Surface roughness

The surface roughness is a parameter used to evaluate the quality of the mechanical parts which predominantly affects its functionality and production costs (^{Mata-Cabrera, Hanafi, Khamlichi, Jabbouri & Bezzazi, 2013}; ^{Schultheiss, Hãgglund, Bushlya, Zhou & Stâhl, 2014}). The average roughness (Ra) is the arithmetical mean of the examined roughness value in the machined zone. This is the most used parameter of roughness value due to its practicality, and it can be calculated by using the Equation (1):

where Ln is the evaluation length and Z is the distance between two points of the profile (ASME, 1995).

Equipment and material used in the experiments

The die-sinking EDM machine of type Surefirst ED-203 was used in to machining of stainless steel workpieces as shows in Figure 1.

In the study, AISI 304 stainless steel was selected as the workpiece material, the specimens were made with dimensions of 100 mm x 25 mm x 6,35 mm. This steel is frequently used for chemical and food processing equipment; brewing equipment; cryogenic vessels; gutters; downspouts; flashings (^{Oberg, Jones, Horton & Ryffel, 2008}). Its main properties are displayed in Table 2.

Table 2 Properties of the workpiece material 

Source: ^{Oberg et al., 2008}

Source: Authors

Figure 1 The used EDM machine. 

Graphite is one of the most used electrode material for EDM applications, because of its good thermal and electric properties (^{Klocke, Schwade, Klink & Veselovac, 2013}). The experiments in this study were conducted using grade GSP-70 graphite electrodes, they were made with dimensions of 30 mm x 10 mm x 13 mm, and a new electrode was used in each replica of the experimental design. The grade GSP-70 graphite is an isotropic fine grain material with high purity and density levels, and as such is an ideal element to use with tasks involving EDM. Table 3 displays the most significant properties of the used electrodes material.

Table 3 Properties of the electrodes material 

Source: Grupo Rooe, 2018

Figure 2 shows the workpiece and electrode materials used in this investigation.

Source: Authors

Figure 2 Workpiece and electrode materials. 

Design of experiments

The two-level factorial design was used in this study with the three parameters concerned: the pulse current (I_A, A), the pulse on time (T_ON, |js) and the pulse off time (T_OFF, μs). Therefore, a two-level factorial design with three factors (2³) was selected consistent with eight combinations for the factor levels, producing two replicas for each combination. The low and high levels for each factor were codified as -1 and +1, respectively.

Table 4 displays the used factors of this work with their levels, which are established on the used electric-discharge machine.

Table 4 Factors and levels selected for the experiments 

Source: Authors

Analysis of surface roughness

The machined surfaces were produced for each combination of levels of I_A, T_ON and T_OFF, and then based on the factors values established in the factorial design. The average roughness (R_a, pm) of the machined surfaces was measured by using the Mitutoyo SJ-402 series 178 profilometer, as shown in Figure 3. The results of the experiment of design 2³ technique mentioned in this study are displayed in Table 5.

Source: Authors

Figure 3 Machined surfaces and profilometer. 

Table 5 Design of experiments matrix for the second-order model 

Source: Authors

Regression model

The second order model related to the average roughness (R_a) and machining parameters (I_A, T_ON and T_OFF) generated in terms of the levels codified of the aforementioned parameters is displayed in Equation (2).

Table 6 shows the ANOVA results produced to check the adequacy of the second order. It can be noted that the P-value is less than α = 0,05, which means that the model possesses a confidence level of 95%, that represents the relationship between average roughness (R_a) and machining parameters (I_A, T_ON and T_OFF).

Table 6 Analysis of Variance for the regression model 

Source: Authors

In Table 7, the ANOVA analysis for the individual model coefficients is displayed. It can be noted that there are three parameters with P-value inferior to α = 0,05, meaning that these are indications of a confidence level of 95%. These significant parameters are: the pulse current (I_A), the pulse on time (TON) and the interaction between them.

Table 7 Analysis of variance of Ra (μη־ι) 

Source: Authors

In addition to this, the coefficient of determination R² = 94,55% obtained through the ANOVA technique explains the amount of reduction in the Ra variability obtained by using the machining parameters (I_A, T_ON and T_OFF) in the model.

On the other hand, it can be observed in Figure 4 that the residues from average roughness are in line with normal distribution and the second order regression model has extracted all the information available from the experiment data.

Source: Authors

Figure 4 Normal probability plot of the residuals. 

Main effects

Figure 5 displays the graphical representations of the main effects of the resulting average roughness (Ra) and the parameters of the experimental design (I_A, T_ON and T_OFF). Figure 5a shows that the levels of pulse current (I_A) significantly influence the obtained average roughness (R_a) values, and as increased the pulse current, the average roughness increased. In Figure 5b, it can be observed that the average roughness increases as the pulse on time (T_ON) increases, meaning that the pulse current can significantly affect average roughness values. Figure 5c shows that the pulse off time does not affect the average roughness (R_a), as there is no significant variation between the mean data for each parameter level.

Source: Authors

Figure 5 Main effects for the Ra (pm) and the experimental parameters of the design (a) I_A, (b) T_ON and (c) T_OFF.  

Cube plot

The cube plot in Figure 6 shows that the lowest average figure for average roughness is 2,260 pm between the eight combinations of levels for the experiment parameters, obtained with levels -1(1,25 A), +1 (10 ps) and -1 (1 ps) for I_A, T_ON and T_OFF, respectively. The highest R_a value is 7,600 pm, obtained through a combination of 1, 1 and -1, which corresponds to I_A of 5,0 A, T_ON of 150 ps and T_OFF of 1 ps.

Source: Authors

Figure 6 Cube plot (data means) for Ra. 

Figure 7 displays the differences between the surface finishes values obtained under different machining conditions. Figure 7a shows a surface roughness micrograph of 2,54 pm value machined using a pulse current (IA) of 1,25 A, a pulse on time (T_ON) of 10 ps and a pulse off time (T_OFF) of 3 ps. Likewise, Figure 7b displays a surface finish micrograph with a value of 8,40 pm obtained using a pulse current (I_A) of 5,00 ps, a pulse on time (T_ON) of 150 ps and a pulse off time (T_OFF) of 1 ps.

Source: Authors

Figure 7 Surfaces roughness micrograph (a) Ra = 2,54 pm and (b) Ra = 8,40 pm. 

Mean absolute percent error

The mean absolute percent error (MAPE) is the average of the absolute differences between the adjusted and experimental R values, expressed as a percent of experimental values (^{Heizer & Render, 2011}) and is computed with using the Equation (3):

Table 8 shows the absolute percent errors computed. The sum of percent errors is 152,131%, therefore, the value of MAPE is 9,508%. MAPE expresses the error as a percent of the experimental values, undistorted by a single large value.

Table 8 Absolute percent errors 

Source: Authors