# Simulation and Experimental Study on the Shrub-Cutting Performance of Quasi-Planetary Cutter
## 3 Methods and Experimental Design
### Finite-Element Single-Factor Simulation Experiment
#### 3.1.2 Finite-Element Modelling  
In the finite-element simulation of cutting, the quasi-planetary shrub cutter and shrub models were simplified to improve computational efficiency, reduce simulation complexity, and minimise the probability of errors. The bolts, nuts, and washers of the cutter were omitted, leaving only the teeth, cutter flange, and part of the spindle. The shrub was simplified into a cylindrical shape, with its axis perpendicular to the ground and fully constrained at the bottom. Simplified 3D models of the quasi-planetary shrub cutter and shrub were created using SolidWorks 2022 software. The 3D models were then imported into LS-PrePost 2024, the pre-processing and post-processing software of LS-DYNA, in STEP format to establish the finite-element cutting model. The cutter material was defined as a bilinear kinematic hardening plastic model (MAT_PLASTIC_KINEMATIC). This model is primarily used to describe the elastic-plastic behaviour of materials and is particularly suitable for metals. It was applied to a 65 Mn cutter to improve computational efficiency and facilitate the extraction of the cutter's stress and strain. The material parameters of 65 Mn are listed in Table 4. The flange used to mount and secure the cutter head was modelled as a rigid material, with 45# steel (equivalent to AISI 1045) as the selected material. Its properties are as follows: a density of 7850 kg/m\({}^{3}\), a Young's modulus of 206 Gpa, and a Poisson's ratio of 0.269. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Poisson’s** & **Density** & **Elastic** & **Yield Limit** & **Shear** \\  & **Ratio** & **(kg/m\({}^{3}\))** & **Modulus** & **(Gpa)** & **Modulus** \\ \hline
65 Mn & 0.3 & 7850 & 206 & 0.44 & 78.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Physical parameters of a circular saw. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Level** & \(n\) **(r/min)** & \(v\) **(mm/s)** & _D_\text{a (mm)} \\ \hline
1 & 1000 & 30 & 15 \\
2 & 1250 & 45 & 20 \\
3 & 1500 & 60 & 25 \\
4 & 1750 & 75 & 30 \\
5 & 2000 & 90 & 35 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Single Test Factors and Levels. The three shrubs selected were modelled using a linear elastic orthogonal anisotropic material model [27], which best matched the mechanical properties of wood. Additionally, the keyword MAT_ADD_EROSION was included to simulate material failure during cutting. The material compositions are listed in Table 1.  
A mesh is crucial in finite-element simulations since it decomposes complex geometries into simpler elements, making numerical calculations feasible. A well-designed mesh enhances computational accuracy and efficiency while also influencing the stability and convergence of the solution. Although finer meshes capture more physical phenomena, they also increase computational costs. Therefore, achieving a balance in mesh design is essential. Due to the complex structure of the cutter, tetrahedral meshing was employed to improve mesh quality and enhance computational efficiency and accuracy. The mesh density was increased around the serrated parts of the cutter. For the simplified shrub, hexahedral meshing was applied, with a higher mesh density in the cutting section that comes into contact with the cutter teeth. The total meshes of the model were 137,085. The total nodes of the model were 74,123. The mesh number was doubled, revealing that when the total mesh number was 274,170, the maximum stress value in the blade slightly decreased (i.e., by 2%). Therefore, the coarser meshing scheme of 137,085 elements was applied to all the models in the simulation tests. The finite-element model after meshing is shown in Figure 6.  
To simulate shrub-root fixation, a full constraint was applied to the bottom surface of the simplified shrub model. Simultaneously, the rotational speed along the Z-direction and feeding speed along the XY-plane were applied to the entire cutter. The cutting height was set to 10 cm, using the bottom surface of the shrub as the reference plane.