Method for calculating abrasion loss in bolt connecting and tightening process

Abstract

The invention relates to the field of mechanical engineering, in particular to a method for calculating the abrasion loss in the bolt connecting and tightening process, and establishes an abrasion prediction calculation model in the bolt tightening process by combining a fractal contact theory, a Yamamoto equation and an improved Archard abrasion theory. The fractal contact theory and the improved Archard wear theory are both calculated on the premise of uniform load, so that the threaded surface is subjected to sub-region division, the actual axial load distribution condition of the meshing surface is fully considered, and the axial load on each sub-region of the threaded surface is obtained through a Yamamoto equation. And after the contact state of each sub-region is calculated by utilizing a fractal contact theory, the abrasion loss distribution of the whole thread meshing surface is calculated in combination with an improved Archard abrasion model. A calculation model for accurately calculating the abrasion loss in the bolt tightening process is provided, so that accurate abrasion loss prediction is achieved, and the situation of thread seizure is effectively prevented.

Description

Technical Field

[0001] The invention relates to the technical field of mechanical engineering, and in particular to a method for calculating wear amount during a bolt connection tightening process. Background Art

[0002] Bolt connection is an important connection form. Due to its low cost, strong repeatability and convenient operation, it is widely used in railways, vehicles, ships, aerospace and other fields. However, during the installation process, due to improper operation, bolts are prone to seizure failure. Especially for stainless steel bolts and nuts, which have low hardness and high plasticity, thread seizure occurs frequently. Thread seizure makes it difficult to continue tightening or disassembling the bolts. If necessary, destructive methods can only be used to dismantle them, causing huge economic losses.

[0003] Research shows that thread seizure is the most serious wear condition, and there are two main explanations for its occurrence: one view is that a large amount of frictional heat is generated during the sliding process of the internal and external threads, causing the local temperature to reach the melting point of the material, resulting in local welding; the other view is that during the tightening process, severe adhesive wear occurs on the thread surface, resulting in continuous accumulation of wear debris. As the amount of wear debris increases, the relative movement of the internal and external threads is hindered, eventually leading to thread seizure failure. In summary, the combined wear form of abrasive wear and adhesive wear is likely to be the root cause of thread seizure, and accurately calculating the amount of wear during the tightening of bolted connections is crucial to preventing thread seizure. Summary of the invention

[0004] In view of the above problems, an embodiment of the present invention provides a method for calculating the wear amount during the tightening process of a bolt connection.

[0005] An embodiment of the present invention provides a method for calculating the wear amount during the tightening process of a bolt connection, comprising:

[0006] S1. According to the uneven distribution characteristics of the bolt axial load, the thread surface is divided into several sub-areas, wherein the axial load distribution on each sub-area is uniform;

[0007] S2. Calculate the nominal contact force of each sub-area based on the axial load distribution theory, consider the actual microscopic morphology of the thread surface, and use the fractal contact theory to establish the actual contact force calculation model of each sub-area;

[0008] S3, based on the nominal contact force and actual contact force calculation model, the maximum contact area of ​​a single micro-convex body in each sub-region is calculated by an iterative calculation method;

[0009] S4, for each sub-region, performing an integral operation based on the maximum contact area of ​​a single micro-convex body in the sub-region to obtain an 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 Archard wear theory combined with adhesion correction theory to obtain the wear distribution of the thread surface.

[0011] Compared with the prior art, the beneficial effect of the present invention is that it provides a calculation model for accurately calculating the wear amount during the bolt tightening process, thereby achieving accurate wear amount prediction and effectively preventing the occurrence of thread seizure.

[0012] Optionally, in S2, the actual microscopic morphology of the thread surface is considered, and the process of establishing the actual contact force calculation model of each sub-region using fractal contact theory includes:

[0013] According to the actual microscopic morphology, the deformation stages of the micro-convex body are divided into: elastic deformation stage, elastic-plastic first deformation stage, elastic-plastic second deformation stage and plastic deformation stage;

[0014] The fractal contact theory is used to determine the variation range of the contact area of ​​the micro-asperity at each deformation stage, as well as the calculation equation of the actual contact force of the micro-asperity at each deformation stage.

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

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

[0017] S3-2, according to the current maximum contact area a l The current deformation stage of the micro-convex body is determined in combination with the variation range of the contact area of ​​the micro-convex body, and the actual contact force of the current deformation stage of the micro-convex body and the previous deformation stages is calculated;

[0018] S3-3. Calculate the sum of the actual contact forces at each deformation stage of the micro-convex body to obtain the total actual contact force ΔP n , calculate the total actual contact force ΔP of the micro-asperity n The absolute value of the difference between the nominal contact force ΔP of the sub-region to which the asperity belongs;

[0019] S3-4, determine whether the absolute value is less than the calculation accuracy CA, if it is less than the current maximum contact area a l As the maximum contact area of ​​the micro-convex body; if it is not less than, it will grow according to the set step size Δa l Increase the maximum contact area of ​​the current setting a l And return to execute S3-2.

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

[0021] The calculation model between wear volume and friction coefficient, wear coefficient, actual contact area and relative sliding distance is derived by combining Archard wear theory with adhesion correction theory:

[0022]

[0023] μ=(σ y / τ b ) 2

[0024] Where 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;

[0025] Considering the elastic deformation stage, the first elastic-plastic deformation stage, the second elastic-plastic deformation stage and the plastic deformation stage, the wear calculation model during the bolt tightening process is obtained by substituting the actual contact area:

[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 is the elastic contact wear coefficient, K e2 is the elastic-plastic contact wear coefficient, K e3 is the plastic contact wear coefficient, D is the fractal dimension, ψ is a constant; [0, a ec ] is the integral range of contact area in the elastic deformation stage, [a ec , a epc] represents the integral range of the contact area in the first elastic-plastic deformation stage, [a epc , a pc ] represents the integral range of the contact area in the second elastic-plastic deformation stage, [a pc , a l ] represents the integral range of the contact area in the plastic deformation stage; a is the contact area of ​​the micro-convex body, ω is the deformation of the micro-convex body, and a and ω have different implicit function corresponding relationships in different deformation stages:

[0028] 1) Elastic deformation stage

[0029]

[0030] 2) Elastic-plastic first deformation stage

[0031]

[0032] 3) Elastic-plastic second deformation stage

[0033]

[0034] 4) Plastic deformation stage

[0035]

[0036] Among them, C1-C7 are all constants. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The drawings described herein are used to provide a further understanding of the present invention, constitute a part of the present application, and do not constitute a limitation of the present invention. In the drawings:

[0038] Figure 1 A principle block diagram of a method for calculating wear during the tightening process of a bolt connection provided by an embodiment of the present invention;

[0039] Figure 2 A principle block diagram of an embodiment of the present invention for calculating the maximum contact area of ​​a single micro-protrusion in each sub-region by an iterative calculation method. DETAILED DESCRIPTION

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

[0041] See also Figure 1 , a method for calculating the wear amount during the tightening process of a bolt connection provided by an embodiment of the present invention comprises:

[0042] S1. According to the uneven distribution characteristics of the bolt axial load, the thread surface is divided into several sub-areas, wherein the axial load distribution on each sub-area is uniform.

[0043] In practice, the Yamamoto equation can be used to obtain the axial load on the bolt thread surface.

[0044] S2. The nominal contact force of each sub-area is calculated based on the axial load distribution theory. At the same time, the actual micromorphology of the thread surface is considered, and the actual contact force calculation model of each sub-area is established using the fractal contact theory.

[0045] In the implementation, the deformation stages of the micro-convex body are divided into: elastic deformation stage, elastic-plastic first deformation stage, elastic-plastic second deformation stage and plastic deformation stage according to the actual microscopic morphology;

[0046] The fractal contact theory is used to determine the range of contact area of ​​the micro-convex body in each deformation stage. Specifically, the range of change in the elastic deformation stage is expressed as [0, a ec ], the range of the first elastic-plastic deformation stage is expressed as [a ec , a epc ], the range of the second elastic-plastic deformation stage is expressed as [a epc , a pc ], the plastic deformation stage variation range is expressed as greater than a pc , and the calculation equations of the actual contact force of the micro-convex body at each deformation stage.

[0047] S3. Based on the nominal contact force and actual contact force calculation model, an iterative calculation method is used to calculate the maximum contact area of ​​a single micro-convex body in each sub-area.

[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 is to calculate the maximum contact area of ​​a single micro-convex body, thereby determining the integration range. Figure 2 , the specific calculation process of the maximum contact area of ​​a single microconvex body includes:

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

[0050] S3-2, according to the current maximum contact area a l The current deformation stage of the micro-convex body is determined in combination with the variation range of the contact area of ​​the micro-convex body, and the actual contact force of the current deformation stage of the micro-convex body and the previous deformation stages is calculated;

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

[0052] S3-4, determine whether the absolute value is less than the calculation accuracy CA, if it is less than the current maximum contact area a l As the maximum contact area of ​​the micro-convex body; if it is not less than, it will grow according to the set step size Δa l Increase the maximum contact area of ​​the current setting a l And return to execute S3-2.

[0053] S4. For each sub-region, an integral operation is performed based on the maximum contact area of ​​a single micro-convex body in the sub-region to obtain the actual contact area of ​​the sub-region.

[0054] In the implementation, the lower limit of the range of contact area of ​​the micro-convex body determined by fractal contact theory is used as the lower limit of the integral to obtain the maximum contact area a of the micro-convex body. 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 Archard wear theory combined with adhesion correction theory to obtain the wear distribution of the thread surface.

[0056] In practice, Archard theory is a classic theory for contact surface wear calculation. 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 take into account the effect of the rough surface, it is improved accordingly in this application so that it can be applied to the microscopic scale of the rough surface, fully considering the normal stress and tangential stress of the contact surface, and according to the adhesion correction theory, the relationship between the wear amount and the 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, the elastoplastic contact stage and the 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, so the present invention considers the composite form of these two mechanisms. The classical Archard wear theory can be used to evaluate the degree of composite wear, and its original form is:

[0058]

[0059] During the tightening process, the meshing thread surfaces of the bolt and the nut form a friction pair, which continuously generates sliding friction. There are both normal stress and tangential stress 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] Combined with the above formula, note that F / σ is the actual contact area A r , so we can get based on A r A modified form of the Archard wear model:

[0062]

[0063] μ=(σ y / τ b ) 2

[0064] Among them, 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 Indicates 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, the wear calculation model during the bolt tightening process is obtained by substituting the actual contact area:

[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 is the elastic contact wear coefficient, K e2 is the elastic-plastic contact wear coefficient, K e3 is the plastic contact wear coefficient, D is the fractal dimension, ψ is a constant; [0, a ec ] is the integral range of the contact area in the elastic deformation stage, [a ec , a epc ] represents the integral range of the contact area in the first elastic-plastic deformation stage, [a epc , a pc ] represents the integral range of the contact area in the second elastic-plastic deformation stage, [a pc , a l ] represents the integral range of the contact area in the plastic deformation stage; H is the material hardness, and it should be noted that [a pc , a l ] l That is, the maximum value of the maximum contact area of ​​all micro-convex bodies in the plastic deformation stage is determined, which is used to determine the upper limit of the integration of the variable a. The same is true for other stages;

[0068] a is the contact area of ​​the micro-convex body, which is a variable. When two rough surfaces come into contact, the contact areas formed by different micro-convex bodies are different due to the different heights and sizes of the micro-convex bodies. a is used to represent the contact area formed by these micro-convex bodies. l represents the maximum value of these contact areas; that is, the maximum contact area of ​​the micro-convex body calculated by the iteration method, ω is the deformation of the micro-convex body, and a and ω have different implicit function correspondences at different deformation stages:

[0069] 1) Elastic deformation stage

[0070]

[0071] 2) Elastic-plastic first deformation stage

[0072]

[0073] 3) Elastic-plastic second deformation stage

[0074]

[0075] 4) Plastic deformation stage

[0076]

[0077] Among them, C1-C7 are all constants.

[0078] The embodiments of the present invention provide a calculation model for accurately calculating the wear amount during the tightening process of the bolt, thereby achieving accurate wear amount prediction and effectively preventing the occurrence of thread seizure.

[0079] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A method for calculating the wear amount during the tightening process of a bolt connection, characterized in that: include: S1. According to the uneven distribution characteristics of the bolt axial load, the thread surface is divided into several sub-areas, wherein the axial load distribution on each sub-area is uniform; S2. Calculate the nominal contact force of each sub-area based on the axial load distribution theory, consider the actual microscopic morphology of the thread surface, and use the fractal contact theory to establish the actual contact force calculation model of each sub-area; S3, based on the nominal contact force and actual contact force calculation model, the maximum contact area of ​​a single micro-convex body in each sub-region is calculated by an iterative calculation method; S4, for each sub-region, performing an integral operation based on the maximum contact area of ​​a single micro-convex body in the sub-region to obtain an 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 using Archard wear theory combined with adhesion correction theory to obtain the wear distribution of the thread surface.

2. The method for calculating the wear amount during the tightening process of bolt connection according to claim 1, characterized in that: In S2, the actual microscopic morphology of the thread surface is considered, and the process of establishing the actual contact force calculation model of each sub-region using fractal contact theory includes: According to the actual microscopic morphology, the deformation stages of the micro-convex body are divided into: elastic deformation stage, elastic-plastic first deformation stage, elastic-plastic second deformation stage and plastic deformation stage; The fractal contact theory is used to determine the variation range of the contact area of ​​the micro-asperity at each deformation stage, as well as the calculation equation of the actual contact force of the micro-asperity at each deformation stage.

3. The method for calculating the wear amount during the tightening process of bolt connection according to claim 2, characterized in that: The process of calculating the maximum contact area of ​​a single micro-convex body in each sub-region by iterative calculation in S3 includes: S3-1. Set the calculation accuracy CA and the maximum contact area a l The initial value of S3-2, according to the current maximum contact area a l The current deformation stage of the micro-convex body is determined in combination with the variation range of the contact area of ​​the micro-convex body, and the actual contact force of the current deformation stage of the micro-convex body and the previous deformation stages is calculated; S3-3. Calculate the sum of the actual contact forces at each deformation stage of the micro-convex body to obtain the total actual contact force ΔP n , calculate the total actual contact force ΔP of the micro-asperity n The absolute value of the difference between the nominal contact force ΔP of the sub-region to which the asperity belongs; S3-4, determine whether the absolute value is less than the calculation accuracy CA, if it is less than the current maximum contact area a l As the maximum contact area of ​​the micro-convex body; if it is not less than, it will grow according to the set step size Δa l Increase the maximum contact area of ​​the current setting a l And return to execute S3-2.

4. The method for calculating the wear amount during the tightening process of bolt connection according to claim 1, characterized in that: The process of calculating the wear amount of the sub-region in S5 based on the actual contact area of ​​the sub-region using Archard wear theory combined with adhesion correction theory includes: The calculation model between wear volume and friction coefficient, wear coefficient, actual contact area and relative sliding distance is derived by combining Archard wear theory with adhesion correction theory: μ=(σ y / t b ) 2 Where 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 first elastic-plastic deformation stage, the second elastic-plastic deformation stage and the plastic deformation stage, the wear calculation model during the bolt tightening process is obtained by substituting the actual contact area: 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 is the elastic contact wear coefficient, K e2 is the elastic-plastic contact wear coefficient, K e3 is the plastic contact wear coefficient, D is the fractal dimension, ψ is a constant; [0, a ec ] is the integral range of contact area in the elastic deformation stage, [a ec , a epc ] represents the integral range of the contact area in the first elastic-plastic deformation stage, [a epc , a pc ] represents the integral range of the contact area in the second elastic-plastic deformation stage, [a pc , a l ] represents the integral range of the contact area in the plastic deformation stage; a is the contact area of ​​the micro-convex body, ω is the deformation of the micro-convex body, 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 Among them, C1-C7 are all constants.

Images