Method and system for automatically generating finite element mesh of parameterized spur bevel gear

Abstract

This invention discloses a method and system for automatically generating parametric finite element meshes for spur bevel gears, comprising: generating an end face tooth profile geometric model using control parameters of the spur bevel gear; generating a 2D end face half-side mesh on the generated geometric model and mirroring it symmetrically to generate a full end face tooth mesh; converting the full end face tooth mesh to the actual spatial position of the end face, and generating a 3D gear tooth mesh using linear interpolation between the two end face 2D full tooth meshes; generating a 3D gear spoke mesh based on a 2D cross-sectional geometric model of the gear spoke; connecting the gear tooth 3D mesh with the gear spoke 3D mesh to generate a gear cyclic symmetric mesh containing single teeth, and rotating and copying the gear cyclic symmetric mesh to generate a full-ring gear finite element 3D mesh. This achieves automatic parametric mesh generation, capable of generating 20-node hexahedral finite element meshes with high accuracy.

Description

Technical Field

[0001] This invention belongs to the field of gear simulation technology. It relates to a method and system for automatically generating finite element meshes for parametric spur bevel gears. Background Technology

[0002] Gear drives are widely used in engineering due to their advantages such as high efficiency, high power, long life, compact structure, and reliable operation, including in aircraft engine accessory transmission systems and helicopter transmission systems. Aircraft gears require lightweight and high reliability, making their design challenging. The finite element method (FEM) is often used in the strength, vibration, and life design of gear drives, and the quality of the FEM mesh significantly affects the accuracy of the analysis. Currently, commercial software is commonly used to generate FEM meshes for structures, with only tetrahedral elements being relatively mature 3D meshes. However, tetrahedral elements have low accuracy, resulting in poor shape simulation precision. Furthermore, commercial software struggles to automatically generate parametric meshes, posing challenges to structural shape optimization design.

[0003] Application No. 202110824112.9 discloses a fully parametric gear meshing analysis method based on the finite element method. It identifies parameters affecting gear geometry and material properties, then obtains the tooth profile based on the parametric equations of the involute and transition curves, generating a complete gear tooth profile and a 3D gear solid model. Next, it performs APDL implementation of the parametric mapped mesh, segments the end face, and selects appropriate mesh elements to generate a complete parametric gear model. This method requires generating a complete gear tooth profile and a 3D gear solid model, resulting in a large computational load, and its accuracy needs further improvement. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for automatically generating parametric finite element meshes for straight bevel gears, which can generate 20-node 6-sided finite element meshes for straight bevel gears with high accuracy.

[0005] The technical solution to achieve the purpose of this invention is as follows:

[0006] A method for automatically generating finite element meshes for parametric spur bevel gears includes the following steps:

[0007] S01: Generate the end face tooth profile geometric model using the control parameters of a straight bevel gear;

[0008] S02: Generate a 2D end face half mesh on the generated geometric model and mirror symmetrically map it to generate a full end face mesh;

[0009] S03: Convert the end face full tooth mesh to the actual spatial position of the end face, and use linear interpolation between the two end face 2D full tooth meshes to generate the tooth 3D volume mesh;

[0010] S04: Generate a 3D volume mesh of the gear spokes based on the 2D cross-sectional geometric model of the gear spokes;

[0011] S05: Connect the 3D mesh of the gear teeth with the 3D mesh of the gear spokes to generate a cyclic symmetric mesh of the gear containing a single tooth. The cyclic symmetric mesh of the gear is rotated and copied to generate a full-ring gear finite element 3D mesh.

[0012] In a preferred embodiment, the method for generating the end face tooth profile geometric model in step S01 includes:

[0013] S11: Obtain the base circle radius based on the end face module, pressure angle, and number of teeth, and then obtain the involute equation;

[0014] S12: Obtain the first arc segment of the addendum circle and the involute based on the addendum circle diameter and the involute equation;

[0015] S13: Obtain the second arc segment of the root circle based on the root circle diameter and the involute equation;

[0016] S14: Obtain the remaining arc segments based on the rim thickness;

[0017] S15: Perform rounding operation on two intersecting curves based on the given tooth root rounding radius;

[0018] S16: Generate a quadrilateral 8-node mesh for the closed curve to obtain the geometric model of the generated end face tooth profile.

[0019] In the preferred technical solution, during the mirror symmetry mapping in step S02, overlapping nodes on the symmetry line are deleted, nodes with smaller node numbers are retained, and all nodes are renumbered consecutively in order of size.

[0020] In a preferred embodiment, the method for converting the end-face full-tooth mesh to the actual spatial position of the end face in step S03 includes:

[0021] The coordinate system is translated and transformed, and the grid points are geometrically transformed. The relationship between the new coordinates (x', y') and the old coordinates (x, y) of the grid points after the coordinate system translation is as follows:

[0022] x' = x, y' = y - 0.5d

[0023] d is the pitch circle diameter;

[0024] Rotate the grid points about the x' axis by δ i Spend;

[0025] Translate Δy′ = 0.5d in the y' direction. i ;

[0026] Translate in the z-direction by Δz = 0.5d itan(δ i );

[0027] Where i = 1 and 2 represent the first end face and the second end face, respectively.

[0028] In a preferred embodiment, the method for generating the 3D volumetric mesh of the gear teeth in step S03 includes:

[0029] The node coordinates of each section in the middle are obtained by linear interpolation of the node coordinates of the 2D full-tooth mesh of the two end faces. The redundant nodes in the 3D element are deleted, and all nodes are renumbered continuously in order of size. A 20-node hexahedral element mesh is generated linearly from the first end face to the second end face.

[0030] In a preferred embodiment, the method for generating the 3D volumetric mesh of the gear spokes in step S04 includes:

[0031] The number of gear spoke 2D elements generated from the gear spoke cross-sectional geometric model is the same as the number of gear tooth thickness elements.

[0032] The gear spokes are generated by rotating and copying around the gear axis. The number of copies is the same as the number of elements at the rim. The rotation and copying angle is 360 / z, resulting in a 3D volume mesh of the gear spokes.

[0033] The present invention also discloses a computer storage medium storing a computer program, which, when executed, implements the above-described method for automatically generating finite element meshes for parameterized spur bevel gears.

[0034] This invention also discloses a parametric spur bevel gear finite element mesh automatic generation system, comprising:

[0035] The end face tooth profile geometry model construction module uses the control parameters of spur bevel gears to generate the end face tooth profile geometry model.

[0036] The end face full tooth mesh generation module generates a 2D end face half mesh on the generated geometric model and mirrors it symmetrically to generate an end face full tooth mesh.

[0037] The gear tooth 3D volume mesh generation module converts the end face full tooth mesh to the actual spatial position of the end face, and generates the gear tooth 3D volume mesh by linear interpolation between the two end face 2D full tooth meshes;

[0038] The 3D volumetric mesh generation module for gear spokes generates a 3D volumetric mesh for gear spokes based on the 2D cross-sectional geometric model of the gear spokes.

[0039] The full-ring gear finite element 3D mesh generation module connects the gear tooth 3D body mesh with the gear spoke 3D body mesh to generate a gear cyclic symmetric mesh containing single teeth. The gear cyclic symmetric mesh is then rotated and copied to generate the full-ring gear finite element 3D mesh.

[0040] In a preferred embodiment, the method for generating the end face tooth profile geometric model by the end face tooth profile geometric model construction module includes:

[0041] S11: Obtain the base circle radius based on the end face module, pressure angle, and number of teeth, and then obtain the involute equation;

[0042] S12: Obtain the first arc segment of the addendum circle and the involute based on the addendum circle diameter and the involute equation;

[0043] S13: Obtain the second arc segment of the root circle based on the root circle diameter and the involute equation;

[0044] S14: Obtain the remaining arc segments based on the rim thickness;

[0045] S15: Perform rounding operation on two intersecting curves based on the given tooth root rounding radius;

[0046] S16: Generate a quadrilateral 8-node mesh for the closed curve to obtain the geometric model of the generated end face tooth profile.

[0047] In a preferred embodiment, the method for converting the end face full-tooth mesh to the actual spatial position of the end face in the tooth 3D volume mesh generation module includes:

[0048] The coordinate system is translated and transformed, and the grid points are geometrically transformed. The relationship between the new coordinates (x', y') and the old coordinates (x, y) of the grid points after the coordinate system translation is as follows:

[0049] x' = x, y' = y - 0.5d

[0050] d is the pitch circle diameter;

[0051] Rotate the grid points about the x' axis by δ i Spend;

[0052] Translate Δy′ = 0.5d in the y' direction. i ;

[0053] Translate in the z-direction by Δz = 0.5d i tan(δ i );

[0054] Where i = 1 and 2 represent the first end face and the second end face, respectively.

[0055] Compared with the prior art, the significant advantages of this invention are:

[0056] 1. This method can automatically generate parametric meshes, thus achieving high efficiency: saving a lot of manpower, shortening calculation time, and providing a mesh generation basis for gear optimization design.

[0057] 2. The 20-node hexahedral 3D element used is the most accurate and shape-simulating element among commonly used 3D elements in finite element analysis, thus enabling subsequent finite element analysis to achieve high accuracy. Attached Figure Description

[0058] Figure 1 A flowchart illustrating the automatic generation method of parametric finite element mesh for straight bevel gears, as shown in this embodiment;

[0059] Figure 2 This is a schematic diagram of the node numbering of a 20-node hexahedral element in an embodiment.

[0060] Figure 3 This is a schematic diagram of an 8-node quadrilateral 2D unit as shown in the embodiment.

[0061] Figure 4 This is a schematic diagram of the parameters of a spur bevel gear in an embodiment;

[0062] Figure 5 This is a schematic diagram of the shaft intersection angle and pitch cone angle of the spur bevel gear in the embodiment;

[0063] Figure 6 This is a schematic diagram of the involute curve in an embodiment;

[0064] Figure 7 This is a schematic diagram of the 2D geometric model of the end face half in the embodiment;

[0065] Figure 8 The end face full tooth mesh diagram is shown in the embodiment.

[0066] Figure 9 Big-endian and little-endian mesh diagrams for an embodiment;

[0067] Figure 10 A schematic diagram of interpolation-generated 3D meshes for an example embodiment;

[0068] Figure 11 A schematic diagram of the geometric model of the gear spoke cross-section in the embodiment;

[0069] Figure 12 Schematic diagram of the 2D unit of the gear spokes in the embodiment;

[0070] Figure 13 Schematic diagram of the 3D unit of the gear spokes in the embodiment;

[0071] Figure 14 Gear cycle symmetrical mesh diagram of the embodiment;

[0072] Figure 15The full-ring gear mesh diagram of the embodiment;

[0073] Figure 16 This is a schematic diagram of the automatic generation system for parameterized finite element meshes of spur bevel gears, as shown in the embodiment. Detailed Implementation

[0074] The principle of this invention is as follows: a 3D mesh is generated between the 2D meshes on both end faces using linear interpolation. A full-ring gear finite element 3D mesh is then generated by rotating and replicating the cyclically symmetric mesh. This allows for automatic generation of parametric meshes with high efficiency. It can generate a 20-node, hexahedral finite element mesh for a spur bevel gear with high accuracy.

[0075] Example 1:

[0076] like Figure 1 As shown, an automatic method for generating finite element meshes for parametric spur bevel gears includes the following steps:

[0077] S01: Generate the end face tooth profile geometric model using the control parameters of a straight bevel gear;

[0078] S02: Generate a 2D end face half mesh on the generated geometric model and mirror symmetrically map it to generate a full end face mesh;

[0079] S03: Convert the end face full tooth mesh to the actual spatial position of the end face, and use linear interpolation between the two end face 2D full tooth meshes to generate the tooth 3D volume mesh;

[0080] S04: Generate a 3D volume mesh of the gear spokes based on the 2D cross-sectional geometric model of the gear spokes;

[0081] S05: Connect the 3D mesh of the gear teeth with the 3D mesh of the gear spokes to generate a cyclic symmetric mesh of the gear containing a single tooth. The cyclic symmetric mesh of the gear is rotated and copied to generate a full-ring gear finite element 3D mesh.

[0082] The generated 3D finite element mesh for the full-ring gear is a 20-node hexahedral finite element mesh. The node numbers for the 20-node hexahedral elements are as follows: Figure 2 As shown, it consists of 8-node quadrilateral 2D elements. Each element's edge connects two corner points and one midpoint. Each of the six end faces has eight nodes. Figure 3 As shown. The midpoints of each side form 3 mid-planes, and each mid-plane has 4 points forming a quadrilateral.

[0083] The teeth of a spur bevel gear are distributed on a conical surface. The module, tooth height, tooth thickness, etc. are different along the tooth phase, and the parameters of the large end are usually taken into account. Figure 4This is a schematic diagram of a spur bevel gear structure, including the large end 40, small end 41, root cone 42, top cone 43, pitch cone 44, front cone 45, and back cone 46. Some parameters are shown in the diagram, such as the shaft intersection angle and pitch cone angle of the spur bevel gear. Figure 5 As shown in Table 1, the main geometric parameters and calculation formulas for spur bevel gears are listed below.

[0084] Table 1. Symbols and Calculation Formulas for Main Parameters of Straight Bevel Gears

[0085]

[0086]

[0087] In a preferred implementation, the method for generating the end face tooth profile geometry model in step S01 includes:

[0088] S11: Obtain the base circle radius based on the end face module, pressure angle, and number of teeth, and then obtain the involute equation;

[0089] S12: Obtain the first arc segment of the addendum circle and the involute based on the addendum circle diameter and the involute equation;

[0090] S13: Obtain the second arc segment of the root circle based on the root circle diameter and the involute equation;

[0091] S14: Obtain the remaining arc segments based on the rim thickness;

[0092] S15: Perform rounding operation on two intersecting curves based on the given tooth root rounding radius;

[0093] S16: Generate a quadrilateral 8-node mesh for the closed curve to obtain the geometric model of the generated end face tooth profile.

[0094] Specifically, end face module, pressure angle, rim thickness, and number of teeth are important parameters for parameter control.

[0095] The base circle radius can be obtained from the end face module, pressure angle, and number of teeth (see Table 1):

[0096] R b =0.5zmcosα;

[0097] And the equation of the involute is obtained:

[0098] θ = tanω - ω, x = R b cosθ / cosω, y=R b sinθ / cosω (1)

[0099] Where: R bLet θ be the radius of the base circle, θ be the angle between the line connecting the intersection point K of the involute and the generating line and the origin O, and the positive direction of the X-axis, and ω be the angle between the line connecting the intersection point N of the generating line and the base circle and the origin O, and the positive direction of the X-axis (see details). Figure 6 ).

[0100] Pressure angle: α = ω - θ, radius of curvature at any point K: R k =R b ω, radius of curvature at the pitch circle: d is the pitch circle diameter.

[0101] Generated from the involute equation Figure 7 As shown, the BCD segment curve is used, and a 2D geometric model of the end face half is further generated based on relevant gear parameters such as rim thickness, addendum circle diameter, and dedendum circle diameter. Its coordinate system is XOY (see...). Figure 6 The geometric model is located in the XY plane, where point "H" is the intersection of the pitch circle and AG.

[0102] The specific implementation includes the following steps:

[0103] 1. From the tooth tip circle diameter parameter d a And the AB arc segment of the tooth tip circle is obtained from the involute equation (1);

[0104] 2. From the involute equation (1), we can obtain the involute as: BCD circular arc segment;

[0105] 3. From the root circle diameter parameter d f The maximum circumferential range angle Φ of half a tooth and the involute equation (1) are used to obtain the DE arc segment of the root circle;

[0106] 4. From the rim thickness Hy and Φ, the arc segments EF and FG can be obtained;

[0107] 5. Based on the given tooth root fillet radius, perform the fillet operation of the two intersecting curves at point D, that is, the tangency operation with the arc;

[0108] 6. Connect them into a closed curve to generate a 2D geometric model of the end face half.

[0109] In a preferred implementation, during the mirror symmetry mapping in step S02, overlapping nodes on the symmetry line are deleted, nodes with smaller node numbers are retained, and all nodes are renumbered consecutively in order of size.

[0110] Based on the obtained geometric model, existing quadrilateral mesh generation methods (such as the segmentation method, paving method, etc.) are used to generate the end face half mesh (see...). Figure 8 Then, the end face full tooth mesh is generated by mirror mapping, and the overlapping nodes on the symmetry line AG are deleted, keeping the smaller node number. All nodes are then renumbered consecutively in order of size.

[0111] In a preferred implementation, the method for converting the end face full-tooth mesh to the actual spatial position of the end face in step S03 includes:

[0112] The coordinate system is translated and transformed, and the grid points are geometrically transformed. The relationship between the new coordinates (x', y') and the old coordinates (x, y) of the grid points after the coordinate system translation is as follows:

[0113] x' = x, y' = y - 0.5d

[0114] d is the pitch circle diameter;

[0115] Therefore, the origin of the coordinate system is moved to... Figure 6 Point H is shown.

[0116] Rotate the grid points about the x' axis by δ i Spend;

[0117] Translate Δy′ = 0.5d in the y' direction. i ;

[0118] Translate in the z-direction by Δz = 0.5d i tan(δ i );

[0119] Where i = 1 and 2 represent the first end face and the second end face, i.e., the big end and the little end, respectively.

[0120] This converts the finite element mesh to... Figure 4 For the actual spatial location of the end face shown, please refer to [reference needed]. Figure 9 .

[0121] In a preferred implementation, the method for generating the 3D volumetric mesh of the gear teeth in step S03 includes:

[0122] The node coordinates of each section in the middle are obtained by linear interpolation of the node coordinates of the 2D full-tooth mesh of the two end faces. The redundant nodes in the 3D element are deleted, and all nodes are renumbered continuously in order of size. A 20-node hexahedral element mesh is generated linearly from the first end face to the second end face.

[0123] A 3D 20-node hexahedral mesh is generated between two 2D 8-node quadrilateral meshes on both ends using linear interpolation. Figure 10 A 3D mesh diagram was generated for interpolation, and a total of 8 layers of cells were generated.

[0124] Depend on Figure 2 As shown, the 20-node hexahedral element has 8 nodes on its end face, which is consistent with... Figure 3 The 8-node quadrilateral 2D element shown corresponds to this, but... Figure 2The mid-section shown has only 4 nodes, and the dashed line segment in the figure has no intermediate nodes, which is 4 fewer than the 2D element. However, linear interpolation includes all nodes of the 2D element, so the mid-section of the 3D element will have some extra nodes that are not connected to the element. These can be retained or deleted, and then reordered continuously in order of size.

[0125] In a preferred implementation, the method for generating the 3D volumetric mesh of the gear spokes in step S04 includes:

[0126] The number of gear spoke 2D elements generated from the gear spoke cross-sectional geometric model is the same as the number of gear tooth thickness elements.

[0127] The gear spokes are generated by rotating and copying around the gear axis. The number of copies is the same as the number of elements at the rim. The rotation and copying angle is 360 / z, resulting in a 3D volume mesh of the gear spokes.

[0128] Figure 11 For the geometric model of the gear spoke cross-section, the 2D elements of the gear spoke are generated using the segmentation method or the paving method, such as... Figure 12 As shown, the number of units for line segment P in the diagram is 8, which is consistent with... Figure 11 The number of tooth thickness units is consistent.

[0129] Rotate around the gear axis to generate 3D units of the gear spokes, the number of copies being equal to the number of copies. Figure 11 The number of units at the rim is consistent, 6 units.

[0130] The rotation and copy angle is 360° / z. See the generated 3D mesh. Figure 13 .

[0131] The 3D mesh of the gear teeth is docked with the 3D mesh of the spokes to generate a cyclically symmetric mesh of the gear containing single teeth. Each point at the docking point has two overlapping nodes. The node with the larger number is deleted, and all nodes are renumbered consecutively in ascending order. See the mesh below. Figure 14 This model can be used for vibration analysis of gears.

[0132] The gear cyclic symmetric mesh is rotated and copied to generate a full-ring gear finite element 3D mesh. Coincident nodes on the overlapping surfaces are deleted, and all nodes are renumbered sequentially according to size. See the mesh below. Figure 15 .

[0133] The finite element model of a full-ring gear can be used for static strength analysis or vibration analysis of gears.

[0134] In another embodiment, a computer storage medium stores a computer program that, when executed, implements the above-described method for automatically generating finite element meshes for parameterized spur bevel gears.

[0135] In another embodiment, such as Figure 16As shown, a parametric spur bevel gear finite element mesh automatic generation system includes:

[0136] The end face tooth profile geometric model construction module 10 uses the control parameters of a spur bevel gear to generate the end face tooth profile geometric model.

[0137] The end face full tooth mesh generation module 20 generates a 2D end face half mesh on the generated geometric model and mirrors it symmetrically to generate an end face full tooth mesh.

[0138] The gear tooth 3D volume mesh generation module 30 converts the end face full tooth mesh to the actual spatial position of the end face, and generates the gear tooth 3D volume mesh by linear interpolation between the two end face 2D full tooth meshes.

[0139] The 3D volumetric mesh generation module 40 for gear spokes generates a 3D volumetric mesh for gear spokes based on the 2D cross-sectional geometric model of the gear spokes.

[0140] The full-ring gear finite element 3D mesh generation module 50 connects the gear tooth 3D body mesh with the gear spoke 3D body mesh to generate a gear cyclic symmetric mesh containing single teeth. The gear cyclic symmetric mesh is rotated and copied to generate the full-ring gear finite element 3D mesh.

[0141] The following describes in detail the workflow of the parameterized spur bevel gear finite element mesh automatic generation system using a preferred embodiment as an example:

[0142] The finite element mesh of the gear tooth can be generated from the parameters, formulas, and involute equation (1) listed in Table 1. The gear tooth has two end faces, and the tooth profile of the end faces is symmetrical. Figure 7 This represents the right half of a tooth profile on a certain end face (the coordinate system in the figure is right-handed). AG is the line of symmetry of the tooth profile, coinciding with the y-axis in the figure. EF is determined by the angle Φ.

[0143]

[0144] set up Figure 7 The image shows the right half of the tooth profile on end face 1. The steps for generating the finite element mesh for the gear tooth are as follows:

[0145] 1) Begin;

[0146] 2) Input gear parameters (see Table 1) and mesh control parameters (mesh cell side length dimensions);

[0147] 3) From the tooth tip circle diameter parameter d a And the AB arc segment of the tooth tip circle is obtained from the involute equation (1);

[0148] 4) From the involute equation (1), we can obtain the involute: BCD;

[0149] 5) From the root circle diameter parameter df The DE arc segment of the tooth root circle is obtained from Φ and the involute equation (1);

[0150] 6) The arc segments EF and FG can be obtained from the rim thickness Hy and Φ;

[0151] 7) Based on the given tooth root fillet radius, perform the fillet operation of the two intersecting curves at point D, that is, the tangency operation with the arc;

[0152] 8) Figure 7 The closed curve shown is subjected to quadrilateral 8-node mesh generation to obtain a 2D mesh for one half tooth of the end face, see... Figure 8 Right side grid;

[0153] 9) Using AG as the plane of symmetry, mirror-replicate half of the 2D mesh and delete the overlapping nodes on the symmetry line. Renumber all nodes sequentially according to their size to obtain the following result: Figure 8 The end face full tooth 2D mesh shown;

[0154] 10) Perform similar operations (3)-9) on end face 2 to obtain the following result: Figure 9 The small end face 2 full tooth 2D mesh is shown;

[0155] 11) A 20-node hexahedral element mesh is linearly generated by sweeping from end face 1 to end face 2 (see...). Figure 10 That is, the node coordinates of each section in the middle are obtained by linear interpolation of the 2D mesh node coordinates of the two end faces, redundant nodes in the 3D unit are deleted, and all nodes are renumbered continuously in order of size.

[0156] 12) Based on the 2D cross-sectional geometric model of the gear spokes (see...) Figure 11 Generate a 2D mesh for the gear spokes (see...) Figure 12 );

[0157] 13) Generate a 3D mesh of the gear spokes by rotating and copying the 2D mesh, delete overlapping nodes, and renumber all nodes sequentially according to their size (see...). Figure 13 );

[0158] 14) Add the 3D mesh of the gear teeth (see...) Figure 10 ) and 3D mesh of the spokes (see Figure 13 For a cyclically symmetric mesh containing a single toothed gear, delete overlapping nodes and renumber all nodes sequentially in size order (see...). Figure 14 );

[0159] 15) Rotate and copy the cyclic symmetric mesh of the gear to generate a full-ring gear 3D mesh model, delete overlapping nodes, and renumber all nodes consecutively in size order (see...). Figure 15 );

[0160] 16) Output gear mesh data;

[0161] 17) Stop.

[0162] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for automatically generating parametric finite element meshes for spur bevel gears, characterized in that, Includes the following steps: S01: Generate the end face tooth profile geometric model using the control parameters of a straight bevel gear; S02: Generate a 2D end face half mesh on the generated geometric model and mirror symmetrically map it to generate a full end face mesh; S03: Convert the end face full tooth mesh to the actual spatial position of the end face, and use linear interpolation between the two end face 2D full tooth meshes to generate the tooth 3D volume mesh; The method for converting the end face full-tooth mesh to the actual spatial position of the end face includes: The coordinate system is translated and transformed, and the grid points are geometrically transformed. The relationship between the new coordinates (x', y') and the old coordinates (x, y) of the grid points after the coordinate system translation is as follows: x'=x, y'=y-0.5d d is the pitch circle diameter; Rotate the grid points around the x' axis Spend; Translate in the y' direction ; Translate in the z direction ; Where: i=1,2 represent the first end face and the second end face, respectively; S04: Generate a 3D volume mesh of the gear spokes based on the 2D cross-sectional geometric model of the gear spokes; S05: Connect the 3D mesh of the gear teeth with the 3D mesh of the gear spokes to generate a cyclic symmetric mesh of the gear containing a single tooth. The cyclic symmetric mesh of the gear is rotated and copied to generate a full-ring gear finite element 3D mesh.

2. The method for automatically generating parametric finite element meshes for spur bevel gears according to claim 1, characterized in that, The method for generating the end face tooth profile geometric model in step S01 includes: S11: Obtain the base circle radius based on the end face module, pressure angle, and number of teeth, and then obtain the involute equation; S12: Obtain the first arc segment of the addendum circle and the involute based on the addendum circle diameter and the involute equation; S13: Obtain the second arc segment of the root circle based on the root circle diameter and the involute equation; S14: Obtain the remaining arc segments based on the rim thickness; S15: Perform rounding operation on two intersecting curves based on the given tooth root rounding radius; S16: Generate a quadrilateral 8-node mesh for the closed curve to obtain the geometric model of the generated end face tooth profile.

3. The method for automatically generating parametric finite element meshes for spur bevel gears according to claim 1, characterized in that, In step S02, during the mirror symmetry mapping, overlapping nodes on the symmetry line are deleted, nodes with smaller node numbers are retained, and all nodes are renumbered consecutively in order of size.

4. The method for automatically generating parametric finite element meshes for spur bevel gears according to claim 2, characterized in that, The method for generating the 3D volumetric mesh of the gear teeth in step S03 includes: The node coordinates of each section in the middle are obtained by linear interpolation of the node coordinates of the 2D full-tooth mesh of the two end faces. The redundant nodes in the 3D element are deleted, and all nodes are renumbered continuously in order of size. A 20-node hexahedral element mesh is generated linearly from the first end face to the second end face.

5. The method for automatically generating parametric finite element meshes for spur bevel gears according to claim 1, characterized in that, The method for generating the 3D volumetric mesh of the gear spokes in step S04 includes: The number of gear spoke 2D elements generated from the gear spoke cross-sectional geometric model is the same as the number of gear tooth thickness elements. The gear spokes are generated by rotating and copying around the gear axis. The number of copies is the same as the number of elements at the rim. The rotation and copying angle is 360 / z, resulting in a 3D volume mesh of the gear spokes.

6. A computer storage medium having a computer program stored thereon, characterized in that, When the computer program is executed, it implements the automatic generation method for parameterized finite element mesh of straight bevel gears as described in any one of claims 1-5.

7. A parametric finite element mesh automatic generation system for spur bevel gears, characterized in that, include: The end face tooth profile geometry model construction module uses the control parameters of spur bevel gears to generate the end face tooth profile geometry model. The end face full tooth mesh generation module generates a 2D end face half mesh on the generated geometric model and mirrors it symmetrically to generate an end face full tooth mesh. The gear tooth 3D volume mesh generation module converts the end face full tooth mesh to the actual spatial position of the end face, and generates the gear tooth 3D volume mesh by linear interpolation between the two end face 2D full tooth meshes; The method for converting the end face full-tooth mesh to the actual spatial position of the end face includes: The coordinate system is translated and transformed, and the grid points are geometrically transformed. The relationship between the new coordinates (x', y') and the old coordinates (x, y) of the grid points after the coordinate system translation is as follows: x'=x, y'=y-0.5d d is the pitch circle diameter; Rotate the grid points around the x' axis Spend; Translate in the y' direction ; Translate in the z direction ; Where: i=1,2 represent the first end face and the second end face, respectively; The 3D volumetric mesh generation module for gear spokes generates a 3D volumetric mesh for gear spokes based on the 2D cross-sectional geometric model of the gear spokes. The full-ring gear finite element 3D mesh generation module connects the gear tooth 3D body mesh with the gear spoke 3D body mesh to generate a gear cyclic symmetric mesh containing single teeth. The gear cyclic symmetric mesh is then rotated and copied to generate the full-ring gear finite element 3D mesh.

8. The automatic generation system for parameterized spur bevel gear finite element meshes according to claim 7, characterized in that, The method for generating the end face tooth profile geometric model by the end face tooth profile geometric model construction module includes: S11: Obtain the base circle radius based on the end face module, pressure angle, and number of teeth, and then obtain the involute equation; S12: Obtain the first arc segment of the addendum circle and the involute based on the addendum circle diameter and the involute equation; S13: Obtain the second arc segment of the root circle based on the root circle diameter and the involute equation; S14: Obtain the remaining arc segments based on the rim thickness; S15: Perform rounding operation on two intersecting curves based on the given tooth root rounding radius; S16: Generate a quadrilateral 8-node mesh for the closed curve to obtain the geometric model of the generated end face tooth profile.

9. The automatic generation system for parametric spur bevel gear finite element meshes according to claim 7, characterized in that, The method for converting the end face full tooth mesh to the actual spatial position of the end face in the tooth 3D volumetric mesh generation module includes: The coordinate system is translated and transformed, and the grid points are geometrically transformed. The relationship between the new coordinates (x', y') and the old coordinates (x, y) of the grid points after the coordinate system translation is as follows: x'=x, y'=y-0.5d d is the pitch circle diameter; Rotate the grid points around the x' axis Spend; Translate in the y' direction ; Translate in the z direction ; Where i=1 and 2 represent the first end face and the second end face, respectively.

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