## 3 Multibody Dynamics Simulation
### Design Variables  
In this study, the effects of assembly tolerance, material, and structural configuration on noise levels were determined using multibody dynamic analysis. First, the effects of assembly tolerance on noise levels were analyzed. Case 1 was designed to allow the main shaft which is connected to the driven gear to be displaceable by a maximum of 0.3 mm in the axial direction. Case 2 was prepared with a bearing tolerance of 0.02 mm. These design variations are represented in Figure 7. Two additional cases were prepared to test the effects of the materials. For Case 3, the top cover material was changed from polycarbonate to Al6061-T6. Aluminum has a better sound absorption property than engineering plastic polycarbonate and was expected to reduce the gear noise level. For case 4, the material for the driven gear was changed from S45C to polycarbonate. In general, plastic gears produce less noise than metal gears, but the durability issue needs to be considered [19]. Polyacetal has a small wear and friction coefficient and is also wear-resistant with good mechanical properties compared to ordinary plastics [20]. Because the driver gear is exposed to a fatigue load four times higher than that of the driven gear, the material for the driver gear was fixed with S45C. The components tested with different materials are shown in Figure 8.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Part**} & \multirow{2}{*}{**Material**} & \multicolumn{2}{c}{**Young’s**} & \multirow{2}{*}{**Poisson’s Ratio**} & \multirow{2}{*}{**Density [kg/m\({}^{3}\)]**} \\  & & **Modulus [GPa]** & & \\ \hline \multirow{2}{*}{External cover} & Polycarbonate & 2.2 & 0.37 & 1210 \\  & Polyacetal & 3.3 & 0.35 & 1420 \\ \multirow{2}{*}{Gear} & S45C & 210 & 0.3 & 7865 \\ \multirow{2}{*}{Etc.} & Al6061-T6 & 68.9 & 0.33 & 2698 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Material properties.  
Figure 7: Design variable–Assembly tolerance: (**a**) Case 1: Main shaft; (**b**) Case 2: Bearing.  
The effects of structure on noise levels were tested with four additional cases. The purpose of structural modifications is to reduce noise levels by enhancing structural rigidity within the scope of the basic design. For Case 5, the structural frame next to the gear case was changed to a solid type (Figure 9a). Gears are the major source of noise, and as such enhanced rigidity of the frame close to the gears may reduce noise generation. For Case 6, an arch-shaped reinforcement was added transversely in the middle of the frame without interfering with other internal components (Figure 9b). For Case 7, the thickness of the top cover was increased from 1 mm to 2 mm (Figure 9c). This was the maximum thickness increase allowed without interfering with other structural components. For Case 8, the gear thickness was reduced from 8 mm to 6 mm (Figure 9d). The lower the thickness of the gears, the smaller the contact area, resulting in lower noise levels.  
Figure 8: Design variable-Material: (**a**) Case 3: Top cover material change from polycarbonate to Al6061-T6; (**b**) Case 4: Driven gear material from S45C to polycarbonate.  
Figure 9: Design variable–Structure: (**a**) Case 5: Change frame to solid type; (**b**) Case 6: Add arched frame; (**c**) Case 7: Increase the thickness of the top cover; (**d**) Case 8: Reduced gear thickness.