# Dynamic Performance Optimization of Circular Sawing Machine Gearbox
## 3 Gearbox Structure Optimization
### Topology Optimization  
In this report, ANSYS numerical simulation software was used to numerically simulate the box, and to quantify the problems involved in the structure optimization process. Based on the acquired data, the potential problems can be identified and data support can be provided for the optimization direction of the box. Modal analysis of the numerical calculations of multi-body dynamics of mechanical structures is a relatively basic linear dynamic analysis method used to describe the frequency characteristics of structures, including the natural frequencies and modes of participation. Figure 2: Schematic diagram of gearbox structure: 1-lateral plate, 2-bearing, 3-gear, 4-output shaft, 5-gearbox, 6-input shaft, 7-differential shaft. Considering the aforementioned challenges, a numerical model for the sawing gearbox was established, as shown in Figure 3. The geometrical dimensions and material parameters were initially set according to the specifications of the manufacturing process of the gearbox. For the holes and parts near the model boundary, stress concentration can easily occur, and local refinement was performed. The numerical model grid has a total of 99,774 nodes and 61,174 solid elements, and is verified by grid independence. The contact position between the gearbox and slider is imposed as a completely fixed constraint, which limits the model base to six degrees of freedom in the X, Y, and Z directions, and satisfies the initial structural optimization requirements [46; 47]. Considering the significant reduction in the computational burden due to the meshing of various parts in the assembly, the conservation of computing resources, and accuracy of the solution, the calculation model is solved using this approach by adding point mass [48; 49]. The mass and centroid coordinates of the transmission shaft (including bearings, gears and other components) are determined by the physical model of the gearbox. The mass and centroid coordinates are added to the gearbox as point masses, as shown in Figure 4.  
Based on this method, the original ten-order modes of the gearbox before optimization can be obtained, as shown in Table 1.  
When the frequency of the external excitation is close to the value in the table, the possibility of large vibration deformation of the structure is relatively high. In this instance, resonance may occur, which causes extreme damage to the structure. Therefore, frequency values close to that listed in the table should be avoided in engineering design. According to the calculation formula of saw cutting force, the maximum saw cutting force can be obtained when circular saw blade saws circular bar. Considering the safety factor, the sawing force is \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Order** & **Frequency** & **Order** & **Frequency** \\ \hline
1 & 491.9 & 6 & 1327.0 \\
2 & 662.6 & 7 & 1440.1 \\
3 & 765.2 & 8 & 1536.2 \\
4 & 1233.0 & 9 & 1566.6 \\
5 & 1285.4 & 10 & 1644.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Original box body modal before structure optimization. Figure 4: Mass point distribution of gearbox. Figure 3: Gearbox numerical model. 1500 N, and the direction is the negative direction of the feed. The saw blade is mounted on the output shaft, and the shaft and box are installed using bearings. The force diagram of the output shaft can be established. Based on calculations, the reaction forces of the two bearings are obtained as 334.69 N and 1030.64 N, respectively. Considering the sawing force as resistance, the direction of the force acting on the gearbox can be determined according to the relationship between the force and reaction force.