When the tractor gear has defects, in the process of meshing transmission, the defects will have an impact on the tractor. In the vibration signal, the phenomena of amplitude modulation and frequency modulation appear. Different faults have different manifestations in the spectrum. Identifying faults from the spectrum is generally based on the characteristics of meshing frequency and its harmonic frequency. There are several common fault spectrum identification methods:
1) Fundamental frequency identification
If the number of teeth of the tractor gear is Z and the speed is n (RPM), the meshing frequency is: F (n) = Z × n/60。 In the past, the increase of the amplitude of the fundamental frequency component was often used as the basis for the occurrence of faults. However, due to many factors affecting the fundamental frequency, when the fault is not obvious enough, the change of the amplitude of the meshing frequency is very small, and it is often difficult to identify the fault frequency.
2) Spectrum identification
Diagnosis is based on the spacing of harmonic frequencies. In the spectrum with high resolution, uniform spikes can often be seen, and there is a harmonic relationship between the corresponding frequencies. Measuring the spacing can judge the location of the fault.
3) Side frequency identification
Side frequency identification is one of the most commonly used methods in tractor gear fault diagnosis. Because tractor gear failure will generally cause signal modulation, by identifying the side frequency spacing on the spectrum. The fault impulse frequency causing modulation can be known, so that the location of the fault can be inferred. However, due to the simultaneous existence of amplitude modulation and frequency modulation, the side frequency often becomes complex and asymmetric. Especially when there are multiple modulation sources and low-frequency modulation, it is often difficult to identify the side frequency directly.
The emergence of spectrum refinement technology enables people to refine any small local frequency band in the spectrum, greatly improves the resolution of the spectrum, and solves the problem that the side frequency is sometimes difficult to identify directly. However, the frequency band of the refined spectrum is very narrow, which is generally used only in combination with the spectrum, that is, select the frequency band to be refined.
Among the methods of tractor gear fault diagnosis, cepstrum method has special advantages Especially in the side frequency identification, it provides the information of periodic structures in the spectrum, such as harmonic family and side frequency.
Traditionally, power cepstrum is defined as “power spectrum of logarithmic power spectrum”, and its expression is as follows:
Where GX (f) is the self power spectrum of the signal; CP (q) is the power cepstrum.
The commonly used expression in practical engineering is：
Ca (q) is called amplitude cepstrum, or cepstrum for short.
The main reason for the cepstrum transformation of the power spectrum is that the component of the signal can be easily identified in the cepstrum, which is convenient to extract the signal components we are concerned about. In the cepstrum, the peak is caused by the sideband system, and the cepstrum of the peak indicates the period of the modulation signal, and its reciprocal is just the modulation frequency, The modulation frequency is the fault information we are looking for.
The inverted frequency can also eliminate the influence of the path on the source, separate the source from the path, and obtain important information of the source, such as the impulse response function H (T) of a system, the input is x (T), and the output is y (T) = x (t) * H (T).
From the convolution theorem:
Then power spectrum:
This formula shows that if two cepstrums are known among the three quantities, the other cepstrum can be obtained. The input signal and the impulse response signal of the system are separated in the cepstrum. In the fault diagnosis of the tractor gearbox, we can use this performance to separate the effect of the signal source from the effect of the transmission path. When the two vibration sensors have different power spectra due to different positions, but the important signal components in the cepstrum are the same, It is only slightly different at the low inverted frequency, which is only caused by different transfer paths, that is, different transfer functions.