# Design and Experimental Study of the General Mechanical Pneumatic Combined Seed Metering Device
## 3 Key Component Parameter Design and Analysis
### Seed Cleaning Process Analysis
Taking the centroid of the pressed seed in Figure 4 as the origin, the kinematics equations were set following the tangential and normal directions of the seed's movement in the hole:  
\[\left\{ \begin{array}{c}F_{D1}+G=F_{r2}+N_{1}sin\frac{\theta}{2}+N_{2}sin\frac{ \theta}{2}\\ N_{1}cos\frac{\theta}{2}=N_{2}cos\frac{\theta}{2}\end{array} \right\} \tag{7}\]  
where \(F_{D1}\) denotes the force exerted by the cleaning airflow on the seed, \(N\); \(N_{1}\) represents the supporting force of the right wall of the hole on the seed, \(N\); \(N_{2}\) expresses the supporting force of the left wall of the hole on the seed, \(N\). If should be ensured that the seed cleaning airflow could normally press the seeds to the bottom of the hole without being thrown out by the centrifugal force. Then, the sidewall had no force on the seeds. The critical condition for this should meet the following equation:  
\[F_{D1}+G\geq F_{r2} \tag{8}\]  
According to the combination of (6) and (8), if the seeds were not thrown out by the centrifugal force of the feeding drum in the transport area and a seed was pressed to the bottom of the hole in the seed cleaning area, it would be only necessary to meet the requirements of the seed transport area. The conditions were enough to be thrown out by the centrifugal force of the drum. In practical work, the force of the cleaning airflow on the cleaned seeds is illustrated in Figure 5, the airflow force on the pressed seeds exerted a pressing effect on the seeds. After the seed was pressed to the bottom of the hole, the hole was blocked, and the cleaning air could not pass through the hole normally. Thus, the hole could be considered a closed inverted cone. In accordance with the principle of fluid mechanics, the force on the seed cleaned out of the hole was the flow resistance, as expressed below:  
\[F_{D2}=\frac{1}{2}\rho v_{3}^{2}AC \tag{9}\]  
where \(\rho\) denotes the air density, 1.21 kg/m\({}^{3}\); \(A\) represents the windward area of the seed, m\({}^{2}\); \(v_{3}\) expresses the airflow velocity of the seed cleaning, m/s; \(C\) is the dimensionless resistance coefficient, related to the shape of the seed, the surface state and the Reynolds number of the fluid. If the seed was similar to a spherical rigid body, the maximum windward area would be obtained:  
\[A=\frac{\pi d^{2}}{4} \tag{10}\]  
Figure 5: The force map of seeds cleaned out of filling hole. For seeds cleaned through the hole, the resistance of the seeds to the flow might originate from various directions. When the direction of resistance to the flow of the seeds was opposite to the direction of gravity on the seeds, the required air velocity would be the smallest. At this time, the seeds which were stuck in the holes were easiest cleaned by the airflow. Taking this special situation as a prerequisite, the minimum airflow velocity required for seed cleaning could be determined. At this time, the seed was not subject to the force of the side wall, and the force of the seed is illustrated in Figure 5.  
Taking the seed that had been cleaned from the hole as the origin in Figure 5, the critical equation of kinematics was set along the opposite direction of gravity. \[F_{D2}+F_{r3}cos\alpha=G \tag{11}\]  
By combining Equations (5) and (9)-(11), the critical condition for seeds to be cleaned by air flow was calculated as:  
\[v_{3}\geq\sqrt{\frac{8m(g-\omega^{2}rcos\alpha)}{\rho\pi d^{2}C}} \tag{12}\]  
From Equations (8) and (12), whether the seeds could be cleaned is related to the rotation angular velocity \(\omega\) of the drum, the cleaning airflow velocity \(v_{3}\), the cone angle of the hole \(\theta\), the airflow parameters, and the characteristics exhibited by the seed material, etc. Given the previous experiment in this study, the airflow velocity of soybean and corn seed cleaning ranged from 8 m/s to 21 m/s, and the airflow velocity of rapeseed cleaning was 2-12 m/s.