A Parametric Mesh Implementation Method for Involute Spline Contact Pairs

Abstract

The present invention discloses a parametric mesh implementation method for an involute spline contact pair, including: generating an stp file of the involute spline contact pair geometric model based on a Python script; importing the stp file into Gmsh software for mesh generation and outputting an inp file containing mesh information; importing the inp file into abaqus simulation software for mechanical analysis. The present invention can automatically, quickly and accurately generate the geometric model of the involute spline contact pair, perform high-quality mesh dissection, and perform mechanical property analysis.

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:

[0005] A parameterized mesh implementation method for an involute spline contact pair, comprising:

[0006] Generate stp file of involute spline contact geometry model based on Python script;

[0007] Import the stp file into the Gmsh software for meshing, and output an inp file containing mesh information;

[0008] Import the inp file into abaqus simulation software for mechanical analysis.

[0009] Beneficial effects of the present invention:

[0010] 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

[0011] 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;

[0012] Figure 2 Schematic diagram of the modeling and simulation process for the embodiments of the present invention;

[0013] Figure 3 Schematic diagram of the generation of involute;

[0014] Figure 4 In the embodiments of the present invention Schematic diagram for understanding angles;

[0015] Figure 5 Schematic diagram of the geometric model of the involute spline contact pair for the embodiments of the present invention;

[0016] Figure 6 Schematic diagram of the node numbering of the refined model of the involute external spline for the embodiments of the present invention;

[0017] Figure 7 Schematic diagram of the mesh division of the involute external spline for the embodiments of the present invention;

[0018] Figure 8 Schematic diagram of the mesh division of the involute internal spline for the embodiments of the present invention;

[0019] Figure 9 Schematic diagram of the mesh division of the involute spline contact pair for the embodiments of the present invention;

[0020] Figure 10 Normal stress nephogram of the tooth surface of the external spline for the embodiments of the present invention;

[0021] Figure 11 Mises stress nephogram of the external spline for the embodiments of the present invention. Detailed implementation manners

[0022] The following further describes the present invention in detail with reference to specific embodiments, but the implementation manners of the present invention are not limited thereto.

[0023] As an object-oriented programming language, Python has numerous powerful function libraries and application programming interfaces, supports convenient data input and excellent result analysis and visualization functions, and has good scalability.

[0024] Gmsh is a powerful mesh generation software, widely used in the meshing stage of finite element analysis (FEM), especially suitable for use in conjunction with tools such as Python and Abaqus. In meshing, Gmsh can automatically generate high-quality meshes based on the defined geometric model, support various geometric structures such as 2D and 3D, and can effectively adapt to models of different sizes and complexities. Users can also precisely control parameters such as the size, density, and shape of the mesh to meet the requirements of different analyses. Gmsh also has an efficient mesh optimization function, which can optimize the mesh after generation to improve the mesh quality (such as element shape, size uniformity, etc.) to improve the accuracy and stability of simulation calculations.

[0025] Currently, the modeling method of involute splines relies on manual operations, which is inefficient and error-prone. To address this issue, the present invention uses Python and Gmsh software for modeling and meshing, and combines Abaqus software for simulation analysis, providing a parametric mesh implementation method for involute spline contact pairs. Please refer to Figure 1 and Figure 2 for understanding. This method may include the following steps:

[0026] S1, Generate an stp file of the geometric model of the involute spline contact pair based on a Python script;

[0027] In the embodiments of the present invention, the Python version may be Python 3.8.20, but this is not limited.

[0028] The present invention uses a Python script to automatically construct the geometric model of the involute spline contact pair through programming.

[0029] Specifically, S1 may include the following steps:

[0030] S11, Run the Python script, and set the module, number of teeth, and pressure angle of the involute spline contact pair in the Python script according to the spline design standard;

[0031] Among them, the spline design standard may be the relevant standard of GB / T 3478.1-2008 cylindrical straight-tooth involute splines, which contains the relevant parameter values of spline design. The embodiments of the present invention can specifically select according to the required spline configuration.

[0032] S12, Based on the module, number of teeth, and pressure angle, calculate the base circle diameter, and then generate an initial involute equation;

[0033] Among them, the formula used to calculate the base circle diameter is:

[0034] (1);

[0035] Among them, the base circle is the involute base circle; represents the base circle diameter; represents the module; represents the number of teeth; represents the pressure angle.

[0036] The involute is a curve commonly used in mechanical transmissions, especially in the design of gears and splines. It is a curve gradually developed from the outer tangent (or inner tangent) of a circle and has very special geometric properties, which can ensure smooth transmission characteristics when gears or splines are meshed.

[0037] Please refer to Figure 3 the shown involute generation diagram. When the straight line performs a pure rolling motion along a certain circumference, a certain point on it forms a locus which is the involute of this circumference. This circumference is the involute base circle, and its radius is ; the straight line is the involute generating line; the angle is the involute angle of point

[0038] The involute has the following characteristics: the length of the involute generating line segment is equal to the arc length rolled by the base circle; the normal line at any point on the involute is tangent to the base circle and its center of curvature is the tangent point , and the radius of curvature is the line segment ; the size of the base circle is the determining factor of the involute shape.

[0039] Figure 3 In , point is the meshing point of the involute and its conjugate tooth profile, and can also be regarded as the intersection point of the involute and the pitch circle. is the radius vector of point . Define the acute angle formed between the direction of the positive pressure borne by the tooth profile at and the direction of the velocity of this point as the pressure angle of the involute at . In triangle

[0040] (2);

[0041] Among them, represents the length of the line segment .

[0042] Also, since there is:

[0043] (3);

[0044] Thus, it can be obtained that:

[0045] (4);

[0046] It can be known that the involute angle is a function related to the pressure angle and is defined as the involute function represented by inv , that is:

[0047] inv (5);

[0048] According to formulas (2) to (5), the involute and the coordinate equation are obtained as:

[0049] (6);

[0050] Thus, in the rectangular coordinate system, the initial involute equation is expressed as:

[0051] (7);

[0052] Among them, when the straight line performs a pure rolling motion along the circumference of the base circle, the locus formed by the point is the involute of the base circle circumference, and the points and are points on the base circle; and are the coordinates of the point in the involute equation; is the base circle radius; is the included angle between the straight line formed by the center of the base circle and the point , and the straight line .

[0053] S13, mirror the initial involute equation to obtain the tooth profiles at both ends of a single tooth of the external spline;

[0054] Compared with rectangular splines, involute splines with involute tooth profiles are more suitable for connections with large loads, high centering accuracy, and large dimensions. Since their tooth profiles are involutes, the key teeth bear radial forces during loading, thereby automatically centering the spline pair and equalizing the loads on each tooth, thus increasing the working life.

[0055] S13 may include:

[0056] Based on the equation of the symmetry axis ray of the involute profile, the initial involute equation is mirrored to obtain the tooth profiles at both ends of a single tooth of the external spline.

[0057] Specifically, after drawing the involute using Python, the involute needs to be mirrored. From simple geometry, the equation of the symmetry axis ray of the involute profile is:

[0058] (8);

[0059] Where, represents the angle between the center line of the starting area of the external spline and the x-axis, For the schematic of the angle, please refer to Figure 4 for understanding; represents the involute angle; represents the number of teeth.

[0060] Based on the above formula (8), the initial involute equation can be mirrored to obtain the tooth profiles at both ends of a single tooth of the external spline. Those skilled in the art can combine this part with Figure 4 for understanding and no detailed description will be given here.

[0061] S14. Set the basic dimension parameters of the involute spline contact pair according to the spline design standard to obtain the tooth grooves at both ends of a single tooth of the internal spline;

[0062] Among them, the basic dimension parameters include:

[0063] Pitch diameter, base circle diameter, pressure angle, major diameter dimension of the external spline, minor diameter dimension of the external spline, tooth form allowance, major diameter dimension of the internal spline, minor diameter dimension of the internal spline, upper deviation of the working tooth thickness of the external spline, total tolerance of the spline.

[0064] Specifically, according to GB / T3478.1-2008 Cylindrical straight tooth involute splines (metric module, side fit) Part 1: General principles, the present invention first establishes a basic dimension of a 30° flat root:

[0065] (9);

[0066] (10);

[0067] (11);

[0068] (12);

[0069] (13);

[0070] (14);

[0071] (15);

[0072] (16);

[0073] (17);

[0074] (18);

[0075] (19);

[0076] (20);

[0077] Wherein, represents the pitch diameter, in millimeters; represents the module; represents the number of teeth; represents the base circle diameter, in millimeters; represents the pressure angle; represents the major diameter dimension of the external spline, in millimeters; represents the minor diameter dimension of the external spline, in millimeters; represents the major diameter dimension of the internal spline, in millimeters; represents the minor diameter dimension of the internal spline, in millimeters; represents the maximum value of the starting circle diameter of the involute of the external spline; represents the tooth form margin, in millimeters; represents the distance from the center of the tooth root chamfer to the base circle; represents the upper deviation of the working tooth thickness of the external spline, in micrometers, determined by looking up the table; represents the total tolerance of the spline, determined by looking up the table; represents the maximum value of the working tooth space width;

[0078] S14, including:

[0079] S141, according to the basic dimension parameters of the involute spline contact pair, obtain the equation of the symmetry axis ray of the involute of the internal spline tooth profile and the initial involute; wherein, the initial involute is determined according to the initial involute equation;

[0080] According to the information of formulas (9) to (20), the equation of the symmetry axis ray of the involute of the internal spline tooth profile and the initial involute can be obtained as:

[0081] (21);

[0082] Wherein, represents the angle between the center line of the starting area of the internal spline and the x-axis; Indicates the spreading angle.

[0083] 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 spaces at both ends of a single tooth of the internal spline.

[0084] Reference can be made to Figure 4 and the part of the external spline to understand the relevant content of the internal spline, which will not be elaborated here.

[0085] S15. Obtain the complete cross-section of the meshing of the internal and external splines according to the tooth profiles at both ends of the single tooth of the external spline and the tooth spaces at both ends of the single tooth of the internal spline, and stretch the cross-section to obtain the stp file of the geometric model of the involute spline contact pair.

[0086] Among them, the stp file of the geometric model of the involute spline contact pair contains all the parameters of the geometric model of the involute spline contact pair.

[0087] Please refer to Figure 5 to understand the geometric model of the involute spline contact pair. This geometric model is formed by the meshing of the external spline and the internal spline.

[0088] It can be understood that in the embodiment of the present invention, for the involute spline contact pair to be designed, through parameter selection, the modeling is automatically completed using a Python script. By modifying the relevant parameters, any stp file of the geometric model of the involute spline contact pair that meets the standards can be generated according to this method.

[0089] S2. Import the stp file into Gmsh software for mesh generation, and output the inp file containing mesh information;

[0090] Gmsh software is used for mesh generation of the geometric model of the involute spline contact pair. In the embodiment of the present invention, the version of Gmsh software can be Gmsh4.11.1, but there is no limitation on this.

[0091] Specifically, S2 can include the following steps:

[0092] S21. In the Gmsh software, for the geometric model of the involute spline contact pair generated from the imported stp file, set the node parameters of the mesh generation unit;

[0093] Taking the involute external spline as an example, please refer to Figure 6 , the node parameters include the number of nodes between two teeth in the circumferential direction , the number of nodes on a single tooth in the circumferential direction , the number of nodes on a single tooth in the tooth height direction , the number of nodes in the radial direction of the external spline shaft section . Figure 6 The three regions corresponding to the yellow lines in form a mesh generation unit.

[0094] S22. Generate a regular planar quadrilateral mesh for a mesh division unit using the node parameters.

[0095] Please refer to Figure 6 , and the Gmsh software uses the transfinite surface function in Gmsh for each region of the above-mentioned mesh division unit to generate a regular planar quadrilateral mesh for this mesh division unit.

[0096] S23. Array the regular planar quadrilateral mesh of the above-mentioned mesh division unit on the involute spline contact pair geometric model to obtain a circumferential single-layer quadrilateral mesh of the involute spline contact pair geometric model.

[0097] The Gmsh software arrays the regular planar quadrilateral mesh of the above-mentioned mesh division unit on the involute spline contact pair geometric model, and a circumferential single-layer quadrilateral mesh is obtained, thus completing the single-layer mesh division.

[0098] S24. Use the extrude function of the Gmsh software to stretch the circumferential single-layer quadrilateral mesh of the involute spline contact pair geometric model to obtain a complete mesh of C3D8 elements, and output the corresponding mesh information in the form of an inp file.

[0099] Specifically, by stretching the circumferential single-layer quadrilateral mesh along the radial direction, a complete mesh of C3D8 elements can be obtained, thus completing all the mesh divisions of the involute spline contact pair geometric model. These mesh information are exported to an inp file through the output function of the Gmsh software.

[0100] For the mesh division results of the involute external spline, the mesh division results of the involute internal spline, and the mesh division results of the involute spline contact pair in the embodiments of the present invention, please refer to Figure 7 , Figure 8 , Figure 9 respectively for illustration.

[0101] In the embodiments of the present invention, by using the Gmsh software to first divide the regionalized planar mesh, circularly array to obtain a complete planar quadrilateral mesh, and then stretch through the built-in function of Gmsh to finally obtain a refined C3D8 mesh and output an inp file, high-quality mesh dissection is realized, which can ensure the finite element calculation accuracy.

[0102] S3. Import the inp file into the abaqus simulation software for mechanical analysis.

[0103] Specifically, S3 may include:

[0104] Import the inp file into the Abaqus simulation software. After defining material parameters, creating analysis steps, setting boundary conditions and loads, run the simulation to obtain relevant stress nephograms for analyzing stress and deformation results.

[0105] Specifically, the material parameters include elastic modulus, Poisson's ratio, etc. Setting boundary conditions includes fixed-end constraints, applying torque, etc.

[0106] The following gives a simulation example:

[0107] Refer to relevant standards and design methods to select the parameters of the involute spline contact pair. The pitch circle pressure angle Adopt the common pressure angle of 30°; according to the structural design of the helicopter reducer and the input torque of the system, the module Take 3mm. The aviation application has high requirements for the accuracy of the spline pair. Usually, the tolerance grade of the spline pair should be less than grade 6, and the selection of the tooth profile 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 this model is taken as 0.2.

[0108] Table 1 Basic parameters of involute spline contact pair

[0109]

[0110] The contact analysis of the spline pair drive simulation belongs to highly nonlinear calculation, which has extremely high requirements for the computer configuration, mesh quality and accuracy. Therefore, it is difficult to select a suitable mesh type and mesh size and obtain accurate and efficient convergence results. In the finite element calculation software, to ensure the accuracy of the solution results, a sufficiently small mesh size is required, while the solution time also increases accordingly and the occupation of computing resources further expands. To reduce the mesh quality and improve the calculation efficiency, in the actual simulation operation, the present invention realizes the mesh refinement of the contact area by parameterization.

[0111] In finite element contact analysis, the master surface and the slave surface form a contact pair. When defining a 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 penetrate the slave surface, but the slave surface cannot. The contact direction at the nodes is along the normal direction of the master surface. The abaqus simulation software describes two settings for the relative slip between two contact surfaces: small slip and finite slip. For finite slip, the relative sliding between the two contact surfaces is not restricted, and the abaqus simulation software continuously judges the area where the master surface nodes and the slave surface nodes come into contact. For small slip, the abaqus simulation software determines the area on the master surface that will act on all the nodes on the slave surface, and these relationships will persist throughout the analysis process. Since there is a large relative slip between the contacting tooth surfaces during the meshing process of the spline, the finite slip method is adopted for the contact problem of the spline.

[0112] In the abaqus simulation software, there are two discrete methods for contact pairs: face-to-face discretization and point-to-face discretization. Face-to-face discretization establishes contact relationships over the entire slave surface and takes into account the shape changes of the slave surface and the master surface during the analysis process; point-to-face discretization establishes contact relationships 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 adopted when solving the contact problem of the spline. 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. Therefore, when the influence of friction on the model is small, the influence of friction can be ignored. In the spline contact pair setting, the Frictionless (frictionless) type is selected.

[0113] The boundary conditions of the spline must be applied to the rotational degrees of freedom about its axis. However, the three-dimensional solid elements in the abaqus simulation software usually do not have rotational degrees of freedom. Therefore, reference points need to be established in the local coordinate systems of the internal and external splines, and coupling constraints need to be established between the spline and the reference points.

[0114] The final calculation results are as Figure 10 and Figure 11 shown. Figure 10 is the normal stress nephogram of the external spline tooth surface, Figure 11 is the von Mises stress nephogram of the external spline.

[0115] In the parametric mesh implementation method of the involute spline contact pair provided by the embodiments of the present invention, the geometric parametric modeling of the spline is realized through Python scripts, the mesh generation is carried out using Gmsh, and the finite element analysis is carried out in abaqus, realizing a method for parametric modeling and simulation of involute splines based on Python, Gmsh, and abaqus, which can automatically, quickly, and accurately generate a spline model and perform mechanical property analysis on it.

[0116] In the method of the present invention, by simple parameter settings, the number of teeth, module, pressure angle, fit clearance, and grid density of internal and external splines can be changed in real time. Through simulation, the stress distribution and deformation of involute splines under different load conditions can be obtained. The results show that the method of the present invention can quickly and accurately evaluate the mechanical properties of splines, provide data support for optimized design, has a high degree of automation and accuracy, and can be used for rapid design and evaluation of spline structures to improve engineering efficiency.

[0117] It should be noted that in the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention.

[0118] In addition, the terms "first" and "second" are only used for descriptive purposes and should not be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, "a plurality" means two or more, unless otherwise specifically defined.

[0119] In the description of this specification, the description with reference to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials, or characteristics described in connection 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 can be combined in a suitable manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine the different embodiments or examples described in this specification.

[0120] The above 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 parametric mesh implementation method for an involute spline contact pair, characterized in that Including: Generating an stp file of the involute spline contact pair geometric model based on a Python script; Import the stp file into Gmsh software for mesh generation, and output an inp file containing mesh information; among them, importing the stp file into Gmsh software for mesh generation and outputting an inp file containing mesh information includes: in the Gmsh software, set the node parameters of the mesh generation element for the involute spline contact pair geometric model generated from the imported stp file; the node parameters include the number of nodes between two teeth in the circumferential direction , the number of nodes on a single tooth in the circumferential direction , the number of nodes on a single tooth in the tooth height direction , the number of nodes in the radial direction of the external spline shaft section ; use the transfinite surface function in Gmsh for each region of a mesh generation element with the node parameters to generate a regular planar quadrilateral mesh for the mesh generation element; array the regular planar quadrilateral mesh of the mesh generation element on the involute spline contact pair geometric model to obtain a circumferential single-layer quadrilateral mesh of the involute spline contact pair geometric model; use the extrude function of the Gmsh software to stretch the circumferential single-layer quadrilateral mesh of the involute spline contact pair geometric model to obtain a complete mesh of C3D8 elements, and output the corresponding mesh information in the form of an inp file through the output function of the Gmsh software; Importing the inp file into the abaqus simulation software for mechanical analysis; Among them, generating an stp file of the involute spline contact pair geometric model based on a Python script includes: Running the Python script and setting the module number, 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 number, number of teeth, and pressure angle, calculating the base circle diameter and then generating an initial involute equation; Mirroring the initial involute equation to obtain the tooth profiles at both ends of a single tooth of the external spline; Setting the basic dimension parameters of the involute spline contact pair according to the spline design standard to obtain the tooth grooves at both ends of a single tooth of the internal spline; Obtaining a complete cross-section of the internal and external spline meshing based on the tooth profiles at both ends of a single tooth of the external spline and the tooth grooves at both ends of a single tooth of the internal spline, and stretching the cross-section to obtain an stp file of the involute spline contact pair geometric model; Among them, setting the basic dimension parameters of the involute spline contact pair according to the spline design standard to obtain the tooth grooves at both ends of a single tooth of the internal spline includes: Obtaining the equation of the ray of the axis of symmetry between the involute of the internal spline tooth profile and the initial involute according to the basic dimension parameters of the involute spline contact pair; where the initial involute is determined according to the initial involute equation; Based on the equation of the ray of the axis of symmetry between the involute of the internal spline tooth profile and the initial involute, obtaining the tooth grooves at both ends of a single tooth of the internal spline.

2. The parametric mesh implementation method of the involute spline contact pair according to claim 1, wherein, The formula for calculating the base circle diameter is: ； Among them, represents the base circle diameter; represents the module; represents the number of teeth; represents the pressure angle.

3. The parametric grid implementation method of the involute spline contact pair according to claim 1, characterized in that, The initial involute equation is expressed as: ； Among them, when the straight line performs a pure rolling motion along the circumference of the base circle, the locus formed by the point is the involute of the base circle circumference, and the points and are points on the base circle; and are the coordinates of the point in the involute equation; is the radius of the base circle; is the center of the base circle and the point constitute the straight line , and the included angle with the straight line .

4. The parametric mesh implementation method of the involute spline contact pair according to claim 1, characterized in that Mirroring the initial involute equation to obtain the tooth profiles at both ends of a single tooth of the external spline includes: Based on the equation of the ray of the axis of symmetry of the involute tooth profile, mirroring the initial involute equation to obtain the tooth profiles at both ends of a single tooth of the external spline.

5. The parametric mesh implementation method of the involute spline contact pair according to claim 1, characterized in that, The basic dimension parameters include: Pitch circle diameter, base circle diameter, pressure angle, major diameter dimension of the external spline, minor diameter dimension of the external spline, tooth form allowance, major diameter dimension of the internal spline, minor diameter dimension of the internal spline, upper deviation of the working tooth thickness of the external spline, total tolerance of the spline.

6. The parametric mesh implementation method of the involute spline contact pair according to claim 1, wherein Importing the inp file into the abaqus simulation software for mechanical analysis includes: Importing the inp file into the abaqus simulation software, defining material parameters, creating an analysis step, setting boundary conditions and loads, and then running the simulation to obtain relevant stress nephograms to analyze stress and deformation results.

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