## 5 Results and Discussion
### Effect of Interaction  
Based on the analysis results of Table 4, the quadratic polynomials and the regression model were analyzed; its initial equation is shown in (15). The regression response surface model of BGR and UGR is shown in Equation (16), and the model of BGR and UGR after removing the terms of nonsignificance is shown in Equation (17). In order to observe certain curvature regions and interactions among the three parameters, the response surfaces of Equations (16) and (17) are established, as shown in Figure 13.  
\[\left\{ \begin{array}{l}BGR=Const_{1}+a_{11}A+a_{12}B+a_{13}C+a_{14}AB+a_{15} AC+a_{16}BC+a_{17}A^{2}+a_{18}B^{2}+a_{19}C^{2}\\ UGR=Const_{2}+a_{21}A+a_{22}B+a_{23}C+a_{24}AB+a_{25}AC+a_{26}BC+a_{27}A^{2}+a_{ 28}B^{2}+a_{29}C^{2}\end{array} \right. \tag{15}\]  
\[\left\{ \begin{array}{l}BGR=1.74+1.44A-0.54B+0.34C+0.088 AB-0.14 AC+0.04 BC+0.99A^ {2}+0.44B^{2}+0.56C^{2}\\ UGR=1.38-1.23A+0.36B+0.46C+0.73 AB+0.29 AC-0.29 BC+1.77A^{2}+1.25B^{2}-0.35C^{2} \end{array} \right. \tag{16}\]  
\[\left\{ \begin{array}{l}BGR=1.92+1.44A-0.54B+0.34C+1.01A^{2}+0.59C^{2}\\ UGR=1.97+1.44A-0.54B+0.34C+0.088 AB+1.02A^{2}+0.47B^{2}\end{array} \right. \tag{17}\]  
where \(Const_{1}\), \(Const_{2}\) is the constant value of \(BGR\) and \(UGR\) regression equations, respectively; \(a_{11}\), \(a_{12}\), and \(a_{13}\) are the principal effect coefficients of \(A\), \(B\), and \(C\) for \(BGR\), respectively; \(a_{14}\), \(a_{15}\), and \(a_{16}\) are the interaction coefficients of \(AB\), \(AC\), and \(BC\) for \(BGR\), respectively; \(a_{17}\), \(a_{18}\), and \(a_{19}\) are the quadratic coefficients of \(A^{2}\), \(B^{2}\), and \(C^{2}\) for \(BGR\), respectively; \(a_{21}\), \(a_{22}\), and \(a_{23}\) are the principal effect coefficients of \(A\), \(B\), and \(C\) for \(UGR\), respectively; \(a_{24}\), \(a_{25}\), and \(a_{26}\) are the interaction coefficients of \(AB\), \(AC\), and \(BC\) for \(UGR\), respectively; \(a_{27}\), \(a_{28}\), and \(a_{29}\) are the quadratic coefficients of \(A^{2}\), \(B^{2}\), and \(C^{2}\) for \(UGR\), respectively. Figure 13: _Cont._As shown in the contour map of Figure 13d, (1) the central color is obviously darker than the other figures and it indicates that the interaction of factors A and B on the UGR is more significant, which is consistent with the measurement results. (2) When the C-feeding amount is constant, the BCR gradually increases with an increase of A-cylinder rotational speed and a decrease of B-clearance between the cylinder and the concave plate. This is because the grain is subjected to an increase of collision force during movement, the impact between the ear, the threshing element, and the concave, and the collision between the ear and ear, leading to an increase of BGR, but not the reduction of UGR. (3) When factor B is a constant, the BCR gradually increases with an increase of factor A and factor C. The UGR first decreases and then increases as factor A increases; this is because the smaller factors A and C are, the smaller the impact force between ears and threshing elements; hence, the UGR is larger. When factor A is larger, the UGR will also increase due to the insufficient threshing of the ears. (4) When factor A is a constant, the BCR decreases with an increase of factor B and a decrease of factor C, while the UGR first decreases and then increases with an increase of factor B; this is because a value of factor B that is too large or too small will lead to a failure of threshing the ears. In combination with the ANOVA analysis results in Tables 5 and 6, the effect order of factors like the rotational speed of the cylinder, the clearance of the concave and the cylinder, and feed amount was consistent, just the degree of action was different.