## 3 Results
### Surface Free Energy (SFE) after Milling
However, analyzing the detailed error results and differences for individual cases and taking into account its practical purpose, it would be more reasonable to use network 6. This network was the product of 200 iterations and the activation function in both the hidden and output layers is logistic. The numerical results from the total simulation of the surface roughness parameter, Rz, for AZ31 and AZ91D alloy after milling are shown in Figure 18 while those after milling and brushing are shown in Figure 19. Once \(\rm{v_{c}}\) and \(\rm{s_{tr}}\) were fed into Statistica, the surface roughness parameters, Rz, for both alloys were obtained. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Network No.** & **Network Name** & **Quality (Training, \%)** & **Quality (Validation, \%)** & **Error (Training)** & **Error (Validation)** & **Activation (Hidden)** & **Activation (Output)** \\ \hline \multicolumn{8}{c}{AZ31 alloy} \\ \hline
1 & RBF 2-8-1 & 93.96 & 99.99 & 0.008 & 0.024 & Gaussian & Linear \\
2 & RBF 2-5-1 & 92.20 & 99.98 & 0.011 & 0.025 & Gaussian & Linear \\
3 & RBF 2-6-1 & 92.36 & 99.98 & 0.011 & 0.032 & Gaussian & Linear \\ \hline \multicolumn{8}{c}{AZ91D alloy} \\ \hline
4 & MLP 2-5-1 & 95.01 & 99.22 & 0.016 & 0.027 & Tanh & Logistic \\
5 & MLP 2-3-1 & 91.37 & 97.68 & 0.026 & 0.005 & Tanh & Sinus \\
6 & MLP 2-4-1 & 95.01 & 99.97 & 0.016 & 0.027 & Logistic & Logistic \\ \hline \end{tabular}
\end{table} 
Table 4: Characteristics of MLP and RBF networks for AZ31 and AZ91D alloy for surface roughness parameters, Rz, after brushing. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Network No.** & **Network Name** & **Quality (Training, \%)** & **Quality (Validation, \%)** & **Error (Training)** & **Error (Validation)** & **Activation (Hidden)** & **Activation (Output)** \\ \hline \multicolumn{8}{c}{AZ31 alloy} \\ \hline
1 & MLP 2-9-1 & 91.44 & 89.39 & 0.528 & 0.532 & Logistics & Sinus \\
2 & RBF 2-8-1 & 96.31 & 99.98 & 0.233 & 0.729 & Gaussian & Linear \\
3 & MLP 2-8-1 & 98.97 & 99.96 & 0.002 & 0.647 & Logistics & Linear \\ \hline \multicolumn{8}{c}{AZ91D alloy} \\ \hline
4 & MLP 2-6-1 & 96.96 & 99.65 & 0.031 & 0.042 & Tanh & Exponential \\
5 & MLP 2-8-1 & 97.95 & 99.37 & 0.032 & 0.072 & Tanh & Exponential \\
6 & MLP 2-8-1 & 98.99 & 99.53 & 0.011 & 0.012 & Tanh & Logistic \\ \hline \end{tabular}
\end{table} 
Table 3: Characteristics of multi-layered perceptron (MLP) and radial basis function (RBF) networks for AZ31 and AZ91D alloy for surface roughness parameters, Rz, after milling. The accuracy of the modelled networks (Figures 20 and 21) enables the comparison of the surface roughness parameter, Rz, measured for the milling and brushing of the AZ31 alloy (Figure 20) and the AZ91D alloy (Figure 21) material, with the numerical values reflecting the changes in the cutting speed, v\({}_{\rm c}\), at a fixed trochoidal step of s\({}_{\rm tr}\) = 15. From their comparison, it can be seen that the relative error between the real values of the simulated parameters did not exceed 10% for milling, and 15% for after milling and brushing. Figure 19: Numerical results of the surface roughness parameters, Rz, after brushing for the (**a**) AZ31 alloy (RBF 2-8-1) and (**b**) AZ91D alloy (MLP 2-4-1) depending on the cutting speed, v\({}_{\rm c}\), and trochoidal step, s\({}_{\rm tr}\). Figure 18: Numerical results of surface roughness parameters, Rz, after milling for the (**a**) AZ31 alloy (MLP 2-8-1) and (**b**) AZ91D alloy (MLP 2-8-1) depending on the cutting speed, v\({}_{\rm c}\), and trochoidal step, s\({}_{\rm tr}\). The results from the simulations show a permissible level of error, lower than 15%. This indicates that ANNs are fully capable of simulating parameters of milling or brushing. The obtained data may give grounds for the development of effective numerical models. This property of artificial neural networks earmarks them as a perfect machining process simulation tool.