Ảnh hưởng của độ cứng Workpiece đến hiệu suất EDM

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International Journal of Machine Tools & Manufacture 49 (2009) 744–748

International Journal of Machine Tools & Manufacture

journal homepage: www.elsevier.com/locate/ijmactool

Short Communication

Inﬂuence of workpiece hardness on EDM performance Jose´ Duarte Marafona (cid:2), Arlindo Arau´ jo

a r t i c l e i n f o

a b s t r a c t

The aim of this research is to show the inﬂuence of the hardness of the alloy steel on the material removal rate and on the workpiece surface roughness.

The Taguchi methodology was used to study that inﬂuence. The result of the veriﬁcation test for workpiece surface roughness was a strong conﬁrmation. This type of outcome allows the use of the additive model to predict the workpiece surface roughness with an average error of 0.4%.

Departamento de Engenharia Mecaˆnica e Gesta˜o Industrial, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal

The result of the veriﬁcation test for material removal rate was a poor conﬁrmation due to an interaction of parameters. This type of outcome does not allow the additive model to predict the material removal rate with accuracy. Therefore, a linear regression model was developed for material removal rate using workpiece hardness and its interactions, among other variables. This model predicts the material removal rate with an average error of 1.06%.

These results show that workpiece hardness and its interactions have inﬂuence on the material

removal rate and on the workpiece surface roughness.

Article history: Received 22 October 2008 Received in revised form 13 March 2009 Accepted 13 March 2009 Available online 27 March 2009

Introduction

surface of the workpiece is submitted to a heat treatment (locally), where the time of stage is the pulse duration and the temperature reached by the workpiece is due to the applied current intensity being followed by a quick cooling of the workpiece. These variables affect the metallurgic constituent of the white layer and consequently its hardness [8–10] and its thermal conductivity.

Electrical discharge machining (EDM) is a non-traditional manufacturing process where the material is removed by a succession of electrical discharges, which occur between the electrode and the workpiece. These are submersed in a dielectric liquid such as kerosene or deionised water. The electrical discharge machining process is widely used in the aerospace, automobile and moulds industries to machine hard metals and its alloys.

It is also known that during the cut by EDM the material removal rate (MRR) decreases, which is due to process instability according to [11]. However, the decrease of material removal rate is due to the change of metallurgic constituent in the zone affected by the heat, according to the authors. Therefore, the authors have decided to investigate the effect of the initial workpiece hardness on the material removal rate and workpiece surface roughness.

2. Experimental methodology

During the electrical discharge, a discharge channel is created where the temperature reaches approximately 12,000 1C [1], removing material by evaporation and melting [2–4] from both the electrode and the workpiece. When the discharge ceases there is a high cooling on the surface of the workpiece creating a zone affected by the heat that contains the white layer. This layer contains several hollows, spheroids, ﬁssures and micro ﬁssures. Carbon is the main element of the white layer composition inﬂuencing simultaneously its hardness and thermal conductivity [5]. The white layer thickness depends on the workpiece material, on the power used to cut the workpiece and on the applied electrical polarity.

Electrical discharge machining is governed by a thermal phenomenon [6,7], therefore not only removes material from the workpiece but also changes the metallurgical constituents in the zone affected by the heat. Thus, during machining by EDM the

(cid:2) Corresponding author. Tel.: +351 225 081 520; fax: +351 225 081 445.

Keywords: Electrical discharge machining (EDM) Alloy steel hardness Material removal rate (MRR) Workpiece surface roughness Taguchi methodology Linear regression model

The effect of the workpiece hardness on the material removal rate and workpiece surface roughness was studied using the Taguchi method, which is generally applied to improve the quality of a product. The Taguchi method is mainly used to optimise a single output. However, some authors [12] use the orthogonal array L18 and the grey relational analysis to optimise various outputs simultaneously. The authors used the orthogonal array L18, the analysis of variance (ANOVA), additive model and linear regression to understand the relationship between various inputs and a single output.

E-mail address: jdmar@fe.up.pt (J.D. Marafona).

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Nomenclature

Ram cycle (s) interval of time between lift-offs Compression (%) degree of deterioration (number of eroded

particles during EDM) in the gap

Ram speed (mm/min) speed at which the ram lifts off the electrode from the workpiece at regular intervals of time

3. Experimental results

According to Taguchi, ‘‘it is desirable to treat the interactions including these in the noise, which is not generally done. Only a main effect that exceeds the value of interactions can be used safely in robust project.’’ Thus, the orthogonal array L18 should be used because this array has the property of distributing interac- tions to all the columns and treats the interactions as equivalent to noise. This array can handle seven parameters at three levels and one parameter at two levels and deﬁnes eighteen individual experiments. If all combinations of parameters and levels were used, 4374 (21 (cid:2) 37) experiments would be involved, and thus, there is a signiﬁcant reduction in the number of experiments performed and thereby a signiﬁcant reduction in cost and time.

The importance of the input parameters in the EDM process was determined. There are eight input parameters (Table 1) that affect the EDM performance. Some of these parameters are likely to have a more signiﬁcant effect on electrical discharge machining performance than others. The levels of the input parameters, S1–S8, were allocated using the values of rough cut of EDM, given in the AGIE manual. These values are indicated in Table 1. The experimental results of each setting of input parameters of the orthogonal array L18 are given in Table 1. These are the average of two experiments.

3.1. Effect of the workpiece hardness on the material removal rate

3.1.1. Analysis of variance

This methodology was designed and performed in a die- sinking EDM machine, AGIE COMPACT 3, equipped with adaptive control facilities. The adaptive control optimization (ACO) system enables the process to be optimised automatically and it was switched off so that the results can be generalized to all machines. The electrode and workpiece materials are electrolytic copper and steel AISI/SAE-D2, respectively. Two steel AISI/SAE-D2 bars were used in the research. One bar was quenched and tempered yielding a hardness of 60 HRC; the hardness of the normalized bar was 235 HB. The treated bar and the normalized bar were parallelepipeds with dimensions of 300 (cid:2) 60 (cid:2) 25 mm3. The electrodes used were copper rods 16 mm in diameter and a length of 160 mm. The EDM performance is related to the efﬁciency which is determined in the EDM process by the material removal rate and by the electrode wear ratio (EWR). Quality is determined by the accuracy and the surface roughness—only the latter will be considered here. Surface roughness was characterised using the arithmetic average roughness (Ra) value. This was measured using a Hommelewerk T4000 measurement instrument.

The results of the analysis of variance show that the most signiﬁcant contributors to the material removal rate are current intensity, duty factor, compression and ram cycle with degrees of signiﬁcance greater or equal to 90%. The pooling of the small variances [variance ratio lesser or equal to 2%] increases not only the variance error of the overall average but also the degrees of signiﬁcance of the most important contributors. The results of the pooling of the small variances show that the most signiﬁcant contributors to the material removal rate are current intensity (17%), duty factor (14%), compression (16%), ram cycle (33%) and pulse duration (9%) with degrees of signiﬁcance greater or equal to 97.5%. The variance error attributed to unknown sources in obtaining the maximum material removal rate is 10%. These results can be seen in Table 2.

This experimental methodology enables the workpiece hard- ness and its interactions to be signiﬁcant contributors to the material removed rate and also the workpiece surface roughness to be determined.

Nevertheless, the two bars have signiﬁcantly different work- piece hardness, the material removal rate decreases slightly. It is important to point out that the interactions of parameters were not studied because the orthogonal array has the property of

J.D. Marafona, A. Arau´jo / International Journal of Machine Tools & Manufacture 49 (2009) 744–748 745

Table 1 Orthogonal array L18 and experimental data.

Number of trials Steel hardness Current intensity Applied voltage Pulse duration Duty factor Ram speed Compression Ram cycle MRR (ave.), mm3/min Ra (ave.), mm (S1) NC (S2) NC (S3) NC (S4) % (S5) mm/min (S6) % (S7) s (S8)

0.3 2 30 30

0.3 2 30

0.3 2 0.3 2 30 2 30

0.3 2 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1(235 HB) 1 1 1 1 1 1 1 1 2(60 HRC) 2 2 2 2 2 2 2 2 10 10 10 11 11 11 12 12 12 10 10 10 11 11 11 12 12 12 2 4 6 2 4 6 2 4 6 2 4 6 2 4 6 2 4 6 16 18 19 16 18 19 18 19 16 19 16 18 18 19 16 19 16 18 50 65 80 65 80 50 50 65 80 80 50 65 80 50 65 65 80 50 350 525 700 525 700 350 700 350 525 525 700 350 350 525 700 700 350 525 20 30 40 40 20 30 30 40 20 30 40 20 40 20 30 20 30 40 0.3 2.89 17.66 27.82 33.90 11.40 16.92 30.80 13.24 31.32 7.62 22.05 5.68 34.95 7.93 14.03 21.81 43.68 14.54 7.1 7.7 7.2 7.6 9 9 10.8 10.8 9.5 7.3 6.5 8.6 9.2 9.7 7.4 11 9.2 11.8

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Table 2 Results of the analysis of variance (ANOVA) for MRR.

ANOVA results for MRR

St S3 S4 S5 S6 S7 S8 Se S1 S2

2288 17 42 2 21 235 2 117 360 2 180 20 2 10 389 2 195 778 2 389 10 1 10 428 2 214 8.9 1.6 2 10 0.7 1 26 2 13 1 1.1 0.8 0 13.7 16 90 14.8 17 90 29.6 34 95 Sum of squares Degree of freedom Variance Variance ratio Percentage of contribution Degree of signiﬁcance 16.3 19 90

– – –

208 2 104 332 2 166 361 2 180 750 2 375 400 2 200

7.4 9 97.5 11.8 14 99 12.8 16 99.5 26.7 33 99.5 Pooling of small variances into the error 98 Sum of squares 7 Degree of freedom 14 Variance 1 Variance ratio Percentage of contribution 10 Degree of signiﬁcance 14.2 17 99.5

Table 3 Results of the ANOVA assessment for the linear regression model.

Source Degrees of freedom (DOF) Sum of squares (SS) Mean square (MS) Variance ratio (F) Probability (P)

2275.340 0.000(cid:2) 163.380 0.072 14 3 17 2287.317 0.215 2287.532

(cid:2) Highly signiﬁcant.

Regression Residual error Total R2 ¼ 1.000 Adjusted R2 ¼ 0.999

Table 4 Experimental data and predicted values for the rate of material removal and surface roughness.

distributing interactions to all the columns and treats the interactions as equivalent to noise. The veriﬁcation test indicates that material removal rate is affected by interactions of para- meters. Therefore, the variance error of 10% attributed to unknown sources can be explained by the effect of the workpiece hardness and its interactions on the material removal rate, according to the authors.

3.1.2. Linear regression model

MRR (mm3/min) Ra (mm) Relative error (%) Relative error (%) Number of trials Experimental Predicted Experimental Predicted

Some models for EDM performance parameters were built using the additive model from Taguchi methodology and the response surface methodology [12,13]. In this study, the veriﬁca- tion test from Taguchi method shows a poor conﬁrmation due to an interaction of parameters, so additive model predicts material removal rate with high accuracy errors, say in the order of 10%. Therefore, a linear regression model was developed for material removal rate using workpiece hardness and its interactions besides others interactions of input parameters. The capability of the linear model to represent the experimental data was assessed through the analysis of variance. The results of the analysis of variance for the linear model are shown in Table 3. This linear model presents a regression square (R2) of 1.0 and an adjusted regression square (adj. R2) of 0.999, meaning that the predicted values and the experimental data agree very well.

Eq. (1) shows the coefﬁcients of the linear regression model,

using the data and the results presented in Table 1.

The predicted values of the linear regression model and the experimental data are shown in Table 4. The linear regression model predicts material removal rate with an average error of 1.06%.

MRR ¼ (cid:3) 106:518 þ 209:729nS1 þ 1:550nS2 þ 21:424nS3

(cid:3) 11:353nS4 (cid:3) 1:269nS5

þ 0:339nS6 þ 4:588nS7 (cid:3) 0:616nS8 þ 2:948nS12

(cid:3) 14:545nS13 (cid:3) 0:619nS14

(1)

þ 0:327nS15 (cid:3) 0:218nS16 (cid:3) 2:709nS17

The results of the linear regression model show that the material removal rate is dependent on the workpiece hardness and its interactions. Its results, presented in Eq. (1), show that the contributions of the unknown sources to the material removal i.e. rate variance are mainly composed of combined effects,

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 7.1 7.7 7.2 7.6 9 9 10.8 10.8 9.5 7.3 6.5 8.6 9.2 9.7 7.4 11 9.2 11.8 7.06 7.66 7.16 7.66 9.01 9.01 10.84 10.84 9.54 7.34 6.54 8.64 9.19 9.69 7.39 10.96 9.16 11.76 0.6 0.5 0.6 0.8 0.1 0.1 0.4 0.4 0.4 0.5 0.6 0.5 0.1 0.1 0.1 0.4 0.4 0.3 2.89 17.66 27.82 33.90 11.40 16.92 30.80 13.24 31.32 7.62 22.05 5.68 34.95 7.93 14.03 21.81 43.68 14.54 3.04 17.64 28.02 33.87 11.44 16.88 30.94 13.33 31.42 7.63 22.20 5.76 35.29 8.20 14.43 22.02 43.64 14.60 5.2 0.1 0.7 0.1 0.3 0.2 0.4 0.6 0.3 0.1 0.6 1.4 0.9 3.3 2.8 0.9 0.1 0.4

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Table 5 Results of the analysis of variance (ANOVA) for Ra.

ANOVA results for Ra

Se S1 S2 S3 S4 S5 S6 S7 S8 St

29.521 2 41.124 17 0.222 1 0.222 14.761 8.874 2 4.437 1.021 2 0.511 0.388 2 0.194 1.021 2 0.511 20.9 1386 416.6 47.9 18.2 47.9 0.021 2 0.011 1 0.05 0.54 0.034 2 0.017 1.6 0.08 2.48 0.94 2.48 0.021 2 0.011 1 0.05 Sum of squares Degree of freedom Variance Variance ratio Percentage of contribution Degree of signiﬁcance 95 71.8 99.5 21.58 99.5 97.5 90 97.5

29.496 – – 2 0.209 1 0.209 14.748 8.849 2 4.424 0.996 2 0.498 0.362 2 0.181 0.996 2 0.498

Ys1, Ys2, y, Ys7 are the average values levels for parameters S1, S2, y, S7, respectively.

statistical interactions, of parameter. The workpiece hardness is the parameter that interacts with all remaining parameters. The exception is the interaction between the workpiece hardness and the ram cycle, which does not inﬂuence the material removal rate variance.

4. Conclusion

3.2. Effect of the workpiece hardness on the average surface roughness (Ra)

3.2.1. Analysis of variance

The results of this research show that the material removal rate and the workpiece surface roughness are directly dependent on the workpiece hardness. This is demonstrated by the mathema- tical models used in the research.

The results of this research show that the material removal rate is dependent on the workpiece hardness and its interactions with exception of the interaction between the workpiece hardness and the ram cycle. The material removal rate is predicted with an average error of 1.06%.

It is also demonstrated that workpiece surface roughness is dependent on the workpiece hardness and other input para- meters. The additive model predicts the workpiece surface roughness values with an average error of 0.4%.

In conclusion,

this knowledge demonstrates

that

the electrical discharge machining process is not only inﬂuenced by the thermal properties of the workpiece but also by its hardness.

The results of the analysis of variance show that the most important contributors to the workpiece surface roughness are current intensity, pulse duration, duty factor, compression, work- piece hardness and ram speed, with degrees of signiﬁcance greater or equal to 90%. The pooling of the small variances conﬁrm that the most important contributors to the workpiece surface roughness are current intensity (71.7%), pulse duration (21.5%), duty factor (2.4%), compression (2.4%), workpiece hardness (0.5%) and ram speed (0.9%), with degrees of signiﬁcance greater or equal to 99%. The variance error attributed to unknown sources in obtaining the workpiece surface roughness is 0.5%. The small variance error value indicates that the average surface roughness is obtained by the isolated effect of the workpiece hardness, current intensity, pulse duration, duty factor, ram speed and compression parameter. These results can be seen in Table 5.

References

The veriﬁcation test indicates a strong conﬁrmation. These results show that the workpiece hardness is inﬂuent on the workpiece surface roughness.

0.077 6 0.013 1 0.5 16.4 0.5 14.1 0.9 Pooling of small variances into the error Sum of squares Degree of freedom Variance Variance ratio Percentage of contribution Degree of signiﬁcance 99 1152.2 71.7 99.5 345.7 21.5 99.5 38.9 2.4 99.5 99 38.9 2.4 99.5

3.2.2. Additive model

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The result of the veriﬁcation test allows the additive model to predict the workpiece surface roughness. The values predicted and the experimental data show a high degree of agreement, as shown in Table 4. In this study, the ram cycle and the applied voltage are not signiﬁcant contributors to the workpiece surface roughness, as shown in the additive model described in Eq. (2):

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[4] F. van Dijck, Physic-mathematical analysis of the electro discharge machining process, Ph.D. Thesis, Katholieke University, Heverlee, Netherlands, 1973, pp. 61–62.

(2)

Ra ¼ Y exp (cid:3) ðY exp (cid:3) Y S1Þ (cid:3) ðY exp (cid:3) Y S2Þ (cid:3) ðY exp (cid:3) Y S4Þ (cid:3) (cid:4) (cid:4) (cid:4) (cid:3) ðY exp (cid:3) Y S7Þ

[5] J.D. Marafona, Black layer affects the thermal conductivity of the surface of copper–tungsten electrode, International Journal of Advanced Manufacturing Technology, doi:10.1007/s00170-008-1613-3.

The Ra value is obtained by a combination of levels of the parameters of the orthogonal array, where Yexp is the overall average response of the Ra for the entire orthogonal array and the

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