The time domain waveform of vibration data measured when the planetary gear is cracked is shown in Figure 1. It can be seen from Figure 1 that the time domain waveform of the vibration signal tested is very complex, and it is difficult to distinguish the fault impact characteristics caused by the planetary gear crack; In the vibration signal spectrum, there is no obvious peak value at 1 times of the meshing frequency FM, and the maximum peak value appears at 2 times of the meshing frequency 2fm, and there are several sidebands on both sides of the sideband. The interval of the sideband is the rotation frequency fc of the planetary carrier, which belongs to the normal frequency component. Therefore, it is impossible to judge whether the planetary gear is faulty only by Fourier transform.
In order to extract fault feature information, the proposed apoelmd method is used to decompose the planetary gear fault vibration signal. The amplitude and integration times of white noise are fixed to 0.01sd and 2 respectively, and the upper limit frequency of white noise is determined by RRMSE. Figure 2 (a) shows the relative root mean square error values at different upper frequencies. It can be seen from Figure 2 (a) that the optimal upper limit frequency of white noise added to planetary gear fault signal is 71.68 kHz (14 times of sampling frequency). Figure 2 (b) shows the decomposition result of apoelmd. The instantaneous frequency of the first product function (Pf1 component) decomposed by apoelmd fluctuates 6 times around the meshing frequency, as shown in Fig. 2 (c). Therefore, Pf1 component is still selected for further demodulation analysis. In the envelope spectrum diagram 2 (d) of Pf1 component, the amplitudes of each peak frequency are greater than the normal signal, in which the third harmonic 3fp and the sixth harmonic 6fp of the planetary gear fault characteristic frequency are dominant, and the other peaks mainly appear in the frequency doubling NFP of the planetary gear local fault characteristic frequency and the combination NFP + FC of the planetary gear fault characteristic frequency fc. In the Pf1 component instantaneous frequency Fourier transform spectrum 2 (E), it can also be found that the amplitudes of double frequency NFP, carrier rotation frequency fc, and the combination of both NFP + FC of planetary gear fault characteristic frequency are obvious, and they are more prominent than the normal signal. These characteristics show that the planetary gear has a local fault, which is consistent with the experimental simulation of planetary gear root crack fault state.
As a contrast, the traditional elmd and EEMD methods are used to decompose the planetary gear fault signal. At this time, the amplitude of white noise is set to 0.2sd, and the number of integration is set to 200. The envelope spectrum and instantaneous frequency Fourier spectrum of the decomposed sensitive component are analyzed, and the results are shown in Figure 3. It can be seen from the envelope spectrum in Fig. 3 (a) and the instantaneous frequency Fourier spectrum in Fig. 3 (b) that the amplitudes of the processing results of the proposed apoelmd method at the frequency doubling NFP of the local fault characteristic frequency of the planetary gear, the rotation frequency fc of the planetary carrier, and the combination NFP + FC with the rotation frequency fc of the planetary carrier are significantly higher than those of the traditional elmd and EEMD In addition, the interference of other irrelevant frequency components in the spectrum is small, while there are many noise frequency components with large amplitude in the processing results of elmd and EEMD methods, which brings great interference to the fault diagnosis of planetary gear and is not conducive to make correct judgment. Through the above comparative analysis, it can also be concluded that the proposed apoelmd method is superior to the traditional elmd and EEMD methods in signal decomposition performance, weak fault feature extraction and noise suppression.