A method for extracting extended stress of thread contact surface

Abstract

A method for extracting extended stress of thread tooth contact surface belongs to the field of bolt connection and finite element simulation, and includes the following steps: step 1: determining the theoretical formula of normal stress and shear stress of any contact surface of thread; step 2: calculating the direction cosine of the external normal; step 3: establishing a thread tooth contact surface model in finite element; step 4: extracting the extended stress of the thread tooth bevel; step 5: importing the extended stress into the original finite element mesh model according to the mesh node coordinates to obtain the extended stress distribution. The present invention can apply theoretical calculation to finite element simulation, provide great help for stress analysis of thread pair, and can be applied to stress analysis calculation of any other connection interface.

Description

Technical Field

[0001] The invention belongs to the field of bolt connection and finite element simulation, and particularly relates to a method for extracting extended stress of a thread contact surface. Background Art

[0002] Threaded connections are widely used in aerospace, construction machinery, and other fields due to their reliable vibration resistance, anti-loosening, and reusability. However, due to their structural characteristics, threaded connections commonly suffer from uneven load distribution between threads and stress concentration at the thread root, which, to a certain extent, affects the strength and reliability of threaded connections. Although scholars at home and abroad have conducted in-depth research and exploration on thread pair stress analysis, and have developed three methods for studying thread pair load distribution: analytical methods, photoelastic testing, and finite element methods, each method has its own limitations, and it is difficult to combine theoretical calculations with finite element simulations. The normal stress perpendicular to the thread contact surface and the shear stress on the thread contact surface can accurately describe the load distribution of thread pairs and clarify the structural performance of threaded connections. Currently, theoretical research on bolted connections has analyzed the normal stress perpendicular to the thread contact surface and the shear stress on the thread contact surface. However, in finite element analysis, the normal stress, shear stress, equivalent stress, and principal stress in all directions of the component are usually analyzed. There is no method to extract the normal stress and shear stress on any contact surface of the component, which limits the study of thread stress. Summary of the Invention

[0003] Based on the above technical problems, the present invention proposes a method for extracting the extended stress of the contact surface of the thread teeth, establishes an extraction method that can accurately calculate the extended stress of the contact surface of the thread teeth, and can apply theoretical calculations to finite element simulation, providing great help for the stress analysis of the thread pair, and can be applied to the stress analysis calculation of any other connection interface.

[0004] The present invention adopts the following technical solutions:

[0005] A method for extracting extended stress from a thread contact surface comprises the following steps:

[0006] Step 1: Determine the theoretical formulas for normal stress and shear stress on any contact surface of the thread:

[0007] Select a point P on any contact surface and take a plane ABC near it. The stress components at the point P on the contact surface are σ x ,σ y ,σ z ,τ xy ,τ yz ,τ xz The forces on the plane ABC near point P in the three coordinate axis directions are p and x ,p y ,pz , the external normal N of plane ABC and the direction cosines of the three coordinate axes x, y, and z are l, m, and n respectively. When plane ABC approaches point P, the following relationship exists:

[0008]

[0009] Let the normal stress and shear stress of plane ABC be σ n and τ n , then:

[0010] σ n =lp x +mp y +np z (2)

[0011]

[0012] The external normal N and the direction cosines of the three coordinate axes x, y, and z are l, m, and n respectively as follows:

[0013]

[0014] Step 2: Calculate the coordinates of the external normal at any position on the thread contact surface, and then calculate the direction cosine of the external normal;

[0015] According to formula (9)

[0016]

[0017] Substitute the coordinates (x0, y0, z0) of any point on the thread contact surface into (9) to obtain the vector coordinates of the external normal N: (F x (x0,y0,z0),F y (x0,y0,z0),F z (x0, y0, z0)), according to the coordinates, the external normal N and the direction cosines of the three coordinate axes x, y, and z are l, m, and n respectively;

[0018] Step 3: Establish the thread contact surface model in the finite element method;

[0019] Step 4: Extract the coordinates of each grid node in the selected area and the corresponding stress components on the grid nodes, and extract the extended stress of the thread bevel;

[0020] Step 5: Import the expanded stress into the original finite element mesh model according to the mesh node coordinates to obtain the expanded stress distribution.

[0021] Furthermore, the step 2 is specifically as follows:

[0022] Establish the expression of the thread contact surface in the cylindrical coordinate system:

[0023]

[0024] Where r is the distance from a point on the thread contact surface to the bolt axis, r0 is half of the bolt diameter, and r min =r0, r max is half of the bolt's major diameter, α / 2 is the thread profile half angle, P is the thread pitch, and z is the height of any point on the thread tooth slope in the cylindrical coordinate system. is the azimuth in the cylindrical coordinate system;

[0025] Convert the expression in the circular coordinate system into the surface expression in the Cartesian coordinate system:

[0026]

[0027] Right now:

[0028]

[0029] The thread contact surface spatial expression (7) is converted into an implicit surface equation:

[0030] F(x,y,z)=0 (8)

[0031] Formula (9) is obtained by converting formula (8).

[0032] Furthermore, the step 3 specifically includes first establishing a bolt model, then simulating the tightening process, setting the bottom surface of the bolt as a fixed constraint, applying angular displacement to the nut, and loading a pre-tightening force to achieve pre-tightening.

[0033] Furthermore, the extended stress of the thread bevel extracted in step 4 is extracted by Matlab programming. Specifically, the contact stress of the thread bevel is extracted as follows: first, the structural parameters of the bolt and the coordinates of the grid nodes are input into the program, and the coordinates of the normal vector N of each grid node are calculated by formula (9) using the input data; then the direction cosines l, m, n of each point are calculated by formula (4), and finally the σ of each grid node is input. x ,σ y ,σ z ,τ xy ,τ yz ,τ xz , and calculate the expanded stress σ of each grid node through formulas (1)-(3) n and τ n .

[0034] Beneficial effects of the present invention:

[0035] The present invention proposes a method for extracting the extended stress of the thread tooth contact surface, which can accurately extract the extended stress at any point on the threaded connection contact surface in finite element simulation and obtain the stress distribution law of the threaded contact surface. This method fills the gap in finite element analysis of stress; this method is not limited by the form of the contact surface and can provide a stress calculation method for contact surfaces of different shapes. The calculation results are accurate and reliable. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a schematic diagram of the three-dimensional stress at any point on any contact surface of the thread;

[0037] Figure 2 is the bolt model established in the finite element method;

[0038] Figure 3 It is the equivalent stress distribution diagram of the selected area in the bolt model of the finite element model;

[0039] Figure 4 This is the stress extraction flow chart for the thread contact surface;

[0040] Figure 5 is the extended stress σ on the thread contact surface n distribution map;

[0041] Figure 6 is the thread contact surface expansion stress τ n Distribution map. DETAILED DESCRIPTION

[0042] The specific implementation of the present invention is described in detail below with reference to the accompanying drawings and examples.

[0043] The present invention provides a method for extracting extended stresses on the contact surface of a threaded thread. In this method, the normal stress and shear stress of any contact surface of a component can be considered an extension of traditional stress analysis and are therefore defined as extended stresses. The method comprises the following steps:

[0044] Step 1: Determine the theoretical formulas for normal stress and shear stress at any contact surface of the thread

[0045] In this embodiment, in order to calculate the normal stress and shear stress on any contact surface, first select a point P on any contact surface and take a plane ABC near it, such as Figure 1 As shown in the figure, the normal stress and shear stress components at a point P on the contact surface are σ x ,σ y ,σ z ,τ xy ,τ yz ,τ xz The forces on the plane ABC near point P in the three coordinate axis directions are p and x ,py ,p z , the external normal N of plane ABC and the direction cosines of the three coordinate axes x, y, and z are l, m, and n respectively. When plane ABC approaches point P, the following relationship exists:

[0046]

[0047] Let the normal stress and shear stress of plane ABC be σ n and τ n , then:

[0048] σ n =lp x +mp y +np z (2)

[0049]

[0050] The external normal N and the direction cosines of the three coordinate axes x, y, and z are l, m, and n respectively as follows:

[0051]

[0052] Step 2: Calculate the coordinates of the external normal at any position on the thread contact surface, and then calculate the direction cosine of the external normal

[0053] In this embodiment, to calculate the normal stress and shear stress at any position on the thread contact surface using the method given in step 1 in the finite element method, it is first necessary to calculate the coordinates of the external normal at any position on the thread contact surface, and then calculate the direction cosines of the external normal. In order to determine the coordinates of the external normal N of the thread contact surface and calculate its direction cosines, it is necessary to determine the expression of the thread contact surface. Therefore, first establish the expression of the thread contact surface in the cylindrical coordinate system:

[0054]

[0055] Where r is the distance from a point on the thread contact surface to the bolt axis, r0 is half of the bolt diameter, and r min =r0, r max is half of the bolt's major diameter, α / 2 is the thread profile half angle, P is the thread pitch, and z is the height of any point on the thread tooth slope in the cylindrical coordinate system. is the azimuth in the cylindrical coordinate system.

[0056] Convert the expression in the circular coordinate system into the surface expression in the Cartesian coordinate system:

[0057]

[0058] Right now:

[0059]

[0060] Change the thread contact surface spatial expression (7) into an implicit surface equation:

[0061] F(x,y,z)=0 (8)

[0062] Derivative of formula (8):

[0063]

[0064] Finally, the coordinates (x0, y0, z0) of any point on the thread contact surface are brought into (9), and the vector coordinates of the external normal N are obtained as (F x (x0,y0,z0),F y (x0,y0,z0),F z (x0, y0, z0)), based on this coordinate, we can get the external normal N and the direction cosines of the three coordinate axes x, y, and z, respectively, l, m, and n.

[0065] Step 3: Create a thread contact surface model in finite element analysis

[0066] In this embodiment, the method given in step 1 is used to calculate the normal stress and shear stress at any position of the thread contact surface in the finite element method. First, a high-fidelity bolt model including all details such as the nut, screw, thread, and head fillet is established, such as Figure 2 As shown in the figure. In the model, the bolt and self-locking nut are made of GH738, with an elastic modulus of E = 213 GPa and a Poisson's ratio of γ = 0.3. The connected part is made of TC17, with an elastic modulus of E = 200 GPa and a Poisson's ratio of γ = 0.3. The bolts, nuts, and connected parts in the calculation model are all constructed using hexahedral C3D8R elements. Secondly, to simulate the tightening process, the bottom surface of the bolt is set as a fixed constraint, an angular displacement is applied to the nut, and a preload is applied to achieve the preload effect. The thread pitch p of both the bolt and nut is 1 mm, and the thread profile half-angle α / 2 is 30°.

[0067] Step 4: Extract the coordinates of each grid node in the selected area and the corresponding stress components on the grid nodes, and extract the extended stress of the thread bevel

[0068] In this embodiment, first select Figure 3 The area shown in the figure is used to extract the coordinates x, y, z of each grid node in the area and the corresponding σ on the grid node. x ,σ y ,σ z ,τ xy ,τ yz ,τ xz Then, follow the steps below. Figure 4The process shown is to extract the contact stress of the thread bevel through Matlab programming. Figure 4 The process shown is as follows: First, input the structural parameters of the bolt (pitch P, thread half angle α / 2) and the coordinates of the grid nodes in the program, and use the input data to calculate the coordinates of the normal vector N of each grid node through formula (9); then calculate the direction cosine l, m, n of each point through formula (4). Finally, input the σ of each grid node. x ,σ y ,σ z ,τ xy ,τ yz ,τ xz , and calculate the expanded stress σ of each grid node through formulas (1)-(3) n and τ n .

[0069] Step 5: Import the extended stress into the original finite element mesh model according to the mesh node coordinates to obtain the extended stress distribution

[0070] In this embodiment, the extended stress on the thread bevel calculated in step 4 is imported into the original finite element mesh model according to the mesh node coordinates, and the same stress can be obtained. Figure 3 The extended stress distribution on the same area. Extended stress σ n and τ n The distribution of Figure 5 and Figure 6 shown.

Claims

1. A method for extracting extended stress of thread contact surface, characterized in that: The steps include: Step 1: Determine the theoretical formula for normal stress and shear stress on any contact surface of the thread: Select a point P on any contact surface and take a plane ABC near it. The stress components at any point P on the contact surface are σ x ,σ y ,σ z ,τ xy ,τ yz ,τ xz , the forces on the plane ABC near point P in the three coordinate axis directions are p x ,p y ,p z , the external normal N of plane ABC and the direction cosines of the three coordinate axes x, y, and z are l, m, and n respectively. When plane ABC approaches point P, the following relationship exists: Let the normal stress and shear stress of plane ABC be σ n and τ n , then: σ n =lp x +mp y +np z (2) The external normal N and the direction cosines of the three coordinate axes x, y, and z are l, m, and n respectively as follows: Step 2: Calculate the coordinates of the external normal line at any position on the thread contact surface, and then calculate the direction cosine of the external normal line; According to formula (9) Substituting the coordinates (x0, y0, z0) of any point on the thread contact surface into (9), we can obtain the vector coordinates of the external normal N as (F x (x0,y0,z0),F y (x0,y0,z0),F z (x0, y0, z0)), according to the coordinates, the external normal N and the direction cosines of the three coordinate axes x, y, and z are l, m, and n respectively; Step 3: Establish the thread contact surface model in the finite element method; Step 4: Extract the coordinates of each grid node in the selected area and the corresponding stress components on the grid nodes, and extract the extended stress of the thread bevel surface; Step 5: Import the extended stress into the original finite element mesh model according to the mesh node coordinates to obtain the extended stress distribution.

2. According to a method for extracting extended stress of thread contact surface according to claim 1, it is characterized in that: The step 2 is specifically as follows: Establish the expression of thread contact surface in cylindrical coordinate system: Where r is the distance from a point on the thread contact surface to the bolt axis, r0 is half of the bolt minor diameter, and r min =r0,r max is half of the bolt's major diameter, α / 2 is the thread profile half angle, P is the thread pitch, and z is the height of any point on the thread tooth slope in the cylindrical coordinate system. is the azimuth in the cylindrical coordinate system; Convert the expression in the circular coordinate system into the surface expression in the Cartesian coordinate system: Right now: The thread contact surface spatial expression (7) is changed into an implicit surface equation: F(x,y,z)=0 (8) By derivatizing equation (8), we can obtain equation (9).

3. According to a method for extracting extended stress of thread contact surface according to claim 1, it is characterized in that: The step 3 specifically includes first establishing a bolt model, then simulating the tightening process, setting the bottom surface of the bolt as a fixed constraint, applying an angular displacement to the nut, and loading a pre-tightening force to achieve pre-tightening.

4. According to a method for extracting extended stress of thread contact surface according to claim 1, it is characterized in that: The process of extracting the extended stress of the thread bevel surface in step 4 is to extract the contact stress of the thread bevel surface through Matlab programming, specifically: firstly, input the structural parameters of the bolt and the coordinates of the grid nodes in the program, and use the input data to calculate the coordinates of the normal vector N of each grid node through formula (9); then calculate the direction cosine l, m, n of each point through formula (4), and finally input the σ of each grid node x ,σ y ,σ z ,τ xy ,τ yz ,τ xz , and calculate the extended stress σ of each grid node through formulas (1)-(3) n and τ n .

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