Method for generating transition grid of finite element axis and outer hexagonal contour of bolt
By automatically generating C3D8 format bolt finite element axis and external hexagonal contour transition meshes, the problem of large number of bolt precision finite element meshes and poor computational convergence is solved, realizing efficient and accurate mesh generation and calculation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-30
- Publication Date
- 2026-04-10
AI Technical Summary
The existing precision finite element mesh for bolts has a huge number of meshes, poor computational convergence, and the transition mesh operation is cumbersome and relies on manual drawing, resulting in low computational efficiency.
A transition mesh generation method using the bolt finite element axis and external hexagonal contour is adopted. By automatically generating a C3D8 format mesh, the number of meshes in non-interest areas is reduced, ensuring mesh regularity and computational accuracy, and reducing computational difficulty.
It greatly reduces the difficulty of mesh drawing, improves drawing efficiency and accuracy, reduces the number of meshes, reduces the computational scale and convergence difficulty, and improves the efficiency of finite element calculation.
Smart Images
Figure CN121837548A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of precision finite element technology for bolts, specifically relating to the design of a method for generating a transition mesh between the finite element axis and the external hexagonal contour of a bolt. Background Technology
[0002] There are two ways to handle the axial mesh in traditional bolt finite element methods. One is to not use a transition mesh, so that the mesh at the axial center is completely consistent with the mesh at the thread. Although this method is simple, it greatly increases the number of meshes in the overall model, and the convergence difficulty and computation time will also increase significantly. The other method is to use a pentahedral mesh, which directly divides the cylinder at the axial center into multiple pentahedral elements according to the diameter. Although this method reduces the number of meshes, the included angles of the elements are sharp, and the convergence difficulty of the calculation is even greater.
[0003] Traditional methods for processing external hexagonal contour meshes do not use transition meshes. Axial transition meshes and external hexagonal contour transition meshes in bolt finite element analysis are special techniques in the field of bolt precision finite element subdivision. Their function is to quickly and regularly transition the sleeve-shaped finite element mesh of the bolt shank to the axis, and the sleeve-shaped finite element nodes of the bolt head or nut to the outermost hexagonal physical contour. This method ensures that the shape of the finite element mesh is sufficiently regular and that the mesh closely matches the physical contour of the object, thus improving the computational accuracy and convergence of bolt precision finite element calculations. Summary of the Invention
[0004] The purpose of this invention is to solve the problems of existing bolt precision finite element meshes having a huge number of meshes, poor computational convergence, difficult transition mesh operations, and complete reliance on manual drawing. It proposes a method for generating transition meshes between the bolt finite element axis and the external hexagonal contour, which greatly reduces the complexity of the operation, improves the fault tolerance rate, and reduces the mesh size of the axis and bolt head.
[0005] The technical solution of this invention is: a method for generating a transition mesh between the finite element axis and the external hexagonal profile of a bolt, comprising the following steps: S1. Obtain the circumferential layer number, the number of inner layers of the current transition layer of the bolt, and the Cartesian coordinates of the first base point.
[0006] S2. Obtain the number of circular lattice nodes N of the current transition layer in the plane where the first base point is located, based on the circumferential layer number of the current transition layer.
[0007] S3. Draw the boundary of a square or regular hexagon based on the number of nodes N and the transition contour type.
[0008] S4. Divide the boundary of the square or regular hexagon into N equal parts.
[0009] S5. Rename the address of the first base point according to the number of transition layers to obtain the renamed base point.
[0010] S6. Generate and output the axis and external hexagonal contour transition mesh in C3D8 format based on the renamed base point.
[0011] Furthermore, step S3 includes the following sub-steps: S31. If the transition contour type is square, determine whether the number of nodes N is divisible by 4. If so, proceed to step S32; otherwise, subsequent calculations cannot be performed, and the process ends.
[0012] If the transition contour type is a regular hexagon, then determine whether the number of nodes N is divisible by 6. If so, proceed to step S32; otherwise, subsequent calculations cannot be performed, and the process ends.
[0013] S32. If the transition contour type is square, then connect the first base point A and the origin O of the Cartesian coordinate system to obtain line segment AO, and set the point on line segment AO that is 0.7L away from the origin O as the second base point B.
[0014] If the transition profile type is a regular hexagon, then connect the origin O of the Cartesian coordinate system to the first base point A and extend it. Based on the actual physical length of the bolt's outer hexagonal profile, obtain the extension distance of line segment OA, and set the endpoint of the extension line as the second base point B.
[0015] S33. Using the second base point B as the corner point of the square or regular hexagon and the origin O as the centroid of the square or regular hexagon, draw the boundary of the square or regular hexagon.
[0016] Furthermore, in step S4, all points after being divided into N equal parts are arranged clockwise as B0, B0+1, B0+2, ..., B0+N-1, where the initial point B0 is the second base point B.
[0017] Furthermore, in step S5, the address of the first base point A is renamed according to the number of transition layers n, resulting in the renamed base point B. n .
[0018] Furthermore, step S6 includes the following sub-steps: S61. Connect the N points on a square or regular hexagon with the initial address B0 to the points on a circular lattice with the renamed base point B0. n Connect each pair of N points starting from the address to obtain N lines.
[0019] S62. Divide each line into n equal parts, and obtain n-1 points on each line excluding the two endpoints.
[0020] S63. Move the initial point B0 to the renamed base point B. nThe n-1 points B1~B n-1 Using the initial point B0 as the base point, connect the corresponding points on each line clockwise to obtain n-1 circles, from the initial point B0 to the renamed base point B. n The direction stores the addresses of N points in each ring, thus obtaining the transition zone between the circular dot matrix and the square or regular hexagon.
[0021] S64. Let j be the number of C2D4 grids in the m-th ring of the transition zone, with an initial value of 1 for j and an initial value of 0 for nx.
[0022] S65. Determine if j=N. If yes, proceed to step S67; otherwise, proceed to step S66.
[0023] S66. Generate a C2D4 mesh in the cylindrical coordinate plane at Z=0, with the node address combination being [B m +j-1,B m +j,B m+1 +j,B m+1 [+j-1], increment the value of grid number j by 1, and return to step S65.
[0024] S67. Generate a C2D4 mesh in the cylindrical coordinate plane at Z=0, with the node address combination being [B m +j-1,B m B m+1 B m+1 +j-1].
[0025] S68. Determine whether m>n is satisfied. If yes, proceed to step S69; otherwise, increment the value of m by 1 and return to step S66.
[0026] S69. Stretch all C2D4 meshes in the Z-axis direction to generate and output a C3D8 format mesh with a transition between the axis and the outer hexagonal contour.
[0027] The beneficial effects of this invention are: (1) In the precision finite element mesh of bolts, the present invention uses axial transition mesh and external hexagonal contour transition mesh, which greatly reduces the number of meshes in non-interest areas. While ensuring the calculation accuracy, it makes the meshes at the core of the screw and the contour of the bolt head more regular, which greatly reduces the scale of finite element calculation and the difficulty of convergence.
[0028] (2) The present invention adopts a fully automatic generation technology, and the three-dimensional information of each key node does not require manual calculation intervention, which reduces the difficulty of drawing the precision finite element mesh of the bolt. Compared with manual drawing, it greatly improves the drawing efficiency and accuracy of the mesh. Attached Figure Description
[0029] Figure 1The diagram shown is a flowchart of a method for generating a transition mesh between the finite element axis and the external hexagonal contour of a bolt, according to an embodiment of the present invention.
[0030] Figure 2 The diagram shown is a schematic diagram of the equal division of square and regular hexagonal nodes provided in an embodiment of the present invention.
[0031] Figure 3 The diagram shown is a node address rule diagram within the square and regular hexagonal transition zone provided in an embodiment of the present invention.
[0032] Figure 4 The diagram shown is a schematic of the transition mesh between the axis and the outer hexagonal contour when the Z-axis stretching number is 3, provided in an embodiment of the present invention.
[0033] Figure 5 The figure shown is a schematic diagram of a complete finite element model of a bolt using a transition mesh, provided in an embodiment of the present invention. Detailed Implementation
[0034] Exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be understood that the embodiments shown and described in the drawings are merely exemplary and are intended to illustrate the principles and spirit of the invention, and are not intended to limit the scope of the invention.
[0035] This invention provides a method for generating a transition mesh between the finite element axis and the external hexagonal profile of a bolt, such as... Figure 1 As shown, the process includes the following steps S1 to S6: S1. Obtain the circumferential layer number, the number of inner layers of the current transition layer of the bolt, and the Cartesian coordinates of the first base point.
[0036] S2. Obtain the number N of circular lattice nodes in the plane where the first base point is located in the current transition layer based on the circumferential layer number of the current transition layer. Figure 2 As shown in the circular dot matrix.
[0037] S3. Draw the boundary of a square or regular hexagon based on the number of nodes N and the transition contour type.
[0038] Step S3 includes the following sub-steps S31 to S33: S31. If the transition contour type is square, determine whether the number of nodes N is divisible by 4. If so, proceed to step S32. Otherwise, since the number of dot matrix nodes does not meet the requirements, subsequent calculations cannot be performed, and the process ends.
[0039] If the transition contour type is a regular hexagon, then determine whether the number of nodes N is divisible by 6. If so, proceed to step S32; otherwise, since the number of lattice nodes does not meet the requirements, subsequent calculations cannot be performed, and the process ends.
[0040] S32. If the transition contour type is square, then connect the first base point A and the origin O of the Cartesian coordinate system to obtain line segment AO. Set the point on line segment AO that is 0.7L away from the origin O as the second base point B. Figure 2 As shown in (a).
[0041] If the transition profile type is a regular hexagon, then connect the origin O of the Cartesian coordinate system to the first base point A and extend it. Based on the actual physical length of the bolt's outer hexagonal profile, obtain the extension distance of line segment OA, and set the endpoint of the extension line as the second base point B. Figure 2 As shown in (b).
[0042] S33. Using the second base point B as the corner point of the square or regular hexagon and the origin O as the centroid of the square or regular hexagon, draw the boundary of the square or regular hexagon.
[0043] S4. Divide the boundary of the square or regular hexagon into N equal parts.
[0044] like Figure 2 As shown, the points after dividing the boundary of a square or regular hexagon into N equal parts are B0, B0+1, B0+2, ..., B0+N-1 in clockwise order, where the initial point B0 is the second base point B.
[0045] S5. Rename the address of the first base point according to the number of transition layers to obtain the renamed base point.
[0046] like Figure 3 As shown, the address of the first base point A is renamed according to the transition inner layer number n, resulting in the renamed base point B. n .
[0047] S6. Generate and output the axis and external hexagonal contour transition mesh in C3D8 format based on the renamed base point.
[0048] Step S6 includes the following sub-steps S61 to S69: S61. Connect the N points on a square or regular hexagon with the initial address B0 to the points on a circular lattice with the renamed base point B0. n Connect each pair of N points starting from the address with a line, resulting in N connecting lines, such as... Figure 3 As shown.
[0049] S62. Divide each line into n equal parts, resulting in n-1 points on each line excluding the two endpoints, such as... Figure 3 As shown.
[0050] S63. Move the initial point B0 to the renamed base point B. n The n-1 points B1~B n-1Using the initial point B0 as the base point, connect the corresponding points on each line clockwise to obtain n-1 circles, from the initial point B0 to the renamed base point B. n The direction stores the addresses of N points in each ring, resulting in the transition zone between the circular dot matrix and the square or regular hexagon, where... Figure 3 (a) represents the transition zone between the circular lattice and the square. Figure 3 (b) is the transition zone between the circular lattice and the regular hexagon.
[0051] S64. Let j be the number of C2D4 grids in the m-th ring of the transition zone, with an initial value of 1 for j and an initial value of 0 for nx.
[0052] S65. Determine if j=N. If yes, proceed to step S67; otherwise, proceed to step S66.
[0053] S66. Generate a C2D4 mesh in the cylindrical coordinate plane at Z=0, with the node address combination being [B m +j-1,B m +j,B m+1 +j,B m+1 [+j-1], increment the value of grid number j by 1, and return to step S65.
[0054] S67. Since the maximum address of the matrix is B nx +j-1 and B nx+1 +j-1, therefore, in the last loop, the pointer address will exceed the maximum dimension. To ensure the address closure of the ring lattice, a C2D4 mesh is generated in the cylindrical coordinate plane at Z=0, with the node address combination being [B m +j-1,B m B m+1 B m+1 +j-1].
[0055] In this embodiment of the invention, Z represents the height of a point in the cylindrical coordinate system.
[0056] S68. Determine whether m>n is satisfied. If yes, proceed to step S69; otherwise, increment the value of m by 1 and return to step S66.
[0057] S69. Stretch all C2D4 meshes in the Z-axis direction to generate and output a C3D8 format mesh with a transition between the axis and the outer hexagonal contour.
[0058] In this embodiment of the invention, C2D4 refers to a 2D 4-node mesh, and C3D8 refers to a 3D hexahedral 8-node mesh.
[0059] like Figure 4 The image shows the actual finite element model of the generated axis-to-external hexagonal profile transition mesh. Figure 5The image shows a complete example of a precision finite element model of a bolt using this transition method.
[0060] In this embodiment of the invention, the cylindrical finite element mesh is transitioned to a cubic finite element mesh for the bolt core, ensuring that the core region consists of regular hexahedral elements, significantly reducing the number of mesh elements and the difficulty of computational convergence. Simultaneously, at the bolt head, a single- or multi-turn transition mesh is used to transition the cylindrical mesh to an external hexagonal profile, ensuring the regularity of the mesh shape. This allows the finite element model of the bolt head to perfectly correspond to its physical dimensions without increasing the model's convergence difficulty.
[0061] The challenge of creating circular transition polygons lies in the significant mesh distortion at the polygon's corner points, which affects the computational convergence. This invention employs a multiple equal-division method: the polygon is divided into equal parts and connected to the original circular lattice point by line, and then all line segments are further divided into equal parts. Each ring of nodes, except for the inner and outer boundary points, is actually located in a non-equal-divided position within that ring. The advantage of this node arrangement is that the mesh shape distortion at the polygon's corner points is minimal, ensuring the model can converge normally in computation.
[0062] This invention introduces the concept of the number of transition inner layers. The value of the number of transition inner layers is a key value for controlling the transition mesh size and corner mesh distortion. The larger the number of transition inner layers n, the smaller the mesh size and the finer the mesh, but the distortion of the corner mesh will also increase accordingly. The smaller the number of transition inner layers n, the larger the mesh size and the fewer the meshes, while the distortion of the corner mesh will decrease.
[0063] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.
Claims
1. A method for generating a finite element bolt axis and external hexagon profile transition mesh, characterized by, The method comprises the following steps: S1, acquiring the number of circumferential sub-layers of the current transition layer of the bolt, the number of inner transition sub-layers and the Cartesian coordinates of the first base point; S2, acquiring the number N of circular lattice nodes of the current transition layer in the plane where the first base point is located according to the number of circumferential sub-layers of the current transition layer; S3, drawing the boundary of a square or a regular hexagon according to the number N of nodes and the transition profile type; S4, equally dividing the boundary of the square or the regular hexagon by N; S5, renaming the address of the first base point according to the number of inner transition sub-layers to obtain a renamed base point; S6, generating a C3D8 format transition mesh of the shaft and the outer hexagonal profile and outputting the same according to the renamed base point.
2. The method of claim 1, wherein, The step S3 comprises the following steps: S31, if the transition profile type is a square, determining whether the number N of nodes can be divided by 4, if yes, entering step S32, otherwise, the subsequent calculation cannot be performed, and the process ends; if the transition profile type is a regular hexagon, determining whether the number N of nodes can be divided by 6, if yes, entering step S32, otherwise, the subsequent calculation cannot be performed, and the process ends; S32, if the transition profile type is a square, connecting the first base point A and the origin O of the Cartesian coordinate system to obtain a line segment AO, and setting a point position at a position 0.7L away from the origin O on the line segment AO as a second base point B; if the transition profile type is a regular hexagon, connecting the origin O of the Cartesian coordinate system to the first base point A and extending, obtaining an extension distance of the line segment OA according to the actual physical length of the outer hexagonal profile of the bolt, and setting the end point of the extension line as the second base point B; S33, taking the second base point B as a corner point of the square or the regular hexagon, and taking the origin O as the center of the square or the regular hexagon, to draw the boundary of the square or the regular hexagon.
3. The method of claim 2, wherein, After being equally divided by N in the step S4, all the point positions are sequentially B0, B0+1, B0+2, …, B0+N-1 in clockwise direction, wherein the initial point B0 is the second base point B.
4. The method of claim 3, wherein, The step S5 renames the address of the first base point A according to the transition inner division number n, to obtain a renamed base point B n .
5. The method of claim 4, wherein, The step S6 comprises the following steps: S61. Connect the N points on a square or regular hexagon with the initial address B0 to the points on a circular lattice with the renamed base point B0. n Connect each pair of N points starting from the address to obtain N connecting lines; S62, equally dividing each line by n to obtain n-1 points on each line except the two end points; S63, rename the initial point B0 to the base point B n S64, connect the corresponding point positions on each line clockwise to obtain n-1 circles, and store the addresses of the N points of each circle in the direction from the initial point B0 to the renamed base point B n-1 n S65, obtain the transition zone between the circular point array and the square or regular hexagon. S64, setting j as the number of C2D4 meshes of the mth circle on the transition zone, and setting the initial value of j as 1 and the initial value of nx as 0; S65, determining whether j=N is satisfied, if yes, entering step S67, otherwise, entering step S66; S66, generate a C2D4 grid in the cylindrical coordinate plane of Z=0, the node address combination is [B m +j-1, B m +j, B m+1 +j, B m+1 +j-1], let the value of grid number j be increased by 1, and return to step S65; S67, generate a C2D4 grid in the cylindrical coordinate plane of Z=0, node address combination is [B m +j-1, B m , B m+1 , B m+1 +j-1]; S68, determining whether m>n is satisfied, if yes, entering step S69, otherwise, increasing the value of m by 1 and returning to step S66; S69, stretching all C2D4 meshes in the Z-axis direction to generate a C3D8 format transition mesh of the shaft and the outer hexagonal profile and output the same.