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CN-115859707-B - Automatic generation method and system for finite element grid of parameterized straight bevel gear

CN115859707BCN 115859707 BCN115859707 BCN 115859707BCN-115859707-B

Abstract

The invention discloses an automatic generation method and system of a parameterized straight-tooth conical gear finite element grid, comprising the steps of generating an end face tooth form geometric model by adopting control parameters of the straight-tooth conical gear, generating a 2D end face half grid on the generated geometric model, performing mirror symmetry mapping to generate an end face full-tooth grid, converting the end face full-tooth grid to an actual space position of the end face, generating a gear tooth 3D body grid between the two end face 2D full-tooth grids by adopting a linear interpolation method, generating a 3D body grid of a gear web according to the 2D section geometric model of the gear web, butting the gear tooth 3D body grid with the 3D body grid of the gear web to generate a gear cycle symmetrical grid containing single teeth, and rotationally replicating the gear cycle symmetrical grid to generate the full-ring gear finite element 3D grid. The parameterized grid is automatically generated, the 20-node 6-plane finite element grid can be generated, and higher precision is obtained.

Inventors

  • XUE YUANYUAN
  • DAI YU
  • ZHAO YUNSHENG
  • DING JIANGUO
  • CAI XIANXIN

Assignees

  • 太仓点石航空动力有限公司

Dates

Publication Date
20260505
Application Date
20221107

Claims (9)

  1. 1. The automatic generation method of the parameterized straight bevel gear finite element grid is characterized by comprising the following steps of: s01, generating an end face tooth form geometric model by adopting control parameters of a straight tooth conical gear; S02, generating 2D end face half grids on the generated geometric model, and performing mirror symmetry mapping to generate end face full-tooth grids; S03, converting the end face full-tooth grid into an actual space position of the end face, and generating a gear tooth 3D body grid between the two end face 2D full-tooth grids by adopting a linear interpolation method, wherein the method for converting the end face full-tooth grid into the actual space position of the end face comprises the following steps: Translation conversion is carried out on a coordinate system, geometric conversion is carried out on grid points, and the relation between new coordinates (x ', y') and old coordinates (x, y) of the grid points after translation of the coordinate system is carried out: x'=x,y'=y-0.5d d is the diameter of the reference circle; Rotating the grid points around the x' axis A degree; translation in the y' direction ; Translation in z-direction ; Wherein i=1, 2 represents a first end face and a second end face, respectively; s04, generating a 3D body grid of the gear web according to the 2D section geometric model of the gear web; and S05, butting the gear tooth 3D body grid with the gear radial plate 3D body grid to generate a gear cycle symmetrical grid containing single teeth, and rotationally copying the gear cycle symmetrical grid to generate a full-ring gear finite element 3D grid.
  2. 2. The method for automatically generating the finite element mesh of the parameterized straight bevel gear according to claim 1, wherein the method for generating the end face tooth form geometric model in the step S01 comprises the following steps: s11, obtaining a base circle radius according to the end surface modulus, the pressure angle and the tooth number, and obtaining an involute equation; S12, obtaining a first arc section and an involute of the addendum circle according to the diameter of the addendum circle and an involute equation; s13, obtaining a second arc section of the root circle according to the diameter of the root circle and an involute equation; s14, obtaining the rest arc sections according to the thickness of the wheel rim; S15, carrying out rounding operation of two intersecting curves according to a given root rounding radius; s16, generating a 4-sided 8-node grid for the closed curve to obtain a generated end face tooth form geometric model.
  3. 3. The method for automatically generating the finite element mesh of the parameterized spur-conical gear according to claim 1, wherein in the step S02, nodes overlapped on a symmetry line are deleted during mirror symmetry mapping, nodes with smaller node numbers are reserved, and all the nodes are numbered again continuously according to the order of size.
  4. 4. The method for automatically generating a finite element mesh for a parameterized spur gear conical gear according to claim 2, wherein the method for generating a 3D volume mesh for gear teeth in step S03 comprises: Node coordinates of each middle section are obtained through linear interpolation of node coordinates of 2D full-tooth grids of two end faces, redundant nodes of the middle section of a 3D unit are deleted, all the nodes are continuously renumbered according to the size sequence, and a 20-node 6-plane unit grid is generated linearly from a first end face to a second end face.
  5. 5. The method for automatically generating a finite element mesh for a parameterized spur-conical gear according to claim 1, wherein the method for generating a 3D body mesh for a gear web in step S04 comprises: the number of the gear web 2D units generated according to the gear web section geometric model is consistent with the number of the gear tooth thickness units; And (3) rotating and copying the gear wheel disc around the gear axis to generate 3D units of the gear wheel disc, wherein the copying number is consistent with the number of the units at the wheel rim, and the rotating and copying angle is 360/z, so that the 3D body grid of the gear wheel disc is obtained.
  6. 6. A computer storage medium having stored thereon a computer program, characterized in that the computer program, when executed, implements the parameterized straight bevel gear finite element mesh automatic generation method of any of claims 1-5.
  7. 7. An automatic generation system for a finite element mesh of a parameterized spur-conical gear, comprising: the end face tooth form geometric model construction module adopts control parameters of the straight tooth conical gear to generate an end face tooth form geometric model; The end face full-tooth grid generating module generates 2D end face half-side grids on the generated geometric model and performs mirror symmetry mapping to generate end face full-tooth grids; The gear tooth 3D body grid generating module converts the end face full-tooth grid into an actual space position of the end face, generates the gear tooth 3D body grid between the two end face 2D full-tooth grids by adopting a linear interpolation method, and the method for converting the end face full-tooth grid into the actual space position of the end face comprises the following steps: Translation conversion is carried out on a coordinate system, geometric conversion is carried out on grid points, and the relation between new coordinates (x ', y') and old coordinates (x, y) of the grid points after translation of the coordinate system is carried out: x'=x,y'=y-0.5d d is the diameter of the reference circle; Rotating the grid points around the x' axis A degree; translation in the y' direction ; Translation in z-direction ; Wherein i=1, 2 represents a first end face and a second end face, respectively; The 3D body grid generating module of the gear web generates a 3D body grid of the gear web according to the 2D section geometric model of the gear web; and the full-ring gear finite element 3D grid generation module is used for butting the gear tooth 3D body grid and the gear radial plate 3D body grid to generate a gear circularly symmetric grid containing single teeth, and the gear circularly symmetric grid is rotationally duplicated to generate the full-ring gear finite element 3D grid.
  8. 8. The parameterized straight bevel gear finite element mesh automatic generation system of claim 7, wherein the method of generating the face tooth geometry model by the face tooth geometry model construction module comprises: s11, obtaining a base circle radius according to the end surface modulus, the pressure angle and the tooth number, and obtaining an involute equation; S12, obtaining a first arc section and an involute of the addendum circle according to the diameter of the addendum circle and an involute equation; s13, obtaining a second arc section of the root circle according to the diameter of the root circle and an involute equation; s14, obtaining the rest arc sections according to the thickness of the wheel rim; S15, carrying out rounding operation of two intersecting curves according to a given root rounding radius; s16, generating a 4-sided 8-node grid for the closed curve to obtain a generated end face tooth form geometric model.
  9. 9. The parameterized spur gear conical gear finite element mesh automatic generation system of claim 7, wherein the method of transforming the end face full-tooth mesh into the actual spatial position of the end face in the gear tooth 3D volume mesh generation module comprises: Translation conversion is carried out on a coordinate system, geometric conversion is carried out on grid points, and the relation between new coordinates (x ', y') and old coordinates (x, y) of the grid points after translation of the coordinate system is carried out: x'=x,y'=y-0.5d d is the diameter of the reference circle; Rotating the grid points around the x' axis A degree; translation in the y' direction ; Translation in z-direction ; Wherein i=1, 2 represents the first end face and the second end face, respectively.

Description

Automatic generation method and system for finite element grid of parameterized straight bevel gear Technical Field The invention belongs to the technical field of gear simulation, and relates to an automatic generation method and system for a finite element grid of a parameterized straight bevel gear. Background The gear transmission has the advantages of high efficiency, high power, long service life, compact structure, reliable work and the like, and is widely applied to engineering, including an aircraft engine accessory transmission system and a helicopter transmission system. The aviation gear is required to be light in weight and high in reliability, so that the design difficulty is high. In the design of the vibration life of the gear transmission intensity, a finite element method is often needed, and the quality of a finite element grid has a great effect on analysis accuracy. At present, commercial software is commonly used for generating a finite element grid of a structure, and a relatively mature 3D grid only has 4 faces. However, the 4-surface unit has low accuracy and poor shape simulation accuracy. In addition, the commercial software is difficult to realize automatic generation of the parameterized grid, and certain difficulty is brought to the optimal design of the structural shape. Application number 202110824112.9 discloses a full-parameterized gear meshing analysis method based on finite elements, which is used for confirming parameters affecting the geometric shape and materials of gears, obtaining tooth profiles based on involute and transition curve parameter equations and generating complete gear tooth profiles and a three-dimensional gear solid model, carrying out APDL realization of parameterized mapping grids, dividing end faces, and selecting proper grid units to generate the complete gear parameterized model. The method needs to generate the complete gear tooth profile and the three-dimensional gear solid model, so that the calculated amount is large, and the precision is still to be improved. Disclosure of Invention The invention aims to provide a parameterized automatic generation method and system for a finite element grid of a straight bevel gear, which can realize the automatic generation of the parameterized grid and can generate a 6-plane finite element grid of a node of the straight bevel gear 20 to obtain higher precision. The technical solution for realizing the purpose of the invention is as follows: a parameterized straight bevel gear finite element grid automatic generation method comprises the following steps: s01, generating an end face tooth form geometric model by adopting control parameters of a straight tooth conical gear; S02, generating 2D end face half grids on the generated geometric model, and performing mirror symmetry mapping to generate end face full-tooth grids; s03, converting the end face full-tooth grids to actual space positions of the end faces, and generating gear tooth 3D body grids between the two end face 2D full-tooth grids by adopting a linear interpolation method; s04, generating a 3D body grid of the gear web according to the 2D section geometric model of the gear web; and S05, butting the gear tooth 3D body grid with the gear radial plate 3D body grid to generate a gear cycle symmetrical grid containing single teeth, and rotationally copying the gear cycle symmetrical grid to generate a full-ring gear finite element 3D grid. In a preferred technical scheme, the method for generating the end face tooth form geometric model in the step S01 comprises the following steps: s11, obtaining a base circle radius according to the end surface modulus, the pressure angle and the tooth number, and obtaining an involute equation; S12, obtaining a first arc section and an involute of the addendum circle according to the diameter of the addendum circle and an involute equation; s13, obtaining a second arc section of the root circle according to the diameter of the root circle and an involute equation; s14, obtaining the rest arc sections according to the thickness of the wheel rim; S15, carrying out rounding operation of two intersecting curves according to a given root rounding radius; s16, generating a 4-sided 8-node grid for the closed curve to obtain a generated end face tooth form geometric model. In the preferred technical scheme, in the mirror symmetry mapping in the step S02, the nodes overlapped on the symmetry line are deleted, the node with smaller node number is reserved, and all the nodes are numbered again continuously according to the size sequence. 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: Translation conversion is carried out on a coordinate system, geometric conversion is carried out on grid points, and the relation between new coordinates (x ', y') and old coordinates (x, y) of the grid points after translation of the coordin