A bearing damage positioning method based on acoustic emission signal lamb wave dispersion mode matching

Abstract

The application relates to a bearing damage positioning method based on Lamb wave dispersion mode matching of acoustic emission signals, wherein different frequency band components of original acoustic emission signals with the same frequency interval are obtained; a time of arrival curve is obtained; a theoretical dispersion curve of Lamb wave propagation in a bearing is solved, then a coordinate system is unified with the signal time of arrival curve; the dispersion curve and the time curve are matched through a Pearson correlation coefficient index; a formula is established according to a speed difference and a time difference, and a bearing damage distance is calculated; the sensor is moved by a certain distance to be measured again, and the damage position is determined through the two results. The method of matching the Lamb wave propagation mode can determine the propagation speed of the acoustic emission signals with different frequencies, the accuracy of the time difference positioning method is greatly improved, the bearing damage position can be directly found through a single sensor, the bearing fault diagnosis can be realized without depending on the bearing rotating speed, the installation difficulty can be effectively reduced, and the detection cost can be reduced.

Description

A bearing damage localization method based on Lamb wave dispersion mode matching of acoustic emission signals Technical Field

[0001] This invention relates to a bearing damage localization method based on Lamb wave dispersion mode matching of acoustic emission signals. It is a single-sensor bearing damage localization method that confirms the signal propagation mode and propagation speed by matching the propagation mode. Background Technology

[0002] The mainstream bearing fault diagnosis method is based on envelope analysis to extract bearing fault types by frequency. This method requires specific rotational speed information. A more direct approach, however, can pinpoint the location of bearing damage, enabling fault diagnosis independent of bearing rotational speed and facilitating fault confirmation and repair.

[0003] Studies have shown that the waveform of the acoustic emission signal is fixed along the propagation path between the acoustic emission source and the sensor. Furthermore, compared to the propagating elastic stress wave, a low-speed bearing can be considered nearly static. Therefore, the propagation of the acoustic emission signal can be calculated through appropriate hardware and sensor layout. In media with thin-plate-like structures, the acoustic emission signal mainly propagates as a Lamb wave. Lamb waves exhibit dispersion characteristics; combining this with the acoustic emission signal can improve positioning accuracy and diagnostic efficiency. Summary of the Invention

[0004] This invention provides a bearing damage localization method based on Lamb wave dispersion mode matching of acoustic emission signals, which solves the problem of difficulty in determining the signal propagation mode when using acoustic emission signals to locate the fault location of large bearings.

[0005] The technical solution adopted in this invention is as follows: a bearing damage localization method based on Lamb wave dispersion mode matching of acoustic emission signals, the method comprising the following steps:

[0006] S1: Conduct a lead breakage experiment on the outer ring of the bearing on a low-speed bearing failure simulation test bench to simulate the acoustic emission signal of bearing outer ring damage.

[0007] S2: Obtain the components of the original acoustic emission signal at the same frequency interval through continuous wavelet transform (CWT);

[0008] S3: Use the Akaike Information Criterion (AIC) to calculate the actual arrival time of signals for each frequency band and obtain the arrival time curve;

[0009] S4: Substitute the bearing structural parameters into the Rayleigh-Lamb equation to solve the theoretical dispersion curve of the Lamb wave propagating in the bearing, and then unify the coordinate system with the signal arrival time curve.

[0010] S5: Match the dispersion curve and the time curve using the Pearson correlation coefficient to determine the propagation mode and propagation speed of the acoustic emission Lamb wave;

[0011] S6: Establish a formula based on the speed difference and time difference to calculate the location of bearing damage.

[0012] S7: Move the sensor a certain distance and measure again, using the two results to determine the location of the damage.

[0013] As a further aspect of the present invention, in S1, a lead-breaking experiment is performed on the outer ring of the bearing on a low-speed bearing failure simulation test bench to simulate the acoustic emission signal of the bearing outer ring damage. The sampling unit is V, the sampling rate is 2MHz, and the pencil lead is an HB pencil with a tip extension length of 3-5mm when the lead breaks.

[0014] As a further aspect of the present invention, in step S2, the components of the original acoustic emission signal with the same frequency interval are obtained through continuous wavelet transform (CWT). The processing procedure is as follows:

[0015] A continuous wavelet transform is performed on the acquired acoustic emission signal s(t) to obtain signals in each frequency band with equal frequency intervals. The formula is as follows: Where a is the dimensionless scale parameter, b is the translation parameter, and Ψ * (t) is the complex conjugate of the mother wavelet Ψ(t), and the complex Morlet mother wavelet is used here, which is defined as: f b and f c These are the bandwidth parameter and the center frequency, respectively. Scale parameter. Where f s Let f be the sampling frequency of s(t), and f be the actual corresponding frequency. The real part of CWT can be considered as the center frequency and standard deviation being equal to f and f, respectively. A Gaussian bandpass filter. By selecting appropriate bandwidth parameters and center frequency, and then setting the actual frequency sequence, the components of the acoustic emission signal in different frequency bands can be obtained through CWT.

[0016] As a further aspect of the present invention, in step S3, the actual arrival time of the signal in each frequency band is calculated using the Akaike Information Criterion (AIC) to obtain an arrival time curve. The calculation process is as follows:

[0017] For a time series x of length T, AIC can be defined as:

[0018] AIC(t) = tlog 10 (var{x(1:t)})+(Tt-1)log 10The function is defined as `(varr{(x(t:T))})`, where `var` represents the variance of the time series `x`, and the length `T` extends from the start of the signal to the point of maximum peak. The AIC function divides the signal into two vectors: `{x(1:t)}` and `{x(t:T)}`. The vector before `t` represents high-entropy, uncorrelated noise, while the vector after `t` represents a significantly correlated, low-entropy signal. The minimum point `t` when the AIC function reaches its minimum value is the signal arrival time. The calculated arrival times are then plotted on a time-frequency coordinate system.

[0019] As a further aspect of the present invention, in step S4, the bearing structural parameters are substituted into the Rayleigh-Lamb equation to solve for the theoretical dispersion curve of the Lamb wave propagating in the bearing. The calculation process is as follows:

[0020] Lamb waves propagate in solid materials in symmetric and antisymmetric modes, which can be described by the Rayleigh-Lamb equations:

[0021] The symmetry pattern is: The antisymmetric mode is:

[0022] In the formula: Where k is the wavenumber of the Lamb wave along the horizontal direction of the plate, h is the plate thickness, ω is the angular frequency, ω=2πf, C l For the longitudinal wave velocity, C s The velocity is the transverse wave velocity. The dispersion curve can be calculated by substituting the material structure parameters into the Rayleigh-Lamb equation.

[0023] As a further aspect of the present invention, in step S4, the coordinate system is unified with the signal arrival time curve. Specifically, there are inherent errors in actual signal acquisition and calculation, and further calculation may amplify the errors. Therefore, the coordinate system of the theoretical dispersion curve is transformed to the coordinate system of the arrival time curve.

[0024] As a further aspect of the present invention, in step S5, the dispersion curve and the time curve are matched using the Pearson correlation coefficient to determine the specific propagation mode and propagation speed of the acoustic emission Lamb wave. The formula is as follows:

[0025] The Pearson correlation coefficient r(X, Y) for a sample is defined as:

[0026]

[0027] Where Cov(X, Y) is the covariance of the dispersion curve X and the time curve Y, Var[X] is the variance of curve X, and Var[Y] is the variance of curve Y. If r = 0, then there is no linear correlation between the two curves X and Y. The larger the absolute value of the correlation coefficient, the stronger the correlation. After selecting a suitable interval, its accuracy can be verified by the slope.

[0028] As a further aspect of the present invention, in step S6, a formula is established based on the speed difference and time difference to calculate the bearing damage location. The positioning formula is as follows:

[0029] Let the transmission distance of the acoustic emission signal be d. For any frequency band of the same acoustic emission signal, the distance d remains constant; therefore, the transmission time is inversely proportional to the transmission speed. The distance from the damage source to the sensor can be expressed as:

[0030] Where v1 and v2 are the propagation speeds of signals in different frequency bands, and t1 and t2 are the propagation times of the acquired signals (hereinafter referred to as acquisition time). Due to the advance pickup characteristic of the acquisition system, the acquisition time is not the actual propagation time of the acoustic emission signal. Let t AE The difference between the actual propagation time of the acoustic emission signal and the acquisition time is given by the relationship between the acquisition time and t. AE The difference is the signal propagation time.

[0031] As a further aspect of the present invention, in step S7, the sensor is moved a certain distance and measured again. The damage location is determined by the two results. The significance of this is that the bearing ring structure is a symmetrical structure. Calculating the damage distance once can only determine two symmetrical damage locations. Moving the sensor and calculating the distance again can determine a unique result.

[0032] The beneficial effects of this invention are:

[0033] 1. This invention employs a single sensor to directly locate bearing damage, enabling bearing fault diagnosis without relying on bearing speed. Clear fault location information facilitates prediction of the bearing's remaining life. Furthermore, using a single sensor reduces installation difficulties in actual operating conditions and effectively reduces data acquisition costs.

[0034] 2. This invention addresses the problem of difficulty in determining the signal propagation mode when using acoustic emission signals to locate faults in large bearings. It performs continuous wavelet transform on the signal and uses the AIC criterion to obtain the signal arrival time curve. Then, it uses the Pearson correlation coefficient index to match it with the theoretical dispersion curve, providing a method to determine the Lamb wave propagation mode and propagation speed. Attached Figure Description

[0035] Figure 1 is an overall flowchart of the present invention;

[0036] Figure 2 is a time-domain waveform diagram of the lead breakage signal collected by the present invention;

[0037] Figure 3 is a schematic diagram of the arrival time curve calculated by the present invention;

[0038] Figure 4 is a theoretical dispersion curve of the Lamb wave of the bearing material of the present invention.

[0039] Figure 5 is a schematic diagram of the theoretical dispersion curve after coordinate transformation according to the present invention;

[0040] Figure 6 shows the Pearson correlation coefficient within the selected interval of this invention;

[0041] Figure 7 shows the location of bearing damage according to the present invention; Detailed Implementation

[0042] The present invention will be further described below with reference to the embodiments.

[0043] Figure 1 shows a flowchart of the method of the present invention. The bearing damage localization method based on Lamb wave dispersion mode matching of acoustic emission signals provided by the present invention includes the following steps:

[0044] Step S1: Perform a lead-breaking experiment on the outer ring of the bearing on a low-speed bearing failure simulation test bench to simulate the acoustic emission signal of the bearing outer ring damage. The sampling unit is V, the sampling rate is 2MHz, the pencil lead is HB pencil, and the tip protrusion length is 3-5mm. The lead-breaking position is 120° away from the sensor position. The collected signal is shown in Figure 2.

[0045] Step S2: Obtain the components of the original acoustic emission signal at the same frequency interval through continuous wavelet transform (CWT). The processing procedure is as follows:

[0046] A continuous wavelet transform is performed on the acquired acoustic emission signal s(t) to obtain signals in each frequency band with equal frequency intervals. The formula is as follows: Where a is the dimensionless scale parameter, b is the translation parameter, and Ψ * (t) is the complex conjugate of the mother wavelet Ψ(t), and the complex Morlet mother wavelet is used here, which is defined as: f b and f c These are the bandwidth parameter and the center frequency, respectively, with f as the reference value. b =0.5, f c =5. Scale parameter Where f s Let f be the sampling frequency of s(t), and f be the actual corresponding frequency. The real part of CWT can be considered as the center frequency and standard deviation being equal to f and f, respectively. A Gaussian bandpass filter. Using the selected bandwidth parameters and center frequency, and then setting the required actual frequency sequence, the frequency components of different frequency bands of the acoustic emission signal can be obtained through CWT, wherein the frequency interval of the actual frequency sequence is 1kHz.

[0047] Step S3: Use the Akaike Information Criterion (AIC) to calculate the actual arrival time of the signal for each frequency band and obtain the arrival time curve. The calculation process is as follows:

[0048] For a time series x of length T, AIC can be defined as:

[0049] AIC(t) = tlog 10 (var{x(1:t)})+(Tt-1)log 10 The AIC function (var{(x(t:T))}) divides the signal into two vectors: {x(1:t)} and {x(t:T)}. The vector before t represents high-entropy, uncorrelated noise, while the vector after t represents a significantly correlated, low-entropy signal. The arrival time is defined as the minimum point t of the AIC function. The calculated arrival times are plotted on a time-frequency coordinate system; a schematic diagram of the arrival time curve is shown in Figure 3.

[0050] S4: Substitute the bearing structural parameters into the Rayleigh-Lamb equation to solve the theoretical dispersion curve of the Lamb wave propagating in the bearing, and then unify the coordinate system with the signal arrival time curve.

[0051] In step S4, the bearing structural parameters are substituted into the Rayleigh-Lamb equation to solve for the theoretical dispersion curve of the Lamb wave propagating in the bearing. The calculation process is as follows:

[0052] Lamb waves propagate in solid materials in symmetric and antisymmetric modes, which can be described by the Rayleigh-Lamb equations:

[0053] The symmetry pattern is: The antisymmetric mode is:

[0054] In the formula: Where k is the wavenumber of the Lamb wave along the horizontal direction of the plate, h is the plate thickness, ω is the angular frequency, ω=2πf, C l For the longitudinal wave velocity, C s Let C be the transverse wave velocity. Take Cl = 6016 m / s, C... s =3216m / s, and the dispersion curve is calculated by substituting it into the Rayleigh-Lamb equation, as shown in Figure 4.

[0055] In step S4, the coordinate system is unified with the signal arrival time curve. Specifically, inherent errors exist in actual signal acquisition and calculation, and further calculation may amplify these errors. Therefore, the coordinate system of the theoretical dispersion curve is transformed to the arrival time curve coordinate system. To make the arrival time differences of signals in different frequency bands more obvious, the propagation distance is assumed to be the farthest distance, i.e., half the circumference. Below 82kHz, there are only three possible propagation modes, and the trends of their curves differ significantly. Therefore, signals below 82kHz are selected, and their trends are matched to these three propagation modes to determine the propagation speed. The result after transformation is shown in Figure 5.

[0056] S5: Match the dispersion curve and the time curve using the Pearson correlation coefficient to determine the propagation mode and propagation speed of the acoustic emission Lamb wave;

[0057] In step S5, the dispersion curve and time curve are matched using the Pearson correlation coefficient to determine the specific propagation mode and propagation speed of the acoustic emission Lamb wave. The formula is as follows:

[0058] The Pearson correlation coefficient r(X, Y) for a sample is defined as:

[0059]

[0060] Where Cov(X, Y) is the covariance of the dispersion curve X and the time curve Y, Var[X] is the variance of curve X, and Var[Y] is the variance of curve Y. If r = 0, then there is no linear correlation between the two curves X and Y. The larger the absolute value of the correlation coefficient, the stronger the correlation. After selecting a suitable interval, the accuracy is verified by the slope. The correlation is calculated by stepping 1kHz each time with an interval length of 10kHz. The S0 mode with better correlation coefficient calculation results is shown in Figure 6. It can be seen that the correlation between 20-40kHz and 60-80kHz is relatively high. However, comparing Figure 3 and Figure 5, the slope of 20-40kHz is far from the theoretical dispersion curve, confirming that the propagation mode of 60-80kHz is the S0 mode.

[0061] Step S6: Establish a formula based on the speed difference and time difference to calculate the bearing damage location. The location formula is as follows:

[0062] Let the transmission distance of the acoustic emission signal be d. For any frequency band of the same acoustic emission signal, the distance d remains constant; therefore, the transmission time is inversely proportional to the transmission speed. The distance from the damage source to the sensor can be expressed as:

[0063] Where v1 and v2 are the propagation speeds of signals in different frequency bands, and t1 and t2 are the propagation times of the acquired signals (hereinafter referred to as acquisition time). Due to the advance pickup characteristic of the acquisition system, the acquisition time is not the actual propagation time of the acoustic emission signal. Let t AE The difference between the actual propagation time of the acoustic emission signal and the acquisition time is given by the relationship between the acquisition time and t. AE The difference is the signal propagation time.

[0064] S7: Move the sensor a certain distance and measure again. Determine the damage location using the two results. The significance is that the bearing's annular structure is symmetrical; a single calculation of the damage distance can only determine two symmetrical damage locations. Moving the sensor and calculating the distance again determines a unique result. The second measurement location is achieved by moving the sensor counterclockwise by 45°. The lead breakage is performed 20 times each, with a frequency interval of 1kHz. All positioning results from steps S6 and S7 are shown in Figure 7.

Claims

1. A bearing damage localization method based on Lamb wave dispersion mode matching of acoustic emission signals, characterized in that, The process includes the following steps: S1: Conduct a lead breakage experiment on the outer ring of the bearing on a low-speed bearing fault simulation test bench to simulate the acoustic emission signal of the bearing outer ring damage; S2: Obtain the different frequency band components of the original acoustic emission signal at the same frequency interval through continuous wavelet transform (CWT); S3: Calculate the actual arrival time of each frequency band signal using the Akaike Information Criterion (AIC) to obtain the arrival time curve; S4: Substitute the bearing structural parameters into the Rayleigh-Lamb equation to solve the theoretical dispersion curve of the Lamb wave propagating in the bearing, and then unify the coordinate system with the signal arrival time curve; S5: Match the dispersion curve and the time curve using the Pearson correlation coefficient index to determine the propagation mode and propagation speed of the acoustic emission Lamb wave; S6: Establish a formula based on the velocity difference and time difference to calculate the bearing damage location; S7: Move the sensor a certain distance and measure again to determine the damage location through the two results; In S2, obtaining the different frequency band components of the original acoustic emission signal at the same frequency interval through continuous wavelet transform (CWT) involves processing the acquired acoustic emission signal... Perform continuous wavelet transform to obtain signals in frequency bands with equal frequency intervals. The formula is as follows: ,in It is a dimensionless scale parameter. These are translation parameters. It is the mother wavelet The complex conjugate of the complex Morlet mother wavelet is used here, and it is defined as: ， and These are the bandwidth parameter, center frequency, and scale parameter. ,in yes sampling frequency, The actual corresponding frequency; the real part of CWT is considered as the center frequency and standard deviation, respectively equal to and A Gaussian bandpass filter; by selecting the bandwidth parameter and center frequency and setting the actual frequency sequence, the components of the acoustic emission signal in different frequency bands can be obtained through CWT; in S4, the bearing structure parameters are substituted into the Rayleigh-Lamb equation to solve the theoretical dispersion curve of the Lamb wave propagating in the bearing. The calculation process is as follows: The propagation of the Lamb wave in solid materials has symmetric and antisymmetric modes, described by the Rayleigh-Lamb equation: The symmetric mode is: The antisymmetric mode is: In the formula: ， ,in Let be the wave number of the Lamb wave along the horizontal direction of the plate. For plate thickness, Angular frequency, ， For the longitudinal wave velocity, Given the transverse wave velocity, the dispersion curve is calculated by substituting the material structural parameters into the Rayleigh-Lamb equation.

2. The bearing damage localization method based on Lamb wave dispersion mode matching of acoustic emission signals according to claim 1, characterized in that: In S1, a lead-breaking experiment is conducted on the outer ring of the bearing on a low-speed bearing failure simulation test bench to simulate the acoustic emission signal of the bearing outer ring damage. The sampling unit is V, the sampling rate is 2MHz, and the pencil lead is an HB pencil with a tip extension length of 3-5mm.

3. The bearing damage localization method based on Lamb wave dispersion mode matching of acoustic emission signals according to claim 1, characterized in that: In step S3, the Akaike Information Criterion (AIC) is used to calculate the actual arrival time of signals in each frequency band, obtaining an arrival time curve. The calculation process is as follows: for a length of... time series AIC is defined as: , where var represents the variance of the time series x, and the length T extends from the start of the signal to the maximum peak value; when the AIC function reaches its minimum value, the minimum point t is the signal arrival time, and the calculated arrival time is plotted in the time-frequency coordinate system.

4. The bearing damage localization method based on Lamb wave dispersion mode matching of acoustic emission signals according to claim 1, characterized in that: In step S4, the coordinate system is unified with the signal arrival time curve. The specific process is as follows: There are inherent errors in actual signal acquisition and calculation. Further calculation may amplify the errors. Therefore, the coordinate system of the theoretical dispersion curve is transformed to the coordinate system of the arrival time curve.

5. The bearing damage localization method based on Lamb wave dispersion mode matching of acoustic emission signals according to claim 1, characterized in that: In step S5, the dispersion curve and time curve are matched using the Pearson correlation coefficient to determine the specific propagation mode and propagation speed of the acoustic emission Lamb wave. The formula is: Pearson correlation coefficient of the sample. Defined as: ;in, Let X be the covariance between the dispersion curve X and the time curve Y. Let X be the variance of curve X. Let Y be the variance of the curve Y; if If there is no linear correlation between the two curves X and Y, the larger the absolute value of the correlation coefficient, the stronger the correlation. After selecting a suitable interval, the accuracy is verified by the slope.

6. The bearing damage localization method based on Lamb wave dispersion mode matching of acoustic emission signals according to claim 1, characterized in that: In step S6, a formula is established based on the speed difference and time difference to calculate the bearing damage location. The positioning formula is as follows: Let the acoustic emission signal transmission distance be... For any frequency band of the same acoustic emission signal, the distance Since both remain unchanged, the transmission time is inversely proportional to the transmission speed; the distance from the damage source to the sensor is expressed as: ,in 、 For the propagation speed of signals in different frequency bands, 、 The acquisition time is the propagation time of the acquired signal, hereinafter referred to as the acquisition time. Due to the advance pickup characteristic of the acquisition system, the acquisition time is not the actual propagation time of the acoustic emission signal. The difference between the actual propagation time of the acoustic emission signal and the acquisition time is the sum of the acquisition time and the time between the acquisition time and the acquisition time. The difference is the signal propagation time.

7. The bearing damage localization method based on Lamb wave dispersion mode matching of acoustic emission signals according to claim 1, characterized in that: In step S7, the sensor is moved a certain distance and measured again. The damage location is determined by the two results. The significance is that the bearing ring structure is a symmetrical structure. Calculating the damage distance once can only determine two symmetrical damage locations. Moving the sensor and calculating the distance again can determine a unique result.

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