Firstly, the vibration signal is resampled in the angular domain, and the input shaft speed curve (as shown in Figure 1) and the resampled signal in the angular domain (as shown in Figure 2) can be obtained by using the computational order tracking technique.
After resampling, the order spectrum of the original signal can be obtained by Fourier transform (Fig. 3). From the figure, we can see that the smear phenomenon in the spectrum has been significantly improved, and the spectrum peak is more prominent. However, there are many main order signals and their high order harmonic ratios (Oc, Om, 2Om, 3Om, 4Om, Om1, 2Om1) in the order. The order information is abundant, and the modulation phenomenon is obvious in the picture. The accurate fault information can not be extracted only by calculating the order tracking technique, so that it is impossible to diagnose the faults.
VMD analysis method is used to denoise the angle domain signal after equal angle sampling, and the IMF component with the largest kurtosis is extracted. The number of selected mode decomposition is k = 5, and the penalty factor is α = 4 000.
Figure 4 shows the order spectrum of IMF component obtained by VMD decomposition. It can be seen from the figure that according to the different order ratio of the center, the original signal is decomposed into five components, the kurtosis value of each component is calculated, and the IMF component with the most obvious fault information is selected according to the kurtosis criterion. Among them, the kurtosis value of imf2 is the highest, which is used as a fault signal for fast spectral kurtosis analysis.
Through the calculation of Fast Spectral Kurtosis Algorithm, the fast spectral kurtosis diagram shown in Fig. 5 is obtained. It can be seen from the diagram that the signal with the largest spectral kurtosis value in the fault signal is the signal with the center order ratio of FC = 398.4259 and the bandwidth of BW = 113.836. Taking the calculation results as input parameters, a band-pass filter is constructed, and the filtered signal is enveloped in angle domain. As shown in Fig. 6B, the modulation phenomenon still exists in the envelope diagram. Then, square envelope demodulation is performed to obtain the square envelope order spectrum as shown in Fig. 6C.
In Fig. 6C, it can be observed that the rotational speed order of input shaft OC, meshing order of intermediate shaft driving wheel (G3) om, double order ratio 2om and triple order ratio 3om, and it can be found that both sides of meshing order ratio have obvious side bands, with the phenomenon of large number, large amplitude and wide distribution. This is consistent with the fault characteristics of broken teeth. Therefore, it can be judged that the fault is broken teeth, and the fault gear is intermediate shaft driving gear (G3). This is consistent with the actual situation, which verifies the effectiveness of the method.