# Design and Test of Vertical Axis Rotating Cutters for Cutting Corn Roots and Crown
## 2 Materials and Methods
### Materials
#### 2.1.1 Preparation of Soil and Root-Crowns
The 0-3 cm soil layer was defined as the shallow soil layer. This layer, being the uppermost, is most susceptible to being disturbed, and it plays a protective role for the soil. Therefore, when designing the cutter edge for the shallow soil layer, it was ensured that the cutter could smoothly penetrate the soil while effectively cutting the roots, minimizing soil damage. Therefore, the sinusoidal curve characteristic was employed to design the cutter edge for the shallow soil layer to reduce soil disturbance [8] as shown in Equation (3). The 3-6 cm soil layer was defined as the middle soil layer. In this layer, corn roots play a pivotal role in the absorption and transportation of water and nutrients [22], with a relatively concentrated distribution. The Archimedean spiral cutter could effectively cut and guide roots, producing a \"pulling-out\" effect while causing lower soil disturbance [10]. This curve was employed to design the cutter edge for cutting roots in the middle soil layer as shown in Equation (4). The 6-9 cm soil layer was defined as the deep soil layer, representing the maximum depth attainable by the cutter. In this layer, the corn roots are more dispersed. To ensure that the root lengths after cutting could meet the requirements, the cutter needed to have a large sweeping area and preserve the low energy consumption, so an involute cutter edge was employed as shown in Equation (5). The involute curve has a relatively uniform force distribution characteristic, which could effectively reduce energy consumption during cutting roots [5; 23]. \[f(x_{3})=9.52\sin(-0.62x_{3})\qquad(-0.52<x_{3}<0) \tag{3}\]  
\[ \begin{array}{l}x_{4}=4.67(1+0.5t_{4})\cos(t_{4})-3.41\\ f(t_{4})=4.67(1+0.5t_{4})\sin(t_{4})+1.48\end{array} \qquad(-0.413<t_{4}<0.3) \tag{4}\]  
Figure 2: (**a**) Bionic cutter for cutting crown. (**b**) Multi-curve cutter for cutting roots. (**c**) Device integrated by cutters. \[x_{5} =6.11(\cos t_{5}+t_{5}\sin t_{5})+4.4\] \[f(t_{5}) =6.11(\sin t_{5}-t_{5}\cos t_{5})+14.56\] (1.74 \[<t_{5}<2.28\] )  
The device was integrated by cutters rotated vertically for cutting corn root-crowns and could synchronously cut roots and crowns with low soil disturbance. The overlapping length between the moving and fixed cutters directly affected the effect of cutting the crown. Although a longer overlapping length could more thoroughly cut the crown, it would increase the risk of cutter collision. Based on the agricultural machinery design manual, the overlapping length between the moving and fixed cutters was recommended to be 75-85%. Considering assembly errors, the overlapping length was set to 120 mm. To meet agronomic requirements, the length of the crown after cutting should be less than or equal to 50 mm, and a shorter length of the crown after cutting results in a faster decomposition rate. Considering the vibration would occur during the process of cutting the crown, which might cause a change in the relative positions of the moving and fixed cutters. The vertical spacing between the moving cutter and the fixed cutter should not be too small, and it was set to 20 mm after comprehensive consideration. According to the operational requirements of combine harvesters, the height of the corn crown after harvest should be less than 10 cm. Due to uneven terrain, field measurements showed that the crown height ranged from 0 to 15 cm. To adapt to the different heights of the corn crown, the height of the moving cutters should be designed higher than 150 mm. However, if the height of the moving cutters was too large, the stability of the cutter shaft would be affected. After comprehensive consideration, the height of the moving cutters was determined to be 210 mm. Two multi-curve cutters for cutting roots were installed opposite each other at the lower end of the cutter shaft. The device integrated by cutters rotated vertically is shown in Figure 2c.