## 2 Materials and Methods
### Cutting Simulation Single-Factor Experiment Results
#### 3.2.4 Quadratic Regression Orthogonal Combination Experimental Results and Analysis  
Simulation tests are performed on the constructed cutting device to evaluate the repeated-cutting rate (\(Y_{1}\)) and the miss-cutting rate (\(Y_{2}\)) under different working conditions, and the experimentally obtained results are provided in Table 6. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Experimental Factors**} & \multicolumn{3}{c}{**Experimental Indicators**} \\ \cline{2-6}
**Test No.** & \(\mathbf{x_{1}}\) & \(\mathbf{x_{2}}\) & \(\mathbf{x_{3}}\) & \
\begin{tabular}{c} **Repeated-Cutting** \\ **Rate \(Y_{1}\)/(\%)** \\ \end{tabular} &
\begin{tabular}{c} **Miss-Cutting** \\ **Rate \(Y_{2}\)/(\%)** \\ \end{tabular} \\ \hline  
) & \(21.19\) & \(3.01\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Experimental program and results. Figure 16: Cutting device operating law for three crank lengths. The individual coefficients of the main regression equation can be obtained from the combination design calculations provided in Table 6. Therefore, the regression equations between the three influencing factors of crank length (\(x_{1}\)), crank rotation speed (\(x_{2}\)), and forward speeds (\(x_{3}\)) and the two evaluation indicators, including the repeated-cutting rate (\(Y_{1}\)) and the miss-cutting rate (\(Y_{2}\)), can be established in the following form:  
\[ \begin{array}{c}Y_{1}=21.19+4.36x_{1}+8.98x_{2}-9.2x_{3}+0.4943x_{1}x_{2}-0. 4603x_{1}x_{3}-0.9701x_{2}x_{3}\\ \hskip 14.226378 pt-0.275x_{1}^{2}-1.04x_{2}^{2}+2.13x_{3}^{2}\\ \hskip 14.226378 ptY_{2}=3.01-0.8913x_{1}-2.51x_{2}+2.32x_{3}+0.5172x_{1}x_{2}- 0.4577x_{1}x_{3}-1.19x_{2}x_{3}\\ \hskip 14.226378 pt+0.0089x_{1}^{2}+0.9904x_{2}^{2}+0.1902x_{3}^{2}\end{array}  \tag{9}\]  
The variance analysis of the regression equation is given in Table 7. The analysis results reveal that the model \(p\)-values of both repeated-cutting rate (\(Y_{1}\)) and miss-cutting rate (\(Y_{2}\)) are less than 0.01. This obviously indicates that the model has an extremely significant impact, and the regression equation obtained from the fitting of experimentally observed data exhibits a high degree of fit, which can be effectively utilized to carry out the influential analysis of each test factor on the evaluation indicators. The significance test for each test factor, in the repeated-cutting rate \(Y_{1}\) model, shows that the \(p\)-values of \(x_{1}\), \(x_{2}\), \(x_{3}\), \(x_{2}x_{3}\), \(x_{2}^{2}\), and \(x_{3}^{2}\) are less than 0.01, which demonstrates an extremely significant impact. Further, the \(p\)-values of \(x_{1}x_{2}\) and \(x_{1}x_{3}\) are also lower than 0.05, which indicates a significant impact; however, the \(p\)-value of \(x_{1}^{2}\) is more than 0.05, which means no significant impact. Concerning the model for the miss-cutting rate (\(Y_{2}\)), the \(p\)-values of \(x_{1}\), \(x_{2}\), \(x_{3}\), \(x_{1}x_{2}\), \(x_{1}x_{3}\), \(x_{2}x_{3}\), and \(x_{2}^{2}\), are less than 0.01, which indicates the extremely significant impact of the model, whereas the \(p\)-values of \(x_{1}^{2}\) and \(x_{3}^{2}\) are higher than 0.05, which means no significant impact.