Variable-speed working condition rolling bearing fault diagnosis method based on improved wavelet packet transformation and envelope order tracking

Abstract

The invention discloses a variable-speed working condition rolling bearing fault diagnosis method based on improved wavelet packet transformation and envelope order tracking, and the method specifically comprises the steps: carrying out the equal-angle resampling of a vibration signal according to the phase of a rotating shaft, and carrying out the wavelet packet transformation of an angle domain vibration signal through an improved wavelet packet transformation algorithm, and finally, fault diagnosis is carried out according to the transformed envelope order spectrum of the wavelet packet coefficient of each node. According to the method, time domain signals are converted into angle domain signals through equal-angle resampling, frequency spectrum fuzziness caused by rotating speed changes is eliminated, and the angle domain signals are divided to different order bands through the excellent frequency domain decomposition capacity of an improved wavelet packet transformation algorithm so that sub-signals with the high signal-to-noise ratio can be obtained. And finally, solving the envelope spectrum of the sub-signal to further highlight the fault characteristics. According to the method, the problem of difficulty in fault diagnosis of the variable-speed working condition bearing is solved, meanwhile, the process of determining a high-frequency resonance frequency band by means of a kurtosis graph and extracting a high-frequency resonance signal through band-pass filtering is avoided, and the diagnosis method is simple, efficient and high in accuracy.

Description

Technical Field

[0001] This invention relates to the fields of digital signal processing and mechanical fault diagnosis, specifically to a fault diagnosis method for rolling bearings in variable speed conditions based on improved wavelet packet transform and envelope order tracking. Background Technology

[0002] Rolling bearings are a key component of rotating machinery systems, playing a vital role in industrial production. In actual industrial production, rolling bearings often operate in complex and harsh environments, making them prone to failure. Therefore, condition monitoring of rolling bearings and real-time fault diagnosis are of great significance in ensuring the safe and stable operation of equipment.

[0003] Rolling bearings often operate under variable speed conditions, generating non-periodic fault pulses that cannot be accurately determined using Fourier analysis. To address the ambiguity of the bearing vibration signal spectrum under variable speed conditions, an order tracking method using equal-angle resampling of the vibration signal based on the shaft phase has been proposed and widely used. Studies have shown that the angle between the load and the radial plane changes with the position of the balls during the rotation of a rolling bearing, causing random slippage in the time interval of the fault pulses. This random slippage leads to spectral ambiguity in the equally sampled signal spectrum. To highlight fault characteristics, its envelope spectrum is often used for analysis. The fault diagnosis method combining order tracking and envelope analysis is called envelope order tracking. This method is simple, efficient, and has been widely applied in bearing fault diagnosis.

[0004] Because vibration signals contain a large amount of noise, fault features in the envelope order spectrum of the original vibration signal are often masked by the noise. To improve the signal-to-noise ratio (SNR), a suitable frequency band is often selected for bandpass filtering of the original signal, and then envelope order tracking is applied to the filtered signal to extract fault features. In engineering, the fast kurtosis plot algorithm is generally used to determine the high-frequency resonance band of the signal, and the original signal is then bandpass filtered based on the resonance band before fault diagnosis. However, when the SNR is low, the fast kurtosis plot algorithm sometimes cannot accurately determine the resonance band, causing fault features in the filtered signal to be masked by noise. Accurately determining the high-frequency resonance band through some method is crucial for applying envelope order tracking to diagnose faults in rolling bearings operating under variable speed conditions.

[0005] In recent years, wavelet packet transform has been widely used in bearing fault diagnosis due to its excellent time-frequency analysis capabilities. However, wavelet packet transform algorithms based on Mallat multiresolution analysis suffer from spectral aliasing, which can mask fault characteristics in the wavelet packet coefficient spectrum. Removing redundant frequency components from the wavelet packet coefficients can avoid spectral aliasing and improve the frequency domain analysis capabilities of the wavelet packet transform. By improving the wavelet packet transform algorithm, removing redundant frequency components from the wavelet packet coefficients, and then utilizing the excellent frequency decomposition capabilities of the wavelet packet to obtain high-frequency resonance signals, the final combination of wavelet packet transform and envelope order tracking can achieve fault diagnosis of variable speed bearings. Summary of the Invention

[0006] To address the spectral aliasing problem in wavelet packet transform algorithms, this invention utilizes Fourier transform and inverse Fourier transform to remove redundant frequency components from wavelet packet coefficients, thus eliminating spectral aliasing. Furthermore, to achieve fault diagnosis of rolling bearings operating under variable speed conditions, this invention combines an improved wavelet packet transform algorithm with envelope order tracking, proposing a novel method for fault diagnosis of variable speed bearings. Simulation experiments have verified the effectiveness of this method.

[0007] A fault diagnosis method for rolling bearings under variable speed conditions based on improved wavelet packet transform and envelope order tracking includes the following steps:

[0008] 1. Data Collection

[0009] High-sampling-rate accelerometers and incremental encoders were used to collect the vibration acceleration and shaft phase on the bearing base under test, respectively.

[0010] 2. Iso-angle resampling

[0011] The vibration signal is resampled at equal angles based on the phase of the rotating shaft, converting the time-domain signal into an angle-domain signal.

[0012] 3. Wavelet packet transform

[0013] An improved wavelet packet transform algorithm is used to perform wavelet packet transform on the angle domain signal.

[0014] The wavelet packet transform algorithm based on Mallat's multiresolution analysis is as follows:

[0015]

[0016] In the formula, x(n) is a discrete-time signal, n = 0, 1, ... B-1; Let be the wavelet packet coefficients of the i-th node in the j-th layer, j = 0, 1, ..., log₂N, i = 1, 2, ..., 2 j H and G are the low-pass and high-pass filters for wavelet decomposition, respectively.

[0017] Operators C and D are used to remove redundant frequency components from the wavelet packet coefficients of each node to avoid frequency aliasing.

[0018] The formula for operator C is:

[0019]

[0020] In the formula, N j Let x(n) represent the length of x(n), k = 0, 1, ..., N. j -1, It is the output of operator C.

[0021] The formula for calculating operator D is:

[0022]

[0023] In the formula, N j Let x(n) represent the length of x(n), k = 0, 1, ..., N. j -1, It is the output of operator D.

[0024] 4. Calculate the envelope of the wavelet packet node coefficients in the last layer using the following formula:

[0025]

[0026] In the formula, p i (n) represents the wavelet packet coefficients of the i-th node in the J-th layer, where J is the decomposition layer number. p i Hilbert transform of (n), For p i (n) The magnitude of the analytic signal, i.e., the envelope.

[0027] 5. Calculate the envelope order spectrum

[0028] The envelope order spectrum is obtained by performing a Fourier transform on the square of the wavelet packet coefficient envelope of each node.

[0029] 6. Fault Diagnosis

[0030] By comparing the characteristic order in the wavelet packet coefficient envelope order spectrum of each node with the characteristic order of bearing fault, the bearing fault type can be determined.

[0031] Beneficial effects

[0032] This invention proposes a novel method for fault diagnosis of rolling bearings operating under variable speed conditions based on improved wavelet packet transform and envelope order tracking. Specifically, after resampling the time-domain vibration signal at equal angles according to the shaft phase, an improved wavelet packet transform algorithm is used to perform wavelet packet transform on the angle-domain signal. Fault diagnosis is then performed by analyzing the envelope spectrum of the wavelet packet coefficients at the last layer nodes. This invention utilizes Fourier transform and inverse transform to remove redundant frequency components from the wavelet packet coefficients, avoiding spectral aliasing in traditional wavelet packet transform algorithms, improving the frequency resolution of the wavelet packet transform, and enhancing its frequency domain decomposition capability. Compared with traditional wavelet packet algorithms, the improved wavelet packet algorithm can use wavelet filters of lower order due to the elimination of spectral aliasing, indirectly improving the algorithm's efficiency. Furthermore, resampling the time-domain vibration signal at equal angles before the wavelet packet transform eliminates spectral ambiguity caused by speed variations, and calculating the envelope spectrum of the wavelet packet coefficients after the wavelet packet transform further enhances the fault diagnosis capability of this method. Attached Figure Description

[0033] Figure 1 The flowchart is shown below for the fault diagnosis method of rolling bearing under variable speed conditions based on improved wavelet packet transform and envelope order tracking proposed in this invention.

[0034] Figure 2 Schematic diagram of the improved wavelet packet transform algorithm;

[0035] Figure 3 The time-domain waveforms of bearing vibration signals in Embodiment 3 of the present invention are shown.

[0036] Figure 4 This refers to the shaft phase pulse signal of the bearing in Embodiment 3 of the present invention;

[0037] Figure 5 The angular domain waveform of the bearing vibration signal in Embodiment 3 of the present invention;

[0038] Figure 6 This is the envelope order spectrum of the wavelet packet coefficients of the third-layer node of the vibration signal of the healthy bearing in this embodiment of the invention;

[0039] Figure 7 This is the envelope order spectrum of the wavelet packet coefficients of the third layer node of the vibration signal of the inner ring fault bearing in an embodiment of the present invention.

[0040] Figure 8 This is the envelope order spectrum of the wavelet packet coefficients of the third-layer node of the vibration signal of the outer ring fault bearing in an embodiment of the present invention. Detailed Implementation

[0041] The present invention will now be described in conjunction with the accompanying drawings and embodiments.

[0042] This invention uses the University of Ottawa bearing dataset for testing. The experimental bearing is an ER16K ball bearing. An accelerometer and an incremental encoder were used to collect the vibration acceleration of the bearing housing and the phase of the shaft, respectively, with a sampling frequency of 200kHz. The bearing operates under variable speed conditions, and the inner ring fault order f... i =5.43, outer ring fault order f o =3.57. The embodiments of this invention were implemented in the Matlab 2022b software environment.

[0043] like Figure 1 As shown, the specific steps of the fault diagnosis method proposed in this invention are as follows:

[0044] S1. Data Acquisition

[0045] A high-sampling-rate accelerometer (ICP accelerometer, Model 623C01) and an incremental encoder (EPCmodel 775) were used to acquire the vibration acceleration and shaft phase on the bearing base under test, respectively. The sampling frequency was 200kHz for both, and the incremental encoder generated 1024 pulses per revolution of the shaft. The vibration signals and phase pulse signals of the healthy bearing, the bearing with an inner ring fault, and the bearing with an outer ring fault are shown below. Figure 3 and Figure 4 As shown (only a portion of the signal is displayed for ease of observation).

[0046] S2. Isoangular resampling

[0047] The vibration signal is resampled at equal angles based on the phase of the rotating shaft, specifically as follows:

[0048] (1) Determine the index of the points with equal phase intervals based on the phase pulse signal of the rotating shaft.

[0049] (2) The vibration signal is resampled according to the index, that is, the signal value at the index is taken as the signal after equal-angle resampling, and the sampling frequency is 1024 sample points / revolution. The signals after equal-angle resampling for healthy bearings, inner ring fault bearings, and outer ring fault bearings are as follows: Figure 5 As shown (only a portion of the signal is displayed for ease of observation).

[0050] S3. Wavelet Packet Transform

[0051] Using the Daubechies wavelet 'db4' as the mother wavelet, an improved wavelet packet transform algorithm is used to perform a three-level wavelet packet transform on the angle domain signal.

[0052] S4. Find the envelope of the wavelet packet coefficients of the 3rd layer node.

[0053] S5. Calculate the square of the envelope of the wavelet packet coefficients at the 3rd layer nodes, and perform a Fast Fourier Transform (FFT) on the squared envelope to obtain the envelope order spectrum of the wavelet packet coefficients at each node. The envelope order spectra of the wavelet packet coefficients at the 3rd layer nodes for the healthy bearing, the inner ring fault bearing, and the outer ring fault bearing are shown below. Figure 6 , 7 As shown in Figure 8.

[0054] S6. Perform fault diagnosis on the bearing based on the envelope order spectrum of the wavelet packet coefficients of the third-level node and the order of the rolling bearing fault characteristics. Figure 6 The inner fault order f is absent in the envelope order spectrum of wavelet packet coefficients at all nodes. i and outer ring fault order f o The harmonic order indicates that the bearing has not experienced any inner or outer ring failure. Figure 7 In almost all nodes, there is an inner-circle fault order f. i The harmonic order indicates that the bearing has an inner ring failure. Figure 8 The presence of obvious outer ring fault characteristic order and harmonic order at nodes (3,2) and (3,3) indicates that an outer ring fault has occurred in the bearing.

Claims

1. A fault diagnosis method for rolling bearings under variable speed conditions based on improved wavelet packet transform and envelope order tracking, characterized in that, Includes the following steps: (1) Data acquisition: High sampling rate accelerometer and incremental encoder are used to acquire the vibration acceleration and shaft phase on the bearing base under test, respectively; (2) Equal angle resampling: The vibration signal is resampled at equal angles according to the phase of the rotating shaft collected in step (1), and the time domain signal is converted into the angle domain signal. (3) Wavelet packet transform: The improved wavelet packet transform algorithm is used to perform wavelet packet transform on the angle domain signal obtained in step (2); (4) Find the envelope: Find the envelope of the wavelet packet coefficients of the last layer node in step (3); (5) Find the envelope order spectrum: Find the envelope spectrum of the wavelet packet coefficients of the nodes in step (4); (6) Fault diagnosis: Based on the envelope order spectrum of wavelet packet coefficients of each node in step (5) and the bearing fault characteristic order, the bearing is diagnosed for fault.

2. The method for fault diagnosis of rolling bearings under variable speed conditions based on improved wavelet packet transform and envelope order tracking according to claim 1, characterized in that, The step (2) of equal-angle resampling specifically involves: (2.1) Determine the index of the points with equal phase intervals based on the phase pulse signal of the rotating shaft; (2.2) Take the signal value at the index as the signal after equal angle resampling, and the sampling frequency is the number of pulses generated by the incremental encoder when the shaft rotates one revolution.

3. The method for fault diagnosis of rolling bearings under variable speed conditions based on improved wavelet packet transform and envelope order tracking according to claim 1, characterized in that, The wavelet packet transform in step (3) is specifically as follows: The Fast Fourier Transform (FFT) and Inverse Fourier Transform (IFFT) are used to remove redundant frequency components from the wavelet packet coefficients, avoiding spectral aliasing. The calculation formulas for operators C and D are as follows: In the formula, N j Let x(n) represent the length of x(n), k = 0, 1, ..., N. j -1, It is the output of operator C; In the formula, N j Let x(n) represent the length of x(n), k = 0, 1, ..., N. j -1, It is the output of operator D.

4. The method for fault diagnosis of rolling bearings under variable speed conditions based on improved wavelet packet transform and envelope order tracking according to claim 1, characterized in that, Step (4) involves calculating the envelope, specifically: (4.1) Find the analytic signal of the last layer of node coefficients in the wavelet packet transform of the angle domain signal; (4.2) Find the modulus of the analytic signal of the last layer of node coefficients in the wavelet packet transform of the angle domain signal.

5. The method for fault diagnosis of rolling bearings under variable speed conditions based on improved wavelet packet transform and envelope order tracking according to claim 1, characterized in that, Step (5) involves obtaining the envelope order spectrum, specifically as follows: Find the square of the envelope of the last layer of node coefficients in the wavelet packet transform of the angle domain signal, and then perform a Fourier transform on it to obtain the envelope order spectrum.

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