Influence of workpiece hardness on EDM performance

ARTICLE IN PRESS<br /> International Journal of Machine Tools & Manufacture 49 (2009) 744–748<br /> <br /> Contents lists available at ScienceDirect<br /> <br /> International Journal of Machine Tools & Manufacture<br /> journal homepage: www.elsevier.com/locate/ijmactool<br /> <br /> Short Communication<br /> <br /> Influence of workpiece hardness on EDM performance<br /> ´<br /> ´<br /> Jose Duarte Marafona Ã, Arlindo Araujo<br /> ˆ<br /> ˜<br /> Departamento de Engenharia Mecanica e Gestao Industrial, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal<br /> <br /> steel AISI/SAE-D2,<br /> a r t i c l e in f o<br /> <br /> a b s t r a c t<br /> <br /> Article history:<br /> Received 22 October 2008<br /> Received in revised form<br /> 13 March 2009<br /> Accepted 13 March 2009<br /> Available online 27 March 2009<br /> <br /> The aim of this research is to show the influence of the hardness of the alloy steel on the material<br /> removal rate and on the workpiece surface roughness.<br /> The Taguchi methodology was used to study that influence. The result of the verification test for<br /> workpiece surface roughness was a strong confirmation. This type of outcome allows the use of the<br /> additive model to predict the workpiece surface roughness with an average error of 0.4%.<br /> The result of the verification test for material removal rate was a poor confirmation due to an<br /> interaction of parameters. This type of outcome does not allow the additive model to predict the<br /> material removal rate with accuracy. Therefore, a linear regression model was developed for material<br /> removal rate using workpiece hardness and its interactions, among other variables. This model predicts<br /> the material removal rate with an average error of 1.06%.<br /> These results show that workpiece hardness and its interactions have influence on the material<br /> removal rate and on the workpiece surface roughness.<br /> & 2009 Elsevier Ltd. All rights reserved.<br /> <br /> Keywords:<br /> Electrical discharge machining (EDM)<br /> Alloy steel hardness<br /> Material removal rate (MRR)<br /> Workpiece surface roughness<br /> Taguchi methodology<br /> Linear regression model<br /> <br /> 1. Introduction<br /> Electrical discharge machining (EDM) is a non-traditional<br /> manufacturing process where the material is removed by a<br /> succession of electrical discharges, which occur between the<br /> electrode and the workpiece. These are submersed in a dielectric<br /> liquid such as kerosene or deionised water. The electrical<br /> discharge machining process is widely used in the aerospace,<br /> automobile and moulds industries to machine hard metals and its<br /> alloys.<br /> During the electrical discharge, a discharge channel is created<br /> where the temperature reaches approximately 12,000 1C [1],<br /> removing material by evaporation and melting [2–4] from both<br /> the electrode and the workpiece. When the discharge ceases there<br /> is a high cooling on the surface of the workpiece creating a zone<br /> affected by the heat that contains the white layer. This layer<br /> contains several hollows, spheroids, fissures and micro fissures.<br /> Carbon is the main element of the white layer composition<br /> influencing simultaneously its hardness and thermal conductivity<br /> [5]. The white layer thickness depends on the workpiece material,<br /> on the power used to cut the workpiece and on the applied<br /> electrical polarity.<br /> Electrical discharge machining is governed by a thermal<br /> phenomenon [6,7], therefore not only removes material from<br /> the workpiece but also changes the metallurgical constituents in<br /> the zone affected by the heat. Thus, during machining by EDM the<br /> Ã Corresponding author. Tel.: +351 225 081 520; fax: +351 225 081 445.<br /> <br /> E-mail address: jdmar@fe.up.pt (J.D. Marafona).<br /> 0890-6955/$ - see front matter & 2009 Elsevier Ltd. All rights reserved.<br /> doi:10.1016/j.ijmachtools.2009.03.002<br /> <br /> surface of the workpiece is submitted to a heat treatment<br /> (locally), where the time of stage is the pulse duration and the<br /> temperature reached by the workpiece is due to the applied<br /> current intensity being followed by a quick cooling of the<br /> workpiece. These variables affect the metallurgic constituent of<br /> the white layer and consequently its hardness [8–10] and its<br /> thermal conductivity.<br /> It is also known that during the cut by EDM the material<br /> removal rate (MRR) decreases, which is due to process instability<br /> according to [11]. However, the decrease of material removal<br /> rate is due to the change of metallurgic constituent in the zone<br /> affected by the heat, according to the authors. Therefore, the<br /> authors have decided to investigate the effect of the initial<br /> workpiece hardness on the material removal rate and workpiece<br /> surface roughness.<br /> <br /> 2. Experimental methodology<br /> The effect of the workpiece hardness on the material removal<br /> rate and workpiece surface roughness was studied using the<br /> Taguchi method, which is generally applied to improve the quality<br /> of a product. The Taguchi method is mainly used to optimise a<br /> single output. However, some authors [12] use the orthogonal<br /> array L18 and the grey relational analysis to optimise various<br /> outputs simultaneously. The authors used the orthogonal array<br /> L18, the analysis of variance (ANOVA), additive model and linear<br /> regression to understand the relationship between various inputs<br /> and a single output.<br /> <br /> ARTICLE IN PRESS<br /> ´<br /> J.D. Marafona, A. Araujo / International Journal of Machine Tools & Manufacture 49 (2009) 744–748<br /> <br /> Nomenclature<br /> <br /> 745<br /> <br /> Ram cycle (s) interval of time between lift-offs<br /> Compression (%) degree of deterioration (number of eroded<br /> particles during EDM) in the gap<br /> <br /> Ram speed (mm/min) speed at which the ram lifts off the<br /> electrode from the workpiece at regular intervals of<br /> time<br /> <br /> According to Taguchi, ‘‘it is desirable to treat the interactions<br /> including these in the noise, which is not generally done. Only a<br /> main effect that exceeds the value of interactions can be used<br /> safely in robust project.’’ Thus, the orthogonal array L18 should be<br /> used because this array has the property of distributing interactions to all the columns and treats the interactions as equivalent<br /> to noise. This array can handle seven parameters at three levels<br /> and one parameter at two levels and defines eighteen individual<br /> experiments. If all combinations of parameters and levels were<br /> used, 4374 (21 Â 37) experiments would be involved, and thus,<br /> there is a significant reduction in the number of experiments<br /> performed and thereby a significant reduction in cost and time.<br /> This methodology was designed and performed in a diesinking EDM machine, AGIE COMPACT 3, equipped with adaptive<br /> control facilities. The adaptive control optimization (ACO) system<br /> enables the process to be optimised automatically and it was<br /> switched off so that the results can be generalized to all machines.<br /> The electrode and workpiece materials are electrolytic copper and<br /> steel AISI/SAE-D2, respectively. Two steel AISI/SAE-D2 bars were<br /> used in the research. One bar was quenched and tempered<br /> yielding a hardness of 60 HRC; the hardness of the normalized bar<br /> was 235 HB. The treated bar and the normalized bar were<br /> parallelepipeds with dimensions of 300 Â 60 Â 25 mm3. The<br /> electrodes used were copper rods 16 mm in diameter and a length<br /> of 160 mm. The EDM performance is related to the efficiency<br /> which is determined in the EDM process by the material removal<br /> rate and by the electrode wear ratio (EWR). Quality is determined<br /> by the accuracy and the surface roughness—only the latter will be<br /> considered here. Surface roughness was characterised using the<br /> arithmetic average roughness (Ra) value. This was measured using<br /> a Hommelewerk T4000 measurement instrument.<br /> This experimental methodology enables the workpiece hardness and its interactions to be significant contributors to the<br /> material removed rate and also the workpiece surface roughness<br /> to be determined.<br /> <br /> 3. Experimental results<br /> The importance of the input parameters in the EDM process<br /> was determined. There are eight input parameters (Table 1) that<br /> affect the EDM performance. Some of these parameters are likely<br /> to have a more significant effect on electrical discharge machining<br /> performance than others. The levels of the input parameters,<br /> S1–S8, were allocated using the values of rough cut of EDM, given<br /> in the AGIE manual. These values are indicated in Table 1.<br /> The experimental results of each setting of input parameters of<br /> the orthogonal array L18 are given in Table 1. These are the average<br /> of two experiments.<br /> <br /> 3.1. Effect of the workpiece hardness on the material removal rate<br /> 3.1.1. Analysis of variance<br /> The results of the analysis of variance show that the most<br /> significant contributors to the material removal rate are current<br /> intensity, duty factor, compression and ram cycle with degrees of<br /> significance greater or equal to 90%. The pooling of the small<br /> variances [variance ratio lesser or equal to 2%] increases not only<br /> the variance error of the overall average but also the degrees of<br /> significance of the most important contributors. The results of the<br /> pooling of the small variances show that the most significant<br /> contributors to the material removal rate are current intensity<br /> (17%), duty factor (14%), compression (16%), ram cycle (33%) and<br /> pulse duration (9%) with degrees of significance greater or equal<br /> to 97.5%. The variance error attributed to unknown sources in<br /> obtaining the maximum material removal rate is 10%. These<br /> results can be seen in Table 2.<br /> Nevertheless, the two bars have significantly different workpiece hardness, the material removal rate decreases slightly. It is<br /> important to point out that the interactions of parameters were<br /> not studied because the orthogonal array has the property of<br /> <br /> Table 1<br /> Orthogonal array L18 and experimental data.<br /> Number of trials Steel hardness Current intensity Applied voltage Pulse duration Duty factor Ram speed<br /> Compression Ram cycle MRR (ave.), mm3/min Ra (ave.), mm<br /> (S1)<br /> NC (S2)<br /> NC (S3)<br /> NC (S4)<br /> % (S5)<br /> mm/min (S6) % (S7)<br /> s (S8)<br /> 1<br /> 2<br /> 3<br /> 4<br /> 5<br /> 6<br /> 7<br /> 8<br /> 9<br /> 10<br /> 11<br /> 12<br /> 13<br /> 14<br /> 15<br /> 16<br /> 17<br /> 18<br /> <br /> 1(235 HB)<br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 1<br /> 2(60 HRC)<br /> 2<br /> 2<br /> 2<br /> 2<br /> 2<br /> 2<br /> 2<br /> 2<br /> <br /> 10<br /> 10<br /> 10<br /> 11<br /> 11<br /> 11<br /> 12<br /> 12<br /> 12<br /> 10<br /> 10<br /> 10<br /> 11<br /> 11<br /> 11<br /> 12<br /> 12<br /> 12<br /> <br /> 2<br /> 4<br /> 6<br /> 2<br /> 4<br /> 6<br /> 2<br /> 4<br /> 6<br /> 2<br /> 4<br /> 6<br /> 2<br /> 4<br /> 6<br /> 2<br /> 4<br /> 6<br /> <br /> 16<br /> 18<br /> 19<br /> 16<br /> 18<br /> 19<br /> 18<br /> 19<br /> 16<br /> 19<br /> 16<br /> 18<br /> 18<br /> 19<br /> 16<br /> 19<br /> 16<br /> 18<br /> <br /> 50<br /> 65<br /> 80<br /> 65<br /> 80<br /> 50<br /> 50<br /> 65<br /> 80<br /> 80<br /> 50<br /> 65<br /> 80<br /> 50<br /> 65<br /> 65<br /> 80<br /> 50<br /> <br /> 350<br /> 525<br /> 700<br /> 525<br /> 700<br /> 350<br /> 700<br /> 350<br /> 525<br /> 525<br /> 700<br /> 350<br /> 350<br /> 525<br /> 700<br /> 700<br /> 350<br /> 525<br /> <br /> 20<br /> 30<br /> 40<br /> 40<br /> 20<br /> 30<br /> 30<br /> 40<br /> 20<br /> 30<br /> 40<br /> 20<br /> 40<br /> 20<br /> 30<br /> 20<br /> 30<br /> 40<br /> <br /> 0.3<br /> 2<br /> 30<br /> 30<br /> 0.3<br /> 2<br /> 30<br /> 0.3<br /> 2<br /> 0.3<br /> 2<br /> 30<br /> 2<br /> 30<br /> 0.3<br /> 2<br /> 30<br /> 0.3<br /> <br /> 2.89<br /> 17.66<br /> 27.82<br /> 33.90<br /> 11.40<br /> 16.92<br /> 30.80<br /> 13.24<br /> 31.32<br /> 7.62<br /> 22.05<br /> 5.68<br /> 34.95<br /> 7.93<br /> 14.03<br /> 21.81<br /> 43.68<br /> 14.54<br /> <br /> 7.1<br /> 7.7<br /> 7.2<br /> 7.6<br /> 9<br /> 9<br /> 10.8<br /> 10.8<br /> 9.5<br /> 7.3<br /> 6.5<br /> 8.6<br /> 9.2<br /> 9.7<br /> 7.4<br /> 11<br /> 9.2<br /> 11.8<br /> <br /> ARTICLE IN PRESS<br /> ´<br /> J.D. Marafona, A. Araujo / International Journal of Machine Tools & Manufacture 49 (2009) 744–748<br /> <br /> 746<br /> <br /> Table 2<br /> Results of the analysis of variance (ANOVA) for MRR.<br /> ANOVA results for MRR<br /> Se<br /> <br /> S2<br /> <br /> S3<br /> <br /> S4<br /> <br /> S5<br /> <br /> S6<br /> <br /> S7<br /> <br /> S8<br /> <br /> St<br /> <br /> 26<br /> 2<br /> 13<br /> 1<br /> 1.1<br /> <br /> Sum of squares<br /> Degree of freedom<br /> Variance<br /> Variance ratio<br /> Percentage of contribution<br /> Degree of significance<br /> <br /> S1<br /> 10<br /> 1<br /> 10<br /> 0.8<br /> 0<br /> <br /> 428<br /> 2<br /> 214<br /> 16.3<br /> 19<br /> 90<br /> <br /> 42<br /> 2<br /> 21<br /> 1.6<br /> 2<br /> <br /> 235<br /> 2<br /> 117<br /> 8.9<br /> 10<br /> <br /> 360<br /> 2<br /> 180<br /> 13.7<br /> 16<br /> 90<br /> <br /> 20<br /> 2<br /> 10<br /> 0.7<br /> 1<br /> <br /> 389<br /> 2<br /> 195<br /> 14.8<br /> 17<br /> 90<br /> <br /> 778<br /> 2<br /> 389<br /> 29.6<br /> 34<br /> 95<br /> <br /> 2288<br /> 17<br /> <br /> –<br /> <br /> 400<br /> 2<br /> 200<br /> 14.2<br /> 17<br /> 99.5<br /> <br /> –<br /> <br /> 208<br /> 2<br /> 104<br /> 7.4<br /> 9<br /> 97.5<br /> <br /> 332<br /> 2<br /> 166<br /> 11.8<br /> 14<br /> 99<br /> <br /> –<br /> <br /> 361<br /> 2<br /> 180<br /> 12.8<br /> 16<br /> 99.5<br /> <br /> 750<br /> 2<br /> 375<br /> 26.7<br /> 33<br /> 99.5<br /> <br /> Pooling of small variances into the error<br /> Sum of squares<br /> 98<br /> Degree of freedom<br /> 7<br /> Variance<br /> 14<br /> Variance ratio<br /> 1<br /> Percentage of contribution<br /> 10<br /> Degree of significance<br /> <br /> Table 3<br /> Results of the ANOVA assessment for the linear regression model.<br /> Source<br /> <br /> Degrees of freedom (DOF)<br /> <br /> Sum of squares (SS)<br /> <br /> Mean square (MS)<br /> <br /> Variance ratio (F)<br /> <br /> Probability (P)<br /> <br /> Regression<br /> Residual error<br /> Total<br /> R2 ¼ 1.000<br /> Adjusted R2 ¼ 0.999<br /> <br /> 14<br /> 3<br /> 17<br /> <br /> 2287.317<br /> 0.215<br /> 2287.532<br /> <br /> 163.380<br /> 0.072<br /> <br /> 2275.340<br /> <br /> 0.000Ã<br /> <br /> Ã Highly significant.<br /> <br /> distributing interactions to all the columns and treats the<br /> interactions as equivalent to noise. The verification test indicates<br /> that material removal rate is affected by interactions of parameters. Therefore, the variance error of 10% attributed to<br /> unknown sources can be explained by the effect of the workpiece<br /> hardness and its interactions on the material removal rate,<br /> according to the authors.<br /> 3.1.2. Linear regression model<br /> Some models for EDM performance parameters were built<br /> using the additive model from Taguchi methodology and the<br /> response surface methodology [12,13]. In this study, the verification test from Taguchi method shows a poor confirmation due to<br /> an interaction of parameters, so additive model predicts material<br /> removal rate with high accuracy errors, say in the order of 10%.<br /> Therefore, a linear regression model was developed for material<br /> removal rate using workpiece hardness and its interactions<br /> besides others interactions of input parameters. The capability<br /> of the linear model to represent the experimental data was<br /> assessed through the analysis of variance. The results of the<br /> analysis of variance for the linear model are shown in Table 3.<br /> This linear model presents a regression square (R2) of 1.0<br /> and an adjusted regression square (adj. R2) of 0.999, meaning<br /> that the predicted values and the experimental data agree<br /> very well.<br /> Eq. (1) shows the coefficients of the linear regression model,<br /> using the data and the results presented in Table 1.<br /> MRR ¼ À 106:518 þ 209:729nS1 þ 1:550nS2 þ 21:424nS3<br /> À 11:353nS4 À 1:269nS5<br /> þ 0:339nS6 þ 4:588nS7 À 0:616nS8 þ 2:948nS12<br /> À 14:545nS13 À 0:619nS14<br /> þ 0:327nS15 À 0:218nS16 À 2:709nS17<br /> <br /> (1)<br /> <br /> Table 4<br /> Experimental data and predicted values for the rate of material removal and<br /> surface roughness.<br /> Number<br /> of trials<br /> <br /> Ra (mm)<br /> <br /> Relative<br /> error (%)<br /> <br /> Experimental Predicted<br /> 1<br /> 2<br /> 3<br /> 4<br /> 5<br /> 6<br /> 7<br /> 8<br /> 9<br /> 10<br /> 11<br /> 12<br /> 13<br /> 14<br /> 15<br /> 16<br /> 17<br /> 18<br /> <br /> 7.1<br /> 7.7<br /> 7.2<br /> 7.6<br /> 9<br /> 9<br /> 10.8<br /> 10.8<br /> 9.5<br /> 7.3<br /> 6.5<br /> 8.6<br /> 9.2<br /> 9.7<br /> 7.4<br /> 11<br /> 9.2<br /> 11.8<br /> <br /> 7.06<br /> 7.66<br /> 7.16<br /> 7.66<br /> 9.01<br /> 9.01<br /> 10.84<br /> 10.84<br /> 9.54<br /> 7.34<br /> 6.54<br /> 8.64<br /> 9.19<br /> 9.69<br /> 7.39<br /> 10.96<br /> 9.16<br /> 11.76<br /> <br /> MRR (mm3/min)<br /> <br /> Relative<br /> error (%)<br /> <br /> Experimental Predicted<br /> 0.6<br /> 0.5<br /> 0.6<br /> 0.8<br /> 0.1<br /> 0.1<br /> 0.4<br /> 0.4<br /> 0.4<br /> 0.5<br /> 0.6<br /> 0.5<br /> 0.1<br /> 0.1<br /> 0.1<br /> 0.4<br /> 0.4<br /> 0.3<br /> <br /> 2.89<br /> 17.66<br /> 27.82<br /> 33.90<br /> 11.40<br /> 16.92<br /> 30.80<br /> 13.24<br /> 31.32<br /> 7.62<br /> 22.05<br /> 5.68<br /> 34.95<br /> 7.93<br /> 14.03<br /> 21.81<br /> 43.68<br /> 14.54<br /> <br /> 3.04<br /> 17.64<br /> 28.02<br /> 33.87<br /> 11.44<br /> 16.88<br /> 30.94<br /> 13.33<br /> 31.42<br /> 7.63<br /> 22.20<br /> 5.76<br /> 35.29<br /> 8.20<br /> 14.43<br /> 22.02<br /> 43.64<br /> 14.60<br /> <br /> 5.2<br /> 0.1<br /> 0.7<br /> 0.1<br /> 0.3<br /> 0.2<br /> 0.4<br /> 0.6<br /> 0.3<br /> 0.1<br /> 0.6<br /> 1.4<br /> 0.9<br /> 3.3<br /> 2.8<br /> 0.9<br /> 0.1<br /> 0.4<br /> <br /> The predicted values of the linear regression model and the<br /> experimental data are shown in Table 4. The linear regression<br /> model predicts material removal rate with an average error of<br /> 1.06%.<br /> The results of the linear regression model show that the<br /> material removal rate is dependent on the workpiece hardness<br /> and its interactions. Its results, presented in Eq. (1), show that the<br /> contributions of the unknown sources to the material removal<br /> rate variance are mainly composed of combined effects, i.e.<br /> <br /> ARTICLE IN PRESS<br /> ´<br /> J.D. Marafona, A. Araujo / International Journal of Machine Tools & Manufacture 49 (2009) 744–748<br /> <br /> 747<br /> <br /> Table 5<br /> Results of the analysis of variance (ANOVA) for Ra.<br /> ANOVA results for Ra<br /> Se<br /> Sum of squares<br /> Degree of freedom<br /> Variance<br /> Variance ratio<br /> Percentage of contribution<br /> Degree of significance<br /> <br /> S1<br /> <br /> S2<br /> <br /> S3<br /> <br /> S4<br /> <br /> S5<br /> <br /> S6<br /> <br /> S7<br /> <br /> S8<br /> <br /> St<br /> <br /> 0.021<br /> 2<br /> 0.011<br /> 1<br /> 0.05<br /> <br /> 0.222<br /> 1<br /> 0.222<br /> 20.9<br /> 0.54<br /> 95<br /> <br /> 29.521<br /> 2<br /> 14.761<br /> 1386<br /> 71.8<br /> 99.5<br /> <br /> 0.034<br /> 2<br /> 0.017<br /> 1.6<br /> 0.08<br /> <br /> 8.874<br /> 2<br /> 4.437<br /> 416.6<br /> 21.58<br /> 99.5<br /> <br /> 1.021<br /> 2<br /> 0.511<br /> 47.9<br /> 2.48<br /> 97.5<br /> <br /> 0.388<br /> 2<br /> 0.194<br /> 18.2<br /> 0.94<br /> 90<br /> <br /> 1.021<br /> 2<br /> 0.511<br /> 47.9<br /> 2.48<br /> 97.5<br /> <br /> 0.021<br /> 2<br /> 0.011<br /> 1<br /> 0.05<br /> <br /> 41.124<br /> 17<br /> <br /> 0.209<br /> 1<br /> 0.209<br /> 16.4<br /> 0.5<br /> 99<br /> <br /> 29.496<br /> 2<br /> 14.748<br /> 1152.2<br /> 71.7<br /> 99.5<br /> <br /> –<br /> <br /> 8.849<br /> 2<br /> 4.424<br /> 345.7<br /> 21.5<br /> 99.5<br /> <br /> 0.996<br /> 2<br /> 0.498<br /> 38.9<br /> 2.4<br /> 99.5<br /> <br /> 0.362<br /> 2<br /> 0.181<br /> 14.1<br /> 0.9<br /> 99<br /> <br /> 0.996<br /> 2<br /> 0.498<br /> 38.9<br /> 2.4<br /> 99.5<br /> <br /> –<br /> <br /> Pooling of small variances into the error<br /> Sum of squares<br /> 0.077<br /> Degree of freedom<br /> 6<br /> Variance<br /> 0.013<br /> Variance ratio<br /> 1<br /> Percentage of contribution<br /> 0.5<br /> Degree of significance<br /> <br /> statistical interactions, of parameter. The workpiece hardness is<br /> the parameter that interacts with all remaining parameters. The<br /> exception is the interaction between the workpiece hardness and<br /> the ram cycle, which does not influence the material removal rate<br /> variance.<br /> <br /> Ys1, Ys2, y, Ys7 are the average values levels for parameters S1,<br /> S2, y, S7, respectively.<br /> <br /> 4. Conclusion<br /> 3.2. Effect of the workpiece hardness on the average surface<br /> roughness (Ra)<br /> 3.2.1. Analysis of variance<br /> The results of the analysis of variance show that the most<br /> important contributors to the workpiece surface roughness are<br /> current intensity, pulse duration, duty factor, compression, workpiece hardness and ram speed, with degrees of significance<br /> greater or equal to 90%. The pooling of the small variances confirm<br /> that the most important contributors to the workpiece surface<br /> roughness are current intensity (71.7%), pulse duration (21.5%),<br /> duty factor (2.4%), compression (2.4%), workpiece hardness (0.5%)<br /> and ram speed (0.9%), with degrees of significance greater or equal<br /> to 99%. The variance error attributed to unknown sources in<br /> obtaining the workpiece surface roughness is 0.5%. The small<br /> variance error value indicates that the average surface roughness<br /> is obtained by the isolated effect of the workpiece hardness,<br /> current intensity, pulse duration, duty factor, ram speed and<br /> compression parameter. These results can be seen in Table 5.<br /> The verification test indicates a strong confirmation. These<br /> results show that the workpiece hardness is influent on the<br /> workpiece surface roughness.<br /> <br /> 3.2.2. Additive model<br /> The result of the verification test allows the additive model to<br /> predict the workpiece surface roughness. The values predicted<br /> and the experimental data show a high degree of agreement, as<br /> shown in Table 4. In this study, the ram cycle and the applied<br /> voltage are not significant contributors to the workpiece surface<br /> roughness, as shown in the additive model described in Eq. (2):<br /> Ra ¼ Y exp À ðY exp À Y S1 Þ À ðY exp À Y S2 Þ<br /> À ðY exp À Y S4 Þ À Á Á Á À ðY exp À Y S7 Þ<br /> <br /> (2)<br /> <br /> The Ra value is obtained by a combination of levels of the<br /> parameters of the orthogonal array, where Yexp is the overall<br /> average response of the Ra for the entire orthogonal array and the<br /> <br /> The results of this research show that the material removal rate<br /> and the workpiece surface roughness are directly dependent on<br /> the workpiece hardness. This is demonstrated by the mathematical models used in the research.<br /> The results of this research show that the material removal rate<br /> is dependent on the workpiece hardness and its interactions with<br /> exception of the interaction between the workpiece hardness and<br /> the ram cycle. The material removal rate is predicted with an<br /> average error of 1.06%.<br /> It is also demonstrated that workpiece surface roughness is<br /> dependent on the workpiece hardness and other input parameters. The additive model predicts the workpiece surface<br /> roughness values with an average error of 0.4%.<br /> In conclusion, this knowledge demonstrates that the<br /> electrical discharge machining process is not only influenced<br /> by the thermal properties of the workpiece but also by its<br /> hardness.<br /> References<br /> [1] K. Albinski, K. Musiol, A. Miernikiewicz, S. Labuz, M. 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