## 4 Discussion  
From a theoretical perspective, one can initially ignore the inter-seed interaction forces and consider the seeds inside the seed metering device as a single seed population to analyze the motion patterns of seeds within a seed metering device. Thus, the problem is simplified to the interaction between the seed population and the seed metering device. Because the seed metering device undergoes sinusoidal vibration due to the action of the eccentric wheel and return spring, its acceleration can be described by the following equation:  
\[a=A\omega^{2}\cos\omega t \tag{6}\]  
where \(a\) represents the acceleration of the seed metering device; \(A\) is the amplitude of the seed metering device's vibration; \(\omega\) is the angular frequency; and \(t\) is time. The seed population inside the seed metering device is subject to the forces of gravity and the vibrational excitation of the seed metering device. If the vibration-induced acceleration exceeds gravitational acceleration, it may cause the seed population to detach from the hole-wheel. This condition is satisfied when the following relationship holds:  
\[A\omega^{2}\cos\omega t>g \tag{7}\]  
Here, \(g\) represents the gravitational acceleration acting on the seed population. Since \(\omega=2\pi\)f, we can express the relationship as follows:  
\[f>\sqrt{\frac{g}{4\pi^{2}A}} \tag{8}\]  
where \(f\) is the vibration frequency of the seed metering device. Figure 7: Sowing performance based on the relationship between vibration frequency and (**a**) seeding quality and (**b**) the seeding uniformity variation coefficient. The seed metering process of the hole-wheel-type seed metering device involves three stages: filling, clearing, and sowing. When the seed metering device operates, the hole-wheel rotates upward in the filling zone. Driven by the rotating hole-wheel, rapeseed seeds form a dynamic circulating seed mass. Under the combined action of gravity, centrifugal force, the support force of the hole-wheel on the rapeseed seeds, the friction between the hole-wheel and the rapeseed seeds, and the pushing force between the seeds, the seeds enter the holes in the wheel in two ways: \"filling space\" and \"scooping\". Therefore, when the vibration frequency of the seed metering device meets the above relationship, the seed population inside the device is intermittently ejected, losing contact with the hole-wheel and creating \"voids\" between the seed mass and the wheel. This causes the seeds that have already filled the holes to be \"flung out\", preventing the wheel from making contact with the seeds and causing it to fail to complete the filling process. Consequently, the discharge rate of the seed metering device decreases, leading to missed seeding and reduced uniformity in seed metering. When the vibration frequency of the seed metering device exceeds 10 Hz, the simulation process clearly shows that seeds are repeatedly ejected from the holes, resulting in a reduced discharge rate as the hole-wheel fails to fill adequately, as shown in Figure 8.  
Based on the research content of this article, the amplitude of vibration for the seed metering device is 3 mm. Inserting this value into the formula, one can calculate that the seed population inside the device will be intermittently ejected when \(f\) > 9.096 Hz. However, due to the interaction forces within the seed population and the friction between the seed population and the seed metering device, the actual vibration frequency needs to be slightly higher than the calculated theoretical vibration frequency to cause intermittent ejection of the seed population. According to the results of the vibration test bench, 10 Hz is the minimum vibration frequency at which the seed population is ejected, which corresponds highly with the theoretical calculations and experimental conclusions. [PERSON] et al.