A prediction method and system for considering the contact stiffness of rough surfaces in elastic-plastic states

Abstract

The present invention discloses a prediction method for considering the contact stiffness of a rough surface in an elastoplastic state. By dividing the contact state interval of asperities and using a polynomial of the natural logarithm function to characterize the relationship between the contact load and the normal deformation of asperities in the elastoplastic stage, an analytical model for the contact of asperities in the elastoplastic state is established. Then, combined with the analytical models in the elastic state and the plastic state, an analytical model for the contact of a single asperity is established, and an analytical model for the contact of the entire rough surface is obtained. By comparing with the calculation results of the finite element model for the contact of the rough surface, the accuracy of the calculation results of the normal contact stiffness of the rough surface is effectively improved, and the error is reduced. The present invention also fully considers the mutual influence between different contact states of asperities on the rough surface, thereby the influence on the normal contact stiffness of the rough surface is overcome, and the problem of inaccurate calculation results of the normal contact stiffness of the rough surface caused by serious deformation of the asperity surface when bearing a large load is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of rough surface contact deformation research, and relates to a prediction method and system for rough surface contact stiffness considering elastic-plastic state. Background Art

[0002] The machined surface of a part is not a smooth plane. At the microscopic scale, it is a rough surface composed of a large number of micro-convex bodies of different sizes, which makes the rough surface interface of the part present complex contact characteristics and is the main reason for the nonlinear dynamic behavior of the rough surface interface. The contact characteristics of the micro-convex bodies will directly affect the contact characteristics of the rough surface interface. Due to the complexity and uncertainty of the distribution of micro-convex bodies and the difficulty of experimental research on the rough surface interface, it has always been a difficult point to establish a mechanical model of the rough surface interface to characterize the complex contact characteristics of the rough surface interface.

[0003] The key to establishing the mechanical model of the rough surface interface is to establish the analytical model of contact stiffness and contact damping. As one of the important parameters to describe the contact characteristics of the interface, contact stiffness and contact damping have a significant impact on the dynamic performance of engineering structures. Studies have shown that 60%-80% of the total stiffness and 90% of the total damping of engineering structures come from interface contact stiffness and contact damping. Inaccurate contact parameter models will produce unacceptable errors in the prediction of the dynamic behavior of mechanical structures.

[0004] In the prior art, the mechanical model of the rough surface joint surface is established to predict the normal contact stiffness of the rough surface micro-convex body, but there is still a large error. Because the micro-convex body of the rough surface is seriously deformed when subjected to a large load, the accuracy of the normal contact stiffness of the rough surface is low and the error is large. Summary of the invention

[0005] In response to the problems existing in the prior art, the present invention proposes a prediction method and system for the contact stiffness of rough surfaces in the elastic-plastic state. By dividing the contact state intervals of micro-convex bodies, modeling is performed separately for different contact states of the rough surface, and the model is verified by finite element simulation, thereby effectively improving the accuracy of the calculation results of the normal contact stiffness of the rough surface and reducing the error.

[0006] The present invention is achieved through the following technical solutions:

[0007] A method for predicting contact stiffness of rough surfaces considering elastic-plastic state, characterized by comprising:

[0008] S1. Establish a single micro-convex body normal contact finite element model, perform finite element simulation verification on the single micro-convex body normal contact finite element model, and calculate the simulation result of the single micro-convex body normal contact finite element;

[0009] S2. Determine the demarcation points of the fully elastic deformation stage, elastoplastic deformation stage, and fully plastic deformation stage of the asperity according to the finite element simulation results of the normal contact of a single asperity described in S1; characterize the relationship between the contact load and the normal deformation of the asperity in the elastoplastic stage by a polynomial of the natural logarithm function and determine the analytical expression, characterize the relationship between the contact area and the normal deformation of the asperity in the elastoplastic deformation stage by a polynomial of the exponential function and determine the analytical expression, and combine the analytical expressions of the fully elastic deformation stage and fully plastic deformation stage of the asperity to establish an analytical model for the normal contact of a single asperity;

[0010] S3. Establish a finite element model of the analytical model for the contact of a rough surface according to the finite element model of the normal contact of a single asperity described in S1;

[0011] S4. Establish an analytical model for the normal contact of a rough surface according to the analytical model for the normal contact of a single asperity described in S2 and the finite element model of the analytical model for the contact of a rough surface described in S3;

[0012] S5. Perform finite element simulation verification on the analytical model for the contact of a rough surface described in S4 according to the finite element model of the analytical model for the contact of a rough surface described in S3, obtain the contact load and contact area of the rough surface, and calculate the normal contact stiffness of the rough surface through analysis.

[0013] Preferably, the specific process of establishing the finite element model of the normal contact of a single asperity in S1 is as follows:

[0014] Establish a finite element model of the contact between the asperity and the rigid plane, constrain the degrees of freedom of the upper surface of the asperity, apply an upward displacement boundary condition to the rigid plane to simulate the loading of the asperity, obtain the variation law of the contact state of a single asperity under normal load, divide each contact interval according to the variation law, and obtain the finite element model of the normal contact of a single asperity.

[0015] Preferably, the expression of the polynomial of the natural logarithm function described in S2 is:

[0016] a 1 lnδ + a 2 δ + a 3

[0017] Wherein: use the logarithmic term a 1 lnδ to control the basic shape of the fitting curve; add the first-order term a 2 δ to meet the smoothness condition; add the constant term a 3 to meet the continuity condition, a 1 、a 2 and a 3 are undetermined coefficients.

[0018] Preferably, the expression of the polynomial of the exponential function in S2 is:

[0019]

[0020] where: using the exponential term c 1 e δ to control the basic shape of the fitting curve; adding the inverse proportional term to meet the smoothness condition; adding the constant term c 3 to meet the continuity condition, c 1 、c 2 and c 3 are undetermined coefficients.

[0021] Preferably, in S2, the Hertz theory is adopted to determine the analytical expressions of the fully elastic deformation stage and the fully plastic deformation stage of the asperities.

[0022] Preferably, in S3, a finite element model of the rough surface contact analytical model is established, and the specific process is as follows:

[0023] Use Matlab programming to simulate and generate the rough surface point cloud matrix, import the generated rough surface point cloud matrix into Solidworks to establish the geometric model of the rough surface, and then import the geometric model of the rough surface into the commercial finite element software ABAQUS to establish the finite element model of the rough surface contact analytical model.

[0024] Preferably, the specific process of the rough surface contact analytical model in S4 is as follows:

[0025] Extract the two-dimensional topography curves in the x-axis and y-axis directions of the finite element model of the rough surface contact analytical model, calculate and average the statistical parameters of the topography curves to obtain the Gaussian distribution function of the asperities, the equivalent asperities of the rough surface, and the density of the asperities; use the Gaussian distribution function of the asperities to integrate the contact load and contact area of the asperities in the fully elastic deformation stage, elastic-plastic deformation stage, and fully plastic deformation stage over the entire rough surface to obtain the relationship between the contact load and contact area of the entire rough surface and the normal deformation, and then combine the equivalent asperities and density of the rough surface to establish the normal contact analytical model of the rough surface.

[0026] Preferably, the specific calculation formulas for the contact load and contact area of the entire rough surface are:

[0027] Fully elastic deformation stage:

[0028] When 0 ≤ δ < δ c ,

[0029]

[0030]

[0031] Elastoplastic first deformation stage:

[0032] When δ c ≤ δ < 6δ c At this time,

[0033]

[0034]

[0035] Elastoplastic second deformation stage:

[0036] When 6δ c ≤ δ < 110δ c At this time,

[0037]

[0038]

[0039] Fully plastic deformation stage:

[0040] When 110δ c ≤ δ < L,

[0041]

[0042]

[0043] Among them: δ is the normal deformation of the microconvex body; δ c is the critical deformation when the elastic stage of the microconvex body transforms into the first elastoplastic stage; 6δ c is the critical deformation when the microconvex body transforms from the first elastoplastic stage to the second elastoplastic stage; δ p = 110δ c is the critical deformation when the microconvex body transforms from the second elastoplastic stage to the plastic stage; the normal load of the microconvex body f = a·p; L is the height of the microconvex body, d is the normal approach amount, L - d = δ, the normal deformation of the microconvex body is equal to the height of the microconvex body minus the normal approach amount, where L = 3σ, that is, the maximum height of the microconvex body; g(z) is the Gaussian function; A is the actual contact area of the rough surface; F is the total contact load of the rough surface; N is the number of microconvex bodies on the rough surface; a e is the contact area of the microconvex body in the elastic stage; a ep1 is the contact area of the microconvex body in the first elastoplastic stage; a ep2 is the contact area of the microconvex body in the second elastoplastic stage; a p is the contact area of the microconvex body in the plastic stage; f e is the contact load of the microconvex body in the elastic stage; fep1 is the contact load of asperities in the first elastoplastic stage; f ep2 is the contact load of asperities in the second elastoplastic stage; f p is the contact load of asperities in the plastic stage.

[0044] Preferably, the finite element simulation verification of the rough surface contact analysis model described in S5 is carried out. The specific process is as follows:

[0045] Assign material properties and boundary conditions to the finite element model of the rough surface contact analysis model, so as to carry out simulation verification on the finite element model of the rough surface contact analysis model, obtain the contact load and contact area of the rough surface, compare the rough surface contact analysis model with the finite element model of the rough surface contact analysis model, verify the accuracy of the rough surface contact analysis model, and obtain the normal contact stiffness of the rough surface by analyzing the curves of the contact load and contact area of the rough surface contact analysis model with the normal deformation.

[0046] A prediction system for the contact stiffness of a rough surface considering the elastoplastic state includes a model establishment module, a calculation module, and a simulation verification module;

[0047] The model establishment module is used to establish a finite element model of the normal contact of a single asperity, an analytical model of the normal contact of a single asperity, a finite element model of the rough surface contact analysis model, and an analytical model of the rough surface normal contact analysis model;

[0048] The calculation module is used to calculate the simulation results of the finite element of the normal contact of a single asperity and calculate the normal contact stiffness of the rough surface;

[0049] The simulation verification module is used to carry out finite element simulation verification on the finite element model of the normal contact of a single asperity and carry out finite element simulation verification on the rough surface contact analysis model.

[0050] Compared with the prior art, the present invention has the following beneficial technical effects:

[0051] The present invention provides a prediction method and system for the contact stiffness of a rough surface considering the elastoplastic state, which divides the contact state intervals of asperities according to the finite element simulation results of a single asperity, models different contact states of the rough surface respectively, and verifies the model through finite element simulation, thereby effectively improving the accuracy of the calculation result of the normal contact stiffness of the rough surface and reducing the error. The present invention also fully considers the mutual influence between different contact states of the asperities on the rough surface, and thus the influence on the normal contact stiffness of the rough surface, overcoming the disadvantage that when a large load is applied, serious deformation occurs on the surface of the asperities, resulting in inaccurate calculation results of the normal contact stiffness of the rough surface. At the same time, the present invention establishes a polynomial of the natural logarithm function to characterize the relationship between the contact load and the normal deformation amount in the elastoplastic deformation stage of the asperity, and establishes a polynomial of the exponential function to characterize the relationship between the contact area and the normal deformation amount in the elastoplastic deformation stage of the asperity, thereby establishing an analytical model of the contact of the asperity in the elastoplastic state. Then, combined with the analytical models in the elastic state and the plastic state, an analytical model of the contact of a single asperity is established. By integrating the Gaussian distribution function over the entire rough surface, an analytical model of the contact of the entire rough surface is obtained. This analytical model of the contact of the rough surface can accurately calculate and predict the normal contact stiffness of the asperities on the rough surface, which has important theoretical and engineering significance for realizing the prediction of the dynamic behavior of mechanical structures. In addition, the model designed by the present invention is analytical, with a simple form, and has characteristics such as reliability and high accuracy, which is beneficial to characterizing the relationship between the normal contact load and the contact area of the metal rough surface and the normal deformation, thereby improving the accuracy of the calculation result of the normal contact stiffness of the rough surface.

[0052] Furthermore, the present invention simultaneously considers three contact states: fully elastic, elastoplastic, and fully plastic, and considers the evolution law of the plastic region in the elastoplastic state of the asperity. Analytical formulas for classical elastic contact and plastic contact are respectively used for modeling in the fully elastic deformation stage and the fully plastic deformation stage, improving the reliability and accuracy of the modeling method, and thus further improving the accuracy of the calculation result of the normal contact stiffness of the rough surface.

[0053] Furthermore, based on the Gaussian distribution of the asperities on the rough surface, the present invention establishes a normal contact model of the rough surface by using the method of probability statistical analysis. Compared with other related models, the present invention avoids the Runge effect caused by high-order polynomial interpolation and the discontinuous and non-smooth problems when the contact state changes. At the same time, the model of the present invention is analytical, with a simple form, effectively solving the problem that when a large load is applied and serious deformation occurs to the asperities on the rough surface, ensuring the accuracy of the normal contact stiffness of the rough surface and small error, and having important engineering application value in the field of dynamics of mechanical structures. Description of the Drawings

[0054] Figure 1This is the technical route of the present invention;

[0055] Figure 2 This is a schematic diagram of a single asperity contact;

[0056] Figure 3 This is a schematic diagram of the contact pressure fitting in the elastic-plastic stage;

[0057] Figure 4 This is a schematic diagram of the contact area fitting in the elastic-plastic stage;

[0058] Figure 5 This is a schematic diagram of the Gaussian distribution of asperities on a rough surface;

[0059] Figure 6 This is a finite element model of a single asperity;

[0060] Figure 7 This is the evolution law of the plastic region of the asperity;

[0061] Figure 8 This is the contact state curve of the finite element model of a single asperity;

[0062] Figure 9 This is the comparison between the analytical model and the finite element model of the asperity;

[0063] Figure 10 This is the Matlab topography of the rough surface;

[0064] Figure 11 This is the geometric model of the rough surface;

[0065] Figure 12 This is the finite element model of the rough surface;

[0066] Figure 13 This is the change process of the contact state of the finite element model of the rough surface;

[0067] Figure 14 This is the calculation result of the contact state of the finite element model of the rough surface;

[0068] Figure 15 This is the comparison between the analytical model and the finite element model of the rough surface. Specific implementation mode

[0069] The following further elaborates on the present invention in conjunction with specific embodiments, which is an explanation rather than a limitation of the present invention.

[0070] Reference Figure 1 This is the technical route of the overall implementation plan of the present invention;

[0071] The present invention provides a prediction method and system for the contact stiffness of a rough surface in an elastic-plastic state, and specifically relates to a normal contact analytical model of a metal rough surface that is based on the Hertz contact theory and considers the elastic-plastic contact state of micro-asperities and obeys Gaussian distribution, and provides a finite element simulation verification method for the model. According to the finite element simulation results of a single micro-asperity, the micro-asperity contact state interval is divided, and the method of characterizing the relationship between the contact load and the normal deformation of the micro-asperity in the elastic-plastic stage based on the natural logarithmic function of the present invention is used to establish an analytical contact model of the micro-asperity in the elastic-plastic state, and then the elastic state and plastic state analytical models are combined to establish a single micro-asperity contact analytical model, and the Gaussian distribution function is used to integrate to the entire rough surface to obtain the contact analytical model of the entire rough surface. Finally, the calculation results are compared with those of the rough surface contact finite element model established using the ABAQUS commercial finite element software, thereby effectively improving the accuracy of the calculation results of the normal contact stiffness of the rough surface and reducing the error; the present invention also fully considers the mutual influence between the different contact states between the micro-asperities on the rough surface, thereby affecting the normal contact stiffness of the rough surface, overcoming the shortcoming that when subjected to a large load, the micro-asperity surface undergoes severe deformation, resulting in inaccurate calculation results of the normal contact stiffness of the rough surface.

[0072] The present invention proposes a method for predicting the contact stiffness of a rough surface in an elastic-plastic state, which is implemented according to the following specific steps:

[0073] (1) Modeling a single asperity normal contact finite element model, verifying the single asperity normal contact finite element model through finite element simulation, and calculating the simulation results of the single asperity normal contact finite element;

[0074] A finite element model of the contact between a micro-asperity and a rigid plane is established. The degrees of freedom of the upper surface of the micro-asperity are constrained, and an upward displacement boundary condition is imposed on the rigid plane to simulate the loading of the micro-asperity. The change law of the contact state of a single micro-asperity under normal load can be obtained, and each contact interval can be divided according to the change law.

[0075] (2) Modeling of single asperity normal contact analytical model

[0076] According to the finite element simulation results of the normal contact of a single micro-asperity, the dividing points of the micro-asperity's complete elastic deformation stage, elastic-plastic deformation stage and complete plastic deformation stage are determined; the relationship between the contact load and the normal deformation of the micro-asperity in the elastic-plastic stage is characterized by a polynomial of a natural logarithmic function and an analytical expression is determined; the relationship between the contact area and the normal deformation of the micro-asperity in the elastic-plastic deformation stage is characterized by a polynomial of an exponential function and an analytical expression is determined; and combined with the analytical expressions of the complete elastic deformation stage and the complete plastic deformation stage of the micro-asperity, an analytical model of normal contact of a single micro-asperity is established;

[0077] The rough surface is regarded as being composed of micro - convex bodies with statistical probability distribution characteristics. The schematic diagram of the deformation of a single micro - convex body is as shown in Figure 2 the following figure:

[0078] (a) Fully elastic stage

[0079] In the fully elastic stage, according to Hertz contact theory, the contact area a e and the average contact pressure p e between the normal deformation δ can be expressed as:

[0080] a e = πRδ

[0081]

[0082] where: R is the equivalent curvature radius at the top of the micro - convex body; k is the hardness coefficient: k = 0.454 + 0.41ν;

[0083] H is the hardness of the softer material.

[0084] When the normal deformation increases to the elastic critical deformation δ c , the micro - convex body will begin to produce plastic deformation. δ c is related to the material parameters of the softer material, and the expression is as follows:

[0085]

[0086] where: E is the equivalent elastic modulus of the micro - convex body,

[0087] (b) Elastic - plastic stage

[0088] To solve the problem of discontinuity and non - smoothness existing in the existing contact pressure model, this paper proposes a polynomial based on the natural logarithm function to express the change curve of the contact pressure in the elastic - plastic stage. The elastic - plastic stage is divided into two segments, as shown in Figure 3 the following figure. Polynomials of natural logarithm functions in the form of: a 1 lnδ + a 2 δ + a 3 are used to fit the pressure curves of the two stages of elastic - plastic deformation.

[0089] The specific calculation process is as follows:

[0090] Use polynomials of natural logarithm functions in the form of a 1 lnδ + a 2 δ + a 3 to fit the pressure curves of the first deformation stage and the second deformation stage of elastic - plastic deformation; among them: use the logarithmic term a 1 lnδ to control the basic shape of the fitting curve; add the first - order term a2 δ is used to satisfy the smoothness condition; a constant term a is added 3 to satisfy the continuity condition, a 1 , a 2 and a 3 are undetermined coefficients.

[0091] Elastoplastic first deformation stage:

[0092] When δ c ≤δ≤6δ c :

[0093] p ep1 =a 1 lnδ + a 2 δ + a 3

[0094] According to the continuity and smoothness conditions:

[0095] p e (δ c ) = p ep1 (δ c )

[0096] p ep1 (δ c ) = p ep2 (δ c )

[0097] p ep2 (δ p ) = p p (δ p )

[0098] It is obtained that in the formula:

[0099]

[0100] Elastoplastic second deformation stage:

[0101] When 6δ c ≤δ≤110δ c :

[0102] p ep2 =b 1 lnδ + b 2 δ + b 3

[0103] According to the continuity and smoothness conditions, it is obtained that in the formula:

[0104]

[0105] In the formula: δ is the normal deformation of the asperity; δ cis the critical deformation amount for the elastic stage of the microconvex body to transform into the first elastoplastic stage; 6δ c is the critical deformation amount for the microconvex body in the first elastoplastic stage to transform into the second elastoplastic stage; δ p = 110δ c is the critical deformation amount for the microconvex body in the second elastoplastic stage to transform into the plastic stage; p e is the contact pressure of the microconvex body in the elastic stage; p ep1 is the contact pressure of the microconvex body in the first elastoplastic stage; p ep2 is the contact pressure of the microconvex body in the second elastoplastic stage; p p is the contact pressure of the microconvex body in the plastic stage.

[0106] Similarly, to solve the problem of discontinuity and non-smoothness in the existing contact area model, this paper proposes a polynomial based on the exponential function to represent the change curve of the contact pressure in the elastoplastic stage. The elastoplastic stage is divided into two segments, as Figure 4 shown. The exponential function polynomials in the form of: are used to fit the contact area curves in the two elastoplastic stages.

[0107] Using the exponential function polynomial in the form of to fit the contact area curves in the two elastoplastic stages; where: the exponential term c 1 e δ controls the basic shape of the fitting curve; the inverse proportional term is added to meet the smoothness condition; the constant term c 3 is added to meet the continuity condition, c 1 、c 2 and c 3 are undetermined coefficients.

[0108] The first elastoplastic deformation stage:

[0109] When δ c ≤δ≤6δ c :

[0110]

[0111] According to the continuity and smoothness conditions:

[0112] a e (δ c ) = a ep1 (δ c )

[0113] a ep1 (δ c ) = a ep2 (δ c )

[0114] aep2 (δ p ) = a p (δ p )

[0115] to obtain in the formula:

[0116]

[0117]

[0118] The second elastoplastic deformation stage:

[0119] When 6δ c ≤δ≤110δ c :

[0120]

[0121] Obtained according to the continuity and smoothness conditions, in the formula:

[0122]

[0123] (c) Fully plastic state

[0124] When the normal deformation amount is greater than the critical deformation amount δ p , that is, 110 times δ c , the asperity enters the fully plastic state. At this time, the average pressure in the contact area of the asperity is equal to the hardness of the softer material. The contact area a p and the average contact pressure p p The relationship with the normal deformation amount δ can be expressed as:

[0125] a p = 2πRδ

[0126] p p = H

[0127] (3) Finite element simulation verification of the analytical model for rough surface contact

[0128] A square rough surface is generated by a two-dimensional digital filtering method. The point cloud of the rough surface is generated by Matlab, and the point cloud matrix is imported into Solidworks for geometric modeling. The established geometric model of the rough surface is imported into the commercial finite element software ABAQUS to establish a finite element model of the rough surface contact analysis model. A Frictionless contact is added between the upper surface of the rough surface and the lower surface of the rigid plane, and a fixed constraint is added to the lower end of the rough surface model. Then, the finite element model is meshed, the lower end of the model is fixed, and the rough surface is compressed downward by the rigid plane to obtain the relationship between the normal contact load, the contact area and the deformation of the rough surface. The present invention simultaneously considers three contact states of full elasticity, elastoplasticity and full plasticity, and considers the evolution law of the plastic region in the elastoplastic state of the microconvex body. Analytical formulas of classical elastic contact and plastic contact are used for modeling in the full elastic deformation stage and the full plastic deformation stage respectively, which improves the reliability and accuracy of the modeling method, and further improves the accuracy of the calculation result of the normal contact stiffness of the rough surface.

[0129] (4) Modeling method for the normal contact analysis model of the rough surface

[0130] (a) Parameter calculation

[0131] Extract multiple two-dimensional topography curves in the x and y directions of the finite element model of the rough surface, calculate the statistical parameters of the topography curves, and obtain the Gaussian distribution function of the microconvex body. Substitute the statistical parameters of the rough surface topography curve into the following formula to calculate the equivalent and density of the microconvex body of the rough surface;

[0132]

[0133] where, R is the equivalent curvature radius at the top of the microconvex body, σ′ is the root mean square slope of the two-dimensional topography curve; σ″ is the root mean square curvature of the two-dimensional topography curve.

[0134]

[0135] where, ρ is the density of the microconvex body, σ′ is the root mean square slope of the two-dimensional topography curve, and σ″ is the root mean square curvature of the two-dimensional topography curve.

[0136] As a preferred implementation mode of the present invention, 5 two-dimensional topography curves in the x and y directions of the finite element model of the rough surface are extracted;

[0137] (b) Model establishment

[0138] Assume that the height of the microconvex body on the rough surface follows a Gaussian distribution, as Figure 5As shown, the maximum asperity height is 3σ. The total contact load of the rough surface is the sum of the contact areas and contact loads on all contacting asperities. Using the method of probability statistical analysis proposed in the GW model, for the contact area and contact load models of asperities with fully elastic, elastoplastic, and fully plastic deformations respectively, under a given normal approach d, by integrating in segments over the entire rough surface using the Gaussian distribution function according to the contact state of the asperities, the contact area and contact load of the entire rough surface can be obtained as follows:

[0139] Fully elastic deformation stage:

[0140] When 0 ≤ δ < δ c :

[0141]

[0142]

[0143] First elastoplastic deformation stage

[0144] When δ c ≤ δ < 6δ c :

[0145]

[0146]

[0147] Second elastoplastic deformation stage:

[0148] When 6δ c ≤ δ < 110δ c :

[0149]

[0150]

[0151] Fully plastic deformation stage:

[0152] When 110δ c ≤ δ < L:

[0153]

[0154]

[0155] Where: δ is the normal deformation of the asperity; δ c is the critical deformation at which the elastic stage of the asperity changes to the first elastoplastic stage; 6δ c is the critical deformation at which the asperity changes from the first elastoplastic stage to the second elastoplastic stage; δ p = 110δ cis the critical deformation amount when the microconvex body changes from the elastoplastic second stage to the plastic stage; the normal load f of the microconvex body = a·p; L is the height of the microconvex body, d is the normal approach amount, L - d = δ, and the normal deformation of the microconvex body is equal to the height of the microconvex body minus the normal approach amount, where L = 3σ, which is the maximum height of the microconvex body; g(z) is the Gaussian function; A is the actual contact area of the rough surface; F is the total contact load of the rough surface; N is the number of microconvex bodies on the rough surface; a e is the contact area of the microconvex body in the elastic stage; a ep1 is the contact area of the microconvex body in the first elastoplastic stage; a ep2 is the contact area of the microconvex body in the second elastoplastic stage; a p is the contact area of the microconvex body in the plastic stage; f e is the contact load of the microconvex body in the elastic stage; f ep1 is the contact load of the microconvex body in the first elastoplastic stage; f ep2 is the contact load of the microconvex body in the second elastoplastic stage; f p is the contact load of the microconvex body in the plastic stage.

[0156] In addition, the model designed in the present invention is analytical, with a simple form, and has characteristics such as reliability and high accuracy. It is beneficial to characterize the relationship between the normal contact load and contact area of the metal rough surface and the normal deformation, thereby improving the accuracy of the calculation result of the normal contact stiffness of the rough surface.

[0157] Based on the Gaussian distribution of the microconvex bodies on the rough surface, the present invention establishes a normal contact model of the rough surface by using the method of probability statistical analysis. Compared with other related models, the present invention avoids the Runge effect caused by high-order polynomial interpolation and the discontinuous and non-smooth problems when the contact state changes. At the same time, the model of the present invention is analytical, with a simple form, effectively solves the problem that when the microconvex bodies on the rough surface are severely deformed under a large load, ensures the accuracy of the normal contact stiffness of the rough surface and has a small error, and has important engineering application value in the field of dynamics of mechanical structures.

[0158] Perform finite element simulation verification on the analytical model of rough surface contact. The specific process is as follows: endow the finite element model of the analytical model of rough surface contact with material properties and boundary conditions, thereby perform simulation verification on the finite element model of the analytical model of rough surface contact, obtain the contact load and contact area of the rough surface, compare the analytical model of rough surface contact with the finite element model of the analytical model of rough surface contact, verify the accuracy of the analytical model of rough surface contact, and obtain the normal contact stiffness of the rough surface by analyzing the curves of the contact load and contact area of the analytical model of rough surface contact and the normal deformation.

[0159] A prediction system for considering the contact stiffness of a rough surface in the elastic-plastic state, including a model establishment module, a calculation module, and a simulation verification module;

[0160] The model establishment module is used to establish a finite element model of the normal contact of a single microconvex body, an analytical model of the normal contact of a single microconvex body, a finite element model of the analytical model of the rough surface contact, and an analytical model of the normal contact of the rough surface;

[0161] The calculation module is used to calculate the simulation results of the finite element of the normal contact of a single microconvex body and calculate the normal contact stiffness of the rough surface;

[0162] The simulation verification module is used to perform finite element simulation verification on the finite element model of the normal contact of a single microconvex body and perform finite element simulation verification on the analytical model of the rough surface contact.

[0163] The following gives a specific application example and verifies the effectiveness of the present invention in establishing an analytical model of rough surface contact and finite element simulation:

[0164] The first step: Modeling of the finite element model of the normal contact of a single microconvex body. Establish a finite element model of the contact between the microconvex body and the rigid plane. The microconvex body is a symmetric structure, and 1 / 4 of it is taken for modeling. The radius of the microconvex body is 6 μm, the material is hard aluminum alloy, the elastic modulus is 70 GPa, the Poisson's ratio is 0.3, and the yield strength is 300 Mpa. The finite element model is as Figure 6 shown. Constrain the degrees of freedom on the upper surface of the microconvex body, and apply an upward displacement boundary condition to the rigid plane to simulate the loading of the microconvex body. The yield evolution process of the microconvex body is as Figure 7 shown, and the simulation results of the finite element of the normal contact of a single microconvex body are calculated;

[0165] According to the finite element results, when the normal deformation reaches δ c , the microconvex body begins to produce plastic yield, and the plastic yield first occurs inside the microconvex body. When the normal deformation increases to 6δ c , the plastic yield region extends to the surface of the microconvex body. As the normal deformation continues to increase, the plastic yield region of the microconvex body gradually extends on the surface of the microconvex body. The contact area and contact pressure curves of the 1 / 4 microconvex body finite element model are as Figure 8 shown;

[0166] The second step: Modeling of the analytical model of the normal contact of a single microconvex body. Based on the polynomial of the natural logarithm function, characterize the relationship between the contact load and the normal deformation of the microconvex body in the elastic-plastic stage and determine the analytical expression. Combine the analytical expressions in the elastic stage and the plastic stage of the microconvex body to establish an analytical model of the normal contact of a single microconvex body, and compare the calculation results of the analytical model with the finite element simulation results of a single microconvex body. The contact area and normal contact pressure curves calculated by comparing the finite element model and the analytical model are asFigure 9 As shown, the calculation results of the analytical model are in good agreement with the finite element simulation results of a single microconvex body;

[0167] Step 3: Finite element simulation verification of the analytical model for rough surface contact. Figure 10 、 Figure 11 and Figure 12 Figure 0000529 shows the modeling process of the finite element model for rough surface contact. Matlab programming is used to simulate a rough surface with statistical characteristics. The generated rough surface point cloud matrix is imported into Solidworks to establish the geometric modeling of the rough surface, and the geometric model is imported into the commercial finite element software ABAQUS to establish the finite element model and assign material properties and boundary conditions to the model. The lower end of the model is fixed, and the rough surface is compressed downward by a rigid plane. From Figure 0000529, it can be seen that as the normal load increases, the number of microconvex bodies undergoing contact plastic deformation gradually increases. Summing up the contact states of each node on the contact surface of the finite element model, the relationship between the normal contact area, contact load, and deformation of the rough surface is obtained, as shown in Figure 0000530; Figure 13 As can be seen from Figure 0000529, as the normal load increases, the number of microconvex bodies undergoing contact plastic deformation gradually increases. Summing up the contact states of each node on the contact surface of the finite element model, the relationship between the normal contact area, contact load, and deformation of the rough surface is obtained, as shown in Figure 0000530; Figure 14 as shown;

[0168] Step 4: Modeling of the analytical model for normal contact of rough surfaces. Extract 5 two-dimensional topography curves in the x and y directions of the finite element rough surface respectively, calculate the statistical parameters of the two-dimensional topography curves and take the average to obtain the Gaussian distribution function of the microconvex bodies. Using the method of probability statistical analysis proposed in the GW model, the contact load and contact area models of microconvex bodies in complete elastic, elastoplastic deformation, and complete plastic deformation are respectively integrated in segments to the entire rough surface using the Gaussian distribution function to obtain the relationship between the contact load and normal deformation of the entire rough surface, and compare it with the finite element contact model of the rough surface, as shown in Figure 0000533. As can be seen from the figure, the analytical model for normal contact of rough surfaces of the present invention is in good agreement with the analytical model for contact state of rough surfaces (1 / 4FEM model), verifying the accuracy of the analytical model for normal contact of rough surfaces of the present invention. Figure 15 As shown in Figure 0000533, it can be seen from the figure that the analytical model for normal contact of rough surfaces of the present invention is in good agreement with the analytical model for contact state of rough surfaces (1 / 4FEM model), verifying the accuracy of the analytical model for normal contact of rough surfaces of the present invention.

[0169] Although the embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the above specific embodiments and application fields. The above specific embodiments are merely illustrative and guiding, rather than restrictive. Under the inspiration of the specification, those of ordinary skill in the art can also make many forms without departing from the scope protected by the claims of the present invention, and these all belong to the scope of protection of the present invention.

Claims

1. A prediction method for considering the contact stiffness of rough surfaces in elastic-plastic states, characterized in that, it includes, S1. Establish a finite element model for the normal contact of a single asperity. Through finite element simulation verification of the finite element model for the normal contact of a single asperity, calculate the simulation results of the finite element for the normal contact of a single asperity; S2. According to the finite element simulation results of the normal contact of a single asperity described in S1, determine the demarcation points of the fully elastic deformation stage, elastic-plastic deformation stage, and fully plastic deformation stage of the asperity; characterize the relationship between the contact load and the normal deformation amount in the elastic-plastic stage of the asperity through a polynomial of the natural logarithm function and determine the analytical expression, characterize the relationship between the contact area and the normal deformation amount in the elastic-plastic deformation stage of the asperity through a polynomial of the exponential function and determine the analytical expression, and combine the analytical expressions of the fully elastic deformation stage and the fully plastic deformation stage of the asperity to establish an analytical model for the normal contact of a single asperity; The expression of the polynomial of the natural logarithm function is: Using logarithmic terms to control the basic shape of the fitting curve; adding a linear term to meet the smoothness condition; adding a constant term to meet the continuity condition, 、 and being undetermined coefficients; The expression of the polynomial of the exponential function is: Using exponential terms to control the basic shape of the fitting curve; adding an inverse proportional term to satisfy the smoothness condition; adding a constant term to satisfy the continuity condition, 、 and are coefficients to be determined; S3. According to the finite element model for the normal contact of a single asperity described in S1, establish a finite element model for the analytical model of rough surface contact; S4. According to the analytical model for the normal contact of a single asperity described in S2 and the finite element model for the analytical model of rough surface contact in S3, establish an analytical model for the normal contact of a rough surface, including: Extract the two-dimensional topography curves in the x-axis and y-axis directions of the finite element model of the analytical model of rough surface contact, calculate the statistical parameters of the topography curves and take the average to obtain the Gaussian distribution function of the asperities, the equivalent asperities of the rough surface, and the density of the asperities; use the Gaussian distribution function of the asperities to integrate the contact load and contact area of the asperities in the fully elastic deformation stage, elastic-plastic deformation stage, and fully plastic deformation stage over the entire rough surface to obtain the relationship between the contact load and contact area of the entire rough surface and the normal deformation, and then combine the equivalent asperities and density of the rough surface to establish an analytical model for the normal contact of a rough surface; S5. Conduct finite element simulation verification on the analytical model for the normal contact of a rough surface described in S4 according to the finite element model for the analytical model of rough surface contact described in S3, obtain the contact load and contact area of the rough surface, and calculate and analyze to obtain the normal contact stiffness of the rough surface.

2. The prediction method for considering the contact stiffness of rough surfaces in elastic-plastic states according to claim 1, characterized in that, The specific process of establishing the finite element model for the normal contact of a single asperity described in S1 is: Establish a finite element model for the contact between an asperity and a rigid plane, constrain the degrees of freedom on the upper surface of the asperity, apply an upward displacement boundary condition to the rigid plane to simulate the loading of the asperity, obtain the change law of the contact state of a single asperity under normal load, and divide each contact interval according to the change law to obtain the finite element model for the normal contact of a single asperity.

3. The prediction method for considering the contact stiffness of rough surfaces in elastic-plastic states according to claim 1, characterized in that, The analytical expressions for the fully elastic deformation stage and the fully plastic deformation stage of the asperities described in S2 are determined using Hertz theory.

4. A prediction method for the contact stiffness of a rough surface considering the elastoplastic state according to claim 1, wherein, The finite element model for establishing the contact analytical model of the rough surface in S3 is as follows: Use Matlab programming to simulate and generate the point cloud matrix of the rough surface, import the generated point cloud matrix of the rough surface into Solidworks to establish the geometric model of the rough surface, and then import the geometric model of the rough surface into the commercial finite element software ABAQUS to establish the finite element model of the contact analytical model of the rough surface.

5. A prediction method for the contact stiffness of a rough surface considering the elastoplastic state according to claim 1, wherein, The contact load and contact area of the entire rough surface are calculated as follows: Fully elastic deformation stage: When then First elastoplastic deformation stage: When , Second elastoplastic deformation stage: When then Fully plastic deformation stage: When then Wherein: is the normal deformation of the asperity; is the critical deformation when the elastic stage of the asperity transforms into the first elastoplastic stage; is the critical deformation when the first elastoplastic stage of the asperity transforms into the second elastoplastic stage; is the critical deformation when the second elastoplastic stage of the asperity transforms into the plastic stage; the normal load of the asperity ; L is the height of the asperity, d is the normal approach; = i.e., the normal deformation of the asperity is equal to the height of the asperity minus the normal approach, where i.e., the maximum height of the asperity; is the Gaussian function; A is the actual contact area of the rough surface; F is the total contact load of the rough surface; N is the number of asperities on the rough surface; is the contact area of the asperity in the elastic stage; is the contact area of the asperity in the first elastoplastic stage; is the contact area of the asperity in the second elastoplastic stage; is the contact area of the asperity in the plastic stage; is the contact load of the asperity in the elastic stage; is the contact load of the asperity in the first elastoplastic stage; is the contact load of the asperity in the second elastoplastic stage; is the contact load of the asperity in the plastic stage.

6. A prediction method for the contact stiffness of a rough surface considering the elastoplastic state according to claim 1, wherein, The finite element simulation verification of the contact analytical model of the rough surface described in S5 is as follows: Assign material properties and boundary conditions to the finite element model of the contact analytical model of the rough surface, thereby performing simulation verification on the finite element model of the contact analytical model of the rough surface, obtaining the contact load and contact area of the rough surface, comparing the contact analytical model of the rough surface with the finite element model of the contact analytical model of the rough surface, verifying the accuracy of the contact analytical model of the rough surface, and obtaining the normal contact stiffness of the rough surface by analyzing the curves of the contact load and contact area of the contact analytical model of the rough surface versus the normal deformation.

7. A prediction system for the contact stiffness of a rough surface considering the elastoplastic state, wherein, Based on the prediction method described in any one of claims 1-6, it includes a model establishment module, a calculation module, and a simulation verification module; The model establishment module is used to establish a finite element model for the normal contact of a single asperity, an analytical model for the normal contact of a single asperity, a finite element model for the contact analytical model of the rough surface, and an analytical model for the normal contact of the rough surface; The calculation module is used to calculate the simulation results of the finite element for the normal contact of a single asperity and to calculate the normal contact stiffness of the rough surface; The simulation verification module is used to perform finite element simulation verification on the finite element model for the normal contact of a single asperity and to perform finite element simulation verification on the contact analytical model of the rough surface.

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