A multi-scale characterization method for bearing raceway waviness-local defects

Abstract

The present invention provides a bearing raceway waviness-local defect multi-scale characterization method, which belongs to the field of bearing manufacturing technology. The method comprises the following steps: S1, generating a matrix R and a matrix G through a Gaussian distribution function, and generating a matrix Z through convolution calculation; S2, regenerating a matrix R' from the matrix R, defining local defect parameters to obtain a Gaussian filter G of defect scale; S3, obtaining a trend matrix T according to the characteristics of the local defects to be simulated; S4, convolving the matrix R' with the matrix G' to obtain a local defect random matrix D', and then adding the local defect random matrix D' to the trend matrix T to obtain the local defect matrix D; S5, obtaining a waviness curve from step S1 and a local defect curve from step S4 through a slicing method, and obtaining a waviness-local defect multi-scale simulation curve after superposition and smoothing operations, overcoming the problem of insufficient characterization capability when the scale of the waviness and the scale of the local defect morphology are similar and coexist in the bearing raceway, and realizing accurate characterization of local defects of rolling bearings.

Description

Technical Field

[0001] The invention relates to the technical field of bearing manufacturing, and in particular to a bearing raceway waviness-local defect multi-scale characterization method. Background Art

[0002] Rolling bearings are key components in rotating machinery, playing the role of shaft support and motion transmission. Due to their compact structure, high mechanical efficiency and high precision, they are widely used in important fields such as aerospace, wind power generation, and the automotive industry. According to statistics, 30% of the faults in rotating machinery are caused by bearings, and 50% of the faults in wind power gearbox transmission systems are related to bearings. However, the success rate of early fault diagnosis of rolling bearings is low, which is still a research hotspot and engineering difficulty in academia. One of the fundamental reasons is that the internal excitation of early bearing faults is weak, and the vibration characteristics are easily affected by the excitation of waviness, resulting in unclear mapping relationship between vibration characteristics and internal and external excitation of bearings, unclear mechanism of action, and affecting the identification of early fault vibration characteristics. In the actual operation of bearings, early faults are generated in the process of operation. On the one hand, the scale of the early faults is similar to the waviness size, and on the other hand, the surface of the early local defects also has a morphological scale. However, the current characterization methods of waviness, local defects and surface morphology are insufficient for the characterization of the waviness scale and the local defect morphological scale that are similar and coexist in the bearing raceway, which affects the identification of early faults of rolling bearings. Summary of the invention

[0003] The present invention provides a bearing raceway waviness-local defect multi-scale characterization method to overcome the problem of insufficient characterization capability when the waviness scale and the local defect morphology scale are similar and coexist on the bearing raceway, thereby achieving accurate characterization of local defects of rolling bearings.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is:

[0005] A bearing raceway waviness-local defect multi-scale characterization method comprises the following steps:

[0006] S1, generating a random matrix R through a Gaussian distribution function, and obtaining a Gaussian filter function according to the Gaussian distribution function, selecting parameters of the Gaussian filter function according to the parameters of the waviness to be simulated to define a Gaussian filter, thereby generating a Gaussian filter matrix G, and generating a bearing raceway random waviness matrix Z through convolution calculation of the random matrix R and the Gaussian filter matrix G;

[0007] S2, defining a preset size area from the random matrix R as a local defect interval, regenerating a random matrix for the local defect area using a Gaussian distribution function as a defect random matrix R', defining the depth of the local defect and defining a Gaussian filter according to the defect scale to obtain a Gaussian filter G' of the defect scale;

[0008] S3, selecting a local defect trend simulation function according to the characteristics of the local defect to be simulated, and obtaining a trend matrix T;

[0009] S4, convolving the defect random matrix R' with the Gaussian filter matrix G' of the defect scale to obtain a local defect random matrix D', and then adding the local defect random matrix D' to the trend matrix T to obtain a local defect matrix D;

[0010] S5, select a corrugation curve that meets the requirements from the raceway random corrugation matrix Z obtained in step S1 and a local defect curve that meets the requirements from the local defect matrix D obtained in step S4 by a slicing method, and superimpose and smooth the selected corrugation curve and local defect curve to form a unified matrix of the bearing raceway that meets the requirements, that is, the corrugation-local defect multi-scale simulation curve.

[0011] Furthermore, in step S1, the bearing raceway waviness matrix Z can be expressed as:

[0012]

[0013] Where R represents a random data matrix with a normal distribution and a mean of 0 and a standard deviation of σ generated by the Gaussian distribution function G(x,y), and a size of N×N. G represents a Gaussian filter matrix generated based on the Gaussian filter function G'(x,y) and capable of reflecting the characteristics of the corrugation.

[0014]

[0015] Where cl represents the relevant length of the waviness along the x and y directions, N w is the assumed bearing waviness order to be simulated, L p is the raceway diameter of the raceway, λ i is the wave distance of each order of corrugation, is the average wave distance of the waviness, and s represents the correlation length control coefficient.

[0016] Furthermore, regression analysis shows that when s=0.55, the simulation effect is optimal.

[0017] Further, in step S3,

[0018] Define the ideal local defect length L, width B and the starting position of spalling (x 0 ,y 0 );

[0019] According to the characteristics of the local defect to be simulated, a trend function is selected from commonly used trend functions as a local defect trend simulation function;

[0020] The trend matrix T is obtained by combining multiple selected local defect trend simulation functions to achieve accurate description of the actual complex morphology.

[0021] Furthermore, in step S4, the defect random matrix R' in the defect interval is convolved with the Gaussian filter matrix G' of the defect scale according to formula (11), and the local defect random matrix D' is added with the trend matrix T according to formula (12):

[0022]

[0023] D=D′+T ​​(12)

[0024] Furthermore, the selected waviness curve and the local defect curve are superimposed according to formula (13), and the superimposed curve is smoothed according to formula (14).

[0025] x=[Z(1:x 0 ,m),D(:,q),Z(x 0 :N,m)] (13)

[0026] x=smooth(x) (14)

[0027] Due to the adoption of the above technical solution, the present invention has the following beneficial effects:

[0028] The bearing raceway waviness-local defect multi-scale characterization method of the present invention generates a raceway random waviness matrix Z by defining a Gaussian filter of the waviness scale, and obtains a defect random matrix R' and a Gaussian filter matrix G of the defect scale within the defect interval; obtains a trend matrix T by selecting a suitable trend function; convolves the defect random matrix R' with the Gaussian filter matrix G' of the defect scale to obtain a local defect random matrix D', and then adds the local defect random matrix D' to the trend matrix T to obtain a local defect matrix D; selects a waviness curve that meets the requirements from the raceway random waviness matrix Z and a local defect curve that meets the requirements from the local defect matrix D by a slicing method, superimposes and smoothes the selected waviness curve and the local defect curve to form a bearing raceway surface waviness-local defect multi-scale simulation curve that meets the requirements, thereby improving the characterization capability of the rolling bearing, overcoming the problem of insufficient characterization capability when the waviness scale and the local defect morphology scale are similar and coexist on the bearing raceway, and realizing accurate characterization of local defects of the rolling bearing. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a flow chart of a multi-scale characterization method of bearing raceway waviness-local defects according to a preferred embodiment of the present invention;

[0030] Figure 2A schematic diagram of a local defect area of ​​a rolling bearing;

[0031] Figure 3 It is a schematic diagram of the local defect trend simulation function, where Figure 3 (a) is the oblique line function, Figure 3 (b) is a half-sine function, Figure 3 (c) is a rectangular function, Figure 3 (d) is a triangular function, Figure 3 (e) is a trapezoidal function, Figure 3 (f) is a sine function;

[0032] Figure 4 is a schematic diagram of local defects, where Figure 4 (a) is a schematic diagram of the structure of local defect 1. Figure 4 (b) is a schematic diagram of the structure of local defect 2;

[0033] Figure 5 This is a schematic diagram of the corrugation simulation results based on the Gaussian filter, where: Figure 5 (a) is a schematic diagram of a random matrix. Figure 5 (b) is a schematic diagram of the raceway random waviness matrix Z;

[0034] Figure 6 is the multi-scale simulation result of bearing raceway waviness-local defect, where: Figure 6 (a) is the local defect matrix, Figure 6 (b) is the unified matrix of the raceway;

[0035] Figure 7 To select two morphological curves, Figure 7 (a) is the waviness curve that meets the requirements selected from the raceway random waviness matrix Z obtained by the slicing method. Figure 7 (b) is to select the local defect curve that meets the requirements from the local defect matrix D;

[0036] Figure 8 This is a schematic diagram of actual local defects in rolling bearings;

[0037] Fig. 9 This is a test image of the rolling bearing peeling morphology, where Fig. 9 (a) is the peeling morphology near the bearing area. Fig. 9 (b) is the peeling morphology near the center of the bearing area;

[0038] Fig.10 For Fig. 9 The rolling bearing peeling morphology slice curve extracted from Fig.10 (a) is the peeling morphology slice curve near the bearing area. Fig.10(b) is the peeling morphology slice curve near the center of the bearing area;

[0039] Fig.11 The bearing raceway waviness-local defect multi-scale characterization method of the present invention is used to characterize the bearing raceway waviness-local defect multi-scale characterization method. Figure 8 The simulation results obtained by simulating at A in the figure are as follows: Fig.11 (a) is the simulated morphology near the loading area. Fig.11 (b) is the slice curve of the peeling morphology near the bearing area;

[0040] Fig.12 for Fig.11 The bearing raceway waviness-local defect multi-scale characterization method of the present invention is used to characterize the bearing raceway waviness-local defect multi-scale characterization method. Figure 8 The simulation results obtained by simulating at point B in the figure are as follows: Fig.12 (a) is the simulated defect morphology at the center of the load-bearing area. Fig.12 (b) is the slice curve of the peeling morphology near the center of the bearing area;

[0041] Fig.13 is the correlation coefficient between the simulation curve selected by the slicing method and the measured morphology curve, where Fig.13 (a) Figure 8 The correlation coefficient between the simulated curve selected by the slicing method at A and the measured morphology curve, where Fig.13 (b) Figure 8 Correlation coefficient between the simulation curve selected by the slicing method at point B and the measured morphology curve. DETAILED DESCRIPTION

[0042] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0043] It should be noted that when a component is referred to as being "fixed to" another component, it may be directly on the other component or there may also be a component centered. When a component is considered to be "connected to" another component, it may be directly connected to the other component or there may also be a component centered. When a component is considered to be "set on" another component, it may be directly set on the other component or there may also be a component centered. The terms "vertical", "horizontal", "left", "right" and similar expressions used herein are for illustrative purposes only.

[0044] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used herein in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The term "and / or" used herein includes any and all combinations of one or more related listed items.

[0045] In view of the problem that the surface of the local defect of the bearing raceway is uneven, and its early morphological scale is similar to the scale of the waviness, which makes it difficult to identify the vibration characteristics induced by defect excitation, a preferred embodiment of the present invention provides a multi-scale characterization method of bearing raceway waviness-local defect, including the following steps:

[0046] S1, generate a random matrix R through a Gaussian distribution function, and obtain a Gaussian filter function based on the Gaussian distribution function, select parameters of the Gaussian filter function according to the parameters of the corrugation to be simulated to define the Gaussian filter, thereby generating a Gaussian filter matrix G, and generate a bearing raceway random corrugation matrix Z through the convolution calculation of the random matrix R and the Gaussian filter matrix G.

[0047] In step S1, the bearing raceway waviness matrix Z can be expressed as:

[0048]

[0049] Where R represents a random data matrix with a normal distribution and a mean of 0 and a standard deviation of σ generated by the Gaussian distribution function G(x,y), and a size of N×N. G represents a Gaussian filter matrix generated based on the Gaussian filter function G'(x,y) and capable of reflecting the characteristics of the corrugation.

[0050]

[0051] Where cl represents the relevant length of the waviness along the x and y directions, N w is the assumed bearing waviness order to be simulated, L p is the raceway diameter of the raceway, λ i is the wave distance of each order of corrugation, is the average wave distance of the waviness, and s is the correlation length control coefficient. Regression verification shows that when s = 0.55, the simulation effect is the best.

[0052] Step S1 belongs to the prior art. For example, reference may be made to the description of a bearing waviness targeted characterization method based on a Gaussian filter disclosed in Chinese invention patent application CN116842655A. To save space, it will not be described here.

[0053] S2, define a preset size area from the random matrix R as the local defect interval, use the Gaussian distribution function to regenerate a random matrix for the local defect area as the defect random matrix R', define the depth of the local defect and define a Gaussian filter according to the defect scale to obtain a Gaussian filter G' of the defect scale. In this step, by setting the filter parameters, that is, N shown in formula (3, 4) w By changing the size of the order, the scale of the local defect morphology can be changed.

[0054] S3, selecting a local defect trend simulation function according to the characteristics of the local defect to be simulated, and obtaining a trend matrix T.

[0055] In step S3, the ideal local defect length L, width B and the starting position of the peeling are defined in the waviness simulation interval length (x 0 ,y 0 ),like Figure 2 As shown. According to the characteristics of the local defect to be simulated, a local defect trend simulation function is selected, that is, a trend function is selected from the commonly used trend functions as the local defect trend simulation function. Commonly used trend functions include oblique line function, half sine function, rectangular function, triangle function, trapezoidal function and sine function, such as Figure 3 shown.

[0056] The mathematical expression of the oblique line local defect function is formula (5):

[0057]

[0058] In formula (5), L is the length of the local defect, and A is the maximum amplitude of the local defect.

[0059] The mathematical expression of the semi-sinusoidal local defect function is formula (6):

[0060]

[0061] In formula (6), A is the maximum amplitude of the local defect, and L is the length of the local defect.

[0062] The mathematical expression of the rectangular local defect function is formula (7):

[0063]

[0064] In formula (7), A is the maximum amplitude of the local defect, and L is the length of the local defect.

[0065] The mathematical expression of the triangular local defect is formula (8):

[0066]

[0067] In formula (8), L 1, L 2 is the length of each part of the local defect, A is the maximum amplitude of the local defect, and L is the length of the local defect.

[0068] The mathematical expression of the trapezoidal local defect is formula (9):

[0069]

[0070] In formula (9), L 1 , L 2 , L 3 is the length of each part of the local defect, A is the maximum amplitude of the local defect, and L is the length of the local defect.

[0071] The mathematical expression of sinusoidal local defects is formula (10):

[0072]

[0073] In formula (10), A is the maximum amplitude of the local defect, and L is the length of the local defect.

[0074] A method of selecting a trend function from commonly used trend functions as a local defect trend simulation function. For example, when simulating a local defect length L< rolling element diameter d and L< defect depth Dd, Figure 4 (a) shows the local defect 1. In this case, a small rectangular function can be used. When the local defect length L to be simulated is greater than the rolling element diameter d and L>Dd, as shown in Figure 4 For the local defect 2 shown in (b), a trapezoidal function or a sinusoidal function can be used.

[0075] The trend matrix T is obtained by combining multiple selected local defect trend simulation functions to achieve accurate description of the actual complex morphology.

[0076] S4, convolve the defect random matrix R' with the Gaussian filter matrix G' of the defect scale to obtain the local defect random matrix D', and then add the local defect random matrix D' to the trend matrix T to obtain the local defect matrix D.

[0077] In this embodiment, the entire raceway morphology is divided into multiple segments of corrugation-local defects-corrugation. The local defect part is represented by a combination of trend function and random morphology, that is, the trend matrix T and the local defect random matrix D' are added together, and the corrugation part is characterized by the method in step S1. There is only one local defect considered here, not a combination of multiple local defects. The combination mentioned in the patent specifically refers to the addition of the trend matrix T and the local defect random matrix D'. Specifically, in step S4, the defect random matrix R' in the defect interval is convolved with the Gaussian filter matrix G' of the defect scale according to formula (11) to obtain the local defect random matrix D', and the local defect random matrix D' is added to the trend matrix T according to formula (12) to obtain the local defect matrix D:

[0078]

[0079] D=D′+T ​​(12)

[0080] S5, selecting a corrugation curve that meets the requirements from the raceway random corrugation matrix Z obtained in step S1 and a local defect curve that meets the requirements from the local defect matrix D obtained in step S4 by a slicing method, superimposing and smoothing the selected corrugation curve and local defect curve to form a bearing raceway surface corrugation-local defect multi-scale simulation curve that meets the requirements.

[0081] In this embodiment, the selected waviness curve and the local defect curve are superimposed according to formula (13), and the superimposed curve is smoothed according to formula (14). Selecting a curve that meets the requirements from a matrix by a slicing method belongs to the prior art. For example, a method for targeted characterization of bearing waviness based on a Gaussian filter disclosed in Chinese invention patent application CN116842655A can be referred to. For the sake of space, it will not be repeated here.

[0082] x=[Z(1:x 0 ,m),D(:,q),Z(x 0 :N,m)](13)

[0083] x=smooth(x)(14)

[0084] Wherein, m refers to the mth slice in the waviness matrix, q refers to the qth slice in the local defect matrix, and N is the size parameter of the random data matrix, that is, the size of the aforementioned random data matrix is ​​N×N. x is the bearing raceway morphology curve selected by the slicing method, which mainly includes three parts, namely, two waviness curves and one local defect morphology curve. The waviness curve is formed in step S1, and then on this basis, the local defect position is specified, and the local defect morphology curve is generated through steps S2 and S3, which is equivalent to the waviness curve being divided into two parts.

[0085] In summary, by setting the simulated corrugation order N w , the Gaussian filter lateral correlation length coefficient s and standard deviation σ three parameters, can generate the bearing raceway waviness matrix Z; by selecting a suitable trend function and superimposing the waviness curve and defect curve to obtain the waviness-local defect morphology curve that meets the requirements, the characterization capability of the rolling bearing is improved.

[0086] The bearing raceway waviness-local defect multi-scale characterization method of the present invention is described below with a specific embodiment.

[0087] Take deep groove ball bearing 6206 (outer ring raceway diameter is 56.45mm) as an example, N w Set to 9, the standard deviation of the corrugation σ is set to 0.05μm (the corrugation amplitude is 0.2μm), and the random corrugation matrix Z and random matrix R of the raceway are generated according to step S1. Figure 5 shown.

[0088] The area with a length and width of 50 in the random matrix R is selected as the local defect area. In order to describe the morphological characteristics of the local defect area, the Gaussian distribution function is used to regenerate the random matrix as the defect random matrix R'. The depth of the local defect and the Gaussian filter G' defined according to the defect scale are defined. The local defect random matrix D' is obtained by formula (11). The local defect random matrix D' is added to the trend matrix T according to formula (12) to obtain the local defect matrix D.

[0089] Calculate the waviness and local defect related indicators respectively, select the waviness curve that meets the requirements from the raceway random waviness matrix Z obtained in step S1 and select the local defect curve that meets the requirements from the local defect matrix D obtained in step S4 by slicing method, and superimpose and smooth the selected waviness curve and local defect curve according to equations (13)-(14) to obtain the multi-scale simulation curve of bearing raceway surface waviness-local defect that meets the requirements. Figure 7 In order to select two morphology curves, the wavy line segment in the figure is the measured morphology curve with only waviness, while the blue solid line is the measured morphology curve with both waviness and local defects.

[0090] The microscopic morphology of the local defects on the outer ring of the bearing is measured by ultra-depth-of-field microscopy, and the morphology slices are extracted to obtain the local defect curve. The local defects on the outer ring of the deep groove ball bearing 6307 that appear during operation are scanned. The local defects are mainly concentrated near the position entering the load-bearing area and the load-bearing center, such as Figure 8 Among them, the peeling defect in the center of the load-bearing area is relatively large, about 6 mm long along the circumference of the raceway, and there are some smaller intermittent peelings near the load-bearing area, with a minimum length of 300 μm and a maximum length of about 2 mm.

[0091] Select Figure 8 The super-depth-of-field microscope is used to measure the local defects at A and B. A is a small peeling pit just entering the load-bearing area, and B is the edge of a large peeling pit near the center of the load-bearing area. The super-depth-of-field microscope is set to 300 times, and the morphological results of A and B are as follows: Fig. 9 (a) and Fig. 9 (b) Fig. 9 Medium red indicates a larger height value, the darker the red, the greater the height, and blue indicates a smaller depth, the darker the blue, the smaller the height value. Fig. 9 (a) and Fig. 9 (b) is sliced ​​and the morphological curve in the slice is extracted. Fig. 9 The arrow in the middle indicates the direction of the extracted topography curve. Fig.10 shown. Fig.10 The small peeling slice curve near the position just entering the load-bearing area in (a) first decreases and then increases, and the actual peeling shows a certain randomness and is not an ideal rectangle. Fig.10 (b) The morphology of the large peeling edge near the center of the bearing zone is generally a descending curve, and the morphology fluctuates randomly during the descending process.

[0092] according to Figure 8 The morphological characteristics of the peeling at A in the middle are simulated by the bearing raceway waviness-local defect multi-scale characterization method of the present invention, and the simulated local defect curve is obtained and compared with the measured peeling section curve. The size of the random matrix R is set to 256×256, the simulation standard deviation σ is set to 2μm, and the defect depth D d The standard deviation σ of the 30μm corrugation is set to 0.05μm, assuming that the local defect trend is a trigonometric function, and the correlation length control coefficient s=0.5. The simulation results are as follows Fig.11 As shown. Figure 8 The morphology of the peeling at B in the figure. The size of the random matrix R is set to 256×256, the simulation standard deviation σ is set to 2μm, and the defect depth D d=250μm, correlation length control coefficient s=0.8, simulation results are as follows Fig.12 shown.

[0093] The Chinese invention patent application CN116842655A discloses a method for targeted characterization of bearing waviness based on a Gaussian filter, as described in formula (18): R = σ × randn (1, N) = σ × [a 1 a 2 a 3 …a N ], calculate the correlation coefficient between the simulated and measured local defect curves, and analyze the correlation between the simulated surface morphology and the real morphology. The calculation found that Fig.11 The correlation coefficient between the simulated and measured morphology curves is 0.9398. Fig.12 The correlation coefficient between the simulated and measured morphology curves is 0.9435, and the simulated morphology curve has a high correlation with the measured morphology curve. The correlation coefficients of all slices and measured morphology curves are as follows Fig.13 shown.

[0094] The correlation coefficient between the simulated waviness curve obtained by the characterization method of this embodiment and the measured waviness curve is calculated, and the correlation between the simulated waviness and the measured waviness is analyzed. The expression of the Pearson correlation coefficient r is:

[0095]

[0096] In the formula, X a and X b are the simulated morphology and the actual machined surface morphology, is the average value. The larger the value of r is, the higher the correlation between the simulated corrugation and the measured corrugation is.

[0097] By comparing the simulated and measured local defect curves, the waviness-local defect multi-scale characterization method proposed in this chapter can describe the bearing raceway morphology characteristics and realize the true characterization of the raceway morphology.

[0098] The above description is a detailed description of the preferred feasible embodiments of the present invention, but the embodiments are not intended to limit the scope of the patent application of the present invention. All equivalent changes or modified changes completed under the technical spirit suggested by the present invention should fall within the patent scope covered by the present invention.

Claims

1. A multi-scale characterization method for bearing raceway waviness-local defects, It is characterized in that The following steps are involved: S1, generating a random matrix R through a Gaussian distribution function, and obtaining a Gaussian filter function according to the Gaussian distribution function, selecting parameters of the Gaussian filter function according to the parameters of the waviness to be simulated to define a Gaussian filter, thereby generating a Gaussian filter matrix G, and generating a bearing raceway random waviness matrix Z through convolution calculation of the random matrix R and the Gaussian filter matrix G; S2, defining a preset size area from the random matrix R as a local defect interval, regenerating a random matrix for the local defect area using a Gaussian distribution function as a defect random matrix R', defining the depth of the local defect and defining a Gaussian filter according to the defect scale to obtain a Gaussian filter G' of the defect scale; S3, selecting a local defect trend simulation function according to the characteristics of the local defect to be simulated, and obtaining a trend matrix T; S4, convolving the defect random matrix R' with the Gaussian filter matrix G' of the defect scale to obtain a local defect random matrix D', and then adding the local defect random matrix D' to the trend matrix T to obtain a local defect matrix D; S5, select a corrugation curve that meets the requirements from the raceway random corrugation matrix Z obtained in step S1 and a local defect curve that meets the requirements from the local defect matrix D obtained in step S4 by a slicing method, and superimpose and smooth the selected corrugation curve and local defect curve to form a unified matrix of the bearing raceway that meets the requirements, that is, the corrugation-local defect multi-scale simulation curve.

2. The bearing raceway waviness-local defect multi-scale characterization method according to claim 1, It is characterized in that In step S1, the bearing raceway waviness matrix Z can be expressed as: Where R represents a random data matrix with a normal distribution and a mean of 0 and a standard deviation of σ generated by the Gaussian distribution function G(x,y), and a size of N×N. G represents a Gaussian filter matrix generated based on the Gaussian filter function G'(x,y) and capable of reflecting the characteristics of the corrugation. Where cl represents the relevant length of the waviness along the x and y directions, N w is the assumed bearing waviness order to be simulated, L p is the raceway diameter of the raceway, λ i is the wave distance of each order of corrugation, is the average wave distance of the waviness, and s represents the correlation length control coefficient.

3. The bearing raceway waviness-local defect multi-scale characterization method according to claim 2, It is characterized in that Regression verification shows that when s=0.55, the simulation effect is best.

4. The bearing raceway waviness-local defect multi-scale characterization method according to claim 1, It is characterized in that In step S3, Define the ideal local defect length L, width B and the starting position of spalling (x 0 ,y 0 ); According to the characteristics of the local defect to be simulated, a trend function is selected from commonly used trend functions as a local defect trend simulation function; The trend matrix T is obtained by combining multiple selected local defect trend simulation functions to achieve accurate description of the actual complex morphology.

5. The bearing raceway waviness-local defect multi-scale characterization method according to claim 1, It is characterized in that In step S4, the defect random matrix R' in the defect interval is convolved with the Gaussian filter matrix G' of the defect scale according to formula (11), and the local defect random matrix D' is added with the trend matrix T according to formula (12): D=D′+T ​​(12).

6. The bearing raceway waviness-local defect multi-scale characterization method according to claim 1, It is characterized in that The selected waviness curve and local defect curve are superimposed according to formula (13), and the superimposed curve is smoothed according to formula (14): x=[Z(1:x 0 ,m),D(:,q),Z(x 0 :N,m)] (13) x=smooth(x) (14) Where m refers to the mth slice in the random waviness matrix of the bearing raceway, q refers to the qth slice in the local defect matrix, N is the size parameter of the random data matrix; x is the bearing raceway topography curve selected by the slicing method.

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