A bolt loosening test analysis method and system

Abstract

The application discloses a bolt loosening test analysis method, comprising: obtaining the surface topography parameters of the pressure bearing surface of a bolt connection structure; calculating the fractal parameters according to the obtained surface topography parameters of the pressure bearing surface; calculating the static friction coefficient of the pressure bearing surface according to the obtained surface topography parameters of the pressure bearing surface; performing a tensile test on the bolt connection structure, analyzing the residual pre-tightening force of the bolt connection structure, and obtaining the influence law of the static friction coefficient of the pressure bearing surface on bolt loosening. The application considers the influence of the static friction coefficient of the bolt connection pressure bearing surface on the loosening of the bolt connection structure, introduces a domain expansion factor and a micro-convex body elastic-plastic deformation stage to modify the three-dimensional fractal theory, deduces a joint surface static friction coefficient model, and analyzes the loosening trend of the bolt connection structure under the action of a cyclic load through the static friction coefficient model. The bolt connection loosening is analyzed by considering the friction coefficient of the pressure bearing surface, which is more in line with the actual working condition, and a new method is provided for the bolt connection structure loosening research under the actual working condition.

Description

Technical Field

[0001] This invention relates to a bolt loosening test analysis method and system based on a fractal model of the static friction coefficient of the bearing surface, belonging to the field of bolt loosening research. Background Technology

[0002] As is well known, bolted connections are simple, reliable, and easy to install and remove, and are widely used in various assemblies. However, in actual operation, bolted connections are subject to various load impacts that can cause bolts to loosen. Loose bolts can prevent the bolted structure from functioning properly, and in severe cases, can lead to incalculable consequences. Therefore, studying bolt loosening is crucial.

[0003] Currently, most methods for studying bolt loosening involve directly applying cyclic loads without considering the coefficient of friction. However, the coefficient of friction has a significant impact on bolted connections. Therefore, it is essential to consider the static friction coefficient of the bearing surface when conducting research on bolt loosening. Summary of the Invention

[0004] This invention aims to at least solve one of the technical problems existing in the prior art. To this end, this invention provides a bolt loosening test analysis method based on a fractal model of the static friction coefficient of the bearing surface, aiming to provide a new method for predicting the loosening of bolted connections under load in practical work.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a bolt loosening test analysis method, comprising the following steps: obtaining the surface morphology parameters of the bearing surface of the bolt connection structure; calculating the fractal parameters based on the obtained surface morphology parameters of the bearing surface; calculating the static friction coefficient of the bearing surface based on the obtained surface morphology parameters of the bearing surface; conducting a tensile test on the bolt connection structure, analyzing the residual preload of the bolt connection structure, and obtaining the influence law of the static friction coefficient of the bearing surface on bolt loosening.

[0006] The bolt loosening test analysis method, preferably, involves obtaining the surface morphology parameters of the bearing surface of the bolt connection structure by scanning the connector and nut with a NANOWEA three-dimensional non-contact surface morphology instrument to obtain the surface morphology parameters of the connector and nut under different surface roughnesses, and exporting them as TXT format files.

[0007] The bolt loosening test analysis method, preferably, involves calculating the fractal parameters based on the obtained surface morphology parameters of the bearing surface by importing the exported TXT format file into MATLAB and using the structure function method to calculate the fractal parameters.

[0008] The bolt loosening test analysis method, preferably, includes the following steps in calculating the static friction coefficient of the bearing surface based on the obtained surface morphology parameters: calculating the total normal contact load of the mating surface; calculating the total tangential contact load of the mating surface; establishing a three-dimensional fractal static friction coefficient model based on the calculated total normal contact load and total tangential contact load of the mating surface; and substituting the calculated fractal parameters into the established three-dimensional fractal static friction coefficient model to calculate the static friction coefficient of the bearing surface.

[0009] The bolt loosening test analysis method, preferably, involves calculating the total normal contact load of the mating surface as follows: The normal contact load of a single micro-protrusion in the elastic phase is expressed as:

[0010] In the formula, E Indicates the elastic modulus; R Indicates the curvature of a single micro-convexity; This represents the normal deformation of a single micro-convex body; The total normal contact load of the elastic stage of the interface can be obtained by integrating the single micro-protrusion over the critical cross-sectional area:

[0011] In the formula, D Indicates fractal dimension; G Indicates the scaling factor; Representation field expansion factor; The size parameter representing the spectral density; This represents the theoretical contact area of ​​a single micro-protrusion; The critical normal deformation amount representing the elastic and elastoplastic deformation of a single micro-protrusion; The critical cross-sectional area for elastic deformation and elastoplastic deformation of a single micro-protrusion; This represents the critical cross-sectional area for elastic deformation of a single micro-convex body; The normal contact load of a single micro-protrusion during the plastic forming stage is expressed as:

[0012]

[0013] In the formula, Y Indicates yield strength; The total normal contact load during the plastic stage of the interface can be obtained by integrating the individual micro-protrusion over the critical cross-sectional area:

[0014] In the formula, This represents the critical normal deformation amount of an individual micro-protrusion in terms of elastoplastic and plastic deformation. The critical cross-sectional area representing the elastoplastic and plastic deformation of a single micro-protrusion; This represents the size distribution function of the contact points of the micro-protrusion; The normal contact load of a single micro-protrusion in the elastoplastic stage is expressed as:

[0015] In the formula, These represent coefficients related to material properties and fractal parameters of the interface. , v Poisson's ratio; The total normal contact load in the elastoplastic stage of the interface can be obtained by integrating the single micro-protrusion over the critical cross-sectional area:

[0016] Therefore, the total normal contact load on the interface is expressed as: .

[0017] The bolt loosening test analysis method, preferably, involves calculating the total tangential contact load at the mating surface using the following method: The tangential contact load in the elastic stage is expressed as:

[0018] in:

[0019]

[0020] In the formula, This represents the maximum shear stress. The tangential contact load in the elastoplastic stage is expressed as:

[0021] in:

[0022]

[0023] Therefore, the total tangential contact load at the mating surface is expressed as: .

[0024] The bolt loosening test analysis method, preferably, uses a three-dimensional fractal static friction coefficient model as follows: .

[0025] The bolt loosening test analysis method, preferably, involves performing a tensile test on the bolted connection structure to analyze the residual preload and obtain the influence of the static friction coefficient of the bearing surface on bolt loosening. Specifically, this includes the following steps: fixing the bolted connection structure on a fatigue tensile testing machine; applying cyclic load tensile testing with the tightening torque as a control variable, recording the change in residual preload under tangential cyclic load, and establishing the relationship between the residual preload and different static friction coefficients of the bearing surface, thus obtaining the influence of the static friction coefficient of the bearing surface on bolt loosening when the tightening torque is the same; applying cyclic load tensile testing with the preload as a control variable, recording the change in residual preload under tangential cyclic load, and establishing the relationship between the residual preload and different static friction coefficients of the bearing surface, thus obtaining the influence of the static friction coefficient of the bearing surface on bolt loosening when the preload is the same.

[0026] The bolt loosening test analysis method, preferably, when the tightening torque is the same, the influence law of the static friction coefficient of the bearing surface on bolt loosening is as follows: the residual clamping force of the bolt connection structure under tangential contact load is negatively correlated with the static friction coefficient of the bearing surface. The smaller the static friction coefficient of the bearing surface, the greater the initial preload, and the better the anti-loosening effect of the bolt connection. When the preload is the same, the influence of the static friction coefficient of the bearing surface on bolt loosening is as follows: the residual clamping force of the bolt connection structure under tangential contact load is positively correlated with the static friction coefficient of the bearing surface. The larger the static friction coefficient of the bearing surface, the better the anti-loosening effect of the bolt connection.

[0027] Secondly, the present invention provides a bolt loosening test analysis system, comprising: a first processing unit for acquiring surface morphology parameters of the bearing surface of the bolted connection structure; a second processing unit for calculating fractal parameters based on the acquired surface morphology parameters of the bearing surface; a third processing unit for calculating the static friction coefficient of the bearing surface based on the acquired surface morphology parameters of the bearing surface; and a fourth processing unit for conducting a tensile test on the bolted connection structure, analyzing the residual preload of the bolted connection structure, and obtaining the influence law of the static friction coefficient of the bearing surface on bolt loosening.

[0028] The present invention has the following advantages due to the adoption of the above technical solutions: This invention addresses bolted connection structures, considering the influence of the static friction coefficient of the bearing surface on the loosening of the bolted connection. By introducing a domain expansion factor and modifying the three-dimensional fractal theory based on the elastoplastic deformation stage of micro-protrusions, a static friction coefficient model for the mating surface is derived. This static friction coefficient model is then used to analyze the loosening trend of bolted connections under cyclic loading. Considering the friction coefficient of the bearing surface in analyzing the loosening of bolted connections is more consistent with actual working conditions, providing a new method for studying the loosening of bolted connection structures under actual working conditions. Attached Figure Description

[0029] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts. In the drawings: Figure 1 This is a flowchart illustrating the implementation of a bolt loosening test analysis method according to an embodiment of the present invention. Figure 2 The loosening curves of three different surface roughness connectors under the same torque; Figure 3 The diagram shows the loosening curves of three connectors with different surface roughnesses when the preload is the same. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0031] In the description of this invention, it should be noted that the terms "upper", "lower", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the system or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0032] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "assembly," "setup," and "connection" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0033] The following is a detailed description of a bolt loosening test analysis method and system provided by an embodiment of the present invention, with reference to the accompanying drawings.

[0034] Example 1: Please see Figure 1 This embodiment provides a bolt loosening test analysis method, which includes the following steps: S100. Obtain the surface morphology parameters of the bearing surface of the bolted connection structure; In this embodiment, the connector and nut (which together form the bearing surface of the bolted connection structure) can be scanned using a NANOWEA three-dimensional non-contact surface profilometer to obtain the surface profiling parameters of the connector and nut under different surface roughnesses, and then exported as TXT format files.

[0035] S200. Calculate the fractal parameters based on the obtained surface morphology parameters of the bearing surface; In this embodiment, the exported TXT format file is imported into MATLAB, and the fractal parameters are calculated using the structure function method.

[0036] S300. Calculate the static friction coefficient of the bearing surface based on the obtained surface morphology parameters. The specific process is as follows: S301. Calculate the total normal contact load at the mating surface: Micro-protrusions undergo three deformation stages: elastic, plastic, and elastoplastic. By dividing the contact area of ​​the micro-protrusion deformation, the normal contact load of the micro-protrusion in each stage is calculated, providing a basis for calculating the total contact load of the mating surface.

[0037] The normal contact load of a single micro-protrusion in the elastic stage can be expressed as:

[0038] In the formula, E Indicates the elastic modulus; R Indicates the curvature of a single micro-convexity; This represents the normal deformation of a single micro-convex body; The total normal contact load of the elastic stage of the interface can be obtained by integrating the single micro-protrusion over the critical cross-sectional area:

[0039] In the formula, D Indicates fractal dimension; G Indicates the scaling factor; Representation field expansion factor; The size parameter representing the spectral density; This represents the theoretical contact area of ​​a single micro-protrusion; The critical normal deformation amount representing the elastic and elastoplastic deformation of a single micro-protrusion; The critical cross-sectional area for elastic deformation and elastoplastic deformation of a single micro-protrusion; This represents the critical cross-sectional area for elastic deformation of a single micro-convex body; The normal contact load of a single micro-protrusion during the plastic forming stage can be expressed as:

[0040]

[0041] In the formula, Y Indicates yield strength; The total normal contact load during the plastic stage of the interface can be obtained by integrating the individual micro-protrusion over the critical cross-sectional area:

[0042] In the formula, This represents the critical normal deformation amount of an individual micro-protrusion in terms of elastoplastic and plastic deformation. The critical cross-sectional area representing the elastoplastic and plastic deformation of a single micro-protrusion; This represents the size distribution function of the contact points of the micro-protrusion; The normal contact load in the elastoplastic stage can be expressed as:

[0043] In the formula, These represent coefficients related to material properties and fractal parameters of the interface. , v This is Poisson's ratio, with a value of 0.29; The total normal contact load in the elastoplastic stage of the interface can be obtained by integrating the single micro-protrusion over the critical cross-sectional area:

[0044] Therefore, the total normal contact load on the bonding surface can be expressed as: ; S302. Calculate the total tangential contact load at the mating surface: When a micro-forehead has undergone plastic deformation, it will undergo plastic flow under normal loads and will no longer be able to withstand tangential loads. Therefore, it is unnecessary to consider the plastic deformation stage when calculating the tangential load on a micro-forehead.

[0045] The tangential contact load in the elastic stage can be expressed as:

[0046] in:

[0047]

[0048] In the formula, This represents the maximum shear stress. The tangential contact load in the elastoplastic stage can be expressed as:

[0049] in:

[0050]

[0051] Therefore, the total tangential contact load at the mating surface can be expressed as: ; S303. Based on the calculated total normal contact load and total tangential contact load of the mating surface, a three-dimensional fractal static friction coefficient model is established as follows: ; S304. Substitute the fractal parameters obtained in step S200 into the established three-dimensional fractal static friction coefficient model to calculate the static friction coefficient of the bearing surface.

[0052] S400. Tensile tests are conducted on bolted connections to analyze the residual preload and determine the influence of the static friction coefficient of the bearing surface on bolt loosening. The specific process includes the following steps: S401. Fix the bolted connection structure onto the fatigue tensile testing machine; S402. Using the tightening torque as a control variable, perform cyclic load stretching, record the change of residual preload in the bolted connection structure under tangential cyclic load, and establish the relationship between residual preload and static friction coefficient of different bearing surfaces. This will reveal the influence of static friction coefficient of bearing surfaces on bolt loosening when the tightening torque is the same. S403. Using the preload as a control variable, apply cyclic load tension, record the change in residual preload of the bolted connection structure under tangential cyclic load, and establish the relationship between residual preload and static friction coefficient of different bearing surfaces. This will reveal the influence of the static friction coefficient of the bearing surface on bolt loosening when the preload is the same.

[0053] The bolt loosening test analysis method provided in Embodiment 1 above will be further illustrated below through a specific example.

[0054] Step 1: Use NANOWEA 3D non-contact surface profilometer to scan and obtain the surface profilometry parameters of three types of connectors (hereinafter referred to as N1, N2, and N3) and nuts with surface roughness of 0.2, 2.4, and 4.4 respectively, and export them as TXT format files.

[0055] Step 2: Import the above TXT file into MATLAB, and use the structure function method to calculate the fractal parameters. The fractal parameters are shown in the table below:

[0056] Step 3: Substitute the fractal parameters into the established three-dimensional fractal static friction coefficient model to calculate the static friction coefficient of the bearing surface, as shown in the table below:

[0057] Step 4: Fix the bolted connection structure on a fatigue tensile testing machine and subject it to cyclic loading. Record the change in preload under tangential cyclic loading. This experiment is divided into two parts: the effect of the static friction coefficient of the bearing surface on bolt loosening when the tightening torque is the same, and the effect of the static friction coefficient of the bearing surface on bolt loosening when the preload is the same. The test parameters of the fatigue tensile testing machine were set as follows: lateral displacement 0.3 mm, frequency 10 Hz, 3000 cycles. A customized ring pressure sensor was used to record the change in preload in real time. The test results are attached. Figure 2 and attached Figure 3 As shown, the results indicate that when tightening torque is used as the control variable, the residual clamping force of the bolt under tangential contact load is negatively correlated with the static friction coefficient of the bearing surface. The smaller the static friction coefficient of the bearing surface, the larger the initial preload, and the better the anti-loosening effect of the bolt connection. Conversely, when preload is used as the control variable, the residual clamping force of the bolt under tangential contact load is positively correlated with the static friction coefficient of the bearing surface. The larger the static friction coefficient of the bearing surface, the better the anti-loosening effect of the bolt connection.

[0058] Example 2: The above-described embodiment 1 provides a bolt loosening test analysis method. Correspondingly, this embodiment provides a bolt loosening test analysis system. The bolt loosening test analysis system provided in this embodiment can implement the bolt loosening test analysis method of embodiment 1. This system can be implemented through software, hardware, or a combination of both. For example, the system may include integrated or separate functional modules or units to execute the corresponding steps in the methods of embodiment 1. Since the bolt loosening test analysis system of this embodiment is basically similar to the method embodiment, the description process of this embodiment is relatively simple. Relevant details can be found in the description of embodiment 1. The bolt loosening test analysis system of this embodiment is merely illustrative.

[0059] The bolt loosening test analysis system provided in this embodiment includes: The first processing unit is used to obtain the surface morphology parameters of the bearing surface of the bolted connection structure. The second processing unit is used to calculate the fractal parameters based on the obtained surface morphology parameters of the bearing surface of the bolted connection structure. The third processing unit is used to calculate the static friction coefficient of the bearing surface; The fourth processing unit is used to conduct tensile tests on bolted connection structures, analyze the residual preload of bolted connection structures, and obtain the influence law of static friction coefficient of bearing surface on bolt loosening.

[0060] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for analyzing bolt loosening during testing, characterized in that, Includes the following steps: Obtain the surface morphology parameters of the bearing surface of the bolted connection structure; The fractal parameters are calculated based on the obtained surface morphology parameters of the bearing surface; The static friction coefficient of the bearing surface is calculated based on the obtained surface morphology parameters of the bearing surface. Tensile tests were conducted on bolted connections to analyze the residual preload and determine the influence of the static friction coefficient of the bearing surface on bolt loosening. The specific steps included: The bolted connection structure is fixed on the fatigue tensile testing machine; By using the tightening torque as a control variable to apply cyclic load tension, the change in residual preload of the bolted connection structure under tangential cyclic load is recorded, and the relationship between residual preload and static friction coefficient of different bearing surfaces is established. Thus, the influence of static friction coefficient of bearing surface on bolt loosening when the tightening torque is the same can be obtained. By using the preload as a control variable to apply cyclic load tension, recording the change in residual preload in the bolted connection structure under tangential cyclic load, and establishing the relationship between residual preload and the static friction coefficient of different bearing surfaces, the influence of the static friction coefficient of the bearing surface on bolt loosening can be obtained when the preload is the same. When the tightening torque is the same, the influence of the static friction coefficient of the bearing surface on bolt loosening is as follows: the residual clamping force of the bolt connection structure under tangential contact load is negatively correlated with the static friction coefficient of the bearing surface. The smaller the static friction coefficient of the bearing surface, the greater the initial preload, and the better the anti-loosening effect of the bolt connection. When the preload is the same, the influence of the static friction coefficient of the bearing surface on bolt loosening is as follows: the residual clamping force of the bolt connection structure under tangential contact load is positively correlated with the static friction coefficient of the bearing surface. The larger the static friction coefficient of the bearing surface, the better the anti-loosening effect of the bolt connection.

2. The bolt loosening test analysis method according to claim 1, characterized in that, The method for obtaining the surface morphology parameters of the bearing surface of the bolted connection structure is as follows: the connector and nut are scanned using a NANOWEA three-dimensional non-contact surface profilometer to obtain the surface morphology parameters of the connector and nut under different surface roughnesses, and then exported as TXT format files.

3. The bolt loosening test analysis method according to claim 2, characterized in that, The method for calculating fractal parameters based on the obtained surface morphology parameters of the bearing surface is as follows: import the exported TXT format file into MATLAB and use the structure function method to calculate the fractal parameters.

4. The bolt loosening test analysis method according to claim 3, characterized in that, The calculation of the static friction coefficient of the bearing surface based on the obtained surface morphology parameters of the bearing surface specifically includes the following steps: Calculate the total normal contact load at the mating surface; Calculate the total tangential contact load at the mating surface; A three-dimensional fractal static friction coefficient model is established based on the calculated total normal contact load and total tangential contact load of the mating surface; The calculated fractal parameters are substituted into the established three-dimensional fractal static friction coefficient model to calculate the static friction coefficient of the bearing surface.

5. The bolt loosening test analysis method according to claim 4, characterized in that, The method for calculating the total normal contact load at the interface is as follows: The normal contact load of a single micro-protrusion in the elastic phase is expressed as: In the formula, E Indicates the elastic modulus; R Indicates the curvature of a single micro-convexity; This represents the normal deformation of a single micro-convex body; The total normal contact load of the elastic stage of the interface can be obtained by integrating the single micro-protrusion over the critical cross-sectional area: In the formula, D Indicates fractal dimension; G Indicates the scaling factor; Representation field expansion factor; The size parameter representing the spectral density; This represents the theoretical contact area of ​​a single micro-protrusion; The critical normal deformation amount representing the elastic and elastoplastic deformation of a single micro-protrusion; The critical cross-sectional area for elastic deformation and elastoplastic deformation of a single micro-protrusion; This represents the critical cross-sectional area for elastic deformation of a single micro-protrusion. The normal contact load of a single micro-protrusion during the plastic forming stage is expressed as: In the formula, Y Indicates yield strength; The total normal contact load during the plastic stage of the interface can be obtained by integrating the individual micro-protrusion over the critical cross-sectional area: In the formula, The critical cross-sectional area representing the elastic-plastic deformation and plastic deformation of a single micro-convex body; This represents the size distribution function of the contact points of the micro-protrusion; The normal contact load of a single micro-protrusion in the elastoplastic stage is expressed as: In the formula, These represent coefficients related to material properties and fractal parameters of the interface. , v Poisson's ratio; The total normal contact load in the elastoplastic stage of the interface can be obtained by integrating the single micro-protrusion over the critical cross-sectional area: Therefore, the total normal contact load on the interface is expressed as: 。 6. The bolt loosening test analysis method according to claim 5, characterized in that, The method for calculating the total tangential contact load at the mating surface is as follows: The tangential contact load in the elastic stage is expressed as: in: In the formula, This represents the maximum shear stress. The tangential contact load in the elastoplastic stage is expressed as: in: Therefore, the total tangential contact load at the mating surface is expressed as: 。 7. The bolt loosening test analysis method according to claim 6, characterized in that, The three-dimensional fractal static friction coefficient model is as follows: 。 8. A bolt loosening test and analysis system, characterized in that, include: The first processing unit is used to obtain the surface morphology parameters of the bearing surface of the bolted connection structure. The second processing unit is used to calculate fractal parameters based on the obtained surface morphology parameters of the pressure-bearing surface; The third processing unit is used to calculate the static friction coefficient of the bearing surface based on the obtained surface morphology parameters of the bearing surface; The fourth processing unit is used to conduct tensile tests on bolted connections, analyze the residual preload of the bolted connections, and obtain the influence of the static friction coefficient of the bearing surface on bolt loosening. Specifically, it includes the following steps: The bolted connection structure is fixed on the fatigue tensile testing machine; By using the tightening torque as a control variable to apply cyclic load tension, the change in residual preload of the bolted connection structure under tangential cyclic load is recorded, and the relationship between residual preload and static friction coefficient of different bearing surfaces is established. Thus, the influence of static friction coefficient of bearing surface on bolt loosening when the tightening torque is the same can be obtained. By using the preload as a control variable to apply cyclic load tension, recording the change in residual preload in the bolted connection structure under tangential cyclic load, and establishing the relationship between residual preload and the static friction coefficient of different bearing surfaces, the influence of the static friction coefficient of the bearing surface on bolt loosening can be obtained when the preload is the same. When the tightening torque is the same, the influence of the static friction coefficient of the bearing surface on bolt loosening is as follows: the residual clamping force of the bolt connection structure under tangential contact load is negatively correlated with the static friction coefficient of the bearing surface. The smaller the static friction coefficient of the bearing surface, the greater the initial preload, and the better the anti-loosening effect of the bolt connection. When the preload is the same, the influence of the static friction coefficient of the bearing surface on bolt loosening is as follows: the residual clamping force of the bolt connection structure under tangential contact load is positively correlated with the static friction coefficient of the bearing surface. The larger the static friction coefficient of the bearing surface, the better the anti-loosening effect of the bolt connection.

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