Rolling bearing fault feature enhancement method for multi-period accumulation mutual reference correlation coefficient signal reconstruction

Abstract

The invention discloses a rolling bearing fault feature enhancement method for multi-period accumulation mutual reference correlation coefficient signal reconstruction, and belongs to the field of fault diagnosis and signal processing. The method is provided for solving the problem that the installation error and the manufacturing error of an encoder interfere with the fault feature identification of the rolling bearing and the problem that the fault feature of the rolling bearing is weak and difficult to identify under the low-rotating-speed and variable-rotating-speed composite working condition. The rolling bearing fault feature enhancement method based on multi-cycle accumulation mutual reference correlation coefficient signal reconstruction is provided based on the fluctuation characteristics of instantaneous angular velocity signals under the working conditions of different rotating speeds, different radial loads and different fault sizes in combination with multi-cycle differential accumulation characteristics and correlation analysis characteristics. According to the method, interference components such as encoder installation errors, manufacturing errors, instantaneous angular velocity estimation errors and measurement noise are suppressed, and then feature extraction of weak faults of the rolling bearing under the low-rotating-speed and variable-rotating-speed composite working conditions is achieved.

Description

Technical Field

[0001] The present invention relates to a rolling bearing fault feature enhancement method for multi-period cumulative cross-reference correlation coefficient signal reconstruction, belonging to the technical fields of fault diagnosis and signal processing. Background Art

[0002] Low-speed and variable-speed operating conditions are common operating conditions of rotating machinery. As a core component, the health of rolling bearings directly affects the operating accuracy, working efficiency, and service life of rotating machinery. Therefore, fault diagnosis of rolling bearings under low-speed and variable-speed operating conditions has become one of the research hotspots in the field of fault diagnosis.

[0003] On the one hand, encoder signals have advantages such as short transmission paths, no need for external installation, no need for regular calibration, and direct correlation with dynamics. In recent years, fault diagnosis technologies based on instantaneous angular velocity signals have developed rapidly.

[0004] On the other hand, early faults of bearings are relatively weak. In low-speed and variable-speed operating conditions, they are easily affected by errors such as speed trend components and background noise, causing the fault features to be submerged. At the same time, encoder installation errors are inevitable in engineering applications; the energy amplitude of encoder installation errors is positively correlated with the speed, that is, the modulation effect of encoder installation errors on fault signals increases significantly with the increase in speed.

[0005] In summary, it is particularly important to enhance the weak fault features of rolling bearings and suppress interference components. Summary of the Invention

[0006] To solve the above problems, the present invention provides a rolling bearing fault feature enhancement method for multi-period cumulative cross-reference correlation coefficient signal reconstruction (MPCRCC), which solves the problem that the early fault features of the outer ring IAS signal of rolling bearings based on encoder signals are relatively weak and are easily affected by interference components such as encoder manufacturing errors, installation errors, variable-speed trend components, and background noise under low-speed and variable-speed composite operating conditions, resulting in difficult clear identification of bearing fault features.

[0007] Based on the signals collected by an optical encoder, the present invention suppresses interference components such as speed trend components, encoder installation errors, and background noise under variable-speed and low-speed operating conditions, enhances the weak fault features of early rolling bearings, and realizes clear identification of the fault features of the outer ring of rolling bearings.

[0008] The rolling bearing fault feature enhancement method for multi-period cumulative cross-reference correlation coefficient signal reconstruction of the present invention is as follows:

[0009] 1. Collect the instantaneous angular displacement and corresponding time of the optical encoder through the PicoScope signal acquisition system, and calculate the instantaneous angular velocity w using the forward difference method i , and the calculation formula is as follows:

[0010]

[0011] In the formula, w i represents the instantaneous angular velocity at the i-th moment, i = 1, 2, 3,..., N represents the number of grating lines per revolution of the encoder;

[0012] 2. Under the condition of high radial load, obtain the rolling bearing outer ring fault signal with high signal-to-noise ratio as the reference signal w R , and obtain the number P of periods of interest from the reference signal w R , and obtain the fault impact position γ(p) through the extreme value;

[0013] 3. Perform periodic cumulative calculation on the instantaneous angular velocity through the following formula;

[0014]

[0015] In the formula: p = 1, 2,..., P, P is the number of periods of interest; w cj is the j-th column of the row vector of the matrix w c , w c is the matrix form of the instantaneous angular velocity w i , d(·) represents differential calculation, j = 1, 2... J, Nw is the instantaneous angular velocity fault impact angle (i.e., window width parameter) caused by the rolling bearing fault, L fault is the rolling bearing fault size, R is the inner radius of the outer ring, f shaft is the inner ring rotation characteristic frequency, f cage is the cage rotation frequency, Δφ = 2π / N, N represents the number of grating lines per revolution of the encoder;

[0016]

[0017] In the formula: l is the length of the reference signal w R , J = round(K / J)-1, K is the length of the instantaneous angular velocity w i , j = 1, 2... J, T is the transpose operation;

[0018] 4. Calculate the correlation ρ R between the reference signal w c and w wcj,wR through the following formula;

[0019]

[0020] Where: E(·) represents the mean operation, μ represents the sample mean operation, σ represents the sample standard deviation operation, and j = 1, 2, …, J;

[0021] ρ wcj,wR Aiming at having a good correlation between the reference signal w with high signal-to-noise ratio R and the original signal w i when they are phase-aligned, the correlation coefficient of the signal to be analyzed is extracted by sequentially shifting the phase, thereby enhancing the periodic component;

[0022] According to M j and ρ wcj,wR , the reconstructed signal ρm under different cycle numbers p is obtained through the following formula to achieve the enhancement of the fault characteristics of the rolling bearing under different cycle numbers p; the IDF index is used to evaluate the enhancement effect of the fault characteristics under different cycle numbers p, and the optimal cycle p corresponding to the maximum IDF p value is obtained op ;

[0023]

[0024] Where: J = round(K / J) - 1, K is the length of the instantaneous angular velocity w i , round(·) represents the floor operation, and T represents the transpose operation;

[0025] The IDF index is used to evaluate the enhancement effect of the fault characteristics under different cycle numbers p, and the p p corresponding to the maximum value is obtained op ;

[0026] p op = argmax(IDF p );

[0027] Where, argmax(·) is to obtain the p value corresponding to the maximum IDFp value.

[0028] 5. Analyze the order spectrum of the reconstructed signal ρm corresponding to the optimal cycle p op to identify the weak fault characteristics of the outer ring of the rolling bearing and realize the fault feature diagnosis of the rolling bearing.

[0029] The beneficial effects of the present invention are:

[0030] 1. The method of the present invention can effectively enhance the fault characteristics of the rolling bearing, suppress the encoder error, speed trend component and other interference components;

[0031] 2. The present invention realizes the extraction of fault features of rolling bearings under variable speed and low speed composite working conditions based on the Multi-period cumulative cross-reference correlation coefficient signal reconstruction (MPCRCC) algorithm and order spectrum analysis, solves the problem of interference of encoder installation error and manufacturing error on the fault feature identification of rolling bearings, and the problem that the fault features of rolling bearings are weak and difficult to identify under low speed and variable speed composite working conditions. Description of the Drawings

[0032] Figure 1 It is a schematic diagram of the fault signal of the outer ring of the rolling bearing, encoder error, and variable speed simulation composite instantaneous angular velocity; among them, Figure a is the fault signal diagram of the outer ring of the rolling bearing; Figure b is the encoder installation error diagram; Figure c is the encoder etching error diagram; Figure d is the speed trend component diagram of variable speed; Figure e is the time-domain waveform diagram of the variable speed simulation composite instantaneous angular velocity signal; Figure f is the order spectrum diagram of the instantaneous angular velocity signal;

[0033] Figure 2 It is the time-domain waveform diagram (a) of the reference signal w R and the order spectrum diagram (b) of the reference signal;

[0034] Figure 3 It is the fault feature extraction result of the outer ring of the rolling bearing by the MPCRCC algorithm of the present invention; among them, Figure a is the relationship diagram between the optimization period P op and the IDF index; Figure b is the order spectrum diagram of the reconstructed signal ρm corresponding to the optimization period p op ;

[0035] Figure 4 It is the MO analysis diagram (a) of the parameter optimization of the SAM algorithm and the order diagram (b) corresponding to the MO of the parameter optimization of the SAM algorithm;

[0036] Figure 5 It is for N w = 256 cyclic stationary analysis result diagram (a) and N w = 512 cyclic stationary analysis result diagram (b);

[0037] Figure 6 It is a schematic diagram of the structure of the primary transmission test bench;

[0038] Figure 7 It is the fault signal diagram of the outer ring of the rolling bearing; among them, Figure a is the time-domain waveform diagram of the instantaneous angular velocity w i ; Figure b is the order spectrum diagram corresponding to the instantaneous angular velocity w i signal;

[0039] Figure 8 It is the result diagram for the analysis of the MPCRCC algorithm; Diagram a is the reference signal w R diagram; Diagram b is the relationship diagram between the optimized period P op and the IDF index; Diagram c is the reconstructed signal diagram corresponding to the optimized period p op ; Diagram d is the order spectrum diagram of the reconstructed signal;

[0040] Figure 9 It is the MO analysis diagram (a) for the parameter optimization of the SAM algorithm and the corresponding order diagram (b) for the parameter optimization of the SAM algorithm;

[0041] Figure 10 It is for N w = 256 cyclic stationary analysis result diagram (a) and N w = 512 cyclic stationary analysis result diagram (b); Specific implementation manners

[0042] Next, in combination with the accompanying drawings in the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts fall within the scope of protection of the present invention. In this embodiment, if there is no special description for the method, it is a conventional method.

[0043] Embodiment 1: This embodiment is for the diagnosis of the fault signal of the outer ring of a rolling bearing by using the method of the present invention. The specific process includes:

[0044] The calculation formula of the fault signal model of the outer ring of the rolling bearing used in the simulation is as follows:

[0045] w = w bpfo + w o + w ge + w s + w n

[0046] In the formula: w bpfo , w o、 w ge、 w s、 w n are respectively the fault signal of the outer ring of the rolling bearing, the encoder installation error, the encoder etching error, the speed trend component, and the noise.

[0047] Among them, the fault signal w bpfo of the outer ring of the rolling bearing has the following formula:

[0048]

[0049] where A represents the amplitude, ζ represents the damping coefficient, and f n represents the resonance frequency, and f bpfo represents the fault order of the outer ring of the rolling bearing. The simulation signal parameters are set as A = 1, ζ = 0.5, and f n = 5 ×, and f bpfo = 3.6 ×. The fault signal diagram of the outer ring of the rolling bearing is shown in Figure 1 Figure a;

[0050] The formula for the encoder installation error w o is as follows:

[0051] w o = w e + w t

[0052]

[0053] where ρ = Δr / r, which is the encoder eccentricity ratio, r is the radius of the code disk, and Δr is the eccentricity between the encoder center and the rotation center; β is the tilt error angle, θ e is the initial angle of the eccentricity error, and θ t is the initial angle of the tilt error. It can be seen that the encoder installation error w o increases with the increase of the rotational speed. The encoder installation error diagram is shown in Figure 1 Figure b;

[0054] The calculation formula for the encoder etching error w ge is as follows:

[0055]

[0056] where: Δθ ge represents the etching error angle, N represents the number of grating lines per revolution of the encoder. The encoder installation error diagram is shown in Figure 1 Figure c;

[0057] The calculation formula for the speed trend component w s is as follows:

[0058]

[0059] where: A s represents the amplitude, f stc represents the frequency, φs s is the phase, S is the number of speed trend components, θ is the initial angle. The speed trend component diagram under variable rotational speed is shown in Figure 1 Figure d;

[0060] The specific setting values of the above simulation parameters are shown in the following table:

[0061]

[0062] Step 1: Variable speed simulation composite instantaneous angular velocity w i waveform diagram of ( Figure 1 e) composed of Figure 1 a rolling bearing outer ring fault signal, Figure 1 b encoder error, Figure 1 c encoder etching error, Figure 1 d the speed trend component of variable speed superimposed, and from its order spectrum Figure 1 f it can be seen that the fault characteristic spectrum line of the rolling bearing outer ring cannot be effectively identified in the order spectrum, and the DC component of the speed trend dominates.

[0063] Step 2: Obtain a set of rolling bearing outer ring fault signals with obvious fault characteristics (first-stage speed-increasing data under the condition of a radial load of 100 N and a constant speed of 5 rpm) from the first-stage transmission test bench as the reference signal w R , such as Figure 2 a shown, from the order spectrum of the reference signal Figure 2 b it can be seen that the fault impact of the rolling bearing is significant, and the reference signals of the simulation and the experiment are consistent. Obtain the number P of the periods of interest from the reference signal w R , and obtain the fault impact position γ(p) through the extreme value;

[0064] Step 3: Use the MPCRCC algorithm to enhance the fault characteristics of the rolling bearing outer ring

[0065] (1) Perform periodic cumulative calculation on the instantaneous angular velocity through the following formula;

[0066]

[0067] Where: p = 1, 2,..., 20, P is the number of periods of interest; w cj is the j-th column of the row vector of the matrix w c , w c is the matrix form of the instantaneous angular velocity w i , d(·) represents differential calculation, j = 1, 2…J, J = round(K / J)-1, K = 5; Nw is the instantaneous angular velocity fault impact angle caused by the rolling bearing fault, L fault is the rolling bearing fault size, R is the inner radius of the outer ring, f shaft is the inner ring rotation characteristic frequency, f cage is the cage rotation frequency, Δφ = 2π / N, N represents the number of grating lines per revolution of the encoder, and the window width parameter Nw in this embodiment is set to 20;

[0068] (2): Calculate the reference signal w through the following formula Rand w c The correlation ρ wcj,wR ;

[0069]

[0070] where: E(·) represents the mean operation, μ represents the sample mean operation, σ represents the sample standard deviation operation, and j = 1, 2,..., J;

[0071] (3) According to M j , ρ wcj,wR , the reconstructed signal ρm under different cycle numbers p is obtained through the following formula to enhance the fault characteristics of the rolling bearing under different cycle numbers p;

[0072]

[0073] where: J = round(K / J) - 1, K is the length of the instantaneous angular velocity w i , round(·) represents the floor operation, and T represents the transpose operation;

[0074] (4) The IDF index is used to evaluate the enhancement effect of the fault characteristics under different cycle numbers p, and the optimal cycle p p corresponding to the maximum IDF op

[0075] p op = argmax(IDF p );

[0076] where, argmax(·) represents obtaining the extreme value corresponding to the maximum IDF p value,

[0077] The relationship between the optimized cycle P op obtained by the above MPCRCC algorithm and the IDF index is as Figure 3 shown in a, P op = 14, and the order spectrum of the reconstructed signal ρm corresponding to the optimized cycle p op is as Figure 3 shown in b. It can be seen that the fault characteristic spectrum line of the rolling bearing outer ring and its high-order harmonic spectrum lines can be effectively identified. Thus, the fault characteristics of the rolling bearing outer ring are extracted.

[0078] To further verify the feasibility of the method of the present invention for the simulation signal, the traditional SAM algorithm and the traditional cyclic stationary method are used to analyze the above variable-speed simulation composite instantaneous angular velocity w i ;

[0079] 1. Using the traditional SAM algorithm for the variable-speed simulation composite instantaneous angular velocity w iAnalysis is carried out with the parameter MO = -1.5:1.5, and the optimized MO is determined as follows Figure 4 As shown in Fig. a, the optimized MO is 0.5, and the corresponding order spectrum is as follows Figure 4 Fig. b. It can be seen from the figure that the fault characteristic spectrum line of the outer ring of the rolling bearing cannot be effectively identified, and the interference spectrum line dominates;

[0080] 2. The traditional cyclic stationary method is used to analyze the variable rotational speed simulation composite instantaneous angular velocity w i Analysis is carried out, where the window width parameter N w is set to 256 and 512 respectively, and the maximum cyclic frequency α max is set to 100. The obtained cyclic order spectrum is as follows Figure 5 Fig. a, Figure 5 Fig. b. Since the instantaneous angular velocity fluctuation caused by the rolling bearing fault does not have the second-order cyclic stationary characteristic, the traditional cyclic stationary algorithm cannot effectively extract the rolling bearing fault characteristics, that is, the rolling bearing fault characteristic spectrum line cannot be identified in Figure 5 .

[0081] Comparing the algorithm results of the present invention with the traditional SAM and the traditional cyclic stationary method, it can be found that under the interference of strong noise and speed trend components, etc., the fault characteristics of the method proposed in the present invention are more obvious, and the rolling bearing faults or characteristics can be clearly identified.

[0082] Example 2: In this example, the method of the present invention is used to extract the fault characteristics of the outer ring of the rolling bearing on the test bench

[0083] This example uses the first-stage transmission test bench as shown in Figure 6 for verification. The instantaneous angular displacement and the corresponding time are obtained through the Picoscope acquisition system with a sampling rate of 5×10 6 Hz, and the forward difference method is used to calculate the instantaneous angular velocity w i . The encoder model is ETF100-H851007B, the number of grating lines N of the optical encoder is 10000, and the encoder is installed on the pinion shaft;

[0084] The fault bearing model used in this example is 6205. To simulate the outer ring fault of the rolling bearing, a small groove with a width of about 0.3 mm and a depth of about 0.28 mm is machined on the outer ring of the bearing by wire cutting. The roller diameter d is 8 mm, the pitch diameter D is 39 mm, the number of rollers Z is 9, and the contact angle α is 0. The number of teeth of the pinion is 24, the number of teeth of the large gear is 56, and the transmission ratio is 2.33; The fault characteristic orders of the rolling bearing in this experiment are shown in the following table. The radial load in the experiment is 100 N, and the speed change is 0 - 20 rpm;

[0085]

[0086] To verify the effectiveness of the MPCRCC algorithm in enhancing weak feature components, the fault data of the outer ring of a rolling bearing is used for verification in this part, and the instantaneous angular velocity w i The waveform and the corresponding order spectrum are as shown in Figure 7 It can be seen that the spectral lines of the speed trend component dominate, while the fault characteristics of the outer ring of the bearing are relatively weak and cannot be effectively identified ( Figure 7 b);

[0087] Referring to the methods in steps 2 and 3 of Embodiment 1, the instantaneous angular velocity w i The signal is analyzed, where P = 2, 3,..., 20, and the window width parameter Nw in this embodiment is set to 20; the parameter settings in the IDF index are: f bpfo = 8.35×, K = 5; the reference signal w R Is the first-stage speed-up data under the condition of a radial load of 100 N and a constant rotational speed of 5 rpm. The fault period of the outer ring of its rolling bearing is consistent with the period of the signal to be analyzed, as shown in Figure 8 a;

[0088] The relationship between the optimized period P op Obtained by the MPCRCC algorithm and the IDF index is as shown in Figure 8 b, P op = 6, the reconstructed signal ρm corresponding to the optimized period p op And the corresponding order spectrum are as shown in Figure 8 c, 8d; it can be seen that the fault characteristic spectral lines of the outer ring of the rolling bearing and their high-order harmonic spectral lines can be effectively identified. Therefore, the method proposed in the present invention can effectively enhance the fault components of the outer ring of the rolling bearing in the instantaneous angular velocity signal, and further realize the identification of the fault characteristics of the rolling bearing.

[0089] The traditional SAM algorithm is used to analyze the instantaneous angular velocity w i The parameters MO = -1.5:1.5 are used, and the determined optimized MO is as shown in Figure 9 a, the optimized MO is 0.5, and the corresponding order spectrum is as shown in Figure 9 b; it can be seen that the fault characteristic spectral lines of the outer ring of the rolling bearing cannot be effectively identified, while the interference spectral lines dominate.

[0090] The traditional cyclic stationary method is used to analyze the original signal, where the window width parameter N w Is set to 256 and 512 respectively, and the maximum cyclic frequency α max Is set to 100, and the obtained cyclic order spectrum is as shown in Figure 10 a and 10b. Since the IAS fluctuation caused by the rolling bearing fault does not have the second-order cyclic stationary characteristic, the traditional cyclic stationary algorithm cannot effectively extract the rolling bearing fault characteristics, that is, the rolling bearing fault characteristic spectral lines cannot be identified in Figure 10 .

[0091] In summary, the algorithm of the present invention can effectively enhance the fault characteristics of rolling bearings through simulation and experimental verification, and realize the extraction of the fault characteristics of rolling bearings.

Claims

1. A rolling bearing fault feature enhancement method based on multi-period cumulative mutual reference correlation coefficient signal reconstruction, characterized in that: Here are the steps: (1) Collect the instantaneous angular displacement and corresponding time of the optical encoder and calculate the instantaneous angular velocity w using the forward difference method i ; (2) Under high radial load conditions, obtain the rolling bearing outer ring fault signal with high signal-to-noise ratio as the reference signal w R , from the reference signal w R The number of cycles of interest P is obtained in , and the fault impulse position γ(p) is obtained through the extreme value; (3) The instantaneous angular velocity is calculated by periodic accumulation using the following formula: Where: p = 1, 2, ..., P, P is the number of cycles of interest; w cj is the matrix w c The jth column of the column vector, w c is the instantaneous angular velocity w i The matrix form of , d(·) represents differential calculation, j = 1, 2…J, Nw is the instantaneous angular velocity fault impact angle caused by rolling bearing fault, that is, the window width parameter; L fault is the rolling bearing fault size, R is the inner radius of the outer ring, f shaft is the characteristic frequency of the inner ring rotation, f cage is the cage rotation frequency, N represents the number of gratings per revolution of the encoder; Where: l is the reference signal w R length, J = round(K / J)-1, K is the instantaneous angular velocity w i length, j=1,2…J, T is the transpose operation; (4) The multi-period cumulative cross-reference correlation coefficient ρ is calculated by the following formula wcj,wR ; Where: E(·) represents mean operation, μ represents sample mean operation, σ represents sample standard deviation operation, j=1,2,...,J; According to M j , wcj,wR , the reconstructed signal ρm under different cycle numbers p is obtained by the following formula to enhance the fault characteristics of rolling bearings under different cycle numbers p; the IDF index is used to evaluate the enhancement effect of fault characteristics under different cycle numbers p, and the IDF is obtained p The optimal period p corresponding to the maximum value op ; Where: J = round (K / J) - 1, K is the instantaneous angular velocity w i length, round(·) indicates a round-down operation, and T is a transpose operation; (5) For the optimal period p op The order spectrum of the corresponding reconstructed signal ρm is analyzed to identify the weak fault characteristics of the outer ring of the rolling bearing and realize the fault characteristic diagnosis of the rolling bearing.

2. The rolling bearing fault feature enhancement method based on multi-period cumulative mutual reference correlation coefficient signal reconstruction according to claim 1 is characterized in that: Get IDF p The optimal period p corresponding to the maximum value op The formula is as follows: p op =arg max(IDF p ); In the formula, argmax(·) represents the IDF p The p-value corresponding to the maximum value.

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