## 3 Results  
### Model Establishment and Significance Test  
The test results are shown in Table 2 (\(X_{1}\), \(X_{2}\), and \(X_{3}\) are the factor code values), and the regression fitting analyses of the impurity content and the insect impurity rate were conducted using the Design-Expert 8.0.6 software. The regression equations of the impurity content \(Y_{1}\) and the insect rate \(Y_{2}\) were established to conduct the significance test and analysis of the three factors for the test indicators. Lastly, the quadratic polynomial response surface regression model of the significant test factors and evaluation indicators was obtained. The model significance test results are listed in Table 3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Code Value**} & \multicolumn{3}{c}{**Factors**} \\ \cline{2-4}  & **Drum Rotation** & **Nail Tooth Speed** & **Roller Screen** \\  & **Speed** & **nclination** & **nclination** \\  & **x1/(r\_min\({}^{-1}\))** & **x2/(r\_min\({}^{-1}\))** & **x3/(\({}^{\circ}\))** \\ \hline \(-1\) & 38 & 10 & 5 \\
0 & 48 & 25 & 10 \\
1 & 58 & 40 & 15 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Test factor code.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number** & \(X_{1}\) & \(X_{2}\) & \(X_{3}\) & \(Y_{1}\)/\% & \(Y_{2}\)/\% \\ \hline \(1\) & \(-1\) & \(-1\) & 0 & 8.1 & 3.3 \\ \(2\) & \(1\) & \(-1\) & 0 & 10.2 & 2.8 \\ \(3\) & \(-1\) & 1 & 0 & 9.7 & 2.7 \\ \(4\) & \(1\) & 1 & 0 & 9.5 & 2.2 \\ \(5\) & \(-1\) & 0 & \(-1\) & 6.5 & 2.4 \\ \(6\) & \(1\) & 0 & \(-1\) & 7.3 & 2.3 \\ \(7\) & \(-1\) & 0 & 1 & 6.3 & 3.5 \\ \(8\) & \(1\) & 0 & 1 & 7.3 & 2.3 \\ \(9\) & \(0\) & \(-1\) & \(-1\) & 8.4 & 1.1 \\ \(10\) & \(0\) & \(1\) & \(-1\) & 9.2 & 1.1 \\ \(11\) & \(0\) & \(-1\) & 1 & 7.8 & 1.8 \\ \(12\) & \(0\) & 1 & 1 & 8.3 & 1.1 \\ \(13\) & \(0\) & 0 & 0 & 5.2 & 1.5 \\ \(14\) & \(0\) & 0 & 0 & 5.9 & 1.9 \\ \(15\) & \(0\) & 0 & 0 & 5.6 & 1.7 \\ \(16\) & \(0\) & 0 & 0 & 5.3 & 1.6 \\ \(17\) & \(0\) & 0 & 0 & 5.7 & 1.8 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Test design and response results.  
In accordance with Table 3, the response surface models \(P_{1}\) and \(P_{2}\) of the impurity content and the insect rate are both less than 0.0001, indicating that the regression model is extremely significant. The lack of fit was 0.5025 and 0.5413, respectively, both being greater than 0.05. The lack of fit was not significant. In other words, the quadratic regression equation fitted by the model was highly consistent with the actual test, which reflects the relationship between the impurity content \(Y_{1}\), the insect rate \(Y_{2}\), and \(X_{1}\), \(X_{2}\), and \(X_{3}\). The working parameters of the BSF sand can be effectively optimized by the regression model.  
The regression equation of the impurity content is:  
\[Y_{1}=5.54+0.46X_{1}+0.27X_{2}-0.21X_{3}-0.58X_{1}X_{2}+0.05X_{1}X_{3}-0.075X_{ 2}X_{3}+1.13X_{1}{}^{2}+2.71X_{2}{}^{2}+0.18X_{3}{}^{2} \tag{22}\]  
The regression equation of the insect rate is:  
\[Y_{2}=1.70-0.29X_{1}-0.24X_{2}+0.23X_{3}-0.28X_{1}X_{3}-0.17X_{2}X_{3}+1.20X_{ 1}{}^{2}-0.15X_{2}{}^{2}-0.27X_{3}{}^{2} \tag{23}\]  
By analyzing the \(p\) value of each factor, the effect of each factor on the impurity content, in descending order, is: the rotation speed of the trimmed screener, the speed of the spike teeth, and the inclination of the trommel screen. The effect of each factor on the insect rate, in descending order, is: the rotation speed of the trommel screener, the speed of the spike teeth, and the inclination of the trommel screen.