# Analysis of Feed Inlet and Optimal Feeding Amount of Waste Ground Film Impurity Removal Equipment
## 2 Materials and Methods
### Optimal Structural Form and Feeding Volume Determination
#### 2.3.3 Optimal Structural Form and Feeding Volume Determination  
Various forms of inlet structures were simulated. The simulation feeding amount was set according to the proportion of each material mass in the real residual film-impurity mixture. The monitoring area was set up at the position of the red solid line box shown in Figure 9a. The maximum values of the forces on the trommel screen at each moment were determined for each inlet structure. The average value of the statistical results was used as the basis to draw the bar graph shown in Figure 13. The difference between the maximum value and the average value was used as the reference for the error bar. Figure 11: Different forms of inlet area. Figure 12: Feed inlet 3D model: (**a**) square; (**b**) oval; and (**c**) semi-circular inlets. As shown in Figure 13, the overall force of the trommel screen increased and then decreased. At a small feeding volume, the volume of the residual film-impurity mixture agglomerates was small, and the number of materials was small, resulting in a smaller collision force. At a larger feeding volume, the fed residual film-impurity mixture collided with the edge of the feed opening, leading to serious velocity loss and resulting in a smaller collision force. When a square inlet was used, the larger inlet area resulted in more material feeding and no speed loss during the feeding process. At a large feeding volume of 200 kg/h, the maximum force during the operation of the trommel screen was 3.632 N. When an oval inlet was used, the inlet area was the smallest. Because of this, the size of the agglomerates of the residual film-impurity mixture was limited by the decreased feed rate, and the larger agglomerates could not be fed smoothly. The maximum force during the operation of the trommel screen was 3.047 N at a feed rate of 150 kg/h. When the feed opening was semi-circular, the area of the feed opening was between that of the square and oval ones. Compared to the square feed opening, the structure had a rounded boundary, resulting in challenges with material feeding. The structure had a rounded boundary, which avoided collisions during the material feeding process. Compared with the oval inlet, the semi-circular structure had a larger area, allowing more material to be fed. Therefore, the generated force was between those of the above two structures. The maximum force during the operation of the trommel screen was 3.392 N at a feed rate of 200 kg/h. The maximum collision force at all times during the operation of the integrated trommel screen was investigated for different inlet structures. For the square inlet and a feeding volume of 200 kg/h, the collision force between the residual film-impurity mixture agglomerate and the tumbler screen surface was the largest; that is, the agglomerates of the residual film-impurity mixture were most likely to be decluttered. To study the optimal feeding rate of the residual film-impurity mixture under the square feeding port condition, the parameters were further optimized in the range of 150-250 kg/h. The maximum values of the forces on the trommel screen at each moment under different feeding conditions were obtained. The average value was calculated, and a scatter plot was plotted as shown in Figure 14. A curve fit was performed [24; 25; 26; 27; 28]. According to the imported data, the fitting equation was set as a quadratic equation: and the curve was fitted repeatedly. The best fit was achieved when the reduced residual sum of squares (RSSs) was constant. At this point, \(a=-3.58857\times 10^{-4}\), \(b=0.1453\), \(c=-12.46171\), and \(R^{2}\) was 0.99436. The fitted curve equation was given using Equation (8):  
\[y=-0.000358857x^{2}+0.1453x-12.46171 \tag{8}\]  
Figure 13: Trommel screen forces at different feed rates. The quadratic equation was solved when \(x=202.45\), \(y\) had the maximum value of 2.25, and the parameters were rounded.