# Fault Diagnosis of Vehicle Gerboxes Based on Adaptive Wavelet Threshold and LT-PCA-NGO-SVM
## 3 Construction and Analysis of the Gearbox Vibration Test Bench  
In this study, the gearbox of a new energy vehicle is used for engineering practical experiments. Figure 9 displays the gearbox vibration test bench, where the vibration acceleration signal during gearbox operation is captured by a piezoelectric acceleration sensor installed on the gearbox housing. The installation position of the acceleration sensor [31] on the gearbox housing is displayed in Figure 10.  
Figure 8: Schematic diagram of SVM.  
Figure 7: Schematic diagram of LT-PCA.  
Initially, the normal gearbox platform serves as the driving end to provide forward speed, with a single motor as the load delivering forward torque. This setup simulates the working condition of the gearbox driving in the forward direction. The gearbox is then set to first gear with a torque of 300 Nm at the load end. Vibration data are collected at three speed points: 1200 rpm, 1800 rpm, and 2400 rpm, with a minimum of 20 datasets collected at each speed point to mitigate the influence of accidental factors. The collected samples have a length of 10 s, a maximum frequency of effective analysis set at 5000 Hz, and a resolution of 0.1 Hz, and 80 groups of data are extracted for further use. Following the collection of vibration data in the normal state, samples representing the tooth surface of light, moderate, and severe failure states are gathered, as shown in Figure 11. This set of input samples is then used to conduct data feature extraction and dimensionality reduction experiments.  
Figure 11: Faulty gear condition. (**a**) Minor tooth failure state. (**b**) Moderate tooth failure state. (**c**) Severe tooth failure state.  
Figure 9: Gearbox vibration test bench device for a vehicle. (**a—**Drive motor; **b—**Sensor; **c—**transmission; **d—**coupling; **e—**load motor; **f—**Three-phase line; **g—**Cooling water pipe; **h—**Collection toolbox).  
The fault characteristic frequency of the sun gear is as follows:  
\[f_{s}=N*\frac{n_{s}}{60}*\left(\frac{Z_{r}}{Z_{r}+Z_{s}}\right) \tag{25}\]  
The fault characteristic frequency of the planet gear is as follows:  
\[f_{p}=\frac{n_{s}}{60}*\left(\frac{Z_{r}}{Z_{r}+Z_{s}}\right)*\left(\frac{Z_{s} }{Z_{p}}\right) \tag{26}\]  
The fault characteristic frequency of the ring gear is as follows:  
\[f_{r}=N*\frac{n_{s}}{60}*\left(\frac{Z_{r}}{Z_{r}+Z_{s}}\right)*\left(\frac{Z_{ s}}{Z_{r}}\right) \tag{27}\]  
The fault characteristic frequency of the planetary carrier is as follows:  
\[f_{p}=\frac{n_{s}}{60}*\left(\frac{Z_{s}}{Z_{r}+Z_{s}}\right) \tag{28}\]  
The characteristic frequency of meshing faults in the planetary gear train is as follows:  
\[f_{s}=\frac{n_{s}}{60}*\left(\frac{Z_{r}*Z_{s}}{Z_{r}+Z_{s}}\right) \tag{29}\]  
The parameters of the new energy vehicle gearbox used in the bench experiment are shown in Table 5.  
For speeds of 1200, 1800, and 2400 rpm, the fault characteristic frequency is calculated using Formulas (25) to (29), as shown in Table 6.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Input Speed** & **Input Frequency** & **Meshing Frequency** & **Sun Gear** & **Planet Gear** & **Ring Gear** & **Planet Carrier** \\
**(RPM)** & **(Hz)** & **(Hz)** & **(Hz)** & **(Hz)** & **(Hz)** & **(Hz)** \\ \hline
1200 & 20 & 474.84 & 59.35 & 15.32 & 5.16 & 20.65 \\
1800 & 30 & 712.26 & 89.03 & 22.98 & 7.74 & 30.97 \\
2400 & 40 & 949.68 & 118.71 & 30.63 & 10.32 & 41.29 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Fault characteristic frequency of each component under different input speeds.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Sun Gear** & **Planet Gear** & **Ring Gear** \\ \hline Number of teeth & 32 & 31 & 92 \\ Module (mm) & 2.5 & 2.5 & 2.5 \\ Pressure angle (°) & 20 & 20 & 20 \\ Helix angle (°) & 0 & 0 & 0 \\ Addendum coefficient & 1 & 1 & 1 \\ Dedendum coefficient & 0.25 & 0.25 & 0.25 \\ Profile Shift coefficient & 0 & 0 & 1.112 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Planetary gear train parameter settings.