Rolling bearing composite fault diagnosis method based on variable speed working condition

Abstract

The invention relates to a rolling bearing composite fault diagnosis method based on a variable speed working condition. The method is characterized by comprising the following steps: S1, converting a variable-speed bearing fault signal into a relatively stable angular domain signal by adopting a resampling method, and adaptively decomposing the angular domain signal into K modal component signals based on successive variational mode decomposition (SVMD); s2, constructing a weighting factor according to the correlation coefficient and the root-mean-square value, combining the weighting factor with a margin index to establish a weighting margin index (WMF), calculating a WMF value of each component signal, selecting a component greater than a mean value as an effective component, and reconstructing the effective component; and S3, denoising the reconstructed signal by adopting a wavelet soft threshold (WST), demodulating the denoised reconstructed signal through an order spectrum, and contrasting with a theoretical fault order to realize fault diagnosis under a variable-speed working condition within an error allowable range. The SVMD method is combined with the WMF index and the WST noise reduction method, so that the fault order of the bearing can be effectively extracted from the noise environment, and the method has a good effect on composite fault diagnosis under the variable-speed working condition and has a certain practical application value.

Description

Technical Field

[0001] The invention relates to an application of a method for evaluating a modal component of a composite fault signal under a variable speed working condition in the field of bearing faults, and in particular to a method for evaluating a modal component based on a weighted margin index. Background Art

[0002] Rolling bearings are one of the most important parts in mechanical equipment. They have a high failure rate. Their failure can easily cause the entire equipment to stop working. Therefore, bearing fault diagnosis is of great significance in the monitoring and maintenance of mechanical equipment. Compared with single faults, compound faults increase the difficulty of diagnosis. Studies have shown that inner and outer ring faults account for 90% of bearing failures, affecting the normal operation of equipment, and serious ones will cause certain economic losses.

[0003] However, in the actual operation of vehicles, composite bearing failures caused by the start and stop of equipment under variable speed conditions are more common. The fault impact caused by variable speed conditions is no longer periodic in the time domain, and the fault characteristic frequency will change due to the change in speed. At this time, the vibration signal is characterized as a nonlinear non-stationary signal. Only through time-frequency domain analysis will produce "spectral blurring" phenomenon, and it is difficult to effectively extract the fault characteristic information contained in the bearing vibration signal. Therefore, conventional diagnostic methods are no longer applicable. In order to solve the problem that nonlinear non-stationary signals are difficult to process and analyze, some scholars have proposed that the order tracking method can be used to convert the non-stationary signal under variable speed conditions into a relatively stable angular domain signal, and then the order spectrum analysis can be used to realize bearing fault diagnosis.

[0004] The above method can realize the extraction of bearing fault features under variable speed conditions to a certain extent. However, the fault features of the vibration signals collected in the actual industrial environment are easily interfered by noise, which obscures the characteristic information. Therefore, it is necessary to take certain noise reduction processing on the angular domain signal to highlight the impact component information of the vibration signal, and then perform order spectrum analysis on the noise-reduced signal to realize the accurate extraction of bearing composite fault signals under variable speed conditions.

[0005] Based on the above content, in order to solve the problem that bearing composite faults under variable speed conditions are easily interfered by strong background noise, which leads to the obliteration of important fault feature information, a method of denoising based on SVMD decomposition and weighted margin index using WST is proposed, which can effectively solve the above problem. Summary of the invention

[0006] The present invention proposes a signal decomposition method based on SVMD decomposition and margin index, and reconstructs the signal through WST denoising, and envelope demodulates the reconstructed signal after denoising to solve the problem that fault information is obscured by noise under variable speed conditions.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

[0008] The present invention provides a fault feature extraction method based on weighted margin index and WST denoising method, comprising the following steps:

[0009] S1: The non-stationary signal under variable speed is transformed into a relatively stable angular domain signal through the resampling method, and the angular domain signal is decomposed into K modal component signals using the SVMD method.

[0010] S2: Calculate the weighted margin index of each modal component, select the components above the mean as effective components, and reconstruct the effective components.

[0011] S3: Use WST to reduce noise and reconstruct the signal. Analyze the reconstructed signal after noise reduction based on the order spectrum method, compare it with the theoretical fault characteristic order, and determine the fault type.

[0012] Preferably, the S1 is specifically:

[0013] The composite fault signal of rolling bearing under variable speed condition is taken as the research object. The resampling method is used to convert it into a stable angular domain signal, and then it is decomposed into a series of modal component signals based on the SVMD method.

[0014] Preferably, the calculation process of S2 is as follows:

[0015] S2.1: Solve the root mean square value of the K component signals x after SVMD decomposition to reflect the vibration intensity of the bearing fault signal to better characterize the fault signal characteristics. The expression is:

[0016]

[0017] Where κ is the number of modal components, κ = 1, 2, ···, K, N is the number of signal sampling points.

[0018] S2.2: Solve the correlation coefficient value of the component signal, and its mathematical expression is:

[0019]

[0020] Where E(·) is the mathematical expectation and y is the angular domain signal.

[0021] S2.3 Solve the margin factor value of each component, and its mathematical expression is

[0022]

[0023] where x max is the maximum value among a set of component signals.

[0024] S2.4: Construct weighting factors and establish weighted margin indicators, the mathematical expression of which is:

[0025]

[0026] The WMF value of each component is calculated, and the components greater than the WMF mean are selected as valid components. They are then reconstructed into reconstructed signals in preparation for noise reduction.

[0027] Preferably, the specific process of S3 is:

[0028] S3.1 uses the wavelet soft threshold method to reduce the noise of the reconstructed signal. The commonly used threshold mathematical expression is:

[0029]

[0030] However, when there are too many signal sampling points, the threshold obtained by this method is large and remains unchanged during the threshold quantization process of each layer, resulting in the omission of some useful signals and reducing the accuracy of signal extraction. Therefore, an improved threshold selection rule is adopted to avoid the problem of too many sampling points. Its mathematical expression is:

[0031]

[0032] Where σ is the standard deviation of noise, θ is the number of decomposition layers, λ is the threshold, and λ θ is the threshold value on the corresponding θ layer.

[0033] S3.2 uses the order spectrum method to envelope the reconstructed signal after demodulation and noise reduction, identifies and extracts the actual fault order of the bearing in the order spectrum, and compares it with the theoretical fault order within the allowable error range to determine the fault type. When a certain frequency has many multiples, it can be considered that the bearing has this type of fault.

[0034] The theoretical failure order of the bearing can be calculated and determined based on the size parameters, and its expression is as follows:

[0035] Outer ring theoretical fault characteristic order:

[0036]

[0037] Theoretical fault order of inner ring:

[0038]

[0039] Theoretical failure order of rolling element:

[0040]

[0041] Theoretical fault characteristic order of cage:

[0042]

[0043] Where Z is the number of rolling elements, d is the rolling element diameter, and D is the raceway pitch diameter. is the contact angle.

[0044] The present invention has the following advantages:

[0045] In order to accurately extract the characteristic information of bearing composite fault signal under variable speed working condition, the present invention uses SVMD to decompose the fault signal, selects the effective component based on the weighted sparsity index, uses the WST method to reduce the noise and reconstruct the effective component signal, and realizes the bearing composite fault diagnosis under variable speed working condition by envelope demodulation. This method can effectively extract the characteristic information of bearing fault obliterated by background noise and improve the accuracy of fault extraction. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 A flow chart of a rolling bearing composite fault signal diagnosis method based on variable speed conditions is provided for the implementation of this example.

[0047] Figure 2 It is the time domain of vibration signal under braking and deceleration conditions.

[0048] Figure 3 is the time domain of the modal components after SVMD decomposition.

[0049] Figure 4 Comparison of the reconstructed signal before and after noise reduction.

[0050] Figure 5 is the order spectrum of the reconstructed signal after denoising. DETAILED DESCRIPTION

[0051] In order to clarify the purpose, technical solutions and advantages of the present invention, the present invention is further described in detail in conjunction with specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0052] Example

[0053] The composite fault signal of rolling bearing under braking and deceleration conditions is taken as the research object. The theoretical fault order of the bearing can be obtained through the size parameters. The size parameters of the experimental bearing are: bearing diameter D = 38.52mm, rolling element diameter d = 7.94mm, number of rolling elements Z = 9, contact angle

[0054] Outer ring theoretical fault characteristic order:

[0055]

[0056] Theoretical fault order of inner ring:

[0057]

[0058] Theoretical failure order of rolling element:

[0059]

[0060] Theoretical fault characteristic order of cage:

[0061]

[0062] according to Figure 1 The flowchart shown in the figure, this example provides a diagnosis method based on the composite fault signal of the rolling bearing under the variable speed working condition, the method comprises the following steps:

[0063] S1: The non-stationary signal under variable speed is transformed into a relatively stable angular domain signal through the resampling method, and the angular domain signal is decomposed into 19 modal component signals using the SVMD method.

[0064] S2: Calculate the weighted margin index of each modal component, select the components above the mean as effective components, and reconstruct the effective components.

[0065] S2.1: Solve the root mean square value of the 19 component signals x after SVMD decomposition to reflect the vibration intensity of the bearing fault signal in order to better characterize the fault signal characteristics. The expression is:

[0066]

[0067] Where κ is the number of modal components, κ=1, 2,..., K, K=19, and N is the number of signal sampling points, N=15000.

[0068] S2.2: Solve the correlation coefficient value of the component signal, and its mathematical expression is:

[0069]

[0070] Where E(·) is the mathematical expectation and y is the angular domain signal.

[0071] S2.3 Solve the margin factor value of each component, and its mathematical expression is

[0072]

[0073] where x max is the maximum value among a set of component signals.

[0074] S2.4: Construct weighting factors and establish the weighted margin indicator WMF, whose mathematical expression is:

[0075]

[0076] The WMF value of each component is calculated, and the calculated mean value is 0.0018. The components with WMF values ​​greater than 0.0018 are selected as valid components, and they are reconstructed to form reconstructed signals.

[0077] S3: Use WST to reduce noise and reconstruct the signal. Analyze the reconstructed signal after noise reduction based on the order spectrum method, compare it with the theoretical fault characteristic order, and determine the fault type.

[0078] S3.1 uses the wavelet soft threshold method to reduce the noise of the reconstructed signal. The commonly used threshold mathematical expression is:

[0079]

[0080] However, when there are too many signal sampling points, the threshold obtained by this method is large and remains unchanged during the threshold quantization process of each layer, resulting in the omission of some useful signals and reducing the accuracy of signal extraction. Therefore, an improved threshold selection rule is adopted to avoid the problem of too many sampling points. Its mathematical expression is:

[0081]

[0082] Where σ is the noise standard deviation, σ = 0.0312, θ is the number of decomposition layers, k = 20, λ is the threshold, λ θ is the threshold value corresponding to the θ layer, min(λ)=0.045.

[0083] S3.2 uses the order spectrum method to envelope the demodulated and denoised reconstructed signal, and extracts the actual bearing fault order within the allowable error range. According to the order spectrum, it can be clearly observed that O i =5.42, O o =3.43, O b =4.53 and its corresponding 2 times frequency and 3 times frequency, and then determine the fault type.

[0084] The specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A rolling bearing composite fault diagnosis method under variable speed conditions, characterized in that: The following steps are involved: S1: Based on the resampling method, the variable speed composite fault signal is converted into a stable angular domain signal, and the angular domain signal is decomposed using successive variational mode decomposition (SVMD) to obtain K modal component signals. S2: Calculate the weighted sparsity value of each modal component signal, select the components greater than the mean as the effective components, and reconstruct the effective component signals. S3: The wavelet soft threshold method is used to reduce noise and reconstruct the signal. The reconstructed signal after noise reduction is analyzed by order spectrum and compared with the theoretical fault order to realize compound fault diagnosis under variable speed conditions.

2. The rolling bearing composite fault diagnosis method under variable speed conditions according to claim 1 is characterized in that: Specifically, S1 takes the composite fault signal of the rolling bearing under variable speed working condition as the research object, converts it into an angular domain signal by using a resampling method, and decomposes it into a series of component signals based on the SVMD method.

3. The rolling bearing composite fault diagnosis method under variable speed conditions according to claim 1 is characterized in that: The weighted margin index in S2 is an evaluation index that comprehensively reflects the vibration intensity of the bearing fault signal, the correlation between the original signal and the component signal, and the signal impact characteristics. The calculation process is as follows: S2.1: Solve the root mean square value of the K component signals x after SVMD decomposition to reflect the vibration intensity of the bearing fault signal in order to better characterize the fault signal characteristics. The mathematical expression is: Where κ is the number of modal components, κ = 1, 2, ···, K, N is the number of signal sampling points. S2.2: Solve the correlation coefficient value of the component signal, and its mathematical expression is: Where E(·) is the mathematical expectation and y is the angular domain signal. S2.3 Solve the margin factor value of each component, and its mathematical expression is where x max is the maximum value among a set of component signals. S2.4: Construct weighting factors and establish weighted margin indicators, the mathematical expression of which is: The WMF value of each component is calculated, and the components greater than the mean value of the weighted margin index are selected as effective components. They are reconstructed into reconstructed signals in preparation for noise reduction.

4. The rolling bearing composite fault diagnosis method under variable speed conditions according to claim 1 is characterized in that: The specific process of S3 is as follows: S3.1 uses wavelet soft threshold to reduce noise of reconstructed signal. The commonly used threshold mathematical expression is: However, when there are too many signal sampling points, the threshold obtained by this method is large and remains unchanged during the threshold quantization process of each layer, resulting in the omission of some useful signals and reducing the accuracy of signal extraction. Therefore, an improved threshold selection rule is adopted to avoid the problem of too many sampling points. Its mathematical expression is: Where σ is the standard deviation of noise, θ is the number of decomposition layers, λ is the threshold, and λ θ is the threshold value on the corresponding θ layer. S3.2 uses the order spectrum method to envelope the reconstructed signal after demodulation and noise reduction, identifies and extracts the actual fault order of the bearing in the order spectrum, and compares it with the theoretical fault order within the allowable error range to determine the fault type. When a certain frequency has many multiples, it can be considered that the bearing has this type of fault. The theoretical failure order of the bearing can be calculated and determined based on the size parameters, and its expression is as follows: Outer ring theoretical fault characteristic order: Theoretical fault order of inner ring: Theoretical failure order of rolling element: Theoretical fault characteristic order of cage: Where Z is the number of rolling elements, d is the rolling element diameter, and D is the raceway pitch diameter. is the contact angle.

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