# Bionic Design of a Winding Roller and Experiments for Cleaning Long Foreign Matter from Raw Cotton
## 2 Materials and Methods
### Module Design of Multi-Roller Cleaning Device  
To improve the cleaning efficiency of the mechanical device, a multi-roller module was designed. As shown in Figure 3, a standard module includes two feeding rollers and four winding rollers. Each module's side dimension is 600 \(\times\) 600 mm. To meet different cleaning requirement, the multi-module configuration can be arranged in parallel based on the standard module. In this paper, equipment with three modules is proposed. The multi-roller functioning of a standard module is listed as follows:  
1. First stage: cotton feeding. The two above feeding rollers have large dimensions and load-bearing ability. As shown in Figure 4, when the raw cotton is loaded from the upper inlet, the feeding rollers rotate in opposite directions at a low speed of 3-6 r/min. In this case, uniform cotton flow is formed under gravity and extrusion, and is transported downward simultaneously. The forces are mainly loaded on the feeding rollers, which need mechanical calculation. 2. Second stage: LFM rough winding. The adjacent winding roller below each feeding roller has a high rotation speed. The cotton flow mixed with LFM is separated layer-by-layer via interaction with the teeth. Then, the cotton layer is transported by the centrifugal force, and the LFM on the teeth can be cleaned during rotating and winding. Figure 2: Model of a winding roller. 3. Third stage: precise LFM winding. The cotton layer interacts with the teeth of the lower winding rollers again to further clean the LFM, and the cleaning principle is similar to the second stage. When the cleaned cotton layer reaches the outlet, a vacuum tube collects it for the next process. Based on practical experience, the rotating speed of the feeding roller was designed as 3-6 r/min based on the requirements of a stable cotton supply and hard structural stiffness. Here, the key parameter of the equipment is the diameter design of the feeding roller, designed as follows. The weight of the cotton placed on every module is nearly one ton. Because the feeding rollers rotate in opposite directions and the cotton is highly compressed, another one ton of extrusion force is generated. In this paper, the above forces is derived from test data from the Shandong FuHao Optoelectronic Technology Co., Ltd. (Jinan, China). The maximum deflection of the feeding roller is calculated by  
\[\omega_{\text{max}}=\frac{5 qL^{4}}{384 EI}=\frac{5\frac{G+F_{extra}}{L}L^{4}}{384 E\frac{\pi D_{f}^{4}}{32}}=\frac{5(G+F_{extra})L^{3}}{12E\pi D_{f}^{4}}\leq 10\text{ mm} \tag{1}\]  
where \(G\) is the weight of cotton, \(F_{extra}\) is the extrusion force, \(E\) is the elasticity modulus of steel, \(I\) is the inertia moment of the cross section, \(L\) is the length of the feeding roller, \(D_{f}\) is the diameter of the feeding roller, and \(\omega_{\text{max}}\) is the maximum deflection, which is limited to 10 mm as test data for vibration control. If it is over 10 mm, the roller's deflection is obvious and the transmission system overloads. The vibration of the chain is dangerous and unavoidable. Figure 4: Model of a feeding roller. Figure 3: 3-Module design of multi-roller cleaning system. In addition, the diameter can be calculated by a modified equation (Equation (2)), based on Equation (1), as follows:  
\[D\geq\sqrt{\frac{5(G+F_{extru})L^{3}}{12E\pi\omega_{\mathrm{max}}}}=\sqrt{\frac{ 4\frac{5\cdot(10^{4}+10^{4})\cdot 2000^{3}}{12\cdot 210\cdot 10^{9}\pi\cdot 10}}}=56 \;\mathrm{mm} \tag{2}\]  
Therefore, the diameter of the feeding roller is designed as 60 mm. The length and diameter of the feeding teeth are 120 mm and 18 mm (as shown in Figure 3), respectively, which can be calculated from the above procedures considering the equipment dimensions. To separate cotton and wind LFM, the speed of the winding roller is designed with a high value. According to test data, the forces are non-significant design factors and the speed is the most significant factor.