# Design and Evaluation of a Shaping and Pruning Machine for Dwarf and Densely Planted Jujube Trees
## 3 Results
### Results of the Quadratic Regression Orthogonal Test
#### 3.1.2 Response Surface Analysis  
The pruning effect was determined by the missed pruning rate and stubble breakage rate when the machine pruned jujube trees. The response surface diagram was drawn using Design-Expert V8.0.6.1 data analysis software in this paper [48]. In addition, the effects for the interaction of experimental factors on the rates of missed pruning and stubble breakage were analyzed. According to variance analysis, the interaction between the rotation speed of the cutter \(X_{1}\) and the diameter of the cutter \(X_{2}\) had a significant influence on the missed pruning rate. After excluding the other non-significant interaction factors, the response surface diagram for the influence of significant interaction factors on the missed pruning rate was generated by Design-Expert 8.0.6.1 data analysis software. Figure 13 shows the response surface diagram of the influence of the interaction between rotation speed of the cutter and diameter of the cutter on the missed pruning rate of jujube trees when the forward speed is at the central level (0.65 m/s). Figure 13 shows that the missed pruning rate decreases when the rotation speed of the cutter increases from 1700 r/min to 2300 r/min. When the rotation speed of the cutter was constant, the missed pruning rate first decreased and then increased as the diameter of the cutter increased from 200 mm to 300 mm. Finally, it could be concluded that the influence of the rotation speed of the cutter on the missed pruning rate was more significant. According to variance analysis, the interaction between the rotation speed of the cutter \(X_{1}\) and the diameter of the cutter \(X_{2}\) as well as the interaction between rotation speed of the cutter \(X_{1}\) and forward speed \(X_{3}\) had significant effects on the stubble breakage rate. After excluding the other non-significant interaction factors, the response surface diagrams of  
Figure 13: Response surface diagram of the influence of significant interaction factors on the missed pruning rate. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Evaluation Indexes** & **Difference Source** & **Sum of Squares** & **Degree of Freedom** & **Mean Square** & **\(F\) Value** & **\(P\) Value** \\ \hline \multirow{3}{*}{Missed pruning rate \(P_{1}\)/\%} & Model & 81.95 & 5 & 16.39 & 119.19 & \textless{}0.0001 \\  & Residual & 1.65 & 12 & 0.14 & & \\  & Lack of Fit & 1.28 & 7 & 0.18 & 2.44 & 0.1713 \\  & Pure Error & 0.37 & 5 & 0.075 & & \\ \hline \multirow{3}{*}{Stubble breakage rate \(P_{2}\)/\%} & Model & 55.39 & 6 & 9.23 & 64.10 & \textless{}0.0001 \\  & Residual & 1.58 & 11 & 0.14 & & \\ \cline{1-1}  & Lack of Fit & 1.07 & 6 & 0.18 & 1.74 & 0.2803 \\ \cline{1-1}  & Pure Error & 0.51 & 5 & 0.10 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Variance analysis table of regression models. the influence of significant interaction factors on the stubble breakage rate were generated, as shown in Figure 14.  
Figure 14a shows the response surface diagram of the influence of the interaction between rotation speed of the cutter and diameter of the cutter on the stubble breakage rate of juibube trees when the forward speed is at the central level (0.65 m/s). It showed that the stubble breakage rate decreased when the rotation speed of the cutter increased from 1700 r/min to 2300 r/min. When the rotation speed of the cutter was constant, the stubble breakage rate first decreased and then increased as the diameter of the cutter increased from 200 mm to 300 mm. It could be concluded that the influence of the rotation speed of the cutter on the stubble breakage rate was more significant. Figure 14b shows the response surface diagram of the influence of the interaction between rotation speed of the cutter and forward speed on the stubble breakage rate of juibube trees when the diameter of the cutter was located at the central level (250 mm). It showed that the stubble breakage rate decreased when the rotation speed of the cutter increased from 1700 r/min to 2300 r/min.