The frequency component becomes very rich after the signal is phase-modulated. Due to the characteristics of the Bessel function Jn(m), the amplitude at the fundamental frequency no longer has a maximum value, and the side frequencies generated on both sides of the fundamental frequency are no longer symmetrically distributed around the fundamental frequency, thereby making the gears using the characteristic spectrum method. Fault diagnosis brings great difficulties.
Let the characteristic frequency of a fault signal of the gear be 100 Hz. It is the time domain and frequency domain diagram of the modulated signal when the original signal is m=0.7, 3, 10. It can be seen that the spectral characteristics of the signal have begun to change when the modulation factor is 0.7, but the modulation has little effect. As the value of the modulation factor increases, the influence of modulation increases, and the spectral characteristics of the signal are severely distorted.
Demodulation of the gear phase-modulated vibration signal When performing the vibration signal sampling of the gear, a fixed sampling frequency method is usually used. The sampled signals are equally spaced on the time axis, ie, isochronous. After the gear vibration signal is affected by phase modulation, assuming time from t0 to t, according to equation (2), its instantaneous phase can be expressed as: (t) = [t mcospt] t0 (8) Obviously, the instantaneous phase is not only related to the fundamental frequency. It is also affected by the modulation factor and modulation, so the signal is distorted and its spectral characteristics will also change. In this paper, a phase modulation signal demodulation method based on spatial sampling method is proposed. The basic principle is to follow the principle of constant phase difference between adjacent sampling points to sample the gear vibration signal. Start with the spatial sampling of the signal to achieve its purpose of signal demodulation corresponding to time.
During the test, since the instantaneous speed value of the measured gear changes with the load fluctuation, (t) is not constant, that is, the collected vibration signal S(t) has a modulation phenomenon, which is disadvantageous for analysis and diagnosis. Regardless of how (t) varies with time t, the phase of rotation of every two adjacent teeth is constant because the teeth on the gears are equally spaced over the circumference of the wheel. If a photoelectric encoder is installed next to the monitored gear and the sampling is triggered by the photoelectric encoder, S(t) can be sampled at a fixed phase interval (spatial sampling), and the collected vibration signal can be expressed as: Y(n)=Acosn(9) where: Y(n) is the amplitude of the nth sampling point; it is the phase interval of two adjacent pulses of the photoelectric encoder, =2/N; N is the gear rotation one encoder The number of pulses produced.
In this way, when the instantaneous speed changes rapidly, the sampling speed also changes accordingly; when the instantaneous speed becomes small, the sampling speed also becomes smaller, thereby correcting the twisted gear vibration signal. By performing a Fourier analysis on the spatially sampled signal, an equivalent spectrum can be obtained, which should have the spectral characteristics of the original signal. When the signal of m=10 is selected, the analysis result after spatial sampling is as shown.
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