Method for calculating wear during bolt tightening

Abstract

This invention relates to the field of mechanical engineering, specifically to a method for calculating wear during bolt tightening. Combining fractal contact theory, the Yamamoto equation, and a modified Archard wear theory, a wear prediction calculation model for bolt tightening is established. Since both fractal contact theory and the modified Archard wear theory assume uniform load, the thread surface is divided into sub-regions to fully consider the actual axial load distribution on the meshing surface. The axial load on each sub-region of the thread surface is obtained using the Yamamoto equation. After calculating the contact state of each sub-region using fractal contact theory, the wear distribution of the entire thread meshing surface is calculated using the modified Archard wear model. This provides an accurate calculation model for bolt tightening wear, enabling accurate wear prediction and effectively preventing thread seizure.

Description

Technical Field

[0001] This invention relates to the field of mechanical engineering technology, and in particular to a method for calculating wear during bolt tightening. Background Technology

[0002] Bolted connections are an important form of connection, widely used in railways, vehicles, ships, aerospace, and other fields due to their low cost, high repeatability, and ease of operation. However, during installation, improper handling can easily lead to bolt seizing failure. This is especially true for stainless steel bolts and nuts, which have low hardness and high plasticity, making thread seizing frequent. Seized threads make it difficult to tighten or loosen the bolt, sometimes requiring destructive removal methods and resulting in significant economic losses.

[0003] Studies have shown that thread seizure is the most severe wear condition, and its cause can be explained by two main theories: one is that a large amount of frictional heat is generated during the sliding of internal and external threads, causing the local temperature to reach the melting point of the material, thus resulting in localized fusion welding; the other is that severe adhesive wear occurs on the thread surface during tightening, leading to the continuous accumulation of wear debris. As the amount of wear debris increases, the relative movement of the internal and external threads is hindered, ultimately leading to thread seizure failure. In summary, the combined wear pattern of abrasive wear and adhesive wear is likely the root cause of thread seizure, and accurately calculating the wear during bolt tightening is crucial for preventing thread seizure. Summary of the Invention

[0004] To address the above problems, embodiments of the present invention provide a method for calculating wear during bolt tightening.

[0005] This invention provides a method for calculating wear during bolt tightening, comprising:

[0006] S1. Based on the non-uniform distribution characteristics of the bolt axial load, the threaded surface is divided into several sub-regions, where the axial load distribution is uniform in each sub-region.

[0007] S2. Calculate the nominal contact force of each sub-region based on the axial load distribution theory, while considering the actual micromorphology of the threaded surface, and establish the actual contact force calculation model of each sub-region using the fractal contact theory.

[0008] S3. Based on the calculation model of nominal contact force and actual contact force, the maximum contact area of ​​a single micro-protrusion in each sub-region is calculated by iterative calculation.

[0009] S4. For each sub-region, perform an integral calculation based on the maximum contact area of ​​a single micro-protrusion in the sub-region to obtain the actual contact area of ​​the sub-region.

[0010] S5. Based on the actual contact area of ​​the sub-region, the wear amount of the sub-region is calculated using the Arcard wear theory combined with the adhesion correction theory, thereby obtaining the wear distribution of the thread surface.

[0011] Compared with the prior art, the beneficial effects of the present invention are: to provide an accurate calculation model for calculating the wear amount during bolt tightening, thereby achieving accurate wear prediction and effectively preventing thread seizure.

[0012] Optionally, in S2, considering the actual microstructure of the threaded surface, the process of establishing the actual contact force calculation model for each sub-region using fractal contact theory includes:

[0013] Based on the actual microstructure, the deformation stages of the micro-protrusion are divided into the following stages: elastic deformation stage, first elastic-plastic deformation stage, second elastic-plastic deformation stage, and plastic deformation stage.

[0014] The range of change of the contact area of ​​the micro-protrusion under each deformation stage is determined by fractal contact theory, and the calculation equation of the actual contact force of the micro-protrusion under each deformation stage is also determined.

[0015] Optionally, the process of calculating the maximum contact area of ​​a single micro-protrusion in each sub-region using an iterative calculation method in S3 includes:

[0016] S3-1. Set the calculation precision CA and the maximum contact area a. l The initial value;

[0017] S3-2, Based on the currently set maximum contact area a l The deformation stage of the micro-protrusion is determined by combining the range of change of the contact area of ​​the micro-protrusion, and the actual contact force of the micro-protrusion in the current deformation stage and each previous deformation stage is calculated.

[0018] S3-3. Calculate the sum of the actual contact forces at each deformation stage of the micro-convexity to obtain the total actual contact force ΔP. n Calculate the total actual contact force ΔP of the micro-protrusion. n The absolute value of the difference between the nominal contact force ΔP and the subregion to which the micro-protrusion belongs;

[0019] S3-4. Determine if the absolute value is less than the calculation precision CA. If it is less, adjust the currently set maximum contact area a. l This serves as the maximum contact area of ​​the micro-protrusion; if it is not less than this, it will increase according to the set increment Δa. l Increase the currently set maximum contact area a l Then return to execute S3-2.

[0020] Optionally, the process in S5 for calculating the wear amount of a sub-region based on the actual contact area of ​​the sub-region using Archard wear theory combined with adhesion correction theory includes:

[0021] Using Archard's wear theory combined with adhesion correction theory, a calculation model is derived to relate wear amount to friction coefficient, wear coefficient, actual contact area, and relative sliding distance:

[0022]

[0023] μ=(σ y / τ b ) 2

[0024] Where W represents the amount of wear, K e Here, f represents the wear coefficient, f represents the friction coefficient, S represents the sliding distance, and A represents the sliding distance. r σ represents the actual contact area. y τ represents the yield strength. b Indicates tangential yield strength;

[0025] Considering the elastic deformation stage, the first elastic-plastic deformation stage, the second elastic-plastic deformation stage, and the plastic deformation stage, and substituting the actual contact area, we obtain the model for calculating the wear during bolt tightening:

[0026]

[0027] Where g1(x)=πC2(D / 2)ψ 1-D / 2 a l D / 2 g2(x) = 0.93C4 -1.136 a ec (D / 2)ψ 1-D / 2 a l D / 2 g3(x) = 0.94C4 -1.146 a ec (D / 2)ψ 1-D / 2 a l D / 2 g4(x)=2πC2(D / 2)ψ 1-D / 2 a l D / 2 ;K e1 K is the elastic contact wear coefficient. e2 K is the coefficient of elastic-plastic contact wear. e3 The coefficient of plastic contact wear is given by D, where D is the fractal dimension and ψ is a constant; [0, a] ec [a] represents the integral range of the contact area during the elastic deformation stage. ec a epc[a] represents the integral range of the contact area during the first stage of elastic-plastic deformation. epc a pc [a] represents the integral range of the contact area during the second stage of elastic-plastic deformation. pc a l ] represents the integral range of the contact area during the plastic deformation stage; a is the contact area of ​​the micro-convexity, and ω is the deformation of the micro-convexity. a and ω have different implicit functional relationships in different deformation stages:

[0028] 1) Elastic deformation stage

[0029]

[0030] 2) First stage of elastic-plastic deformation

[0031]

[0032] 3) Second stage of elastic-plastic deformation

[0033]

[0034] 4) Plastic deformation stage

[0035]

[0036] Where C1-C7 are all constants. Attached Figure Description

[0037] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, are not intended to limit the scope of the invention. In the drawings:

[0038] Figure 1 A schematic diagram illustrating the principle of a method for calculating wear during bolt tightening, as provided in an embodiment of the present invention.

[0039] Figure 2 This is a block diagram illustrating the principle of calculating the maximum contact area of ​​a single micro-protrusion in each sub-region using an iterative calculation method, as provided in an embodiment of the present invention. Detailed Implementation

[0040] 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 embodiments and accompanying drawings. Here, the illustrative embodiments and descriptions of this invention are used to explain the invention, but are not intended to limit the invention.

[0041] See Figure 1 The present invention provides a method for calculating wear during bolt tightening, comprising:

[0042] S1. Based on the non-uniform distribution characteristics of the bolt axial load, the threaded surface is divided into several sub-regions, where the axial load distribution is uniform in each sub-region.

[0043] In practice, the axial load on the bolt thread surface can be obtained using the Yamamoto equation.

[0044] S2. Calculate the nominal contact force of each sub-region based on the axial load distribution theory, and at the same time consider the actual micromorphology of the threaded surface, establish the actual contact force calculation model of each sub-region using fractal contact theory.

[0045] In practice, based on the actual micromorphology, the deformation stages of the micro-protrusions are divided into the following stages: elastic deformation stage, first elastic-plastic deformation stage, second elastic-plastic deformation stage, and plastic deformation stage.

[0046] The variation range of the contact area of ​​the micro-convex body under each deformation stage is determined using fractal contact theory. Specifically, the variation range in the elastic deformation stage is expressed as [0, a]. ec The range of variation in the first stage of elastic-plastic deformation is expressed as [a] ec a epc The range of variation in the second stage of elastic-plastic deformation is expressed as [a] epc a pc The range of variation in the plastic deformation stage is expressed as greater than a. pc And the calculation equations for the actual contact force of the micro-protrusions at each deformation stage.

[0047] S3. Based on the calculation model of nominal contact force and actual contact force, the maximum contact area of ​​a single micro-protrusion in each sub-region is calculated by iterative calculation.

[0048] In practice, when using fractal contact theory to calculate the contact state of each sub-region, the actual contact area of ​​the sub-region is required as input. The key to calculating the actual contact area lies in calculating the maximum contact area of ​​a single micro-convex body, thereby determining the integration range. (See also...) Figure 2 The specific calculation process for the maximum contact area of ​​a single micro-protrusion includes:

[0049] S3-1. Set the calculation precision CA and the maximum contact area a. l The initial value; during implementation, the maximum contact area a l The initial value can be calculated iteratively starting from 0;

[0050] S3-2, Based on the currently set maximum contact area a l The deformation stage of the micro-protrusion is determined by combining the range of change of the contact area of ​​the micro-protrusion, and the actual contact force of the micro-protrusion in the current deformation stage and each previous deformation stage is calculated.

[0051] S3-3. Calculate the sum of the actual contact forces at each deformation stage of the micro-convexity to obtain the total actual contact force ΔP. n Calculate the total actual contact force ΔP of the micro-protrusion. n The absolute value of the difference between the nominal contact force ΔP of the subregion to which the micro-protrusion belongs; for example, the total actual contact force ΔP when the micro-protrusion is in the first stage of elastic-plastic deformation. n This is the sum of the actual contact forces during the elastic deformation stage and the first plastic deformation stage;

[0052] S3-4. Determine if the absolute value is less than the calculation precision CA. If it is less, adjust the currently set maximum contact area a. l This serves as the maximum contact area of ​​the micro-protrusion; if it is not less than this, it will increase according to the set increment Δa. l Increase the currently set maximum contact area a l Then return to execute S3-2.

[0053] S4. For each sub-region, perform an integral calculation based on the maximum contact area of ​​a single micro-protrusion in the sub-region to obtain the actual contact area of ​​the sub-region.

[0054] In practice, the lower limit of the variation range of the contact area of ​​the micro-protrusion, determined by fractal contact theory, is used as the lower limit of integration during the integral calculation to obtain the maximum contact area 'a' of the micro-protrusion. l As the upper limit of points.

[0055] S5. Based on the actual contact area of ​​the sub-region, the wear amount of the sub-region is calculated using the Arcard wear theory combined with the adhesion correction theory, thereby obtaining the wear distribution of the thread surface.

[0056] In practice, the Archard theory is the classic theory for calculating wear on contact surfaces. The original Archard formula can obtain the wear amount of the contact surface through normal force, relative sliding distance, wear coefficient, and material yield strength. Since the original formula is a macroscopic form of wear calculation and does not consider the effect of rough surfaces, this application modifies it to be applicable to the microscopic scale considering rough surfaces, fully considering the normal and tangential stresses of the contact surface. Based on the adhesion correction theory, the relationship between wear amount and friction coefficient, wear coefficient, actual contact area, and relative sliding distance is derived. The actual contact area is the sum of the actual contact areas in the elastic contact stage, elastoplastic contact stage, and plastic contact stage, which can be calculated by fractal contact theory; specifically:

[0057] Microscopic contact analysis shows that both adhesive wear and abrasive wear occur during bolt tightening; therefore, this invention considers a combination of these two mechanisms. The classic Archard wear theory can be used to evaluate the degree of combined wear; its original form is:

[0058]

[0059] During the tightening process, the meshing thread surfaces of the bolt and nut form a friction pair, continuously generating sliding friction. Both normal and tangential stresses exist on the contact surface. According to the adhesion correction theory, the yield strength σ... y The relationship between normal stress σ and tangential stress τ is:

[0060] σ 2 +μτ 2 =σ y 2

[0061] Combining the above formula, and noting that F / σ is the actual contact area A r Therefore, we can obtain a result based on A. r An improved form of the Archard wear model:

[0062]

[0063] μ=(σ y / τ b ) 2

[0064] Where W represents the wear amount, K e Here, f represents the wear coefficient, f represents the friction coefficient, S represents the sliding distance, and A represents the sliding distance. r σ represents the actual contact area. y τ represents the yield strength. b This represents the tangential yield strength; generally, μ = 9; τ = fσ.

[0065] Considering the elastic deformation stage, the first elastic-plastic deformation stage, the second elastic-plastic deformation stage, and the plastic deformation stage, and substituting the actual contact area, we obtain the model for calculating the wear during bolt tightening:

[0066]

[0067] Where g1(x)=πC2(D / 2)ψ 1-D / 2 a l D / 2 g2(x) = 0.93C4 -1.136 a ec (D / 2)ψ 1-D / 2 a l D / 2 g3(x) = 0.94C4 -1.146 a ec (D / 2)ψ 1-D / 2 a l D / 2 g4(x)=2πC2(D / 2)ψ1-D / 2 a l D / 2 ;K e1 K is the elastic contact wear coefficient. e2 K is the coefficient of elastic-plastic contact wear. e3 The coefficient of plastic contact wear is given by D, where D is the fractal dimension and ψ is a constant; [0, a] ec [a] represents the integral range of the contact area during the elastic deformation stage. ec a epc [a] represents the integral range of the contact area during the first stage of elastic-plastic deformation. epc a pc [a] represents the integral range of the contact area during the second stage of elastic-plastic deformation. pc a l [] represents the integral range of the contact area during the plastic deformation stage; H is the material hardness, and it should be noted that [a pc a l ] in l That is, the maximum value among all the maximum contact areas of micro-protrusions in the plastic deformation stage is determined, and is used to determine the upper limit of the integration with respect to variable a. The same applies to other stages.

[0068] The contact area of ​​the micro-protrusion, denoted by 'a', is a variable. When two rough surfaces come into contact, the contact area formed by different micro-protrusions varies due to differences in their height and size. Let 'a' represent the contact area formed by these micro-protrusions. l This represents the maximum value among these contact areas; that is, the maximum contact area of ​​the micro-protrusion calculated by the iterative method, where ω is the deformation of the micro-protrusion. a and ω have different implicit functional relationships at different deformation stages:

[0069] 1) Elastic deformation stage

[0070]

[0071] 2) First stage of elastic-plastic deformation

[0072]

[0073] 3) Second stage of elastic-plastic deformation

[0074]

[0075] 4) Plastic deformation stage

[0076]

[0077] Where C1-C7 are all constants.

[0078] This invention provides a calculation model for accurately calculating the wear amount during bolt tightening, thereby achieving accurate wear prediction and effectively preventing thread seizing.

[0079] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A method of calculating an amount of wear in a bolt fastening process, characterized by, The method comprises the following steps: S1, according to the uneven distribution characteristics of the axial load of the bolt, the thread surface is divided into a plurality of sub-regions, wherein the axial load distribution on each sub-region is uniform; S2, according to the axial load distribution theory, the nominal contact force of each sub-region is calculated, and the actual micro topography of the thread surface is considered, and a calculation model of the actual contact force of each sub-region is established by using the fractal contact theory; S3, based on the nominal contact force and the actual contact force calculation model, the maximum contact area of a single micro asperity in each sub-region is calculated by using an iterative calculation method; S4, for each sub-region, the maximum contact area of a single micro asperity in the sub-region is integrated to obtain the actual contact area of the sub-region; S5, based on the actual contact area of the sub-region, the wear amount of the sub-region is calculated by using the Archard wear theory combined with the adhesion correction theory, so as to obtain the wear amount distribution of the thread surface; In S2, the actual micro topography of the thread surface is considered, and the calculation model of the actual contact force of each sub-region is established by using the fractal contact theory, which comprises the following steps: According to the actual micro topography, the micro asperity deformation stage is divided into an elastic deformation stage, an elastic-plastic first deformation stage, an elastic-plastic second deformation stage and a plastic deformation stage; The change range of the micro asperity contact area in each deformation stage is determined by using the fractal contact theory, and the calculation equation of the actual contact force of the micro asperity in each deformation stage is determined; In S5, the actual contact area of the sub-region is used to calculate the wear amount of the sub-region by using the Archard wear theory combined with the adhesion correction theory, which comprises the following steps: The calculation model of the wear amount and the friction coefficient, the wear coefficient, the actual contact area and the relative sliding distance is derived by using the Archard wear theory combined with the adhesion correction theory: μ = (σ y / τ b ) 2 wherein W represents the wear amount, K e represents the wear coefficient, f represents the friction coefficient, S represents the sliding distance, A r represents the actual contact area, σ y represents the yield strength, τ b represents the tangential yield strength; Considering the elastic deformation stage, the elastic-plastic first deformation stage, the elastic-plastic second deformation stage and the plastic deformation stage, the wear amount calculation model in the bolt tightening process is obtained by substituting the actual contact area: wherein g1(x) = πC2(D / 2)ψ 1-D / 2 a l D / 2 , g2(x) = 0.93C4 -1.136 a ec (D / 2)ψ 1-D / 2 a l D / 2 , g3(x) =0.94C4 -1.146 a ec (D / 2)ψ 1-D / 2 a l D / 2 , g4(x) = 2πC2(D / 2)ψ 1-D / 2 a l D / 2 ; K e1 is an elastic contact wear coefficient, K e2 is an elastoplastic contact wear coefficient, K e3 is a plastic contact wear coefficient, D is a fractal dimension, and ψ is a constant; [0, a ec ] is an elastic deformation stage contact area integration range, [a ec , a epc ] represents an elastoplastic first deformation stage contact area integration range, [a epc , a pc ] represents an elastoplastic second deformation stage contact area integration range, and [a pc , a l ] represents a plastic deformation stage contact area integration range; a is a microconvex contact area, and ω is a microconvex deformation amount, and a and ω have different implicit function corresponding relationships in different deformation stages. 1) Elastic deformation stage 2) Elastic-plastic first deformation stage 3) Elastic-plastic second deformation stage 4) Plastic deformation stage Wherein, C1-C7 are constants.

2. The method of claim 1, wherein In S3, the maximum contact area of a single micro asperity in each sub-region is calculated by using an iterative calculation method, which comprises the following steps: S3-1, set the calculation accuracy CA and the maximum contact area a l of the initial value; S3-2, maximum contact area a according to current setting l The current deformation stage of the micro-convex body is determined according to the range of the change of the contact area of the micro-convex body, and the actual contact force of the current deformation stage and the actual contact force of each previous deformation stage are calculated. S3-3, calculate the sum of the actual contact forces of each deformation stage of the micro asperities to obtain the total actual contact force , calculate the total actual contact force of the micro asperities and the absolute value of the difference between the nominal contact force of the sub-region to which the micro asperity belongs ​ S3-4, judge whether the absolute value is smaller than the calculation accuracy CA, if smaller, increase the current set maximum contact area a l as the maximum contact area of the micro convex body; if not smaller, increase the current set maximum contact area a l by the set growth step Δa l and return to execute S3-2.

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