Method for realizing parameterized grids of involute spline contact pair

Abstract

The invention discloses a parameterized grid implementation method for an involute spline contact pair. The parameterized grid implementation method comprises the steps of generating an stp file of a geometric model of the involute spline contact pair based on a Python script; importing the stp file into Gmsh software to carry out grid division, and outputting an inp file containing grid information; and importing the inp file into abaqus simulation software for mechanical analysis. According to the method, the geometric model of the involute spline contact pair can be automatically, quickly and accurately generated, high-quality mesh generation is carried out, and mechanical property analysis is carried out.

Description

Technical Field

[0001] The invention belongs to the field of involute spline modeling, and in particular relates to a parameterized grid realization method for an involute spline contact pair. Background Art

[0002] Involute splines are widely used in the field of mechanical transmission. This is because involute splines have many advantages over rectangular splines, such as more teeth, thick tooth ends and tooth roots, strong load-bearing capacity, easy automatic centering, high installation accuracy, and large spline diameter under the same external dimensions, which is conducive to increasing the rigidity of the shaft. In addition, involute splines are easy to use cold rolling, cold beating, cold extrusion and other chipless processing methods, with high production efficiency, high precision, and can save materials.

[0003] The structural parameters of involute splines have a significant impact on mechanical properties. However, traditional modeling methods rely on manual operations, which are inefficient and prone to errors. Summary of the invention

[0004] In order to solve the above problems existing in the prior art, the present invention provides a parameterized mesh implementation method for an involute spline contact pair. The technical problem to be solved by the present invention is achieved through the following technical solutions: A parameterized mesh implementation method for an involute spline contact pair, comprising: Generate stp file of involute spline contact geometry model based on Python script; Import the stp file into the Gmsh software for meshing, and output an inp file containing mesh information; Import the inp file into the abaqus simulation software for mechanical analysis.

[0005] Beneficial effects of the present invention: In the parametric mesh implementation method of the involute spline contact pair provided in an embodiment of the present invention, spline geometry parametric modeling is implemented through a Python script, meshing is performed using Gmsh, and finite element analysis is performed in abaqus. A method for parametric modeling and simulation of involute splines based on Python, Gmsh and abaqus is implemented, which can automatically, quickly and accurately generate a spline model and perform mechanical property analysis on it. BRIEF DESCRIPTION OF THE DRAWINGS

[0006] Figure 1 A schematic flow chart of a method for implementing a parameterized mesh of an involute spline contact pair provided by an embodiment of the present invention; Figure 2 A schematic diagram of a modeling and simulation process according to an embodiment of the present invention; Figure 3 This is a schematic diagram for generating an involute; Figure 4 In the embodiment of the present invention Diagram for understanding angles; Figure 5 Schematic diagram of an involute spline contact pair geometric model of an embodiment of the present invention; Figure 6 A schematic diagram of node numbering of an involute external spline refinement model according to an embodiment of the present invention; Figure 7 A schematic diagram of mesh division of an involute external spline in an embodiment of the present invention; Figure 8 A schematic diagram of mesh division of an involute internal spline in an embodiment of the present invention; Fig. 9 A schematic diagram of mesh division of an involute spline contact pair in an embodiment of the present invention; Fig.10 is a normal stress cloud diagram of the external spline tooth surface in an embodiment of the present invention; Fig.11 It is the mises stress cloud diagram of the external spline in the embodiment of the present invention. DETAILED DESCRIPTION

[0007] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0008] As an object-oriented programming language, Python has many powerful function libraries and application programming interfaces, supports convenient data input and excellent result analysis and visualization functions, and has good scalability.

[0009] Gmsh is a powerful mesh generation software, which is widely used in the meshing stage of finite element analysis (FEM), and is particularly suitable for use with tools such as Python and abaqus. In meshing, Gmsh can automatically generate high-quality meshes based on the defined geometric model, supports a variety of geometric structures such as 2D and 3D, and can effectively adapt to models of different sizes and complexities. Users can also accurately control the size, density, shape and other parameters of the mesh to meet the needs of different analyses. Gmsh also has an efficient mesh optimization function, which can optimize the mesh after it is generated, improve the quality of the mesh (such as unit shape, size uniformity, etc.), and improve the accuracy and stability of the simulation calculation.

[0010] At present, the modeling method of involute spline relies on manual operation, which is inefficient and prone to errors. To solve this problem, the present invention uses Python and Gmsh software for modeling and meshing, and combines abaqus software for simulation analysis, and provides a parametric mesh implementation method for involute spline contact pair. Please refer to Figure 1 and Figure 2It is understood that the method may include the following steps: S1, generates the stp file of the involute spline contact geometry model based on Python script; In the embodiment of the present invention, the Python version may be Python 3.8.20, but this is not limited.

[0011] The present invention uses Python script to automatically realize the construction of the involute spline contact pair geometric model through programming.

[0012] Specifically, S1 may include the following steps: S11, running a Python script, and setting the module, number of teeth, and pressure angle of the involute spline contact pair in the Python script according to the spline design standard; The spline design standard may be the relevant standard of GB / T3478.1-2008 cylindrical spur involute spline, which contains relevant parameter values ​​of spline design. The embodiment of the present invention may be specifically selected from the standard according to the required spline configuration.

[0013] S12, calculating the base circle diameter based on the module, the number of teeth, and the pressure angle, and then generating an initial involute equation; The formula used to calculate the base circle diameter is: (1); Among them, the base circle is the involute base circle; Indicates the base circle diameter; Represents the modulus; Indicates the number of teeth; Represents the pressure angle.

[0014] An involute is a curve commonly used in mechanical transmission, especially in the design of gears and splines. It is a curve that is gradually developed from the circumtangent (or intangent) of a circle. It has very special geometric properties and can ensure smooth transmission characteristics when the gears or splines are meshed.

[0015] See also Figure 3 The involute curve shown in the figure is generated when the straight line When a circle is in pure rolling motion, a point on it The trajectory formed This circle is the involute of the circle. This circle is the involute base circle, and its radius is ;straight line That is the involute generating line; angle Point on the involute The exhibition angle.

[0016] The involute has the following characteristics: The length of the line segment and the length of the arc rolled over the base circle Equal; any point on the involute The normal of the position is tangent to the base circle and The center of curvature is the tangent point , the radius of curvature is the line segment ; The size of the base circle is the determining factor of the involute shape.

[0017] Figure 3 midpoint It is the meshing point of the involute and its conjugate tooth profile, and can also be regarded as the intersection of the involute and the pitch circle. For point The radial direction defines the tooth profile. The acute angle between the direction of the positive pressure at the point and the direction of the velocity at this point is the involute The pressure angle at middle: (2); in, Represents a line segment Length.

[0018] And because of the existence of: (3); So we can get: (4); Known angle is the pressure angle The relevant function is defined as using inv The involute function represented by is: inv (5); According to formula (2) to formula (5), the involute and coordinate equations are obtained as follows: (6); Then, in the rectangular coordinate system, the initial involute equation is expressed as: (7); Among them, the straight line When the point is in pure rolling motion along the circumference of the base circle, The trajectory formed is the involute of the base circle, point and Point is a point on the base circle; and is the midpoint of the involute equation The coordinates of is the base circle radius; is the center of the base circle and Point The straight line , and the straight line Angle.

[0019] S13, mirroring the initial involute equation to obtain tooth profiles at both ends of a single external spline tooth; Compared with rectangular splines, involute splines with involute tooth profiles are more suitable for connections with large loads, high centering accuracy and large sizes. Because the tooth profile is involute, the key teeth bear radial forces when loading, thereby automatically centering the spline pair, making each tooth evenly loaded and thus increasing the service life.

[0020] S13 may include: Based on the equation of the symmetry axis ray of the involute tooth profile, the initial involute equation is mirrored to obtain the tooth profiles at both ends of the external spline single tooth.

[0021] Specifically, after drawing the involute using Python, the involute needs to be mirrored. From simple geometry, we know that the equation of the symmetry axis ray of the involute tooth profile is: (8); in, It represents the angle between the center line of the external spline starting area and the x-axis. For a diagram of the angle, see Figure 4 understand; represents the aspect angle; Indicates the number of teeth.

[0022] Based on the above formula (8), the initial involute equation can be mirrored to obtain the tooth profiles at both ends of the external spline single tooth. Figure 4 Understood, no detailed explanation is given here.

[0023] S14, setting basic dimension parameters of the involute spline contact pair according to the spline design standard to obtain tooth grooves at both ends of a single tooth of the internal spline; The basic size parameters include: Pitch circle diameter, base circle diameter, pressure angle, external spline major diameter, external spline minor diameter, tooth profile allowance, internal spline major diameter, internal spline minor diameter, external spline effective tooth thickness deviation, and total spline difference.

[0024] Specifically, according to the standard GB / T3478.1-2008 Cylindrical Spur Involute Spline (Metric Module Side Fit) Part 1: General, the present invention first establishes a basic dimension of a 30° flat tooth root: (9); (10); (11); (12); (13); (14); (15); (16); (17); (18); (19); (20); in, Indicates the pitch circle diameter in millimeters; Represents the modulus; Indicates the number of teeth; Indicates the base circle diameter in millimeters; represents the pressure angle; Indicates the major diameter of the external spline, in millimeters; Indicates the minor diameter of the external spline in millimeters; Indicates the major diameter of the internal spline, in millimeters; Indicates the minor diameter of the internal spline in millimeters; Indicates the maximum value of the starting circle diameter of the external spline involute; Indicates the tooth profile allowance in millimeters; Indicates the distance from the center of the tooth root chamfer to the base circle; Indicates the upper deviation of the effective tooth thickness of the external spline, in microns, determined by looking up the table; Indicates the total difference of the spline, determined by looking up the table; Indicates the maximum effective tooth groove width; S14, including: S141, according to the basic size parameters of the involute spline contact pair, obtain the equation of the involute of the internal spline tooth profile and the symmetry axis ray of the initial involute; wherein the initial involute is determined according to the initial involute equation; According to the information in formulas (9) to (20), the equations of the involute of the internal spline tooth profile and the symmetry axis ray of the initial involute can be obtained as follows: (twenty one); in, Indicates the angle between the center line of the internal spline starting area and the x-axis; Indicates the angle of expansion.

[0025] S142, based on the equation of the involute of the internal spline tooth profile and the symmetry axis ray of the initial involute, obtain the tooth grooves at both ends of the single tooth of the internal spline.

[0026] You can refer to Figure 4 As well as the part about external splines, understanding the relevant content of internal splines will not be explained in detail here.

[0027] S15, obtaining a complete cross section of internal and external spline meshing according to the tooth profiles at both ends of the external spline single tooth and the tooth grooves at both ends of the internal spline single tooth, and stretching the cross section to obtain an STP file of the involute spline contact pair geometric model.

[0028] Among them, the stp file of the involute spline contact pair geometry model contains all the parameters of the involute spline contact pair geometry model.

[0029] See also Figure 5 Understand the involute spline contact geometry model. This geometry model is composed of the meshing of external splines and internal splines.

[0030] It can be understood that the embodiment of the present invention automatically completes modeling of the involute spline contact pair to be designed by selecting parameters and using Python scripts. By modifying relevant parameters, an stp file of any involute spline contact pair geometric model that meets the standard can be generated according to this method.

[0031] S2, importing the stp file into the Gmsh software for meshing, and outputting an inp file containing mesh information; The Gmsh software is used to perform meshing on the involute spline contact pair geometric model. In the embodiment of the present invention, the Gmsh software version may be Gmsh4.11.1, but this is not limited.

[0032] Specifically, S2 may include the following steps: S21, in the Gmsh software, for the involute spline contact pair geometric model generated by the imported stp file, setting the node parameters of the mesh division unit; For an example of an involute external spline, see Figure 6 The node parameters include the number of nodes between two teeth in the circumferential direction , Number of nodes on a single circumferential tooth , Number of nodes on a single tooth in the tooth height direction , Number of nodes in radial direction of external spline shaft segment . Figure 6 The three areas corresponding to the yellow lines in the middle form a grid division unit.

[0033] S22, generating a regular plane quadrilateral mesh of a mesh division unit using the node parameters; See also Figure 6 The Gmsh software uses the transfinite surface function in Gmsh for each area of ​​the above-mentioned grid division unit to generate a regular plane quadrilateral grid of the grid division unit.

[0034] S23, arraying the regular plane quadrilateral mesh of the one mesh division unit on the involute spline contact pair geometry model to obtain a circumferential single-layer quadrilateral mesh of the involute spline contact pair geometry model; The Gmsh software arrays the regular plane quadrilateral mesh of the above-mentioned mesh division unit on the involute spline contact pair geometry model to obtain a circumferential single-layer quadrilateral mesh, thereby completing the single-layer mesh division.

[0035] S24, using the extrude function of the Gmsh software to stretch the circumferential single-layer quadrilateral mesh of the involute spline contact pair geometry model to obtain a complete C3D8 unit mesh, and output the corresponding mesh information in the form of an inp file.

[0036] Specifically, by stretching the circumferential single-layer quadrilateral mesh along the radial direction, a complete C3D8 unit mesh can be obtained, thereby completing the entire mesh division of the involute spline contact pair geometry model, and exporting these mesh information to the inp file through the output function of the Gmsh software.

[0037] The meshing results of the involute external spline, the meshing results of the involute internal spline, and the meshing results of the involute spline contact pair in the embodiment of the present invention are shown in FIG. Figure 7 , Figure 8 , Fig. 9 Hint.

[0038] The embodiment of the present invention utilizes the Gmsh software to first divide the regionalized plane grid, and the annular array obtains a complete plane quadrilateral grid, and then stretches it through the built-in function of Gmsh to finally obtain a refined C3D8 grid and output an inp file, thereby achieving high-quality grid division and ensuring the accuracy of finite element calculation.

[0039] S3, importing the inp file into abaqus simulation software for mechanical analysis.

[0040] Specifically, S3 may include: Import the inp file into the abaqus simulation software, define material parameters, create analysis steps, set boundary conditions and loads, run the simulation, and obtain the relevant stress cloud diagram to analyze the stress and deformation results.

[0041] Specifically, material parameters include elastic modulus, Poisson's ratio, etc. Setting boundary conditions includes fixed end constraints, applied torque, etc.

[0042] The following is a simulation example: Refer to relevant standards and design methods to select the parameters of the involute spline contact pair. The commonly used pressure angle is 30°; according to the structural design of the helicopter reducer and the torque input by the system, the modulus Take 3mm. Aviation applications have high requirements for spline pair precision. Usually the spline pair tolerance grade should be less than grade 6. The selection of tooth curve and parameters refers to GB / T3478.1-2008. The basic geometric parameters and material properties of the spline pair are shown in Table 1. The friction coefficient between the inner and outer spline contact surfaces of the model Take 0.2.

[0043] Table 1 Basic parameters of involute spline contact pair

[0044] The contact analysis of spline transmission simulation is a highly nonlinear calculation, which has extremely high requirements on the configuration of the computer and the quality and accuracy of the grid. Therefore, it is difficult to select the appropriate grid type and grid size and obtain accurate and efficient convergence results. In the finite element calculation software, in order to ensure the accuracy of the solution results, a sufficiently small grid size is required, and the solution time is also increased accordingly, and the occupation of computing resources is further expanded. In order to reduce the quality of the grid and improve the computing efficiency, in the actual simulation operation, the present invention uses parameterization to achieve the mesh refinement of the contact area.

[0045] In finite element contact analysis, the master surface and the slave surface constitute a contact pair. When defining the contact pair, the master surface and the slave surface must be accurately selected. In the abaqus simulation software, the nodes on the master surface can invade the slave surface, but the slave surface cannot. The contact direction at the node is along the normal of the master surface. The abaqus simulation software describes the relative slip between the two contact surfaces with two settings: small slip and limited slip. For limited slip, the relative slip between the two contact surfaces is not restricted, and the abaqus simulation software will continue to determine the area where the master surface nodes and the slave surface nodes are in contact. For small slip, the abaqus simulation software determines the area on the master surface that will interact with all the nodes on the slave surface, and these relationships will continue throughout the analysis process. Since the spline has a large relative slip when contacting the tooth surface during the meshing process, the limited slip method is used to solve the contact problem of the spline.

[0046] The abaqus simulation software includes two contact pair discretization methods: face-to-face discretization and point-to-face discretization. Face-to-face discretization is to establish a contact relationship on the entire slave surface, and the changes in the shapes of the slave surface and the master surface will be considered during the analysis process; point-to-face discretization is to establish a contact relationship between the nodes on the slave surface and their projection points on the master surface. The calculation accuracy of the point-to-face discretization method is lower than that of the face-to-face discretization method. The face-to-face discretization method is used to solve the contact problem of splines. In the contact simulation of the abaqus simulation software, the discontinuity of the bonding and slip states may lead to non-convergence problems in the calculation, so when the influence of friction on the model is small, the influence of friction can be ignored. In the spline contact pair settings, select the Frictionless frictionless type.

[0047] The boundary conditions of the spline must be applied to the rotational freedom around its axis, but the three-dimensional solid elements in the abaqus simulation software usually do not have rotational freedom, so it is necessary to establish a reference point on the local coordinate system of the internal and external splines, and establish a coupling constraint between the spline and the reference point.

[0048] The final calculation result is as follows Fig.10 and Fig.11 As shown, Fig.10 is the normal stress cloud diagram of the external spline tooth surface, Fig.11 This is the mises stress cloud diagram of the external spline.

[0049] In the parametric mesh implementation method of the involute spline contact pair provided in an embodiment of the present invention, spline geometry parametric modeling is implemented through a Python script, meshing is performed using Gmsh, and finite element analysis is performed in abaqus. A method for parametric modeling and simulation of involute splines based on Python, Gmsh and abaqus is implemented, which can automatically, quickly and accurately generate a spline model and perform mechanical property analysis on it.

[0050] In the method of the present invention, the number of teeth, module, pressure angle, fit clearance, and mesh density of the internal and external splines can be changed in real time by simple parameter settings. The stress distribution and deformation of the involute spline under different load conditions can be obtained through simulation. The results show that the method of the present invention can quickly and accurately evaluate the mechanical properties of the spline and provide data support for the optimization design. It has a high degree of automation and accuracy and can be used to quickly design and evaluate the spline structure and improve engineering efficiency.

[0051] It should be noted that, in the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise" and the like indicating directions or positional relationships are based on the directions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore should not be understood as a limitation on the present invention.

[0052] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0053] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification.

[0054] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A parameterized mesh implementation method for an involute spline contact pair, characterized in that: include: Generate stp file of involute spline contact geometry model based on Python script; Import the stp file into the Gmsh software for meshing, and output an inp file containing mesh information; Import the inp file into abaqus simulation software for mechanical analysis.

2. The parameterized mesh implementation method of the involute spline contact pair according to claim 1, characterized in that: The stp file of the involute spline contact pair geometry model generated based on the Python script includes: Running a Python script, and setting the module, number of teeth, and pressure angle of the involute spline contact pair in the Python script according to the spline design standard; Based on the module, the number of teeth, and the pressure angle, the base circle diameter is calculated, and then an initial involute equation is generated; Mirroring the initial involute equation, the tooth profiles at both ends of the external spline single tooth are obtained; According to the spline design standard, the basic dimension parameters of the involute spline contact pair are set to obtain the tooth grooves at both ends of the single tooth of the internal spline; A complete cross section of internal and external spline meshing is obtained according to the tooth profiles at both ends of the external spline single tooth and the tooth grooves at both ends of the internal spline single tooth, and the cross section is stretched to obtain an STP file of the involute spline contact pair geometric model.

3. The parameterized mesh implementation method of the involute spline contact pair according to claim 2, characterized in that: The formula used to calculate the base circle diameter is: ； in, Indicates the base circle diameter; Represents the modulus; Indicates the number of teeth; Represents the pressure angle.

4. The parameterized mesh implementation method of the involute spline contact pair according to claim 2, characterized in that: The initial involute equation is expressed as: ； Among them, the straight line When the point is in pure rolling motion along the circumference of the base circle, The trajectory formed is the involute of the base circle, point and Point is a point on the base circle; and is the midpoint of the involute equation The coordinates of is the base circle radius; is the center of the base circle and Point The straight line , and the straight line Angle.

5. The parameterized mesh implementation method of the involute spline contact pair according to claim 2, characterized in that: The initial involute equation is mirrored to obtain the tooth profiles at both ends of the external spline single tooth, including: Based on the equation of the symmetry axis ray of the involute tooth profile, the initial involute equation is mirrored to obtain the tooth profiles at both ends of the external spline single tooth.

6. The parameterized mesh implementation method for involute spline contact pair according to claim 2, characterized in that: The basic size parameters include: Pitch circle diameter, base circle diameter, pressure angle, external spline major diameter, external spline minor diameter, tooth profile allowance, internal spline major diameter, internal spline minor diameter, external spline effective tooth thickness deviation, and total spline difference.

7. The parameterized mesh implementation method of the involute spline contact pair according to claim 2, characterized in that: According to the spline design standard, the basic size parameters of the involute spline contact pair are set to obtain the tooth grooves at both ends of the internal spline single tooth, including: According to the basic size parameters of the involute spline contact pair, the equations of the involute of the internal spline tooth profile and the symmetry axis ray of the initial involute are obtained; wherein the initial involute is determined according to the initial involute equation; Based on the equation of the involute of the internal spline tooth profile and the symmetry axis ray of the initial involute, the tooth grooves at both ends of the single tooth of the internal spline are obtained.

8. The parameterized mesh implementation method for involute spline contact pair according to claim 2, characterized in that: Import the stp file into the Gmsh software for meshing, and output an inp file containing mesh information, including: In the Gmsh software, for the involute spline contact pair geometric model generated by the imported stp file, the node parameters of the mesh division unit are set; Generating a regular plane quadrilateral grid of a grid division unit using the node parameters; Arraying the regular plane quadrilateral mesh of the one mesh division unit on the involute spline contact pair geometry model to obtain a circumferential single-layer quadrilateral mesh of the involute spline contact pair geometry model; The extrude function of the Gmsh software is used to stretch the circumferential single-layer quadrilateral mesh of the involute spline contact pair geometry model to obtain a complete C3D8 unit mesh, and the corresponding mesh information is output in the form of an inp file.

9. The parameterized mesh implementation method of the involute spline contact pair according to claim 8, characterized in that: The node parameters include the number of nodes between two teeth in the circumferential direction , Number of nodes on a single circumferential tooth , Number of nodes on a single tooth in the tooth height direction , Number of nodes in radial direction of external spline shaft segment .

10. The parameterized mesh implementation method of involute spline contact pair according to claim 1, characterized in that: Import the inp file into the abaqus simulation software for mechanical analysis, including: Import the inp file into the abaqus simulation software, define material parameters, create analysis steps, set boundary conditions and loads, run the simulation, and obtain the relevant stress cloud diagram to analyze the stress and deformation results.

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