#
Multi-Response Optimization of Electrical Discharge Machining Using the Desirability Function^{ †}

^{*}

^{†}

## Abstract

**:**

_{on,}and the time interval t

_{off}, on the surface roughness (Sa), the thickness of the white layer (WL), and the MRR, during the machining of tool steel 55NiCrMoV7. The surface and subsurface integrity were evaluated using an optical microscope and a scanning profilometer. Analysis of variance (ANOVA) was used to establish the statistical significance parameters. The calculated contribution indicated that the discharge current had the most influence (over the 50%) on the Sa, WL, and MRR, followed by the discharge time. The multi-response optimization was carried out using the desirability function for the three cases of EDM: Finishing, semi-finishing, and roughing. The confirmation test showed that maximal errors between the predicted and the obtained values did not exceed 6%.

## 1. Introduction

_{3}N

_{4}-TiN. The authors used RSM to determine the optimal parameters for the machining of ceramic composites. The conducted research showed that the MRR and surface roughness of the manufactured parts depended on the value of the discharge current and the pulse time, and the results were consistent with the results for the processing of tool steel [41]. Kumaran et al. [42] used a grey fuzzy logic approach to optimize the EDM parameters during the machining of carbon fiber reinforced plastic composite. Their research showed that established optimal parameters in ultrasonic-assisted EDM allowed improvements in the deburring rate, with a simultaneous improvement in the tool wear rate (TWR). Gu et al. [43] indicated that the machining of new alloys, which have a high melting point and good thermal conductivity, like titanium–zirconium–molybdenum, require optimizations of the EDM in connection with the analysis. The presented results showed that the crater diameter was much smaller than the plasma-affected zone. To improve the machining performance (Ra, MRR), the response surface methodology was used. Dang [44] proposed the Kriging regression model and particle swarm in the optimization of EDM of P20 steel. The authors indicated that the Kriging model could capture the nonlinear characteristics and was better able to obtain the optimum parameters for the MRR, tool wear, and surface roughness. Mohanty et al. [45] pointed out that the choice of the electrode material should be considered in the optimization of the EDM process. The authors found that in the machining of Inconel 718, the material removal rate and tool wear could be improved by using a graphite electrode and to improve surface integrity, the better choice was a brass and copper electrode. Using the utility concept and the quantum particle swarm optimization (QPSO) algorithm, the optimal parametric setting was developed with the objectives to maximize the MRR and minimize tool wear, surface roughness, and radial overcut. Research presented by Maity et al. [46] on the influence of EDM parameters on the thickness of the recast layer, material removal rate, and overcut on the machining of Inconel 718, showed that the optimization parameters using the RSM and Artificial Bee Colony algorithm gave an average prediction accuracy of about 3.5% in relation to confirmation tests. The predictive efficiency of neural networks may be affected by different factors like noise corruption, spatial distribution, and the size of the data used to construct the artificial neural network (ANN) model. Tripathy et al. [47], in order to optimize the powder mixed (SiC) electro-discharge machining of H-11 die steel, which seeks to maximize the MRR and minimize electrode wear and surface roughness, used a different method of optimization. The authors used the grey relational analysis and the technique for the order of preference by similarity, where the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) solution achieved a similar effect of an improved performance of the quality characteristics. Nguyen et al. [48] investigated the influence of powder mixed (Ti) electro-discharge machining of SKD61, SKD11, SKT4 steel on the surface roughness (SR), MRR, and microhardness. The presented results showed that the addition of Ti powder in dielectric resulted in reduced SR and increased microhardness. The authors indicated that optimization with the Taguchi–TOPSIS made it difficult to select the optimal parameters. The presented research showed that the measured distance could lead to confusion in selecting the best alternative. A fuzzy analytic hierarchy process (AHP) and fuzzy TOPSIS method were used by Roy et al. [49] to optimize multiple responses of the material removal rate, tool wear, and tool overcut in EDM based on various process parameters. Kandpal et al. [50] investigated the influence of EDM parameters on the MRR, tool wear, and overcut of aluminum matrix composites. The authors showed optimization with the utility concept, which provided the collective optimization of both responses for improving the mean of the process. D’Urso et al. [51] proposed the optimization of EDM micro drilling using a cost index which combined two opposite effects of the material removal rate and tool wear. The minimization of the cost index enabled optimal working conditions. Parsana et al. [52] indicated that in the optimization process of EDM drilling, an important point to consider was the roundness of the holes. Using the RSM and passing vehicle search algorithm, normalized weights proved to be useful in obtaining the Pareto fronts for a combination of different objectives at a time. Research carried out by Hadad et al. [53] showed that the analysis of the optimal parameters of EDM machining, in addition to the electrical parameters, should also include the initial roughness of the working electrodes, which has significant effects on the machining performance during the finishing, semi-rough, and rough EDM processes.

## 2. Materials and Methods

#### 2.1. Uncertainty Evaluation Procedure

_{PROF}was calculated according to the following equation:

_{cal}is the standard calibration uncertainty of the roughness standard; u

_{p}is the standard uncertainty related to the measurement procedure and is calculated as a standard deviation of ten repeated measurements on the calibrated standard; and u

_{res,PROF}is the resolution standard uncertainty related to the declared 3 nm vertical resolution of the scanning profilometer for measuring range 0.2 mm.

_{S}

_{a,EDM}is calculated using the standard deviation of repeated Sa measurements on the electrical discharge machining sample. Table 1 presents the uncertainty budget.

_{OM}was calculated according to the following equation:

_{cal}is the standard calibration uncertainty of the calibration slide, u

_{p}is the standard uncertainty related to the measurement procedure and is calculated as the standard deviation of ten repeated measurements on the calibrated slide; and u

_{res,OM}is the resolution standard uncertainty related to the objective magnification (50x). The expanded uncertainty of the thickness of the white layer measurement was calculated as follows:

_{m}

_{1}is the standard uncertainty related to the measurement procedure and is calculated as the standard deviation of the ten repeated measurements of the sample, u

_{res,}is the resolution uncertainty related to the declared resolution of the balance with a readability 0.01 mg for the measuring samples of a maximum capacity 50 g, u

_{i}is the uncertainty related to a balance indication error, and u

_{ie}is the uncertainty on a determining indication error.

#### 2.2. Analyses of Current and Voltage Waveforms.

_{on}. Then, during the t

_{off}interval, the conditions in the gap stabilized, and the process was cyclically repeated.

- I = the height of the peak current during discharging,
- Uz = open circuit voltage, this is the system voltage when the EDM circuit is in the open state, and the energy has been built up for discharge,
- Uc = discharge voltage,
- t
_{on}= pulse time, the time required for the current to rise and fall during discharging, - t
_{off}= time interval, this is the time from the end of one pulse to the beginning of the next pulse with the current.

_{off}, the plasma channel may not be completely deionized, which increases the probability of another discharge being in the same place. Furthermore, the ineffective removal of the products of erosion from the gap causes a reduction in the dielectric resistance and destabilization of the conditions. There is a high probability of a short circuit. The machine's control system resists the phenomena described above by increasing the gap (temporarily raising the electrode), whilst at the same time extending the break time (Figure 3).

_{on}= 10–400 µs, and time interval t

_{off}= 10–150 μs, with the following constants :open voltage U

_{0}= 225 V, discharge voltage Uc = 25 V. Table 4 shows the levels of machining parameters carried out in the experimental design.

## 3. Results and Discussion

#### 3.1. Analysis of Surface Integrity

#### 3.2. Response Surface Methodology

_{on}, t

_{off}) ± ε

_{on}(μs) the pulse time, and t

_{off}(μs) the time interval are independent parameters. In the study, the polynomial regression model was chosen to fit the response function to the experimental results.

_{on}, and time interval t

_{off}was built. The results of the experimental studies are presented in Table 5. The surface roughness (Sa) was in the range of 1.88 µm to 12.7 µm. The maximal thickness of the white layer was in the range of 5.5 µm to 33.5 µm. The material removal rate was in the range 0.1 mm

^{3}/min to 29.19 mm

^{3}/min. The obtained value of roughness (Sa), the maximal thickness of the white layer, and the MRR corresponded to the finishing and roughing machining.

^{2}− 0.0004 t

_{on}+ 0.00002 t

_{on}

^{2}+ 0.00006 I t

_{on}

− 0.000007 I t

_{on}

^{2}+ 0.0003 I

^{2}t

_{on}

^{2}− 0.101 t

_{on}+ 0.0003 t

_{on}

^{2}− 0.002 t

_{off}+ 0,035 I t

_{on}− 0.0001 I t

_{on}

^{2}

− 0.0014 I

^{2}t

_{on}+ 0.000005 I

^{2}t

_{on}

^{2}+ 0.00027 t

_{on}t

_{off}− 0.000001 t

_{on}

^{2}t

_{off}

^{2}− 0.00817 t

_{on}+ 0.00004 t

_{on}

^{2}+ 0.02287 t

_{off}

+ 0.00096 I t

_{on}− 0.00001 I t

_{on}

^{2}+ 0.00057 I

^{2}t

_{on}− 0.00668 I t

_{off}

_{on}, and time interval t

_{off}on the Sa, WL, and MRR is shown in Figure 14, Figure 15 and Figure 16, respectively.

_{i}(${\hat{y}}_{i}$), and it has a range from zero to one (one being the most desirable). Different desirable functions can be built, depending on the adopted optimization criteria which determine the desirable value, maximal (upper-U

_{i}) or minimal (lower-L

_{i}). If the response for the investigated parameter should be minimized, then d

_{i}(${\hat{y}}_{i}$) can be calculated according to the following equation:

_{i}or maximum U

_{i}).

^{3}/min), with the possibility of minimizing the surface roughness and white layer thickness. In the last case, the optimal parameters for roughing EDM were considered. In this task, the goal of optimization was to achieve the maximum MRR possible, with the possibility of minimizing the surface roughness and white layer thickness. These three cases of the optimization of electrical discharge machining were carried out using the desirability function, based on the regression Equations (10)–(12). It should be maintained that the success of the optimization with the desirability function mainly depends on the quality of the regressions models. In this study, each established model had a coefficient of determination, R-squared, that was over 98%, and the differences between the R-squared and the R-adjustable were smaller than 0.2, which indicated that the models were adequate in representing the process. For each EDM parameter (discharge current, pulse time, time interval) there was a simultaneous analysis of every combination of the factors for each of the nine responses (Figure 14, Figure 15 and Figure 16). A multi-response optimization procedure was performed for the global desirability function. The ranges for the constraints and factors for optimization are shown in Table 9.

_{on}= 176 µs, and pulse interval t

_{off}= 10 µs. The predicted surface roughness (1.7 µm) and the white layer thickness (6 µm) after optimization were close to the results obtained in the experimental studies for sample number four. Nevertheless, the material removal rate grew almost seven times and reached an MRR = 1.1 mm

^{3}/min. The increase of the MRR was achieved, along with the minimization of the surface roughness and the white layer thickness, which has a significant effect on productivity.

_{on}= 52 µs, and pulse interval t

_{off}= 24 µs. In this case, if the material removal rate reached 14.5 mm

^{3}/min (i.e., the average value of the MRR from experimental studies), the optimized surface roughness and the white layer thickness were as follows: Sa = 5.2 µm and WL = 15 µm. Figure 21 and Table 10 present the results of the optimization for roughing EDM. Values of the optimal EDM parameters as follows: I = 14 A, t

_{on}= 361 µs, and t

_{off}= 24 µs. The optimized material removal rate, surface roughness, and white layer thickness were as follows: MRR = 29.2 mm

^{3}/min, Sa = 12.1 µm, WL = 28.8 µm.

## 4. Conclusions

- Experimental research on the influence of discharge current, pulse time, and pulse interval on the surface roughness (Sa), white layer thickness, and the MRR showed that the discharge current had the main effect on Sa, WL, and the MRR. With an increase in the discharge current and pulse time, the amount of energy delivered to the workpiece caused the melting and evaporation of a higher volume of material, which generated craters with a larger depth and diameter. However, more material which melted in the single crater was not removed from the surface of the workpiece and it re-solidified on the core. The time interval between pulses did not significantly affect the change in surface integrity and the MRR, but it played an important role in the stability of the process.
- The desirability function was used in the multi-response optimization of three functions: Sa, WL, and MRR. For the three cases of EDM—finishing, semi-finishing, and roughing operations—the optimal parameters were established. The confirmation tests for the established optimal parameters showed that the maximal errors between the predicted and the obtained values did not exceed 6%, which could be considered as a very good result.
- The developed regression equations could be used in electrical discharge machining as a guideline for the selection of EDM parameters.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**The recorded voltage and current waveforms for the following parameters: (

**a**) U

_{c}= 25 V, U

_{z}= 230 V, I = 3 A, t

_{on}= 400 µs, t

_{off}= 100 µs; (

**b**) U

_{c}= 25 V, U

_{z}= 230 V, I = 3 A, t

_{on}= 13 μs, t

_{off}= 13 μs.

**Figure 5.**The surface texture of the tool steel 55NiCrMoV7 after electrical discharge machining (EDM): (

**a**) U

_{c}= 25 V, I = 8.5 A, t

_{on}= 400 µs, t

_{off}= 150 µs; (

**b**) U

_{c}= 25 V, I = 3 A, t

_{on}= 400 µs, t

_{off}= 80 µs.

**Figure 7.**The metallographic structure of tool steel 55NiCrMoV7 after EMD: Uc = 25 V, I = 14 A, t

_{on}= 13 µs, t

_{off}= 10 µs.

**Figure 8.**The metallographic structure of tool steel 55NiCrMoV7 after EMD: (

**a**) Uc = 25 V, I = 3 A, t

_{on}= 206 µs, t

_{off}= 80 µs; (

**b**) Uc = 25 V, I = 14 A, t

_{on}= 400 µs, t

_{off}= 80 µs.

**Figure 9.**The structure of the surface after EMD: Uc = 25 V, I = 14 A, t

_{on}= 400 µs, t

_{off}= 150 µs.

**Figure 10.**The comparison between the results of experimental studies to the values calculated based on the developed models for (

**a**) surface roughness (Sa); (

**b**) maximal thickness of white layer (WL); (

**c**) material removal rate (MRR).

**Figure 11.**The plots to check the model for surface roughness (Sa): (

**a**) the normal plot of residuals; (

**b**) the residuals versus the predicted values; and (

**c**) the residuals versus the case values.

**Figure 12.**The plots to check the model for maximal white layer thickness: (

**a**) the normal plot of residuals; (

**b**) the residuals versus the predicted values; and (

**c**) the residuals versus the case values.

**Figure 13.**The plots to check the model MRR: (

**a**) the normal plot of residuals; (

**b**) the residuals versus the predicted values; and (

**c**) the residuals versus the case values.

**Figure 14.**The estimated response surface plot for roughness (Sa): (

**a**) constant t

_{off}= 80 µs; (

**b**) constant t

_{on}= 206 µs; and (

**c**) constant I = 8.5 A.

**Figure 15.**The estimated response surface plot for the WL: (

**a**) constant t

_{off}= 80 µs; (

**b**) constant t

_{on}= 206 µs; and (

**c**) constant I = 8.5 A.

**Figure 16.**The estimated response surface plot for the MRR: (

**a**) constant t

_{off}= 80 µs; (

**b**) constant t

_{on}= 206 µs; and(

**c**) constant I = 8.5 A.

**Table 1.**The uncertainty contributions for the Sa roughness measurements on the scanning profilometer.

Uncertainty Contributions (nm) | |||||
---|---|---|---|---|---|

u_{cal} | u_{p} | u_{res,PROF} | U_{PROF} | U_{Sa, EDM} | U_{95,Sa} |

20 | 2 | 3 | 20.5 | 5 | 42 |

**Table 2.**The uncertainty contributions for the thickness of the white layer measurements on microscope.

Uncertainty Contributions (μm) | ||||
---|---|---|---|---|

u_{cal} | u_{p} | u_{res,OM} | U_{OM} | U_{95,WL} |

0.060 | 0.048 | 0.312 | 0.321 | 0.6 |

Uncertainty Contributions (mg) | |||||
---|---|---|---|---|---|

u_{m}_{1} | u_{res} | u_{i} | u_{ie} | U_{B} | U_{95,W} |

0.02 | 0.0029 | 0.0058 | 0.01 | 0.023 | 0.046 |

EDM Parameters | Level 1 | Level 2 | Level 3 |
---|---|---|---|

discharge current I (A) | 3 | 8.5 | 14 |

pulse time t_{on} (μs) | 13 | 206 | 400 |

time interval t_{off} (μs) | 9 | 80 | 150 |

Exp. no. | EDM Parameters | Observed Values | ||||
---|---|---|---|---|---|---|

Discharge Current I (A) | Pulse Time t_{on} (μs) | Time Interval t _{off} (μs) | Surface Roughness Sa (μm) | Maximal Thickness of the White Layer (μm) | MRR (mm ^{3}/min) | |

1 | 3 | 13 | 10 | 2.0 | 5.5 | 0.54 |

2 | 8.5 | 13 | 10 | 3.1 | 11.5 | 3.47 |

3 | 14 | 13 | 10 | 3.8 | 12 | 11.06 |

4 | 3 | 13 | 80 | 1.9 | 6 | 0.17 |

5 | 8.5 | 13 | 80 | 3.0 | 12 | 1.18 |

6 | 14 | 13 | 80 | 3.4 | 11.5 | 3.21 |

7 | 3 | 13 | 150 | 1.9 | 6 | 0.10 |

8 | 8.5 | 13 | 150 | 3.0 | 11.5 | 0.55 |

9 | 14 | 13 | 150 | 3.3 | 12 | 1.31 |

10 | 3 | 206 | 10 | 1.9 | 7 | 0.51 |

11 | 8.5 | 206 | 10 | 6.2 | 22 | 8.09 |

12 | 14 | 206 | 10 | 9.3 | 25.4 | 28.46 |

13 | 3 | 206 | 80 | 1.9 | 10 | 0.36 |

14 | 8.5 | 206 | 80 | 6.0 | 24 | 5.77 |

15 | 14 | 206 | 80 | 10.5 | 28 | 19.23 |

16 | 3 | 206 | 150 | 1.8 | 10 | 0.29 |

17 | 8.5 | 206 | 150 | 5.4 | 25 | 4.68 |

18 | 14 | 206 | 150 | 11.7 | 32 | 15.48 |

19 | 3 | 400 | 10 | 2.4 | 12 | 0.37 |

20 | 8.5 | 400 | 10 | 3.9 | 17 | 6.58 |

21 | 14 | 400 | 10 | 12.3 | 28 | 29.19 |

22 | 3 | 400 | 80 | 2.4 | 13.5 | 0.34 |

23 | 8.5 | 400 | 80 | 4.0 | 20 | 5.61 |

24 | 14 | 400 | 80 | 12.7 | 29 | 24.84 |

25 | 3 | 400 | 150 | 2.5 | 14 | 0.28 |

26 | 8.5 | 400 | 150 | 4.9 | 18.4 | 2.56 |

27 | 14 | 400 | 150 | 11.5 | 33.5 | 20.31 |

28 | 8.5 | 206 | 80 | 6.1 | 24.5 | 5.88 |

Source | Sum of Squares | Degrees of Freedom | Mean Square | F-Value | Prob > f | Contribution % |
---|---|---|---|---|---|---|

Model | 344.7600 | 7 | 49.027 | 150.95 | <0.0001 | - |

I | 198.5468 | 1 | 198.5468 | 611.29 | <0.0001 | 57.6 |

I^{2} | 5.8097 | 1 | 5.8097 | 17.88 | 0.0004 | 1.7 |

t_{on} | 54.1840 | 1 | 54.1840 | 166.82 | <0.0001 | 15.7 |

t_{on}^{2} | 16.1085 | 1 | 16.1085 | 49.59 | <0.0001 | 4.7 |

I t_{on} | 50.0208 | 1 | 50.0208 | 154.01 | <0.0001 | 14.5 |

I t_{on}^{2} | 8.9235 | 1 | 8.9235 | 27.47 | <0.0001 | 2.6 |

I^{2} t_{on} | 11.1696 | 1 | 11.1696 | 34.39 | <0.0001 | 3.2 |

Error | 6.4953 | 20 | 0.32479 | - | - | - |

Total SS | 351.2560 | 27 | R-sqr = 0.98 | R-Adj = 0.97 |

Source | Sum of Squares | Degrees of Freedom | Mean Square | F-Value | Prob > f | Contribution % |
---|---|---|---|---|---|---|

Model | 1886.366 | 11 | 171.48 | 141.26 | <0.0001 | - |

I | 896.656 | 1 | 896.656 | 738.59 | 0.0022 | 47.5 |

I^{2} | 16.041 | 1 | 16.041 | 13.21 | <0.0001 | 0.8 |

t_{on} | 524.880 | 1 | 524.880 | 432.35 | <0.0001 | 27.8 |

t_{on}^{2} | 174.366 | 1 | 174.366 | 143.62 | 0.0002 | 9.2 |

t_{off} | 27.406 | 1 | 27.406 | 22.57 | <0.0001 | 1.4 |

I t_{on} | 90.750 | 1 | 90.750 | 74.75 | 0.0004 | 4.8 |

I t_{on}^{2} | 61.584 | 1 | 61.583 | 50.72 | 0.0031 | 3.3 |

I^{2}t_{on} | 37.210 | 1 | 37.210 | 30.65 | 0.0071 | 2.0 |

I^{2}t_{on}^{2} | 44.018 | 1 | 44.017 | 36.25 | <0.0001 | 2.3 |

t_{on}t_{off} | 5.603 | 1 | 5.603 | 4.61 | <0.0001 | 0.3 |

t_{on}^{2}t_{off} | 7.860 | 1 | 7.859 | 6.47 | 0.0473 | 0.4 |

Error | 19.424 | 16 | 1.2140 | 738.59 | 0.0216 | - |

Total SS | 1905.799 | 27 | R-sqr = 0.99 | R-Adj = 0.98 |

Source | Sum of Squares | Degrees of Freedom | Mean Square | F-Value | Prob > f | Contribution % |
---|---|---|---|---|---|---|

Model | 2243.49 | 9 | 247.881 | 208.65 | <0.0001 | - |

I | 1253.287 | 1 | 1253.287 | 1055.08 | <0.0001 | 55.9 |

I^{2} | 126.243 | 1 | 126.243 | 106.27 | <0.0001 | 5.6 |

t_{on} | 260.655 | 1 | 260.655 | 219.43 | <0.0001 | 11.6 |

t_{on}^{2} | 56.489 | 1 | 56.489 | 47.55 | <0.0001 | 2.5 |

t_{off} | 101.381 | 1 | 101.381 | 85.34 | <0.0001 | 4.5 |

I t_{on} | 285.948 | 1 | 285.948 | 240.72 | <0.0001 | 12.7 |

I t_{on}^{2} | 36.030 | 1 | 36.030 | 30.33 | <0.0001 | 1.6 |

I^{2}t_{on} | 44.106 | 1 | 44.106 | 37.13 | <0.0001 | 2.0 |

I t_{off} | 79.350 | 1 | 79.350 | 66.80 | <0.0001 | 3.5 |

Error | 21.381 | 18 | 1.188 | - | - | - |

Total SS | 2264.87 | 27 | R-sqr = 0.99 | R-Adj = 0.99 |

Factors | Goal | Lower Limit | Upper Limit | Weight | Importance | ||
---|---|---|---|---|---|---|---|

Finishing EDM | Semi-Finishing | Roughing | |||||

I (A) | In range | 3 | 14 | 1 | - | - | - |

t_{on} (µs) | In range | 13 | 400 | 1 | - | - | - |

t_{off} (µs) | In range | 10 | 150 | 1 | - | - | - |

Sa (µm) | Minimize | 1.85 | 12.7 | 1 | t = 5 | t = 3 | t = 0.3 |

WL (µm) | Minimize | 5.5 | 33.5 | 1 | t = 5 | t = 3 | t = 0.3 |

MRR (mm^{3}/min) | Maximize | 0.01 | 29.19 | 1 | s = 0.3 | s = 3 | s = 5 |

Optimal EDM Parameters | Summary of Values Obtained in Optimization | ||||
---|---|---|---|---|---|

Response | Predicted | Experimental Verification | Error% | ||

Finishing | I = 3 A t _{on} = 176 µst _{off} = 10 µs | Sa (µm) | 1.7 | 1.8 | 6 |

WL (µm) | 6 | 6.3 | 5 | ||

MRR (mm^{3}/min) | 1.13 | 1.06 | 6 | ||

Semi- finishing | I = 14 A t _{on} = 52 µst _{off} = 24 µs | Sa (µm) | 5.2 | 5.4 | 4 |

WL (µm) | 15 | 15.8 | 5 | ||

MRR (mm^{3}/min) | 14.5 | 15 | 3 | ||

Roughing | I = 14 A t _{on} = 361 µst _{off} = 24 µs | Sa (µm) | 12.1 | 12.7 | 5 |

WL (µm) | 28.8 | 30.5 | 6 | ||

MRR (mm^{3}/min) | 29.2 | 28.1 | 4 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Świercz, R.; Oniszczuk-Świercz, D.; Chmielewski, T.
Multi-Response Optimization of Electrical Discharge Machining Using the Desirability Function. *Micromachines* **2019**, *10*, 72.
https://doi.org/10.3390/mi10010072

**AMA Style**

Świercz R, Oniszczuk-Świercz D, Chmielewski T.
Multi-Response Optimization of Electrical Discharge Machining Using the Desirability Function. *Micromachines*. 2019; 10(1):72.
https://doi.org/10.3390/mi10010072

**Chicago/Turabian Style**

Świercz, Rafał, Dorota Oniszczuk-Świercz, and Tomasz Chmielewski.
2019. "Multi-Response Optimization of Electrical Discharge Machining Using the Desirability Function" *Micromachines* 10, no. 1: 72.
https://doi.org/10.3390/mi10010072