## 3 Results
### The Results and Analysis for Milling Force  
The milling performance during the machining process is notably influenced by a diverse array of milling parameters. Table 8 precisely presents the alterations in the milling force, \(F\), under the different spindle speed, \(n\), feed rate, \(v_{\text{f}}\), and axial milling depth, \(a_{\text{p}}\). A range and variance analysis was conducted on the milling force, \(F\), presented in Table 8, with the results detailed in Tables 9 and 10. The range analysis indicates that the influence of milling parameters on milling force \(F\) follows a descending order: axial milling depth \(a_{\text{p}}>\) feed rate \(v_{\text{f}}>\) spindle speed \(n\). As depicted in Figure 7, to minimize the milling force exerted on the tool while ensuring milling efficiency and tool life, the optimal milling parameters are identified as \(n=\) 12,000 \(\text{r}/\min\), \(v_{\text{f}}=\) 1000 \(\text{mm}/\min\), and \(a_{\text{p}}=\) 3 mm. By setting the significance level at \(\alpha=0.05\), the analysis of variance results reveal that F (\(a_{\text{p}}>\) F (\(v_{\text{f}}\)) \(>\) F\({}_{\text{critical value}}>\) F (\(n\)), which implies that the significance order of the influence of milling parameters on milling force \(F\) is \(a_{\text{p}}>v_{\text{f}}>n\). Figure 6: The variation relationship between the wear width, \(b\), of the rake face and the spindle speed, \(n\), the feed rate, \(v_{\text{f}}\), as well as the axial milling depth, \(a_{\text{p}}\). (**a**) The \(b\)-\(n\) variation curve; (**b**) the \(b\)-\(v_{\text{f}}\) variation curve; (**c**) the \(b\)-\(a_{\text{p}}\) variation curve. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No**} & \multicolumn{3}{c}{**Parameters**} & **Results** \\ \cline{2-5}  & \(n\) **(r/min)** & \(v_{\text{f}}\) **(mm/min)** & \(a_{\text{p}}\) **(mm)** & \(F\) **(N)** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 8: The results of orthogonal experiment for milling force. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Item** & \(K_{\text{i}}\) & \(n\) **(r/min)** & \(v_{\text{f}}\) **(mm/min)** & \(a_{\text{p}}\) **(mm)** \\ \hline  & \(K_{1}\) & 48.496 & 44.776 & 43.642 \\ \(F\) (N) & \(K_{2}\) & 48.981 & 50.060 & 49.514 \\ \(K_{3}\) & 50.453 & 53.094 & 54.773 \\ Range & 1.957 & 8.318 & 11.131 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Range Analysis of milling force. Figure 7: The effect curve of milling parameters on milling force, \(F\). The data presented in Table 8 were fitted using Equation (7) and analyzed with 1 stopt software (version 15.0), yielding the fitting results of the multi-quadratic regression model as shown in Table 11. The coefficient of determination, R2, amounts to 0.904. This value implies that variations in the milling parameters have a significant and predictable impact on the milling force, \(F\). Additionally, the fitting model demonstrates excellent performance and can effectively predict alterations in the milling force of the tool, providing valuable references and theoretical support for the actual milling processing procedures. When the fitting results are substituted into Equation (7), the following can be derived:  
\[ \begin{array}{c}F=33.681-2.980\times 10^{-3}n+2.738\times 10^{-2}v_{\text{f}}-0.8 73a_{\text{p}}-4.217\times 10^{-7}nv_{\text{f}}+5.736\times 10^{-4}na_{\text{p}}\\ +1.917\times 10^{-4}v_{\text{f}}a_{\text{p}}+5.481\times 10^{-8}n^{2}-4.5\times 10^{-6 }v_{\text{f}}^{2}-0.307a_{\text{p}}^{2}\end{array}  \tag{9}\]  
Figure 8a-c illustrate the relationship between milling force, \(F\), and the spindle speed, \(n\), feed rate, \(v_{\text{f}}\), and axial milling depth, \(a_{\text{p}}\). As observed in Figure 8a,b, the milling force exhibits an increase with rising feed rate and axial milling depth. This phenomenon can be attributed to the fact that an increase in feed rate results in a greater machining travel distance and volume per unit time.