Implementation method of bolt finite element mesh 4-2 transition layer

Abstract

The invention discloses an implementation method of a bolt finite element grid 4-2 transition layer. The arrangement mode and position information of the whole transition layer are controlled by using three parameters of a base point coordinate, a generation plane and a generation direction. In combination with dot matrix generation, special point abandoning and node re-numbering methods, all possible arrangement and position conditions of 4-2 transition layers involved in bolt precision finite elements are covered through as few parameters as possible and as simple input as possible. According to the method, the bolt finite element 4-2 transition layer mesh meeting the requirements can be automatically generated at the base point position, a practitioner in the bolt precision finite element industry is helped to rapidly generate the bolt mesh of a plurality of transition layers, and the problems that manual drawing of the bolt precision finite element transition area is too tedious and complex, low in efficiency and low in error-tolerant rate are solved.

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 implementing a 4-2 transition layer of a bolt finite element mesh. Background Technology

[0002] The 4-2 transition layer in finite element meshing is one of two special methods in the finite element method (FEM) field, the other being the 3-1 transition layer. The 3-1 transition layer serves to transition from a dense mesh to a sparse mesh. In the field of precision finite element subdivision for bolts, to ensure a sufficiently dense mesh at the threads while reducing the mesh count in non-interesting areas, it is typically necessary to transition the dense mesh at the threads inwards to a sparse mesh in the bolt core. Compared to ordinary finite element methods, the number of dense meshes in precision finite element methods for bolts is extremely large, requiring the calculation of the 3D coordinates of multiple key points. Manual drawing is cumbersome and has a low error tolerance; if the coordinates of key nodes are calculated incorrectly, the entire transition layer mesh is rendered useless. Therefore, a technique for automatically implementing the 4-2 transition layer is needed. Summary of the Invention

[0003] The purpose of this invention is to solve the problems of the tedious and complex, inefficient and fault-tolerant nature of manually drawing the precision finite element transition zone of bolts. It proposes a method for implementing the 4-2 transition layer of the finite element mesh of bolts, which solves the dependence on manual operation in the prior art and greatly improves the drawing efficiency of the transition mesh.

[0004] The technical solution of this invention is: a method for implementing a 4-2 transition layer of a bolt finite element mesh, comprising the following steps: S1. Obtain the physical parameters of the bolt and the Cartesian coordinates of the first base point.

[0005] S2. Set the number of cycles, operating plane and operating axis according to the physical parameters of the bolt. Create a second base point according to the Cartesian coordinates of the first base point and generate a 3*4 dot matrix.

[0006] S3. Select the nodes in the 3*4 dot matrix and renumber them.

[0007] S4. Determine if the last loop has been entered. If yes, proceed to step S6; otherwise, proceed to step S5.

[0008] S5. Generate 6 C2D4 grids in each loop within the operation plane, increment the loop count by 1, and return to step S4.

[0009] S6. Redirect the renumbered nodes.

[0010] S7. Stretch the C2D4 mesh in the operation plane along the operation axis to generate the C3D8 transition mesh.

[0011] S8 outputs the bolt finite element mesh in C3D8 format, 4-2 transition layer, and the Cartesian coordinates of the second base point.

[0012] Furthermore, the physical parameters of the bolt in step S1 include the diameter of the current transition layer mesh, the number of single-pitch layers, the number of circumferential layers, and the orientation and plane of the mesh to be generated.

[0013] Furthermore, in step S2, if the plane containing the mesh to be generated is the Z=C plane, then the number of iterations is set to i=2π / 4Δθ, the operation plane is the Z=C plane, and the operation axis is the Z-axis, where C is a constant.

[0014] If the plane containing the mesh to be generated is the θ=0 plane, then set the number of loops to i=2π / Δθ, the operation plane to the θ=0 plane, and the operation axis to the θ axis.

[0015] Furthermore, the method for creating the second base point based on the Cartesian coordinates of the first base point in step S2 is as follows: Convert the Cartesian coordinates of the first base point to cylindrical coordinates, and offset it along the r-axis by 2dΔr to obtain the cylindrical coordinates of the second base point. Then convert the cylindrical coordinates of the second base point to Cartesian coordinates, where d represents the direction.

[0016] Furthermore, the values ​​of the direction quantity d are: If the direction of the mesh to be generated is the negative direction of the r-axis, then the direction quantity d = -1.

[0017] If the direction of the mesh to be generated is the positive direction of the r-axis, then the direction quantity d=1.

[0018] Furthermore, the specific method for generating the 3*4 dot matrix in step S2 is as follows: If the plane containing the mesh to be generated is the Z=C plane with the direction of the negative r-axis, then the first base point is taken as the upper left corner of the point matrix to be generated, and i 3*4 point matrices are generated on the operation plane, numbered sequentially from 12i-11 to 12i.

[0019] If the plane containing the mesh to be generated is the Z=C plane with the positive direction of the r-axis, then the first base point is taken as the lower left corner of the point matrix to be generated, and i 3*4 point matrices are generated on the operation plane, numbered sequentially from 12i-11 to 12i.

[0020] If the plane containing the mesh to be generated is the θ=0 plane and the direction is the negative direction of the r-axis, then the first base point is taken as the upper right corner of the point matrix to be generated, and i 3*4 point matrices are generated on the operation plane, numbered sequentially from 12i-11 to 12i.

[0021] If the plane containing the mesh to be generated is the θ=0 plane and the direction is the positive direction of the r-axis, then the first base point is taken as the lower right corner of the point matrix to be generated, and i 3*4 point matrices are generated on the operation plane, numbered sequentially from 12i-11 to 12i.

[0022] Furthermore, the node spacing of the r-axis of the 3*4 dot matrix is ​​set to Δr, and the node spacing of the other axis is set to Δθ or ΔZ according to the configured operation axis.

[0023] Further, in step S3, the nodes numbered [12i-11, 12i-9, 12i-8, 12i-7, 12i-5, 12i-4, 12i-3, 12i-2, 12i-1] in the 3*4 matrix are selected and renumbered sequentially from 9i-8 to 9i.

[0024] Furthermore, the node combinations of the six C2D4 meshes generated in step S5 are [9i-8,9i-7,9i-5,9i-6], [9i-6,9i-5,9i-3,9i-4], [9i-7,9i-5,9i-3,9i-2], [9i-4,9i-3,9i,9i-1], [9i-3,9i-2,9i+2,9i] and [9i-1,9i,9i+2,9i+1].

[0025] Further, in step S6, node number 9i+1 is redirected to 1, and node number 9i+2 is redirected to 2.

[0026] The beneficial effects of this invention are as follows: This invention can automatically generate a 4-2 transition layer mesh for bolts at the base point location, helping practitioners in the bolt precision finite element industry to quickly generate bolt meshes with multiple transition layers in two planes. For users, after drawing the mesh of the outer threaded component, specifying the base point location for generating the transition layer and the physical parameters of the bolt, a single-layer 4-2 transition mesh can be generated. By repeating the above operation, multiple transition meshes in different planes can be quickly generated. After simple processing, a complete bolt model can be obtained, greatly shortening the operator's mesh generation time, improving the fault tolerance rate, and allowing the arrangement of the transition layers to be freely modified according to the user's wishes. Attached Figure Description

[0027] Figure 1 The diagram shown is a flowchart of a method for implementing a transition layer of a bolt finite element mesh 4-2 according to an embodiment of the present invention.

[0028] Figure 2 The diagram shown is a schematic diagram of the 4-2 transition layer between the θ=0 plane and the Z=C plane provided in an embodiment of the present invention.

[0029] Figure 3The diagram shown is a schematic diagram of node renumbering provided in an embodiment of the present invention.

[0030] Figure 4 The figure shown is a schematic diagram of a local precision finite element model of a bolt using a 5-layer 4-2 transition layer provided in an embodiment of the present invention. Detailed Implementation

[0031] 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.

[0032] This invention provides a method for implementing a transition layer of a bolt finite element mesh 4-2, such as... Figure 1 As shown, the process includes the following steps S1 to S8: S1. Obtain the physical parameters of the bolt and the Cartesian coordinates of the first base point.

[0033] In this embodiment of the invention, the physical parameters of the bolt include the diameter of the current transition layer mesh, the number of single-pitch layers, the number of circumferential layers, and the orientation and plane of the mesh to be generated. The physical parameters of the bolt can be used to calculate the size information of the smallest elements, such as Δθ, Δr, and ΔZ.

[0034] In this embodiment of the invention, the θ axis, r axis, and Z axis are the three axes of the cylindrical coordinate system, where r represents the radial distance from the point to the Z axis, θ represents the azimuth angle of the point, Z represents the height of the point, and Δθ, Δr, and ΔZ refer to the coordinate difference between two adjacent points.

[0035] S2. Set the number of cycles, operating plane and operating axis according to the physical parameters of the bolt. Create a second base point according to the Cartesian coordinates of the first base point and generate a 3*4 dot matrix.

[0036] In this embodiment of the invention, if the plane where the mesh to be generated is located is the Z=C plane, then the number of iterations is set to i=2π / 4Δθ, the operation plane is the Z=C plane, and the operation axis is the Z-axis, where C is a constant.

[0037] If the plane containing the mesh to be generated is the θ=0 plane, then set the number of iterations to i=2π / Δθ, the operation plane to the θ=0 plane, and the operation axis to the θ-axis. Different planar meshes are as follows: Figure 2 As shown.

[0038] In this embodiment of the invention, the Cartesian coordinates of the first base point are converted to cylindrical coordinates and offset along the r-axis by 2dΔr to obtain the cylindrical coordinates of the second base point, and the cylindrical coordinates of the second base point are converted to Cartesian coordinates, where d represents the direction quantity.

[0039] In this embodiment of the invention, the base point is the reference point for generating a set of 4-2 transition layers. In the finite element mesh, there may be multiple 4-2 transition layer meshes. If it is necessary to generate a second transition layer, it is necessary to offset the first base point to the second base point as required to generate the second transition layer.

[0040] In this embodiment of the invention, if the direction of the mesh to be generated is the negative direction of the r-axis, then the direction quantity d = -1.

[0041] If the direction of the mesh to be generated is the positive direction of the r-axis, then the direction quantity d=1.

[0042] In this embodiment of the invention, the specific method for generating a 3*4 dot matrix is ​​as follows: If the plane containing the mesh to be generated is the Z=C plane with the direction of the negative r-axis, then the first base point is taken as the upper left corner of the point matrix to be generated, and i 3*4 point matrices are generated on the operation plane, numbered sequentially from 12i-11 to 12i.

[0043] If the plane containing the mesh to be generated is the Z=C plane with the positive direction of the r-axis, then the first base point is taken as the lower left corner of the point matrix to be generated, and i 3*4 point matrices are generated on the operation plane, numbered sequentially from 12i-11 to 12i.

[0044] If the plane containing the mesh to be generated is the θ=0 plane and the direction is the negative direction of the r-axis, then the first base point is taken as the upper right corner of the point matrix to be generated, and i 3*4 point matrices are generated on the operation plane, numbered sequentially from 12i-11 to 12i.

[0045] If the plane containing the mesh to be generated is the θ=0 plane and the direction is the positive direction of the r-axis, then the first base point is taken as the lower right corner of the point matrix to be generated, and i 3*4 point matrices are generated on the operation plane, numbered sequentially from 12i-11 to 12i.

[0046] In this embodiment of the invention, the node spacing of the r-axis of the 3*4 dot matrix is ​​set to Δr, and the node spacing of the other axis is set to Δθ or ΔZ according to the pre-defined operating axis. If the operating axis is the Z-axis, the node spacing of the other axis is set to ΔZ; if the operating axis is the θ-axis, the node spacing of the other axis is set to Δθ.

[0047] S3. Select the nodes in the 3*4 dot matrix and renumber them.

[0048] In this embodiment of the invention, nodes without physical meaning are removed, and the nodes numbered [12i-11, 12i-9, 12i-8, 12i-7, 12i-5, 12i-4, 12i-3, 12i-2, 12i-1] in the 3*4 lattice are selected and renumbered sequentially from 9i-8 to 9i. For example... Figure 3 As shown, Figure 3(a) represents the initial node numbering in the 3*4 dot matrix. Figure 3 (b) represents the selected node. Figure 3 (c) The result of renumbering the nodes.

[0049] S4. Determine if the last loop has been entered. If yes, proceed to step S6; otherwise, proceed to step S5.

[0050] S5. Generate 6 C2D4 grids in each loop within the operation plane, increment the loop count by 1, and return to step S4.

[0051] In embodiments of the present invention, such as Figure 3 As shown in (c), the node combinations of the six generated C2D4 meshes are [9i-8,9i-7,9i-5,9i-6], [9i-6,9i-5,9i-3,9i-4], [9i-7,9i-5,9i-3,9i-2], [9i-4,9i-3,9i,9i-1], [9i-3,9i-2,9i+2,9i] and [9i-1,9i,9i+2,9i+1].

[0052] S6. Redirect the renumbered nodes.

[0053] In this embodiment of the invention, since the maximum value of the node number is 9i, the numbers 9i+1 and 9i+2 generated in the last step will exceed the matrix dimension. In order to ensure the circular closure of the nodes, the node number 9i+1 is redirected to 1 and the node number 9i+2 is redirected to 2.

[0054] S7. Stretch the C2D4 mesh in the operation plane along the operation axis to generate the C3D8 transition mesh.

[0055] S8 outputs the bolt finite element mesh in C3D8 format, 4-2 transition layer, and the Cartesian coordinates of the second base point.

[0056] In this embodiment of the invention, C2D4 refers to a 2D 4-node mesh, and C3D8 refers to a 3D hexahedral 8-node mesh.

[0057] This invention uses a method of dot matrix generation, special point discarding, and node address renumbering to achieve the one-time generation of six different shaped meshes within a single cycle of the transition layer. The operation steps are as follows: generate a 3*4 dot matrix and number it, discard nodes without corresponding mesh nodes, and renumber the remaining points in the dot matrix. Finally, through six numbering pointer groups [9i-8,9i-7,9i-5,9i-6], [9i-6,9i-5,9i-3,9i-4], [9i-7,9i-5,9i-3,9i-2], [9i-4,9i-3,9i,9i-1], [9i-3,9i-2,9i+2,9i], and [9i-1,9i,9i+2,9i+1], the six different shaped meshes within a single cycle are obtained.

[0058] This invention uses three parameters—base point coordinates, generation plane, and generation direction—to control the arrangement and position information of the entire transition layer. With as few parameters as possible and as simple as possible input, it covers all possible arrangements and positions of the 4-2 transition layer involved in bolt precision finite element analysis.

[0059] This invention uses the diameter of the current transition layer, the number of layers per pitch, and the number of circumferential layers to calculate Δr, Δθ, and ΔZ to control the size information of the transition layer. No bolt profile information or any mechanical parameters are required; all possible dimensions of the 4-2 transition layer in the complete model can be determined using only these three parameters.

[0060] This embodiment of the invention will output updated base point information for easy access in subsequent operations. If multiple transition layers need to be generated, simply re-enter the output base point information and the physical parameters of the bolts back into the program; no manual calculation of key node information is required. Figure 4 The image shows a local bolt model (excluding the threaded region mesh) generated by the bolt finite element mesh 4-2 transition layer implementation method provided in this embodiment of the invention, which is used 5 times in a cycle. From the outside to the inside, they are the θ=0 plane transition layer, the θ=0 plane transition layer, the Z=C plane transition layer, the θ=0 plane transition layer and the Z=C plane transition layer.

[0061] 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 implementing a 4-2 transition layer of a bolt finite element mesh, characterized in that, Includes the following steps: S1. Obtain the physical parameters of the bolt and the Cartesian coordinates of the first base point; S2. Set the number of cycles, operating plane and operating axis according to the physical parameters of the bolt, create the second base point according to the Cartesian coordinates of the first base point, and generate a 3*4 dot matrix; S3. Select the nodes in the 3*4 dot matrix and renumber them; S4. Determine whether to enter the last loop. If yes, proceed to step S6; otherwise, proceed to step S5. S5. Generate 6 C2D4 grids in each loop within the operation plane, increment the loop count by 1, and return to step S4. S6. Redirect the renumbered nodes; S7. Stretch the C2D4 mesh in the operation plane along the operation axis to generate the C3D8 transition mesh; S8 outputs the bolt finite element mesh in C3D8 format, 4-2 transition layer, and the Cartesian coordinates of the second base point.

2. The method for implementing the transition layer of the bolt finite element mesh 4-2 according to claim 1, characterized in that, The physical parameters of the bolt in step S1 include the diameter of the current transition layer mesh, the number of single-pitch layers, the number of circumferential layers, and the orientation and plane of the mesh to be generated.

3. The method for implementing the transition layer of the bolt finite element mesh 4-2 according to claim 2, characterized in that, In step S2, if the plane containing the mesh to be generated is the Z=C plane, then the number of iterations is set to i=2π / 4Δθ, the operation plane is the Z=C plane, and the operation axis is the Z-axis, where C is a constant. If the plane containing the mesh to be generated is the θ=0 plane, then set the number of loops to i=2π / Δθ, the operation plane to the θ=0 plane, and the operation axis to the θ axis.

4. The method for implementing the transition layer of the bolt finite element mesh 4-2 according to claim 2, characterized in that, The method for creating the second base point based on the Cartesian coordinates of the first base point in step S2 is as follows: Convert the Cartesian coordinates of the first base point to cylindrical coordinates, and offset it along the r-axis by 2dΔr to obtain the cylindrical coordinates of the second base point. Then convert the cylindrical coordinates of the second base point to Cartesian coordinates, where d represents the direction.

5. The method for implementing the transition layer of the bolt finite element mesh 4-2 according to claim 4, characterized in that, The value of the direction quantity d is: If the direction of the mesh to be generated is the negative direction of the r-axis, then the direction quantity d = -1; If the direction of the mesh to be generated is the positive direction of the r-axis, then the direction quantity d=1.

6. The method for implementing the transition layer of the bolt finite element mesh 4-2 according to claim 3, characterized in that, The specific method for generating the 3*4 dot matrix in step S2 is as follows: If the plane containing the mesh to be generated is the Z=C plane and the direction is the negative direction of the r-axis, then the first base point is taken as the upper left corner of the point matrix to be generated, and i 3*4 point matrices are generated on the operation plane, numbered sequentially from 12i-11 to 12i. If the plane containing the mesh to be generated is the Z=C plane and the direction is the positive direction of the r-axis, then the first base point is taken as the lower left corner of the point matrix to be generated, and i 3*4 point matrices are generated on the operation plane, numbered sequentially from 12i-11 to 12i. If the plane containing the mesh to be generated is the θ=0 plane and the direction is the negative direction of the r-axis, then the first base point is taken as the upper right corner of the point matrix to be generated, and i 3*4 point matrices are generated on the operation plane, numbered sequentially from 12i-11 to 12i. If the plane containing the mesh to be generated is the θ=0 plane and the direction is the positive direction of the r-axis, then the first base point is taken as the lower right corner of the point matrix to be generated, and i 3*4 point matrices are generated on the operation plane, numbered sequentially from 12i-11 to 12i.

7. The method for implementing the transition layer of the bolt finite element mesh 4-2 according to claim 6, characterized in that, The node spacing of the r-axis of the 3*4 dot matrix is ​​set to Δr, and the node spacing of the other axis is set to Δθ or ΔZ according to the configured operation axis.

8. The method for implementing the transition layer of the bolt finite element mesh 4-2 according to claim 6, characterized in that, In step S3, nodes numbered [12i-11, 12i-9, 12i-8, 12i-7, 12i-5, 12i-4, 12i-3, 12i-2, 12i-1] in the 3*4 matrix are selected and renumbered sequentially from 9i-8 to 9i.

9. The method for implementing the transition layer of the bolt finite element mesh 4-2 according to claim 6, characterized in that, The node combinations of the six C2D4 meshes generated in step S5 are [9i-8,9i-7,9i-5,9i-6], [9i-6,9i-5,9i-3,9i-4], [9i-7,9i-5,9i-3,9i-2], [9i-4,9i-3,9i,9i-1], [9i-3,9i-2,9i+2,9i] and [9i-1,9i,9i+2,9i+1].

10. The method for implementing the transition layer of the bolt finite element mesh 4-2 according to claim 9, characterized in that, In step S6, node number 9i+1 is redirected to 1, and node number 9i+2 is redirected to 2.

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