A method for generating a precise finite element model of a 30° wedge-shaped anti-loosening thread

Abstract

The present invention discloses a method for generating a precise finite element model of a 30° wedge-shaped anti-loosening thread, comprising the following steps: S1: Obtain the physical parameters of the nut, the data of the contour segmentation points, and the three-dimensional coordinate information of the finite element mesh nodes of the thread, and determine the basic structural parameters of the nut thread profile according to the 30° wedge-shaped anti-loosening thread profile to be generated; S2: Calculate the minimum axial node spacing and the minimum circumferential node spacing of the thread, and determine the tolerance value; S3: Obtain the finite element mesh nodes of the nut, and perform coordinate transformation on the finite element mesh nodes of the nut; S4: Perform contour offset operation according to the finite element mesh nodes of the nut after coordinate transformation, generate a finite element model of the 30° wedge-shaped anti-loosening thread according to the basic structural parameters of the nut thread profile, and determine the tolerance value. The 30° wedge-shaped anti-loosening thread profile formula proposed by the present invention can quickly generate the 30° wedge-shaped anti-loosening thread profile. This profile formula is a necessary condition and premise for the finite element study of the anti-loosening performance of the 30° wedge-shaped anti-loosening thread.

Description

Technical Field

[0001] The present invention belongs to the technical field of screw thread finite element models, and particularly relates to a method for generating a precise finite element model of a 30° wedge-shaped locking screw thread. Background Art

[0002] Currently, in the field of precision finite element research on bolts, domestic and foreign research mainly focuses on the research of standard metric screw threads. Due to the limitations of finite element model technology and the lack of relevant research on the profile formula of the 30° wedge-shaped locking screw thread in domestic and foreign literature. The absence of the profile formula has led to no research on the precise finite element calculation of the 30° wedge-shaped locking screw thread. Summary of the Invention

[0003] The purpose of the present invention is to solve the problem that the lack of a corresponding profile formula for the 30° wedge-shaped locking screw thread leads to the inability to generate a precise finite element model, and a method for generating a precise finite element model of a 30° wedge-shaped locking screw thread is proposed.

[0004] The technical solution of the present invention is: A method for generating a precise finite element model of a 30° wedge-shaped locking screw thread includes the following steps:

[0005] S1: Obtain the physical parameters of the nut, the data of the profile segmentation points, and the three-dimensional coordinate information of the finite element mesh nodes of the screw thread, and determine the basic structural parameters of the nut thread profile according to the 30° wedge-shaped locking screw thread profile to be generated;

[0006] S2: Calculate the minimum axial node spacing and the minimum circumferential node spacing of the screw thread according to the physical parameters of the nut and the three-dimensional coordinate information of the finite element mesh nodes of the screw thread, and determine the tolerance value according to the minimum axial node spacing and the minimum circumferential node spacing of the screw thread;

[0007] S3: Obtain the finite element mesh nodes of the nut, and perform coordinate transformation on the finite element mesh nodes of the nut;

[0008] S4: Perform profile offset operation according to the finite element mesh nodes of the nut after coordinate transformation, generate a finite element model of the 30° wedge-shaped locking screw thread according to the basic structural parameters of the nut thread profile, and determine the tolerance value.

[0009] Further, in step S1, the physical parameters of the nut include the nominal diameter D of the internal thread, the intercept P, the number of equal parts N of the pitch P , the number of equal parts N in the circumferential direction r , the number of dense grid layers n m and the thread helix direction;

[0010] The data of the profile segmentation points include the first profile segmentation point θ1, the second profile segmentation point θ2, the third profile segmentation point θ3, and the fourth profile segmentation point θ4; where

[0011]

[0012] The basic structural parameters of the nut thread profile include the original triangular height H of the thread and the basic minor diameter D1 of the internal thread.

[0013] Further, in step S2, the minimum axial node spacing A of the thread m is calculated by the formula:

[0014]

[0015] where h m represents the height of the dense grid layer, P represents the thread pitch, and N P represents the number of equal parts of the pitch;

[0016] In step S2, the polar coordinates (r p1 , θ p1 ) of the finite element mesh node numbered 1 of the thread in the Cartesian coordinate system are converted into rectangular coordinates (x p1 , y p1 ), and the polar coordinates (r p2 , θ p2 ) of the finite element mesh node numbered 2 of the thread in the Cartesian coordinate system are converted into rectangular coordinates (x p2 , y p2 ), and the minimum circumferential node spacing C of the thread is calculated according to the rectangular coordinates m , and its calculation formula is:

[0017]

[0018] where θ p1 = 0 x p1 represents the x-axis coordinate of the finite element mesh node numbered 1 of the thread in the Cartesian coordinate system, y p1 represents the y-axis coordinate of the finite element mesh node numbered 1 of the thread in the Cartesian coordinate system, x p2 represents the x-axis coordinate of the finite element mesh node numbered 2 of the thread in the Cartesian coordinate system, y p2 represents the y-axis coordinate of the finite element mesh node numbered 2 of the thread in the Cartesian coordinate system, r p1 represents the polar radius of the finite element mesh node numbered 1 of the thread in the Cartesian coordinate system, θ p1 represents the polar angle of the finite element mesh node numbered 1 of the thread in the Cartesian coordinate system, r p2 represents the polar radius of the finite element mesh node numbered 2 of the thread in the Cartesian coordinate system, θ p2 represents the polar angle of the finite element mesh node numbered 2 of the thread in the Cartesian coordinate system, D represents the nominal diameter of the internal thread, and N r represents the number of equal parts in the circumferential direction;

[0019] In step S2, if the minimum axial node spacing A of the thread m is less than the minimum circumferential node spacing C of the thread m , the calculation formula for the tolerance value Err is:

[0020] Err = Errp × A m

[0021] where Errp represents the tolerance coefficient;

[0022] If the minimum axial node spacing A of the thread m is greater than or equal to the minimum circumferential node spacing C of the thread m , the calculation formula for the tolerance value Err is:

[0023] Err = Errp × C m .

[0024] Further, in step S3, the specific method for coordinate transformation is: within the range of 0 - 2π rad of the θ-axis coordinate in the cylindrical coordinate system, perform the transformation from Cartesian coordinates to cylindrical coordinates for all nut finite element mesh nodes.

[0025] Further, step S4 includes the following sub-steps:

[0026] S41: Determine the multi-layer dense grid nodes based on the nut finite element mesh nodes after coordinate transformation;

[0027] S42: Perform a profile offset operation on the multi-layer dense grid nodes;

[0028] S43: Set the radial direction interpolation coefficient of the multi-layer dense grid nodes, and update the cylindrical coordinates of the multi-layer dense grid nodes after performing the profile offset operation;

[0029] S44: Convert the cylindrical coordinates of the updated multi-layer dense grid nodes into Cartesian coordinates, and replace the nut finite element mesh nodes with the multi-layer dense grid nodes converted into Cartesian coordinates to generate a 30° wedge-shaped anti-loosening thread finite element model and determine the tolerance value.

[0030] Further, in step S41, the nut finite element mesh nodes with the R-axis coordinate value in the cylindrical coordinates between and are used as the multi-layer dense grid nodes, where D represents the nominal diameter of the internal thread, n m represents the number of dense grid layers, and h m represents the height of the dense grid layer.

[0031] Further, in step S42, the calculation formula for performing the profile offset operation is:

[0032]

[0033] Among them, R'(θ, z) represents a function with the data of the two coordinate axes θ and z as independent variables and the R coordinate as the dependent variable in the cylindrical coordinate system, P represents the thread pitch, D represents the nominal diameter of the internal thread, D1 represents the original basic minor diameter of the internal thread, H represents the original triangular height of the thread, θ1 represents the first contour segmentation point, θ2 represents the second contour segmentation point, θ3 represents the third contour segmentation point, and θ4 represents the fourth contour segmentation point.

[0034] Furthermore, in step S43, the radial interpolation coefficient k of the multi-layer dense grid nodes R The calculation formula is:

[0035]

[0036] Among them, R i represents the R-axis coordinate value of the multi-layer dense grid node numbered i in the cylindrical coordinate system, R min represents the R-axis coordinate value of the innermost node of the multi-layer dense grid node after the contour offset operation, and R max represents the R-axis coordinate value of the outermost node of the multi-layer dense grid node after the contour offset operation;

[0037] In step S43, the coordinate expression of the updated multi-layer dense grid node is i”(R i ”, θ i , z i ). The expression of the R-axis coordinate R i ” of the cylindrical coordinate is R i ” = k R R i (θ i , z i ) + (1 - k R )R min . Among them, R i ” represents the R-axis coordinate after two transformation operations, θ i represents the θ-axis coordinate of the node numbered i in the cylindrical coordinate system, and z i represents the z-axis coordinate of the node numbered i in the cylindrical coordinate system.

[0038] The beneficial effects of the present invention are:

[0039] (1) The 30° wedge-shaped thread locking profile formula proposed by the present invention can quickly generate the 30° wedge-shaped thread locking profile. This profile formula is a necessary condition and premise for the finite element study of the thread locking performance of the 30° wedge-shaped thread locking.

[0040] (2) The present invention can efficiently, highly accurately, and in large quantities obtain 30° wedge-shaped anti-loosening thread precision finite element models under various size parameters in the case of full-automatic calculation. It has advanced the complex 30° wedge-shaped anti-loosening profile grid drawing work from being unable to draw to pure algorithm drawing after inputting the calculation profile formula, laying a technical foundation for the subsequent research and improvement of the stress distribution and anti-loosening performance of the 30° wedge-shaped anti-loosening profile.

[0041] (3) The thread profile grid generation method adopted by the present invention is to deform the dense grid in the undeformed bolt model into a thread profile by means of node offset. The node offset operation only affects the shape of the dense grid and will not affect any mechanical parameters of the bolt. At the same time, controlling the outermost layer of the grid to remain unchanged, after the innermost layer of the grid fits the profile, a unified offset operation is then performed on the intermediate layer nodes. The advantage of this algorithm is that the number of dense grid layers can be set arbitrarily without modifying the algorithm itself, and it has strong applicability.

[0042] (4) The present invention uses a radial interpolation coefficient to update the node coordinates of the internal multi-layer grids. The key point of this algorithm is that the selection of the interpolation coefficient has a great influence on controlling the distortion of the internal grids, and the degree of grid distortion determines the convergence of this model. By changing the linearity and non-linearity of the interpolation coefficient, a more ideal grid can be obtained. Description of the Drawings

[0043] Figure 1 It is a flowchart for generating a 30° wedge-shaped anti-loosening thread precision finite element model;

[0044] Figure 2 It is a schematic cross-sectional structure diagram of a 30° wedge-shaped anti-loosening nut;

[0045] Figure 3 It is a schematic diagram of transforming the nut dense grid into an internal thread grid. Detailed Embodiment

[0046] The following further describes the embodiments of the present invention with reference to the drawings.

[0047] As Figure 1 shown, the present invention provides a method for generating a 30° wedge-shaped anti-loosening thread precision finite element model, including the following steps:

[0048] S1: Obtain the physical parameters of the nut, the data of the profile segmentation points, and the three-dimensional coordinate information of the thread finite element grid nodes, and determine the basic structure parameters of the nut thread profile according to the 30° wedge-shaped anti-loosening thread profile to be generated;

[0049] S2: Calculate the minimum axial node spacing and the minimum circumferential node spacing of the thread based on the physical parameters of the nut and the three-dimensional coordinate information of the thread finite element mesh nodes, and determine the tolerance value according to the minimum axial node spacing and the minimum circumferential node spacing of the thread;

[0050] S3: Obtain the nut finite element mesh nodes and perform coordinate transformation on the nut finite element mesh nodes;

[0051] S4: Perform a contour offset operation based on the nut finite element mesh nodes after coordinate transformation, generate a 30° wedge-shaped locking thread finite element model according to the basic structural parameters of the nut thread profile, and determine the tolerance value.

[0052] Before describing the computer program flow, it is first necessary to present the contour formula of the 30° wedge-shaped locking thread. Compared with the ordinary internal thread whose tooth bottom is a circular arc structure, the tooth bottom structure of the 30° wedge-shaped locking thread is a 30° wedge, as Figure 2 shown. The segmentation points of the 30° wedge-shaped locking thread contour are basically the same as those of the ordinary thread, only the third contour segmentation point θ3 is slightly different.

[0053] In the embodiment of the present invention, in step S1, the physical parameters of the nut include the nominal diameter D of the internal thread, the intercept P, the number of equal parts N of the pitch P , the number of equal parts N in the circumferential direction r , the number of dense grid layers n m and the thread helix direction;

[0054] The contour segmentation point data includes the first contour segmentation point θ1, the second contour segmentation point θ2, the third contour segmentation point θ3, and the fourth contour segmentation point θ4; among them,

[0055]

[0056] The basic structural parameters of the nut thread profile include the original triangular height H of the thread and the basic minor diameter D1 of the internal thread.

[0057] In the embodiment of the present invention, in step S2, the minimum axial node spacing A m of the thread is calculated by the formula:

[0058]

[0059] where h m represents the height of the dense grid layer, P represents the thread intercept, and N P represents the number of equal parts of the pitch;

[0060] In step S2, convert the polar coordinates (r p1 , θ p1 ) of the thread finite element mesh node numbered 1 in the Cartesian coordinate system into rectangular coordinates (x p1 , yp1 ) Convert the polar coordinates (r p2 , θ p2 ) of the finite element mesh node numbered 2 in the Cartesian coordinate system to rectangular coordinates (x p2 , y p2 ), and calculate the minimum circumferential node spacing C of the thread according to the rectangular coordinates m . Its calculation formula is:

[0061]

[0062] Where θ p1 = 0, x p1 represents the x-axis coordinate of the finite element mesh node numbered 1 in the Cartesian coordinate system, and y p1 represents the y-axis coordinate of the finite element mesh node numbered 1 in the Cartesian coordinate system, x p2 represents the x-axis coordinate of the finite element mesh node numbered 2 in the Cartesian coordinate system, and y p2 represents the y-axis coordinate of the finite element mesh node numbered 2 in the Cartesian coordinate system, r p1 represents the polar radius of the finite element mesh node numbered 1 in the Cartesian coordinate system, θ p1 represents the polar angle of the finite element mesh node numbered 1 in the Cartesian coordinate system, r p2 represents the polar radius of the finite element mesh node numbered 2 in the Cartesian coordinate system, θ p2 represents the polar angle of the finite element mesh node numbered 2 in the Cartesian coordinate system, D represents the nominal diameter of the internal thread, and N r represents the number of circumferential equal divisions;

[0063] In step S2, if the minimum axial node spacing A of the thread m is less than the minimum circumferential node spacing C of the thread m , then the calculation formula for the tolerance value Err is:

[0064] Err = Errp × A m

[0065] Where Errp represents the tolerance coefficient;

[0066] If the minimum axial node spacing A of the thread m is greater than or equal to the minimum circumferential node spacing C of the thread m , then the calculation formula for the tolerance value Err is:

[0067] Err = Errp × C m .

[0068] In an embodiment of the present invention, in step S3, the specific method for coordinate transformation is as follows: within the range of 0 - 2π rad of the θ-axis coordinate in the cylindrical coordinate system, perform Cartesian coordinate to cylindrical coordinate transformation on all nut finite element mesh nodes.

[0069] In an embodiment of the present invention, step S4 includes the following sub-steps:

[0070] S41: Determine multi-layer dense mesh nodes according to the nut finite element mesh nodes after coordinate transformation;

[0071] S42: Perform a profile offset operation on the multi-layer dense mesh nodes;

[0072] S43: Set the radial direction interpolation coefficient of the multi-layer dense mesh nodes, and update the cylindrical coordinates of the multi-layer dense mesh nodes after performing the profile offset operation;

[0073] S44: Convert the cylindrical coordinates of the updated multi-layer dense mesh nodes into Cartesian coordinates, and replace the nut finite element mesh nodes with the multi-layer dense mesh nodes converted into Cartesian coordinates to generate a 30° wedge-shaped locking thread finite element model and determine the tolerance value.

[0074] In an embodiment of the present invention, as Figure 3 shown, in step S41, the nut finite element mesh nodes with the R-axis coordinate value in the cylindrical coordinates within to are used as the multi-layer dense mesh nodes, where D represents the nominal diameter of the internal thread, n m represents the number of dense mesh layers, and h m represents the height of the dense mesh layer.

[0075] In an embodiment of the present invention, in step S42, the calculation formula for performing the profile offset operation is:

[0076]

[0077] where R'(θ, z) represents a function with the data of the two coordinate axes θ and z in the cylindrical coordinate system as independent variables and the R coordinate as the dependent variable. The subscript of R' indicates the R coordinate after a single transformation operation. θ represents the data of the independent variable of the θ coordinate axis in the cylindrical coordinate system, P represents the thread pitch, z represents the data of the independent variable of the z coordinate axis in the cylindrical coordinate system, D represents the nominal diameter of the internal thread, D1 represents the original basic minor diameter of the internal thread, H represents the original height of the thread triangle, θ1 represents the first profile segmentation point, θ2 represents the second profile segmentation point, θ3 represents the third profile segmentation point, and θ4 represents the fourth profile segmentation point.

[0078] When the thread helix direction is right-handed, the angular independent variable is θ. When the thread helix direction is left-handed, θ needs to be replaced by 2π - θ. R'(θ,z) is periodic both circumferentially and axially:

[0079] R'(θ,z) = R'(θ + 2mπ,z + nP) m,n = 1,2,3,…

[0080] In the embodiment of the present invention, in step S43, the radial interpolation coefficient k of the multi-layer dense grid nodes R The calculation formula is:

[0081]

[0082] where, R i represents the R-axis coordinate value of the multi-layer dense grid node numbered i in the cylindrical coordinate system, R min represents the R-axis coordinate value of the innermost node of the multi-layer dense grid node after the contour offset operation, R max represents the R-axis coordinate value of the outermost node of the multi-layer dense grid node after the contour offset operation;

[0083] In step S43, the coordinate expression of the updated multi-layer dense grid node is i”(R i ”,θ i ,z i ). The expression of the R-axis coordinate R i ” of the cylindrical coordinate is R i ” = k R R i (θ i ,z i )+(1 - k R )R min , where, R i ” represents the R-axis coordinate after two transformation operations, θ i represents the θ-axis coordinate of the node numbered i in the cylindrical coordinate system, z i represents the z-axis coordinate of the node numbered i in the cylindrical coordinate system.

[0084] The beneficial effects of the present invention are:

[0085] (1) The 30° wedge-shaped thread locking profile formula proposed by the present invention can quickly generate the 30° wedge-shaped thread locking profile. This profile formula is a necessary condition and premise for the finite element study of the thread locking performance of the 30° wedge-shaped thread locking.

[0086] (2) The present invention can efficiently, highly accurately, and in large quantities obtain 30° wedge-shaped anti-loosening thread precision finite element models under various size parameters in the case of fully automatic calculation. It has advanced the complex 30° wedge-shaped anti-loosening profile grid drawing work from impossible to draw to pure algorithm drawing after inputting the calculation profile formula, laying a technical foundation for the subsequent research and improvement of the stress distribution and anti-loosening performance of the 30° wedge-shaped anti-loosening profile.

[0087] (3) The thread profile grid generation method adopted by the present invention is to deform the dense grid in the undeformed bolt model into a thread profile by means of node offset. The node offset operation only affects the shape of the dense grid and does not affect any mechanical parameters of the bolt. At the same time, controlling the outermost layer of the grid to remain unchanged, after the innermost layer of the grid fits the profile, a unified offset operation is performed on the intermediate layer nodes. The advantage of this algorithm is that the number of dense grid layers can be set arbitrarily without modifying the algorithm itself, and it has strong applicability.

[0088] (4) The present invention uses a radial interpolation coefficient to update the node coordinates of the internal multi-layer grid. The key point of this algorithm is that the selection of the interpolation coefficient has a great influence on controlling the distortion of the internal grid, and the degree of grid distortion determines the convergence of this model. By changing the linear and non-linear interpolation coefficients, a more ideal grid can be obtained.

[0089] Those of ordinary skill in the art will realize that the embodiments described herein are for helping the reader understand the principles of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific deformations and combinations that do not depart from the essence of the present invention based on these technical revelations disclosed by the present invention, and these deformations and combinations are still within the protection scope of the present invention.

Claims

1. A method for generating a precision finite element model of a 30° wedge-shaped anti-loosening thread, characterized in that, Including the following steps: S1: Obtain the physical parameters of the nut, the data of the contour segmentation points, and the three-dimensional coordinate information of the finite element mesh nodes of the thread, and determine the basic structural parameters of the nut thread profile according to the 30° wedge-shaped anti-loosening thread profile to be generated; S2: Calculate the minimum axial node spacing and the minimum circumferential node spacing of the thread according to the physical parameters of the nut and the three-dimensional coordinate information of the finite element mesh nodes of the thread, and determine the tolerance value according to the minimum axial node spacing and the minimum circumferential node spacing of the thread; S3: Obtain the finite element mesh nodes of the nut, and perform coordinate transformation on the finite element mesh nodes of the nut; S4: Perform a contour offset operation according to the finite element mesh nodes of the nut after coordinate transformation, generate a finite element model of the 30° wedge-shaped anti-loosening thread according to the basic structural parameters of the nut thread profile, and determine the tolerance value; In the step S2, the minimum axial node pitch of the thread A m is calculated by the formula: Among them, h m represents the height of the dense grid layer, P represents the thread intercept, N P represents the number of equal parts of the pitch; In step S2, the polar coordinates ( r p1 , θ p1 ) of the thread finite element mesh node numbered 1 in the Cartesian coordinate system are converted into rectangular coordinates ( x p1 , y p1 ). The polar coordinates ( r p2 , θ p2 ) of the thread finite element mesh node numbered 2 in the Cartesian coordinate system are converted into rectangular coordinates ( x p2 , y p2 ), and the minimum circumferential node pitch C m of the thread is calculated based on the rectangular coordinates. The calculation formula is as follows: r p1 , θ p1 ) x p1 , y p1 ) r p2 , θ p2 ) x p2 , y p2 ) C m , Among them, , , , , x p1 represents the x axial coordinate of the thread finite element mesh node numbered 1 in the Cartesian coordinate system, y p1 represents the y axial coordinate of the thread finite element mesh node numbered 1 in the Cartesian coordinate system, x p2 represents the x axial coordinate of the thread finite element mesh node numbered 2 in the Cartesian coordinate system, y p2 represents the y axial coordinate of the thread finite element mesh node numbered 2 in the Cartesian coordinate system, r p1 represents the polar radius of the thread finite element mesh node numbered 1 in the Cartesian coordinate system, θ p1 represents the polar angle of the thread finite element mesh node numbered 1 in the Cartesian coordinate system, r p2 represents the polar radius of the thread finite element mesh node numbered 2 in the Cartesian coordinate system, θ p2 represents the polar angle of the thread finite element mesh node numbered 2 in the Cartesian coordinate system, D represents the nominal diameter of the internal thread, N r represents the number of equal circumferential divisions; In the said step S2, if the minimum axial pitch of the threads A m is less than the minimum circumferential pitch of the threads C m , then the tolerance value Err is calculated by the formula: Among them, Errp represents the tolerance coefficient; If the minimum axial node spacing of the thread A m is greater than or equal to the minimum circumferential node spacing of the thread C m , then the calculation formula for the tolerance value Err is as follows: 。 2. The method for generating a precise finite element model of a 30° wedge-shaped anti-loosening thread according to claim 1, wherein In the step S1, the physical parameters of the nut include the nominal diameter of the internal thread D , intercept P , number of equal pitches N P , number of equal circumferences N r , number of dense grid layers n m and thread helix direction; The contour segmentation point data includes the first contour segmentation point θ 1. The second contour segmentation point θ 2. The third contour segmentation point θ 3. And the fourth contour segmentation point θ 4; Wherein, The basic structural parameters of the nut thread profile include the height of the original thread triangle H and the basic minor diameter of the internal thread D 1.

3. The method for generating a precise finite element model of a 30° wedge-shaped lock-preventing thread according to claim 1, wherein In the step S3, the specific method for coordinate transformation is as follows: within the range where the θ axis coordinate in the cylindrical coordinate system is 0 - 2π rad, perform the transformation from Cartesian coordinates to cylindrical coordinates for all nut finite element mesh nodes.

4. The method for generating a 30° wedge-shaped anti-loosening thread precision finite element model according to claim 1, wherein The step S4 includes the following sub-steps: S41: Determine the multi-layer dense mesh nodes according to the finite element mesh nodes of the nut after coordinate transformation; S42: Perform a contour offset operation on the multi-layer dense mesh nodes; S43: Set the radial direction interpolation coefficient of the multi-layer dense mesh nodes, and update the cylindrical coordinates of the multi-layer dense mesh nodes after performing the contour offset operation; S44: Convert the cylindrical coordinates of the updated multi-layer dense mesh nodes into Cartesian coordinates, and replace the finite element mesh nodes of the nut with the multi-layer dense mesh nodes converted into Cartesian coordinates to generate a finite element model of the 30° wedge-shaped anti-loosening thread and determine the tolerance value.

5. The method for generating a precise finite element model of a 30° wedge-shaped anti-loosening thread according to claim 4, wherein In the step S41, the R axis coordinate values of the cylindrical coordinates are to nut finite element mesh nodes as multi-layer dense mesh nodes, where D represents the nominal diameter of the internal thread, n m represents the number of dense mesh layers, h m represents the height of the dense mesh layer.

6. The method for generating a 30° wedge-shaped anti-loosening thread precision finite element model according to claim 4, characterized in that In the step S42, the calculation formula for performing the contour offset operation is: Among them, represents a function with the data of two coordinate axes θ and z as independent variables in the cylindrical coordinate system, and coordinate as the dependent variable, P represents the thread pitch, D represents the nominal diameter of the internal thread, D 1 represents the original basic minor diameter of the internal thread, H represents the original triangular height of the thread, θ 1 represents the first contour segmentation point, θ 2 represents the second contour segmentation point, θ 3 represents the third contour segmentation point, θ 4 represents the fourth contour segmentation point.

7. The method for generating a 30° wedge-shaped loosening-preventing thread precision finite element model according to claim 4, wherein In the said step S43, the radial direction interpolation coefficient of the multi-layer dense grid nodes k R is calculated by the following formula: Among them, R i represents the i axial coordinate value in the cylindrical coordinate system of the multi-layer dense grid node numbered R ; R min represents the R axial coordinate value of the innermost node of the multi-layer dense grid node after the contour offset operation; R max represents the R axial coordinate value of the outermost node of the multi-layer dense grid node after the contour offset operation; In the step S43, the coordinate expression of the updated multi-layer dense grid nodes is , and the R axis coordinate in the cylindrical coordinate system has the expression , where represents the R axis coordinate after two transformation operations, θ i represents the i axis coordinate of the node with the serial number θ in the cylindrical coordinate system z i represents the i axis coordinate of the node with the serial number z in the cylindrical coordinate system.

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