## 3 Influence Factors Discussion
### Spoke Number  
Wheels consist of spokes and rims. Since the rim follows specific standards, the spokes, as the connection between the rim and hub, are highly designable. In this section, the effect of the number of spokes on power flow transmission is investigated. When adjusting the design scheme, the shape of the rim remained the same while the hub was simplified as a support, and the spokes number was adjusted to four, five, six, seven, eight or nine. To keep the total wheel mass unchanged, the center angle each spoke covered varied with the spoke number. For the wheel with four spokes, the center angle of each spoke was \(45^{\circ}\). As the spoke number increased, the center angle of a single spoke changed to \(36^{\circ}\), \(30^{\circ}\), \(25.7^{\circ}\), \(22.5^{\circ}\) or \(20^{\circ}\). Simplified wheel models with different numbers of spokes are shown in Figure 18.  
Then, the input and output power flows of those simplified wheels were calculated. Taking the 15-inch aluminum alloy wheels as an example in Figure 19 (a similar conclusion could be drawn from the 14-inch wheels), the wheels with odd-numbered spokes showed greater input and output power flows than the ones with even-numbered spokes. In addition, the input and output power flows increased in the case of the higher odd number of spokes. As the wheels with even-numbered spokes showed a lower transmission efficiency of vibration energy, therefore, in order to suppress TACR energy propagation, the wheels with even-numbered spokes should be adopted for the wheel structure in this work. According to the above results, the wheel with four or eight spokes should be chosen in the case of the same wheel size and structure. Then, the structure intensity distributions of the 15-inch wheel with 5, 7 or 9 spokes were given as in Figure 20. The maximum values of the structure intensity in those wheels increased as the number of spokes varied from 5 to 9, and the maximum values were located near the inboard flanges, which were located at the node of the cosine load model. The greater deformation was due to the lower stiffness of the inboard flanges than the outboard ones. Additionally, it can be seen that the structure intensity decreased as the energy went through the spokes to the bolt holes, where the wheel and suspension connect together. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Structure**} & \multicolumn{4}{c}{**Power Flow (\(10^{-3}\) W)**} \\ \cline{2-5}  & \multicolumn{2}{c}{**14-Inch Wheel**} & \multicolumn{2}{c}{**15-Inch Wheel**} \\ \cline{2-5}  & **Input** & **Output** & **Input** & **Output** \\ \hline
0.01 & 192.87 (100\%) & 9.9672 (100\%) & 493.16 (100\%) & 1.5855 (100\%) \\
0.015 & 130.01 (\(-32.6\%\)) & 6.8411 (\(-31.7\%\)) & 309.23 (\(-37.3\%\)) & 1.1138 (\(-29.8\%\)) \\  
To know how the power flow propagated in the wheels and clarify the influence mechanism of the spoke number, the simplified round disk models (RDMs) without and with spokes of different numbers were constructed as shown in Figure 21. The RDMs with a 10 mm thickness had the same cross-section shape as the simplified wheel in Figure 20, which was used to analyze the influence of the spoke number on the power flow transmission. Vector graphs of their structure intensities under the same sound pressure excitation are shown in Figure 22.  
In the vector graphs, the length and the arrow direction of the vector represent the amount and direction of the power flow at a specific point, respectively, so the power flow distribution in the wheel can be clearly observed. From the comparison of the  
Figure 19: Input and output power flow in the simplified 15-inch wheels: (**a**) input power flow and (**b**) output power flow. Figure 20: Structure intensity distributions in simplified wheels with spokes of different numbers: (**a**) five-spoke wheel; (**b**) seven-spoke wheel; and (**c**) nine-spoke wheel.