## 3 Design of Main Working Parts
### Rotary Tillage Soil-Covering Device
#### 3.3.2 Analysis of Axial Soil-Transporting Performance of Rotary Tillage Knife  
In order to ensure the axial covering range of soil while the rotary tillage knife tilts soil, it is necessary to determine the mechanical conditions of soil axial movement. The force of rotary tillage is mainly determined by the structural parameters and soil parameters of rotary tillage. Suppose that there is no relative displacement of soil particles on the rotary tillage knife and there is no interaction between the soil particles. Figure 12 shows the spatial mechanical analysis of a single soil particle at the moment of separation. Taking the center line of the blade axis as the origin \(O_{1}\), the direction of the center line of the blade axis as \(x_{1}\), the direction of the machine as \(y_{1}\) and the direction of the vertical horizontal plane as \(Z_{1}\), the origin of the coordinate system \(O_{1}\) is translated along the plane \(y_{1}O_{1}z_{1}\) to the center of the soil particle \(O_{2}\) to obtain the spatial coordinate system. Supposing the instantaneous motion direction of the soil particle when it breaks away from the tangent plane of the rotary tillage blade \(A_{z1}\), is it can be concluded that, at the moment it breaks away from the tangent plane of the rotary tillage knife, it is affected by the comprehensive action of normal force \(F_{n}\), friction force\(f_{1}\), gravity \(G_{1}\), and centrifugal force \(F_{c}\). The stress of soil particles in \(x_{2}o_{2}z_{2}\) the coordinate system is decomposed into the coordinate system, as shown in Figure 13, and the resultant forces of soil particles along the direction of \(x_{2}\) and \(z_{2}\) are, respectively,  
\[\left\{ \begin{array}{l}F_{x2}=\dfrac{F_{c}\cos\alpha_{1}+G_{1}}{\cos\beta_{2 }}\sin\beta_{2}-f_{1}\cos\beta_{2}\sin\gamma_{1}\\ F_{z2}=F_{n}\cos\beta_{2}-F_{c}\cos\alpha_{1}-G_{1}\end{array} \right. \tag{23}\]  
where \(\alpha_{1}\) is rotation angle of the cutter shaft when a soil particle is detached, (\({}^{\circ}\));  
\(\beta_{2}\) is the angle between the surface of \(x_{2}o_{2}z_{2}\) and the tangent edge of the rotary tillage blade, (\({}^{\circ}\));  
\(\gamma_{1}\) is the angle between the projection of \(A_{z1}\) on the surface of \(x_{2}o_{2}z_{2}\) and \(y_{2}\) the axis, (\({}^{\circ}\));  
\(F_{x2}\) is the resultant force of soil particles along the \(x_{2}\) axis, (N);  
\(F_{z2}\) is the resultant force of soil particles along the \(z_{2}\) axis, (N). Figure 12: Spatial force of a single soil particle. The expressions of centrifugal force \(F_{c}\), gravity \(G_{1}\), and friction \(f_{1}\) are put into Equation (23) to obtain  
\[F_{x2}=-\left(m\omega_{1}{}^{2}R\cos\alpha_{1}+mg\right)\cot\theta-\mu_{1}\left( m\omega_{1}{}^{2}R\cos\alpha_{1}+mg\right)\sin\gamma_{1} \tag{24}\]  
where \(m\) is the mass of soil particles (kg);  
\(R\) is the rotation radius of soil particle movement (mm);  
\(\mu_{1}\) is the friction factor between the soil particle and surface of the rotary tillage knife;  
\(g\) is acceleration of gravity (m/s\({}^{2}\));  
\(\theta\) is the angle of the tangent edge bend. In Equation (24), the relation between \(\beta_{2}\) (the surface of \(x_{2}o_{2}y_{2}\) and the tangent edge of the rotary tillage knife) and \(\theta\) (the bending angle of the tangent edge) is \(\beta_{2}=\theta-\pi/2\), and the angle of the tool shaft \(\alpha_{1}\) ranges from 0\({}^{\circ}\) to 90\({}^{\circ}\)[27]. In order to determine the axial motion displacement conditions of soil particles, it is necessary to determine the motion process after the action of the rotary tillage knife on soil particles. Setting the action time of the rotary tillage knife on soil particles as \(t_{1}\), the component speed along the direction of \(x_{2}\) at the moment when the soil particles leave the positive section of the rotary tillage blade as \(v_{x}\) and the component speed along the direction of \(z_{2}\) as \(v_{z}\), it can be obtained from the momentum theorem that  
\[\left\{