*2.2. Finite Element Modeling and Analysis*

### 2.2.1. Geometric Model

The three-dimensional geometric model of the reciprocating cutting system unit was established by applying the modeling software SolidWorks. In order to improve the accuracy of the solution and shorten simulation operation time, the cutting system model was appropriately optimized, and a cutting unit was extracted for calculating the simulation when constructing the physical model of the cutting system [23,29]. In Figure 3, the simulation model includes three parts: the upper cutting blade, the bottom cutting blade, and the stalk of Chinese little greens.

**Figure 3.** The structural diagram of the geometric model: 1—upper cutting blade; 2—bottom cutting blade; 3—stalk.

The cutting blade was regarded as the same integral rigid body, whose features such as the drive motor and transmission components were omitted, but the oblique angle was retained. In the modeling of the greens, it grew with no inclination angle to the ground, and no branches on the stems. The difference between cortex and xylem was ignored. At the same time, each stem to be cut was assumed to be relatively independent, and there was no implicated force between the stems. In addition, the gap between the cutting blade and stem was narrowed as much as possible to reduce the computing time and the amount of calculation. In Table 1, the primary geometric parameters are listed. The three-dimensional geometric model of the reciprocating cutting system unit is shown in Figure 3. The model was saved in Parasolid (\*.x\_t) format.

**Table 1.** Primary parameters of the geometric model.


### 2.2.2. Material Property Parameters

The ANSYS Workbench has a rich database of materials, and structural steel material was selected as the material for the cutter. The cutting process of the stalk is essentially a state of penetration destruction, and large deformation and destruction inevitably occur as the material fails. The model of the stem adopts linear elastic anisotropic material properties; the constitutive parameters of the materials are shown in Table 2 [30].

**Table 2.** Main material parameters of the geometric model.


#### 2.2.3. Meshing

The ANSYS Workbench contains multiple built-in meshing methods. In this simulation, a hexahedral meshing method was adopted. In order to ensure the accuracy of the simulation, proper mesh densification was performed on the part where the cutter contacts during meshing [31,32]. The model element size of the cutter and the stalk were both 0.8 mm, and the element size of the dense part of the stalk was 0.6 mm. The total number of elements in the cutting model was 8280 together with 11,842 nodes. The finite element model meshing is shown in Figure 4.

**Figure 4.** The finite element model.

### 2.2.4. Loads and Constraints

Initial conditions and boundary constraints were determined according to actual working conditions. It was assumed that there was hard soil. The constraint of the ground on the stalks was assumed to be a cantilever beam constraint. The stalks were constrained in the *X* and *Z* directions at its bottom to limit the displacement in both the *X* and *Z* directions. The speed in the *Y* direction was given, and then the same speed of the harvesting machine was simulated. The influence of the mechanical vibration of the cutter during the cutting process was ignored, and it was assumed that the cutting blade always moves in the same plane.

The constraint of the cutting blade was the displacement constraint in the fixed *Y* and *Z* directions; that is, the cutting blade only moves in the opposite direction of the *X* direction, and the speeds of the upper cutter and the bottom cutter were equal in reverse. During the cutting process, the interaction between the cutting blade and the stalk belongs to the category of stab. Hence, the contact type was defined as surface-to-surface erosion contact. The dynamic friction coefficient between the cutter and the stalk was set to 0.38, and the static friction coefficient was set to 0.4 [20].

#### *2.3. Orthogonal Test Design*

The central–composite test design was adopted [33]. By taking the maximum cutting equivalent stress σ1 of the upper cutting blade and the maximum cutting equivalent stress σ2 of the bottom cutting blade as the target value, then the cutting blade sliding–cutting angle, oblique angle, and the average cutting speed were the three factors used to design an orthogonal test with three factors and five levels. The sliding–cutting angle is an important parameter that affects the shape of the blade, which is the angle between the absolute motion direction and the normal direction of the cutting edge [7]. The larger the sliding–cutting angle is, the smaller the cutting force, but a sliding–cutting angle that is too large is not conducive to stable clamping, so its value ranges from 20◦ to 30◦. The oblique angle is the edge angle of the cutter. If the oblique angle is too small, the service life of the cutter is reduced, and if it is too large, the cutting resistance is increased. In this paper, the oblique angle of the cutter ranges from 35◦ to 45◦ [6]. The average cutting speed is the ratio of a single cutting displacement to the reciprocating movement time of the cutter. It is an important indicator to measure the cutting performance. Some studies have found that when the cutting speed is too fast, the cutting resistance increases, obviously, and when the cutting speed is too small, the cutting motion becomes difficult [20]. Therefore, the average cutting speed was set at 300 to 500 mm/s. The test was divided into 20 groups, and the coding table of test factor levels is shown in Table 3.


**Table 3.** Levels and codes of experimental variables.
