# 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  
#### 2.3.1 Force Analysis of Residual Film-Impurity Mixtures  
Force analysis (Figure 10) for the residual film-impurity mixture from the feeding device to the first collision stage with the tremmel screen was used to study the movement of the residual film-impurity mixture inside the film-hybrid wind separator.  
Figure 9 shows the residual film-impurity mixture in the wind separator inside the residual film-impurity mixture through the I feeding stage and II cleaning stage. The residual film-impurity mixture was subjected to gravity (mg), friction force (\(f\)), and support force (\(F_{N}\)) during stage I. The direction of displacement of the residual film-impurity mixture was along the inlet slope and downward. There was an acute angle between the direction of gravity and the direction of motion, which resulted in positive work; the direction of friction was opposite to the direction of motion, which resulted in negative work.  
Figure 9: Simulation test: (**a**) schematic diagram of fluid-solid coupling test; (**b**) force diagram of different positions of tumbler screen at different moments.  
The direction of the support force was perpendicular to the direction of motion, resulting in zero work. The law of conservation of energy was represented using Equation (6).  
\[mg\cos\frac{\pi}{4}\cdot l-f\cdot l=\frac{1}{2}{m{v_{1}}^{2}}-\frac{1}{2}{m{v_{1} }^{2}} \tag{6}\]  
Friction occurred due to a collision between the residual film-impurity mixture and the inlet, which offset part of the work done by gravity on the residual film-impurity mixture. Compared to the case of no collision, there was velocity loss. Therefore, when the residual film-impurity mixture was fed into the residual film-impurity mixture wind separator, the collision between the material and the inlet had to be minimized.  
There was a flow field with a horizontal angle \(\alpha=8^{\circ}\) inside the tumbler screen. The velocity of the material entering the device was \(v_{1}\), and the direction was the same as the inlet slope, that is, \(\beta=45^{\circ}\). The residual film-impurity mixture was subjected to vertical downward gravity (mg) and airflow resistance (\(F_{t}\)) relative to the direction of material velocity, 7, during stage II; the direction of airflow resistance was the same as the direction of movement of the material relative to the airflow, and the airflow resistance, \(F_{t}\), was calculated using Equation (7):  
\[F_{t}=\frac{1}{2}CA\rho_{S}\
u^{2} \tag{7}\]  
where \(C\) is the air resistance coefficient; \(A\) is the material windward area (m\({}^{2}\)); and \(\rho_{S}\) is the air density (kg/m\({}^{3}\)).  
As shown in Equation (7), after the material entered the device, in addition to the airflow, which was necessary for clearing the airflow imposed by the air resistance, no other factors affected the speed of the material. Therefore, to ensure maximum speed of the residual film-impurity mixture and the drum sieve collision, the structure of the feed opening should be optimized; this also minimizes the speed loss during the feeding process.