## 3 Results
### Neural Network Models and SHAP Analysis
#### 3.1.2 Neural Network Model and SHAP Analysis for Case 2  
Figure 6 shows the impact of cutting speed \(v_{c}\), feed rate \(f\), and depth of cut \(a_{p}\) on \(R_{a}\) based on SHAP values. It can be seen that \(a_{p}\) has a much higher impact compared to \(f\) and \(v_{c}\), where \(f\) has the lowest impact on the \(R_{a}\) value. The higher values of \(a_{p}\) increase and the lower values decrease the value of \(R_{a}\). The same pattern is observed for \(f\), while with the increase in \(v_{c}\), the value of \(R_{a}\) decreases.  
Figure 7 depicts the impact of cutting speed \(v_{c}\), feed rate \(f\), and depth of cut \(a_{p}\) on the main cutting force \(F_{c}\). In Figure 7, it can be seen that \(a_{p}\) has the highest impact on \(F_{c}\), where with the increase in \(a_{p}\), the values of \(F_{c}\) increase, followed by \(f\) with the same pattern. The cutting speed \(v_{c}\) has a small impact on \(F_{c}\), where with the increase in \(v_{c}\), the values of \(F_{c}\) decrease.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Metrics** & \(R_{a}\) & \(F_{c}\) & \(F_{p}\) & \(F_{f}\) \\ \hline \(R^{2}\) & 38.70\% & 92.66\% & 70.54\% & 90.48\% \\ \(MSE\) & 0.0214 & 0.0036 & 0.0148 & 0.0044 \\ \(MAE\) & 0.1121 & 0.0457 & 0.0875 & 0.0504 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Evaluation of the model’s performance on \(R_{a}\), \(F_{c}\), \(F_{p}\), and \(F_{f}\) for case 1.  
Figure 6: Impact of \(v_{c}\), \(f\), and \(a_{p}\) on \(R_{a}\) based on SHAP values for case 2.  
Figure 8 shows the impact of cutting speed \(v_{c}\), feed rate \(f\), and depth of cut \(a_{p}\) on the the passive force \(F_{p}\) based on SHAP values for case 2. In the figure, it can be seen that with an increasing value of input features \(a_{p}\) and \(f\), the value of \(R_{a}\) increases, and with an increasing value of \(v_{c}\), the value of \(R_{a}\) decreases. Based on SHAP values, the highest impact on \(F_{p}\) is exerted by the feed rate \(a_{p}\), followed by the depth of cut \(f\). The lowest impact on \(F_{p}\) is exerted by the cutting speed \(v_{c}\).  
Figure 9 shows the impact of cutting speed \(v_{c}\), feed rate \(f\), and depth of cut \(a_{p}\) on the feed force \(F_{f}\). The increase in cutting speed \(v_{c}\) causes the value of \(F_{f}\) to decrease, although it has the smallest impact. The value of \(F_{f}\) increases as the values of \(f\) and \(a_{p}\) increase. The depth of cut \(a_{p}\) has the greatest impact, followed by the feed rate \(f\).  
Table 5 shows the contributions of features \(v_{c}\), \(f\), and \(a_{p}\) to \(R_{a}\), \(F_{c}\), \(F_{p}\), and \(F_{f}\) for case 2. Table 5 shows that \(a_{p}\) has the highest contribution to \(R_{a}\), \(F_{c}\), and \(F_{f}\), exceeding 50%, with the highest contribution of 84.39% to \(R_{a}\). The highest contribution of 74.29% to \(F_{p}\) comes from \(f\).  
Figure 8: Impact of \(v_{c}\), \(f\), and \(a_{p}\) on \(F_{p}\) based on SHAP values for case 2.  
Figure 7: Impact of \(v_{c}\), \(f\), and \(a_{p}\) on \(F_{c}\) based on SHAP values for case 2.  
The evaluation metrics for the performance of the developed models for \(R_{a}\), \(F_{c}\), \(F_{p}\), and \(F_{f}\) are shown in Table 6 as the mean squared error (\(MSE\)), mean absolute error (\(MAE\)), and coefficient of determination (\(R^{2}\)). With the exception of \(R_{a}\) and \(F_{p}\), the developed model performs well on \(F_{c}\) and \(F_{f}\), with the values of \(R^{2}=93.03\%\) and \(R^{2}=83.92\%\), respectively.