## 3 Design of Main Working Parts
### Rotary Tillage Soil-Covering Device
\tag{15}\]  
where \(x_{0}\) is the pitch of soil cutting, and its coordinates meet  
\[x_{0}=\frac{2\pi V_{m}}{Z\omega_{1}} \tag{16}\]  
where:  
\(Z\) is the number of rotary tillage knives in the same direction, 3. By synthesizing Equations (13)-(16), it can be calculated that the soil-cutting area \(S\) is  
\[S=\!\!\int_{0}^{h_{a}}x_{2(y)}dy-\!\!\int_{0}^{h_{a}}x_{1(y)}dy \tag{17}\]  
Figure 11: Area of soil cut by rotary tillage blade. From the equation, times \(t_{1},t_{3},t_{4},\) and \(t_{5}\) of the rotary tillage knife passing through \(P_{1}\), \(P_{3}\), \(P_{4}\), and \(P_{5}\) can be calculated as  
\[\left\{ \begin{array}{l}\omega_{1}t_{1}=\sin^{-1}(1-\frac{h_{a}}{R})\\ t_{3}=\frac{\pi}{2\omega_{1}}\\ t_{4}=\frac{7\pi}{6\omega_{1}}\\ t_{5}=t_{1}+\frac{2\pi}{3\omega_{1}}\end{array} \right. \tag{18}\]  
where: \(t\) is time (s);  
\(h_{a}\) is the tillage depth (mm);  
\(R\) is the radius of the rotary tillage knife (mm);  
\(\omega_{1}\) is the angular speed of the rotary tillage blade (rad/s). Combined with Equations (17) and (18), the soil-cutting area \(S\) can be calculated as  
\[S= \frac{A\cos 2\omega_{1}t_{1}+B\sin 2\omega_{1}t_{1}+C\cos\omega_{1}t_{1}+D \sin\omega_{1}t_{1}-\frac{1}{2}R^{2}t_{1}+E}{\omega_{1}} \tag{19}\]  
where:  
\[\left\{ \begin{array}{l}A=\frac{(\omega_{1}+\sqrt{3})R^{2}}{8\omega_{1}}\\ B=\frac{(1+\sqrt{3}\omega_{1})R^{2}}{8\omega_{1}}\\ C=\frac{3\sqrt{3}+3\omega_{0}R+3 RV_{m}-3\sqrt{3}\omega_{1}RV_{m}t_{1}-2\sqrt{3} RV_{m}}{6\omega_{1}}\\ D=\frac{3-3\sqrt{3}RV_{m}t_{1}-3\sqrt{3}\omega_{0}R+2\pi RV_{m}+3\omega RV_{m} t_{1}+3\sqrt{3}RV_{m}}{6\omega_{1}}\\ E=\frac{12\sqrt{3}+14\pi RV_{m}-(6\pi+3\sqrt{3}+3\omega_{1})R^{2}-12\sqrt{3} \omega_{0}R}{24\omega_{1}}-\frac{2 RV_{m}+\sqrt{3}\pi RV_{m}}{4\omega_{1}{}^{2}} \end{array} \right. \tag{20}\]  
The area of soil cut by a single rotary tillage knife in one rotation cycle can be approximately calculated as the product of the area of soil cutting and the thickness of soil cutting \(T\), and the formula for calculating the thickness of soil cutting \(T\) is [27]  
\[T=L_{1}\sin(\pi-\theta) \tag{21}\]  
where \(L_{1}\) is the cutting length of the rotary tillage knife's tangent edge, mm;  
\(\theta\) is the angle of the tangent edge. According to Equations (19) and (21), the covering volume \(V\) of a seedbed soil-covering belt for one rotation of the blade pivot is  
\[ \begin{array}{l}V=TSZ\\ =\frac{3L_{1}\sin\theta}{\omega_{1}}\Big{[}A\cos 2\omega_{1}t_{1}+B\sin 2 \omega_{1}t_{1}+C\cos\omega_{1}t_{1}+D\sin\omega_{1}t_{1}-\frac{1}{2}R^{2}t_{1 }+E\Big{]}\end{array}  \tag{22}\]  
According to Equations (18), (20) and (22), the volume of disturbed soil \(V\) is related to such parameters as \(\omega_{1}\), \(R\), \(L_{1}\), \(\theta\), \(h_{a}\), \(Z\), and \(V_{m}\). When the parameters of the rotary tillage knife are determined, \(R\), \(L_{1}\), and \(\theta\) are fixed values, so the amount of soil of the seedbed is mainly affected by the depth of tillage \(h_{a}\), rotary angular speed \(\omega_{1}\), numbers of rotary tillage knives \(Z\), and forward speed of the machine \(V_{m}\). When the forward speed of the machine \(V_{m}\) is certain, the rotation angular speed and tillage depth are the main factors affecting the soil thickness. Therefore, the adjustment of the depth of rotary tillage is taken into consideration in the design of the component.