Through theory and experiment, it is proved that when the tractor gearbox has no fault, the vibration signal energy is basically concentrated in the low-frequency band. When there is a fault, the impact force or friction caused by the fault excites the high-frequency vibration of the tractor gearbox, and the energy is transferred to the medium frequency band and high-frequency band. The power spectrum of the signal reflects the distribution of the energy of the signal with the frequency, that is, the frequency components in the vibration signal and the energy of each frequency component. When the energy ratio of each frequency component in the signal changes and the power spectrum component increases, the energy distribution on the power spectrum is dispersed. When the intermediate frequency component of the signal decreases, the energy distribution on the power spectrum is concentrated. It can be seen that the frequency domain characteristic change of the signal can be better described by the change of the position of the main frequency band in the power spectrum and the dispersion degree of its energy distribution.

Frequency domain parameters mainly include the following:

1) Center of gravity frequency

2) Mean square frequency

3) Root mean square frequency

4) Frequency variance

5) Frequency standard deviation

S (f) in the above formulas is the power spectrum of the vibration signal (F is the frequency). The center of gravity frequency, mean square frequency and root mean square frequency all describe the change of the position of the main frequency band of the power spectrum, while the frequency variance and standard deviation describe the dispersion of spectral energy.

Using the property of Fourier transform, the frequency domain parameters of signal {Xi} (I = 1-N sampling points) can be obtained. The fast time domain algorithm is as follows

Where: X * (I) = [x (I) – x (i-1)]/ Δ。Δ Is the sampling interval, and N is the number of sampling points.

These time-domain and frequency-domain characteristic parameters have their own characteristics and scope of application, but they can only be used for simple diagnosis of tractor gearbox. In practical application, they are often used together with other methods to obtain better fault diagnosis effect.