A method for rolling bearing fault diagnosis

Abstract

The present invention provides a method for rolling bearing fault diagnosis, which belongs to the technical field of bearing fault diagnosis. It solves the problem that the existing methods have poor signal adaptability and cannot accurately identify their fault characteristics. The method for rolling bearing fault diagnosis includes: obtaining a vibration signal f1 and a speed signal f2; using a mathematical model of a second-order synchronous extraction Chirplet transform to convert the vibration signal f1 into a time-frequency diagram; determining whether there is a bearing fault by analyzing the time-frequency ridges in the time-frequency diagram, and when there is a bearing fault, extracting a high-definition time-frequency ridge from the time-frequency ridges, and then obtaining the fault characteristic frequency FCF from the high-definition time-frequency ridges; converting the measured speed signal f2 to obtain a rotation frequency f r , the fault characteristic frequency FCF and the transfer frequency f r Divide the phase to obtain the fault factor f a , according to the failure factor f a Determine the type of bearing fault. The present invention can achieve the accuracy of bearing fault diagnosis under variable speed.

Description

Technical Field

[0001] The invention belongs to the technical field of bearing fault diagnosis, and relates to a method for rolling bearing fault diagnosis. Background Art

[0002] Rotating machinery refers to machinery that mainly relies on rotation to complete specific functions. It is the largest and most widely used type of machinery among various types of mechanical equipment. Typical rotating machinery includes steam turbines, gas turbines, centrifugal and axial compressors, fans, pumps, turbines, generators and aircraft engines, etc., which are widely used in power, petrochemical, metallurgy and aerospace sectors. Rolling bearings are a kind of precision mechanical components that convert the sliding friction between the running shaft and the shaft seat into rolling friction, thereby reducing friction losses. It plays a vital role in rotating machinery. Therefore, once a rolling bearing fails, the losses and impacts will be very serious.

[0003] At present, there are many methods for rolling bearing fault diagnosis. As for the diagnosis methods based on signal processing technology, they can be mainly divided into two categories: one is the traditional signal processing diagnosis method, such as the method based on spectrum analysis technology, resonance demodulation technology, etc.; the other is the modern signal processing diagnosis method, such as the method based on modern spectrum analysis technology, time-frequency analysis technology, etc. When a rolling bearing fails, the corresponding fault characteristics will be manifested in the vibration signal, but the transmission system of rotating machinery is very complex, and the vibration signal is usually submerged in the background signal and noise, making it difficult to be accurately identified. In addition, in actual industrial production, the equipment often works in a variable speed operation state. At this time, the fault signal of the rolling bearing is a non-stationary signal, and the traditional signal processing method cannot accurately identify its fault characteristics. As one of the modern signal processing technologies, time-frequency analysis also encounters different degrees of difficulties in the specific diagnosis process due to its inherent characteristics. For example, short-time Fourier transform, once the parameters are selected, the signal is divided into a fixed grid. If the signal does not conform to the selected fixed grid, it cannot describe the characteristics of the signal well, and lacks signal adaptability. Therefore, the current fault diagnosis methods have the problem of poor signal adaptability and inability to accurately identify fault characteristics. Summary of the invention

[0004] The purpose of the present invention is to address the above problems existing in the prior art and to propose a method for rolling bearing fault diagnosis. The technical problem to be solved is: how to achieve the accuracy of bearing fault diagnosis under variable speed.

[0005] The object of the present invention can be achieved by the following technical solution: A method for rolling bearing fault diagnosis comprises the following steps:

[0006] A. Measure the vibration signal f from the rolling bearing 1 and the speed signal f2 ;

[0007] B. Using the mathematical model of second-order synchronous extraction Chirplet transform established based on Chirplet transform, the vibration signal f 1 Convert to time-frequency diagram;

[0008] C. Determine whether there is a bearing fault by analyzing the time-frequency ridges in the time-frequency diagram. When there is a bearing fault, extract the time-frequency ridges with high clarity from the time-frequency ridges, and then obtain the fault characteristic frequency FCF from the time-frequency ridges with high clarity;

[0009] D. The measured speed signal f 2 Perform conversion processing to obtain the frequency f r , the fault characteristic frequency FCF and the transfer frequency f r Divide the phase to obtain the fault factor f a , according to the failure factor f a Determine the type of bearing failure.

[0010] Working principle: First, a mathematical model of the second-order synchronous extraction Chirplet transform is established based on the Chirplet transform, and then the vibration signal is collected. The collected vibration signal is converted into a time-frequency diagram using the established mathematical model of the second-order synchronous extraction Chirplet transform. The Chirplet transform is a parameterized time domain analysis method. The established second-order synchronous extraction Chirplet transform is a further optimization of the Chirplet transform. The vibration signal is converted by the second-order synchronous extraction Chirplet transform. The obtained time-frequency diagram has a stronger time-frequency focus, which achieves a more accurate estimation of the instantaneous frequency. The time-frequency diagram converted from the vibration signal reflects multiple time-frequency ridges with different clarity. The smoothness of the time-frequency ridges of the time-frequency diagram is judged. When the time-frequency ridge is a non-smooth ridge, it is judged to be a bearing fault. The time-frequency ridge with high clarity is extracted from the multiple time-frequency ridges. The fault characteristic frequency is obtained by analysis based on the extracted time-frequency ridge with high clarity. Finally, the fault characteristic frequency is divided by the rotation frequency to obtain the fault coefficient. According to the size of the fault coefficient, it is judged which type of bearing fault it is, such as the bearing outer ring fault, the bearing inner ring fault, the bearing rolling element fault or the bearing retainer fault. The method realizes the diagnosis of bearing faults under variable speeds, and can accurately judge which type of bearing fault it is. The fault judgment is more accurate, which is convenient for targeted troubleshooting in the later stage.

[0011] In the above-mentioned method for rolling bearing fault diagnosis, in step B, the operation steps of establishing the mathematical model of the second-order synchronous extraction Chirplet transform include:

[0012] B1. Perform Chirplet transformation on the signal x(t) to obtain

[0013] B2. Perform a second-order estimate on the signal x(t) to obtain the instantaneous frequency of the second-order signal

[0014] B3. Based on the instantaneous frequency of the second-order signal Get the second-order synchronous extraction operator

[0015] B4. The obtained With the second-order synchronous extraction operator Perform multiplication calculation to obtain a mathematical model of second-order synchronous extraction Chirplet transform, the formula of the mathematical model is:

[0016]

[0017] The established mathematical model of second-order synchronous extraction of Chirplet transform can effectively identify time-varying characteristics, correctly extract the time-frequency ridges of different components, has strong time-frequency focusing, can perform more accurate instantaneous frequency estimation, and realize accurate diagnosis of bearing faults under variable speed.

[0018] In the above-mentioned method for rolling bearing fault diagnosis, in step B1, a pair of signals x(t) is subjected to Chirplet transformation by the following formula to obtain: Formula 1 is:

[0019]

[0020] Where j is a complex number; is the phase of the kth signal component of the x(t) signal; i is a complex number; R is a positive integer; Yes A k The r-order derivative of (t); A k (t) is the amplitude of the kth signal component of the x(t) signal; is the r-order derivative of the window function after frequency shift; is the derivative of the phase; ω is the frequency.

[0021] In the above-mentioned method for rolling bearing fault diagnosis, in step B2, the second-order signal instantaneous frequency is obtained by performing a second-order estimation on the signal x(t) using the following formula: The formula 2 is:

[0022]

[0023] in, represents the Chirplet transform with window function g, Respectively represent Chirplet transforms with window functions g″(t), tg′(t), and g′(t); To extract q x t+p x The sign of the imaginary part of . To extract symbols from mathematical formulas.

[0024] In the above-mentioned method for rolling bearing fault diagnosis, in step B3, based on the instantaneous frequency of the second-order signal Get the second-order synchronous extraction operator The operations include:

[0025] In judgment When

[0026] In judgment When

[0027] In the above-mentioned method for rolling bearing fault diagnosis, in step C, the operation of determining whether there is a bearing fault by analyzing the time-frequency ridge line in the time-frequency diagram is:

[0028] By analyzing the smoothness of the time-frequency ridges in the time-frequency diagram, when the time-frequency ridges are smoothly transitioned ridges, it is judged that the rolling bearing is not faulty; conversely, when the time-frequency ridges are not smooth and have turning ridges, it is judged that the rolling bearing is faulty. When the bearing fails, the time-frequency ridges on the time-frequency diagram of the vibration signal will show ridges with concentrated energy, and the ridges at this time are not smooth and have turning states, so it can be judged that the rolling bearing is faulty at this time. The present invention uses a mathematical model of second-order synchronous extraction Chirplet transformation to process the vibration signal, and the time-frequency energy aggregation is better, which can more accurately judge whether the rolling bearing is faulty; if the bearing is not faulty, the time-frequency ridges at this time will show smooth transition ridges.

[0029] In the above-mentioned method for rolling bearing fault diagnosis, in step D, the measured speed signal f 2 Perform conversion processing to obtain the frequency f r The operations are:

[0030] The measured speed signal f 2 Divide by 60 to get the rotation frequency f r .

[0031] In the above-mentioned method for rolling bearing fault diagnosis, in step D, according to the fault coefficient f a The operations to determine the type of bearing fault include:

[0032] Preset coefficient f for judging bearing outer ring fault 0 and the coefficient f used to judge the bearing inner ring fault i , the coefficient f of the bearing outer ring failure 0 The coefficient f of the bearing inner ring failure is obtained by the following formula 3: i Obtained by the following formula 4;

[0033] Formula 3: f 0 =0.4×z×f r

[0034] Formula 4: f i =0.6×z×f r

[0035] Where z is the number of balls in the bearing, f r is the speed signal f 2 The frequency conversion is obtained after the conversion process;

[0036] In judging the failure factor f α With coefficient f 0 When the bearing outer ring is close to the bearing outer ring, it is judged to be a fault. The fault coefficient f α With coefficient f i If they are close, it is judged as a bearing inner ring failure.

[0037] In the above-mentioned method for rolling bearing fault diagnosis, in step D, according to the fault coefficient f a The operations to determine the type of bearing fault also include:

[0038] Preset coefficient f for judging bearing rolling element failure b , the coefficient f of the bearing rolling element failure b Obtained by the following formula 5;

[0039] Formula 5: When z < 10, f b =0.23×z×f r ;

[0040] When z ≥ 10, f b =0.18×z×f r ;

[0041] Where z is the number of balls in the bearing, f r is the speed signal f 2 The frequency conversion is obtained after the conversion process;

[0042] In judging the failure factor f α With coefficient f b When approaching, it is judged to be a bearing rolling element failure.

[0043] In the above-mentioned method for rolling bearing fault diagnosis, in step D, according to the fault coefficient f a The operations to determine the type of bearing fault also include:

[0044] Preset coefficient f for judging bearing cage failure c , the bearing cage failure coefficient f c Obtained by the following formula 6;

[0045] Formula 6: f c =(0.38 to 0.4)f r ;

[0046] Where z is the number of balls in the bearing, f r is the speed signal f 2 The frequency conversion is obtained after the conversion process;

[0047] In judging the failure factor f α With coefficient f c If it is close, it is judged to be a bearing retainer failure.

[0048] The coefficients of various bearing failures are set in advance through numerous tests. α Compare with the coefficient of each bearing fault, the fault coefficient f α The bearing fault is determined to be the one whose value is closer to its coefficient, thus achieving accurate identification of fault characteristics.

[0049] Compared with the prior art, the method for rolling bearing fault diagnosis has the following advantages:

[0050] 1. The mathematical model of the second-order synchronous extraction Chirplet transform established in the present invention has less noise interference information on the time-frequency plane when processing vibration signals, has better time-frequency analysis capabilities for multi-component signals, can perform more accurate instantaneous frequency estimation, and the time-frequency ridges obtained by processing have better time-frequency focusing, which can more accurately diagnose rolling bearing faults.

[0051] 2. The present invention can also specifically diagnose which type of bearing fault it is, and the fault diagnosis accuracy is high. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a control flow chart of the present invention.

[0053] Figure 2 It is the ridge extraction result of the vibration signal time-frequency diagram of the present invention. DETAILED DESCRIPTION

[0054] The following are specific embodiments of the present invention and the accompanying drawings to further describe the technical solution of the present invention, but the present invention is not limited to these embodiments.

[0055] When a bearing fails, the corresponding fault characteristics will be reflected in the vibration signal, so fault feature extraction from the vibration signal can effectively diagnose the rolling bearing fault. Figure 1 As shown, the method for rolling bearing fault diagnosis performs the following operations on bearing fault diagnosis: pre-establishing a mathematical model for second-order synchronous extraction of Chirplet transform, the mathematical model is established based on Chirplet transform, and the specific operations are:

[0056] First, perform Chirplet transformation on the signal x(t) to obtain Where j is a complex number; is the phase of the kth signal component of the x(t) signal; i is a complex number; R is a positive integer; Yes A k The r-order derivative of (t); A k (t) is the amplitude of the kth signal component of the x(t) signal; is the r-order derivative of the window function after frequency shift; is the derivative of the phase; ω is the frequency.

[0057] Then perform a second-order estimate on the signal x(t) to obtain the instantaneous frequency of the second-order signal The operation is:

[0058] definition Among them, t 0 is the initial test time, s is the operator, a, b, c are constants, A x Represents the amplitude function, and the derivative of the signal x(t) with respect to t yields:

[0059]

[0060] The derivative of x(t) with respect to t is the product of a complex plane function with the derivative of the logarithm of the amplitude with respect to t as the real part and the derivative of the phase with respect to t as the imaginary part and x(t). A(t) represents the amplitude function, represents the phase function.

[0061] The first-order partial derivative with respect to t is:

[0062] Similarly, The second-order partial derivative with respect to t is:

[0063]

[0064] in, Represents the Chirplet transform with window function H, that is They represent Chirplet transforms with window functions g″(t), tg′(t), and g′(t) respectively.

[0065] Combination The formulas for the first-order partial derivative and the second-order partial derivative of t are obtained by the parameter elimination method:

[0066]

[0067] Therefore, the instantaneous frequency IF of the signal is estimated to obtain the instantaneous frequency of the second-order signal in, Extract symbols from mathematical formulas.

[0068] Afterwards, based on the instantaneous frequency of the second-order signal Get the second-order synchronous extraction operator Among them, in judging When In judgment When

[0069] Finally, the first step With the second-order synchronous extraction operator Perform multiplication calculation to obtain the mathematical model of the second-order synchronous extraction Chirplet transform. The formula of the mathematical model is:

[0070]

[0071] After the mathematical model of the second-order synchronous extraction Chirplet transform is established, the rolling bearing fault is diagnosed by using the mathematical model of the second-order synchronous extraction Chirplet transform. First, the vibration signal f is measured from the rolling bearing. 1 and the speed signal f 2 , vibration signal f 1 and the speed signal f 2 The vibration signal f is measured by a sensor from a rolling bearing, and then the mathematical model of the second-order synchronous extraction Chirplet transform is used to extract the vibration signal f 1 Perform time-frequency analysis to obtain the vibration signal f 1 The time-frequency graph is then analyzed to determine whether there is a bearing fault. When the time-frequency ridge is a smooth transition ridge, it is determined that the rolling bearing is fault-free; on the contrary, when the time-frequency ridge is an uneven ridge with a turning point, it is determined that the rolling bearing is faulty. The time-frequency ridge with high clarity is extracted from the time-frequency ridge. High clarity refers to the obvious time-frequency ridge that appears in the time-frequency graph, such as Figure 2 As shown in the figure, the time-frequency ridge with high definition is extracted, among which the undulating ridge means that the bearing has a fault. The FCF in the figure is called the "fault characteristic frequency", and 2FCF is the double frequency of the fault characteristic frequency. Therefore, the fault characteristic frequency FCF can be obtained from the time-frequency ridge with high definition;

[0072] The measured speed signal f 2 Divide by 60 to get the rotation frequency f r , the fault characteristic frequency FCF and the transfer frequency f r Divide the phase to obtain the fault factor f a ,Right now Finally, according to the failure factor f a Determine the type of bearing fault. The operations include:

[0073] Preset coefficient f for judging bearing outer ring fault 0 , coefficient f used to judge bearing inner ring fault i , coefficient f used to judge bearing rolling element failure b And the factor f used to judge the bearing cage failure c , the coefficient f of bearing outer ring failure 0 Obtained by the following formula: 0 =0.4×z×f r ; Coefficient f of bearing inner ring failure i Obtained by the following formula: i =0.6×z×f r ; Bearing cage failure coefficient f c Obtained by the following formula: c =(0.38 to 0.4)f r ; The coefficient f of bearing rolling element failure b Obtained by the following formula:

[0074] When z<10, f b =0.23×z×f r ;

[0075] When z ≥ 10, f b =0.18×z×f r ;

[0076] Where z is the number of balls in the bearing, f r is the speed signal f 2 The frequency conversion is obtained after the conversion process;

[0077] In judging the failure factor f α With coefficient f 0 When the bearing outer ring is close to the bearing outer ring, it is judged to be a fault. The fault coefficient fα With coefficient f i When it is close to the inner ring of the bearing, it is judged to be a fault; when the fault coefficient f is obtained, α With coefficient f b When the bearing is close to the rolling element, it is judged to be a bearing rolling element failure; when the failure coefficient f is obtained α With coefficient f c When the bearing is close to the bearing cage, it is judged to be a bearing cage failure. This method realizes the bearing fault diagnosis under variable speed and can accurately determine the type of bearing fault. The fault judgment is more accurate, which is convenient for targeted troubleshooting in the later stage.

[0078] The specific embodiments described herein are merely examples of the spirit of the present invention. Those skilled in the art may make various modifications or additions to the specific embodiments described or replace them in similar ways, but they will not deviate from the spirit of the present invention or exceed the scope defined by the appended claims.

Claims

1. A method for rolling bearing fault diagnosis, characterized in that: The steps include: A. Measure and obtain vibration signals from rolling bearings and speed signal ; B. Use the mathematical model of second-order synchronous extraction Chirplet transform based on Chirplet transform to convert the vibration signal Converted into a time-frequency diagram; the operation steps of establishing a mathematical model of second-order synchronous extraction Chirplet transform based on Chirplet transform include: B1, through the following formula a pair of signals Perform Chirplet transformation to obtain , formula 1 is: ， Where j is a complex number; for The phase of the kth signal component of the signal; i is a complex number; R is a positive integer; yes The r-order derivative of ; for The amplitude of the kth signal component of the signal; is the r-order derivative of the window function after frequency shift; is the derivative of the phase; is the frequency; B2. Use the following formula 2 to perform a second-order estimate on the signal x(t) to obtain the instantaneous frequency of the second-order signal , the formula 2 is: in, , The window function is Chirplet transform, , , They represent the window functions as , , Chirplet transform; For extraction The sign of the imaginary part of ; i is a complex number; is the frequency; B3. Based on the instantaneous frequency of the second-order signal Get the second-order synchronous extraction operator , the operations include: In judgment When ; In judgment When ; B4. The obtained With the second-order synchronous extraction operator Perform multiplication calculation to obtain a mathematical model of second-order synchronous extraction Chirplet transform, the formula of the mathematical model is: ； C. By analyzing the smoothness of the time-frequency ridge line in the time-frequency diagram, when the time-frequency ridge line is a smoothly transitioned ridge line, it is judged that the rolling bearing has no fault; on the contrary, when the time-frequency ridge line is an unsmooth ridge line with a turning point, it is judged that the rolling bearing has a fault; when there is a bearing fault, a time-frequency ridge line with high clarity is extracted from the time-frequency ridge line, and then the fault characteristic frequency FCF is obtained from the time-frequency ridge line with high clarity; D. The measured speed signal Convert the frequency , the fault characteristic frequency FCF and the transfer frequency Divide the phase to obtain the failure factor , according to the failure coefficient Determine the type of bearing fault. The operations include: Preset coefficients for judging bearing outer ring faults , coefficient used to judge bearing inner ring fault , coefficient used to judge bearing rolling element failure and coefficients for determining bearing cage failure ; The coefficient of the bearing outer ring failure The coefficient of bearing inner ring failure is obtained by the following formula 3: The coefficient of the bearing rolling element failure is obtained by the following formula 4: Obtained by the following formula 5: The coefficient of the bearing cage failure Obtained by the following formula 6; Formula 3: ; Formula 4: ; Formula 5: ; exist ; Formula 6: ; Where z is the number of balls in the bearing, The speed signal is measured The frequency conversion is obtained after the conversion process; In judging the failure coefficient With coefficient When the bearing is close to the outer ring, it is judged to be a bearing outer ring fault. With coefficient If the bearing inner ring is close to the inner ring, it is judged to be a bearing inner ring fault. With coefficient When the bearing is close to the rolling element, it is judged to be a bearing rolling element failure. With coefficient If it is close, it is judged to be a bearing retainer failure.

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