Method and device for obtaining surface stiffness parameters of a scribed surface based on digital simulation

Abstract

The application discloses a kind of based on digital simulation scraping surface rigidity parameter acquisition method, comprising: respectively calculating the power spectral density of x direction and y direction scraping surface topography data, to obtain mean power spectral density;According to mean power spectral density, obtain bifractal characteristic parameter;Bifractal characteristic parameter is input into topography simulation formula, and simulation bifractal surface is obtained;Setting section height is truncated to simulation bifractal surface, forms truncated region and truncated part;The area of each truncated region and corresponding truncated part volume are calculated;Truncated part is regarded as microconvex, and the deformation of each microconvex is determined;According to the deformation of microconvex and deformation critical value, the deformation stage of each microconvex is determined;According to the deformation stage where each microconvex is located, the rigidity of each microconvex is calculated, and then the total rigidity is summed up.The application proposes the scraping surface rigidity digital simulation calculation method without using distribution law, realizes the more accurate, more efficient digital simulation prediction of the rigidity of scraping this kind of multi-process machining surface.

Description

Technical Field

[0001] This invention relates to a method and apparatus for obtaining stiffness parameters of scraped surfaces based on digital simulation, belonging to the field of digital simulation of stiffness of scraped surfaces and multi-process surfaces. Background Technology

[0002] The structure of machining equipment is typically composed of numerous interconnected parts via mating surfaces, among which the guide rail mating surfaces have a crucial impact on the overall machine performance. The presence of these mechanical mating surfaces results in structural discontinuities, directly affecting the dynamic characteristics of the entire machine. Stiffness, as an important dynamic parameter of the mating surfaces, requires effective methods to verify whether the machined surfaces meet design requirements.

[0003] Traditionally, compression tests are used to measure surface stiffness, but this method can damage the surface morphology. Therefore, simulation calculations to predict stiffness have gradually become an important supplementary method. Surfaces obtained from actual machining are not ideally smooth planes, but complex rough structures composed of multi-scale morphological features. Such surfaces can usually be characterized by a series of micro-protrusions. Most existing simulation methods are based on the study of the contact behavior of individual micro-protrusions, and then extend the results to the entire contact area using distribution laws to calculate the total surface stiffness. For example, the stiffness of fractal surfaces is calculated using Mandelbrot's area distribution law. However, such methods assume that the surface has fractal characteristics and are suitable for general rough surfaces, but they are difficult to handle mating surfaces that have undergone multiple processes such as scraping. Scraping, as a traditional precision surface machining process, is widely used in the machining of guide rail mating surfaces to improve surface fit quality and mechanical properties. The surfaces formed by scraping have unique morphological characteristics, exhibiting a bifractal structure, that is, regions containing two different fractal characteristics simultaneously. Therefore, the traditional stiffness calculation method based on Mandelbrot's area distribution law cannot be directly applied.

[0004] Therefore, there is an urgent need for a novel digital simulation method that does not rely on the distribution law for simulating the stiffness of scraped surfaces. To this end, this invention proposes a digital simulation method for the stiffness of scraped surfaces that does not depend on the distribution law. Summary of the Invention

[0005] This invention provides a method and apparatus for obtaining the stiffness parameters of scraped surfaces based on digital simulation, which can be used for digital simulation prediction of the stiffness of scraped surfaces, a special type of machining.

[0006] The technical solution of this invention is:

[0007] According to a first aspect of the present invention, a method for obtaining the stiffness parameters of a scraped surface based on digital simulation is provided, comprising:

[0008] Step 1: Measure the one-dimensional profile of the scraped surface in the x and y directions to obtain the surface morphology data in the x and y directions.

[0009] Step 2: Calculate the power spectral density of the scraped surface morphology data in the x and y directions respectively to obtain the mean power spectral density.

[0010] Step 3: Obtain bifractal characteristic parameters based on the mean power spectral density; wherein, the bifractal characteristic parameters include the first fractal dimension, the second fractal dimension, the first fractal coefficient, the second fractal coefficient, the maximum frequency index, and the critical frequency index.

[0011] Step 4: Input the bifractal feature parameters into the topography simulation formula to obtain the simulated bifractal surface.

[0012] Step 5: Set the cross-section height to truncate the simulated bifractal surface, forming truncated regions and truncated parts; calculate the area of ​​each truncated region and the volume of the corresponding truncated part; treat the truncated part as a micro-protrusion and determine the deformation of each micro-protrusion.

[0013] Step 6: Determine the deformation stage of each micro-protrusion based on its deformation amount and critical deformation value; calculate the stiffness of each micro-protrusion based on its deformation stage, and then sum them to obtain the total stiffness.

[0014] Further, step 2 specifically includes:

[0015] Step 2.1: Adjust the mean line of the scraped surface morphology data in the x and y directions to zero to obtain the scraped surface morphology data in the x and y directions after the mean line is zeroed.

[0016] Step 2.2: Calculate the power spectral density based on the surface morphology data in the x and y directions after the mean line is zeroed.

[0017] Step 2.3: Perform a double logarithmic transformation on the power spectral density in the x and y directions, and take the mean of the double logarithmic power spectral density in the x and y directions as the mean power spectral density.

[0018] Furthermore, step 3 specifically includes:

[0019] Step 3.1: Construct a fitting equation based on the Sigmoid function; use the mean power spectral density as the input to the fitting equation to obtain the parameters to be determined.

[0020] Step 3.2: Based on the parameters to be determined, calculate the first fractal dimension, the second fractal dimension, the maximum frequency index, and the critical frequency index.

[0021] Step 3.3: Calculate the first fractal coefficient and the second fractal coefficient based on the undetermined parameters and fractal dimension.

[0022] Furthermore, the morphological simulation formula is as follows:

[0023] ;

[0024] Where Z(x,y) represents the simulated bifractal surface; L is a constant; L represents the length of the bifractal surface; M is the number of superimposed cosine waves; , These are the first and second fractal coefficients, respectively. , The first and second fractal dimensions; n is the critical frequency exponent; n is the frequency exponent. It is a random distribution in the interval [0, 2π]. The x-coordinate of the data point on the bifractal surface; The ordinate of the data point on the bifractal surface; This is the maximum frequency index.

[0025] Further, step 5 specifically includes:

[0026] Step 5.1: Set the cross-section height to truncate the simulated bifractal surface, forming the truncated region and the truncated part, and use the octet method to identify each truncated region on the cross-section.

[0027] Step 5.2: Calculate the area of ​​each cut-off region and the volume of each cut-off part.

[0028] Step 5.3: Treat the cut-off portion as a micro-protrusion, determine the base length of each micro-protrusion based on the area of ​​the cut-off region and the corresponding volume of the cut-off portion; determine the deformation amount of each micro-protrusion based on the base length of each micro-protrusion.

[0029] Furthermore, the formula for calculating the deformation ω is:

[0030] ω = G D − 2 l 3 − D [ 1 − cos ( π r l ) ] ;

[0031] in, , The area of ​​the cut-off region; if ,but = , = ;like ,but = , = ; and The first and second fractal dimensions are, and These are the first and second fractal coefficients; This is the critical frequency index. It is a constant; is the length of the micro-convex substrate.

[0032] Furthermore, step 6 specifically includes:

[0033] Step 6.1: Based on the deformation amount and the critical value of the deformation amount of the micro-protrusion, determine the deformation stage of each micro-protrusion as the elastic deformation stage, the first elastic-plastic deformation stage, the second elastic-plastic deformation stage, or the fully plastic deformation stage.

[0034] Step 6.2: Calculate the contact area, contact load, and contact stiffness of each micro-protrusion based on its deformation stage.

[0035] Step 6.3: Sum the contact area, contact load, and contact stiffness of all micro-protrusions to obtain the total contact area, total contact load, and total contact stiffness of the micro-protrusions.

[0036] Furthermore, the determination of the deformation order of each micro-protrusion based on its deformation amount and critical deformation value specifically involves: when the deformation amount... ≤ At that time, the micro-protrusion is in the elastic deformation stage; when < ≤6 At that time, the micro-protrusion is in the first stage of elastic-plastic deformation; when 6 < ≤110 At that time, the micro-protrusion is in the second stage of elastic-plastic deformation; when 110 < The micro-protrusions are in the stage of complete plastic deformation; among them, This is the critical value for deformation.

[0037] According to a second aspect of the present invention, a device for obtaining the stiffness parameters of scraped surfaces based on digital simulation is provided, comprising modules of any of the methods described above.

[0038] According to a third aspect of the present invention, a terminal is provided, comprising a processor, a memory, and a computer program stored in the memory and executable on the processor, the processor being configured to perform the steps of the method described in any one of the foregoing descriptions.

[0039] The beneficial effects of this invention are: This invention proposes a digital simulation calculation method for the stiffness of scraped surfaces without the need to utilize the distribution law; this method overcomes the shortcomings of traditional stiffness simulation calculation methods that cannot be applied to the simulation calculation of surface stiffness in multi-process machining such as scraping, and realizes more accurate and efficient digital simulation prediction of the stiffness of multi-process machining surfaces such as scraping. Attached Figure Description

[0040] Figure 1 This is a flowchart of the method of the present invention.

[0041] Figure 2 The morphology of the scraped surface is measured.

[0042] Figure 3 The result is the fitting result of the power spectral density curve of the scraped surface profile.

[0043] Figure 4 It is a bifractal simulation surface.

[0044] Figure 5 This is a schematic diagram of the cross-sectional cut surface.

[0045] Figure 6 This is a schematic diagram of the 8-connected-domain method.

[0046] Figure 7 This is a schematic diagram for calculating the length of the micro-convex substrate.

[0047] Figure 8 This is a comparison chart of simulation calculation results and experimental results in the embodiments of the present invention. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be arbitrarily combined with each other.

[0049] Example 1: As Figures 1-8 As shown, according to a first aspect of the present invention, a method for obtaining the stiffness parameters of a scraped surface based on digital simulation is provided, comprising:

[0050] Step 1: Measure the one-dimensional profile of the scraped surface in the x and y directions to obtain the surface morphology data in the x and y directions. and .

[0051] Step 2: Calculate the power spectral density of the scraped surface morphology data in the x and y directions respectively to obtain the mean power spectral density.

[0052] Step 3: Obtain bifractal characteristic parameters based on the mean power spectral density; among which, the bifractal characteristic parameters include fractal dimension, fractal coefficient, maximum frequency index, and critical frequency index.

[0053] Step 4: Input the bifractal feature parameters into the topography simulation formula to obtain the simulated bifractal surface.

[0054] Step 5: Set the cross-section height to truncate the simulated bifractal surface, forming truncated regions and truncated parts; calculate the area of ​​each truncated region and the volume of each truncated part; treat the truncated part as a micro-protrusion and determine the deformation of each micro-protrusion.

[0055] Step 6: Determine the deformation stage of each micro-protrusion based on its deformation amount and critical deformation value; calculate the stiffness of each micro-protrusion based on its deformation stage, and then sum them to obtain the total stiffness.

[0056] Furthermore, it also includes:

[0057] Step 7: Change the section height and repeat steps 5 and 6 to calculate the load-stiffness curve.

[0058] Step 8: Repeat steps 4, 5, 6 and 7, and take the average value of all load-stiffness curves for the same section height as the final result.

[0059] Further, step 2 specifically includes:

[0060] Step 2.1: Scrape the surface morphology data in the x and y directions. and The mean line was adjusted to zero, and the surface morphology data of the scraped surface in the x and y directions after the mean line was zeroed were obtained. and .

[0061] Step 2.2: Based on the surface morphology data in the x and y directions after zeroing the mean line, calculate the power spectral density respectively. The calculation formula is:

[0062]

[0063] in, For Fourier transform, This represents the surface morphology data of the scraped surface in the x or y direction after the mean line has been zeroed. To measure the number of measurement points in the x or y direction of the scraped surface (when calculating the power spectral density based on the x-direction scraped surface morphology data after zeroing the mean line, then...) To measure the number of measurement points in the x-direction of the scraped surface; when calculating the power spectral density based on the y-direction scraped surface morphology data after zeroing the mean line, then... (To measure the number of measurement points in the y-direction of the scraped surface) Sampling frequency, This refers to the spatial frequency.

[0064] Step 2.3: Perform a double logarithmic transformation on the power spectral density in the x and y directions, and take the mean of the double logarithmic power spectral density in the x and y directions as the mean power spectral density. .

[0065] Furthermore, step 3 specifically includes:

[0066] Step 3.1: Construct a fitting equation based on the Sigmoid function; use the mean power spectral density as the input to the fitting equation to obtain the parameters to be determined.

[0067] The fitting formula is:

[0068] y 1 = [ 1 − U ( x 1 ) ] ⋅ ( k 1 x 1 + b 1 ) + L ( x 1 ) ( k 2 x 1 + b 2 ) ;

[0069] in, , , , , , and These are parameters to be determined. , ; For spatial frequency, This represents the mean power spectral density.

[0070] Step 3.2: Calculate the first fractal dimension based on the parameters to be determined. Second fractal dimension Maximum frequency index and critical frequency index .

[0071] The and The expression is:

[0072] ;

[0073] ;

[0074] The and The expression is:

[0075] n max = int [ log( f max ) log( γ ) ] ;

[0076] n c = int [ c log( γ ) ] ;

[0077] Where int represents integer division. It is the frequency of maximum mean power spectral density. The constant is taken as 1.5.

[0078] Step 3.3: Calculate the first fractal coefficient based on the undetermined parameters and fractal dimension. Second fractal coefficient The and The expression is:

[0079] ;

[0080] ;

[0081] in, Represents the natural constant.

[0082] Furthermore, the morphological simulation formula is as follows:

[0083] ;

[0084] Where Z(x,y) represents the simulated bifractal surface, that is, the height of the corresponding data point on the bifractal surface represents the simulated bifractal surface; L represents the length of the bifractal surface; This represents the spectrum of a bifractal surface; M is the number of superimposed cosine waves, typically M=10; n is the frequency index; It is a random distribution in the interval [0, 2π]. It is a constant; is the x-coordinate of the data point on the bifractal surface; y is the ordinate of the data point on the bifractal surface.

[0085] Further, step 5 specifically includes:

[0086] Step 5.1: Set the section height h t The simulated bifractal surface is truncated to form truncated regions and truncated portions, and each truncated region on the cross-section is identified using the 8-connected domain method; among them... , For the maximum surface height, This is the cutoff factor; reference Figure 5 The simulated bifractal surface is truncated at a set cross-sectional height, and multiple truncated regions are formed at the cross-sectional height of the simulated bifractal surface. The part that is detached from the simulated bifractal surface is the truncated part. One truncated region corresponds to one truncated part, that is, the number of truncated regions and truncated parts are equal.

[0087] Step 5.2: Calculate the area of ​​each cut-off region and the volume of each cut-off part.

[0088] The formula for calculating the area of ​​the cut-off region is:

[0089] ;

[0090] in, This represents the number of data points in the truncated region. The sampling interval is denoted as .

[0091] The formula for calculating the volume of the truncated portion is:

[0092] ;

[0093] in, The height of the data points on the truncated section from the cross-section.

[0094] Step 5.3: Treat the cut-off portion as a micro-protrusion, determine the base length of each micro-protrusion based on the area of ​​the cut-off region and the corresponding volume of the cut-off portion; determine the deformation amount of each micro-protrusion based on the base length of each micro-protrusion.

[0095] The length of the micro-convex body substrate is determined based on the area of ​​the cut-off region and the corresponding volume of the cut-off portion, expressed as follows:

[0096] v c = G D − 2 l 5 − D π [ 2 c o s ( π r l ) − 2 − ( π r l ) 2 c o s ( π r l ) + 2 π r l s i n ( π r l ) ]

[0097] Among them, the equivalent radius of the truncated region ,like ,but = , = ;like ,but = , = ; and The first and second fractal dimensions are, and These are the first and second fractal coefficients; This is the critical frequency index. Let 1.5 be a constant. Given the area of ​​the cut-off region and the corresponding volume of the cut-off portion, the length of the micro-convex substrate can be determined using the above formula. .

[0098] The formula for calculating the deformation ω is: ω = G D − 2 l 3 − D [ 1 − cos ( π r l ) ] .

[0099] Furthermore, step 6 specifically includes:

[0100] Step 6.1: Based on the deformation amount and the critical value of the deformation amount of the micro-protrusion, determine the deformation stage of each micro-protrusion as the elastic deformation stage, the first elastic-plastic deformation stage, the second elastic-plastic deformation stage, or the fully plastic deformation stage.

[0101] The deformation level of each micro-protrusion is determined based on its deformation amount and critical deformation value. Specifically, when the deformation amount... ≤ At that time, the micro-protrusion is in the elastic deformation stage; when < ≤6 At that time, the micro-protrusion is in the first stage of elastic-plastic deformation; when 6 < ≤110 At that time, the micro-protrusion is in the second stage of elastic-plastic deformation; when 110 < The micro-protrusions are in the stage of complete plastic deformation.

[0102] The critical value of deformation for:

[0103] ;

[0104] Critical value of contact area for:

[0105] ;

[0106] in, This is the hardness coefficient. , is Poisson's ratio; E is the equivalent elastic modulus; H is the material hardness.

[0107] Step 6.2, according to the... The deformation stage of the micro-convex body is calculated. Contact area of ​​each micro-protrusion Contact load Contact stiffness ;Specifically:

[0108] If the micro-protrusion is in the elastic deformation stage, then the contact area of ​​the micro-protrusion in the elastic deformation stage is... Contact load and contact stiffness The expression is:

[0109] ;

[0110] ;

[0111] ;

[0112] in, This represents the radius of curvature of the micro-convex body.

[0113] If the micro-protrusion is in the first elastic-plastic deformation stage, then the contact area of ​​the micro-protrusion in the first elastic-plastic deformation stage is... Contact load and contact stiffness The expression is:

[0114] ;

[0115] ;

[0116] ;

[0117] in, ;

[0118] If the micro-protrusion is in the second elastic-plastic deformation stage, then the contact area of ​​the micro-protrusion in the second elastic-plastic deformation stage is... Contact load and contact stiffness The expression is:

[0119] ;

[0120] ;

[0121] ;

[0122] If the micro-protrusion is in the fully plastic deformation stage, then the contact area of ​​the micro-protrusion in the fully plastic deformation stage is... Contact load and contact stiffness The expression is:

[0123] ;

[0124] ;

[0125] .

[0126] Based on the above, when the first The deformation stages of each micro-convex body are different, therefore the first... Contact area of ​​each Contact load Contact stiffness The calculation methods differ, and the contact area will be used as an example. If the micro-protrusion is in the elastic deformation stage, then... Pick If the micro-protrusion is in the first stage of elastic-plastic deformation, then Pick If the micro-protrusion is in the second stage of elastic-plastic deformation, then Pick If the micro-protrusion is in the fully plastic deformation stage, then Pick Contact load Contact stiffness Similarly.

[0127] Step 6.3: Sum the contact area, contact load, and contact stiffness of all micro-protrusions to obtain the total contact area, total contact load, and total contact stiffness of the micro-protrusions.

[0128] , ,

[0129] in, Indicates the total number of micro-protrusions; ; , , These represent the total contact area, total contact load, and total contact stiffness of the micro-protrusion, respectively.

[0130] As can be seen from the above, by repeatedly executing steps 5.2, 5.3, 6.1, and 6.2, we can analyze... We can obtain the total contact area, total contact load, and total contact stiffness of each micro-protrusion by summing them up.

[0131] Furthermore, in step 7, the cross-sectional height h is changed. t Repeat steps 5 and 6 to calculate the load-stiffness curve.

[0132] Further, in step 8, steps 4, 5, 6 and 7 are repeated, and the average value of all load-stiffness curves for the same cross-sectional height is taken as the final result.

[0133] Taking a real scraped surface as an example, according to Figure 1 The flowchart shown illustrates the principle of the present invention: digital simulation calculation method for the stiffness of scraped surfaces.

[0134] 1) A contact profilometer was used to measure the actual scraped surface, and one-dimensional height data in the x and y directions of the scraped surface were extracted as the scraped surface morphology data. and ,like Figure 2 As shown.

[0135] 2) Calculate the power spectral density of the scraped surface morphology data in the x and y directions respectively to obtain the mean power spectral density:

[0136] 2.1) Collect surface morphology data in the x and y directions. and The mean line was adjusted to zero to obtain the surface morphology data of the scraped surface in the x and y directions after the mean line was zeroed.

[0137] 2.2) Based on the surface morphology data in the x and y directions after zeroing the mean line, calculate the power spectral density respectively, such as... Figure 3 The PSD curve shown.

[0138] 2.3) Perform a double logarithmic transformation on the power spectral density in the x and y directions, and take the mean of the double logarithmic power spectral density in the x and y directions as the mean power spectral density.

[0139] 3) Obtain bifractal characteristic parameters based on the mean power spectral density; among which, the bifractal characteristic parameters include fractal dimension, fractal coefficient, maximum frequency index, and critical frequency index.

[0140] 3.1) Construct a fitting formula based on the Sigmoid function; use the fitting formula to fit the curve, and the fitting result is as follows: Figure 3 As shown, the first asymptote The second asymptote The fitting yielded =-1.24、 =-2.37、 =-26.6765、 =-17.5879、 =0.49 and =7.92.

[0141] 3.2) Calculate the first fractal dimension based on the undetermined parameters. Second fractal dimension Maximum frequency index and critical frequency index ,get =2.88、 =2.315、 =25 and =19.

[0142] 3.3) Calculate the first fractal coefficient based on the undetermined parameters and fractal dimension. Second fractal coefficient Specific values: =3× m、 =4× m.

[0143] 4) Input the bifractal feature parameters into the topography simulation formula to obtain the simulated bifractal surface. The results are as follows: Figure 4 As shown.

[0144] 5) Set the cross-sectional height to truncate the simulated bifractal surface, forming truncated regions and truncated portions; calculate the area of ​​each truncated region and the volume of each truncated portion; treat the truncated portion as a micro-protrusion and determine the deformation of each micro-protrusion:

[0145] 5.1) Set the cross-sectional height to simulate a bifractal surface, such as... Figure 5 As shown. , initial value The value is 1. Each truncated region is identified using the 8-connected component method. Figure 6 This is a schematic diagram of the method.

[0146] 5.2) Calculate the area of ​​each cut-off region and the volume of each cut-off part.

[0147] 5.3) Treating the truncated portion as a micro-protrusion, determine the base length of each micro-protrusion based on the area of ​​the truncated region and the corresponding volume of the truncated portion; determine the deformation amount of each micro-protrusion based on the base length of each micro-protrusion. Figure 7 This is a schematic diagram of the method.

[0148] 6) Based on the deformation amount and critical value of each micro-protrusion, determine the deformation stage of each micro-protrusion; calculate the stiffness of each micro-protrusion based on its deformation stage, and then sum them to obtain the total stiffness.

[0149] 6.1) Determine the deformation stage of each micro-protrusion.

[0150] 6.2) Calculate the contact area, contact load, and contact stiffness of each micro-protrusion based on its deformation stage.

[0151] 6.3) Summing up the contact area, contact load, and contact stiffness of all micro-protrusions respectively, we can obtain the total contact area, total contact load, and total contact stiffness of the micro-protrusions.

[0152] 7) Change the cutoff coefficient with a step size of 0.01 (in this embodiment) It takes values ​​in the range of 1 to 0.4, the first... The cutoff coefficient in the next cycle satisfy: , Step size, (Initial value is 1, total number of cycles is preset value), change the section height, repeat steps 5) and 6) to calculate the load-stiffness curve.

[0153] 8) Repeat steps 4), 5), 6), and 7), and take the average value of all load-stiffness curves as the final simulation result, such as... Figure 8 As shown. A compression experiment was conducted on a real surface, and the experimental results are as follows. Figure 8As shown, the load-stiffness curve results are in good agreement, verifying the rationality of the method provided by this invention.

[0154] According to a second aspect of the present invention, a device for acquiring the stiffness parameters of a scraped surface based on digital simulation is provided, comprising modules of any of the methods described above. Specifically, it includes: a first module for performing step 1: measuring the one-dimensional profile of the scraped surface in the x and y directions to obtain surface topography data in the x and y directions; a second module for performing step 2: calculating the power spectral density of the surface topography data in the x and y directions respectively to obtain the mean power spectral density; a third module for performing step 3: obtaining bifractal characteristic parameters based on the mean power spectral density; wherein the bifractal characteristic parameters include a first fractal dimension, a second fractal dimension, a first fractal coefficient, a second fractal coefficient, a maximum frequency exponent, and a critical frequency exponent; and a fourth module. The first module is used to execute step 4: inputting the bifractal feature parameters into the topography simulation formula to obtain the simulated bifractal surface; the second module is used to execute step 5: setting the cross-sectional height to truncate the simulated bifractal surface, forming truncated regions and truncated parts; calculating the area of ​​each truncated region and the volume of the corresponding truncated part; treating the truncated part as a micro-protrusion and determining the deformation amount of each micro-protrusion; the third module is used to execute step 6: determining the deformation stage of each micro-protrusion based on the deformation amount and the deformation threshold; calculating the stiffness of each micro-protrusion based on the deformation stage of each micro-protrusion, and then summing them to obtain the total stiffness. For parts of each module not described in detail, please refer to the relevant descriptions in other embodiments.

[0155] According to a third aspect of the present invention, a terminal is provided, including a processor, a memory, and a computer program stored in the memory and executable on the processor, the processor being configured to perform the steps of the method described in any one of the foregoing embodiments.

[0156] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for obtaining the stiffness parameters of scraped surfaces based on digital simulation, characterized in that, include: Step 1: Measure the one-dimensional profile of the scraped surface in the x and y directions to obtain the surface morphology data in the x and y directions; Step 2: Calculate the power spectral density of the scraped surface morphology data in the x and y directions respectively to obtain the mean power spectral density; Step 3: Obtain the bifractal characteristic parameters based on the mean power spectral density; wherein, the bifractal characteristic parameters include the first fractal dimension, the second fractal dimension, the first fractal scale constant, the second fractal scale constant, the maximum frequency exponent, and the critical frequency exponent; Step 4: Input the bifractal feature parameters into the topography simulation formula to obtain the simulated bifractal surface; Step 5: Set the cross-section height to truncate the simulated bifractal surface, forming the truncated region and the truncated part; calculate the area of ​​each truncated region and the volume of the corresponding truncated part; treat the truncated part as a micro-protrusion and determine the deformation of each micro-protrusion. Step 6: Determine the deformation stage of each micro-protrusion based on its deformation amount and critical deformation value; calculate the stiffness of each micro-protrusion based on its deformation stage, and then sum them to obtain the total stiffness. Step 3 specifically includes: Step 3.1: Construct a fitting equation based on the Sigmoid function; use the mean power spectral density as the input to the fitting equation to obtain the parameters to be determined. Step 3.2: Based on the parameters to be determined, calculate the first fractal dimension, the second fractal dimension, the maximum frequency index, and the critical frequency index; Step 3.3: Based on the undetermined parameters and fractal dimension, calculate the first fractal scale constant and the second fractal scale constant; ； ； in, The first fractal dimension, The second fractal dimension, , These are parameters to be determined. Step 5 specifically involves: Step 5.1: Set the cross-section height to truncate the simulated bifractal surface, forming the truncated region and the truncated part, and use the octet method to identify each truncated region on the cross-section; ; For the cross-sectional height, For the maximum surface height, The cutoff factor is denoted by a preset step size; the cutoff factor is changed by a preset step size, and the truncation factor is denoted by a preset step size. Cutoff coefficient in the next cycle satisfy: , Step size, for Initial value; Step 5.2: Calculate the area of ​​each cut-off region and the volume of each cut-off portion; Step 5.3: Treat the cut-off portion as a micro-protrusion, determine the base length of each micro-protrusion based on the area of ​​the cut-off region and the corresponding volume of the cut-off portion; determine the deformation amount of each micro-protrusion based on the base length of each micro-protrusion.

2. The method for obtaining the stiffness parameters of scraped surfaces based on digital simulation according to claim 1, characterized in that, Step 2 specifically includes: Step 2.1: Adjust the mean line of the scraped surface morphology data in the x and y directions to zero to obtain the scraped surface morphology data in the x and y directions after the mean line is zeroed. Step 2.2: Calculate the power spectral density based on the surface morphology data in the x and y directions after zeroing the mean line; Step 2.3: Perform a double logarithmic transformation on the power spectral density in the x and y directions, and take the mean of the double logarithmic power spectral density in the x and y directions as the mean power spectral density.

3. The method for obtaining the stiffness parameters of scraped surfaces based on digital simulation according to claim 1, characterized in that, The morphological simulation formula is as follows: ； in, This represents a simulated bifractal surface. It is a constant; Indicates the length of the bifractal surface; To determine the number of superimposed cosine waves; , These are the first and second fractal scale constants, respectively; , The first and second fractal dimensions; The critical frequency index; It is the frequency index; It is a random distribution in the interval [0, 2π]. The x-coordinate of the data point on the bifractal surface; The ordinate of the data point on the bifractal surface; is the maximum frequency index; m is the index of the superimposed cosine wave.

4. The method for obtaining the stiffness parameters of scraped surfaces based on digital simulation according to claim 1, characterized in that, The formula for calculating the deformation ω is: ； in, , The area of ​​the cut-off region; if ,but = , = ;like ,but = , = ; and The first and second fractal dimensions are, and These are the first and second fractal scale constants; This is the critical frequency index. It is a constant; is the length of the micro-convex substrate.

5. The method for obtaining the stiffness parameters of scraped surfaces based on digital simulation according to claim 1, characterized in that, Step 6 specifically includes: Step 6.1: Based on the deformation amount and the critical value of the deformation amount of the micro-protrusion, determine the deformation stage of each micro-protrusion as the elastic deformation stage, the first elastic-plastic deformation stage, the second elastic-plastic deformation stage, or the fully plastic deformation stage. Step 6.2: Calculate the contact area, contact load, and contact stiffness of each micro-protrusion based on its deformation stage. Step 6.3: Sum the contact area, contact load, and contact stiffness of all micro-protrusions to obtain the total contact area, total contact load, and total contact stiffness of the micro-protrusions.

6. The method for obtaining the stiffness parameters of scraped surfaces based on digital simulation according to claim 5, characterized in that, The deformation stage of each micro-protrusion is determined based on its deformation amount and critical deformation value. Specifically, when the deformation amount... ≤ At that time, the micro-protrusion is in the elastic deformation stage; when < ≤6 At that time, the micro-protrusion is in the first stage of elastic-plastic deformation; when 6 < ≤110 At that time, the micro-protrusion is in the second stage of elastic-plastic deformation; when 110 < The micro-protrusions are in the stage of complete plastic deformation; among them, This is the critical value for deformation.

7. A device for obtaining the stiffness parameters of scraped surfaces based on digital simulation, characterized in that, The module includes the method described in any one of claims 1-6.

8. A terminal, characterized in that: The method includes a processor, a memory, and a computer program stored in the memory and executable on the processor, the processor being configured to perform the method according to any one of claims 1-6.

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