CN106991219A - A kind of normal direction interface rigidity Forecasting Methodology for considering three-dimensional fractal - Google Patents

Abstract

The invention relates to a method for predicting the stiffness of a normal interface considering three-dimensional fractal. The steps are: improving the function describing the two-dimensional fractal curve into a correction function for simulating the three-dimensional fractal shape, and expressing the amplitude difference between the peak and the valley described by this function as The amount of contact deformation; if the contact between two rough asperities is equivalent to the contact between a rigid plane and an equivalent asperity, then the actual contact area between the equivalent asperity and the rigid plane; calculate the elastic deformation stage respectively , Deformation in elastic-plastic deformation stage; calculation of area distribution function and actual contact area; calculation of single asperity stiffness and total interface stiffness; calculation of elastic stage stiffness k _n1 and elastic-plastic stage stiffness k _n2 and total interface stiffness. The present invention provides a simple and easy-to-operate prediction method for the acquisition of stiffness between precision mechanical interfaces, considering the elastoplastic deformation of asperities, the friction coefficient between contacts and the influence of three-dimensional fractal distribution, and the obtained results can be predicted and controlled Interface dynamic features provide technical reference.

Description

A Prediction Method of Normal Interface Stiffness Considering 3D Fractal

technical field

The invention relates to a technique of mechanical interface mechanics, in particular to a method for predicting the stiffness of a normal interface considering three-dimensional fractals.

Background technique

The surface of the part processed by the machine tool is smooth from the macroscopic point of view, but it shows a large number of rough bodies from the microscopic point of view, that is, the part has a rough surface morphology. Rough surface topography has an important influence on the friction, fatigue and vibration noise on the interface. Through the observation of metal surface topography, scholars have found that the surface topography at different measurement scales has statistical self-affine and self-similar characteristics, so the fractal theory is introduced and widely used in the description and contact of rough surface topography. analyze. Accurate modeling of the characteristic parameters (mainly contact stiffness and contact damping) on the rough contact interface to analyze and predict the static and dynamic characteristics of the whole machine will be a key technology in the process of general mechanical research and development and analysis.

At present, my country has implemented the "Made in China 2025" strategy. The high-end precision CNC machine tool in the strategy is known as a symbol of a country's high-end equipment manufacturing. As a typical complex electromechanical equipment, there are a large number of interfaces. The static and dynamic characteristics of these interfaces To a large extent, it determines the static and dynamic characteristics of the entire machine tool, that is, it determines the work efficiency, stability and machining accuracy during the machining process of the machine tool. Carefully studying the contact behavior on the interface theoretically and establishing a high-precision prediction model for relevant important dynamic characteristics not only provides a basis for accuracy error compensation, but also provides technical reference for predicting and controlling the dynamic characteristics of the interface, which has extensive engineering significance.

The strategic background of intelligent manufacturing requires that the dynamic characteristics of the entire equipment can be well predicted in the early stage of mechanical design, and this characteristic depends largely on the stiffness characteristics of the interface. In the past, people had many limitations in obtaining mechanical interface stiffness, mainly these problems: First, people often use finite element software to deal with interface contact problems, but this method is more complicated and difficult to divide meshes, and the calculation efficiency is low; secondly, based on The analytical method of fractal theory ignores the characteristics of the friction coefficient and the fractal distribution of the three-dimensional surface of the asperity. Obviously, these assumptions and limitations cannot be directly used in the analysis of high-precision mechanical interfaces (such as precision micro-nano devices, precision robot joint reducers, etc.) , appears to be insufficient in accuracy.

Contents of the invention

Aiming at the inefficiency and poor accuracy of obtaining the mechanical interface stiffness in the prior art, the problem to be solved by the present invention is to provide a method that considers three-dimensional fractals that makes it easy to obtain the interface stiffness that is difficult to detect and improves the accuracy of prediction. A method for predicting interface stiffness.

In order to solve the problems of the technologies described above, the technical solution adopted in the present invention is:

A method for predicting the stiffness of a normal interface considering three-dimensional fractals of the present invention comprises the following steps:

1) Three-dimensional surface topography simulation: improve the function describing two-dimensional fractal curves into a correction function for simulating three-dimensional fractal topography, and express the peak and valley amplitude difference described by this function as contact deformation δ=2G ^D-2 (lnγ ) ^0.5 (2r′) ^3-D , where D is the fractal dimension of the three-dimensional surface topography, 2<D<3, G is the fractal roughness of the surface topography, γ is the frequency density parameter, r′ is the asperity cut-off radius;

2) Asperity contact equivalent treatment: if the contact between two rough asperities is equivalent to the contact between a rigid plane and an equivalent asperity, then the actual contact area between the equivalent asperity and the rigid plane a=πRδ; wherein, δ is the amount of contact deformation of the asperity, and R is the radius of curvature of the asperity;

3) Asperity deformation includes three stages, namely, elastic deformation stage, elastoplastic deformation stage and plastic deformation stage; respectively calculate the deformation amount of elastic deformation stage and elastoplastic deformation stage;

4) Calculation of area distribution function and actual contact area: the area distribution function on the entire contact interface is The actual contact area of the entire contact interface is Among them, D is the fractal dimension of the three-dimensional surface topography, 2<D<3, a _l represents the largest contact area among all asperities; a is the actual contact area;

5) Calculation of the stiffness of a single asperity and the total interface stiffness: the stiffness of a single asperity includes two stages of elastic deformation and elastoplastic deformation, that is, the stiffness k _n1 of the elastic stage and the stiffness k _n2 of the elastic plastic stage,

The total interface stiffness is:

Among them, L _e is the load of a single asperity in the elastic stage, a _e is the critical elastic deformation area of a single asperity, a _l represents the largest contact area among all asperities in contact, and δ is the contact deformation of the asperity , D is the fractal dimension of the three-dimensional surface topography, 2<D<3, L _ep is the load in the elastic-plastic stage of a single asperity, G is the fractal roughness of the surface topography, a _p is the critical plastic deformation area, σ _y Indicates the softer yield strength in the materials in contact with each other, λ is the defined coefficient, a is the actual contact area, and n is the material hardness index.

The calculation of deformation in the elastic deformation stage includes the elastic critical deformation of the loaded asperity, the critical elastic deformation area of a single asperity, and the load in the elastic stage of a single asperity, where,

The elastic critical deformation of the loaded asperity is:

Where k _μ is the friction correction coefficient, φ is the characteristic coefficient of the material, and R is the radius of curvature of the asperity;

The critical elastic deformation area of a single asperity is:

Among them, D is the fractal dimension of the three-dimensional surface topography, 2<D<3, G is the fractal roughness of the surface topography, γ is the frequency density parameter, and k _μ is the friction correction coefficient;

The load in the elastic stage of a single asperity is:

Among them, E is the equivalent elastic modulus of the interface two-phase contact material, expressed as E ₁ , E ₂ are the elastic modulus of the two-phase contact materials, and v ₁ , v ₂ are the Poisson's ratios of the two-phase contact materials, which represent the basic material properties of the two-phase contact materials.

The calculation of the deformation amount in the elastic-plastic deformation stage includes the critical plastic deformation amount of the loaded asperity in the elastic-plastic stage, the critical plastic deformation area of the loaded asperity, and the load of a single asperity in the elastic-plastic stage, where:

The critical plastic deformation of the loaded asperity in the elastic-plastic stage is:

Among them, D is the fractal dimension of the three-dimensional surface topography, 2<D<3, k _μ is the friction correction coefficient, φ is the characteristic coefficient of the material, γ is the frequency density parameter, and G is the fractal roughness of the surface topography.

The critical plastic deformation area of the loaded asperity in the elastic-plastic stage is:

Among them, D is the fractal dimension of the three-dimensional surface topography, 2<D<3, G is the fractal roughness of the surface topography, γ is the frequency density parameter, k _μ is the friction correction coefficient, and φ is the characteristic coefficient of the material.

The load in the elastoplastic stage of a single asperity is:

Among them, σ _y represents the softer yield strength in the mutual contact materials, λ is a defined coefficient, λ=H/σ _y , H is the hardness of the softer material in the two mutual contact materials, n is the material hardness index, expressed as a _e is the critical elastic deformation area of a single asperity.

The present invention has the following beneficial effects and advantages:

1. The present invention provides a simple and easy-to-operate prediction method for obtaining the stiffness between precision mechanical interfaces, which makes it easy to obtain interface stiffness that is difficult to detect, overcomes the defects of traditional methods, and considers the elastoplastic deformation of asperities , friction coefficient between contacts and the influence of three-dimensional fractal distribution, the obtained results can provide technical reference for predicting and controlling the dynamic characteristics of the interface.

Description of drawings

Fig. 1 is the flowchart of prediction method of the present invention;

The three-dimensional surface topography simulation fractal diagram that Fig. 2 inventive method involves;

Fig. 3 is the contact equivalent diagram of the mutual contact asperities involved in the method of the present invention;

Figure 4 is an interface equivalent processing diagram related to the method of the present invention;

Fig. 5 is a verification diagram of a vibration test involved in the method of the present invention.

detailed description

The present invention will be further elaborated below in conjunction with the accompanying drawings of the description.

As shown in Figure 1, a kind of normal interface stiffness prediction method considering three-dimensional fractal of the present invention comprises the following steps:

1) Three-dimensional surface topography simulation: improve the function describing the two-dimensional fractal curve into a correction function for simulating the three-dimensional fractal topography, and express the peak and trough amplitude difference described by this function as the contact deformation δ=2G ^D-2 (lnγ ) ^0.5 (2r′) ^3-D , where D is the fractal dimension of the three-dimensional surface topography, 2<D<3, G is the fractal roughness of the surface topography, γ is the frequency density parameter, r′ is the asperity cut-off radius;

2) Asperity contact equivalent treatment: if the contact between two rough asperities is equivalent to the contact between a rigid plane and an equivalent asperity, then the actual contact area between the equivalent asperity and the rigid plane a=πRδ; where, δ is the contact deformation of the asperity, and R is the equivalent radius of curvature of the asperity;

3) The asperity deformation stage is divided into three stages, namely elastic deformation stage, elastoplastic deformation stage and plastic deformation stage; respectively calculate the deformation amount of elastic deformation stage and elastoplastic deformation stage;

4) Calculation of area distribution function and actual contact area: the area distribution function on the entire contact interface is The actual contact area of the entire contact interface is Among them, a _l represents the largest contact area among all asperities in contact;

5) Calculation of the stiffness of a single asperity and the total interface stiffness: the stiffness of a single asperity includes two stages of elastic deformation and elastoplastic deformation, that is, the stiffness k _n1 of the elastic stage and the stiffness k _n2 of the elastic plastic stage,

The total interface stiffness is:

In step 1), the method of the present invention first improves the Weierstrass-Mandelbrot (WM) function describing the two-dimensional fractal curve into a modified WM function for simulating the three-dimensional fractal appearance, as shown in Figure 2, which is the three-dimensional function involved in the method of the present invention Surface topography simulated fractal diagram. In this embodiment, the given simulation parameters are: the fractal dimension of the three-dimensional surface topography D=2.45, the fractal roughness of the surface topography G=5.42×10 ⁻⁸ m, and the frequency density parameter γ=1.5.

In step 2), according to the classical Hertzian theory, the contact between two rough asperities is equivalent to the contact between a rigid plane and an equivalent asperity after loading, as shown in Fig. 3 . The equivalent plane crosses the equivalent asperity body to form the nominal contact area and the actual contact area, so it is analyzed to obtain the actual contact area a=πRδ between the equivalent asperity body and the rigid plane, where R is the asperity equivalent radius of curvature;

In step 3), the deformation of the asperity is carefully divided into three stages, namely elastic deformation, elastic-plastic deformation and plastic deformation. The calculation of the deformation amount in the elastic deformation stage includes the elastic critical The amount of deformation, the critical elastic deformation area of a single asperity, and the load in the elastic stage of a single asperity, where,

The elastic critical deformation of the loaded asperity is:

Where k _μ is the friction correction coefficient, φ is the characteristic coefficient of the material, and R is the radius of curvature of the asperity;

The critical elastic deformation area of a single asperity is:

Among them, D is the fractal dimension of the three-dimensional surface topography, G is the fractal roughness of the surface topography, γ is the frequency density parameter, and k _μ is the friction correction coefficient;

The load in the elastic stage of a single asperity is:

Among them, E is the equivalent elastic modulus of the interface two-phase contact material, expressed as E ₁ , E ₂ , v ₁ , v ₂ are the basic material properties of the two-phase contact materials, E ₁ , E ₂ are the elastic modulus of the two-phase contact materials, v ₁ , v ₂ are the poise Songby.

In step 3), the calculation of the amount of deformation in the elastic-plastic deformation stage includes the critical plastic deformation amount of the loaded asperity in the elastic-plastic stage, the critical plastic deformation area of the loaded asperity and the load of a single asperity in the elastic-plastic stage, in:

The critical plastic deformation of the loaded asperity in the elastic-plastic stage is:

The critical plastic deformation area of the loaded asperity in the elastic-plastic stage is:

The load in the elastoplastic stage of a single asperity is:

Among them, σ _y represents the softer yield strength of the materials in contact with each other, λ is a defined coefficient, λ=H/σ _y , H is the hardness of the softer material in the two materials in contact with each other, n is the material hardness index, expressed as a _e is the critical elastic deformation area of a single asperity.

In order to verify the prediction accuracy of the method of the present invention, a vibration modal test is now carried out with two reproducible simple specimens, namely two 45 steel plates. The steel plate is 400mm long, 50mm wide, and 6mm thick, connected by 16 M6 bolts, and the interface is processed by milling. The relevant engineering parameters are shown in Table 1.

Table 1 Test steel plate parameters

According to the literature "Li X, Liang Y, Zhao G, et al.Dynamic characteristics of joint surface considering friction and vibration factors based on fractal theory[J].Journal of Vibroengineering,2013,15(2):872-883.", will The interface is subjected to equivalent treatment as shown in Figure 4, and the elastic modulus of the equivalent layer is obtained respectively. The shear modulus and Poisson’s ratio can be embedded in the normal interface stiffness, so that the natural frequency of the calculation mode can be obtained. This result is compared with the vibration test modal frequency in Figure 5, as shown in Table 2. Table 2 also gives the theoretical calculation results when 3D fractals are ignored. It can be seen that the error of ignoring 3D fractals is larger than that of considering 3D fractal surface topography.

Table 2 Comparison of calculation and test results

The above description is the specific implementation of the present invention, but the protection scope of the present invention is not limited thereto, and any easy modification and transformation all belong to the protection scope of the present invention.

Claims (3)

1. A method for predicting the stiffness of a normal interface considering three-dimensional fractal, characterized in that it comprises the following steps: 1) Three-dimensional surface topography simulation: improve the function describing two-dimensional fractal curves into a correction function for simulating three-dimensional fractal topography, and express the peak and valley amplitude difference described by this function as contact deformation δ=2G ^D-2 (lnγ ) ^0.5 (2r′) ^3-D , where D is the fractal dimension of the three-dimensional surface topography, 2<D<3, G is the fractal roughness of the surface topography, γ is the frequency density parameter, r′ is the asperity cut-off radius; 2) Asperity contact equivalent treatment: if the contact between two rough asperities is equivalent to the contact between a rigid plane and an equivalent asperity, then the actual contact area between the equivalent asperity and the rigid plane a=πRδ; wherein, δ is the amount of contact deformation of the asperity, and R is the radius of curvature of the asperity; 3) Asperity deformation includes three stages, namely, elastic deformation stage, elastoplastic deformation stage and plastic deformation stage; respectively calculate the deformation amount of elastic deformation stage and elastoplastic deformation stage; 4) Calculation of area distribution function and actual contact area: the area distribution function on the entire contact interface is The actual contact area of the entire contact interface is Among them, D is the fractal dimension of the three-dimensional surface topography, 2<D<3, a _l represents the largest contact area among all asperities; a is the actual contact area; 5) Calculation of the stiffness of a single asperity and the total interface stiffness: the stiffness of a single asperity includes two stages of elastic deformation and elastoplastic deformation, that is, the stiffness k _n1 of the elastic stage and the stiffness k _n2 of the elastic plastic stage, ${\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; E\&pi;</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 0.5</span>}}}{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1.5</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ;</span>$ ${\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; p</span>}}}{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2.79</span>}{\mathrm{<span\; class="notranslate">\; \&lambda;\&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 5.5</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; G</span>}}^{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 0.5</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 0.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1.5</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1.5</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>$ The total interface stiffness is: ${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2.79</span>}{\mathrm{<span\; class="notranslate">\; \&lambda;\&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 0.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 6.5</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; G</span>}}^{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 0.5</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 0.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1.5</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1.5</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1.5</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; E\&pi;</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 0.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; )</span>$ Among them, L _e is the load of a single asperity in the elastic stage, a _e is the critical elastic deformation area of a single asperity, a _l represents the largest contact area among all asperities in contact, and δ is the contact deformation of the asperity , D is the fractal dimension of the three-dimensional surface topography, 2<D<3, L _ep is the load in the elastic-plastic stage of a single asperity, G is the fractal roughness of the surface topography, a _p is the critical plastic deformation area, σ _y Indicates the softer yield strength in the materials in contact with each other, λ is the defined coefficient, a is the actual contact area, and n is the material hardness index. 2. by the normal interface stiffness prediction method of three-dimensional fractal consideration of claim 1, it is characterized in that: the deformation amount calculation of elastic deformation stage comprises the elastic critical deformation amount of loaded asperity, the critical elasticity of single asperity Deformed area, load in the elastic phase of a single asperity, where, The elastic critical deformation of the loaded asperity is: ${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 33</span>}{\mathrm{<span\; class="notranslate">\; \&pi;k</span>}}_{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}\mathrm{<span\; class="notranslate">\; \&phi;</span>}}{\mathrm{<span\; class="notranslate">\; 40</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; R</span>}$ Among them, k _μ is the friction correction coefficient, φ is the characteristic coefficient of the material, and R is the curvature radius of the asperity; The critical elastic deformation area of a single asperity is: ${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 33</span>}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}\mathrm{<span\; class="notranslate">\; \&phi;</span>}}{\mathrm{<span\; class="notranslate">\; 40</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; G</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$ Among them, D is the fractal dimension of the three-dimensional surface topography, 2<D<3, G is the fractal roughness of the surface topography, γ is the frequency density parameter, and k _μ is the friction correction coefficient; The load in the elastic stage of a single asperity is: ${\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; E\&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 0.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 7.5</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 0.5</span>}}{\mathrm{<span\; class="notranslate">\; G</span>}}^{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}}$ Among them, E is the equivalent elastic modulus of the interface two-phase contact material, expressed as E ₁ , E ₂ are the elastic modulus of the two-phase contact materials, and v ₁ , v ₂ are the Poisson's ratios of the two-phase contact materials, which represent the basic material properties of the two-phase contact materials. 3. by the normal interface stiffness prediction method of three-dimensional fractal consideration of claim 1, it is characterized in that: the deformation amount calculation of elastic-plastic deformation stage comprises the critical plastic deformation amount of loaded micro-convex body in elastic-plastic stage, loaded The critical plastic deformation area of an asperity and the load in the elastoplastic stage of a single asperity, where: The critical plastic deformation of the loaded asperity in the elastic-plastic stage is: ${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 110</span>}{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 33</span>}{\mathrm{<span\; class="notranslate">\; \&pi;k</span>}}_{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}\mathrm{<span\; class="notranslate">\; \&phi;</span>}}{\mathrm{<span\; class="notranslate">\; 40</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 1.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 5.5</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; 0.5</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; G</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}^{\mathrm{<span\; class="notranslate">\; 0.5</span>}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}}$ Among them, D is the fractal dimension of the three-dimensional surface topography, 2<D<3, k _μ is the friction correction coefficient, φ is the characteristic coefficient of the material, γ is the frequency density parameter, G is the fractal roughness of the surface topography, The critical plastic deformation area of the loaded asperity in the elastic-plastic stage is: ${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&lsqb;</span>\frac{\mathrm{<span\; class="notranslate">\; 110</span>}{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 33</span>}{\mathrm{<span\; class="notranslate">\; \&pi;k</span>}}_{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}\mathrm{<span\; class="notranslate">\; \&phi;</span>}}{\mathrm{<span\; class="notranslate">\; 40</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}^{\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; G</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \&rsqb;</span>}^{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; D.</span>}}}$ Among them, D is the fractal dimension of the three-dimensional surface topography, 2<D<3, G is the fractal roughness of the surface topography, γ is the frequency density parameter, k _μ is the friction correction coefficient, and φ is the characteristic coefficient of the material; The load in the elastoplastic stage of a single asperity is: Among them, σ _y represents the softer yield strength of the materials in contact with each other, λ is a defined coefficient, λ=H/σ _y , H is the hardness of the softer material in the two materials in contact with each other, n is the material hardness index, expressed as a _e is the critical elastic deformation area of a single asperity.