
n<br />
i=1<br />
<br />
2<br />
yi<br />
<br />
(2)<br />
<br />
where yi is the ith observation of a treatment combination and n<br />
is the number of replications.<br />
The factor level which produces the largest η is detected as<br />
the factor level which pertains to the optimal condition. Accordingly, the optimal levels of A, B, C, D, and E factors would be<br />
equal to 2, 1, 1, 4, and 1, respectively. The corresponding value<br />
of each factor level can be found out referring to Table 1.<br />
4. Conclusions<br />
Fig. 4. Plot of residuals vs. ﬁts.<br />
<br />
In this research, an experimental investigation was performed<br />
to consider the electrode wear in EDM process of DIN 1.2714<br />
tool steel and the following results were concluded:<br />
1. On-time, current, and pre-EDM roughing as factors along<br />
with on-time/current, on-time/pre-EDM roughing, and<br />
current/pre-EDM roughing as interactions, were found to<br />
have signiﬁcant effect on electrode wear.<br />
2. The predictive model was derived out of regression analysis.<br />
3. The adequacy of predictive model was approved.<br />
4. Optimal level of factors was presented using S/N ratio analysis.<br />
Acknowledgements<br />
<br />
Fig. 5. Plot of residuals vs. the order of the data.<br />
<br />
The authors appreciate Abzaran Co. and Industrial Cooperation Ofﬁce of Isfahan University of Technology for supporting<br />
this research. Also, a special thanks to M. Pourehsan and M.<br />
Neshatpour for their close cooperation.<br />
References<br />
<br />
Fig. 6. Normal plot of residuals.<br />
<br />
3.3. Determination of the optimal condition<br />
Optimal condition is detected by means of S/N ratio method.<br />
The rationale behind this method is to ﬁnd a condition under<br />
which the effect of signals (controllable factors) is the greatest<br />
<br />
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