## 3 Results
### Neural Network Models and SHAP Analysis
#### 3.1.1 Neural Network Model and SHAP Analysis for Case 1  
Figure 2 shows the impact of cutting speed \(v_{c}\), feed rate \(f\), and depth of cut \(a_{p}\) on \(R_{a}\) based on SHAP values for case 1. In Figure 2, it can be seen that with the increasing value of all input features, the value of \(R_{a}\) increases. Based on SHAP values, the highest impact on \(R_{a}\) is exerted by the feed rate \(f\), followed by depth of cut \(a_{p}\). The lowest impact on \(R_{a}\) is exerted by the cutting speed \(v_{c}\).  
The impact of cutting speed \(v_{c}\), feed rate \(f\), and depth of cut \(a_{p}\) on the main cutting force \(F_{c}\) is presented in Figure 3. Unlike when \(R_{a}\) was analyzed, with an increase in the cutting speed \(v_{c}\), the value of the main cutting force \(F_{c}\) decreases, although, as with \(R_{a}\), it has the smallest impact. With an increase in the value of \(f\) and \(a_{p}\), the value of \(F_{c}\) also  
Figure 2: Impact of \(v_{c}\), \(f\), and \(a_{p}\) on \(R_{a}\) based on SHAP values for case 1.  
increases, only in this case, the depth of cut \(a_{p}\) has the highest impact, followed by the feed rate \(f\).  
Figure 4 depicts the impact of cutting speed \(v_{c}\), feed rate \(f\), and depth of cut \(a_{p}\) on the passive force \(F_{p}\). It can be seen that the impact of input features on \(F_{p}\) is almost the same as the impact on \(F_{c}\), where the increase and decrease in the values of input features impact the output value in the same way as \(F_{c}\), while the impact values differ slightly.  
In Figure 5, the impact of \(v_{c}\), feed rate \(f\), and depth of cut \(a_{p}\) on the feed force \(F_{f}\) is shown. It can be seen that all input features impact \(F_{f}\), where with an increase in the values of the input features, the value of \(F_{f}\) increases. Input features \(f\) and \(a_{p}\) have the highest impact on \(F_{f}\).  
Table 3 shows the contributions of features \(v_{c}\), \(f\), and \(a_{p}\) to \(R_{a}\), \(F_{c}\), \(F_{p}\), and \(F_{f}\). In Table 3, it can be seen that \(v_{c}\) has, overall, the lowest contribution to all output values, with the lowest contribution of 3.53% to \(F_{c}\) and the highest contribution of 15.90% to \(R_{a}\). Feature  
Figure 4: Impact of \(v_{c}\), \(f\), and \(a_{p}\) on \(F_{p}\) based on SHAP values for case 1.  
Figure 5: Impact of \(v_{c}\), \(f\), and \(a_{p}\) on \(F_{f}\) based on SHAP values for case 1.  
Figure 3: Impact of \(v_{c}\), \(f\), and \(a_{p}\) on \(F_{c}\) based on SHAP values for case 1.  
has the highest contribution to \(R_{a}\) and the lowest contribution to \(F_{f}\), with values varying from 58.64% and 25.77%, respectively. The highest impact of feature \(a_{p}\) is on \(F_{f}\) and \(F_{c}\), with contributions of 67.28% and 55.39%, respectively, and the lowest impact is on \(F_{p}\) and \(R_{a}\), with contributions of 37.75% and 25.46%, respectively.  
Table 4 shows the evaluation metrics of coefficient of determination (\(R^{2}\)), mean squared error (\(MSE\)), and mean absolute error (\(MAE\)) for the performance of the developed models for \(R_{a}\), \(F_{c}\), \(F_{p}\), and \(F_{f}\). It can be seen that the developed models demonstrate good performance on all outputs, except for \(R_{a}\). The model has the highest performance in predicting the output value of \(F_{c}\), with \(R^{2}=92.66\%\), \(MSE=0.0036\), and \(MAE=0.0457\). The model's performance on \(R_{a}\) is \(R^{2}=38.70\%\), \(MSE=0.0214\), and \(MAE=0.1121\), indicating that the input features do not explain the variability of \(R_{a}\) as well as the other outputs of \(F_{c}\), \(F_{p}\), and \(F_{f}\).