Angle-Time Cycle Steady Rolling Bearing Fault Diagnosis Method without Tachometer

Abstract

An angle-time cyclostationary rolling bearing fault diagnosis method without a tachometer is disclosed. In this method, measuring points are arranged at the bearing housing end cover of the rolling bearing, and a vibration acceleration sensor is used to collect vibration signals. The preliminary speed of the motor is estimated based on the vibration signals through the short-time Fourier transform peak search method. The precise speed of the motor is calculated using the Vold-Kalman filter and the preliminary speed. Based on the precise speed, angle-time cyclostationary analysis is performed on the vibration signals to obtain a cyclic spectral density diagram. Whether there is a bearing fault characteristic order is observed in the cyclic order domain of the cyclic spectral density diagram, and at the same time, the oscillation frequency of the fault impact waveform is determined in the spectral frequency domain to complete the fault diagnosis.

Description

Technical Field

[0001] The present invention relates to the technical field of rolling bearing fault diagnosis, and particularly to a rolling bearing fault diagnosis method with angle-time cyclic stationarity without a tachometer. Background Art

[0002] As an important supporting component of rotating machinery, rolling bearings often bear large loads and impacts, and are vulnerable components in rotating machinery. Once a fault occurs, it will cause the equipment to stop running at least, affecting operation and production, and at worst, it will cause catastrophic accidents such as equipment damage and casualties. Therefore, carrying out rolling bearing fault monitoring and diagnosis is an effective way to reduce operation and maintenance losses and ensure the safe operation of equipment, and has important engineering significance. The angle-time cyclic stationarity analysis method can analyze the information in both the time domain and the angle domain of vibration signals, and diagnose the faults of rolling bearings under variable speed conditions. However, in some high-temperature, high-pressure or enclosed environments, the rotational speed information of the bearing cannot be obtained, which affects the feature identification of the angle domain information of the vibration signal, and it is difficult to extract the early weak fault features of rolling bearings only from the time domain information. Therefore, it is advisable to adopt the proposed angle-time cyclic stationarity analysis method that combines bearing vibration signal to reconstruct rotational speed to solve the problem of cyclic stationarity feature identification without rotational speed.

[0003] The above information disclosed in the background art section is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0004] The purpose of the present invention is to provide a rolling bearing fault diagnosis method with angle-time cyclic stationarity without a tachometer, which solves the problem that the existing cyclic stationarity analysis method of bearings cannot be used without rotational speed, reconstructs the rotational speed and performs cyclic stationarity feature identification under variable speed conditions.

[0005] In order to achieve the above purpose, the present invention provides the following technical solutions:

[0006] A rolling bearing fault diagnosis method with angle-time cyclic stationarity without a tachometer of the present invention includes:

[0007] Step 1, arranging measuring points at the bearing housing end cover of the rolling bearing, and collecting vibration signals by using a vibration acceleration sensor;

[0008] Step 2, estimating the preliminary rotational speed of the motor according to the vibration signal by using the short-time Fourier transform peak search method;

[0009] Step 3, calculating the accurate rotational speed of the motor by using the Vold-Kalman filter and the preliminary rotational speed;

[0010] Step 4: Perform angle-time cyclic stationary analysis on the vibration signal according to the accurate rotational speed to obtain a cyclic spectral density diagram;

[0011] Step 5: Observe whether there is a significant increase in the cyclic spectral density function at a certain abscissa in the cyclic spectral density diagram. This abscissa is the bearing fault characteristic order. At the same time, find the ordinate of the highest point of the cyclic spectral density function at the bearing fault characteristic order of the abscissa as the oscillation frequency of the fault impact waveform to complete the fault diagnosis;

[0012] In a rolling bearing fault diagnosis method with angle-time cyclic stationarity without a tachometer, the rolling bearing is a motor bearing.

[0013] In a rolling bearing fault diagnosis method with angle-time cyclic stationarity without a tachometer, the vibration acceleration sensor is arranged in the vertical direction of the motor bearing end cover.

[0014] In a rolling bearing fault diagnosis method with angle-time cyclic stationarity without a tachometer, the sampling frequency of the vibration acceleration sensor is 10.24 KHz.

[0015] In a rolling bearing fault diagnosis method with angle-time cyclic stationarity without a tachometer, the short-time Fourier transform peak search method for estimating the preliminary rotational speed of the motor includes the following steps

[0016] Step 2-1: Perform short-time Fourier transform on the vibration signal to obtain a frequency spectrum diagram:

[0017]

[0018] where \(x(t)\) is the vibration signal, \(t\) is time, \(\gamma(\tau)\) is the analysis window function, \(\tau\) is the position of the analysis window function, \(f\) is the frequency, and \(X(t, f)\) is the spectral density;

[0019] Step 2-2: Locate the frequency component related to the rotational speed by observing the frequency spectrum diagram, and then apply the maximum tracking algorithm of the frequency component to calculate the preliminary instantaneous frequency:

[0020] f max (t)=\(\argmax|X(t, f)|\) 2 , / \(\in\Delta f\) t ,

[0021] \(\Delta f\) t \(\in\{f\) max (t - d\tau)-\(\delta f\), f max (t - d\tau)+\(\delta f\}\),

[0022] where \(\delta f\) is the given maximum detected frequency tolerance, \(\Delta f\) t is the frequency component related to the rotational speed observed in advance, \(f\) maxis the instantaneous frequency;

[0023] Step 2-3: Calculate the instantaneous phase based on the preliminary instantaneous frequency.

[0024] ω(t) = 2πf max (t),

[0025]

[0026] Step 2-4: Based on the instantaneous phase calculated in Step 2-3, perform angular resampling on the vibration signal and filter the resampled signal using a band-pass filter to retain only the components related to rotation.

[0027] Step 2-5: Use the instantaneous phase to resample the vibration signal back into the time domain.

[0028] Step 2-6: Perform a short-time Fourier transform on the vibration signal after filtering and resampling to obtain a spectrogram, calculate the instantaneous frequency through the maximum amplitude tracking algorithm, and then calculate the preliminary motor speed through ω = 2πf max Calculate the preliminary motor speed.

[0029] In a rolling bearing fault diagnosis method based on angle-time cyclostationarity without a tachometer, using a Vold-Kalman filter and the preliminary speed to calculate the accurate motor speed includes the following steps.

[0030] Step 3-1: Construct the Vold-Kalman filter order analysis structural equation; x(n) - 2cos(ωΔt)x(n + 1) + x(n + 2) = ε(n). Let the coefficient term of x(n + 1) be c(n) = 2cos(ωΔt), and the matrix expansion of the structural equation is:

[0031] Its matrix form is Ax = ε,

[0032] where ε(n) is the non-consistent term of the structural equation, x(n) is the order fraction component to be tracked, and n is the number of sampling points.

[0033] Step 3-2: Design the Vold-Kalman filter order analysis data equation;

[0034] y(n) = x(n) + η(n),

[0035] where η(n) is the background noise and y(n) is the value of the nth sampling point of the vibration signal.

[0036] Step 3-3: Establish the sum of squares of the heterogeneous term and the error term through the least squares method as the loss function: J = r 2 ε T ε + η Tη. Additionally, the error term is the square ε of the inconsistent term ε of the structural equation T ε. The isomer term is the square η of the background noise η T η, where r is the weighting factor

[0037] Step 3-4: Solve for the minimum value of the loss function J. Since ε = Ax and η(n) = y(n) - x(n), then J = r 2 x T A T Ax+(y - x) T (y - x). Let to obtain the equation: x = (r 2 A T A + I) -1 y, where I is the identity matrix

[0038] Step 3-5: Solve the equation to obtain the rotational speed harmonic components

[0039] Step 3-6: After using the Vold-Kalman filtering method, accurate rotational speed harmonic components are obtained. Perform a short-time Fourier transform on the rotational speed harmonic components to obtain a spectrogram, calculate the instantaneous frequency through the maximum amplitude tracking algorithm, and then calculate the accurate rotational speed through ω = 2πf max , and calculate the accurate rotational speed

[0040] In a method for diagnosing rolling bearing faults with angle-time cyclostationarity without a tachometer, the vibration signal is subjected to angle-time cyclostationarity analysis to obtain a cyclic spectral density map, and the steps are as follows

[0041] Step 4-1: Use the method of periodic time averaging to estimate the angle-time autocorrelation function of the vibration signal

[0042]

[0043] where θ is the angle variable, τ is the delay is the cyclic order, and E{*} is the ensemble average operator

[0044] Step 4-2: Discretize the angle-time autocorrelation function to obtain R 2x (n, m), where n and m respectively correspond to the discrete samples of the angle θ and the delay τ: θ = nΔ; τ = mΔ, and Δ is the sampling period

[0045] Step 4-3: Find the discrete Fourier series coefficients of the angle-time autocorrelation function R 2x [n, m] with respect to the discrete angle nΔ

[0046]

[0047] where R x[m; α i are the discrete Fourier series coefficients, where α i is a certain cyclic order; L is the signal length corresponding to the discrete angle nΔ,

[0048] Step 4-4, then perform discrete-time Fourier transform on the discrete delay mΔ to obtain the cyclic spectral density function:

[0049]

[0050] where f is the frequency.

[0051] In the above technical solution, a method for diagnosing rolling bearing faults with angle-time cyclic stationarity without a tachometer provided by the present invention has the following beneficial effects: The method for diagnosing rolling bearing faults with angle-time cyclic stationarity without a tachometer of the present invention realizes the identification of the angle-time cyclic stationary characteristics of the bearing vibration signal without the rotational speed, and reconstructs the rotational speed from the vibration signal by using the method combining short-time Fourier transform and Vold-Kalman filter correction. It overcomes the disadvantage that the angle-time cyclic stationary analysis method is limited in application due to the inability to obtain the rotational speed under certain extreme working conditions. Brief Description of the Drawings

[0052] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings.

[0053] Figure 1 It is a schematic layout diagram of the motor bearing fault simulation test bench for the method for diagnosing rolling bearing faults with angle-time cyclic stationarity without a tachometer in the present invention;

[0054] Figure 2 It is the time-domain diagram of the vibration signal in the present invention;

[0055] Figure 3 It is the flow chart of the short-time Fourier transform peak search method for the method for diagnosing rolling bearing faults with angle-time cyclic stationarity without a tachometer in the present invention;

[0056] Figure 4 It is the preliminary rotational speed diagram estimated by the short-time Fourier transform peak search method in the present invention;

[0057] Figure 5 It is the schematic diagram of the Vold-Kalman order tracking filter process for the method for diagnosing rolling bearing faults with angle-time cyclic stationarity without a tachometer in the present invention;

[0058] Figure 6It is the cyclic stationary analysis flowchart of the rolling bearing fault diagnosis method with angle-time cycle stationarity without a tachometer in the present invention;

[0059] Figure 7 It is the cyclic spectral density diagram obtained by diagnosing the inner ring fault of the bearing using the method of the present invention. Specific embodiments

[0060] To make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are 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 creative efforts fall within the scope of protection of the present invention.

[0061] Therefore, the following detailed description of the embodiments of the present invention provided in the appendix Figures 1 to 7 is not intended to limit the scope of the present invention claimed, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.

[0062] It should be noted that similar reference numerals and letters denote similar items in the following figures. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0063] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as limiting the present invention.

[0064] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, "a plurality" means two or more unless otherwise specifically defined.

[0065] In the present invention, unless otherwise clearly specified or limited, the terms "mounted", "connected", "coupled", "fixed", etc. shall be construed in a broad sense. For example, it may be a fixed connection, a detachable connection, or integrated; it may be directly connected, or indirectly connected through an intermediate medium, and it may be the communication inside two elements or the interaction relationship between two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0066] In the present invention, unless otherwise clearly specified or limited, the first feature being "on" or "under" the second feature may include the direct contact between the first and second features, or may include the situation where the first and second features are not in direct contact but in contact through additional features therebetween. Moreover, the first feature being "above", "over" and "on top of" the second feature includes that the first feature is directly above and obliquely above the second feature, or merely indicates that the horizontal height of the first feature is higher than that of the second feature. The first feature being "under", "beneath" and "underneath" the second feature includes that the first feature is directly below and obliquely below the second feature, or merely indicates that the horizontal height of the first feature is lower than that of the second feature.

[0067] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings. As Figures 1 to 7 shown, a rolling bearing fault diagnosis method with angle-time cyclic stationarity without a tachometer includes

[0068] Step 1: Arrange measuring points at the bearing housing end cover of the rolling bearing, and collect vibration signals using a vibration acceleration sensor;

[0069] Step 2: Estimate the initial speed of the motor according to the vibration signal by the peak search method of short-time Fourier transform;

[0070] Step 3: Calculate the accurate speed of the motor using a Vold-Kalman filter and the initial speed;

[0071] Step 4: Perform angle-time cyclic stationarity analysis on the vibration signal according to the accurate speed to obtain a cyclic spectrum density map;

[0072] Step 5, observe in the cyclic spectral density graph whether there is a significantly high cyclic spectral density function at a certain abscissa, which is the bearing fault characteristic order. At the same time, find the ordinate of the highest point of the cyclic spectral density function at the bearing fault characteristic order of the abscissa as the oscillation frequency of the fault impact waveform to complete the fault diagnosis. The abscissa of the cyclic spectral density graph is the cyclic order, which is a multiple of the rotational speed, and the ordinate is the spectral frequency. Each point on the graph represents the energy value at this cyclic order and spectral frequency. If there is a certain bearing fault characteristic order, the energy value at this order on the cyclic spectral density graph will be very high and can be observed. The bearing fault characteristic order is the ratio of the fault characteristic frequency to the rotational speed, determined by the cyclic spectral density graph. Observe the point with a high energy value in the graph, and the spectral frequency of this point is the oscillation frequency.

[0073] In a preferred embodiment of a method for diagnosing rolling bearing faults with angle-time cyclic stationarity without a tachometer, the rolling bearing is a motor bearing.

[0074] In a preferred embodiment of a method for diagnosing rolling bearing faults with angle-time cyclic stationarity without a tachometer, the vibration acceleration sensor is arranged in the vertical direction of the motor bearing end cover.

[0075] In a preferred embodiment of a method for diagnosing rolling bearing faults with angle-time cyclic stationarity without a tachometer, the sampling frequency of the vibration acceleration sensor is 10.24 KHz.

[0076] In a preferred embodiment of a method for diagnosing rolling bearing faults with angle-time cyclic stationarity without a tachometer, the steps for estimating the preliminary rotational speed of the motor by the short-time Fourier transform peak search method include the following steps.

[0077] Step 2-1, perform short-time Fourier transform on the vibration signal to obtain a spectrogram:

[0078]

[0079] Step 2-2, locate the frequency components related to the rotational speed by observing the spectrogram, and then apply the maximum tracking algorithm of the frequency components to calculate the preliminary instantaneous frequency:

[0080] f max (t) = argmax|X(t, f)| 2 ,

[0081] Δf t ∈{f max (t - dτ) - δf, f max (t - dτ) + δf}, after performing short-time Fourier transform on the signal, a spectrogram will be obtained. Since the amplitude of the frequency components related to the rotational speed is the largest, it is located by the amplitude of the spectral lines on the spectrogram.

[0082] Step 2-3: Calculate the instantaneous phase based on the preliminary instantaneous frequency, and perform angular resampling on the vibration signal.

[0083]

[0084] Step 2-4: Filter the resampled signal using a band-pass filter to retain only the components related to rotation.

[0085] Step 2-5: Use the instantaneous phase to resample the vibration signal back into the time domain.

[0086] Step 2-6: Repeat Steps 2-1 and 2-2 to calculate the preliminary rotational speed of the motor.

[0087] In a preferred embodiment of a method for diagnosing faults in rolling bearings with angle-time cyclostationarity without a tachometer, using a Vold-Kalman filter and the preliminary rotational speed to obtain the accurate rotational speed of the motor includes the following steps.

[0088] Step 3-1: Construct the Vold-Kalman filter order analysis structural equation: x(n) - 2cos(ωΔt)x(n + 1) + x(n + 2) = ε(n). Let the coefficient term of x(n + 1) be c(n) = 2cos(ωΔt). The matrix expansion of the structural equation is:

[0089] Its matrix form is Ax = ε.

[0090] Step 3-2: Design the Vold-Kalman filter order analysis data equation: y(n) = Cx(n) + η(n).

[0091] Step 3-3: Establish the sum of squares of the heterogeneous term and the error term through the least squares method, which is called the loss function: J = r 2 ε T ε + η T η.

[0092] Step 3-4: Solve for the minimum value of J to obtain the equation: x = (r 2 A T A + E) -1 C H y.

[0093] Step 3-5: Solve the equation to obtain the rotational speed harmonic components.

[0094] Step 3-6: Apply the method in (2) to recalculate the accurate rotational speed of the motor.

[0095] In an optimal implementation manner of a rolling bearing fault diagnosis method with angle-time cyclic stationarity without a tachometer, the vibration signal is subjected to angle-time cyclic stationarity analysis, and the steps for obtaining the cyclic spectral density diagram are as follows:

[0096] Step 4-1: Use the method of periodic time averaging to estimate the angle-time autocorrelation function of the vibration signal:

[0097]

[0098] Step 4-2: Discretize the angle-time autocorrelation function to obtain R 2x (n, m), where n and m respectively correspond to the discrete sampling of the angle θ and the delay τ; θ = nΔ; τ = mΔ, and Δ is the sampling period.

[0099] Step 4-3: Obtain the discrete Fourier series coefficients of the periodic function with respect to the discrete angle n:

[0100]

[0101] Step 4-4: Then perform a discrete-time Fourier transform on the discrete delay m to obtain the cyclic spectral density function:

[0102]

[0103] In one implementation manner, the motor bearing local pitting fault diagnosis method of the present invention includes the following steps:

[0104] (1) Use an acceleration vibration sensor to collect the vibration signal of the motor bearing.

[0105] Among them, the sensor is arranged in the vertical direction of the motor bearing end cover, as Figure 1 shown. In this embodiment, the vibration signal is collected by the acceleration sensor, conditioned and collected by the data acquisition system, and finally processed and displayed on the computer. The sampling frequency is 10.24 KHz. The collected vibration signal is as Figure 2 shown.

[0106] (2) According to the measured vibration signal, preliminarily estimate the motor speed by the peak search method of short-time Fourier transform. The specific steps are as follows:

[0107] a) Perform a short-time Fourier transform on the vibration signal to obtain a spectrogram

[0108]

[0109] b) First, locate the frequency component related to the shaft speed by observing the spectrogram. Then apply the maximum tracking algorithm of the selected component to preliminarily calculate the instantaneous frequency

[0110] fmax (t) = argmax|X(t, f)| 2

[0111] Δf t ∈{f max (t - dτ) - δf, f max (t - dτ) + δf}

[0112] c) Based on this preliminary estimated instantaneous frequency, calculate the instantaneous phase and resample the vibration signal in terms of angle.

[0113]

[0114] d) Filter the resampled signal using a band - pass filter to retain only the components related to rotation.

[0115] e) Utilize the instantaneous phase to resample the vibration signal back into the time domain.

[0116] f) Repeat steps a) and b) to calculate the preliminary rotational speed of the motor.

[0117] (3) According to the preliminary rotational speed of the motor obtained in step (2), use the Vold - Kalman order tracking filtering technique to extract the harmonics related to the rotational speed. The specific steps are as follows:

[0118] a) Design the structural equation for Vold - Kalman filtering order analysis;

[0119] x(n) - 2cos(ωΔt)x(n + 1) + x(n + 2) = ε(n)

[0120] Let the coefficient term of x(n + 1) be c(n) = 2cos(ωΔt), and expand the matrix of the structural equation

[0121]

[0122] Its matrix form is Ax = ε.

[0123] b) Design the data equation for Vold - Kalman filtering order analysis;

[0124] y(n) = Cx(n) + η(n)

[0125] c) Establish the sum of squares of the heterogeneous term and the error term through the least - squares method, which is called the loss function;

[0126] J = r 2 ε T ε + η T η

[0127] d) Solve for the minimum value of J, and we can get:

[0128] x = (r 2 A T A + E) -1 C H y

[0129] e) Solving this equation can obtain the rotational speed harmonic components;

[0130] f) Apply the method in step 2 to recalculate the accurate rotational speed of the motor. After using the Vold-Kalman filtering method, the accurate rotational speed harmonic components are obtained. Perform a short-time Fourier transform on the rotational speed harmonic components to obtain a spectrogram. Calculate the instantaneous frequency through the amplitude maximum tracking algorithm, and then calculate the accurate rotational speed through...;

[0131] (4) According to the accurate rotational speed of the motor obtained in step (3), perform an angle-time cyclostationary analysis on the vibration signal and draw a cyclic spectral density diagram. The specific steps are as follows:

[0132] a) Use the method of periodic time averaging to estimate the angle-time autocorrelation function of the signal:

[0133]

[0134] b) Discretize the autocorrelation function to obtain R 2x (n, m), where n and m correspond to the discrete samplings of the angle θ and the delay τ respectively; θ = nΔ; τ = mΔ, and Δ is the sampling period.

[0135] c) Calculate the discrete Fourier series coefficients of the periodic function with respect to the discrete angle n:

[0136]

[0137] d) Then perform a discrete-time Fourier transform on the discrete delay m, and the cyclic spectral density function can be obtained

[0138]

[0139] Observe whether there is a bearing fault characteristic order in the cyclic spectral density diagram, and at the same time determine the oscillation frequency of the fault impact waveform. Furthermore, complete the fault diagnosis. After obtaining the cyclic spectral density function, use the cyclic order as the X-axis, the spectral frequency as the Y-axis, and the cyclic spectral density function value as the Z-axis. Draw the spectral density function diagram.

[0140] See Figure 5Cyclic spectral density diagram for the case of bearing inner ring fault diagnosis. In this case, there is a fault in the bearing inner ring, the bearing model is 6203, and the frequency of this fault is 4.9475 times the bearing rotation speed frequency. Therefore, in the cyclic spectral density diagram, the abscissa represents the cyclic order, indicating the multiple of the rotation speed. Because of the fault with a frequency of 4.9475 times the rotation speed, the value of the cyclic spectral density function at the position where the abscissa is 4.9475 is significantly higher, and there is a bright line. The oscillation frequency of the fault impact waveform is obtained from the ordinate. The ordinate of the point with the highest value of the cyclic spectral density function at the fault order is the oscillation frequency, which can be obtained through Matlab. In one embodiment, there is a fault in the bearing inner ring, the bearing model is 6203, and the frequency of this fault is 4.9475 times the bearing rotation speed frequency. Therefore, in the cyclic spectral density diagram, the abscissa represents the cyclic order, indicating the multiple of the rotation speed. Because of the fault with a frequency of 4.9475 times the rotation speed, the value of the cyclic spectral density function at the position where the abscissa is 4.9475 is significantly higher, and there is a bright line. The oscillation frequency of the fault impact waveform is obtained from the ordinate. The ordinate of the point with the highest value of the cyclic spectral density function at the fault order is the oscillation frequency. Finally, it should be noted that: the described embodiments are only a part of the embodiments of the present application, rather than all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative efforts belong to the scope protected by the present application.

[0141] Only some exemplary embodiments of the present invention have been described by way of illustration above. Undoubtedly, for those of ordinary skill in the art, the described embodiments can be modified in various different ways without departing from the spirit and scope of the present invention. Therefore, the above drawings and description are illustrative in nature and should not be construed as limiting the scope of the claims of the present invention.

Claims

1. A method for diagnosing faults of rolling bearings with stable angular time cycle without a tachometer, characterized in that It includes the following steps: Step 1: Arrange measuring points at the bearing housing end cover of the rolling bearing, and collect vibration signals using a vibration acceleration sensor; Step 2: Estimate the preliminary rotational speed of the motor by the peak search method of short-time Fourier transform according to the vibration signals; Step 3: Calculate the accurate rotational speed of the motor using the Vold-Kalman filter and the preliminary rotational speed; Step 4: Conduct angle-time cyclic stationary analysis on the vibration signals according to the accurate rotational speed to obtain a cyclic spectrum density map; Step 5: Observe whether there is a significant deviation in the cyclic spectrum density function at a certain abscissa in the cyclic spectrum density map. This abscissa is the bearing fault characteristic order. At the same time, find the ordinate of the highest point of the cyclic spectrum density function at the bearing fault characteristic order of the abscissa as the oscillation frequency of the fault impact waveform to complete the fault diagnosis; Among them, Step 4 specifically includes the following steps: Step 4-1: Use the method of periodic time averaging to estimate the angle-time autocorrelation function of the vibration signals: ， where is the angle, is the time delay, is the cycle order, is the ensemble averaging operator, is the angle-time cyclic correlation function, represents angle resampling of the vibration signal, is the imaginary unit; Step 4-2, discretize the angular time autocorrelation function to obtain , where n and m respectively correspond to and discrete sampling of: ; , is the sampling period, Step 4-3, find the angular time autocorrelation function with respect to the discrete angle and the discrete Fourier series coefficients of: ， wherein are the discrete Fourier series coefficients, where is a certain cyclic order; is the discrete angle corresponding to the signal length; Step 4-4, then perform discrete delay and conduct discrete-time Fourier transform to obtain the cyclic spectral density function : ， where is the frequency.

2. A method for diagnosing faults of a rolling bearing with stable angle-time cycle without a tachometer according to claim 1, characterized in that, The rolling bearing is a motor bearing.

3. A method for diagnosing faults of a rolling bearing with stable angle-time cycle without a tachometer according to claim 2, characterized in that, The vibration acceleration sensor is arranged in the vertical direction of the motor bearing end cover.

4. A rolling bearing fault diagnosis method with stable angle-time cycle without a tachometer according to claim 1, characterized in that The sampling frequency of the vibration acceleration sensor is 10.24 KHz.

5. A method for diagnosing faults of a rolling bearing with stable angular time cycle without a tachometer according to claim 1, characterized in that The peak search method of short-time Fourier transform for estimating the preliminary rotational speed of the motor includes the following steps: Step 2-1: Conduct short-time Fourier transform on the vibration signals to obtain a first spectrum map; ， In the formula is the vibration signal, is the time, is the analysis window function, is the position of the analysis window function, is the frequency, is the spectral density; Step 2-2: Locate the frequency components related to the rotational speed by observing the spectrogram, and then apply the maximum tracking algorithm for the said frequency components to calculate the maximum frequency , and take this frequency as the preliminary instantaneous frequency: ， ， ， wherein is the given maximum detected frequency tolerance, is the rotation speed-related frequency component observed beforehand, is the maximum frequency estimated at the previous moment; Step 2-3: Calculate the instantaneous phase based on the preliminary instantaneous frequency; ， ， where is the instantaneous angular frequency, is the instantaneous phase, is the time variable; Step 2-4: Based on the instantaneous phase calculated in Step 2-3, conduct angle resampling on the vibration signals, and then use a band-pass filter to filter the resampled vibration signals, only retaining the components related to rotation; Step 2-5, using the instantaneous phase described in Step 2-3 , resample the filtered vibration signal back into the time domain; Step 2-6: Perform short-time Fourier transform on the vibration signal processed in Step 2-5 to obtain a second spectrogram, and calculate the final instantaneous frequency through Step 2-2. , and then through calculate the preliminary rotational speed of the motor.

6. A rolling bearing fault diagnosis method without a tachometer for angle-time cycle stability, according to claim 5, characterized in that Calculating the accurate rotational speed of the motor using the Vold-Kalman filter and the preliminary rotational speed includes the following steps: Step 3-1, construct the Vold-Kalman filtering order analysis structural equation; , let The coefficient term of is, and the matrix expansion of the structural equation is: ， Its matrix form is , In the formula is the inconsistent term of the structural equation, is the order ratio component to be tracked, is the number of sampling points, Step 3-2: Design a data equation for Vold-Kalman filter order analysis; ， where is the background noise, is the value of the -th sampling point of the vibration signal, Step 3-3: Establish the sum of squares of heterogeneous terms and error terms by the least squares method as the loss function: , in addition, the error term is the inconsistent term of the structural equation squared , the heterogeneous term is the background noise squared , r is the weighting factor Step 3-4, solve the loss function for its minimum value. Since , , so . Let , we get the equation: , where is the identity matrix; Step 3-5: Solve the equation to obtain the rotational speed harmonic components; Step 3-6, after using the Vold-Kalman filtering method, the accurate rotational speed harmonic components are obtained. Perform a short-time Fourier transform on the rotational speed harmonic components to obtain the third spectrogram. Calculate the instantaneous frequency through the maximum amplitude tracking algorithm, and then through , calculate the accurate rotational speed.

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