## 4 Experimental Results
### The Analysis Results of the Defective Planetary Gearbox  
The left transmission train of the azimuth axis had a slight abnormal sound when the measurement ship was sailing in the sea. The vibration signals were measured at a sampling frequency of 12.8 kHz from the measuring points on the planetary gearbox by using ICP acceleration sensors. The AC motor was running at 255 r/m. The signal in time domain is shown in Figure 14(a), periodic transient impulses appear in the signal. The peak-to-peak value is about 0.4 g, which is significantly higher than 0.15 g of the normal planetary gearbox. Its FFT spectrum is shown in Figure 14(b), its components mainly distribute at 500-3,000 Hz. No distinct fault features can be seen in the spectrum.  
Figure 14: **(a)** The vibration signal of the defective planetary gearbox. **(b)** The FFT spectrum.  
Figure 15: The denoising results of the vibration signal using the proposed method.  
The denoising result of the proposed method is shown in Figure 15. During a course of one revolution of the sun gear, three pairs of shock impulses A, B and C occur alternatively. Because there are three planet gears in the first stage of the planetary gearbox. These features indicates that there are several defects in the sun gear. The average time interval between the two neighboring shock impulses in each pair is 0.023 s, corresponding to 43 Hz. It's about 10.5 times of the rotating frequency of the sun gear in the first stage. The frequency 43 Hz is close to the meshing frequency, which suggests that the shock impulses may be caused by defects on two neighboring gear tooth of the sun gear in the first stage.  
Figure 16(a,b,c) display the denoising results of customized multiwavelet using NC, GHM multiwavelet using INC and NC, respectively. As shown in Figure 16(a), periodic impulses can be accurately detected, while the weak impulse at 0.16 s are \"over-killed\" by the chosen threshold. Figure 16(b,c) display similar denoising results. Strong impulses are detected while weak fault features are \"over-killed\". Moreover, GHM multiwavelet cannot accurately separate fault features and the noises are not eliminated completely. The planetary gearbox was disassembled. Figure 17 displays that four incipient pittings denoted as the arrows appear in three regions of 2 \(\times\) 10 mm\({}^{2}\). The field inspection verifies the fault diagnosis conclusion.  
Figure 16: The denoising results of the planetary gearbox signal. **(a)** Customized multiwavelet and NC. **(b)** GHM multiwavelet + INC. **(c)** GHM multiwavelet + NC.  
Figure 17: The defects in the sun gear of the planetary gearbox.  
Figure 18: The analyzed results of the defective planetary gearbox signal using spectral kurtosis. (**a**) The Kurtogram. (**b**) The purified signal. (**c**) The envelop spectrum (low-frequency band).  
The Kurtogram and the resulting signals of spectral kurtosis are illustrated in Figure 18, the maximum kurtosis is 11.5 at level 3, the central frequency is 2,000 Hz and the bandwidth is 800 Hz. The envelope of the filtering signal and its FFT spectrum are shown in Figure 18(b,c), respectively. Only strong impulses could be detected in the envelope of the filtered signal. Figure 18(c) displays a dominant frequency 39.14 Hz, which has a significantly difference with 43 Hz, the meshing frequency of the first stage in the planetary gearbox.