# Design and Test of Vertical Axis Rotating Cutters for Cutting Corn Roots and Crown
## 2 Materials and Methods
### Methods
#### 2.2.2 Full-Factorial Test  
The forward speed of the JD2C-354 tractor is proportional to the rotational speed of the power output shaft, and the relationship between them was obtained by the calibration  
Figure 4: The simulation model of cutters–soil–root–crown. Figure 3: The physical parameters of particles in the simulation. experiment as shown in Equation (6). Through the field pre-test and referring to the Agricultural Machinery Design Manual, the range of the rotational speed of the cutter shaft in the full factor test was determined. The specific forward speeds of the device were obtained based on a calibrated relationship within the rotational speed range of 380 r\(\cdot\)min\({}^{-1}\) to 540 r\(\cdot\)min\({}^{-1}\). The excessive levels in the test might lead to minimal data variation, obscuring outcome differences. Conversely, insufficient levels could introduce excessive data variations, compromising result accuracy and credibility. After comprehensive analysis, five levels were ultimately selected for each factor [30; 31]. \[f(x_{6})=225.92\ln^{x_{6}}+458.39\qquad\left(R^{2}=0.978\right) \tag{6}\]  
where \(f(x_{6})\) is the rotational speed of the cutter shaft (r\(\cdot\)min\({}^{-1}\)) and \(x_{6}\) is the forward speed of the device (m\(\cdot\)s\({}^{-1}\)). To optimize the parameter combination for cutting the root-crown, it was essential to ensure cutting efficiency while minimizing soil disturbance and power consumption. A full-factorial test was designed with forward speed of the device (0.71 m\(\cdot\)s\({}^{-1}\), 0.84 m\(\cdot\)s\({}^{-1}\), 1.01 m\(\cdot\)s\({}^{-1}\), 1.20 m\(\cdot\)s\({}^{-1}\), 1.43 m\(\cdot\)s\({}^{-1}\)) and the rotational speed of the cutter shaft (380 r\(\cdot\)min\({}^{-1}\), 420 r\(\cdot\)min\({}^{-1}\), 460 r\(\cdot\)min\({}^{-1}\), 500 r\(\cdot\)min\({}^{-1}\), 540 r\(\cdot\)min\({}^{-1}\)) as test factors. The qualified rate of root-crown length, the rate of soil disturbance, and the power consumption of the device were selected as indicators. The full-factorial test design is shown in Table 1, with three replicates per group. Through the EDEM post-processing module, the total number of root-crown particles before cutting was denoted as \(S_{1}\), and the number of root-crown particles failing to meet the length requirements after cutting was denoted as \(S_{2}\). The qualified rate of root-crown length \(y_{1}\) in the simulation was calculated via Equation (7):  
\[y_{1}=\left(1-\frac{S_{2}}{S_{1}}\right)\times 100\% \tag{7}\]  
where \(y_{1}\) is the qualified rate of root-crown length in the simulation test. \(S_{1}\) is the total number of root-crown particles. \(S_{2}\) is the total number of root-crown particles that failing to meet the requirements of the cut length. During the process of cutting the root-crown, the disturbed distance by the device was divided into five equidistant segments. The cross-sectional curve of the ridge soil was intercepted, and the cross-sectional areas of each segment were calculated using MATLAB as \(v_{1}\), \(v_{2}\), \(v_{3}\), \(v_{4}\), \(v_{5}\). The volume of the ridge soil was measured as \(v_{0}\). The rate of soil disturbance \(y_{2}\) was calculated via Equation (8). The quintile cross-sectional analysis method was employed to quantitatively characterize the soil disturbance effects during root-crown cutting. However, this method still exhibited significant limitations. Since the ridge was a three-dimensional structure, the disturbance areas were calculated through this method based solely on two-dimensional cross-sections, thereby failing to comprehensively reflect the actual disturbance conditions across the entire ridge. Additionally, the method relied \begin{table}
\begin{tabular}{c c c} \hline \hline
**Test Level** & **Forward Speed of Device (m\(\cdot\)s\({}^{-1}\))** & **Rotational Speed of Cutter Shaft (r\(\cdot\)min\({}^{-1}\))** \\ \hline
1 & 0.71 & 380 \\
2 & 0.84 & 420 \\
3 & 1.01 & 460 \\
4 & 1.20 & 500 \\
5 & 1.43 & 540 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Full-factorial test.