## 5 Model Simulation and Discussion
### Analysis of Main Influencing Factors  
The simulation, based on Equation (9), was performed as shown in Figure 15a-h, which shows the influence of the tool design parameters and milling parameters on \(R_{a}\). Any unnecessary cross-factor analysis was omitted, and the intra-group interaction analysis of the main factors affecting \(R_{a}\) was completed, as shown in Figure 15a-e. Additionally, (a)-(c) represent the cross-factor analysis of the tool design parameters, and (d) and (e) represent the cross-factor analysis of the milling parameters. In particular, the variables and dependent variables displayed on the axis were the objects in the analysis, and the other factors not involved in the images were set as fixed values for comparison \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**TGP** & **T\&WP** & **CWC** & **WEC** & **REC** \\ \hline \(\gamma=5^{\circ}\) & \(a=15255\) & \(K_{1}=9.838\times 10^{-10}\) & \(K=40,923\) & \(K_{0}=2000\) \\ \(\alpha=12^{\circ}\) & \(b=1.6\) & \(K_{2}=6.647\times 10^{-10}\) & \(C=18.13\) & \(C_{0}=0.53\) \\ \(\beta=50^{\circ}\) & \(e=23,054\) & \(K_{3}=2.923\times 10^{-6}\) & & \\ \(R=5\) mm & \(g=3.62\times 10^{-4}\) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation input parameters. Figure 14: Derivation process of \(R_{a}\)-\(VB\) relationship. purposes. For example, in Figure 15c, the independent variables analyzed were \(\beta\) and \(\gamma\), and the dependent variable was \(R_{a}\), then, \(\beta\) and \(\gamma\) were the variables within a certain range, and \(R_{a}\) changed accordingly, while the parameters not involved in Figure 15c were set as constant, such as the tool parameters, radius \(R\), number of teeth \(Z\), flank angle \(\alpha\), machining parameters, feed \(f\), milling depth \(a_{p}\), speed, \(n\), line spacing, \(p\), those of the workpiece being machined, and curvature \(\rho\). The dependent variable generated a surface with the change of the two independent variables, and the surface synthesis reflects the interaction of the two independent variables on the same dependent variable. Figure 15: _Cont._  
As shown in Figure 15, the effect of \(\alpha\) on \(R_{a}\) is more significant than that of \(R\). \(R_{a}\) positively correlates with \(R\), but negatively correlates with \(\alpha\). Thus, to ensure the quality of the processing, unless there is a specific demand, when designing the tool parameters, it is inadvisable to design the tool with a small \(\alpha\) value and large \(R\) value. A similar situation also occurs in the effects of \(\gamma\) and \(R\) on \(R_{a}\), as shown in Figure 15. From Figure 15,b, it can be seen that the effect of \(R\) on \(R_{a}\) is almost linear. However, the effect of \(\alpha\) on \(R_{a}\) appears as a concave function, and the effect of \(\gamma\) on \(R_{a}\) appears as an upper convex function, as shown in Figure 15, comparing the cross factors \(\gamma\) and \(\beta\), \(\beta\) has almost no effect on \(R_{a}\). However, this is relative, as shown in Figure 15; when \(f\) is compared with \(\beta\), \(\beta\) has a greater effect on \(R_{a}\), and as shown in Figure 15, if the two factors \(\beta\) and \(\gamma\) present a great influential difference on \(R_{a}\), the main design or selection object of the tool is \(\gamma\) when the consistency of the tool during processing is insufficient, while \(\beta\) with a relatively weak influence can be selected according to other influencing factors. A similar situation also occurs in the effects of \(\gamma\) and \(R\) on \(R_{a}\), as shown in Figure 15,e,g. It is worth further regarding Figure 15,h. In Figure 15, both \(a_{p}\) and \(\gamma\) negatively correlate with \(R_{a}\), the two factors under this interactive relationship should not be too small simultaneously because the change in the same direction of the two will result in a bigger change rate of \(R_{a}\), but this may also be affected by their respective ranges of variation.