## 2 Materials and Methods
### Cutting Simulation Single-Factor Experiment Results
#### 3.2.4 Quadratic Regression Orthogonal Combination Experimental Results and Analysis
Through the regression equations (Equations (9) and (10)), the order of influence of factors and interactions on the repeated-cutting rate (\(Y_{1}\)) is obtained as \(x_{3}>x_{2}>x_{1}>x_{3}^{2}>x_{2}^{2}x_{2}x_{3}\)\(>x_{1}x_{3}>x_{1}x_{2}>x_{1}^{2}\), and the order of influence on the miss-cutting rate (\(Y_{2}\)) is now derived as  
Figure 17: Contour plots of the influence of various factors on both the repeated-cutting rate and the miss-cutting rate: (**a–c**) Contour graph of repeated-cutting rate; (**d–f**) Contour graph of miss-cutting rate. \(x_{2}>x_{3}>x_{2}x_{3}>x_{2}^{2}>x_{1}>x_{1}x_{2}>x_{1}x_{3}>x_{3}^{2}>x_{1}^{2}\), which is almost consistent with the analysis of variance results. By analyzing the constructed model, the error between the model-adjusted \(R^{2}\) value and the predicted \(R^{2}\) value is within 0.2, and the \(R^{2}\) values are all higher than 0.99. This result reveals that the function model obtained based on both the scientific experimental design and the statistical analysis of data is accurate and reliable. Figure 18a represents the relationship between the predicted and actual values of the repeated-cutting rate of the model constructed in this paper, whereas Figure 18b demonstrates the relationship between the predicted and actual values of the miss-cutting rate of the model constructed in this paper. The plotted results in Figure 18 indicate that the predicted and actual values are very close to each other, which further verifies the accuracy of the constructed model. Therefore, further analyses using the contour plots and the regression equation show that the main factors influencing the repeated-cutting rate of the cutting device operation, in descending order, are forward speed, crank rotation speed, and crank length. Additionally, the chiefly influential factors on the miss-cutting rate of the cutting device operation, in descending order, are crank rotation speed, forward speed, and crank length. In continuing, by removing the non-significant term \(x_{1}^{2}\), which affects the repeated-cutting rate, removing the non-significant terms \(x_{1}^{2}\) and \(x_{3}^{2}\), which affect the miss-cutting rate, and converting the coded values to actual values, the fitting regression equations between the influencing factors and the repeated-cutting rate (\(Y_{1}\)) and the miss-cutting rate (\(Y_{2}\)) are established as follows:  
\[ \begin{array}{ll}Y_{1}=-4.41356&+1.42032x_{1}+0.075461x_{2}-80.44848x_{3}+0.0 00824x_{1}x_{2}\\ &-0.767166x_{1}x_{3}-0.024253x_{2}x_{3}-0.000026x_{2}^{2}+52.97763x_{3}^{2}\\ \\ Y_{2}=8.73978-&0.356588x_{1}-0.041135x_{2}+43.95475x_{3}+0.000862x_{1}x_{2}\\ &-0.762817x_{1}x_{3}-0.029727x_{2}x_{3}+0.000025x_{2}^{2}\end{array}  \tag{11}\]  
Operating Parameter Optimization and Experimental Verification of the Cutting Device 3.3.1. Parameter Optimization  
The results of the quadratic regression orthogonal combination test reveal that the repeated-cutting rate of the cutting device operation ranges from 5.31% to 41.19% and the miss-cutting rate varies from 0.56% to 10.20%. To obtain the optimal combination of  
Figure 18: Plots of the relationship between the model-predicted values and the actual values: (**a**) Relationship between the predicted and actual values of the repeated-cutting rate; (**b**) Relationship between the predicted and actual values of the miss-cutting rate. operating parameters for the cutting device in the orderly harvester for GLVs, the regression model is solved via Design-Expert 13.0.1.0 software with constrained objectives. The performed analyses of the variance results are indicative of the fact that the crank length, the crank rotation speed, the forward speed, and their interactions all have significant effects on the repeated-cutting rate and the miss-cutting rate, and the interaction factors \(x_{2}\) and \(x_{3}\) have more remarkable effects on the repeated-cutting rate and the miss-cutting rate.