## 3 Structure Design of Threshing Cylinder
### Analysis of Factors of Influence on Quality of Threshing Cylinder  
Clarifying the influence factors of the threshing process is an important prerequisite for reducing BGR and UGR. Based on the model of ears in the threshing device during the threshing process, the force of the rasp bar on an ear was analyzed, as shown in Figure 4.  
Figure 3: Diagram of threshing elements. (**a**) Diagram of rasp bar; (**b**) diagram of straight separating bar; (**c**) diagram of spiral excretion rod.  
According to [PERSON]'s second law, the force of an ear impacted by threshing elements F was calculated by Equation (3).  
\[\left\{\begin{array}{l}N\cos\alpha=G+f_{1}\sin\theta+f_{2}\\ F=N\sin\alpha+f_{1}\cos\theta\\ G=mg\\ f_{1}=\mu_{1}N\\ f_{2}=\mu_{2}F\end{array}\right. \tag{3}\]  
\[F=\frac{G(\sin\alpha+\mu_{1}\cos\alpha)}{\cos\alpha(1-\mu_{1}\mu_{2})-\sin \alpha(\mu_{1}+\mu_{2})} \tag{4}\]  
where \(N\) is the holding power of the concave to the ear, \(N\); \(F\) is the holding power of the threshing element to the ear, \(N\); \(f_{1}\) is the friction between the threshing element and the ear, \(N\); \(\mu_{1}\) is the friction coefficient of the threshing element; \(f_{2}\) is the friction between the concave and the ear, \(N\); \(\mu_{2}\) is the friction coefficient of the concave; \(G\) is the gravity of the ear, \(N\); \(m\) is the weight of the ear, g; \(g\) is the gravitational acceleration, 9.8 m/s\({}^{2}\); \(\alpha\) is the angle between force \(N\) and vertical ground, (\({}^{\circ}\)); \(\theta\) is the angle between force \(f_{1}\) and gravity \(G\), (\({}^{\circ}\)).  
From Equation (3), the force \(F\), as well as angle \(\alpha\), are related to friction \(f_{1}\) and angle \(\theta\), where \(\alpha\) and \(\theta\) are complementary. The changing trend of force \(F\) under different friction coefficients, \(\mu_{1}\) and \(\mu_{2}\), is shown in Figure 5.  
As shown in Figure 5, the changing trend of force \(F\) with angle \(\alpha\) is the same when friction coefficients of the threshing element and the concave were different. The maximum value \(Fmax\)  
Figure 4: Model of maize threshing.  
Figure 5: Change rules of force \(F\) with angle \(\alpha\) when \(\mu_{1}\) and \(\mu_{2}\) are different values.  
occurred when angle \(\alpha\) is a constant value, the force \(F\) gradually increases when friction coefficients increase, and curve \(\mu_{1}\) + 0.685 \(\mu_{1}\mu_{2}\) + 0.96 \(\mu_{2}\) = 0.629 (when the value of \(F\) was 150 N in Equation (4)) as the boundary rapidly rises. According to existing literature and previous test results, the maximum destructive power of grain was at the range of 86.5-150 N; this should be considered when selecting materials of the threshing element and the concave. Thus, the threshing element and the concave were made of 50 Mn structural steel and welded to the threshing cylinder through the base. The friction coefficient between 50 Mn structural steel with spray coating and corn was tested as 0.28.  
In order to determine installation parameters of the threshing element, the movement time of ear \(t\) in the threshing device was calculated as Equation (5).  
\[t=\frac{D}{v\sin(\arctan\frac{np}{\pi D})} \tag{5}\]  
where \(D\) is the diameter of the cylinder, mm; \(v\) is the velocity of an ear in the threshing device, m/s; \(n\) is the number of threshing element screw heads; \(p\) is the installation pitch of the threshing elements, mm.  
The relationship between the number of heads \(n\), pitch \(p\), and the length of a spiral l is shown in Figure 7, where the X axial is the number of spirals \(n\), the Y axial is the installation pitch \(p\). Length l gradually decreased with increasing values of \(n\) and \(p\). Equation (5) explains that the less time required for threshing, the higher the threshing efficiency when the velocity of an ear is a constant value.  
Figure 6: Change rule of force \(F\) of an ear with friction coefficient \(\mu_{1}\) and \(\mu_{2}\) when \(\alpha\) is 54.5\({}^{\circ}\).