According to the working principle of Sanc, the separation effect of adaptive filter mainly depends on the selection of delay time Δ, filter length L and filter convergence factor η. The delay time Δ should be set large enough to weaken the autocorrelation of noise, but because the gear vibration signal is not a strict periodic signal, if Δ is too large, it will lead to the attenuation of gear vibration. If the filter length L is too large, the filter will not have enough time to adapt to its convergence criterion. If it is too small, the correlation difference between periodic signal and random signal cannot be reflected. The convergence factor η mainly determines the convergence speed of the filter.
After weighing the above factors, combined with the actual conditions of this test, the Sanc parameters are set as follows: Δ = 1 024, l = 4 096, η = 0.000 01. Limited to space, this paper takes the data of gear broken teeth and bearing outer ring (GoF) as an example to verify the rationality of the parameters selected in this paper. The separated time-domain waveform is shown in Figure 1.
Fig. 1 (a), (b) and (c) respectively show the original signal corresponding to GOF signal and the periodic signal and random signal after Sanc processing. The relevant calculation formula is as follows: fault characteristic frequency Fo of bearing outer ring:
Meshing frequency FG of fixed shaft
Where: Z is the number of bearing rollers; D is the diameter of bearing rollers; D is the pitch diameter of bearing; α is the contact angle; FR is the rotation frequency of bearing; G is the number of pinion teeth. According to the formula, the characteristic order of bearing outer ring fault is about 6.9 ×, and the gear meshing frequency is 32 ×. By resampling the original signal and the separated periodic signal and random signal in the angular domain respectively, the corresponding order spectrum is obtained by Fourier transform, as shown in Figure 2. Fig. 2 (a), (b) and (c) show the order spectrum of the original signal, the order spectrum of the periodic signal and the order spectrum of the random signal respectively. It can be found from Fig. 2 that the strong interference component of the gear is effectively separated from the original signal.
Fig. 3 (a), (b) and (c) are local enlarged graphs of the order spectrum of the original signal, the order spectrum of the periodic signal and the order spectrum of the random signal, respectively. Among them, 7.01 × is the characteristic order of bearing outer ring fault and 32 × is the meshing order of gear. It can be seen from the figure that the bearing signal part in the periodic signal is obviously decreased and the gear signal part in the random signal is effectively suppressed after the Sanc processing, the signal-to-noise ratio of the bearing signal is obviously improved, and the fault feature order is 7.01 × prominent.