A method for calculating contact stiffness of joint surfaces

Abstract

The present invention belongs to the field of machine tools and relates to an algorithm for calculating the normal contact stiffness of a joint surface. The contact stiffness of a joint surface in a machine tool is determined by the contact stiffness of all micro-convex peaks on the contact surface. First, a contact imprint image of the joint surface is obtained, the contact imprint image is loaded into MATLAB software, the image is grayscale processed, and the grayscale-processed contact imprint image is then reversely displayed. The data matrix of the reversely displayed contact imprint image is read using MATLAB software, and an equivalent contact area matrix that takes into account the contact ratio is calculated. The critical contact deformation and critical contact area of the micro-convex peaks on a rough surface are calculated using Hertz contact theory. Based on the contact deformation of the micro-convex peaks, the contact stiffness of the micro-convex peaks during elastic deformation, the contact stiffness during elastic-plastic deformation, and the contact stiffness during plastic deformation are calculated respectively. Based on the three contact stiffness calculation formulas and discrimination methods of the micro-convex peaks, three contact stiffness magnitudes of the equivalent contact area matrix that takes into account the contact ratio are calculated, and the three are summed to obtain the joint surface contact stiffness. This method provides an accurate, convenient, and programmable method for calculating the joint surface contact stiffness.

Description

Technical Field

[0001] The present invention belongs to the field of machine tools, and in particular relates to a method for calculating the contact stiffness of a joint surface. Background Art

[0002] Machine tools are composed of numerous components assembled through various connection methods. Consequently, they contain numerous joint surfaces, which primarily serve as connections and supports. Examples include the connection between the column and the machine bed, and the connection between the motor and the motor base. The static and dynamic characteristics of the entire machine tool are inextricably linked to the contact stiffness of these joint surfaces. Research indicates that 60% to 80% of a machine tool's total stiffness is contributed by the joint stiffness, and over 60% of machine tool vibration problems are related to the dynamic performance of the joint surfaces. Therefore, joint contact stiffness plays a decisive role in the overall stiffness and static and dynamic performance of a mechanical structure. Calculating joint contact stiffness using traditional fractal contact theory is difficult, cumbersome, and suffers from limited accuracy. A new joint contact stiffness calculation method is needed to accurately, conveniently, and programmatically calculate joint contact stiffness. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a method for calculating the contact stiffness of a joint surface in view of the above-mentioned deficiencies in the prior art, so as to achieve accurate, convenient and programmable calculation of the contact stiffness of the joint surface.

[0004] To solve the above technical problems, the technical solution adopted by the present invention is: a method for calculating the contact stiffness of a joint surface, the specific steps of which are as follows:

[0005] Step 1: Obtain a contact imprint image of the bonding surface;

[0006] A layer of red paint was evenly applied to the rough surface of the experimental specimen. The specimen was placed on high-strength tempered glass and a certain pressure load was applied to it. The red paint mark on the actual contact position of the specimen was obtained as a bonding surface contact mark on the tempered glass. A high-resolution contact mark image was taken using a Keyence VHX5000 ultra-depth-of-field microscope.

[0007] Step 2: Combine the grayscale processing of the surface contact mark image and perform reverse display;

[0008] The contact mark image obtained in step 1 is loaded into MATLAB software, and the image is gray-scaled using the software to obtain a contact mark image; the colors of the gray and white positions in the gray-scale processed contact mark image are swapped and displayed to obtain a reversely displayed contact mark image.

[0009] Step 3: Calculate the equivalent contact area matrix of the bonding surface considering the contact ratio;

[0010] Extract the grayscale value data matrix of the reverse display contact mark image in step 2; divide each element in the grayscale value data matrix by the maximum grayscale value in the matrix and then multiply it by the area corresponding to each element in the matrix to obtain an equivalent contact area matrix considering the contact ratio;

[0011] Step 4: Calculate the critical deformation δ of the micro-convex peak on the bonding surface c and critical contact area a c ;

[0012] The critical deformation δ of the micro-convex peak during elastic deformation and elastic-plastic deformation is calculated according to Hertz contact theory. c and critical contact area a c ;

[0013] Step 5: Calculate the contact stiffness of the micro-convex peak under three deformation conditions;

[0014] According to the critical deformation amount and contact area of the micro-convex peak of the bonding surface calculated in step 4, the three deformations of the micro-convex peak are judged, namely elastic deformation, elastoplastic deformation and plastic deformation; the calculation formulas of the contact stiffness of the micro-convex peak during elastic contact deformation, contact stiffness during elastoplastic deformation and contact stiffness during plastic deformation are derived;

[0015] Step 6: Calculate the overall contact stiffness of the joint surface;

[0016] The three deformation judgment criteria of the micro-convex peaks obtained in steps 4 and 5 are used to judge the deformation form of the micro-convex peaks represented by each element of the equivalent contact area matrix considering the contact ratio in step 3; and the three contact stiffness calculation formulas of the micro-convex peaks in step 5 are used to respectively calculate the contact stiffness of the micro-convex peaks represented by each element of the equivalent contact area matrix considering the contact ratio; the calculated contact stiffness of each micro-convex peak is summed to obtain the overall contact stiffness of the bonding surface.

[0017] As preferred embodiment of the present invention, the specific calculation method of step 2 is:

[0018] Assume that the top of each micro-convex peak on the rough surface of the bonding surface is spherical, and its equivalent curvature radius is R. The micro-convex peak contacts the plane under the action of the normal load and produces a normal contact deformation δ; load the contact imprint image obtained in step 1 into the MATLAB software, and use the software's image grayscale processing function to grayscale the contact imprint image to obtain a gray contact imprint image;

[0019] The grayscale processed contact print image is stored in the form of a pixel grayscale value data matrix in the MATLAB software. The grayscale value of the white area in the grayscale processed contact print image is 255, and the grayscale value of the gray area is between 0 and 254. The grayscale value data matrix M of the grayscale processed contact print image is extracted in the MATLAB software. i×i, i and j are the number of rows and columns of the grayscale value data matrix; subtract the grayscale value data matrix M from the grayscale value 255 i×j , so that the grayscale processed contact mark image is reversely displayed and the reverse displayed grayscale value data matrix N is obtained i×j .

[0020] As preferred embodiment of the present invention, the specific calculation method of step 3 is:

[0021] The contact mark specimen is a square with a side length of L, so the gray value data matrix N of the contact mark image is i×j The number of rows and columns is equal, that is, i=j=n, n is the number of pixels in the image; let the gray value data matrix N i×j The area corresponding to each element in is a small circle with a diameter of L / n, and the area of each small circle is π(L / 2n) 2 ; The contact degree and contact deformation size of each micro-convex body are different when they contact, and N i×j Gray value size reflects; extract gray value data matrix N i×j Maximum value N max =MAX{N i×j}, N i×j Divide each element by the maximum value N max Multiply it by the area represented by each element π(L / 2n) 2 Get the equivalent contact area matrix A considering the contact weight i×j for:

[0022]

[0023] As preferred embodiment of the present invention, the specific calculation method of step 4 is:

[0024] When the micro-convex peak contacts the rigid plane, the contact deformation of the micro-convex peak is divided into elastic deformation, elastic-plastic deformation and plastic deformation. c Determine the deformation form of the micro-convex peak; when δ≤δ c When δ c <δ≤110δ c When the micro-convex peak is elastic-plastic deformation, when 110δ c When <δ, the micro-convex peak is plastic deformation;

[0025] Critical deformation δ c Size:

[0026]

[0027] Where E is the equivalent elastic modulus of the bonding surface, E1 and v1 are the elastic modulus and Poisson's ratio of the softer material, respectively; E2 and v2 are the elastic modulus and Poisson's ratio of the harder material, respectively; H is the hardness of the softer material; μ is the contact pressure factor μ = 0.454 + 0.41v1; R is the curvature radius of the micro-convex peak, and the curvature radius is:

[0028]

[0029] Where D is the fractal dimension, G is the characteristic scale coefficient, and D and G are measured by detecting the rough surface morphology; γ is the spatial frequency of the random profile, γ = 1.5, which is an intermediate variable, and the expression of λ is:

[0030]

[0031] According to Hertz contact theory, the critical contact area of the micro-convex peak when it is in the critical state of elastic deformation and elastic-plastic deformation is:

[0032]

[0033] As preferred embodiment of the present invention, the specific calculation method of step 5 is:

[0034] In case of elastic contact deformation, δ≤δ c , that is, a≤a c According to Hertz contact theory, the contact area of the micro-convex peak is:

[0035] a=πRδ (6)

[0036] The relationship between the normal load P and the contact deformation δ is:

[0037]

[0038] By differentiating P with respect to δ, the contact stiffness of the micro-convex peaks in elastic contact is obtained as follows:

[0039]

[0040] Taking δ as the intermediate variable, substitute equation a into k t The relationship between the contact stiffness of the micro-convex peak and its contact area is:

[0041] k t =2Ea 1 / 2 π -1 / 2 (9)

[0042] During elastic-plastic deformation, the deformation range of the elastic-plastic deformation area is δ c <δ≤110δ c , that is, a c <a≤110a c Elastic-plastic contact load P tsfor:

[0043]

[0044] P ts By taking the derivative of δ, we can get the contact stiffness of the micro-convex peak during elastic-plastic deformation:

[0045]

[0046] The contact area of the micro-convex peak during elastic-plastic deformation is:

[0047] a=2πRδ (12)

[0048] δ c Substitute k ts And use δ as the intermediate variable to establish k ts The relationship with a is:

[0049]

[0050] In plastic deformation 110δ c <δ, i.e. 110a c When <a, the contact stiffness of the micro-convex peak is:

[0051] k s =2πRH (14)

[0052] As preferred embodiment of the present invention, the specific calculation method of step 6 is:

[0053] First, the rough surface morphology of the unpressurized specimen is measured to obtain the height of the maximum micro-convex peak as h1, and its position is recorded; after pressurization to form the bonding surface, the rough surface of the specimen is tested to obtain the height of the original maximum micro-convex peak after compression deformation as h2, and the two heights are subtracted to obtain the compression deformation of the maximum micro-convex peak δ max =h1-h2, this deformation is also the maximum deformation of the micro-convex peak of the bonding surface; the contact stiffness of the bonding surface is obtained by connecting the contact stiffness of each micro-convex peak in parallel, so the contact stiffness of the bonding surface is the sum of the contact stiffness generated by each micro-convex peak; the contact stiffness of each micro-convex peak is superimposed to obtain the overall contact stiffness of the bonding surface:

[0054] K=K1+K2+K3 (15)

[0055] Where K1 is the contact stiffness generated by all elastically deformed micro-peaks, and its magnitude is 0≤A ij ≤δ c / δ max ; K2 is the contact stiffness generated by all the micro-convex peaks of elastic-plastic deformation, and its magnitude is δ c / δ max <Aij <110δ c / δ max ; K3 is the contact stiffness generated by all micro-convex peaks of plastic deformation, and its magnitude is 110δ c / δ max ≤A ij ≤1.

[0056] The beneficial effects produced by adopting the above technical scheme are: the present invention provides an algorithm for the normal contact stiffness of the bonding surface; first, a contact mark image of the bonding surface is obtained, the contact mark image is loaded into MATLAB software, the image is grayscale processed, and then the grayscale processed contact mark image is reversely displayed; the data matrix of the reversely displayed contact mark image is read using MATLAB software and the equivalent contact area matrix considering the contact ratio is calculated; the critical contact deformation and critical contact area of the micro-convex peaks on the rough surface are calculated using Hertz contact theory; the contact stiffness of the micro-convex peaks during elastic deformation, elastic-plastic deformation and plastic deformation are calculated according to the contact deformation size of the micro-convex peaks; the three contact stiffness sizes of the equivalent contact area matrix considering the contact ratio are calculated according to the three contact stiffness calculation formulas and discrimination methods of the micro-convex peaks, and the three are summed to obtain the bonding surface contact stiffness; this method is an accurate, convenient and programmable bonding surface contact stiffness calculation method. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 This is a flow chart of a method for calculating contact stiffness of a joint surface provided by an embodiment of the present invention;

[0058] Figure 2 Schematic diagram of compression deformation of micro-convex peaks provided by an embodiment of the present invention;

[0059] Figure 3 This is a contact mark image provided by an embodiment of the present invention;

[0060] Figure 4 This is a grayscale-processed contact mark image provided by an embodiment of the present invention;

[0061] Figure 5 is the grayscale value of the pixel of the contact mark image processed in grayscale according to the embodiment of the present invention;

[0062] Figure 6 The embodiment of the present invention provides a reverse display of the post-contact imprint image;

[0063] Figure 7 It is the pixel grayscale value of the reversely displayed post-contact mark image provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0064] The specific embodiments of the present invention are described in further detail below with reference to the accompanying drawings and examples. These examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0065] This embodiment takes a contact mark picture of a machine tool joint surface as an example, and adopts a joint surface contact stiffness calculation method of the present invention to calculate the contact stiffness of the joint surface.

[0066] In this embodiment, a method for calculating the contact stiffness of a joint surface is provided. Figure 1 The calculation process shown includes the following steps:

[0067] Step 1: Obtain a contact imprint image of the bonding surface;

[0068] A layer of red paint was evenly applied to the rough surface of a square specimen with a side length of L. The specimen was placed on high-strength tempered glass and a certain pressure load was applied to it. The red paint mark at the actual contact position of the specimen obtained a bonding surface contact mark on the tempered glass. The tempered glass with the contact mark was placed on a Keyence VHX5000 ultra-depth-of-field microscope and white paper was placed on the bottom of the tempered glass as a background. The glass was then photographed to produce a high-resolution contact mark image.

[0069] Step 2: Combine the grayscale processing of the surface contact mark image and perform reverse display;

[0070] Assume that the micro-convex peaks on the rough surface of each bonding surface are spherical, the equivalent curvature radius of the micro-convex peaks is R, and the micro-convex peaks contact with the plane under the action of normal load to produce normal contact deformation δ, as shown in Figure 2 As shown. Assume that the contact mark image obtained in step 1 is as follows Figure 3 As shown, the contact imprint picture Figure 3 Load it into MATLAB software and use the software’s image grayscale processing function to Figure 3 Grayscale processing is performed to obtain a gray contact mark image, such as Figure 4 shown. Figure 4 The white area in the middle is the non-contact area of the bonding surface, which does not provide contact stiffness. Figure 4 The medium grey area is the contact region of the bonding surfaces, which provides the contact stiffness.

[0071] The grayscale processed image is stored in the form of a pixel grayscale value data matrix in the MATLAB software. The grayscale value of the white area in the grayscale processed contact mark image is 255, and the grayscale value of the gray area is between 0 and 254. Figure 5 As shown in the figure. The smaller the gray value, the greater the contact deformation, the greater the contact strength and the contact stiffness provided. Figure 5 Gray value data matrix M i×i, i and j are the number of rows and columns of the gray value data matrix, Figure 5 Here, i=j=3.

[0072]

[0073] Because the actual contact area of the bonding surface is small and difficult to calculate, the gray value data matrix M is subtracted from the gray value 255. i× j, grayscale processing Figure 4 Reverse display as Figure 6 As shown. After reverse processing, the gray value data matrix N is obtained i×j . After reverse display, the original image ( Figure 4 ) is displayed as a gray area with a gray value of 0, which is a non-contact area; the remaining areas have non-zero gray values, which are contact areas, such as Figure 7 As shown. Therefore, the gray value matrix N i×j The larger the element grayscale value, the greater the contact deformation, the greater the contact degree and the contact stiffness provided.

[0074]

[0075] Step 3: Calculate the equivalent contact area matrix of the bonding surface considering the contact ratio;

[0076] Since the side length of the test piece is a square L, the gray value data matrix N of the contact mark image is i×j The number of rows and columns is equal, that is, i=j=n, n is the number of pixels in the image, in this example n=3. i×j The area corresponding to each element in is a small circle with a diameter of L / 3, and the area of each small circle is π(L / 6) 2 The contact degree and contact deformation of each micro-convex peak are different, which can be expressed by N i×j The gray value of each element in the image is reflected.

[0077] Extract gray value data matrix N i×j Maximum value N max =MAX{N i×j}. i×j The gray value of each element in is divided by N max Multiply it by the area represented by each element π(L / 6) 2 Get the equivalent contact area matrix A considering the contact weight i×j :

[0078]

[0079] In this example, if the L value is given, the equivalent contact area matrix A considering the contact weight can be determined 3×3 :

[0080]

[0081] Step 4: Calculate the critical deformation δ of the micro-convex peak on the bonding surface c and critical contact area a c ;

[0082] Each non-zero element in the grayscale numerical matrix is formed by the contact of micro-convex peaks. When the micro-convex peaks on the bonding surface contact with the rigid plane, the contact deformation of the micro-convex peaks is divided into elastic deformation, elastic-plastic deformation and plastic deformation. The critical deformation δ of the micro-convex peaks is c Determine the deformation form of the micro-convex peak. When δ≤δ c When δ c <δ≤110δ c When the micro-convex peak is elastic-plastic deformation, when 110δ c When <δ, the micro-convex peak is plastic deformation.

[0083] Critical deformation δ c Size:

[0084]

[0085] Where E is the equivalent elastic modulus of the bonding surface, E1 and v1 are the elastic modulus and Poisson's ratio of the softer material, respectively; E2 and v2 are the elastic modulus and Poisson's ratio of the harder material, respectively; H is the hardness of the softer material; μ is the contact pressure factor μ = 0.454 + 0.41v1; the curvature radius R of the micro-convex peak can be obtained based on the rough surface morphology parameters, and its size is:

[0086]

[0087] Where D is the fractal dimension, G is the characteristic scale coefficient, and D and G are measured by detecting the rough surface morphology; γ is the spatial frequency of the random profile, γ = 1.5, which is an intermediate variable, and the expression of λ is:

[0088]

[0089] According to Hertz contact theory, the critical contact area of the micro-convex peak when it is in the critical state of elastic deformation and elastic-plastic deformation is:

[0090]

[0091] Step 5: Calculate the contact stiffness of the micro-convex peak under three deformation conditions;

[0092] In case of elastic contact deformation, δ≤δ c , that is, a≤a c According to Hertz contact theory, the contact area of the micro-convex peak is:

[0093] a=πRδ (24)

[0094] The relationship between the normal load P and the contact deformation δ is:

[0095]

[0096] By differentiating P with respect to δ, the contact stiffness of the micro-convex peaks in elastic contact is obtained as follows:

[0097]

[0098] Taking δ as the intermediate variable, substitute equation a into k t The relationship between the contact stiffness of the micro-convex peak and its contact area is:

[0099] k t =2Ea 1 / 2 π -1 / 2 (27)

[0100] During elastic-plastic deformation, the deformation range of the elastic-plastic deformation area is δ c <δ≤110δ c , that is, a c <a≤110a c Elastic-plastic contact load P ts for:

[0101]

[0102] P ts By taking the derivative of δ, we can get the contact stiffness of the micro-convex peak during elastic-plastic deformation:

[0103]

[0104] The contact area of the micro-convex peak during elastic-plastic deformation is:

[0105] a=2πRδ (30)

[0106] δ c Substitute k ts And use δ as the intermediate variable to establish k ts The relationship with a is:

[0107]

[0108] In plastic deformation 110δ c <δ, i.e. 110a c When <a, the contact stiffness of the micro-convex peak is:

[0109] k s =2πRH (32)

[0110] Step 6: Calculate the overall contact stiffness of the joint surface;

[0111] First, the rough surface morphology of the unpressurized specimen is measured to obtain the height of the maximum micro-convex peak as h1, and its position is recorded; after pressurization to form the bonding surface, the rough surface of the specimen is tested to obtain the height of the original maximum micro-convex peak after compression deformation as h2, and the two heights are subtracted to obtain the compression deformation of the maximum micro-convex peak δ max =h1-h2, this deformation is also the maximum deformation of the micro-convex peak on the bonding surface.

[0112] The contact stiffness of the joint surface is obtained by connecting the contact stiffness of each micro-convex peak in parallel. Therefore, the contact stiffness of the joint surface is the sum of the contact stiffness generated by each micro-convex peak. According to the different contact forms of each micro-convex peak, the contact stiffness of the joint surface can be obtained as follows:

[0113] K=K1+K2+K3 (33)

[0114] Where K1 is the contact stiffness generated by all elastically deformed micro-peaks, and its magnitude is 0≤A ij ≤δ c / δ max ; K2 is the contact stiffness generated by all the micro-convex peaks of elastic-plastic deformation, and its magnitude is δ c / δ max <A ij <110δ c / δ max ; K3 is the contact stiffness generated by all micro-convex peaks of plastic deformation, and its magnitude is 110δ c / δ max ≤A ij ≤1.

[0115] A i×j ,δmax,δ c , R, E, H and k t , k ts , k s Substituting K1, K2, and K3, we can obtain the contact stiffness K of the bonding surface.

[0116] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some or all of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A method for calculating the contact stiffness of a machine tool joint surface, characterized in that: First, a contact imprint image of the bonding surface is obtained, the contact imprint image is loaded into MATLAB software, the image is grayscale processed, and then the grayscale processed contact imprint image is reversely displayed; the data matrix of the reversely displayed contact imprint image is read using MATLAB software and the equivalent contact area matrix considering the contact ratio is calculated; Calculation of critical contact deformation δ of micro-convex peaks on rough surfaces using Hertz contact theory c and critical contact area a c ; According to the contact deformation size of the micro-convex peak, the contact stiffness of the micro-convex peak during elastic deformation, the contact stiffness during elastic-plastic deformation, and the contact stiffness during plastic deformation are calculated respectively; according to the three contact stiffness calculation formulas and judgment methods of the micro-convex peak, the three contact stiffness sizes of the equivalent contact area matrix considering the contact weight are calculated, and the three are summed to obtain the contact stiffness of the bonding surface; specifically, the following steps are included: Step 1: Obtain the contact imprint image of the bonding surface: A layer of red paint was evenly applied to the rough surface of the experimental specimen. The specimen was then placed on high-strength tempered glass and subjected to a certain pressure load. The red paint mark at the actual contact position of the specimen was then formed on the tempered glass to obtain a contact mark of the bonding surface. A high-resolution image of the contact mark was captured using an ultra-depth-of-field microscope. Step 2: Combine the grayscale processing of the surface contact mark image and perform reverse display: The contact mark image obtained in step 1 is loaded into MATLAB software, and the image is gray-scaled using the software to obtain a contact mark image; the gray and white positions in the gray-scaled contact mark image are swapped and displayed to obtain a reverse-displayed contact mark image; Step 3: Calculate the equivalent contact area matrix of the bonding surface considering the contact ratio: Extract the grayscale value data matrix of the reverse display contact mark image in step 2; divide each element in the grayscale value data matrix by the maximum grayscale value in the matrix and then multiply by the area corresponding to each element in the matrix to obtain an equivalent contact area matrix considering the contact proportion; the contact proportion is determined by dividing each element in the grayscale value data matrix by the maximum grayscale value in the matrix; Step 4: Calculate the critical deformation δ of the micro-convex peak on the bonding surface c and critical contact area a c : The critical deformation δ of the micro-convex peak during elastic deformation and elastic-plastic deformation is calculated according to the Hertz contact theory. c and critical contact area a c ; Step 5: Calculate the contact stiffness of the micro-convex peak under three deformation conditions: According to the critical deformation of the micro-convex peak and the contact area calculated in step 4, the deformation form of the micro-convex peak is judged according to the following judgment criteria: when δ≤δ c When δ c <δ≤110δ c When 110δ c When δ is less than δ, it is plastic deformation. The calculation formulas of contact stiffness during elastic contact deformation, contact stiffness during elastic-plastic deformation, and contact stiffness during plastic deformation of micro-convex peaks are derived. Step 6: Calculate the overall contact stiffness of the joint surface: The three deformation judgment criteria of the micro-convex peaks obtained in steps 4 and 5 are used to judge the deformation form of the micro-convex peaks represented by each element of the equivalent contact area matrix considering the contact ratio in step 3, and the three contact stiffness calculation formulas of the micro-convex peaks in step 5 are used to calculate the contact stiffness of the micro-convex peaks represented by each element of the equivalent contact area matrix considering the contact ratio respectively, and the calculated contact stiffness of each micro-convex peak is summed to obtain the overall contact stiffness of the bonding surface.

2. A method for calculating contact stiffness of a joint surface according to claim 1, characterized in that The specific calculation method of step 2 is: Assume that the top of each micro-convex peak on the rough surface of the bonding surface is spherical, and its equivalent curvature radius is R. When the micro-convex peak is subjected to a normal load and contacts the plane, a normal contact deformation δ is generated. The contact mark image obtained in step 1 is loaded into MATLAB software, and grayscale processing is performed on the contact mark image using the grayscale processing function of the software to obtain a gray contact mark image; The grayscale processed contact print image is stored in the form of a pixel grayscale value data matrix in the MATLAB software. The grayscale value of the white area in the grayscale processed contact print image is 255, and the grayscale value of the gray area is between 0 and 254. The grayscale value data matrix M of the grayscale processed contact print image is extracted in the MATLAB software. i×i , i and j are the number of rows and columns of the grayscale value data matrix; subtract the grayscale value data matrix M from the grayscale value 255 i×j , so that the grayscale processed contact mark image is reversely displayed and the reverse displayed grayscale value data matrix N is obtained i×j .

3. A method for calculating contact stiffness of a joint surface according to claim 2, characterized in that The specific calculation method of step 3 is: The contact mark specimen is a square with a side length of L, so the gray value data matrix N of the contact mark image is i×j The number of rows and columns is equal, that is, i=j=n, n is the number of pixels in the image; let the gray value data matrix N i×j The area corresponding to each element in is a small circle with a diameter of L / n, and the area of each small circle is π(L / 2n) 2 ; The contact degree and contact deformation size of each micro-convex body are different when they contact, and N i×j Gray value size reflects; extract gray value data matrix N i×j Maximum value N max =MAX{N i×j }, N i×j Divide each element by the maximum value N max Multiply it by the area represented by each element π(L / 2n) 2 Get the equivalent contact area matrix A considering the contact weight i×j As shown in formula (1):

4. A method for calculating contact stiffness of a joint surface according to claim 3, characterized in that The specific calculation method of step 4 is: When the micro-convex peak contacts the rigid plane, the contact deformation of the micro-convex peak is divided into elastic deformation, elastic-plastic deformation and plastic deformation. c Determine the deformation form of the micro-convex peak; when δ≤δ c When the micro-convex peak is elastic deformation, when δ c <δ≤110δ c When the micro-convex peak is elastic-plastic deformation, when 110δ c When <δ, the micro-convex peak is plastic deformation; Critical deformation δ c Size: Where E is the equivalent elastic modulus of the bonding surface, E1 and v1 are the elastic modulus and Poisson's ratio of the softer material, respectively; E2 and v2 are the elastic modulus and Poisson's ratio of the harder material, respectively; H is the hardness of the softer material; μ is the contact pressure factor μ = 0.454 + 0.41v1; R is the curvature radius of the micro-convex peak, and the curvature radius is: Where D is the fractal dimension, G is the characteristic scale coefficient, and D and G are measured by detecting the rough surface morphology; γ is the spatial frequency of the random profile, γ = 1.5, which is an intermediate variable, and the expression of λ is: According to Hertz contact theory, the critical contact area of the micro-convex peak when it is in the critical state of elastic deformation and elastic-plastic deformation is shown in formula (5):

5. A method for calculating contact stiffness of a joint surface according to claim 4, characterized in that The specific method of step 5 is as follows: In case of elastic contact deformation, δ≤δ c , that is, a≤a c According to Hertz contact theory, the contact area of the micro-convex peak is: a=πRδ (6) The relationship between the normal load P and the contact deformation δ is: By differentiating P with respect to δ, the contact stiffness of the micro-convex peaks in elastic contact is obtained as follows: Taking δ as the intermediate variable, substitute equation a into k t The relationship between the contact stiffness of the micro-convex peak and its contact area is: k t =2Ea 1 / 2 p -1 / 2 (9) During elastic-plastic deformation, the deformation range of the elastic-plastic deformation area is δ c <δ≤110δ c , that is, a c <a≤110a c Elastic-plastic contact load P ts for: P ts By taking the derivative of δ, we can get the contact stiffness of the micro-convex peak during elastic-plastic deformation: The contact area of the micro-convex peak during elastic-plastic deformation is: a=2πRδ (12) δ c Substitute k ts And use δ as the intermediate variable to establish k ts The relationship with a is: In plastic deformation 110δ c <δ, i.e. 110a c When <a, the contact stiffness of the micro-convex peak is shown in formula (14): k s =2πRH (14)。 6. A method for calculating contact stiffness of a joint surface according to claim 5, characterized in that The specific calculation method of step 6 is as follows: First, the rough surface morphology of the unpressurized specimen is measured to obtain the height of the maximum micro-convex peak as h1, and its position is recorded; after pressurization to form the bonding surface, the rough surface of the specimen is tested to obtain the height of the original maximum micro-convex peak after compression deformation as h2, and the two heights are subtracted to obtain the compression deformation of the maximum micro-convex peak δ max =h1-h2, this deformation is also the maximum deformation of the micro-convex peak of the bonding surface; the contact stiffness of the bonding surface is obtained by connecting the contact stiffness of each micro-convex peak in parallel, so the contact stiffness of the bonding surface is the sum of the contact stiffness generated by each micro-convex peak; the contact stiffness of each micro-convex peak is superimposed to obtain the overall contact stiffness of the bonding surface: K=K1+K2+K3 (15) Where K1 is the contact stiffness generated by all elastically deformed micro-peaks, and its magnitude is 0≤A ij ≤δ c / δ max ; K2 is the contact stiffness generated by all the micro-convex peaks of elastic-plastic deformation, and its magnitude is δ c / δ max <A ij <110δ c / δ max ; K3 is the contact stiffness generated by all the micro-convex peaks of plastic deformation, and its magnitude is 110δ c / δ max ≤A ij ≤1.

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