## 3 Influencing Factors and Interaction Identification of the Machined Surface Error
### Interaction of Influencing Factors of the Machined Surface Error
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Serial** & \(n\) & \(f_{z}\) & \(M\) & \(a\) & **Serial** & \(n\) & \(f_{z}\) & \(M\) & \(a\) \\
**Number** & **(rpm)** & **(mm)** & **(mm)** & **(rpm)** & **(mm)** & **(mm)** & **(mm)** & **(mm)** & **(a)** \\ \hline
1 & 1720 & 0.07 & \(M_{3}\) & \(a_{5}\) & 12 & 1720 & 0.07 & \(M_{3}\) & \(a_{4}\) \\
2 & 1290 & 0.05 & \(M_{1}\) & \(a_{5}\) & 13 & 1290 & 0.09 & \(M_{4}\) & \(a_{5}\) \\
3 & 1720 & 0.07 & \(M_{3}\) & \(a_{3}\) & 14 & 1720 & 0.07 & \(M_{3}\) & \(a_{3}\) \\
4 & 2443 & 0.07 & \(M_{3}\) & \(a_{3}\) & 15 & 1720 & 0.07 & \(M_{2}\) & \(a_{3}\) \\
5 & 1720 & 0.07 & \(M_{2}\) & \(a_{3}\) & 16 & 2150 & 0.05 & \(M_{5}\) & \(a_{1}\) \\
6 & 2150 & 0.09 & \(M_{4}\) & \(a_{1}\) & 17 & 1720 & 0.07 & \(M_{3}\) & \(a_{2}\) \\
7 & 1290 & 0.09 & \(M_{5}\) & \(a_{4}\) & 18 & 1720 & 0.04 & \(M_{3}\) & \(a_{3}\) \\
8 & 1720 & 0.10 & \(M_{3}\) & \(a_{3}\) & 19 & 1720 & 0.07 & \(M_{3}\) & \(a_{3}\) \\
9 & 1720 & 0.07 & \(M_{3}\) & \(a_{3}\) & 20 & 996 & 0.07 & \(M_{3}\) & \(a_{3}\) \\
10 & 2150 & 0.09 & \(M_{1}\) & \(a_{5}\) & 21 & 1290 & 0.05 & \(M_{1}\) & \(a_{1}\) \\
11 & 2150 & 0.05 & \(M_{5}\) & \(a_{5}\) & & & & & \\ \hline \end{tabular}
\end{table} 
Table 5: Simulation scheme of error variation characteristics. the influence of the various characteristics of the machined surface positional and angular errors are shown in Figure 8.  
As shown in Figure 8, where \"\(\times\)\" indicates the interaction between the two, among the design variables of machined surface errors' variation characteristics, probability levels in the range of 0-0.01 are highly influential; probability levels between 0.01 and 0.05 were considered obvious effects, while probability levels greater than 0.05 indicated weak or non-existent interaction with respect to the various characteristics of the machined surface position errors. As shown in the figure, the probability level of spindle speed is between 0 and 0.01, which is less than 0.05, indicating the most significant effect on the machined surface positional error, while the probability level of feed per tooth is between 0.04 and 0.05, with the least effect compared to other factors. The probability level of feed per tooth is between 0 and 0.01, indicating the greatest effect on the machined surface angular error. The probability level of the interaction between spindle speed and tooth error ranged from 0.04 to 0.05, indicating the least influence. According to the results of the significance analysis of the machined surface errors, it can be seen that the interactions of the rotational speed of the milling cutter and cutter tooth error, cutter tooth error and milling vibration, and the feed rate per tooth and milling vibration have obvious effects on the various characteristics of the machined surface positional errors; therefore, these three sets of interaction variables were analyzed separately, and the response surface is shown in Figure 9 according to the response surface methodology [20]. The gentler the surface, the smaller the interaction effect of the two factors on the machined surface positional errors, the more pronounced the curvature of the response surface plot, and the greater the interaction effect of the two factors on the machined surface positional errors. From Figure 9, it can be seen that the combination of the interaction effects of the rotational speed of the milling cutter and the feed rate per tooth with the second group of milling vibration and the rotational speed of the milling cutter has a greater effect on the correlation degree of the surface positional errors of the feature point machining, while the combination of the feed rate per tooth and milling vibration interaction has a small degree of influence. Figure 8: Inherent items of influencing factors of the machined surface error variation characteristics. To analyze the specific extent of the interaction of the influencing factors, the average curvature of the surface reflects the average degree of curvature of the surface in the region.