## 4 Modal Analysis of Driven Gear
### Analysis of Influencing Factors of Inherent Characteristics
#### 4.3.2 Effect of Spoke Plate Thickness on Travelling Wave Resonance Characteristics  
In order to reduce weight and save materials, spoke plate structures are commonly used in aviation gears. The initial thickness of the spoke plate of the driven bevel gear is 17.28 mm. Because the back of the wheel is slotted, the thickness of the spoke plate of the gear model is 10.28 mm, and the fixed temperature is 20 \({}^{\circ}\)C. The thickness of the spoke plate was changed to 6.28 mm, 7.28 mm, 8.28 mm, 9.28 mm, 10.28 mm, 11.28 mm and 12.28 mm, which were divided by the initial thickness of the spoke plate of the driven bevel gear to obtain a dimensionless thickness and observe the influence of spoke plate thickness on the static frequency simulation value. The results are shown in Table 8. Additionally, the trend of the static frequency changing with the spoke plate thickness is shown in Figure 15.  
It can be seen that as the thickness of the spoke plate increases, the static frequency of each vibration mode increases, and the higher the pitch diameter number is, the more obvious the static frequency value increases. At 20 \({}^{\circ}\)C, when the spoke plate thickness changes from 6.28 mm to 12.28 mm, the frequency of the 1 st NC vibration mode of the gear increases by 776.3 Hz, that of the 2 nd NC vibration mode of the gear increases by 1213.1 Hz, that of the 3 rd NC vibration mode of the gear increases by 1079.3 Hz and that of the 4 th NC vibration mode of the gear increases by 1934.5 Hz. The working temperature was set at 20 \({}^{\circ}\)C, the thickness of the gear structure was 17.28 mm, and the thickness of the original model spoke plate was 10.28 mm, accounting for 59% of the total thickness of the gear structure; the spoke plate thickness was changed to 6.28 mm, 7.28 mm, 8.28 mm, 9.28 mm, 10.28 mm, 11.28 mm and 12.28 mm, respectively. The dynamic frequency is approximately equal to the static frequency, and the resonant  
Figure 15: TWR characteristics of gears with different vibration mode at different thickness of spoke plate. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Thickness/\%** & \(f_{1}\)**/Hz** & \(f_{2}\)**/Hz** & \(f_{3}\)**/Hz** & \(f_{4}\)**/Hz** \\ \hline
36.3\% & 2747 & 3565 & 6885 & 11,360 \\
42.1\% & 2892 & 3767 & 6970 & 11,599 \\
47.9\% & 3033 & 3972 & 7168 & 11,866 \\
53.7\% & 3167 & 4176 & 7366 & 12,165 \\
59.5\% & 3293 & 4378 & 7827 & 12,500 \\
65.3\% & 3412 & 4580 & 8116 & 12,876 \\
71.1\% & 3523 & 4779 & 7964 & 13,294 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: TWR characteristics of gears with different vibration at different thickness of spoke plate. rotational speed and resonant frequency of the BTW and FTW of the 3 rd NC and 4 th ND are predicted. The results are shown in Tables 9 and 10. Table 9 shows that when the ratio of the spoke plate thickness to the total thickness increases from 36.3% to 65.3% at a working temperature of 20 \({}^{\circ}\)C, the resonance frequency of the 3 rd ND changes from 6885.1 Hz to 8115.5 Hz, increasing by 1127.4 Hz, and the FTW of the 3 rd ND increases from 7221.6 Hz to 8452 Hz. With an increase of 1230.4 Hz, the frequency of the BTW of the 3 rd ND increases from 6548.6 Hz to 7779 Hz, with an increase of 1230.4 Hz. The FTW resonant rotational speed of the 3 rd ND increases from 9613.5 r/min to 11,331.5 r/min, an increase of 1722 r/min. The frequency of the BTW resonance of the 3 rd ND increases from 8095.6 r/min to 9542.3 r/min, an increase of 1446.7 r/min. As for the influence of the change in the thickness of the spoke plate on the resonance characteristics of the 4 th ND shown in Table 10, when the ratio of the thickness of the spoke plate to the total thickness increases from 36.3% to 65.3%, the frequency of the FTW resonance of the 4 th ND changes from 11,359.5 Hz to 13,294 Hz, an increase of 1934.5 Hz, and the frequency of the BTW resonance of the 4 th ND increases from 11,696 Hz to 13,630.5 Hz.