## 4 Experimental Results
### The Experimental Results of the Normal Planetary Gearbox  
Vibration signals of a normal planetary gearbox in the left transmission train of the azimuth axis were acquired. They are applied to verify the effectiveness of the propose method. The sampling \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Sensitivity** & **Measurement** & **Frequency Range** & **Non-Linearity** & **Sensing Element** \\  & **(\(\pm\)10\%)** & **Range** & **(\(\pm\)10\%)** & **Non-Linearity** & **Element** \\ \hline
333B32 & 100 mv/g & \(\pm\)50,g pk & 0.5–3,000 Hz & \(\leq\)1\% & **C********arcmic \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameters of acceleration sensors. Figure 9: The testing framework of the SCA of a measurement ship. frequency and signal length were 12.8 kHz and 5,760, respectively. The rotating speed of the motor was 150 r/m. The signal in time domain is shown in Figure 10(a), the peak to peak value of the signal is about 0.15 g. Its FFT spectrum is plotted in Figure 10(b), the frequency components are abundant. Evident rotating frequencies, meshing frequencies and sidebands relevant to gearbox faults can hardly be identified in the spectrum. The proposed method chose the customized multiwavelet by using redundant symmetric lifting scheme and the optimal threshold by using INC and it was applied to the measured signal. The signal was decomposed into four levels. As shown in Figure 11(a), the proposed method can depict the distinct features with a period of 0.039 s, that is 25.64 Hz. It is about 10.5 times of the rotation speed of the sun gear in the first stage, which is 2.5 Hz. Figure 11(b) displays the denoising result using customized multiwavelet and conventional neighbouring coefficients with an invariant size of neighbors at different decomposition levels. The impulses between 0.16 s and 0.3 s are very weak, and are nearly \"over-killed\" by the chosen threshold. In addition, unrelated features denoted in the ellipses appear in the denoising result, and these features may influence the validity of fault feature detections. Figure 12(a,b) are the analysis results of GHM multiwavelet denoising using INC and NC, respectively. The denoising results of these two methods are similar, only strong impulses can be detected as shown in the triangles and several singular points appear during 0.02 s and 0.1 s. The impulses in the denoising results are not periodic, which affect the correct fault detections of planetary gearboxes. Figure 10: **(a)** The vibration signal of the normal planetary gearbox. **(b)** The FFT spectrum. Figure 11: The denoising results of the normal planetary gearbox signal using the customized multiwavelet. (**a**) The proposed method (**b**) Conventional neighboring coefficients. Figure 12: The denoising results of the normal planetary gearbox signal using GHM multiwavelet. (**a**) Improved neighboring coefficients. (**b**) Conventional neighboring coefficients. According to the kinetic principles of planetary gearboxes, both contact conditions by means of rolling and sliding exist on the gear tooth when meshing. The force of sliding friction changed its direction at the meshing points, which caused the shocking line impacts. Moreover, when each pair of gear tooth got in or out of contact, the load and deformation of each gear increased or decreased suddenly, causing the meshing shocks. The dynamic load consisted of shocking line impacts and meshing shocks, which caused the meshing vibration of gears. Therefore, the meshing vibration in Figure 11(a) is the inherent dynamic characteristics of gear meshing, it is not relevant with gear defects. The Kurtogram [36,37] and the resulting signals of spectral kurtosis are illustrated in Figure 13. The maximum kurtosis is 2.3 at level 4, the central frequency is 1,000 Hz and the bandwidth is 400 Hz. The envelope of the filtered signal and its FFT spectrum are shown in Figure 13(b,c), respectively.