A method for constructing a unified contact model of rough surface statistics and fractals

Abstract

The present invention relates to the technical field of statistical models, and specifically discloses a method for constructing a unified contact model of rough surface statistics and fractals, comprising the following steps: Step 1: by obtaining the statistical parameters of the rough surface and the distribution of the height of micro-convex bodies, based on the contact mechanical properties of a single micro-convex body, a statistical contact model of the entire rough surface is obtained; Step 2: by using the area distribution function of a single micro-convex body in the contact deformation of the rough surface, a fractal contact model of the real contact area and contact load of the rough surface and the contact area a of the single micro-convex body in the deformation process is established; Step 3: by using the spectral moments of each order to obtain the statistical parameters of the rough surface; Step 4: respectively, under the conditions of the same curvature radius and the minimum cumulative deviation, a unified contact model is established. Taking the fractal results as a benchmark, the non-uniqueness of the statistical results is improved, and a basis is provided for the selection of sampling intervals when measuring the rough surface and obtaining the statistical parameters.

Description

Technical Field

[0001] The invention relates to the technical field of statistical models, in particular to a method for constructing a unified contact model of rough surface statistics and fractals. Background Art

[0002] There are two main methods for studying the contact properties of rough surfaces: statistics and fractals. For a given rough surface, the results of the fractal model are unique, while the results of the statistical model are non-unique due to the uncertainty of the sampling length and sampling interval. Summary of the invention

[0003] A unified contact model between statistics and fractals is established based on the uniqueness of fractal results, aiming at statistical parameters, fractal parameters, power spectrum density function, sampling length and sampling interval.

[0004] A method for constructing a unified contact model of rough surface statistics and fractals of the present invention comprises the following steps:

[0005] Step 1: By obtaining the statistical parameters of the rough surface and the distribution of the height of the micro-asperities, the statistical contact model of the entire rough surface is obtained based on the contact mechanical properties of a single micro-asperity;

[0006] Step 2: Through the area distribution function of a single micro-asperity in the contact deformation of the rough surface, a fractal contact model of the real contact area and contact load of the rough surface and the contact area a of a single micro-asperity in the deformation process is established;

[0007] Step 3: Obtain the zero-order, second-order, and fourth-order spectral moments of the two-dimensional profile through the power spectral density function of the two-dimensional profile of the rough surface, and then obtain the statistical parameters of the rough surface through the spectral moments of each order;

[0008] Step 4: Establish a unified contact model under the conditions of the same curvature radius and minimum cumulative deviation.

[0009] Preferably, the step 1 is specifically:

[0010] The contact between the rough surfaces is simplified to the contact between a rigid plane and a rough plane. The height of the micro-convex body is t, and the distance between the rigid plane and the average height of the micro-convex body is x. When the rough surface contacts the rigid plane, the deformation of the micro-convex body is (tx). The height of the micro-convex body on the entire rough surface obeys the Gaussian distribution, and the probability density function of the height distribution is:

[0011]

[0012] In formula (1): is the probability density function of the height distribution of the micro-convex body, t is the height of the micro-convex body, σ sis the standard deviation of the asperity height;

[0013] The total true contact area of ​​the entire rough surface is:

[0014] A S =A S e +A S ep1 +A S ep2 +A S p (2);

[0015] In formula (2): A S Represents the total real contact area of ​​the rough surface, A S e A represents the actual contact area of ​​the part on the rough surface that is in the elastic deformation stage. S ep1 A represents the real contact area of ​​the rough surface in the first elastic-plastic deformation stage. S ep2 A represents the real contact area of ​​the rough surface in the second elastic-plastic deformation stage. S p Represents the actual contact area of ​​the part on the rough surface that is in the complete plastic deformation stage;

[0016] The total contact load is:

[0017] P S =P S e +P S ep1 +P S ep2 +P S p (3);

[0018] In formula (3), P S Represents the total contact load on the rough surface, P S e P represents the contact load on the rough surface in the elastic deformation stage. S ep1 P represents the contact load on the rough surface in the first elastic-plastic deformation stage. S ep2 P represents the contact load on the rough surface in the second elastic-plastic deformation stage. S p Represents the contact load on the part of the rough surface that is in the complete plastic deformation stage;

[0019] The actual contact area and contact load at each deformation stage are:

[0020]

[0021]

[0022] Among them: A S e A represents the actual contact area of ​​the part on the rough surface that is in the elastic deformation stage. S ep1 A represents the real contact area of ​​the rough surface in the first elastic-plastic deformation stage. S ep2 A represents the real contact area of ​​the rough surface in the second elastic-plastic deformation stage. S p represents the actual contact area of ​​the rough surface in the complete plastic deformation stage, P S e P represents the contact load on the rough surface in the elastic deformation stage. S ep1 P represents the contact load on the rough surface in the first elastic-plastic deformation stage. S ep2 P represents the contact load on the rough surface in the second elastic-plastic deformation stage. S p represents the contact load on the rough surface in the complete plastic deformation stage, ω c is the critical deformation of the micro-convex body for yielding, t is the height of the micro-convex body, x is the distance between the rigid plane and the average height of the micro-convex body, is the probability density function of the height distribution of the micro-convex body, a e is the contact area of ​​a single micro-convex body in the elastic deformation stage, f e is the contact load when a single micro-convex body is in the elastic deformation stage; a ep1 is the contact area of ​​a single micro-convex body in the first elastic-plastic deformation stage, f ep1 is the contact load of a single micro-convex body in the first elastic-plastic deformation stage; a ep2 is the contact area of ​​a single micro-convex body in the second elastic-plastic deformation stage, f ep2 is the contact load of a single micro-convex body in the second elastic-plastic deformation stage; a p The contact area of ​​a single micro-convex body when it is in the stage of complete plastic deformation, f p Contact load of a single asperity when it is in the stage of complete plastic deformation.

[0023] Preferably, the specific steps of step 2 are:

[0024] The area distribution function is:

[0025] m(a)=Da l D / 2 / 2a (D / 2)+1 (6);

[0026] In formula (6), m(a) is the area distribution function of the micro-convexity when the rough surface contacts the rigid plane, D is the fractal dimension of the rough surface, and a l is the maximum contact area of ​​a single micro-asperity, a is the contact area of ​​a single micro-asperity during deformation;

[0027] The total true contact area and total contact load of the entire rough surface are:

[0028] A F =A F e +A F ep1 +A F ep2 +A F p (7);

[0029] P F =P F e +P F ep1 +P F ep2 +P F p (8);

[0030] In formulas (7) and (8), A F Represents the total real contact area of ​​the rough surface, A F e A represents the actual contact area of ​​the part on the rough surface that is in the elastic deformation stage. F ep1 A represents the real contact area of ​​the rough surface in the first elastic-plastic deformation stage. F ep2 A represents the real contact area of ​​the rough surface in the second elastic-plastic deformation stage. F p Represents the actual contact area of ​​the rough surface in the complete plastic deformation stage; P F Represents the total contact load on the rough surface, P F e P represents the contact load on the rough surface in the elastic deformation stage. F ep1 P represents the contact load on the rough surface in the first elastic-plastic deformation stage. F ep2 P represents the contact load on the rough surface in the second elastic-plastic deformation stage.F p Represents the contact load on the part of the rough surface that is in the complete plastic deformation stage;

[0031] The actual contact area and contact load at each deformation stage are:

[0032]

[0033]

[0034] In formula (10), A F e A represents the actual contact area of ​​the part on the rough surface that is in the elastic deformation stage. F ep1 A represents the real contact area of ​​the rough surface in the first elastic-plastic deformation stage. F ep2 A represents the real contact area of ​​the rough surface in the second elastic-plastic deformation stage. F p represents the actual contact area of ​​the rough surface in the complete plastic deformation stage, P F e P represents the contact load on the rough surface in the elastic deformation stage. F ep1 P represents the contact load on the rough surface in the first elastic-plastic deformation stage. F ep2 P represents the contact load on the rough surface in the second elastic-plastic deformation stage. F p represents the contact load on the rough surface in the complete plastic deformation stage, S is the correction coefficient of the multi-scale fractal model for the area distribution function, a nl is the maximum contact area of ​​a single micro-convex body at each frequency level, a nec is the elastic critical contact area of ​​a single asperity at each frequency level, a nepc is the first elastic-plastic critical contact area of ​​a single asperity at each frequency level, a npc is the plastic critical contact area of ​​a single micro-convex body at each frequency level, n ec is the critical frequency index of elasticity, n epc is the critical frequency index of the first elastic-plastic property, n pc is the critical frequency index of the second elastic-plastic property, n min is the frequency level corresponding to the largest asperity on the rough surface, n max is the frequency level corresponding to the smallest asperity on the rough surface, f e is the contact load when a single micro-convex body is in the elastic deformation stage; fep1 is the contact load of a single micro-convex body in the first elastic-plastic deformation stage; f ep2 is the contact load of a single micro-convex body in the second elastic-plastic deformation stage; f p Contact load of a single asperity when it is in the stage of complete plastic deformation.

[0035] Preferably, the specific steps of step 3 are:

[0036] The power spectral density function is:

[0037]

[0038] In formula (11), ζ(ω) is the power spectral density function of the two-dimensional surface profile, ω is the frequency of the wavelength on the two-dimensional surface profile, λ = 2D-4, D is the fractal dimension of the rough surface, G is the scale parameter of the rough surface, γ = 1.5;

[0039] Zero-order spectral moment m 0 , second-order spectral moment m 2 、The fourth-order spectral moment m 4 for:

[0040]

[0041] In formula (12), m 0 is the zero-order spectral moment, m 2 is the second-order spectral moment, m 4 is the fourth-order spectral moment, ω is the frequency of the wavelength on the two-dimensional profile of the surface, and the low cutoff frequency ω l =2π / L, L is the sampling length, high cutoff frequency ω h =2π / Δx, Δx is the sampling interval, λ 1 =2D-4,λ 2 =2D-2,λ 3 =2D; surface statistical parameters are expressed as: average curvature radius of rough surface Rough surface asperity density Standard deviation of rough surface height Asperity height standard deviation Bandwidth parameters Represents the width of the annular spectrum of the isotropic surface, α>1.5.

[0042] Preferably, the specific steps of step 4 are:

[0043] As the distance between the rigid plane and the rough surface continues to decrease, the real contact area of ​​the rough surface continues to increase, and the contact load obtained by the fractal model and the statistical model also continues to increase; the result of the fractal model is unique, while the result of the statistical model changes with the change of the sampling interval under a given sampling length; a unified contact model for the two cases is established by the sampling interval when the curvature radius is equal or the cumulative deviation is the smallest;

[0044] The unified contact model when the radii of curvature are equal is as follows:

[0045] Different frequency levels n in the classification model correspond to different curvature radii. The average curvature radius of the entire rough surface is It is expressed as:

[0046]

[0047] In formula (13), m 4 is the fourth-order spectral moment;

[0048] In the classification model, the low cutoff frequency ω in the fourth-order spectral moment l and high cutoff frequency ω h It is expressed as:

[0049]

[0050] In formula (14), n min is the frequency level corresponding to the largest asperity on the rough surface, n max is the frequency level corresponding to the smallest asperity on the rough surface, γ n Used to control the frequency of the rough surface profile. Usually, γ = 1.5, n is the asperity frequency level;

[0051] Therefore, the average curvature radius of the rough surface in the fractal model is It is expressed as:

[0052]

[0053] In formula (15), D is the fractal dimension of the rough surface, G is the scale parameter of the rough surface, and γ n Used to control the frequency of the rough surface profile. Usually, γ = 1.5, n min is the frequency level corresponding to the largest asperity on the rough surface, n max is the frequency level corresponding to the smallest asperity on the rough surface;

[0054] By letting the mean radius of curvature R in the statistical model S and equal, and obtain the fractal dimension D, frequency level range [nmin ,n max ], the sampling interval Δx of the sampling length L is expressed as:

[0055]

[0056] In formula (16), L is the sampling length, γ = 1.5;

[0057] Based on equations (2), (3), and (16), for the determined fractal parameters and sampling length, a contact model based on curvature radius is established;

[0058]

[0059] In formula (17), A represents the contact area and P represents the contact load;

[0060] Through equations (2), (3) and (7), (8), we can obtain the load-area relationship of the statistical model and the fractal model:

[0061] P S =f 1 (A S ) (18);

[0062] In formula (18), P S is the contact load of the statistical model, A S is the contact area of ​​the statistical model, f 1 is the load-area function relationship of the statistical model;

[0063] P F =f 2 (A F ) (19);

[0064] In formula (19), P F is the contact load of the fractal model, A F is the contact area of ​​the fractal model, f 2 is the load-area function relationship of the fractal model;

[0065] From equations (16), (18), and (19), we can obtain that when the curvature radius is the same and the real contact area is equal, there is a difference between the contact loads of the statistical model and the fractal model:

[0066]

[0067] In formula (20), A is the contact area, f 3 It is the functional relationship of the ratio of contact loads of the statistical model and the fractal model when the radius of curvature is the same;

[0068] The unified contact model for equal areas and minimum load deviation is as follows:

[0069] For the entire rough surface deformation process, the results of the fractal model are unique, while the results of the statistical model vary with the sampling interval under a given sampling length, that is, P S =f 1 (A S ,Δx);

[0070] The optimization model was established using MATLAB, and the same real contact area range [A 1 ,A 2 ] The area of ​​the load-area curve is taken as the benchmark, Δx is adjusted, and the statistical model curve that is closest to the area of ​​the fractal model curve is obtained, so as to establish the objective function W in the optimization model as follows:

[0071]

[0072] In formula (21), ξ F is the area of ​​the load-area curve of the fractal model, ξ S is the area of ​​the statistical model load-area curve, ξ S Related to Δx;

[0073] The sampling interval Δx is obtained as:

[0074] Δx=exp(a+b*n min ) (twenty two);

[0075] a=B a0 +B a1 D+B a2 D 2 +B a3 D 3 , b=B b0 +B b1 D+B b2 D 2 +B b3 D 3 ,

[0076] B a0 =0.47001-11.18509L+18.72477L 2 -6.50791L 3 ,

[0077] B a1 =-3.16844+38.13556L-60.13584L 2 +23.33599L 3 ,

[0078] B a2=1.53991-29.22684L+43.16843L 2 -19.55684L 3 ,

[0079] B a3 =-0.5311+5.99831L-12.68421L 2 +5.16847L 3 ,

[0080] B b0 =0.48226-10.55824L+19.33468L 2 -6.33501L 3 ,

[0081] B b1 =-1.59748+23.55102L-45.66881L 2 +17.58349L 3 ,

[0082] B b2 =1.33746-21.57615L+34.60021L 2 -14.56835L 3 ,

[0083] B b3 =-0.33694+6.53879L-9.00567L 2 +4.56233L 3 ;

[0084] L is the sampling length;

[0085] Based on equations (2), (3), and (22), for the determined fractal parameters and sampling length, a contact model based on cumulative deviation is established:

[0086]

[0087] From equations (18), (19), and (22), we can obtain that when the statistical model results and the fractal model results have the minimum cumulative deviation and the true contact area is equal, there is a relationship between the contact loads:

[0088]

[0089] In formula (24), f 4 It is the functional relationship of the ratio of contact loads of statistical model and fractal model when the cumulative deviation is minimum.

[0090] Compared with the prior art, the present invention has the following beneficial effects:

[0091] Based on the fractal results, the non-uniqueness of the statistical results was improved, which provided a basis for the selection of sampling intervals when measuring rough surfaces and obtaining statistical parameters, and obtained definite statistical results. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 A schematic diagram of the contact between a rigid plane and a rough surface provided by the present invention;

[0093] Figure 2 Load-area curves of the statistical model and the fractal model when the curvature radii of the embodiment of the present invention are equal;

[0094] Figure 3 Loading-area curves of the statistical model and the fractal model with the minimum cumulative deviation according to an embodiment of the present invention. DETAILED DESCRIPTION

[0095] The following will disclose multiple embodiments of the present invention with diagrams. For the purpose of clear description, many physical details will be described together in the following description. However, it should be understood that these physical details should not be used to limit the present invention. In other words, in some embodiments of the present invention, these physical details are not necessary. In addition, for the purpose of simplifying the diagram, some conventional structures and components will be depicted in a simple schematic manner in the diagram.

[0096] In addition, the technical solutions between the various embodiments can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0097] By making the average curvature radius of the rough surface in the statistical model equal to the average curvature radius of the rough surface in the fractal model, the sampling interval based on the fractal parameter and the sampling length is determined:

[0098]

[0099] Through equations (2), (3), and (25), a unified contact model based on curvature radius is obtained:

[0100]

[0101] Based on the results of the fractal model, by adjusting the sampling interval, we obtained an optimization model for the cumulative deviation between the statistical model results and the fractal model results when the real contact area is the same, and found the sampling interval corresponding to the optimal solution:

[0102] Δx 2 =exp(a+b*nmin ) (27);

[0103] Through equations (2), (3), and (27), the unified contact model based on the optimization model is obtained:

[0104]

[0105] The two unified contact models obtained in this way cover the fractal parameters in the fractal model and the sampling length and sampling interval in the statistical model, and obtain a unique solution for a certain rough surface, optimizing the non-uniqueness in the statistical model.

[0106] The above description is only an embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent substitution, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A method for constructing a unified contact model of rough surface statistics and fractals, characterized in that: The steps include: Step 1: By obtaining the statistical parameters of the rough surface and the distribution of the height of the micro-asperities, the statistical contact model of the entire rough surface is obtained based on the contact mechanical properties of a single micro-asperity; Step 2: Through the area distribution function of a single micro-asperity in the contact deformation of the rough surface, a fractal contact model of the real contact area and contact load of the rough surface and the contact area a of a single micro-asperity in the deformation process is established; Step 3: Obtain the zero-order, second-order, and fourth-order spectral moments of the two-dimensional profile through the power spectral density function of the two-dimensional profile of the rough surface, and then obtain the statistical parameters of the rough surface through the spectral moments of each order; Step 4: Establish a unified contact model under the conditions of the same curvature radius and minimum cumulative deviation; The specific steps of step 4 are as follows: As the distance between the rigid plane and the rough surface continues to decrease, the actual contact area of ​​the rough surface continues to increase, and the contact load obtained by the fractal model and the statistical model also continues to increase; the result of the fractal model is unique, while the result of the statistical model changes with the change of the sampling interval under a given sampling length; a unified contact model for the two cases is established through the sampling interval when the curvature radius is equal or the cumulative deviation is minimized.

2. The method for constructing a unified contact model of rough surface statistics and fractals according to claim 1, characterized in that: The step 1 is specifically as follows: The contact between the rough surfaces is simplified to the contact between a rigid plane and a rough plane, and the height of the micro-convex body is t , the distance between the rigid plane and the average height of the micro-convex body is x, and when the rough surface contacts the rigid plane, the deformation of the micro-convex body is (tx); the height of the micro-convex body on the entire rough surface obeys the Gaussian distribution, and the probability density function of the height distribution is: In formula (1): is the probability density function of the height distribution of the micro-convex body, t is the height of the micro-convex body, σ s is the standard deviation of the asperity height; The total true contact area of ​​the entire rough surface is: A S =A S e +A S ep1 +A S ep2 +A S p (2); In formula (2): A S Represents the total real contact area of ​​the rough surface, A S e A represents the actual contact area of ​​the part on the rough surface that is in the elastic deformation stage. S ep1 A represents the real contact area of ​​the rough surface in the first elastic-plastic deformation stage. S ep2 A represents the real contact area of ​​the rough surface in the second elastic-plastic deformation stage. S p Represents the actual contact area of ​​the part on the rough surface that is in the complete plastic deformation stage; The total contact load is: P S =P S e +P S ep1 +P S ep2 σP S p (3); In formula (3), P S Represents the total contact load on the rough surface, P S e P represents the contact load on the rough surface in the elastic deformation stage. S ep1 P represents the contact load on the rough surface in the first elastic-plastic deformation stage. S ep2 P represents the contact load on the rough surface in the second elastic-plastic deformation stage. S p Represents the contact load on the part of the rough surface that is in the complete plastic deformation stage; The actual contact area and contact load at each deformation stage are: Among them: A S e A represents the actual contact area of ​​the part on the rough surface that is in the elastic deformation stage. S ep1 A represents the real contact area of ​​the rough surface in the first elastic-plastic deformation stage. S ep2 A represents the real contact area of ​​the rough surface in the second elastic-plastic deformation stage. S p represents the actual contact area of ​​the rough surface in the complete plastic deformation stage, P S e P represents the contact load on the rough surface in the elastic deformation stage. S ep1 P represents the contact load on the rough surface in the first elastic-plastic deformation stage. S ep2 P represents the contact load on the rough surface in the second elastic-plastic deformation stage. S p represents the contact load on the rough surface in the complete plastic deformation stage, ω c is the critical deformation of the micro-convex body for yielding, t is the height of the micro-convex body, x is the distance between the rigid plane and the average height of the micro-convex body, is the probability density function of the height distribution of the micro-convex body, a e is the contact area of ​​a single micro-convex body in the elastic deformation stage, f e is the contact load when a single micro-convex body is in the elastic deformation stage; a ep1 is the contact area of ​​a single micro-convex body in the first elastic-plastic deformation stage, f ep1 is the contact load of a single micro-convex body in the first elastic-plastic deformation stage; a ep2 is the contact area of ​​a single micro-convex body in the second elastic-plastic deformation stage, f ep2 is the contact load of a single micro-convex body in the second elastic-plastic deformation stage; a p The contact area of ​​a single micro-convex body when it is in the stage of complete plastic deformation, f p Contact load of a single asperity when it is in the stage of complete plastic deformation.

3. The method for constructing a unified contact model of rough surface statistics and fractals according to claim 2, characterized in that: The specific steps of step 2 are as follows: The area distribution function is: m(a)=Da l D / 2 / 2a (D / 2)+1 (6); In formula (6), m(a) is the area distribution function of the micro-convexity when the rough surface contacts the rigid plane, D is the fractal dimension of the rough surface, and a l is the maximum contact area of ​​a single micro-asperity, a is the contact area of ​​a single micro-asperity during deformation; The total true contact area and total contact load of the entire rough surface are: A F =A F e +A F ep1 +A F ep2 +A F p (7); P F =P F e +P F ep1 +P F ep2 +P F p (8); In formulas (7) and (8), A F Represents the total real contact area of ​​the rough surface, A F e A represents the actual contact area of ​​the part on the rough surface that is in the elastic deformation stage. F ep1 A represents the real contact area of ​​the rough surface in the first elastic-plastic deformation stage. F ep2 A represents the real contact area of ​​the rough surface in the second elastic-plastic deformation stage. F p Represents the actual contact area of ​​the rough surface in the complete plastic deformation stage; P F Represents the total contact load on the rough surface, P F e P represents the contact load on the rough surface in the elastic deformation stage. F ep1 P represents the contact load on the rough surface in the first elastic-plastic deformation stage. F ep2 P represents the contact load on the rough surface in the second elastic-plastic deformation stage. F p Represents the contact load on the part of the rough surface that is in the complete plastic deformation stage; The actual contact area and contact load at each deformation stage are: In formula (10), A F e A represents the actual contact area of ​​the part on the rough surface that is in the elastic deformation stage. F ep1 A represents the real contact area of ​​the rough surface in the first elastic-plastic deformation stage. F ep2 A represents the real contact area of ​​the rough surface in the second elastic-plastic deformation stage. F p represents the actual contact area of ​​the rough surface in the complete plastic deformation stage, P F e P represents the contact load on the rough surface in the elastic deformation stage. F ep1 P represents the contact load on the rough surface in the first elastic-plastic deformation stage. F ep2 P represents the contact load on the rough surface in the second elastic-plastic deformation stage. F p represents the contact load on the rough surface in the complete plastic deformation stage, S is the correction coefficient of the multi-scale fractal model for the area distribution function, a nl is the maximum contact area of ​​a single micro-convex body at each frequency level, a nec is the elastic critical contact area of ​​a single asperity at each frequency level, a nepc is the first elastic-plastic critical contact area of ​​a single asperity at each frequency level, a npc is the plastic critical contact area of ​​a single micro-convex body at each frequency level, n ec is the critical frequency index of elasticity, n epc is the critical frequency index of the first elastic-plastic property, n pc is the critical frequency index of the second elastic-plastic property, n min is the frequency level corresponding to the largest asperity on the rough surface, n max is the frequency level corresponding to the smallest asperity on the rough surface, f e is the contact load when a single micro-convex body is in the elastic deformation stage; f ep1 is the contact load of a single micro-convex body in the first elastic-plastic deformation stage; f ep2 is the contact load of a single micro-convex body in the second elastic-plastic deformation stage; f p Contact load of a single asperity when it is in the stage of complete plastic deformation.

4. The method for constructing a unified contact model of rough surface statistics and fractals according to claim 1, characterized in that: The specific steps of step 3 are as follows: The power spectral density function is: In formula (11), ζ(ω) is the power spectral density function of the two-dimensional surface profile, ω is the frequency of the wavelength on the two-dimensional surface profile, λ=2D-4, D is the fractal dimension of the rough surface, G is the Surface scale parameter, γ = 1.5; The zero-order spectral moment m0, the second-order spectral moment m2, and the fourth-order spectral moment m4 are: In formula (12), m0 is the zero-order spectral moment, m2 is the second-order spectral moment, m4 is the fourth-order spectral moment, ω is the frequency of the wavelength on the two-dimensional profile of the surface, and the low cutoff frequency ω is l =2π / L, L is the sampling length, high cutoff frequency ω h =2π / Δx, Δx is the sampling interval, λ1=2D-4,λ2=2D-2,λ3=2D; surface statistical parameters are expressed as: average curvature radius of rough surface Rough surface asperity density Standard deviation of rough surface height Asperity height standard deviation Bandwidth parameters Represents the width of the annular spectrum of the isotropic surface, α>1.

5.

5. The method for constructing a unified contact model of rough surface statistics and fractals according to claim 3, characterized in that: The unified contact model when the radii of curvature are equal is as follows: Different frequency levels n in the classification model correspond to different curvature radii. The average curvature radius of the entire rough surface is It is expressed as: In formula (13), m4 is the fourth-order spectral moment; In the classification model, the low cutoff frequency ω in the fourth-order spectral moment l and high cutoff frequency ω h It is expressed as: In formula (14), n min is the frequency level corresponding to the largest asperity on the rough surface, n max is the frequency level corresponding to the smallest asperity on the rough surface, γ n Used to control the frequency of the rough surface profile. Usually, γ = 1.5, n is the asperity frequency level; Therefore, the average curvature radius of the rough surface in the fractal model is It is expressed as: In formula (15), D is the fractal dimension of the rough surface, G is the scale parameter of the rough surface, and γ n Used to control the frequency of the rough surface profile. Usually, γ = 1.5, n min is the frequency level corresponding to the largest asperity on the rough surface, n max is the frequency level corresponding to the smallest asperity on the rough surface; By letting the mean curvature radius R in the statistical model S and equal, and obtain the fractal dimension D, frequency level range [n min ,n max ], the sampling interval Δx of the sampling length L is expressed as: In formula (16), L is the sampling length, γ = 1.5; Based on equations (2), (3), and (16), for the determined fractal parameters and sampling length, a contact model based on curvature radius is established; In formula (17), A represents the contact area and P represents the contact load; Through equations (2), (3) and (7), (8), we can obtain the load-area relationship of the statistical model and the fractal model: P S =f1(A S )(18); In formula (18), P S is the contact load of the statistical model, A S is the contact area of ​​the statistical model, f1 is the load-area function relationship of the statistical model; P F =f2(A F )(19); In formula (19), P F is the contact load of the fractal model, A F is the contact area of ​​the fractal model, f2 is the load-area function relationship of the fractal model; From equations (16), (18), and (19), we can obtain that when the curvature radius is the same and the real contact area is equal, there is a difference between the contact loads of the statistical model and the fractal model: In formula (20), A is the contact area, and f3 is the functional relationship between the contact load ratio of the statistical model and the fractal model when the curvature radius is the same; The unified contact model for equal areas and minimum load deviation is as follows: For the entire rough surface deformation process, the results of the fractal model are unique, while the results of the statistical model vary with the sampling interval under a given sampling length, that is, P S =f1(A S ,Δx); The optimization model was established using MATLAB. By calculating the area of ​​the load-area curve within the same real contact area range [A1, A2], the result of the fractal model was used as a benchmark, and Δx was adjusted to obtain the statistical model curve that was closest to the area of ​​the fractal model curve. The objective function W in the optimization model was established as follows: In formula (21), ξ F is the area of ​​the load-area curve of the fractal model, ξ S is the area of ​​the statistical model load-area curve, ξ S Related to Δx; The sampling interval Δx is obtained as: Δx=exp(a’+b*n min ) (22); a’=B a0 +B a1 D+B a2 D 2 +B a3 D 3 ,b=B b0 +B b1 D+B b2 D 2 +B b3 D 3 , B a0 =0.47001-11.18509L+18.72477L 2 -6.50791L 3 , <h2 style=";text-align:left;direction:ltr">B<h2 style=";text-align:left;direction:ltr"> a1 <h2 style=";text-align:left;direction:ltr"> =-3.16844+38.13556L-60.13584L<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +23.33599L<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> , B a2 =1.53991-29.22684L+43.16843L 2 -19.55684L 3 , <h2 style=";text-align:left;direction:ltr">B<h2 style=";text-align:left;direction:ltr"> a3 <h2 style=";text-align:left;direction:ltr"> =-0.5311+5.99831L-12.68421L<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +5.16847L<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> , <h2 style=";text-align:left;direction:ltr">B<h2 style=";text-align:left;direction:ltr"> b0 <h2 style=";text-align:left;direction:ltr"> =0.48226-10.55824L+19.33468L<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> -6.33501L<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> , B b1 =-1.59748+23.55102L-45.66881L 2 +17.58349L 3 , B b2 =1.33746-21.57615L+34.60021L 2 -14.56835L 3 , <h2 style=";text-align:left;direction:ltr">B<h2 style=";text-align:left;direction:ltr"> b3 <h2 style=";text-align:left;direction:ltr"> =-0.33694+6.53879L-9.00567L<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +4.56233L<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> ; L is the sampling length; Based on equations (2), (3), and (22), for the determined fractal parameters and sampling length, a contact model based on cumulative deviation is established: From equations (18), (19), and (22), we can obtain that when the statistical model results and the fractal model results have the minimum cumulative deviation and the true contact area is equal, there is a relationship between the contact loads: In formula (24), f4 is the functional relationship of the ratio of the contact load of the statistical model to that of the fractal model when the cumulative deviation is minimum.

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