The influence of the technological parameters on the machining rate at the EDM with thick electrode.

Iuras, Emilia ; Tanasa, Raluca ; Carausu, Constantin 等

1. INTRODUCTION

Regarded by means of technical-economics indicators, the electrical discharge machining (EDM) is one of the processes that achieved a high degree of performance, which assures a high machining rate, with minimal shape and dimension errors. Because of developing and appearance of new industrial fields, but also, of increasing of the requests regarding the productivity, and the economical efficiency, the necessity to optimize the EDM machining process has appeared (Kunieda et. al., 2003) (Momalis et. al., 2004).

Increasing of the productivity could be achieved by means of increasing of the discharging energy [W.sub.i]; the experimental researches show that the increasing of this energy could be achieved only by the increasing of the discharging current I and the pulse time [t.sub.i]; and also by means of the increasing of the discharging frequency f.

2. EXPERIMENTAL CONDITIONS

2.1 Materials, tools and working conditions

The test pieces required for experiments has been made of steel with the following chemical composition: 6.16% wolfram, 4.58% molybdenum, 4.34% chrome, 1.65% vanadium, 0.94% carbon, 0.63% siliceous, 0.343% manganese, 0.0029% sulphur, 0.027% phosphor, 0.57% cobalt, 0.309% nickel.

The pieces used for experiments had a prismatic shape, with the length L = 18 mm, the width l = 13 mm and the thickness g = 7 mm.

Thee tool-electrode is made of cooper, having also a prismatic shape, with the active zone having the following dimensions: length L = 28 mm, width l = 3.5 mm.

2.2 Working Equipment

For performing the experiments, an EDM machine tool endowed with a thick electrode, with numerical control, type FORM 20ZNC (manufactured by Charmilles Company) was used (User' s Manual FORM 20ZNC Charmilles, 2001).

2.3 Planifying of the experiment

In order to perform the experimental plan, the Taguchi method for planify the experiment was used. In order to develop the experiments, a complete factorial plan type [2.sub.3] has been chosen (Ionescu et. al., 2004), (Pillet, 1992).

The main technological factors that could influence the objective function--the productivity of EDM machining [Q.sub.P]-are: the intensity of the electric current I, the pulse time [t.sub.a], the non-pulse time [t.sub.b], the working depth h, the polarity of tool-electrode and tool--piece P User' s Manual FORM 20ZNC Charmilles, 2001), (Kunieda et. al., 2003).

Thus, for the achieved experimental plan, the working depth h=2 [mm], and the polarity of tool--electrode P (-) and tool-piece P (+) were retained as constant, while the values of the parameters current I, duration of a pulse [t.sub.a] and duration between pulses [t.sub.b] were considered at two levels (Pillet, 1992), (User' s Manual FORM 20ZNC Charmilles, 2001).

The values established for I are 8A and 12A, the pulses [t.sub.a] have been chosen at the following two levels: 50[micro]s and 300[micro]s and for the duration between pulses [t.sub.b] 100[micro]s and 500[micro]s.

3. EXPERIMENTAL RESULTS

The experimental plan and also the results of tests are shown in table 1.

The mathematical model (described by means of the Taguchi's method) of the machining rate [Q.sub.P] that describes the influence of the independent factors and the interactions on the objective function could be described by the expression (1) (Ionescu et. al., 2004), (Pillet, 1992):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

After applying the Taguchi's method, it could be noticed that the objective function--the machining rate [Q.sub.P] is maximum for the displacement of the factors at the following levels: I at level 2; [t.sub.a] at level 2; [t.sub.b] at level 1.

By the studying the interactions between factors, it could be noticed that the objective function is maximum for the combinations: [I.sub.2][t.sub.a2], [I.sub.2][t.sub.b1], [t.sub.a2][t.sub.b1].

[FIGURE 1 OMITTED]

In order to obtain a suggestive image (fig. 1) concerning the effects of the factors taken into account, and the interactions of the factors on the objective function, the level 1 (I=8A, [t.sub.a]=50[micro]s, [t.sub.b]=100[micro]s) was examinated.

From the figure 1, one can notice that the greater influence exerted by the factor I, followed by the effects and interactions [t.sub.a], [It.sub.a], [t.sub.b], [It.sub.b], [t.sub.a][t.sub.b].

The theoretical values obtained by means of the matrix model [Q.sub.P]~ for those eight experimental points, and also for the experimental values, for [Q.sub.P] are presented in table 2.

Graphical representation of the values for [Q.sub.P] and [Q.sub.P]~ on the same diagram can be seen in the diagram from figure 2.

By the study of the graphic included in figure 2, one can notice a small difference between the values measured and those obtained by means of the model; this means that there is a good approaching between the theoretical model and the experimental values.

On the other hand, one can notice the smaller influence of the non-controlled factors (for example, the disturbing factors) and a very good accuracy of measures performed for the parameters taken into account.

[FIGURE 2 OMITTED]

One must find out the value "F" according to Fisher law for each factor and interaction. In order to estimate which of the factors has significance, the calculated values are compared with the values included in standard tables (Snedecor Test) for a level of trust 70%. The obtained results are shown in table 3 (Ionescu et. al., 2004), (Pillet, 1992).

In accordance with the data included in table 2, the values of the coefficient Fisher are greater than those displayed in tables, for a certain level of trust of 70%, for the parameters I, [t.sub.a], [t.sub.b], and also in case of interactions [It.sub.a].

All those parameters become significant, and the interactions [t.sub.a][t.sub.b], [It.sub.b], for that F < [F.sub.a] could be considered as not significant and for this reason they could be neglected (Ionescu et. al., 2004), (Pillet, 1992).

The matrix model could be written in a simplified shape, after the elimination of the insignificant interactions as follows (equation 2):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

4. CONCLUSION

Following the experiments, and analyzing the results with Taguchi's method, the problem of the optimization of the EDM process with thick electrode is achieved in this work. Thus, could be formulating the following conclusions.

Analyzing the graphics of influence of the factors and interactions, can be estimated that the maximum machining rate could be achieved if we adjust the factors taken into account at the following levels: I at level (12A), [t.sub.a] at level 2 (300 [micro]s) and [t.sub.b] at level 1 (100 us). Accepting a trust level of 70%, the significant factors are: I, [t.sub.a], [t.sub.b] and interaction [It.sub.a].

A greater discharging energy, required for EDM process, implies a greater intensity of current and also a greater pulse time. Increasing the discharging energy has as effect the local.

5. REFERENCES

Ionescu , R. et. al. (2004). Planification of the experiments efficiency and quality, Publishing House Agir, ISBN 9738466-43-1, Bucharest, Romania

Kunieda, M., et. al. (2003). High speed 3D Milling by dry EDM. Annals of the CIRP, PP. 147-150, vol. 52, no.1, Swissland

Momalis, A.G. et al. (2004). Two-stage electro-discharge machining fabricating superhard cutting tools. Journal of Materials Processing Technology, pp. 318-225, no. 146

Pillet, M. (1992). Introduction aux plans d'experiences, Clamency Publisher, ISBN 2-7081-1442-5, France

User' s Manual FORM 20ZNC Charmilles, (2001). Edipresss Imprimeriers Reunies s.a./Renes, CTSA, Geneva

Tab1. Experimental plane and the values of parameters [Q.sub.P]

 Essay factors

No I [t.sub.a] [t.sub.b] I x [t.sub.a]

1. 1 1 1 1
2. 1 1 2 1
3. 1 2 1 2
4. 1 2 2 2
5. 2 1 1 2
6. 2 1 2 2
7. 2 2 1 1
8. 2 2 2 1

 Essay factors

 [t.sub.a] x [Q.sub.P]--exp.
No I x [t.sub.b] [t.sub.b] [[mm.sup.3]/min]

1. 1 1 2.15441
2. 2 2 0.89939
3. 1 2 2.17240
4. 2 1 2.20973
5. 2 1 3.57463
6. 1 2 2.10414
7. 2 2 8.98734
8. 1 1 5.73916

Tab. 2. The values of the theoretical and experimental
answers and residuum

No. [Q.sub.Pexp] [Q.sub.Pteor] Residuum

1. 2.15441 1.77065 0.38375
2. 0.89939 1.28314 -0.38375
3. 2.17240 2.55615 -0.38375
4. 2.20973 1.82597 0.38375
5. 3.57463 3.95839 -0.38375
6. 2.10414 1.72038 0.38375
7. 8.98734 8.60358 0.38375
8. 5.73916 6.12291 -0.38375

Tab. 3. Analyzing of the variance of the parameter

Source Variability Variant F
 Disp.

I 21.0255 21.0255 17.84
[t.sub.a] 13.4578 13.4578 11.42
[t.sub.b] 4.40504 4.40504 3.73
I [t.sub.a] 7.44863 7.44863 6.32
I [t.sub.b] 1.53210 1.53210 1.30
[t.sub.a] [t.sub.b] 0.02944 0.02944 0.02
Res. 1.1781 1.1781
Total 47.8985

Source [F.sub.[alpha] Significance
 [alpha]=70 F >
 [%] [F.sub.[alpha]

I 3.852 Sig.
[t.sub.a] 3.852 Sig.
[t.sub.b] 3.852 Sig.
I [t.sub.a] 3.852 Sig.
I [t.sub.b] 3.852 Insig.
[t.sub.a] [t.sub.b] 3.852 Insig.
Res.
Total