## 2 Materials and Methods  
### Test Object and Equipment  
#### 2.1.1 Basic Characteristics of the Chassis Frame  
As a core piece of equipment in modern grain harvesting systems, the combine harvester integrates the full process of operations for rice crops, including efficient harvesting, material conveying, threshing and separation, and grain cleaning [46; 47; 48; 49; 50]. Its chassis frame is the main structural component that supports all core working components, such as the engine, cutting header, threshing cylinder, and vibrating screen. The frame is fabricated by welding Q235 structural steel, and its material properties are presented in Table 1.  
\begin{table}
\begin{tabular}{c c c c} \hline Elastic Modulus (MPa) & Poisson’s Ratio & Yield Strength (MPa) &
\begin{tabular}{c} Tensile Strength \\ (MPa) \\ \end{tabular} \\ \hline
2.05 \(\times\) 10\({}^{5}\) & 0.3 & 235 & 375 \\ \hline Hardness (HB) & Density (kg\(\cdot\)mm\({}^{-3}\)) & Shear Modulus (MPa) & Bulk Modulus (MPa) \\ \hline
120 & 7.85 \(\times\) 10\({}^{-6}\) & 7.69 \(\times\) 10\({}^{4}\) & 1.67 \(\times\) 10\({}^{5}\) \\ \hline \end{tabular}
\end{table}
Table 1: Material properties of Q235 steel.  
Modal analysis is a core theoretical method in the field of structural dynamics, and its primary function is to identify the key dynamic parameters of a mechanical system, such as its natural frequencies, modal damping ratios, and mode shapes. From a physical perspective, structural modes represent the inherent dynamic properties that a system exhibits under free vibration. In this study, a modal analysis of the combine harvester chassis frame was conducted using the Modal module in ANSYS Workbench 2023 R1. The finite element model was subjected to a meshing process. To ensure the accuracy of the simulation analysis, the mesh size was set to 12 mm, and a combination of solid and shell elements was selected for the mesh type. The final statistical results of the meshing were 838,840 nodes and 245,398 elements. The modal analysis was performed under free boundary conditions to determine the structure's natural frequencies and mode shapes. The resulting first six free mode shapes of the chassis frame are presented in Figure 1.  
The natural frequencies, maximum deformations, and characteristics of each mode shape are summarized in Table 2.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Order**} & **Natural Frequency** & **Maximum** & **Mode Shape Characteristics** \\  & **(Hz)** & **Deformation (mm)** & **J** \\ \hline
1 & 47.133 & 6.402 & Bilateral frame deformation, with the region of maximum deformation concentrated at the rear end. \\
2 & 50.694 & 7.8578 & Bilateral frame deformation, with the region of maximum deformation concentrated at the rear end. \\
3 & 52.661 & 8.4247 & Unilateral deformation on the left side of the frame, with the region of maximum deformation at the rear end. \\
4 & 55.882 & 14.315 & Deformation concentrated at the frame supporting the operator’s cabin. \\
5 & 56.757 & 6.5279 & Bilateral frame deformation, with the region of maximum deformation concentrated at the rear end. \\
6 & 65.373 & 5.341 & Overall frame deformation, with the region of maximum deformation concentrated on the right side. \\ \hline \hline \end{tabular}
\end{table}
Table 2: Natural frequencies and characteristics of the first six free modes of the chassis frame.  
Figure 1: The first six free mode shapes of the chassis frame.  
The modal analysis results indicate that the first six natural frequencies of the chassis frame are primarily concentrated between 47.133 Hz and 65.373 Hz, with the corresponding mode shapes being predominantly local bending, torsion, and coupled modes. These natural frequencies have the potential to couple with the excitation frequencies of the combine harvester's main working components, making them critical factors for inducing resonance in the chassis frame.