Method for calculating static friction coefficient of joint surface under microscopic contact

Abstract

The invention is applicable to the technical field of machine tool combination and assembly, and provides a method for calculating a static friction coefficient of a joint surface under microscopic contact, which comprises the following steps: acquiring surface characteristic parameters of a joint part; based on a fractal theory and an elastic theory, an equation of additional deformation of a matrix and normal deformation of the micro-convex body is constructed, and deformation geometric parameters of the single micro-convex body are established through microcosmic stress analysis; three deformation stages of the micro-convex body are considered, and the contact area and the contact load of the joint surface are obtained; integrating the real contact area and the contact load of the junction surface at different deformation stages by adopting the corrected island distribution function to obtain the real contact area and the contact load of the junction surface; and establishing a joint part surface static friction coefficient model by considering the influence of the contact surface characteristics on the static friction coefficient. According to the method, a surface static friction coefficient model is established from the microcosmic contact angle, and meanwhile, the interaction between a micro-convex body and a base body and the three stages of elasticity, elastoplasticity and complete plastic deformation of a material are considered.

Description

Technical Field

[0001] The invention belongs to the technical field of machine tool combination assembly, and in particular relates to a method for calculating the static friction coefficient of a combination surface under microscopic contact. Background Art

[0002] The friction coefficient of the joint surface not only affects the electrical conductivity and energy loss of the structure, but also affects the dynamic characteristics, stability and reliability of the structure. A higher static friction coefficient usually increases the friction heat and wear rate between the contact surfaces, thus affecting the service life of the parts. The static friction coefficient is a measure of whether an object is about to slide. For the fixed joint surface of a machine tool, once the joint part slips, the mechanical structure (precision) will fail, directly affecting the normal operation of the machine tool. For the ultra-precision / precision manufacturing field, the mechanical properties of its key components and the machining accuracy of the machine tool are related to the friction coefficient of the joint surface; at the same time, threaded connections in the machinery manufacturing industry account for more than 60% of all connection methods. Therefore, how to calculate the surface static friction coefficient of the bolted joint in the machine tool field is of great significance for the assembly of machine tools. Summary of the invention

[0003] The purpose of the embodiments of the present invention is to provide a method for calculating the static friction coefficient of a bonding surface under microscopic contact, aiming to solve the problems raised in the above-mentioned background technology.

[0004] The embodiment of the present invention is implemented as follows: a method for calculating the static friction coefficient of a bonding surface under microscopic contact comprises the following steps:

[0005] The surface profile data was obtained by a three-dimensional topography instrument, and the equivalent fractal dimension D and fractal roughness G of the bonding surface were calculated using the power spectrum density method.

[0006] Based on fractal theory and elasticity theory, the equations of additional deformation of the matrix and normal deformation of the micro-convex body are constructed. Through microscopic force analysis, the deformation geometric parameters of a single micro-convex body are established.

[0007] Considering the three deformation stages of the micro-convex body, the contact area and contact load of the bonding surface are obtained;

[0008] The modified island distribution function n(a′) is used to integrate the contact area and contact load of the bonding surface at different deformation stages to obtain the real contact area and contact load of the bonding surface.

[0009] Considering the influence of the static friction coefficient on the contact surface characteristics, a static friction coefficient model of the joint surface is established.

[0010] Preferably, the step of constructing the additional deformation equations of the matrix and the normal deformation equations of the micro-convex body based on the fractal theory and the elasticity theory, and establishing the deformation geometric parameters of the single micro-convex body through microscopic force analysis specifically includes:

[0011] According to the definition of the WM function, the convex body is a cosine wave shape, and the three-dimensional morphology is characterized by two dimensions as follows:

[0012]

[0013] In formula (1), r a is the radius of the microconvex cross section; γ is the profile frequency density;

[0014] Under the action of external normal load, the micro-convex body will deform and interact with the matrix. Its actual normal deformation is:

[0015]

[0016] In formula (2), m is the area factor; f is the normal load; A is the local deformation area of ​​the matrix; E is the equivalent Young's modulus;

[0017] The equivalent curvature radius R of the microconvex body satisfies the formula R 2 =(R-δ a ) 2 +r a 2 , since R>>r a , simplified to r a 2 =2Rδ a ;

[0018] When the elastic deformation transitions to the elastic-plastic deformation, the critical deformation Then the critical deformation cross-sectional area at this stage is a′ ec :

[0019]

[0020] When the elastic-plastic deformation transitions to complete plastic deformation, the critical deformation Then the critical deformation cross-sectional area at this stage is a′ pc :

[0021]

[0022] In equations (3) and (4), H is the material hardness and K is the hardness coefficient.

[0023] Preferably, the step of considering the three deformation stages of the micro-convex body to obtain the contact area and contact load of the bonding surface is specifically:

[0024] When the micro-convex body undergoes elastic deformation, according to Hertz theory, the elastic contact area a of a single micro-convex body is e and elastic contact load f e for:

[0025]

[0026] When the micro-convex body undergoes elastic-plastic deformation, the elastic-plastic contact area a of a single micro-convex body is ep and the elastic-plastic contact load f ep for:

[0027]

[0028] When the micro-convex body undergoes complete plastic deformation, the plastic contact area a of a single micro-convex body is p and plastic contact load f p for:

[0029] a p =2πRδ=a′ (9)

[0030] f p =Ha p (10).

[0031] Preferably, the step of integrating the contact area and contact load of the bonding surface at different deformation stages using the modified island distribution function n(a′) to obtain the true contact area and contact load of the bonding surface is to integrate equations (5)-(10) using the modified island distribution function n(a′) to obtain the true contact area A and contact load F of the bonding surface.

[0032] Preferably, the step of integrating equations (5)-(10) using the modified island distribution function n(a′) to obtain the actual contact area A and contact load F of the bonding surface is specifically:

[0033] When a′ satisfies a′ ec <a′<a′ l , a′ l is the maximum micro-contact cross-sectional area, the actual contact area of ​​the micro-convex body A e and contact load F e for:

[0034]

[0035] In formulas (11) and (12), a′ l is the maximum micro-contact cross-sectional area; λ is the interaction factor between the micro-convex body and the substrate;

[0036] When a′ satisfies a′ pc <a′<a′ ec , the actual contact area A of the micro-convex body ep and contact load F ep for:

[0037]

[0038]

[0039] in

[0040]

[0041] When a′ satisfies a′ pc <a′<a′ ec , the actual contact area A of the micro-convex body p and contact load F p for:

[0042]

[0043] From the above equations (11)-(16), the total real contact area A and contact load F of the joint surface can be established as:

[0044]

[0045] Preferably, the step of establishing a static friction coefficient model for the surface of the joint portion by considering the influence of the static friction coefficient on the contact surface characteristics is specifically as follows:

[0046] μ=(1-ξ)μ a +ξμ af +μ df (19)

[0047] In formula (19), ξ represents the percentage of contact area under the plowing effect of micro-convex body; μ a is the friction coefficient under the adhesion of micro-asperities, μ af is the friction coefficient under the action of micro-convex furrow, μ df is the friction coefficient under the action of abrasive plowing, which is expressed as follows:

[0048]

[0049] In equations (20)-(22), τ ai is the adhesion tangential load; S i H is the shear strength of the connecting material; i A is the hardness of the material; di is the contact area under the action of abrasive particles;

[0050] Substituting equations (17), (18) and (20)-(22) into equation (19) can obtain the true static friction coefficient of the joint surface.

[0051] An embodiment of the present invention provides a method for calculating the static friction coefficient of a bonding surface under microscopic contact. A surface static friction coefficient model is established from the perspective of microscopic contact, while considering the interaction between the micro-protrusions and the substrate and the three stages of elasticity, elastoplasticity and complete plastic deformation of the material. Based on fractal theory and Florida theory, a true static friction coefficient model of the bonding surface is derived, and the microscopic contact parameters are further refined, providing theoretical support for predicting the static friction coefficient of rough contact surfaces. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 An equivalent contact diagram of a single microconvex body provided by an embodiment of the present invention;

[0053] Figure 2 A macro-micro contact diagram of a bolted joint provided by an embodiment of the present invention;

[0054] Figure 3 A surface profile measurement result diagram provided by an embodiment of the present invention;

[0055] Figure 4 A power spectral density diagram of a combined surface provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0057] The specific implementation of the present invention is described in detail below in conjunction with specific embodiments.

[0058] A method for calculating the static friction coefficient of a bonding surface under microscopic contact comprises the following steps:

[0059] S1. Obtaining the surface characteristic parameters of the joint:

[0060] like Figure 2 As shown in Figure 1, the microscopic contact surface of the joint is in the form of peaks and valleys. The two connectors are actually in contact with each other through micro-convex bodies. The surface profile data of the connector is scanned by a three-dimensional topography instrument, as shown in Figure 1. Figure 3 As shown;

[0061] The fractal parameters D and G of the rough surface are calculated using the power spectral density method. The results are as follows: Figure 4 As shown;

[0062] S2. Modeling of geometric parameters of micro-convex deformation:

[0063] like Figure 1As shown, the contact between two micro-convex bodies is usually simplified to the contact between a rigid plane and a single micro-convex body. Based on fractal theory and elasticity theory, the deformation geometric parameters of the single micro-convex body can be obtained:

[0064]

[0065] In formula (2), m is the area factor; f is the normal load; A is the local deformation area of ​​the matrix; E is the equivalent Young's modulus;

[0066] The equivalent radius of curvature of the convex body is R, and the formula is R 2 =(R-δ a ) 2 +r a 2 , since R>>r a , which can be simplified to r a 2 =2Rδ a , the expression of R is:

[0067] When the elastic deformation transitions to the elastic-plastic deformation, the critical deformation Then the critical deformation cross-sectional area at this stage is a′ ec :

[0068]

[0069] When the elastic-plastic deformation transitions to complete plastic deformation, the critical deformation Then the critical deformation cross-sectional area at this stage is a′ pc :

[0070]

[0071] In equations (3) and (4), H is the material hardness; K is the hardness coefficient;

[0072] S3. Considering the three deformation stages of the micro-convex body, the real contact area and contact load model of the bonding surface is established:

[0073] When the micro-convex body undergoes elastic deformation, according to Hertz theory, the elastic contact area a of a single micro-convex body is e and elastic contact load f e for:

[0074]

[0075] When the micro-convex body undergoes elastic-plastic deformation, the elastic-plastic contact area a of a single micro-convex body is ep and the elastic-plastic contact load f ep for:

[0076]

[0077] When the micro-convex body undergoes complete plastic deformation, the plastic contact area a of a single micro-convex body is p and plastic contact load f p for:

[0078] a p =2πRδ=a′ (9)

[0079] f p =Ha p (10);

[0080] S4. Use the modified island distribution function n(a′) to integrate equations (5)-(10) to obtain the actual contact area A and contact load F of the bonding surface, specifically:

[0081] When a′ satisfies a′ ec <a′<a′ l , a′ l is the maximum micro-contact cross-sectional area, the actual contact area of ​​the micro-convex body A e and contact load F e for:

[0082]

[0083] In formulas (11) and (12), a′ l is the maximum micro-contact cross-sectional area; λ is the interaction factor between the micro-convex body and the substrate, λ x It can be written as Related to material properties and fractal parameters of the bonding surface;

[0084] When a′ satisfies a′ pc <a′<a′ ec , the actual contact area A of the micro-convex body ep and contact load F ep for:

[0085]

[0086]

[0087] in

[0088]

[0089] When a′ satisfies a′ pc <a′<a′ ec , the actual contact area A of the micro-convex body p and contact load F p for:

[0090]

[0091] From the above equations (11)-(16), the total real contact area A and contact load F of the joint surface can be established as:

[0092]

[0093] S5. Considering the influence of the static friction coefficient on the contact surface characteristics, the interaction between the micro-convex body and the substrate, the fragmentation effect and the plowing effect, as well as the contact load and the division of the contact area between different contact bodies, the Florida model is established as follows:

[0094] μ=(1-ξ)μ a +ξμ af +μ df (19)

[0095] In formula (19), ξ represents the percentage of contact area under the plowing effect of micro-convex body; μ a is the friction coefficient under the adhesion of micro-asperities, μ af is the friction coefficient under the action of micro-convex furrow, μ df is the friction coefficient under the action of abrasive plowing, which is expressed as follows:

[0096]

[0097] In equations (20)-(22), τ ai is the adhesion tangential load; S i H is the shear strength of the connecting material; i A is the hardness of the material; di is the contact area under the action of abrasive particles;

[0098] Substituting equations (17), (18) and (20)-(22) into equation (19) can obtain the true static friction coefficient of the joint surface.

[0099] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for calculating the static friction coefficient of a bonding surface under microscopic contact, characterized in that: The following steps are involved: The surface profile data was obtained by a three-dimensional topography instrument, and the equivalent fractal dimension D and fractal roughness G of the bonding surface were calculated using the power spectrum density method. Based on fractal theory and elasticity theory, the equations of additional deformation of the matrix and normal deformation of the micro-convex body are constructed. Through microscopic force analysis, the deformation geometric parameters of a single micro-convex body are established. Considering the three deformation stages of the micro-convex body, the contact area and contact load of the bonding surface are obtained; The modified island distribution function n(a′) is used to integrate the contact area and contact load of the bonding surface at different deformation stages to obtain the real contact area and contact load of the bonding surface. Considering the influence of the static friction coefficient on the contact surface characteristics, a static friction coefficient model of the joint surface is established.

2. The method for calculating the static friction coefficient of a bonding surface under microscopic contact according to claim 1, characterized in that: The steps of constructing additional deformation equations of the matrix and normal deformation equations of the micro-convex body based on fractal theory and elasticity theory, and establishing deformation geometric parameters of a single micro-convex body through microscopic force analysis specifically include: According to the definition of the WM function, the convex body is a cosine wave shape, and the three-dimensional morphology is characterized by two dimensions as follows: In formula (1), r a is the radius of the microconvex cross section; γ is the profile frequency density; Under the action of external normal load, the micro-convex body will deform and interact with the matrix. Its actual normal deformation is: In formula (2), m is the area factor; f is the normal load; A is the local deformation area of ​​the matrix; E is the equivalent Young's modulus; The equivalent curvature radius R of the microconvex body satisfies the formula R 2 =(R-δ a ) 2 +r a 2 , since R>>r a , simplified to r a 2 =2Rδ a ; When the elastic deformation transitions to the elastic-plastic deformation, the critical deformation Then the critical deformation cross-sectional area at this stage is a′ ec : When the elastic-plastic deformation transitions to complete plastic deformation, the critical deformation Then the critical deformation cross-sectional area at this stage is a′ pc : In equations (3) and (4), H is the material hardness and K is the hardness coefficient.

3. The method for calculating the static friction coefficient of the bonding surface under microscopic contact according to claim 2, characterized in that: The steps of considering the three deformation stages of the micro-convex body to obtain the contact area and contact load of the bonding surface are specifically as follows: When the micro-convex body undergoes elastic deformation, according to Hertz theory, the elastic contact area a of a single micro-convex body is e and elastic contact load f e for: When the micro-convex body undergoes elastic-plastic deformation, the elastic-plastic contact area a of a single micro-convex body is ep and the elastic-plastic contact load f ep for: When the micro-convex body undergoes complete plastic deformation, the plastic contact area a of a single micro-convex body is p and plastic contact load f p for: a p =2πRδ=a′ (9) f p =Ha p (10)。 4. The method for calculating the static friction coefficient of a bonding surface under microscopic contact according to claim 3, characterized in that: The step of integrating the contact area and contact load of the bonding surface at different deformation stages using the modified island distribution function n(a′) to obtain the true contact area and contact load of the bonding surface is to integrate equations (5)-(10) using the modified island distribution function n(a′) to obtain the true contact area A and contact load F of the bonding surface.

5. The method for calculating the static friction coefficient of a bonding surface under microscopic contact according to claim 4, characterized in that: The step of integrating equations (5)-(10) using the modified island distribution function n(a′) to obtain the actual contact area A and contact load F of the bonding surface is specifically as follows: When a′ satisfies a′ ec <a′<a′ l , a′ l is the maximum micro-contact cross-sectional area, the actual contact area of ​​the micro-convex body A e and contact load F e for: In formulas (11) and (12), a′ l is the maximum micro-contact cross-sectional area; λ is the interaction factor between the asperity and the matrix; When a′ satisfies a′ pc <a′<a′ ec , the actual contact area A of the micro-convex body ep and contact load F ep for: in When a′ satisfies a′ pc <a′<a′ ec , the actual contact area A of the micro-convex body p and contact load F p for: From the above equations (11)-(16), the total real contact area A and contact load F of the joint surface can be established as:

6. The method for calculating the static friction coefficient of a bonding surface under microscopic contact according to claim 5, characterized in that: The step of establishing the static friction coefficient model of the joint surface by considering the influence of the contact surface characteristics on the static friction coefficient is specifically as follows: μ=(1-ξ)μ a +xm af +m df (19) In formula (19), ξ represents the percentage of contact area under the plowing effect of micro-convex body; μ a is the friction coefficient under the adhesion of micro-asperities, μ af is the friction coefficient under the action of micro-convex furrow, μ df is the friction coefficient under the action of abrasive plowing, which is expressed as follows: In equations (20)-(22), τ ai is the adhesion tangential load; S i H is the shear strength of the connecting material; i A is the hardness of the material; di is the contact area under the action of abrasive particles; Substituting equations (17), (18) and (20)-(22) into equation (19) can obtain the true static friction coefficient of the joint surface.

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