# Design and Optimization of a Toothed-Plate Single-Roller Crushing Device for Waste Plastic Film
## 3 Design and Theoretical Analysis of the Crushing Component
### Design of the Crushing Roller  
Referring to the relevant rotation crushing device [26; 27], the design of the crushing roller structure is shown in Figure 3. For single-roller plastic-crushing devices, the crushing roller outer diameter is generally not greater than 500 mm. Therefore, the diameter of the tooth tip circle, \(d_{3}\), and the roller diameter, \(d_{1}\), were determined to be 450 mm and 280 mm. Based on a tooth height of 45 mm, it was calculated that the diameter of the toothed bottom circle of the crushing roller, \(d_{2}\), is 360 mm. The length of the toothed plate was 400 mm, and three of them were installed along the axial direction of the crushing roller, resulting in the minimum length of the crushing roller \(L\) being 1200 mm.  
The crushing roller rotation speed should be determined by the crushing principle and material characteristics; for the rotation crushing roller with a fixed toothed plate, the rotation speed can be appropriately reduced. Referring to crop stalk crushing [28], the linear speed of the crushing roller teeth was 6 m/s\(\sim\)16 m/s, which was more effective. Combined with the high ductility characteristics of waste plastic film, the linear speed of the crushing roller teeth, \(V_{\omega}\), was designed at 14 m/s. The theoretical rotation speed of the crushing roller was calculated to be 594 r/min according to Equation (1). Regarding the new plastic-crushing device [29], the maximum speed is set at 900 r/min. Thus, taking into  
Figure 3: The crushing roller structure.  
Figure 2: The structure of the toothed plate. (**a**) Moving toothed plate and (**b**) fixed toothed plate.  
account the problem of rotation speed adjustment in the subsequent test, the rotation speed range of the crushing roller was determined to be from 600 r/min to 900 r/min.  
\[\omega=\frac{60V_{\omega}}{\pi d_{3}} \tag{1}\]  
where \(\omega\) is the crushing roller rotation speed, r/min; \(V_{\omega}\) is the linear speed of the crushing roller toothed tip, m/s; and \(d_{3}\) is the diameter of the toothed tip circle, m.  
The number of toothed plates has a great influence on the working stability and crushing performance of the crushing device. At the same rotation speed, there is an optimum value for the number of toothed plates. When there are too few toothed plates, productivity is low, and the number of crushing times by one rotation of the crushing roller also decreases, leading to the problem of waste plastic film being incompletely crushed or oversized crushed film, which enhances the difficulty of cleaning. Conversely, when there are too many toothed plates, the crushed film size is excessively small, making it difficult to collect and separate. Additionally, having too many toothed plates can impede the timely discharge of crushed film, increasing the possibility of blockages. At present, the toothed plates on the crushing roller are mainly arranged in a spiral pattern, which has a simple structure and a better crushing performance for the material. Thus, three types of crushing rollers were designed, as shown in Figure 4. The toothed plates of the three types were all arranged in a spiral pattern, with the number of toothed plates being the distinguishing factor. Figure 4a-c represent the crushing roller with 6, 12, and 18 toothed plates, referred to as T\({}_{1}\)-, T\({}_{2}\)-, and T\({}_{3}\)-type crushing rollers, respectively.