Microscopic contact under the joint static friction coefficient calculation method

Abstract

The application is suitable for the technical field of machine tool combination assembly, and provides a micro contact joint surface static friction coefficient calculation method, which comprises the following steps: obtaining joint surface characteristic parameters; based on fractal theory and elastic theory, constructing base additional deformation and micro convex body normal deformation equation, through micro stress analysis, establishing single micro convex body deformation geometric parameters; considering three deformation stages of micro convex body, obtaining joint surface contact area and contact load; using modified island distribution function to integrate joint surface real contact area and contact load in different deformation stages, obtaining joint surface real contact area and contact load; considering the influence of static friction coefficient on contact surface characteristics, establishing joint surface static friction coefficient model. The application establishes surface static friction coefficient model from the micro contact angle, and simultaneously considers the interaction of micro convex body and base and three stages of material elastic, elastic-plastic and complete plastic deformation.

Description

Technical Field

[0001] This invention belongs to the field of machine tool assembly technology, and particularly relates to a method for calculating the static friction coefficient of mating surfaces under microscopic contact. Background Technology

[0002] The coefficient of friction at mating surfaces affects not only the electrical conductivity and energy loss of a structure, but also its dynamic characteristics, stability, and reliability. A higher coefficient of static friction typically increases frictional heat and wear rate between contact surfaces, thus affecting the service life of components. The coefficient of static friction is a measure of an object's impending slippage. For fixed mating surfaces in machine tools, slippage at the joint will cause mechanical structure (precision) failure, directly impacting the normal operation of the machine tool. In ultra-precision / precision manufacturing, the mechanical properties of key components and the machining accuracy of machine tools are related to the coefficient of friction at the mating surfaces. Furthermore, threaded connections account for over 60% of all connection methods in the machinery manufacturing industry. Therefore, calculating the surface static friction coefficient of bolted joints in machine tools is of great significance for machine tool assembly. Summary of the Invention

[0003] The purpose of this invention is to provide a method for calculating the static friction coefficient of a bonding surface under microscopic contact, thereby addressing the problems mentioned in the background art.

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

[0005] Surface contour data were obtained using a three-dimensional profilometer, and the equivalent fractal dimension D and fractal roughness G of the bonding surface were calculated using the power spectral density method.

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

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

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

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

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

[0011] According to the definition of the WM function, a micro-convex body has a cosine wave shape, and its three-dimensional morphology can be characterized in two dimensions as follows:

[0012]

[0013] In equation (1), r a γ is the cross-sectional radius of the micro-convex body; γ is the profile frequency density.

[0014] Under external normal load, the micro-protrusion will deform and interact with the matrix. Its actual normal deformation is as follows:

[0015]

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

[0017] The equivalent radius of curvature R of the micro-convex 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] The critical deformation amount when transitioning from elastic deformation to elastoplastic deformation The critical deformation cross-sectional area at this stage is a′ ec :

[0019]

[0020] The critical deformation amount when transitioning from elastoplastic deformation to fully plastic deformation The critical deformation cross-sectional area at this stage is a′ pc :

[0021]

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

[0023] Preferably, the step of considering the three deformation stages of the micro-protrusion to obtain the contact area and contact load of the mating surface specifically includes:

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

[0025]

[0026] When a micro-protrusion undergoes elastoplastic deformation, the elastoplastic contact area 'a' of a single micro-protrusion... ep and elastoplastic contact load f ep for:

[0027]

[0028] When a micro-protrusion undergoes complete plastic deformation, the plastic contact area 'a' of a single micro-protrusion 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 joint surface at different deformation stages using the modified island distribution function n(a′) to obtain the true contact area and contact load of the joint 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 joint 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 as follows:

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

[0034]

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

[0036] When a′ satisfies a′ pc <a′<a′ ec The actual contact area A of the micro-protrusion 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-protrusion p and contact load F p for:

[0042]

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

[0044]

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

[0046] μ=(1-ξ)μ a +ξμ af +μ df (19)

[0047] In equation (19), ξ represents the percentage of contact area under the micro-protrusion furrowing effect; μ a It is the coefficient of friction under the adhesion of micro-protrusions, μ af It is the coefficient of friction under the action of micro-protrusion furrows, μ df It is the coefficient of friction under the action of abrasive furrowing, specifically expressed as follows:

[0048]

[0049] In equations (20)-(22), τ ai For adhesive tangential load; S i H represents the shear strength of the connector material. i The hardness of the material; A di The contact area under the action of abrasive particles;

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

[0051] This invention provides a method for calculating the static friction coefficient of a mating surface under micro-contact conditions. It establishes a surface static friction coefficient model from the perspective of micro-contact, and considers the interaction between the micro-protrusion and the matrix, as well as the three stages of material elasticity, elastoplasticity, and complete plastic deformation. Based on fractal theory and Florida theory, it derives the true static friction coefficient model of the mating surface, further refining the micro-contact parameters and providing theoretical support for predicting the static friction coefficient of rough contact surfaces. Attached Figure Description

[0052] Figure 1 This is an equivalent contact diagram of a single micro-convexity provided in an embodiment of the present invention;

[0053] Figure 2 Macro-micro contact diagram of the bolted joint provided in an embodiment of the present invention;

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

[0055] Figure 4 The power spectral density diagram of the bonding surface provided in the embodiment of the present invention. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0057] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

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

[0059] S1. Obtain the surface feature parameters of the joint:

[0060] like Figure 2 As shown, the microscopic contact surface of the joint is in the form of peaks and valleys. The two connectors are actually in contact between micro-protrusions. The surface contour data of the connectors are scanned using a three-dimensional profilometer, as shown below. Figure 3 As shown;

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

[0062] S2. Modeling of geometric parameters for micro-convexity 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 geometry parameters of the single micro-convex body can be obtained:

[0064]

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

[0066] The equivalent radius of curvature of the micro-convexity is R, and it satisfies the formula R. 2 =(R-δ) a ) 2 +r a 2 Since R >> r a It can be simplified to r a 2 =2Rδ a The expression for R is:

[0067] The critical deformation amount when transitioning from elastic deformation to elastoplastic deformation The critical deformation cross-sectional area at this stage is a′ ec :

[0068]

[0069] The critical deformation amount when transitioning from elastoplastic deformation to fully plastic deformation 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-protrusion, establish a model of the actual contact area and contact load of the mating surface:

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

[0074]

[0075] When a micro-protrusion undergoes elastoplastic deformation, the elastoplastic contact area 'a' of a single micro-protrusion... ep and elastoplastic contact load f ep for:

[0076]

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

[0078] a p =2πRδ=a′ (9)

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

[0080] S4. Integrating equations (5)-(10) using the modified island distribution function n(a′) yields the actual contact area A and contact load F of the mating surface, specifically:

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

[0082]

[0083] In equations (11) and (12), a′ l λ is the maximum micro-contact cross-sectional area; λ is the interaction factor between the micro-protrusion and the substrate. x It can be written as It is related to material properties and fractal parameters of the interface;

[0084] When a′ satisfies a′ pc <a′<a′ ec The actual contact area A of the micro-protrusion 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-protrusion p and contact load F p for:

[0090]

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

[0092]

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

[0094] μ=(1-ξ)μ a +ξμ af +μ df (19)

[0095] In equation (19), ξ represents the percentage of contact area under the micro-protrusion furrowing effect; μ a It is the coefficient of friction under the adhesion of micro-protrusions, μ af It is the coefficient of friction under the action of micro-protrusion furrows, μ df It is the coefficient of friction under the action of abrasive furrowing, specifically expressed as follows:

[0096]

[0097] In equations (20)-(22), τ ai For adhesive tangential load; S i H represents the shear strength of the connector material. i The hardness of the material; A di The contact area under the action of abrasive particles;

[0098] Substituting equations (17), (18) and (20)-(22) into equation (19) yields 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 within 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, Includes the following steps: Surface contour data were obtained using a three-dimensional profilometer, and the equivalent fractal dimension D and fractal roughness G of the bonding surface were calculated using the power spectral density method. Based on fractal theory and elasticity theory, equations for the additional deformation of the matrix and the normal deformation of the micro-convex body are constructed. Through microscopic stress analysis, the deformation geometric parameters of a single micro-convex body are established. Considering the three deformation stages of the micro-protrusion, the contact area and contact load of the mating surface are obtained; Using a modified island distribution function By integrating the contact area and contact load of the joint surface at different deformation stages, the true contact area and contact load of the joint surface are obtained. Considering the influence of contact surface characteristics on the static friction coefficient, a model of the static friction coefficient of the joint surface is established; The steps involved in constructing equations for the additional deformation of the matrix and the normal deformation of the micro-convex body based on fractal theory and elasticity theory, and establishing the deformation geometric parameters of a single micro-convex body through microscopic stress analysis, specifically include: According to the definition of the WM function, a micro-convex body has a cosine wave shape, and its three-dimensional morphology can be characterized in two dimensions as follows: （1） In equation (1), It is the radius of the micro-convex body cross section; It is the profile frequency density; Under external normal load, the micro-protrusion will deform and interact with the matrix. Its actual normal deformation is as follows: （2） In equation (2), m It is a regional factor; It is the normal load; A is the local deformation area of ​​the matrix; E is the equivalent Young's modulus; The equivalent radius of curvature R of the micro-convex body satisfies the formula as follows: ,because Simplified to ; The critical deformation amount when transitioning from elastic deformation to elastoplastic deformation Then the critical deformation cross-sectional area at this stage is : （3） The critical deformation amount when transitioning from elastoplastic deformation to fully plastic deformation Then the critical deformation cross-sectional area at this stage is : （4） In equations (3) and (4), It refers to the hardness of the material; It is the hardness coefficient; The steps for considering the three deformation stages of the micro-protrusion and obtaining the contact area and contact load of the mating surface are as follows: When a micro-protrusion undergoes elastic deformation, the elastic contact area of ​​a single micro-protrusion can be determined according to Hertz's theory. and elastic contact load for: （5） （6） When a micro-protrusion undergoes elastoplastic deformation, the elastoplastic contact area of ​​a single micro-protrusion... and elastoplastic contact loads for: （7） （8） When a micro-protrusion undergoes complete plastic deformation, the plastic contact area of ​​a single micro-protrusion... and plastic contact load for: （9） （10）； The modified island distribution function is adopted. The step of integrating the contact area and contact load at different deformation stages to obtain the true contact area and contact load of the joint surface is used to apply the modified island distribution function. Integrating equations (5)-(10) yields the actual contact area of ​​the mating surfaces. and contact load ; The modified island distribution function is adopted. Integrating equations (5)-(10) yields the actual contact area of ​​the mating surfaces. and contact load The steps are as follows: when satisfy , It is the maximum micro-contact cross-sectional area, the actual contact area of ​​the micro-protrusion. and contact load for: （11） （12） In equations (11) and (12), It is the maximum micro-contact cross-sectional area; It is the interaction factor between the micro-protrusion and the matrix; when satisfy The actual contact area of ​​the micro-protrusion and contact load for: （13） （14） in , , , ; when satisfy The actual contact area of ​​the micro-protrusion and contact load for: （15） （16）； The total true contact area of ​​the mating surface can be established from the above equations (11)-(16). and contact load for: （17） （18）。 2. The method for calculating the static friction coefficient of the interface under microscopic contact according to claim 1, characterized in that, The steps for establishing a static friction coefficient model for the joint surface, considering the influence of contact surface characteristics on the static friction coefficient, are as follows: （19） In equation (19), This represents the percentage of contact area under the micro-protrusion furrowing effect; It is the coefficient of friction under the adhesion of micro-protrusions. It is the coefficient of friction under the action of micro-protrusion furrows. It is the coefficient of friction under the action of abrasive furrowing, specifically expressed as follows: （20） （21） （22） In equations (20)-(22), For adhesion tangential load; Shear strength of the connector material; The hardness of the material; The contact area under the action of abrasive particles; Substituting equations (17), (18) and (20)-(22) into equation (19) yields the true static friction coefficient of the joint surface.

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