A micro-nanoscale friction and wear prediction method

Abstract

The present invention discloses a method for predicting micro- and nano-scale friction and wear. The method comprises: establishing a finite element model, wherein the finite element model is a friction and wear model consisting of a substrate and a sliding body, wherein the sliding body is in sliding contact with the top surface of the substrate; setting boundary conditions for the finite element model, fixing the degrees of freedom of the bottom edge of the substrate, controlling the contact and sliding process between the sliding body and the substrate using displacement, and adding an adhesion force field between the sliding body and the substrate; performing calculations using finite element software according to a set step size, determining the adhesion force based on the relative spacing between the sliding body and the substrate, determining the stress state of the friction and wear region on the substrate surface based on the adhesion force, and calculating the wear amount of the contact region in the current analysis step based on the stress state; and looping through step three until the calculation is complete. The above-described prediction method achieves wear prediction at the micro- and nano-scale, resolving the problem of existing finite element simulation methods that lack consideration of wear due to adhesion.

Description

Technical Field

[0001] The present invention relates to the technical field of friction and wear, and in particular to a method for predicting friction and wear at a micro-nano scale. Background Art

[0002] With the increasing integration and miniaturization of electronic and mechanical components, tribological issues caused by surface and size effects are becoming increasingly prominent. Particularly at the micro- and nanoscale, as device dimensions decrease and specific surface area increases, surface forces and surface effects become the dominant factors affecting the performance and service life of micro- and nano-devices. For example, in micro- and nano-electromechanical systems (such as microgears and micromotors), wear between moving parts is a major cause of system failure. Numerous studies have shown that adhesion is a primary factor contributing to the stability, surface damage, and failure of micro- and nano-devices, directly determining system reliability and lifespan.

[0003] To better study the effects of adhesion, Bradley proposed the first model to consider adhesive contact, which was subsequently followed by the development of the famous Derjaguin-Muller-Toporov (DMT) model and the Johnson-Kendall-Robert (JKR) model. Tabor proposed the dimensionless parameter μ to study the conversion of pullout forces between the DMT model (μ < 0.1) and the JKR model (μ > 3). Furthermore, Maugis used the Dugdale approximation to provide a smooth transition between the DMT and JKR solutions and proposed the MD (Maugis-Dugdale) model. Essentially, the surface interactions considered in the JKR, DMT, and MD theories are simplifications of the Lennard-Jones (LJ) potential, leading Greenwood et al. to model surface adhesion using the LJ potential. In addition to analytical models of adhesive contact, many researchers have also employed numerical methods such as the finite element method to study adhesive contact processes. Kadin et al. used the finite element method and the LJ potential to analyze adhesive contact between a rigid surface and an elastoplastic sphere. Song et al. studied the sudden instability phenomenon during adhesive contact by constructing a virtual nonlinear spring in the finite element model.

[0004] Archard's wear law states that the volume removed by wear is proportional to the applied load and the sliding distance. It is widely applied to both macroscopic and microscopic systems. The finite element method (FEM) is widely used to simulate the wear behavior of materials, and the classic Archard's wear law has long been used to study the wear properties of materials. Combining the FEM with the Archard's wear law can effectively predict material wear behavior.

[0005] Currently, friction and wear models that account for adhesion at the micro- and nanoscale are incomplete, and conducting large-scale, accurate experimental measurements at this scale is extremely difficult. Therefore, it is necessary to consider the effects of adhesion in friction and wear simulations and predictions at this scale. Although existing theoretical models have provided valuable insights into adhesive contact, they only examine the results under normal adhesion, making them difficult to directly apply to stick-slip contacts. To address this issue, a finite element model for stick-slip contact, distinct from previous studies, has been proposed that accounts for tangential forces during the stick-slip process. However, existing stick-slip contact models based on the LJ potential do not account for wear during sliding, making it difficult to assess the interaction between wear and adhesion during sliding. Stick-slip processes are often accompanied by material wear, making it important to consider the effects of van der Waals forces on wear. Regarding wear, although the Archard wear model is a classic adhesive wear model, existing studies have not incorporated the intermolecular forces between contacting surfaces during wear. Furthermore, it is difficult to account for microscopic interfacial adhesion interactions in wear simulations based on macroscopic continuum mechanics finite element methods. Since the adhesion caused by van der Waals forces at the micro-nanoscale cannot be ignored, the existing wear simulation methods need to be improved in order to solve the problem of predicting the wear process considering adhesion at the micro-nanoscale. Summary of the Invention

[0006] In view of this, the present invention provides a micro-nanoscale friction and wear prediction method, which realizes wear prediction at the micro-nanoscale and solves the problem of wear that lacks consideration of adhesion effect in existing finite element simulation methods.

[0007] The present invention adopts the following specific technical solutions:

[0008] A micro-nanoscale friction and wear prediction method, the friction and wear prediction method comprising the following steps:

[0009] Step 1: Establish a finite element model. The finite element model is a friction and wear model consisting of a substrate and a sliding body. The sliding body is in sliding contact with the top surface of the substrate, and a wear area is established in the sliding contact area of ​​the substrate.

[0010] Step 2: Setting boundary conditions for the finite element model, fixing the degrees of freedom of the bottom edge of the substrate, controlling the contact and sliding process between the sliding body and the substrate using displacement, adding an adhesion force field between the sliding body and the substrate, and generating adhesion force at the interface between the sliding body and the substrate through the adhesion force field, so that there is a relative distance between the interface between the sliding body and the substrate;

[0011] Step 3: Use finite element software to perform calculations according to the set step size, determine the adhesion force based on the relative distance between the sliding body and the substrate, determine the stress state of the friction and wear area on the substrate surface based on the adhesion force, and calculate the wear amount of the contact area in the current analysis step based on the stress state;

[0012] Step 4: Repeat step 3 until all analysis steps are completed.

[0013] Furthermore, in step 3, based on the adhesion force model per unit area during sliding proposed by the Lennard-Jones potential function and the continuity law, the adhesion force is determined according to the relative distance between the sliding body and the substrate. The functional relationship between the adhesion force per unit area p(D) and the relative distance D is:

[0014]

[0015] In the above formula, Δγ is the adhesion work, ε is the equilibrium distance between atoms, D is the relative distance between the slider and the substrate, and R is the radius of the slider.

[0016] Furthermore, in step 3, when the stress state of the friction and wear region on the substrate surface is determined based on the adhesion force, the stress σ(x) generated by the adhesion of the sliding body at point x on the substrate is:

[0017]

[0018] In the above formula, F(x)adhesion is the adhesion force of the sliding body on the substrate at point x, and A(x) is the effective contact area between the sliding body and the substrate at point x.

[0019] Furthermore, in step 3, when calculating the wear volume of the contact area in the current analysis step based on the stress state, the Archard wear model is used to represent the wear volume V between the sliding body and the substrate as:

[0020]

[0021] In the above formula, K is the wear coefficient, F is the adhesion force between the sliding body and the substrate, S is the sliding distance, and H is the material hardness;

[0022] The wear depth h between the sliding body and the substrate is:

[0023]

[0024] In the above formula, A is the effective contact area between the sliding body and the substrate;

[0025] Then the wear depth Δh(x) of the sliding body at point x on the substrate is:

[0026]

[0027] In the above formula, ΔS is the sliding distance of the sliding body along the substrate in each analysis step.

[0028] Beneficial effects:

[0029] The micro-nanoscale friction and wear prediction method of the present invention adds an adhesion force field between the sliding body and the substrate when setting the boundary conditions of the finite element model, forms an adhesion force between the interface of the sliding body and the substrate through the adhesion force field, determines the stress state of the friction and wear area on the surface of the substrate according to the adhesion force, and calculates the wear amount of the contact area in the current analysis step according to the stress state; when adopting the friction and wear prediction method of the present invention, an adhesion force field is added between the sliding body and the substrate, and the influence of the adhesion force on the friction and wear is taken into account. Therefore, the friction and wear prediction method realizes wear prediction at the micro-nanoscale, and solves the problem of lack of consideration of wear due to adhesion in existing finite element simulation methods.

[0030] The above-mentioned micro-nanoscale friction and wear prediction method introduces the Lennard-Jones potential function into the finite element through the continuity law and combines it with the macroscopic Archard wear law to realize the adhesion wear prediction at the micro-nanoscale, and realizes the combination of the macroscopic Archard wear theory and the adhesion contact effect based on the microscopic Lennard-Jones potential function, which makes up for the shortcomings of the existing finite element model in micro-nanoscale wear simulation and solves the problem that the existing finite element simulation method lacks consideration of wear due to adhesion.

[0031] The above-mentioned micro-nanoscale friction and wear prediction method can calculate the change of friction coefficient in the friction and wear process considering the adhesion effect, which makes up for the deficiency of providing friction coefficient in most contact friction processes simulated by finite element. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 This is a flow chart of the micro-nanoscale friction and wear prediction method of the present invention;

[0033] Figure 2 Schematic diagram of the principle structure of the finite element model used in the micro-nanoscale friction and wear prediction method of the present invention;

[0034] Figure 3 This is the normal stress contour of the substrate during the friction and wear process considering the adhesion effect;

[0035] Figure 4 This is the shear stress contour of the substrate during the friction and wear process considering the adhesion effect;

[0036] Figure 5The friction force curve of the sliding body during the friction and wear process considering the adhesion effect;

[0037] Figure 6 This is the normal force curve of the sliding body during the friction and wear process considering the adhesion effect;

[0038] Figure 7 The friction coefficient curve during the friction and wear process considering the adhesion effect;

[0039] Figure 8 Wear calculation results for the friction and wear process considering adhesion.

[0040] Among them, 1-base, 2-sliding body, 3-wear area DETAILED DESCRIPTION

[0041] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0042] The embodiment of the present invention provides a method for predicting friction and wear at micro-nano scale, such as Figure 1 As shown, the friction and wear prediction method includes the following steps:

[0043] Step 1 S1, establish a finite element model, such as Figure 2 As shown, the finite element model is a friction and wear model consisting of a substrate 1 and a sliding body 2. The sliding body 2 is in sliding contact with the top surface of the substrate 1, and a wear area 3 is established in the sliding contact area of ​​the substrate 1. The sliding body 2 slides in the direction of arrow A.

[0044] Step 2 S2, setting boundary conditions of the finite element model, fixing the degrees of freedom of the bottom edge of the substrate 1, using displacement to control the contact and sliding process between the sliding body 2 and the substrate 1, adding an adhesion force field P between the sliding body 2 and the substrate 1, and generating an adhesion force at the interface between the sliding body 2 and the substrate 1 through the adhesion force field, with a relative distance D between the interface between the sliding body 2 and the substrate 1;

[0045] Step 3 S3, using finite element software to perform calculations according to a set step size, determining the adhesion force based on the relative distance between the sliding body 2 and the substrate 1, determining the stress state of the friction and wear area 3 on the surface of the substrate 1 based on the adhesion force, and calculating the wear amount of the contact area in the current analysis step based on the stress state;

[0046] When determining the adhesion force based on the relative distance between the sliding body 2 and the substrate 1, the adhesion force per unit area model during sliding is proposed based on the Lennard-Jones potential function and the continuity law. The functional relationship between the adhesion force per unit area p(D) and the relative distance D is:

[0047]

[0048] In the above formula, Δγ is the adhesion work, ε is the interatomic equilibrium distance, D is the relative distance between the slider 2 and the substrate 1, and R is the radius of the slider 2;

[0049] When the stress state of the friction and wear area 3 on the surface of the substrate 1 is determined based on the adhesion force, the stress σ(x) generated by the adhesion of the sliding body 2 at the point x of the substrate 1 is:

[0050]

[0051] In the above formula, F(x)adhesion is the adhesion force of the sliding body 2 at point x on the substrate 1, and A(x) is the effective contact area between the sliding body 2 and the substrate 1 at point x;

[0052] When calculating the wear volume of the contact area in the current analysis step based on the stress state, the Archard wear model is used to express the wear volume V between the sliding body 2 and the substrate 1 as:

[0053]

[0054] In the above formula, K is the wear coefficient, F is the adhesion force between the sliding body 2 and the substrate 1, S is the sliding distance, and H is the material hardness;

[0055] The wear depth h between the sliding body 2 and the substrate 1 is:

[0056]

[0057] In the above formula, A is the effective contact area between the sliding body 2 and the substrate 1;

[0058] Then the wear depth Δh(x) of the sliding body 2 at the base point 1x is:

[0059]

[0060] In the above formula, ΔS is the sliding distance of the sliding body 2 along the substrate 1 in each analysis step;

[0061] Step 4 S4, loop through step 3 until all analysis steps are completed. The calculation results are as follows: Figure 3-8 As shown:

[0062] according to Figure 3 The obtained normal stress cloud map of substrate 1 during the friction and wear process considering adhesion can be obtained. The maximum dimensionless normal stress S during the friction and wear process considering adhesion is: 22 / (Δγ / ε) is 4.347;

[0063] according to Figure 4The obtained shear stress cloud map of substrate 1 during the friction and wear process considering adhesion can be obtained. The maximum dimensionless shear stress S during the friction and wear process is 12 / (Δγ / ε) is 1.034;

[0064] according to Figure 5 The friction force curve of the sliding body 2 during the friction and wear process considering the adhesion effect can be obtained. Under the conditions of λ = 0.172 and y / ε = 0, the dimensionless steady-state friction force is 0.12, where: λ is the Maugis constant, y is the distance from the lowest point of the sliding body 2 to the surface of the substrate 1;

[0065] according to Figure 6 The obtained normal force curve of the sliding body 2 during the friction and wear process considering the adhesion effect can be obtained. Under the conditions of λ = 0.172 and y / ε = 0, the dimensionless steady-state normal force is 3.13;

[0066] according to Figure 7 The obtained friction coefficient curve in the friction and wear process considering the adhesion effect can be obtained. Under the conditions of λ = 0.172 and y / ε = 0, the dimensionless steady-state friction coefficient is 0.04;

[0067] according to Figure 8 The wear calculation results of the friction and wear process considering adhesion effect were obtained under the conditions of λ=0.172 and y / ε=0.

[0068] When setting the boundary conditions of the finite element model, the above-mentioned micro-nanoscale friction and wear prediction method adds an adhesion force field between the sliding body 2 and the substrate 1, and forms an adhesion force between the interface of the sliding body 2 and the substrate 1 through the adhesion force field. The stress state of the friction and wear area 3 on the surface of the substrate 1 is determined according to the adhesion force, and the wear amount of the contact area in the current analysis step is calculated according to the stress state. When using the friction and wear prediction method of the present invention, an adhesion force field is added between the sliding body 2 and the substrate 1, and the influence of the adhesion force on friction and wear is taken into account. Therefore, the friction and wear prediction method realizes wear prediction at the micro-nanoscale, and solves the problem of lack of consideration of wear due to adhesion in existing finite element simulation methods.

[0069] The above-mentioned micro-nanoscale friction and wear prediction method introduces the Lennard-Jones potential function into the finite element through the continuity law and combines it with the macroscopic Archard wear law to realize the adhesion wear prediction at the micro-nanoscale, and realizes the combination of the macroscopic Archard wear theory and the adhesion theory based on the microscopic Lennard-Jones potential function, which makes up for the shortcomings of the existing finite element model in micro-nanoscale wear simulation and solves the problem that the existing finite element simulation method lacks consideration of wear due to adhesion.

[0070] The above-mentioned micro-nanoscale friction and wear prediction method can calculate the change of friction coefficient in the friction and wear process considering the adhesion effect, which makes up for the deficiency of providing friction coefficient in most contact friction processes simulated by finite element.

[0071] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A micro-nanoscale friction and wear prediction method, characterized in that: The following steps are involved: Step 1: Establish a finite element model. The finite element model is a friction and wear model consisting of a substrate and a sliding body. The sliding body is in sliding contact with the top surface of the substrate, and a wear area is established in the sliding contact area of ​​the substrate. Step 2: Setting boundary conditions for the finite element model, fixing the degrees of freedom of the bottom edge of the substrate, controlling the contact and sliding process between the sliding body and the substrate using displacement, adding an adhesion force field between the sliding body and the substrate, and generating adhesion force at the interface between the sliding body and the substrate through the adhesion force field, so that there is a relative distance between the interface between the sliding body and the substrate; Step 3: Use finite element software to perform calculations according to the set step size. Determine the adhesion force based on the relative distance between the sliding body and the substrate. Determine the stress state of the friction and wear area on the substrate surface based on the adhesion force. Calculate the wear volume of the contact area in the current analysis step based on the stress state. Use the Archard wear model to represent the wear volume V between the sliding body and the substrate as: In the above formula, K is the wear coefficient, F is the adhesion force between the sliding body and the substrate, S is the sliding distance, and H is the material hardness; The wear depth h between the sliding body and the substrate is: In the above formula, A is the effective contact area between the sliding body and the substrate; Then the wear depth Δh(x) of the sliding body at point x on the substrate is: In the above formula, ΔS is the sliding distance of the sliding body along the substrate in each analysis step, F(x)adhesion is the adhesion force of the sliding body at point x on the substrate, A(x) is the effective contact area between the sliding body and the substrate at point x, and σ(x) is the stress generated by the adhesion of the sliding body at point x on the substrate. Step 4: Repeat step 3 until all analysis steps are completed.

2. The micro-nanoscale friction and wear prediction method according to claim 1, characterized in that: In step 3, the adhesion force per unit area during sliding is determined based on the relative distance between the sliding body and the substrate, based on the Lennard-Jones potential function and the continuity law. The functional relationship between the adhesion force per unit area p(D) and the relative distance D is: In the above formula, Δγ is the adhesion work, ε is the equilibrium distance between atoms, D is the relative distance between the slider and the substrate, and R is the radius of the slider.

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