# Bionic Design of a Winding Roller and Experiments for Cleaning Long Foreign Matter from Raw Cotton
## 4 Results and Discussion  
As shown in Figure 7, the developed LFM cleaning equipment is able to gather and clean all of the LFM at intervals. The cotton can be fed from the top rollers and cleaned by the winding rollers. Moreover, jamming among teeth can be avoided owing to the comb-like structure. For every experiment, 20 g of LFM, including long hair, plastic films, chemical fibers, and polypropylene twins were mixed uniformly into one ton of raw cotton, and every experiment was repeated three times to obtain authentic results. Because the speed of the feeding roller is determined by the moisture content of the cotton, it has large influence on the extrusion force and feeding efficiency. As shown in Tables 3 and 4, nine experiments were carried out based on the \(L_{9}(3^{4})\) matrix with uniform moisture content value (10%) and speed of feeding roller (5 r/min). In a range analysis, there are two parameters, denoted by \(K_{ji}\) and \(R_{j}\). Here, \(K_{ji}\) is defined as the sum of the indexes of all levels at each factor \(j\), \(\overline{K}_{ji}\) is the average value of each experimental factor at the same level \(i\), \(R_{j}\) is defined as the range between the maximum and minimum value of \(K_{ji}\), and \(K_{ji}\) is used to evaluate the importance of the factors. If \(R_{j}\) is larger, this indicates greater importance of the factor. For example, for the \(L_{9}(3^{4})\) matrix, the calculation for factor \(D\) is as shown below:  
\[K_{D1}=Y_{1}+Y_{2}+Y_{3} \tag{3}\]  
\[K_{D2}=Y_{4}+Y_{5}+Y_{6} \tag{4}\]  
\[K_{D3}=Y_{7}+Y_{8}+Y_{9} \tag{5}\]  
\[\overline{K}_{D1}=\frac{K_{D1}}{3} \tag{6}\]  
\[\overline{K}_{D2}=\frac{K_{D2}}{3} \tag{7}\]  
\[\overline{K}_{D3}=\frac{K_{D3}}{3} \tag{8}\]  
\[R_{j}=\max(\overline{K}_{Di})-\min(\overline{K}_{Di}) \tag{9}\]  
where \(K_{Di}\) is the value of level \(i\) of factor \(D\) and \(Y_{i}\) is the value of the trial number \(i\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Factors**} & \multicolumn{3}{c}{**Level**} \\ \hline
**Parameters** & **Abbreviation** & **1** & **2** & **3** \\ \hline Tooth Diameter & D (mm) & 5 & 6 & 8 \\ Tooth Length & L (mm) & 50 & 60 & 70 \\ Teeth spacing & S (mm) & 60 & 70 & 80 \\ Shaft speed & V (r/min) & 300 & 400 & 500 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Levels and factors affecting LFM cleaning quality. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **D** & **L** & **S** & **V** & **Collected LFMs Amount (g/ton)** \\ \hline
1 & 5 & 50 & 60 & 300 & 12.2 \\
2 & 5 & 60 & 70 & 400 & 13.3 \\
3 & 5 & 70 & 80 & 500 & 15 \\
4 & 6 & 50 & 70 & 500 & 15.6 \\
5 & 6 & 60 & 80 & 300 & 13.2 \\
6 & 6 & 70 & 60 & 400 & 16.7 \\
7 & 8 & 50 & 80 & 400 & 15.1 \\
8 & 8 & 60 & 60 & 500 & 13.4 \\
9 & 8 & 70 & 70 & 300 & 15.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Scheme and results of orthogonal experiments. As shown in Table 3, the LFM amount varied from 12.2 to 16.7 g/ton. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Value Name** & **D** & **L** & **S** & **V** \\ \hline \(\overline{K}_{1}\) & 13.50 & 14.30 & 14.10 & 13.67 \\ \(\overline{K}_{2}\) & 15.17 & 13.30 & 14.83 & 15.03 \\ \(\overline{K}_{3}\) & 14.70 & 15.77 & 14.43 & 14.67 \\ \(R_{j}\) & 1.67 & 2.47 & 0.73 & 1.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Range analysis data. Figure 7: Photo of the designed equipment and LFM cleaning. The test shows the mean values of \(\overline{K}_{ji}\) for different factors with different levels, demonstrating that the higher the mean value of \(\overline{K}_{ji}\) is, the more significant the effect on LFM cleaning quality. Therefore, the best levels of the four factors corresponding to the highest value of \(K_{ji}\) are listed as follows: tooth diameter 6 mm, tooth length 70 mm, teeth spacing 70 mm, and rotating speed of the roller shaft 350 r/min. In addition, the value of \(R_{j}\) demonstrates the significance of the four factors' influence. More specifically, a larger \(R_{j}\) means a more significant effect on the LFM cleaning quality.