A bearing waviness targeted characterization method based on a gaussian filter

Abstract

The application provides a bearing waviness target characterization method based on a Gaussian filter, which generates a random matrix by a Gaussian distribution function to represent the randomness of the waviness, and defines a Gaussian filter according to parameters and the like of the simulated waviness; then, the defined Gaussian filter is used to generate the change of the simulated waviness amplitude, finally, the curve required to describe the waviness is selected by a slicing method and a screening index, and the characterization of the bearing race waviness is realized. The method can completely simulate the actual form of the waviness, can more accurately characterize the characteristics of the real waviness, and thus realizes the accurate characterization of the real waviness of the rolling bearing.

Description

Technical Field

[0001] This invention relates to the field of bearing manufacturing technology, and in particular to a method for targeted characterization of bearing waviness based on a Gaussian filter. Background Technology

[0002] Waviness generated during bearing manufacturing has a significant impact on bearing vibration, noise, and fatigue life during operation. To better assess the impact of bearing waviness on bearing quality and performance during factory inspection, assembly, and use, a common method is to simplify waviness as a sinusoidal waveform or a combination of multiple sinusoidal waveforms. However, the actual waviness curve is neither an ideal sinusoidal waveform nor a non-uniform combination of multiple sinusoidal waveforms; its amplitude and wavelength exhibit non-periodic variations and a degree of randomness. Current sinusoidal function-based characterization methods cannot fully simulate the actual waviness shape, resulting in insufficient representation of displacement and stiffness excitation details in bearing waviness dynamics models, affecting the accuracy of waviness dynamics simulations and the identification of waviness vibration characteristics. Summary of the Invention

[0003] This invention provides a bearing waviness targeting characterization method based on Gaussian filter, thereby overcoming the problem that the characterization method based on sine function cannot completely simulate the actual waviness shape, and realizing accurate characterization of the true waviness of rolling bearings.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for targeted characterization of bearing waviness based on Gaussian filters includes the following steps: S1 generates a random matrix R using a Gaussian distribution function; S2, Obtain the Gaussian filter function based on the Gaussian distribution function from step S1, and select the parameters of the Gaussian filter function according to the ripple parameters to be simulated to define the Gaussian filter, generating the Gaussian filter matrix. G ; S3, through a random matrix R and Gaussian filter matrix G The convolution calculation generates the ripple matrix Z to simulate the change in ripple amplitude; S4. Calculate the waviness order, waviness RMS value, peak-to-peak value, and bandwidth coefficient. Select the curve to describe the waviness from the waviness matrix Z using the slicing method to characterize the bearing raceway waviness.

[0005] Furthermore, in step S1, a random matrix R with a mean of 0 and a standard deviation of σ, following a normal distribution, is generated using a Gaussian distribution function.

[0006] Furthermore, in step S1, a two-dimensional Gaussian distribution function is used, the general form of which can be expressed as: (1) In the formula, μ x and μ y Represent the two-dimensional Gaussian distribution function in x and y The mean of the direction, σ x and σ y Represent the two-dimensional Gaussian distribution function in x and y Variance of direction; when and When the Gaussian distribution function is: (2) The Gaussian distribution function in equation (2) generates a value with a mean of 0 and a standard deviation of . An uncorrelated random matrix R can be expressed as: (3) in Used to control the amplitude of the generated waviness. N This represents the size of the random matrix R.

[0007] Furthermore, in step S2, the height of the Gaussian filter is normalized to 1, and the width of the Gaussian filter is determined by the correlation length. cl Sure: The Gaussian filter function obtained by normalizing equation (2) is expressed as: (4) In the formula, cl The normalized standard deviation is defined as follows: cl For waviness along x and y The relevant length of the direction; The method for selecting the parameters of the Gaussian filter function based on the parameters of the ripple to be simulated is as follows: In the Gaussian filter function... cl The average pitch can be selected based on the order of the simulated waviness and the raceway circumference. According to the characteristics of bearing waviness, it is assumed that the order of the simulated bearing waviness is... The raceway diameter is L , Let be the wave length for each order of waviness, then the average wave length for the waviness is... for: (5) Relevant length cl With waviness mean wavelength The relationship can be represented as: (6) In the formula, s Indicates the relevant length control coefficient; Gaussian filter matrix G for: (7) Furthermore, in step S3, the random matrix R and Gaussian filter matrix G The convolution is: (8) According to the convolution theorem, the spectrum of a function's time-domain convolution is equal to the function's frequency-domain product. (The matrix...) and Performing a Fourier transform and then an inverse Fourier transform on the product, the convolution in equation (8) is transformed into: (9) In the formula, For Fourier transform, The inverse Fourier transform can be expressed as follows: (10) (11) According to equations (8)-(11), the ripple matrix is ​​obtained. Z .

[0008] Furthermore, the formula for calculating the RMS value in step S4 is as follows (12), the formula for calculating the peak-to-peak value is as follows (13), and the formula for calculating the bandwidth coefficient is as follows (14): (12) (13) (14) (15) In the formula, x Each waviness curve represents the waviness. For bandwidth coefficient, Irregular factors f It is a Fourier transform frequency sequence. G(f) This represents the one-sided power spectral density.

[0009] Furthermore, in step S1, the Gaussian distribution function is a one-dimensional Gaussian distribution function, the general form of which can be expressed as: (16) In the formula, μ x Describes the one-dimensional Gaussian distribution function in x The mean of the direction, σ x Describes the one-dimensional Gaussian distribution function in x The variance; when and When, the Gaussian distribution function of equation (16) can be expressed as: (17) The Gaussian distribution function in equation (17) generates a value with a mean of 0 and a standard deviation of . An uncorrelated random matrix R can be expressed as: (18) in Used to control the amplitude of the generated waviness. N This represents the size of the random matrix R.

[0010] Furthermore, in step S2, the height of the Gaussian filter is normalized to 1, and the width of the Gaussian filter is determined by the correlation length. cl Sure: The Gaussian filter function obtained by normalizing equation (17) is expressed as: (19) In the formula, cl The normalized standard deviation is defined as follows: cl For waviness along x The relevant length of the direction; The method for selecting the parameters of the Gaussian filter function based on the parameters of the ripple to be simulated is as follows: In the Gaussian filter function... cl The average pitch can be selected based on the order of the simulated waviness and the raceway circumference. According to the characteristics of bearing waviness, it is assumed that the order of the simulated bearing waviness is... The raceway diameter is L , Let be the wave length for each order of waviness, then the average wave length for the waviness is... for: (20) Relevant length cl With waviness mean wavelength The relationship can be represented as: (twenty one) In the formula, s Indicates the relevant length control coefficient; Gaussian filter matrix G for: . (twenty two) By adopting the above technical solution, the present invention has the following beneficial effects: To address the issue that neither uniform nor non-uniform sine functions can accurately characterize the true waviness characteristics, a Gaussian filter-based targeted characterization method for bearing waviness is proposed. This method uses a Gaussian distribution function to generate a random matrix to represent the randomness of waviness, and defines a Gaussian filter based on the parameters of the waviness to be simulated. Then, the defined Gaussian filter is used to generate variations in the amplitude of the simulated waviness. Finally, the desired curve describing the waviness is selected through a slicing method and a screening index, thus achieving the characterization of bearing raceway waviness. This method can completely simulate the actual waviness shape, enabling it to more accurately characterize the true waviness characteristics, thereby achieving precise characterization of the true waviness of rolling bearings. Attached Figure Description

[0011] Figure 1 A flowchart illustrating a preferred embodiment of the bearing waviness targeting characterization method based on a Gaussian filter according to the present invention. Figure 2 A graph of a random matrix R based on a Gaussian distribution; Figure 3 (a) is a diagram of a Gaussian filter matrix with a specific width and height. Figure 3 (b) is Figure 3 (a) Enlarged view of the Gaussian filter matrix; Figure 4 This is a ripple matrix diagram based on Gaussian filter simulation, i.e., a cluster of ripple curves; Figure 5 The waviness curve that meets the requirements after screening by the slicing method; Figure 6 This represents the order statistics of the ripple matrix, where... Figure 6 (a) represents the order of the waviness of each slice in the waviness matrix Z. Figure 6 (b) is a histogram of all slice orders; Figure 7 The results of the waviness matrix parameter calculation; Figure 8 The selected waviness curves that meet the requirements are, where, Figure 8 (a) is when N w =10, when RMS and peak-to-peak values ​​are relatively large, the ripple curve with sequence number 233 is selected. Figure 8(b) is when N w =10, when RMS and peak-to-peak values ​​are relatively small, the ripple curve with serial number 119 is selected. Figure 8 (c) is N w =10, the ripple curve with sequence number 254 is selected when there is a small degree of randomness. Figure 8 (d) is N w =10, the ripple curve with the sequence number 131 is selected when there is a large degree of randomness; Figure 9 Images showing the measured bearing waviness, among which... Figure 9 (a) is a polar coordinate diagram of the measured bearing waviness. Figure 9 (b) is a rectangular coordinate system diagram of the measured bearing waviness; Figure 10 (a) and Figure 10 (b) The random matrix R and the ripple matrix Z obtained by the bearing ripple-targeting characterization method based on Gaussian filter in this embodiment are respectively. Figure 11 This is a comparison chart of the waviness curve obtained by using the bearing waviness targeting characterization method based on Gaussian filter in this embodiment and the measured waviness curve. Figure 12 (a) represents the correlation coefficients between all slices obtained using the uniform sinusoidal method in the prior art and the measured morphology. Figure 12 (b) represents the correlation coefficients between all slices obtained using the non-uniform sine method in the prior art and the measured morphology. Detailed Implementation

[0012] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0013] It should be noted that when a component is described as "fixed to" another component, it can be directly on the other component or may have a component in between. When a component is considered "connected to" another component, it can be directly connected to the other component or may have a component in between. When a component is considered "set on" another component, it can be directly set on the other component or may have a component in between. The terms "vertical," "horizontal," "left," "right," and similar expressions used in this document are for illustrative purposes only.

[0014] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0015] Please see Figure 1 A preferred embodiment of the present invention provides a method for targeted characterization of bearing waviness based on a Gaussian filter, comprising the following steps: S1 represents the randomness of bearing waviness by generating a random matrix R through a Gaussian distribution function.

[0016] The Gaussian distribution function is used in step S1. G(x,y) A random matrix R with a mean of 0 and a standard deviation of σ, following a normal distribution, is generated. Specifically, in this embodiment, a two-dimensional Gaussian distribution function is used. The general form of a two-dimensional Gaussian distribution function can be expressed as: (1) In the formula, μ x and μ y Represent the two-dimensional Gaussian distribution function in x and y The mean of the direction, σ x and σ y Represent the two-dimensional Gaussian distribution function in x and y Variance of direction.

[0017] when and When, the Gaussian distribution function of equation (1) can be expressed as: (2) The Gaussian distribution function in equation (2) generates a value with a mean of 0 and a standard deviation of . An uncorrelated random matrix R, such as Figure 2 As shown, the random matrix R can be represented as: (3) in Used to control the amplitude of the generated waviness. N This represents the size of the random matrix R.

[0018] S2, based on the Gaussian distribution function in step S1, obtain a Gaussian filter function that reflects the waviness characteristics and has a certain width and height. Then, select the parameters of the Gaussian filter function according to the waviness parameters to be simulated to define the Gaussian filter and generate the Gaussian filter matrix. G .

[0019] In step S2, the height of the Gaussian filter is normalized to 1, and the width of the Gaussian filter is determined by the correlation length. cl Sure: The Gaussian filter function obtained by normalizing equation (2) is expressed as: (4) In the formula, cl The normalized standard deviation is defined as follows: cl For waviness along x and y The relevant length of the direction; The method for selecting the parameters of the Gaussian filter function based on the parameters of the ripple to be simulated is as follows: In the Gaussian filter function... cl The average pitch can be selected based on the order of the simulated waviness and the raceway circumference. According to the characteristics of bearing waviness, it is assumed that the order of the simulated bearing waviness is... The raceway diameter is L , Let be the wave length for each order of waviness, then the average wave length for the waviness is... for: (5) Relevant length cl The average wavelength of the waviness The relationship can be represented as: (6) In the formula, s Indicates the relevant length control coefficient; Gaussian filter matrix G for( Figure 3 ): (7) S3, through a random matrix R and Gaussian filter matrix G The convolution calculation generates the ripple matrix Z to simulate the change in ripple amplitude.

[0020] In step S3, the random matrix R and Gaussian filter matrix G The convolution Z is: (8) According to the convolution theorem, the spectrum of a function's time-domain convolution is equal to the function's frequency-domain product. (The matrix...) and Performing a Fourier transform and then an inverse Fourier transform on the product, the convolution in equation (8) is transformed into: (9) In the formula, For Fourier transform, The Fourier transform formula can be expressed as (10) and the inverse Fourier transform formula can be expressed as (11). Both of these are existing technologies and will not be elaborated here to save space.

[0021] (10) (11) According to equations (8)-(11), the ripple matrix is ​​obtained. Z ( Figure 4 The ripple matrix is ​​obtained by convolving the random matrix R with the Gaussian filter matrix G. Z .

[0022] S4. Calculate the order of waviness, the RMS value of waviness, the peak-to-peak value and the bandwidth coefficient. Select the curve to describe the waviness from the waviness matrix Z using the slicing method to achieve the characterization of bearing raceway waviness.

[0023] The formula for calculating the ripple RMS value in step S4 is as follows (12), the formula for calculating the peak-to-peak value is as follows (13), and the formula for calculating the bandwidth coefficient is as follows (14): (12) (13) (14) (15) In the formula, x Represents the waviness of each waviness curve, max( x ) express x The maximum value, min( x ) express x The minimum value, The bandwidth coefficient represents the degree of randomness in the waviness curve; a larger bandwidth coefficient indicates a greater degree of randomness in the waviness curve. For the calculation of the irregular factor, please refer to formula (15). f It is a Fourier transform frequency sequence. G(f) This represents the one-sided power spectral density. Figure 5This is a curve selected from the ripple matrix Z using the slicing method to describe the rippleness.

[0024] The following specific embodiment will be used to illustrate the bearing waviness targeting characterization method based on Gaussian filter of this implementation.

[0025] Taking the simulated outer ring raceway waviness of a deep groove ball bearing 6206 (outer ring raceway diameter is 56.45mm) as an example, the simulated bearing waviness order is determined. N w Set to 10, standard deviation The value is set to 0.05 μm, and the resulting random matrix R, Gaussian filter G, and wattage matrix Z are as follows: Figure 2 , Figure 3 and Figure 4 As shown, where, Figure 4 The ripple matrix Z diagram, also known as the ripple curve cluster, consists of N curves, where N depends on the dimension of the R matrix. The slicing method involves selecting the desired ripple curve from these N curves.

[0026] The number of peaks for each ripple in the ripple matrix is ​​calculated by peak search, which determines the order of the ripple. Figure 6 (a) is the ripple matrix Z The actual order of each slice, i.e., the order of waviness. Figure 6 (b) Histograms for all slice orders, from Figure 6 It was found that the simulation yielded a ripple level of 10, which was consistent with the simulation requirements.

[0027] Calculate the ripple RMS value, peak-to-peak value, bandwidth coefficient, and other indicators, and normalize each indicator value to [0,1]. The results are as follows: Figure 7 As shown.

[0028] The ripple level should be selected based on actual needs. For example, if a ripple level of 10 is desired and the RMS and peak-to-peak values ​​are relatively high, then it can be selected from... Figure 7 Select as Figure 8 (a) shows the waviness curve with serial number 233. If the desired waviness order is 10 and the RMS and peak-to-peak values ​​are relatively small, then it can be obtained from... Figure 7 Select as Figure 8 (b) shows the waviness curve with serial number 119. If the desired waviness order is 10 and the bandwidth coefficient is small, then it can be obtained from... Figure 7 Select as Figure 8 (c) shows the waviness curve with serial number 254. If the desired waviness order is 10 and the bandwidth coefficient is large, then it can be obtained from... Figure 7 Select as Figure 8 (d) shows the waviness curve for number 131.

[0029] Traditional methods for characterizing waviness typically represent the surface waviness of bearing parts as a sine function or a combination of multiple sine functions.

[0030] The method for characterizing the waviness of a uniform sine function assumes that the waviness curve is composed of... It consists of identical sine waves, and the maximum amplitude of the sine waves is Wavelength is At any position L w At this point, the waviness can be expressed as: (16) The method for characterizing the waviness of a non-uniform sine function assumes that the waviness curve is composed of... It consists of sine waves with different amplitudes and wavelengths, and the maximum amplitude of each sine wave is 10 ... Wavelength is At any position L wi At this point, the waviness can be expressed as: (17) To verify the effectiveness and superiority of the bearing waviness-targeted characterization method based on Gaussian filter proposed in this invention, the actual waviness of the bearing was measured. Characterization simulations were performed using the method of this invention, the uniform sine method, and the non-uniform sine method, and comparative analyses were conducted using Pearson correlation analysis. Cylindrical roller bearing NU307 was selected for raceway waviness measurement. The measurement process was performed according to the national standard "Methods for Measurement and Evaluation of Roundness and Waviness Errors of Rolling Bearing Parts" (JB / T6642-2004). Waviness measurement was performed using a Taylor Hobson PR365 roundness meter. The measured bearing waviness images are shown below. Figure 9 As shown, from Figure 9 It can be seen that the measured order of the waviness of the bearing is 15.

[0031] Set a random matrix R The size is 256×256. R Standard deviation Set to 0.2μm, relevant length control factor s If the value is 0.55, then the waviness matrix Z obtained by the bearing waviness targeting characterization method based on Gaussian filter in this embodiment is as follows: Figure 10 As shown.

[0032] The correlation coefficient between the simulated waviness curve and the measured waviness curve obtained using the characterization method of this embodiment is calculated, and the correlation between simulated waviness and measured waviness is analyzed. The Pearson correlation coefficient is used. rThe expression is: (18) In the formula, and These are the simulated morphology and the actual machined surface morphology, respectively. This is the average value. r The larger the value, the higher the correlation between the simulated ripple and the measured ripple.

[0033] Calculations revealed that the waviness matrix simulated using the characterization method of this embodiment contains a waviness curve of order 15 with a high correlation coefficient to the measured waviness curve. Figure 11 The data shows that the correlation coefficient between the characterization method used in this embodiment and the measured ripple curve is 0.53325.

[0034] The correlation coefficients of the waviness from multiple simulations using the uniform sinusoidal method and the non-uniform sinusoidal method were calculated, and the optimal waviness curves characterized by the two methods are shown below. Figure 12 As shown, at this time, the correlation coefficients between the ripple simulated by the two methods and the measured ripple curves are 0.10119 and 0.38413, respectively, both lower than the correlation coefficient (0.53325) obtained by the characterization method of this embodiment.

[0035] In summary, by setting the order of the simulated ripple... N w Gaussian filter lateral correlation length coefficient s and standard deviation With just three parameters, a Gaussian-distributed surface waviness matrix can be generated. By setting the RMS value, peak-to-peak value, and bandwidth coefficient, a waviness curve that meets the requirements can be selected. Moreover, the waviness simulated by the method in this invention has the greatest correlation with the real waviness, which is better than the commonly used uniform sine method and non-uniform sine method.

[0036] It is understood that in step S1, other types of Gaussian distribution functions can also be used to generate the random matrix R, such as a one-dimensional Gaussian distribution function. In this case, the bearing ripple-targeting characterization method based on Gaussian filter of the present invention includes the following steps: S1 represents the randomness of bearing waviness by generating a random matrix R through a Gaussian distribution function.

[0037] In step S1, a random matrix R with a mean of 0 and a standard deviation of σ, following a normal distribution, is generated using a Gaussian distribution function. Specifically, in this embodiment, a one-dimensional Gaussian distribution function is used, and the general form of a one-dimensional Gaussian distribution function can be expressed as: (19) In the formula, μ xDescribes the one-dimensional Gaussian distribution function in x The mean of the direction, σ x Describes the one-dimensional Gaussian distribution function in x The variance.

[0038] when and When, the Gaussian distribution function of equation (19) can be expressed as: (20) The Gaussian distribution function generated by equation (20) has a mean of 0 and a standard deviation of . An uncorrelated random matrix R can be expressed as: (twenty one) in Used to control the amplitude of the generated waviness. N This represents the size of the random matrix R.

[0039] S2, based on the Gaussian distribution function in step S1, obtain a Gaussian filter function that reflects the waviness characteristics and has a certain width and height. Then, select the parameters of the Gaussian filter function according to the waviness parameters to be simulated to define the Gaussian filter and generate the Gaussian filter matrix. G .

[0040] In step S2, the height of the Gaussian filter is normalized to 1, and the width of the Gaussian filter is determined by the correlation length. cl Sure: The Gaussian filter function obtained by normalizing equation (20) is expressed as: (twenty two) In the formula, cl The normalized standard deviation is defined as follows: cl For waviness along x The relevant length of the direction; The method for selecting the parameters of the Gaussian filter function based on the parameters of the ripple to be simulated is as follows: In the Gaussian filter function... cl The average pitch can be selected based on the order of the simulated waviness and the raceway circumference. According to the characteristics of bearing waviness, it is assumed that the order of the simulated bearing waviness is... The raceway diameter is L , Let be the wave length for each order of waviness, then the average wave length for the waviness is... for: (twenty three) Relevant length cl The average wavelength of the waviness The relationship can be represented as: (twenty four) In the formula, s Indicates the relevant length control coefficient; Gaussian filter matrix G for: (25) S3, through a random matrix R and Gaussian filter matrix G The convolution calculation generates the ripple matrix Z to simulate the change in ripple amplitude.

[0041] In step S3, the random matrix R and Gaussian filter matrix G The convolution Z is: (26) According to the convolution theorem, the spectrum of a function's time-domain convolution is equal to the function's frequency-domain product. (The matrix...) and Performing a Fourier transform and then an inverse Fourier transform on the product, the convolution in equation (26) is transformed into: (27) In the formula, For Fourier transform, The Fourier transform formula can be expressed as (28) and the inverse Fourier transform formula can be expressed as (29). Both of them belong to the prior art and will not be elaborated here to save space.

[0042] (28) (29) According to equations (26)-(29), the ripple matrix is ​​obtained. Z The ripple matrix is ​​obtained by convolving the random matrix R with the Gaussian filter matrix G. Z .

[0043] S4. Calculate the order of waviness, the RMS value of waviness, the peak-to-peak value and the bandwidth coefficient. Select the curve to describe the waviness from the waviness matrix Z using the slicing method to achieve the characterization of bearing raceway waviness.

[0044] The formula for calculating the ripple RMS value in step S4 is as follows (30), the formula for calculating the peak-to-peak value is as follows (31), and the formula for calculating the bandwidth coefficient is as follows (32): (30) (31) (32) (33) In the formula, x Represents the waviness of each waviness curve, max( x ) express x The maximum value, min( x ) express x The minimum value, The bandwidth coefficient represents the degree of randomness in the waviness curve; a larger bandwidth coefficient indicates a greater degree of randomness in the waviness curve. For the calculation of the irregular factor, please refer to formula (33). f It is a Fourier transform frequency sequence. G(f) This represents the one-sided power spectral density.

[0045] The above description is a detailed description of the preferred embodiments of the present invention. However, the embodiments are not intended to limit the scope of the patent application of the present invention. All equivalent changes or modifications made under the technical spirit of the present invention should fall within the patent scope covered by the present invention.

Claims

1. A method for targeted characterization of bearing waviness based on Gaussian filters, characterized in that, Includes the following steps: S1 generates a random matrix R with a mean of 0 and a standard deviation of σ that follows a normal distribution, using a Gaussian distribution function. The Gaussian distribution function used is a two-dimensional Gaussian distribution function, the general form of which is: (1) In the formula, μ x and μ y Let σ represent the mean of the two-dimensional Gaussian distribution function in the x and y directions, respectively. x and σ y Let x and y represent the variances of the two-dimensional Gaussian distribution function in the x and y directions, respectively. when and When the Gaussian distribution function is: (2) The Gaussian distribution function in equation (2) generates a value with a mean of 0 and a standard deviation of . An uncorrelated random matrix R is expressed as: (3) in The magnitude of the generated ripple is used to control the size of the random matrix R. S2, Obtain the Gaussian filter function based on the Gaussian distribution function from step S1, and select the parameters of the Gaussian filter function according to the ripple parameters to be simulated to define the Gaussian filter, generating the Gaussian filter matrix G; the height of the Gaussian filter is normalized to 1, and the width of the Gaussian filter is determined by the relevant length cl: The Gaussian filter function obtained by normalizing equation (2) is expressed as: (4) In the formula, cl is the normalized standard deviation, and cl is defined as the correlation length of the waviness along the x and y directions; The method for selecting the parameters of the Gaussian filter function based on the parameters of the waviness to be simulated is as follows: The cl value in the Gaussian filter function is selected based on the order of the waviness to be simulated and the average wave distance calculated from the raceway circumference. Based on the characteristics of bearing waviness, it is assumed that the order of the bearing waviness to be simulated is... The raceway diameter is L. Let be the wave length for each order of waviness, then the average wave length for the waviness is... for: (5) Relevant length cl and mean wave length of waviness The relationship is represented as: (6) In the formula, s represents the relevant length control coefficient; The Gaussian filter matrix G is: (7) S3 generates a ripple matrix Z by convolving a random matrix R and a Gaussian filter matrix G to simulate the change in ripple amplitude. S4. Calculate the waviness order, waviness RMS value, peak-to-peak value, and bandwidth coefficient. Select the curve to describe the waviness from the waviness matrix Z using the slicing method to characterize the bearing raceway waviness.

2. The bearing waviness targeted characterization method based on Gaussian filter as described in claim 1, characterized in that, In step S3, the convolution of the random matrix R and the Gaussian filter matrix G is: (8) According to the convolution theorem, the spectrum of a function's time-domain convolution is equal to the function's frequency-domain product. (The matrix...) and Performing a Fourier transform and then an inverse Fourier transform on the product, the convolution in equation (8) is transformed into: (9) In the formula, For Fourier transform, The inverse Fourier transform is expressed by the formula: (10) (11) According to equations (8)-(11), the ripple matrix Z is obtained.

3. The bearing waviness targeted characterization method based on Gaussian filter as described in claim 1, characterized in that, The formula for calculating the RMS value in step S4 is (12), the formula for calculating the peak-to-peak value is (13), and the formula for calculating the bandwidth coefficient is (14). (12) (13) (14) (15) In the formula, x represents the waviness of each waviness curve. For bandwidth coefficient, Let f be the irregularity factor, f be the Fourier transform frequency sequence, and G(f) be the one-sided power spectral density.

4. A method for targeted characterization of bearing waviness based on a Gaussian filter, characterized in that, Includes the following steps: S1 generates a random matrix R with a mean of 0 and a standard deviation of σ, following a normal distribution, using a Gaussian distribution function. The Gaussian distribution function used is a one-dimensional Gaussian distribution function, the general form of which is: (16) In the formula, μ x Let σ represent the mean of the one-dimensional Gaussian distribution function in the x-direction. x This represents the variance of the one-dimensional Gaussian distribution function in x; when and When, the Gaussian distribution function of equation (16) is expressed as: (17) The Gaussian distribution function in equation (17) generates a value with a mean of 0 and a standard deviation of . An uncorrelated random matrix R is expressed as: (18) in The magnitude of the generated ripple is used to control the size of the random matrix R. S2, Obtain the Gaussian filter function based on the Gaussian distribution function from step S1, and select the parameters of the Gaussian filter function according to the ripple parameters to be simulated to define the Gaussian filter, generating the Gaussian filter matrix G; the height of the Gaussian filter is normalized to 1, and the width of the Gaussian filter is determined by the relevant length cl: The Gaussian filter function obtained by normalizing equation (17) is expressed as: (19) In the formula, cl is the normalized standard deviation, and cl is defined as the correlation length of the waviness along the x-direction; The method for selecting the parameters of the Gaussian filter function based on the parameters of the waviness to be simulated is as follows: The cl value in the Gaussian filter function is selected based on the order of the waviness to be simulated and the average wave distance calculated from the raceway circumference. Based on the characteristics of bearing waviness, it is assumed that the order of the bearing waviness to be simulated is... The raceway diameter is L. Let be the wave length for each order of waviness, then the average wave length for the waviness is... for: (20) Relevant length cl and mean wave length of waviness The relationship is represented as: (21) In the formula, s represents the relevant length control coefficient; The Gaussian filter matrix G is: ； S3 generates a ripple matrix Z by convolving a random matrix R and a Gaussian filter matrix G to simulate the change in ripple amplitude. S4. Calculate the waviness order, waviness RMS value, peak-to-peak value, and bandwidth coefficient. Select the curve to describe the waviness from the waviness matrix Z using the slicing method to characterize the bearing raceway waviness.

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