## 5 Experimental Verification of Different Combinations of Fault Conditions  
The faulty gear is shown in Figure 10. The experimental bench is shown in Figure 11 below. The acceleration sensor was placed directly above the planetary gearbox. The experimental motor speed was set to 1800 rpm, the actual speed was 1782 rpm, the sampling frequency was 5000 Hz, the sampling time was 4s, and the actual rotation frequency of the sun gear was 29.7 Hz. The gear-related parameters and the characteristic frequency of the gearbox are given in Tables 3 and 4 below. The frequency was taken between 450 Hz and 550 Hz. appears at a frequency of \(f_{m}\pm nf_{c}\) (\(n=1,2,\,\dots\) ), and the sideband interval is the rotation frequency \(f_{c}\) of the planetary frame, as shown in the figure at points 1 and 2, which are \(f_{m}-7f_{c}\) and \(f_{m}+7f_{c}\), respectively, and these phenomena are consistent with the theoretical expectations of the normal planetary gearbox vibration signal and are basically consistent with the simulation in the previous section, which verifies the correctness of the simulation model and the credibility of the results. Experimental Verification of the Combined Fault Conditions of Sun Gear Missing Teeth and Planetary Gear Pitting  
Figure 13 shows the time domain waveform and the Fourier spectrum of the experimental vibration signal under the combined fault conditions of the sun gear teeth missing and planetary gear pitting. The time domain waveform shows a more obvious shock, and the peak of the whole spectrum is more obvious. There is a modulation effect of the \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Meshing** \\ **Frequency** \\ \(f_{m}\) \\ \end{tabular} } & \multicolumn{2}{c}{**Absolute Rotational Frequency**} & \multicolumn{2}{c}{**Local Fault**} \\ \cline{2-5}  & & & **Characteristic Frequency** \\ \cline{2-5}  & **Sun Gear** & **Carrier** & **Sun Gear** & **Planet Gear** \\ \cline{2-5}  & \(f_{s}^{\prime}\) & \(f_{c}\) & \(f_{s}\) & \(f_{p}\) \\ \hline
498.9 Hz & 29.7 Hz & 5.9 Hz & 71.3 Hz & 16.2 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experiment of planetary gearbox characteristic frequency. Figure 12: Experimental vibration signal of sun gear and planetary gear under normal working conditions: (**a**) Time domain waveform; (**b**) Fourier spectrum. planetary frame on the meshing frequency, so there are peaks at \(f_{m}\pm nf_{c}\) on both sides of the meshing frequency \(f_{m}\), where \(n\) is an integer, such that 6, 9 and 7, 8 are \(f_{m}\pm f_{c}\) and \(f_{m}\pm 2f_{c}\), respectively. Due to the presence of three planetary gears, it can also be seen in the figure that peaks appear at the positions \(f_{m}\pm nf_{s}/3\pm nf_{c}\) of the meshing frequency, with sideband intervals of \(nf_{s}/3\) times the characteristic frequencies of the sun gear fault, where \(n\) is an integer, such that 1, 3, 4, 11, 12, and 13 are \(f_{m}-2f_{s}/3\), \(f_{m}-f_{s}/3-f_{c}\), \(f_{m}-f_{s}/3\), \(f_{m}+f_{s}/3\), \(f_{m}+f_{s}/3+f_{c}\), and \(f_{m}+2f_{s}/3\), respectively. Peaks are found at the positions of frequency \(f_{m}\pm nf_{p}/3\pm f_{c}\) associated with the planetary gear fault characteristic frequency \(f_{p}\), such as at 2, 5, and 10 are \(f_{m}-2f_{p}-f_{c}\), \(f_{m}-f_{p}\), and \(f_{m}+f_{p}\), respectively, and it can be seen that the experimental signal is basically consistent with the simulated signal. Therefore, the comprehensive diagnosis is that both the sun gear and the planetary gear are faulty. Experimental Verification of the Combined Fault Conditionsof Sun Gear Missing Tenth and Planetary Gear Missing Tenth  
From Figure 14, it can be seen that the time domain waveform shock is more obvious when the sun gear and planetary gear are missing teeth at the same time. Similarly, peaks \(f_{m}\pm nf_{c}\) on both sides of the meshing frequency \(f_{m}\), where \(n\) is an integer, such as at 3 and 4 are \(f_{m}\pm f_{c}\), respectively.