# Design and Optimization of a Toothed-Plate Single-Roller Crushing Device for Waste Plastic Film
## 5 Analysis and Verification of Crushing Test Results
### Influence of Interaction Factors on Indicators  
(1) The influence of interaction factors on the size qualification rate of crushed film  
As shown in Figure 10, the response surface and contour were generated using Design-Expert 12.0 software to analyze the effects of the feeding speed, the number of toothed plates, and the crushing roller rotation speed on the size qualification rate of crushed film. Figure 10a-c represent the response surface for the effects of \(X_{1}X_{2}\), \(X_{1}X_{3}\), and \(X_{2}X_{3}\) on \(Y_{1}\), respectively. The contours of the three figures are all elliptical, indicating a strong interaction between any two factors. From Figure 10a, it can be observed that when \(X_{1}\) is 0.25 m/s, \(Y_{1}\) initially increases from 74.11% to 85.52% and then decreases to 81.64% with increasing levels of \(X_{2}\). Similarly, when \(X_{1}\) is 0.4 m/s, \(Y_{1}\) initially exhibits an increase from 80.05% to 87.58% and then decreases to 80.47% as the \(X_{2}\) level increases. The curvature of the surface in the direction of \(X_{2}\) is more pronounced than that of \(X_{1}\), indicating that \(X_{2}\) has a more significant impact on \(Y_{1}\), consistent with the previous variance analysis results. This is because, at a constant feeding speed, a higher number of toothed plates can lead to excessive crushing of waste plastic film. Conversely, a lower number of toothed plates can result in incomplete crushing of waste plastic film. Both can lead to a lower size qualification rate of crushed film. Figure 10b shows that when \(X_{3}\) is 600 r/min, \(Y_{1}\) continuously increases from 79.18% to 89.01% as the \(X_{1}\) level increases, and conversely, when \(X_{3}\) is 900 r/min, \(Y_{1}\) continuously decreases to 85.92% as the \(X_{1}\) level increases. Figure 10c reveals that when \(X_{3}\) is at 600 r/min, \(Y_{1}\) initially increases from 76.70% to 84.18% and then decreases to 78.35% as the \(X_{2}\) level increases, and when \(X_{3}\) is at 900 r/min, \(Y_{1}\) initially exhibits an increase from 75.57% to 88.83% and then decreases to 84.26% as the \(X_{2}\) level increases. Additionally, from the number of contour lines, it can be seen that at lower rotation speeds, the number of teeth has a greater impact on \(Y_{1}\). The curvature of the surface in the direction of \(X_{2}\) is more pronounced than that of \(X_{3}\), indicating that \(X_{2}\) has a more significant effect on \(Y_{1}\), consistent with the variance  
Figure 10: Response surfaces and contours for the effect of interaction factors on \(Y_{1}\). (**a**), (**b**) and (**c**) show the interaction effect of \(X_{2}X_{1}\), \(X_{3}X_{1}\) and \(X_{3}X_{2}\) on \(Y_{1}\), respectively. analysis results. This is because at a higher crushing roller rotation speed, the region of crushing is approximately cylindrical, and the influence of the number of toothed plates on the crushing effect is \"masked\" by the high roller rotation speed. (2) The influence of interaction factors on the impurity content of crushed film  
To investigate the impact of interaction factors on the impurity content of the crushed film, the response surface and contour of the impurity content were created, as shown in Figure 11. Figure 11a-c represent the response surfaces for the interaction effects of \(X_{1}X_{2}\), \(X_{1}X_{3}\), and \(X_{2}X_{3}\) on \(Y_{2}\), respectively. The contours for \(X_{1}X_{2}\) and \(X_{2}X_{3}\) are both elliptical, indicating a strong interaction between \(X_{1}\) and \(X_{2}\), as well as \(X_{2}\) and \(X_{3}\). From Figure 11a, it can be observed that when \(X_{2}\) is 6, there is little change in the value of \(Y_{2}\) with an increase in the \(X_{1}\) level. However, when \(X_{2}\) is 18, an increase in the \(X_{1}\) level results in a continuous increase from 15.04% to 18.33% in \(Y_{2}\).