阅读说明：本技术 一种粗糙表面重复加卸载接触的多尺度模型的建模方法 (Modeling method of multi-scale model of repeated loading and unloading contact of rough surface ) 是由 原园 杨凯 王嘉豪 翟赵凯 于 2021-06-03 设计创作，主要内容包括：本发明公开了一种粗糙表面重复加卸载接触的多尺度模型建模方法,包括如下步骤：步骤(1)基于三维WM函数仿真粗糙表面的生成；步骤(2)将两个粗糙表面的接触简化为刚性平板与等效粗糙表面的接触,获得单个微凸体的加、卸载接触模型；步骤(3)根据加卸载循环次数获得重复加卸载情况下的单个微凸体接触模型；步骤(4)根据面积分布函数获得完整粗糙表面分别在加、卸载时的接触力学模型,得出不同加卸载循环次数下的参数变化规律以及面积载荷关系；步骤(5)取不同粗糙度的实验试件进行重复加卸载实验。通过观察表面参数的变化,获得表面形貌在重复载荷下的变化规律。本发明对于机械零件在受到重复载荷情况下的表面失效的预测问题提出了理论指导。(The invention discloses a multi-scale model modeling method for repeated loading and unloading contact of a rough surface, which comprises the following steps: step (1) simulating generation of a rough surface based on a three-dimensional WM function; step (2) the contact of the two rough surfaces is simplified into the contact of a rigid flat plate and an equivalent rough surface, and an adding and unloading contact model of a single micro-convex body is obtained; step (3) obtaining a single microprotrusion contact model under the condition of repeated loading and unloading according to the loading and unloading cycle times; step (4) obtaining a contact mechanical model of the complete rough surface during loading and unloading respectively according to the area distribution function, and obtaining parameter change rules and area load relations under different loading and unloading circulation times; and (5) taking the test pieces with different roughness to perform repeated loading and unloading experiments. And obtaining the change rule of the surface morphology under the repeated load by observing the change of the surface parameters. The method provides theoretical guidance for the prediction problem of the surface failure of the mechanical part under the condition of repeated load.)

1. A multi-scale model modeling method for repeated loading and unloading contact of a rough surface is characterized by comprising the following steps:

step (1) simulating generation of a rough surface based on a three-dimensional WM function;

step (2) the contact of the two rough surfaces is simplified into the contact of a rigid flat plate and an equivalent rough surface, and an adding and unloading contact model of a single micro-convex body is obtained;

step (3) obtaining a single microprotrusion contact model under the condition of repeated loading and unloading according to the loading and unloading cycle times;

step (4) obtaining a contact mechanical model of the complete rough surface during loading and unloading respectively according to the area distribution function, obtaining different area load formulas according to different deformation stages, and obtaining parameter change rules and area load relations under different loading and unloading cycle times;

step 5, taking the test pieces with different roughness to carry out repeated loading and unloading experiments, and observing the surface appearance through a 3D Leica microscope; and calculating to obtain the change rule of the surface morphology parameters according to the morphology of the experimental test piece after each loading and unloading cycle is finished.

2. The method for constructing a multi-scale model of repeated loading and unloading of contact on a rough surface according to claim 1, wherein the step (1) is performed as follows:

the generation of the simulated rough surface z (x) by the WM function is given by equation (1):

in the formula (1), χ represents a displacement coordinate with the surface profile height z; d is the fractal dimension (1)<D<2) (ii) a G is a profile parameter; gamma is a frequency coefficient, and is 1.5 when the contour height of the rough surface generally follows normal distribution; n represents a frequency index, n_minIs the minimum frequency index;

elastic critical frequency index n_ecComprises the following steps:

first elastoplasticity critical frequency index n_epcComprises the following steps:

second elastoplasticity critical frequency index n_pcComprises the following steps:

in the formulas (2), (3) and (4), fix represents an integral part to be evaluated, K is a hardness coefficient, v is a poisson ratio of the material, K is 0.454+0.41v, H is the hardness of the material, E is an equivalent elastic modulus, G is a profile parameter, D is a fractal dimension, and γ is a frequency coefficient.

3. The method for constructing a multi-scale model of repeated loading and unloading of contact from a rough surface according to claim 1, wherein the step (2) is performed as follows:

(1) elastic critical deformation amount omega_necIs composed of

In the formula (5), K is a hardness coefficient, v is a Poisson's ratio of the material, and satisfies that K is 0.454+0.41v, H is the hardness of the material, E is an equivalent elastic modulus, and R is_nIs the curvature radius of the micro-convex body;

given deformationWhen the micro-convex body is elastically deformed, the contact area a corresponding to the load is loaded_nContact pressure F_nIs of the formula

In the formula (6), R_nIs the radius of curvature of the microprotrusion, omega_nE is the equivalent elastic modulus for the loading deformation;

corresponding contact area during unloadingContact pressure withIs of the formula

In the formula (7)In order to unload the amount of deformation,the radius of curvature at unloading, E is the equivalent modulus of elasticity,is the size of the base of the microprotrusion,is the contact area, D is the fractal dimension, and G is the scale parameter;

(2)when the micro-convex body is deformed, the micro-convex body is subjected to first elastic-plastic deformation;

corresponding contact pressure F during loading_nep1And contact area a_nep1Is composed of

In the formula (8), ω_nFor loading of deformation, ω_necIs an elastic critical deformation amount, F_necElastic critical contact load, a_necIs the elastic critical contact area;

corresponding contact pressure during unloadingAnd contact areaIs composed of

In formulae (9) and (10), ω is_nmaxFor loading of deformation, ω_nmaxIn order to load the amount of deformation,to unload the deformation, F_nmaxFor loading with deformation amount of omega_nmaxCorresponding contact load of_nmaxFor loading with deformation amount of omega_nmaxThe contact area is calculated by the formula (11), omega, for the first elastoplastic deformation of the microprotrusions_nresCalculating a formula (12) for the residual deformation;

in the formula (11), F_necAnd a_necRespectively, the elastic critical contact load and the elastic critical contact area, omega_necIs the elastic critical deformation amount, omega_nmaxIs the loading deformation;

residual deformation amount omega_nresAnd maximum deformation omega under load_nmaxIn a relationship of

In the formula (12), ω_nmaxFor loading of deformation, ω_nmaxIs the loading deformation;

radius of dischargeWith the original radius R_nIn a relationship of

E in the formula (13) is the elastic modulus, σ_yIs the yield strength, omega, of the material_necIs the elastic critical deformation amount, omega_nmaxIs the loading deformation;

then the microprotrusions undergo a second elasto-plastic deformation;

corresponding contact pressure F during loading_nep2And contact area a_nep2Is composed of

In formula (14), ω_nFor loading of deformation, ω_necIs an elastic critical deformation amount, F_necElastic critical contact load, a_necIs the elastic critical contact area;

the corresponding contact pressure and contact area in the unloading process are as follows:

in formulae (15) and (16), ω_nmaxIs the loading deformation; omega_nmaxIs the loading deformation;to unload the deformation, F_nmaxFor loading with deformation amount of omega_nmaxCorresponding contact load of_nmaxFor loading with deformation amount of omega_nmaxThe corresponding contact area is calculated as formula (17) for the micro-convex body with the second elastic-plastic deformation; omega_nresCalculating a formula (12) for the residual deformation;

(3)when in use, the microprotrusions are in plastic contact;

when the microprotrusions are plastically deformed, the corresponding contact pressure F during loading_npAnd contact area a_npIs composed of

F_np＝Ha_n，a_np＝2πR_nω_n (18)

In the formula (18), R_nIs the radius of curvature of the microprotrusion, omega_nIs the loading deformation; during unloading, there is no recovery process after the pressure is removed.

4. The method for constructing a multi-scale model of repeated loading and unloading of contact on a rough surface according to claim 1, wherein step 3 is performed as follows:

the first loading and unloading cycle is finished, and the residual deformation omega_nres1And residual radius of curvature R_u1；

In the formula (19), δ₁Is a first load deflection, ω_nres1Is the residual deformation at the end of the first loading, ω_necIs the elastic critical deformation;

in the formula (20), R₁Is the initial radius of curvature, E is the modulus of elasticity, σ_yIs the yield strength, omega, of the material_necIs an elastic critical deformation amount, δ₁Loading deformation for the first time;

the amount of deformation at the second loading is δ₂＝δ₁-ω_res1，ω_nres1The residual deformation at the end of the first loading;

the second loading and unloading cycle is finished and the residual deformation omega is_nres2The calculation method is formula (21), the residual curvature radius R_u2The calculation method is formula (22);

in the formula (21), δ₂For the second loading of the deformation, ω_necIs the elastic critical deformation;

in the formula (22), R_u1Is the radius of curvature at the end of the first loading and unloading, E is the modulus of elasticity, σ_yIs the yield strength, omega, of the material_necIs an elastic critical deformation amount, δ₂Loading the deformation for the second time;

after the third loading and unloading cycle is finished, the calculation methods are expressed by the formulas (15) and (16), and the calculation method of the contact area and the contact load in each loading and unloading cycle is the same as that in the first time.

5. The method for constructing the multi-scale model of the repeated loading and unloading contact of the rough surface as claimed in claim 1, wherein the step 4 is performed as follows:

the area density function formula is as follows (19)

In the formula (23), D is fractal dimension, M is coefficient, the calculation method is the formula (24), a_nlCorresponding to a maximum contact area among the plurality of asperities having a frequency index n;

formula (24)) In (a)_lThe maximum contact area of a single microprotrusion at any depression during surface contact, a_nlCorresponding to the maximum contact area of the plurality of microprotrusions having a frequency index n, n_minIs the minimum frequency index;

(1) the total real contact area during loading is

A_r3＝A_re+A_rep1+A_rep2 (25)

In the formula (25), D is fractal dimension, M is coefficient, a_nlCorresponding to the maximum contact area, a, of the plurality of microprotrusions having a frequency index n_necIs the elastic critical contact area;

total true contact load F_r3Is composed of

F_r3＝F_re+F_rep1+F_rep2 (26)

In the formula (26), D is fractal dimension, G is scale parameter, M is coefficient, K is hardness coefficient, and is related to Poisson ratio v of the material, wherein K is 0.454+0.41v, H is material hardness, a is_necIs an elastic critical contact area, a_nlCorresponding to a maximum contact area among the plurality of asperities having a frequency index n;

(2) true contact area during unloadingIs composed of

In the formula (27), n^u(a^u) As a function of the area distribution,corresponding to the maximum contact area among the plurality of microprotrusions having a frequency index n, D is the fractal dimension,the maximum contact area of the elastic deformation zone,is the first in the unloading processA maximum contact area of the elastic-plastic deformation zone,the largest contact area of the second elastic-plastic deformation area in the unloading process;

true contact loadIs a formula (28)

In the formula (28), K is a hardness coefficient, and is related to the poisson ratio v of the material, and satisfies that K is 0.454+0.41v, H is the hardness of the material, and ω is_necThe elastic critical deformation is the loading deformation omega_nmax，Andrespectively elastic, first elastic-plastic and second elastic-plastic contact pressure during unloading,for the unloading processThe largest contact area of the middle first elastic-plastic deformation zone,the largest contact area of the second elastic-plastic deformation area in the unloading process;

the contact area and the contact load are subjected to dimensionless treatment

(3) Under the condition of repeated loading and unloading, the area load relationship under different loading and unloading times is obtained through repeated loading and unloading.

6. The method for constructing a multi-scale model of repeated loading and unloading of contact of a rough surface as claimed in claim 1, wherein step 5 is performed as follows:

(1) taking different test pieces, namely an upper test piece made of 40Cr steel and a lower test piece made of 45 steel, wherein the roughness of the upper test piece is 0.04 mu m, and the roughness of the lower test piece is 0.4 mu m/0.8 mu m/1.0 mu m/1.2 mu m;

(2) applying a load to an upper test piece, wherein the upper surface of a lower test piece is an experimental surface, and observing the change of the surface appearance through a Leica microscope;

(3) obtaining a surface fractal dimension D and a contour characteristic scale coefficient G by adopting a structure function method;

(4) and drawing related images according to the parameters obtained by calculation, and proving the correctness of the theoretical model.

Technical Field

The invention belongs to the technical field of modeling of contact surfaces between mechanical parts under a microscale, and particularly relates to a multiscale model modeling method for repeatedly loading and unloading contact on a rough surface.

Background

The problem of surface contact has been a hot spot in tribology, in mechanical products, contact surfaces exist everywhere, and the force between the contact surfaces does not remain constant but fluctuates within a certain range, which results in repeated contact forces of rough surfaces. When the surfaces of the parts are continuously subjected to the action of contact force, the micro-protrusions on the surfaces are gradually sheared and ground, so that the surfaces of the parts are crushed and failed, and the performance condition and the service life of the parts are influenced. Starting from the research on the contact friction between single microprotrusions, the problem of contact of rough surfaces is solved, the relation between the mechanical properties of the contact surfaces and the surface characteristics of the contact surfaces is obtained, and the service life and the performance of the parts are improved by controlling the processing of the surfaces of the parts.

When a mechanical part is in a working process, the mechanical part is frequently subjected to repeated loading, for example, when a gear and a bearing are in a working state, the process of loading and unloading is carried out continuously, and therefore, the research on the relationship between the surface appearance and the loading and unloading times is very necessary.

At present, the contact research on rough surfaces is based on a statistical method or a fractal method to load the surfaces, and influences on contact areas, contact loads or contact rigidity are changed by changing the influences of different parameters, and when the loads on the surfaces are removed, influences on the mechanical properties of the surfaces are generated; but neglects the change of surface topography parameters of the surface under the condition of repeated loading and unloading.

Disclosure of Invention

Technical problem to be solved

The invention aims to research the change of the surface appearance and the change rule of parameters of a mechanical part under the condition of repeated load so as to solve one or more of the technical problems. The modeling method can apply the theoretical model calculation result to practical application, and further provides theoretical guidance for solving the problem of mechanical property change of mechanical parts under the condition of repeated load.

(II) technical scheme

In order to achieve the purpose, the invention is realized by the following technical scheme: a multi-scale model modeling method for repeated loading and unloading contact of a rough surface comprises the following steps:

step (1) simulating generation of a rough surface based on a three-dimensional WM function;

step (2) the contact of the two rough surfaces is simplified into the contact of a rigid flat plate and an equivalent rough surface, and an adding and unloading contact model of a single micro-convex body is obtained;

step (3) obtaining a single microprotrusion contact model under the condition of repeated loading and unloading according to the loading and unloading cycle times;

step (4) obtaining a contact mechanical model of the complete rough surface during loading and unloading respectively according to the area distribution function, obtaining different area load formulas according to different deformation stages, and obtaining parameter change rules and area load relations under different loading and unloading cycle times;

step 5, taking the test pieces with different roughness to carry out repeated loading and unloading experiments, and observing the surface appearance through a 3D Leica microscope; and calculating to obtain the change rule of the surface morphology parameters according to the morphology of the experimental test piece after each loading and unloading cycle is finished.

Preferably, the step (1) is performed as follows:

the generation of the simulated rough surface z (x) by the WM function is given by equation (1):

in the formula (1), χ represents a displacement coordinate with the surface profile height z; d is the fractal dimension (1)<D<2) (ii) a G is a profile parameter; gamma is a frequency coefficient, and is 1.5 when the contour height of the rough surface generally follows normal distribution; n represents a frequency index, n_minIs the minimum frequency index;

elastic critical frequency index n_ecComprises the following steps:

first elastoplasticity critical frequency index n_epcComprises the following steps:

second elastoplasticity critical frequency index n_pcComprises the following steps:

in the formulas (2), (3) and (4), fix represents an integral part to be evaluated, K is a hardness coefficient, v is a poisson ratio of the material, K is 0.454+0.41v, H is the hardness of the material, E is an equivalent elastic modulus, G is a profile parameter, D is a fractal dimension, and γ is a frequency coefficient.

3. The method for constructing a multi-scale model of repeated loading and unloading of contact from a rough surface according to claim 1, wherein the step (2) is performed as follows:

(1) elastic critical deformation amount omega_necIs composed of

In the formula (5), K is a hardness coefficient, v is a Poisson's ratio of the material, and satisfies that K is 0.454+0.41v, H is the hardness of the material, E is an equivalent elastic modulus, and R is_nIs the curvature radius of the micro-convex body;

given deformationWhen the micro-convex body is elastically deformed, the contact area a corresponding to the load is loaded_nContact pressure F_nIs of the formula

In the formula (6), R_nIs the radius of curvature of the microprotrusion, omega_nE is the equivalent elastic modulus for the loading deformation;

corresponding contact area during unloadingContact pressure withIs of the formula

In the formula (7)In order to unload the amount of deformation,the radius of curvature at unloading, E is the equivalent modulus of elasticity,is the size of the base of the microprotrusion,is the contact area, D is the fractal dimension, and G is the scale parameter;

(2)when the micro-convex body is deformed, the micro-convex body is subjected to first elastic-plastic deformation;

corresponding contact pressure F during loading_nep1And contact area a_nep1Is composed of

In the formula (8), ω_nTo loadAmount of deformation, ω_necIs an elastic critical deformation amount, F_necElastic critical contact load, a_necIs the elastic critical contact area;

corresponding contact pressure during unloadingAnd contact areaIs composed of

In formulae (9) and (10), ω is_nmaxFor loading of deformation, ω_nmaxIn order to load the amount of deformation,to unload the deformation, F_nmaxFor loading with deformation amount of omega_nmaxCorresponding contact load of_nmaxFor loading with deformation amount of omega_nmaxThe contact area is calculated by the formula (11), omega, for the first elastoplastic deformation of the microprotrusions_nresCalculating a formula (12) for the residual deformation;

in the formula (11), F_necAnd a_necRespectively, the elastic critical contact load and the elastic critical contact area, omega_necIs the elastic critical deformation amount, omega_nmaxIs the loading deformation;

residual deformation amount omega_nresAnd maximum deformation omega under load_nmaxIn a relationship of

In the formula (12), ω_nmaxFor loading of deformation, ω_nmaxIs the loading deformation;

radius of dischargeWith the original radius R_nIn a relationship of

E in the formula (13) is the elastic modulus, σ_yIs the yield strength, omega, of the material_necIs the elastic critical deformation amount, omega_nmaxIs the loading deformation;

then the microprotrusions undergo a second elasto-plastic deformation;

corresponding contact pressure F during loading_nep2And contact area a_nep2Is composed of

In formula (14), ω_nFor loading of deformation, ω_necIs an elastic critical deformation amount, F_necElastic critical contact load, a_necIs the elastic critical contact area;

the corresponding contact pressure and contact area in the unloading process are as follows:

in formulae (15) and (16), ω_nmaxIs the loading deformation; omega_nmaxIs the loading deformation;to unload the deformation, F_nmaxFor loading with deformation amount of omega_nmaxCorresponding contact load of_nmaxFor loading with deformation amount of omega_nmaxThe corresponding contact area is calculated as formula (17) for the micro-convex body with the second elastic-plastic deformation; omega_nresCalculating a formula (12) for the residual deformation;

(3)when in use, the microprotrusions are in plastic contact;

when the microprotrusions are plastically deformed, the corresponding contact pressure F during loading_npAnd contact area a_npIs composed of

F_np＝Ha_n，a_np＝2πR_nω_n (18)

In the formula (18), R_nIs the radius of curvature of the microprotrusion, omega_nIs the loading deformation; during unloading, there is no recovery process after the pressure is removed.

Preferably, step 3 is performed as follows:

the first loading and unloading cycle is finished, and the residual deformation omega_nres1And residual radius of curvature R_u1；

In the formula (19), δ₁Is a first load deflection, ω_nres1For the end of the first loadingAmount of residual deformation of, omega_necIs the elastic critical deformation;

in the formula (20), R₁Is the initial radius of curvature, E is the modulus of elasticity, σ_yIs the yield strength, omega, of the material_necIs an elastic critical deformation amount, δ₁Loading deformation for the first time;

the amount of deformation at the second loading is δ₂＝δ₁-ω_res1，ω_nres1The residual deformation at the end of the first loading;

the second loading and unloading cycle is finished and the residual deformation omega is_nres2The calculation method is formula (21), the residual curvature radius R_u2The calculation method is formula (22);

in the formula (21), δ₂For the second loading of the deformation, ω_necIs the elastic critical deformation;

in the formula (22), R_u1Is the radius of curvature at the end of the first loading and unloading, E is the modulus of elasticity, σ_yIs the yield strength, omega, of the material_necIs an elastic critical deformation amount, δ₂Loading the deformation for the second time;

after the third loading and unloading cycle is finished, the calculation methods are expressed by the formulas (15) and (16), and the calculation method of the contact area and the contact load in each loading and unloading cycle is the same as that in the first time.

Preferably, step 4 is performed as follows:

the area density function formula is as follows (19)

In the formula (23), D is fractal dimension, M is coefficient, the calculation method is the formula (24), a_nlCorresponding to a maximum contact area among the plurality of asperities having a frequency index n;

in the formula (24), a_lThe maximum contact area of a single microprotrusion at any depression during surface contact, a_nlCorresponding to the maximum contact area of the plurality of microprotrusions having a frequency index n, n_minIs the minimum frequency index;

(1) the total real contact area during loading is

A_r3＝A_re+A_rep1+A_rep2 (25)

In the formula (25), D is fractal dimension, M is coefficient, a_nlCorresponding to the maximum contact area, a, of the plurality of microprotrusions having a frequency index n_necIs the elastic critical contact area;

total true contact load F_r3Is composed of

F_r3＝F_re+F_rep1+F_rep2 (26)

In the formula (26), D is fractal dimension, G is scale parameter, M is coefficient, K is hardness coefficient, and is related to Poisson ratio v of the material, wherein K is 0.454+0.41v, H is material hardness, a is_necIs an elastic critical contact area, a_nlCorresponding to a maximum contact area among the plurality of asperities having a frequency index n;

(2) true contact area during unloadingIs composed of

In the formula (27), n^u(a^u) As a function of the area distribution,corresponding to the largest of the plurality of microprotrusions having a frequency index of nThe contact area, D is the fractal dimension,the maximum contact area of the elastic deformation zone,for the largest contact area of the first elastoplastic deformation zone during unloading,the largest contact area of the second elastic-plastic deformation area in the unloading process;

true contact loadIs a formula (28)

In the formula (28), K is a hardness coefficient, and is related to the poisson ratio v of the material, and satisfies that K is 0.454+0.41v, H is the hardness of the material, and ω is_necThe elastic critical deformation is the loading deformation omega_nmax，Andrespectively elastic, first elastic-plastic and second elastic-plastic contact pressure during unloading,for the largest contact area of the first elastoplastic deformation zone during unloading,the largest contact area of the second elastic-plastic deformation area in the unloading process;

the contact area and the contact load are subjected to dimensionless treatment

(3) Under the condition of repeated loading and unloading, the area load relationship under different loading and unloading times is obtained through repeated loading and unloading.

Preferably, step 5 is performed as follows:

(1) taking different test pieces, namely an upper test piece made of 40Cr steel and a lower test piece made of 45 steel, wherein the roughness of the upper test piece is 0.04 mu m, and the roughness of the lower test piece is 0.4 mu m/0.8 mu m/1.0 mu m/1.2 mu m;

(2) applying a load to an upper test piece, wherein the upper surface of a lower test piece is an experimental surface, and observing the change of the surface appearance through a Leica microscope;

(3) obtaining a surface fractal dimension D and a contour characteristic scale coefficient G by adopting a structure function method;

(4) and drawing related images according to the parameters obtained by calculation, and proving the correctness of the theoretical model.

Has the advantages that:

a three-dimensional anisotropic rough surface is generated through Matlab software simulation, a fractal method is used, the specific deformation state of a single micro-convex body on the surface during loading and unloading is analyzed, a mechanical contact model for repeated loading and unloading of the single micro-convex body is established, the area density distribution function is used for expanding the mechanical contact model to the complete surface, and the mechanical contact model of the complete surface under the repeated loading and unloading condition is obtained. And obtaining the change rule of the surface morphology under the repeated load by observing the change of the surface parameters. The method provides theoretical guidance for the prediction problem of the surface failure of the mechanical part under the condition of repeated load.

Drawings

FIG. 1 is a rough surface generated by a three-dimensional WM function simulation of the present invention;

FIG. 2 illustrates the loading of a single microprotrusion according to the invention; (b) a schematic diagram of individual microprotrusion unloading;

FIG. 3 is a schematic view of the present invention illustrating repeated loading and unloading;

FIG. 4 is a schematic diagram of variations in microprotrusion parameters in an embodiment of the present invention;

FIG. 5 is a graph showing the variation of the area load relationship in an embodiment of the present invention;

FIG. 6 shows the real surface topography of the test piece with different roughness (a), (b), (c) and (d) according to the experiment of the present invention;

FIG. 7 is a graph showing the surface topography profile of the test pieces (a), (b), (c) and (d) with different roughness measured by the experiment of the present invention;

FIG. 8 is (a) a change rule of curvature radius of a micro-convex body on the surface of a test piece with the roughness of 0.4 μm measured by experiments; (b) the change rule of the height of the micro-convex body on the surface of the test piece with the roughness of 0.4 mu m is shown.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Referring to fig. 1-8, the present invention provides a technical solution for establishing a mechanical contact model of a rough surface under repeated loading and unloading conditions.

Referring to fig. 4 and 5, the parameters according to the embodiment of the present invention are: fractal dimension D2.4, G1.36 × 10^-11m, as shown in fig. 4(a), is a single microprotrusion when n is 19The parameters of the body are changed under ten loading and unloading cycles, at the moment, the frequency index of the microprotrusions is smaller than the elastic critical frequency index, only elastic deformation occurs, and after the loading and unloading are finished, the shapes of the microprotrusions are completely recovered, so that the heights and the curvature radii of the microprotrusions do not change along with the increase of the loading and unloading times. Fig. 4(b) is a variation rule of a single microprotrusion body when n is 35, where the frequency index of the microprotrusion body is in an elastic-plastic critical deformation range, the height of the microprotrusion body gradually decreases and the curvature radius gradually increases with the increase of the loading and unloading times, and the variation of the parameters gradually slows about ten times, which may be regarded as the microprotrusion body reaching a stable state; FIG. 5(a) shows n_min＝5,n_maxWhen the load is 23, the area of the rough surface is mainly elastically deformed, and under the same load, the contact area of the rough surface is not changed along with the change of the loading and unloading times; FIG. 5(b) shows n_min＝30,n_maxThe area load relationship of the rough surface is 60, the elastic-plastic deformation mainly occurs, the contact area under the same load is gradually increased along with the increase of the loading and unloading times, but after the tenth time, the area change is not obvious, and the stable state is considered to be achieved;

the invention is further improved in that the correctness of the theoretical model is verified through experiments:

taking an upper test piece material which is 40Cr steel, a lower test piece material which is 45 steel, wherein the roughness of the upper test piece is 0.04 mu m, the roughness of the lower test piece is 0.4 mu m/0.8 mu m/1.0 mu m/1.2 mu m, the sampling length is 2500 mu m, the processing methods are grinding, and the thermal treatment is hardening and tempering; FIG. 6 shows the surface topography of the test pieces under different conditions;

by applying load to the upper test piece, the surface of the lower test piece is an experimental surface, and observing the change of the surface appearance through a Leica microscope, as shown in FIG. 7, the change of the height of the surface profile is shown, and the surface profile basically does not change after ten times of loading and unloading, and reaches a stable state at the moment;

the fractal dimension D of the surface with the roughness of 0.4 mu m is 2.455 and the scale parameter G is 3.02 multiplied by 10 by adopting a root mean square method^{- 9}m, the frequency index range of the microprotrusions is 13-25; surface fractal dimension D of 0.8 μm roughness 2.415, rulerDegree parameter G is 3.57 multiplied by 10^-7m, the frequency index range of the microprotrusions is 14-27; roughness 1.0 μm surface fractal dimension D2.381, scale parameter G5.52 × 10^-7m, the frequency index range of the microprotrusions is 16-33; surface fractal dimension D of 1.2 μm 2.346 and scale parameter G of 1.61 × 10^-6m, the frequency index range of the microprotrusions is 17-37;

and drawing a related image according to an experimental result to obtain a surface topography profile and a change rule of a parameter of the microprotrusion, as shown in fig. 8, it can be seen that the height change of the microprotrusion is opposite to the curvature radius along with the increase of the loading and unloading times, and fig. 8 takes a test piece with the surface roughness of 0.4 μm as an example, and the surface topography change trends of other roughnesses are the same.

The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element. Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.