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1 The generalized demodulation time-frequency analysis method of envelope order spectrum based on generalized demodulation time-frequency analysis requires Hilbert transform on the signal before generalized demodulation and wavelet packet decomposition. The obtained wavelet packet decomposition result is a complex number. The component signals, and thus the time domain waveforms of the individual single component signals, are not obtained. Therefore, the literature improves the generalized demodulation time-frequency analysis, not only can effectively decompose multi-component signals, but also obtain the same time-frequency distribution.
When the gear fails, the amplitude and phase of the vibration signal change at the same time, generating amplitude and phase modulation, ignoring the influence of the transfer function on the gear vibration signal. The gear fault vibration signal picked up by the sensor is x(t)=∑Mm =1Xm[1 dm(t)]cos[2Πmzfst Order sampling can be achieved by various order tracking methods. The traditional order tracking method requires special hardware to implement. If the hardware conditions are not allowed, the order tracking method can be used for resampling. At this time, it is only necessary to separately perform the vibration signal and the speed signal at the same time. Interval time domain sampling.
The steps of the envelope order spectrum method based on generalized demodulation time-frequency analysis are as follows: 1) The phase function s(t) is estimated from the gear speed signal r(t).
The gear fault vibration signal contains a lot of noise. At this time, the meshing frequency and its sideband are submerged, so the phase function cannot be estimated from the approximate time-frequency map, but the phase function can be theoretically determined. Specifically for the gear fault vibration signal, it is composed of several frequency groups that are not parallel to each other. According to the gear number and the speed curve r(t), the meshing frequency can be calculated. In order to make the frequency bands of the respective frequency families do not overlap before the wavelet packet decomposition, it is conceivable to first convert the time-frequency curve of the first frequency family (the lowest frequency component) into a straight line parallel to the time coordinate axis, so that the first one can be The frequency family is separated from the other frequency families (refer to Part 3), whereby the phase function s(t)=z∫t0r(Σ)60dΣ can be determined from the gear speed signal r(t) (unit: rmin), where z is the gear Number of teeth. Then determine the phase function s(t) = 2z ∫ t0r (Σ) 60d Σ, separate the second frequency family from the other frequency families, and so on.
2) The improved generalized demodulation time-frequency analysis method is used to analyze the gear vibration signal x(t) to obtain several single-component signals.
2 Application 211 simulation signal analysis sampling frequency is 2048Hz. Directly using D10 orthogonal wavelet to decompose and reconstruct the 2 layers of wavelet packet. As shown in the figure, it can be seen that the wavelet decomposition lacks adaptiveness and cannot be obtained. A single component signal with physical meaning.
Since the time-frequency curves of the two components in the simulated signal overlap each other, the wavelet packet decomposition cannot obtain the two components in the original signal, resulting in the decomposition result. (Consider converting the time-frequency curve of the low-frequency component into a line parallel to the time axis), and then performing generalized demodulation on the simulated signal to obtain a time-frequency distribution (without inverse generalized demodulation). As shown, it can be seen that After the generalized demodulation, the time-frequency curves of the two components have been separated, so that the MODWPT can be used to perform wavelet packet decomposition on the generalized demodulated signal, and the complete time-frequency distribution of the signal is further obtained. The dotted line indicates that the frequency band of [0,1024] Hz is evenly divided into four equal-bandwidth bands, thereby determining the number of decomposition layers J0=2. Selecting the Fe2jer2 Korovkin wavelet filter of length L=22, using improved generalized demodulation After the frequency analysis method analyzes the simulation signal, the decomposition result and the time-frequency distribution are respectively shown. It can be seen from the decomposition result and the time-frequency diagram that the generalized demodulation time-frequency distribution has completely separated the two components in the original signal, and thus the superiority of the method in processing the FM signal can be seen. At the same time, it can be seen that although the theoretical generalized demodulation time-frequency analysis method is suitable for processing multi-component signals in which the time-frequency distribution is a plurality of parallel curves, the time-frequency distribution curves of the respective components are not parallel to each other. The quantity signal, as long as the appropriate phase function is selected, so that the time-frequency distribution curve of each component after the generalized demodulation is distributed in the rectangular time-frequency block of the different wavelet packet time-frequency space, the instantaneous frequency of each component obtained after the wavelet packet decomposition And the instantaneous amplitude still has physical meaning, and still get more accurate results.
It can be seen that there are obvious peaks at the order of 1 and 2, respectively corresponding to the frequency of the gear and its double frequency, indicating that the simulated signal is amplitude modulated by the rotational frequency component, so based on the generalized demodulation time-frequency The analyzed envelope order spectrum can effectively extract the modulation information of the amplitude modulation signal under non-stationary speed, which can be effectively applied to the gear fault diagnosis under non-stationary speed.
212 Experimental Signal Analysis In order to verify the effectiveness of the method, transient experiments were carried out on the gear test bench under normal and broken gear conditions. Two standard spur gears with a modulus of 2 mm and a number of teeth of 55 were used. The acceleration vibration signal is picked up on the gear box, and the speed signal is picked up by the photoelectric speed sensor. The sampling frequency is 2048 Hz. After the band-pass filtering of the vibration acceleration signal, the envelope order spectrum analysis is directly performed, and the result is shown in the figure. The obvious frequency-dependent order can be found because the vibration signal is not only a multi-component amplitude modulation 2 frequency modulation signal, but also the frequency component of the envelope signal (ie, the frequency conversion and its multiple) changes with time, so The FFT of the envelope signal directly cannot extract its rotational frequency component. In order to perform generalized demodulation analysis on the gear vibration signal, it is necessary to determine the phase function. It can be seen from the speed curve that the maximum meshing frequency is 41,215 Hz, so the gear vibration signal contains at most two frequency families. From the analysis method of the first part and the previous simulation signal, it is known that in order to make the frequency bands of the two frequency families do not overlap before the wavelet packet decomposition, the time frequency of the first frequency family (the lowest frequency component) can be simply considered. The curve is transformed into a straight line parallel to the time coordinate axis, whereby the phase function s(t)=55∫t0r(Σ) 60dΣ can be determined. Then, the gear vibration signal is subjected to generalized demodulation time-frequency analysis, and the decomposition result is shown. Further, the envelope order spectrum analysis is performed on each component in the graph. It is found that the envelope order spectrum of the first component c1(t) and the second component c2(t) are obvious at the order of one. The peak value corresponds to the frequency of the gear, which indicates that the gear vibration signal is modulated by the amplitude of the frequency-converting component. This is the characteristic of the vibration signal when the gear has a broken tooth fault, which is consistent with the actual situation. No obvious frequency-related order was found from the figure. The same method as above was used to analyze the envelope order spectrum of each component, and the order related to the frequency conversion could not be found from these figures.
3 Conclusion The essence of order tracking analysis is to convert the non-stationary signal in the time domain into the stable signal of the angular domain by equal angle sampling to better reflect the information related to the rotation speed. When the gear fails, its vibration signal appears as multi-component amplitude modulation 2 frequency modulation during start-stop process. Therefore, in order to extract the amplitude modulation characteristics of the fault signal, it is necessary to separate the multi-component amplitude modulation 2 FM signal on the one hand, and the other In aspect, an order analysis is performed on the envelope of the separated single component signal. Based on this, this paper proposes an envelope order spectrum method based on generalized demodulation time-frequency analysis. The generalized demodulation time-frequency analysis method is used to decompose the gear vibration signal into several single-component amplitude modulation 2 FM signals, and then perform the components. Envelope order spectrum analysis can extract the amplitude modulation characteristics related to frequency conversion, so as to effectively diagnose faults. The method is suitable for processing multi-component amplitude modulation 2 FM signals, which can be used for gear fault diagnosis in the start-stop process, but the phase function needs to be estimated. This is also a key problem in the generalized demodulation time-frequency analysis method. The literature makes a preliminary discussion. But yet to be further research.
When the gear fails, the amplitude and phase of the vibration signal change at the same time, generating amplitude and phase modulation, ignoring the influence of the transfer function on the gear vibration signal. The gear fault vibration signal picked up by the sensor is x(t)=∑Mm =1Xm[1 dm(t)]cos[2Πmzfst
The steps of the envelope order spectrum method based on generalized demodulation time-frequency analysis are as follows: 1) The phase function s(t) is estimated from the gear speed signal r(t).
The gear fault vibration signal contains a lot of noise. At this time, the meshing frequency and its sideband are submerged, so the phase function cannot be estimated from the approximate time-frequency map, but the phase function can be theoretically determined. Specifically for the gear fault vibration signal, it is composed of several frequency groups that are not parallel to each other. According to the gear number and the speed curve r(t), the meshing frequency can be calculated. In order to make the frequency bands of the respective frequency families do not overlap before the wavelet packet decomposition, it is conceivable to first convert the time-frequency curve of the first frequency family (the lowest frequency component) into a straight line parallel to the time coordinate axis, so that the first one can be The frequency family is separated from the other frequency families (refer to Part 3), whereby the phase function s(t)=z∫t0r(Σ)60dΣ can be determined from the gear speed signal r(t) (unit: rmin), where z is the gear Number of teeth. Then determine the phase function s(t) = 2z ∫ t0r (Σ) 60d Σ, separate the second frequency family from the other frequency families, and so on.
2) The improved generalized demodulation time-frequency analysis method is used to analyze the gear vibration signal x(t) to obtain several single-component signals.
2 Application 211 simulation signal analysis sampling frequency is 2048Hz. Directly using D10 orthogonal wavelet to decompose and reconstruct the 2 layers of wavelet packet. As shown in the figure, it can be seen that the wavelet decomposition lacks adaptiveness and cannot be obtained. A single component signal with physical meaning.
Since the time-frequency curves of the two components in the simulated signal overlap each other, the wavelet packet decomposition cannot obtain the two components in the original signal, resulting in the decomposition result. (Consider converting the time-frequency curve of the low-frequency component into a line parallel to the time axis), and then performing generalized demodulation on the simulated signal to obtain a time-frequency distribution (without inverse generalized demodulation). As shown, it can be seen that After the generalized demodulation, the time-frequency curves of the two components have been separated, so that the MODWPT can be used to perform wavelet packet decomposition on the generalized demodulated signal, and the complete time-frequency distribution of the signal is further obtained. The dotted line indicates that the frequency band of [0,1024] Hz is evenly divided into four equal-bandwidth bands, thereby determining the number of decomposition layers J0=2. Selecting the Fe2jer2 Korovkin wavelet filter of length L=22, using improved generalized demodulation After the frequency analysis method analyzes the simulation signal, the decomposition result and the time-frequency distribution are respectively shown. It can be seen from the decomposition result and the time-frequency diagram that the generalized demodulation time-frequency distribution has completely separated the two components in the original signal, and thus the superiority of the method in processing the FM signal can be seen. At the same time, it can be seen that although the theoretical generalized demodulation time-frequency analysis method is suitable for processing multi-component signals in which the time-frequency distribution is a plurality of parallel curves, the time-frequency distribution curves of the respective components are not parallel to each other. The quantity signal, as long as the appropriate phase function is selected, so that the time-frequency distribution curve of each component after the generalized demodulation is distributed in the rectangular time-frequency block of the different wavelet packet time-frequency space, the instantaneous frequency of each component obtained after the wavelet packet decomposition And the instantaneous amplitude still has physical meaning, and still get more accurate results.
It can be seen that there are obvious peaks at the order of 1 and 2, respectively corresponding to the frequency of the gear and its double frequency, indicating that the simulated signal is amplitude modulated by the rotational frequency component, so based on the generalized demodulation time-frequency The analyzed envelope order spectrum can effectively extract the modulation information of the amplitude modulation signal under non-stationary speed, which can be effectively applied to the gear fault diagnosis under non-stationary speed.
212 Experimental Signal Analysis In order to verify the effectiveness of the method, transient experiments were carried out on the gear test bench under normal and broken gear conditions. Two standard spur gears with a modulus of 2 mm and a number of teeth of 55 were used. The acceleration vibration signal is picked up on the gear box, and the speed signal is picked up by the photoelectric speed sensor. The sampling frequency is 2048 Hz. After the band-pass filtering of the vibration acceleration signal, the envelope order spectrum analysis is directly performed, and the result is shown in the figure. The obvious frequency-dependent order can be found because the vibration signal is not only a multi-component amplitude modulation 2 frequency modulation signal, but also the frequency component of the envelope signal (ie, the frequency conversion and its multiple) changes with time, so The FFT of the envelope signal directly cannot extract its rotational frequency component. In order to perform generalized demodulation analysis on the gear vibration signal, it is necessary to determine the phase function. It can be seen from the speed curve that the maximum meshing frequency is 41,215 Hz, so the gear vibration signal contains at most two frequency families. From the analysis method of the first part and the previous simulation signal, it is known that in order to make the frequency bands of the two frequency families do not overlap before the wavelet packet decomposition, the time frequency of the first frequency family (the lowest frequency component) can be simply considered. The curve is transformed into a straight line parallel to the time coordinate axis, whereby the phase function s(t)=55∫t0r(Σ) 60dΣ can be determined. Then, the gear vibration signal is subjected to generalized demodulation time-frequency analysis, and the decomposition result is shown. Further, the envelope order spectrum analysis is performed on each component in the graph. It is found that the envelope order spectrum of the first component c1(t) and the second component c2(t) are obvious at the order of one. The peak value corresponds to the frequency of the gear, which indicates that the gear vibration signal is modulated by the amplitude of the frequency-converting component. This is the characteristic of the vibration signal when the gear has a broken tooth fault, which is consistent with the actual situation. No obvious frequency-related order was found from the figure. The same method as above was used to analyze the envelope order spectrum of each component, and the order related to the frequency conversion could not be found from these figures.
3 Conclusion The essence of order tracking analysis is to convert the non-stationary signal in the time domain into the stable signal of the angular domain by equal angle sampling to better reflect the information related to the rotation speed. When the gear fails, its vibration signal appears as multi-component amplitude modulation 2 frequency modulation during start-stop process. Therefore, in order to extract the amplitude modulation characteristics of the fault signal, it is necessary to separate the multi-component amplitude modulation 2 FM signal on the one hand, and the other In aspect, an order analysis is performed on the envelope of the separated single component signal. Based on this, this paper proposes an envelope order spectrum method based on generalized demodulation time-frequency analysis. The generalized demodulation time-frequency analysis method is used to decompose the gear vibration signal into several single-component amplitude modulation 2 FM signals, and then perform the components. Envelope order spectrum analysis can extract the amplitude modulation characteristics related to frequency conversion, so as to effectively diagnose faults. The method is suitable for processing multi-component amplitude modulation 2 FM signals, which can be used for gear fault diagnosis in the start-stop process, but the phase function needs to be estimated. This is also a key problem in the generalized demodulation time-frequency analysis method. The literature makes a preliminary discussion. But yet to be further research.
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