A finite element parametric modeling method for cylindrical gears with variable hyperbolic arc tooth traces

Abstract

The present application provides a finite element parametric modeling method for a variable hyperbolic arc tooth line cylindrical gear, including: setting geometric parameters and mesh parameters of the variable hyperbolic arc tooth line cylindrical gear; determining the node coordinates of the tooth profile of a single tooth surface at the middle section based on the middle section of the tooth width of a single gear tooth; obtaining the node coordinates of n tooth surfaces at a single layer of the middle section by copying and rotating the node coordinates of a single tooth surface at the middle section; determining the node coordinates of the tooth profile of n tooth surfaces at a non-middle section and the node coordinates of n tooth surfaces at a single layer of the non-middle section in the same way; based on the calculated node coordinates of the variable hyperbolic arc tooth line cylindrical gear, connecting the nodes of two adjacent layers according to the eight-node hexahedral unit node connection order rule, and constructing the corresponding unit number coordinate matrix; establishing the finite element mesh model of the variable hyperbolic arc tooth line cylindrical gear according to the unit number coordinate matrix. The present application can take into account both the calculation accuracy and solution efficiency of modeling.

Description

Technical Field

[0001] The present application relates to the technical field of finite element modeling of gears, and in particular to a finite element parameterized modeling method for variable hyperbolic arc tooth line cylindrical gears. Background Art

[0002] Gear transmission systems are superior to other transmission forms in terms of transmitting torque, changing speed and direction of movement. Therefore, gear transmission systems are widely used in high-speed rail, aerospace, high-precision processing and heavy machinery. In the connection transmission, gear transmission has the advantages of high transmission efficiency, reliable operation, long service life, accurate transmission ratio, compact structure, wide power and speed application range, etc. It is widely used in various mechanical structures, and its transmission performance directly affects the overall performance of the entire mechanical system.

[0003] As mechanical equipment develops towards long life, high speed, high load, low noise, light weight and high precision, higher requirements are put forward for gear transmission performance, so that conventional gears cannot meet the requirements in some occasions. Therefore, researching and developing new gears is a new goal for workers in the field of gear transmission. Variable hyperbolic arc tooth line cylindrical gear (VH-CATT cylindrical gear) is a new type of gear. It has a special tooth surface structure, the tooth line is a circular arc line, the middle section tooth profile is an involute, and the other section tooth profiles parallel to the middle section are the envelope of the variable hyperbola. The contact mode can be point contact and line contact. Its special tooth direction and tooth profile characteristics jointly change the tooth surface shape and tooth surface contact characteristics, making it have good meshing performance, low installation accuracy requirements, large overlap, strong load-bearing capacity and no axial force compared to traditional involute gears (spur teeth, helical teeth, herringbone teeth) in terms of transmission characteristics. It also has the advantages of strong anti-eccentric load capacity and insensitivity to installation errors. It has broad application prospects in the transmission of mechanical equipment such as aerospace, transportation, etc.

[0004] Finite element simulation has significant advantages in studying the processes of gear static contact analysis, dynamic contact analysis, modal analysis, gear root stress, gear bending strength research and other high-precision performance analysis. It is the most powerful means of gear transmission performance analysis. Meshing is the core link of finite element modeling, and its quality directly determines the accuracy of finite element analysis results. In the application of finite element software, the generation of mesh models can be achieved in two ways. First, following the method from geometry to mesh, we first need to build a geometric model of the part, then divide it into regions, and arrange seed points on the boundary to generate a mesh. In this process, the geometric model can be completed in a dedicated finite element software or other 3D modeling software. Secondly, taking the method from node to mesh, we first build nodes based on node information, and then connect the nodes to form units, and finally build a mesh model. The first method, from geometry to mesh, relies on the function of geometric modeling software, so it performs particularly well when dealing with simple parts. For example, through this method, we can generate standard geometric models such as spur gears and helical gears, and even modified gear models. However, these geometric models may have certain limitations in accuracy, and the quality of the generated mesh may not be satisfactory. In addition, when faced with special grid division requirements, such as using a combination of coarse and fine grids, the first method may encounter greater implementation difficulties.

[0005] In the existing finite element performance analysis of gear transmission, finite elements have been widely used in static and dynamic stress analysis of various gears. In order to ensure the reliability of gear finite element meshing quality and calculation accuracy, the current finite element simulation gear finite element parametric modeling process steps are relatively fixed and cumbersome. In the total time of finite element analysis, structural finite element meshing occupies half or more of the time. At the same time, if the finite element meshes are manually re-divided for different gear parameters, it will cost a lot of manpower and be prone to errors. All these limit the further in-depth research of internal and external meshing gear pairs and their transmission systems. In addition, due to the complex geometric shape of variable hyperbolic arc tooth line cylindrical gears, meshing is difficult, and usually a lot of time and effort are required in the finite element preprocessing link. Therefore, how to take into account both calculation accuracy and solution efficiency has become a difficult and hot issue in the finite element analysis of variable hyperbolic arc tooth line cylindrical gears. Summary of the invention

[0006] In order to solve the above technical problems, the present application provides a finite element parametric modeling method for a variable hyperbolic arc tooth line cylindrical gear. The technical solution provided by the present application is as follows:

[0007] A finite element parameterized modeling method for a variable hyperbolic arc tooth line cylindrical gear, comprising:

[0008] Set the geometric parameters and mesh parameters of the variable hyperbolic arc tooth line cylindrical gear;

[0009] Based on the middle section of the tooth width of a single gear tooth, determine the node coordinates of the tooth profile of a single tooth surface at the middle section;

[0010] Based on the node coordinates of a single tooth surface at the middle section, the node coordinates of n tooth surfaces at a single layer of the middle section are obtained by copying and rotating;

[0011] Based on the non-mid-section of the tooth width of n gear teeth, the node coordinates of the tooth profile of n tooth surfaces at the non-mid-section are determined. Based on the node coordinates of a single tooth surface at the non-mid-section, the node coordinates of n tooth surfaces at the single layer of the non-mid-section are obtained by copying and rotating.

[0012] Based on the calculated node coordinates of the variable hyperbolic arc tooth line cylindrical gear, the nodes of two adjacent layers are connected according to the node connection order rule of the eight-node hexahedral unit to construct the corresponding unit number coordinate matrix;

[0013] According to the unit number coordinate matrix, a finite element mesh model of the variable hyperbolic arc tooth line cylindrical gear is established.

[0014] Preferably, in the finite element parametric modeling method of the variable hyperbolic arc tooth line cylindrical gear, the geometric parameters include but are not limited to: cutter disc radius, module, number of teeth, tooth top height coefficient, top clearance coefficient, displacement coefficient, pressure angle, pitch circle radius, base circle radius, root height, tooth top circle radius, root circle radius, gear base boundary radius, tooth full height, slope of the transition curve dividing line, tooth width, distance of the tooth width section from the middle section of the tooth width, straight edge height, tool tip fillet radius, and the number of teeth of the generated gear.

[0015] Preferably, in the finite element parametric modeling method of the variable hyperbolic arc tooth line cylindrical gear, the grid parameters include but are not limited to: the number of grid points of the tooth top circle curve, the number of grid points of the tooth surface working curve, the number of grid points of the transition curve, the number of grid points of the root circle transition curve, the number of straight line grid points of the base part, the total number of point clouds of a single tooth section, the total number of nodes on the longitudinal curve, the number of dividing surfaces of half the tooth width, the total number of section point clouds, the total number of single-layer single-tooth grids, and the number of single-layer grids.

[0016] Preferably, in the finite element parametric modeling method of the variable hyperbolic arc tooth line cylindrical gear, the node coordinates of the tooth profile of a single tooth surface at the middle section are determined based on the middle section of the tooth width of a single gear tooth, including:

[0017] Based on the middle section of the tooth width of a single gear tooth and the predefined key nodes of the single-layer single-tooth area, the matrix of the node coordinates of the middle section gear tooth area and the matrix of the node coordinates of the middle section matrix transition area are determined;

[0018] According to the matrix of the node coordinates of the gear tooth area in the middle section and the matrix of the node coordinates of the transition zone of the matrix in the middle section, the node coordinates are integrated to obtain the node coordinates of the tooth profile of a single tooth surface at the middle section.

[0019] Preferably, in the finite element parametric modeling method of the variable hyperbolic arc tooth line cylindrical gear, the matrix of the node coordinates of the mid-section gear tooth area is determined based on the mid-section of the tooth width of a single gear tooth and the predefined key nodes of the single-layer single-tooth area, including:

[0020] Based on the middle section of the tooth width of a single gear tooth and the predefined key nodes of the single-layer single-tooth area, determine the node coordinates on the longitudinal line segment and the node coordinates on the transverse line segment of the middle section gear tooth area;

[0021] According to the node coordinates on the longitudinal line segment and the node coordinates on the transverse line segment of the mid-section gear tooth area, a matrix of the node coordinates of the mid-section gear tooth area is obtained.

[0022] Preferably, in the finite element parametric modeling method of the variable hyperbolic arc tooth line cylindrical gear, the key nodes of the single-layer single-tooth area include but are not limited to: the intersection of the concave root circle transition curve and the transition curve, recorded as node ; The intersection of the concave transition curve and the tooth surface working curve is recorded as the node ; The intersection of the concave tooth tip circle curve and the tooth surface working surface is recorded as the node ; The intersection of the straight line of the concave base part and the base boundary is recorded as the node ; The intersection of the straight line of the convex base part and the base boundary is recorded as the node ; The intersection of the convex root circle transition curve and the transition curve is recorded as the node ; The intersection of the convex transition curve and the tooth surface working curve is recorded as the node ; The intersection of the convex tooth tip circle curve and the tooth surface working surface is denoted as ; The node The node obtained by rotating one tooth angle counterclockwise around the center of the gear along the tooth width direction ; The node The node obtained by rotating one tooth angle counterclockwise around the center of the gear along the tooth width direction ; The node The corresponding position angle is the node obtained by rotating one tooth angle counterclockwise around the center of the gear along the tooth width direction. ; The node The corresponding position angle is the node obtained by rotating one tooth angle counterclockwise around the center of the gear along the tooth width direction. ; Passing node Make the slope The intersection of the straight line and the center line of a single tooth is recorded as the node ; Passing node Make the slope The intersection of the straight line and the center line of a single tooth is recorded as the node ; The midpoint of the tooth tip circle curve is recorded as the node ; The intersection of the lower boundary curve of the matrix and the center line of the single tooth is recorded as the node .

[0023] Preferably, in the finite element parametric modeling method of the variable hyperbolic arc tooth line cylindrical gear, the node coordinates of a single tooth surface at the middle section are obtained by copying and rotating to obtain the node coordinates of n tooth surfaces at a single layer of the middle section, including:

[0024] A single tooth surface at the middle section is rotated around the center point of the gear circle at a set angle in three-dimensional space at the corresponding tooth spacing angle, and based on the node coordinates of the single tooth surface at the middle section, the node coordinates of n tooth surfaces at a single layer of the middle section are copied.

[0025] Preferably, in the finite element parametric modeling method of the variable hyperbolic arc tooth line cylindrical gear, the node coordinates of the variable hyperbolic arc tooth line cylindrical gear calculated, according to the eight-node hexahedral unit node connection order rule, connect the nodes of two adjacent layers to construct the corresponding unit number coordinate matrix, including:

[0026] Number the divided mesh nodes of the variable hyperbolic arc tooth line cylindrical gear to obtain mesh node numbers;

[0027] Based on the calculated node coordinates and mesh node numbers of the variable hyperbolic arc tooth line cylindrical gear, the nodes of two adjacent layers are connected according to the node connection order rule of the eight-node hexahedral unit to construct the corresponding unit number coordinate matrix.

[0028] Preferably, in the finite element parametric modeling method of the variable hyperbolic arc tooth line cylindrical gear, the grid cell matrix in the unit number coordinate matrix includes the gear tooth area grid cell matrix, the base transition area right boundary grid cell matrix, the base transition area grid cell matrix, and the base transition area left boundary grid cell matrix.

[0029] Preferably, in the finite element parametric modeling method of the variable hyperbolic arc tooth line cylindrical gear, the finite element mesh model of the variable hyperbolic arc tooth line cylindrical gear is established according to the unit number coordinate matrix, including:

[0030] According to the fixed format of the inp file and the unit number coordinate matrix, the node number, coordinate, unit number and corresponding node number are written into the inp file;

[0031] Import the inp file into ABAQUS to obtain the finite element mesh model of the variable hyperbolic arc tooth line cylindrical gear.

[0032] The beneficial effects of this application are:

[0033] 1. This application is to improve the finite element mesh of a variable hyperbolic arc tooth line cylindrical gear, obtain a finite element model of a variable hyperbolic arc tooth line cylindrical gear with better mesh quality, and obtain a more accurate, continuous and smooth stress distribution;

[0034] 2. This application is to parametrically generate a finite element mesh of a variable hyperbolic arc tooth line cylindrical gear. By modifying the geometric parameters, a finite element mesh of a variable hyperbolic arc tooth line cylindrical gear near the tooth profile area can be obtained in a very short time, saving a lot of pre-processing operations;

[0035] 3. This application can set the parameters for controlling the finite element mesh size of the variable hyperbolic arc tooth line cylindrical gear in the program, which is convenient for quickly adjusting and generating finite element models of variable hyperbolic arc tooth line cylindrical gears with different mesh sizes, so it can be reasonably set according to the configuration of the computer used and the required time;

[0036] 4. During the execution of the program in this application, some key intermediate results will be presented in the form of line graphs for quick debugging of the program. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0038] Figure 1 A schematic flow chart of a finite element parametric modeling method for a variable hyperbolic arc tooth line cylindrical gear is provided in an embodiment of the present application;

[0039] Figure 2 A schematic diagram of a single tooth cross-section profile of a variable hyperbolic arc tooth line cylindrical gear provided in an embodiment of the present application;

[0040] Figure 3 It is another schematic diagram of a single tooth cross-section profile of a variable hyperbolic arc tooth line cylindrical gear provided in an embodiment of the present application;

[0041] Figure 4 A schematic diagram of the division of the gear tooth area and the base transition area of ​​the single tooth cross-sectional profile of the variable hyperbolic arc tooth line cylindrical gear provided in an embodiment of the present application;

[0042] Figure 5 This is a partial schematic diagram of the finite element mesh model of the variable hyperbolic arc tooth line cylindrical gear provided in an embodiment of the present application. DETAILED DESCRIPTION

[0043] In order to enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below. Obviously, the described embodiments are only part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0044] In the embodiments provided in the present application, it should be understood that the disclosed method or system can be implemented in other ways. The system embodiments described below are merely schematic. For example, the division of units and modules is only a logical function division. There may be other division methods in actual implementation, such as: multiple units or modules can be combined, or can be integrated into another system, or some features can be ignored, or not executed. In addition, the coupling, direct coupling, or communication connection between the components shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or modules, which can be electrical, mechanical or other forms.

[0045] In addition, all functional units in the embodiments of the present application may be integrated into one processor, or each unit may be a separate device, or two or more units may be integrated into one device; each functional unit in the embodiments of the present application may be implemented in the form of hardware or in the form of hardware plus software functional units.

[0046] A person skilled in the art can understand that all or part of the steps of the following method embodiments can be completed by program instructions and related hardware. The aforementioned program instructions can be stored in a computer-readable storage medium. When the program instructions are executed, the steps of the following method embodiments are executed; and the aforementioned storage medium includes: a mobile storage device, a read-only memory (ROM), a magnetic disk or an optical disk, and other media that can store program codes.

[0047] It should be understood that the use of "system", "device", "unit" and / or "module" in this application is only a method for distinguishing different components, elements, parts, parts or assemblies at different levels. However, if other words can achieve the same purpose, the word can be replaced by other expressions.

[0048] 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 technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of this application, "multiple" and "several" mean two or more, unless otherwise clearly and specifically defined.

[0049] If a flow chart is used in the present application, the flow chart is used to illustrate the operations performed by the system according to the embodiment of the present application. It should be understood that the preceding or following operations are not necessarily performed accurately in order. On the contrary, each step can be processed in reverse order or simultaneously. At the same time, other operations can also be added to these processes, or a certain step or several steps of operations can be removed from these processes.

[0050] It should also be noted that, in this article, terms such as "comprises", "includes" or any other variations thereof are intended to cover non-exclusive inclusion, so that an article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such articles or devices. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the article or device including the above elements.

[0051] The embodiments of the present application are written in a progressive manner.

[0052] like Figure 1 As shown, the embodiment of the present application provides a finite element parameterized modeling method for a variable hyperbolic arc tooth line cylindrical gear, comprising:

[0053] S1. Set the geometric parameters and mesh parameters of the variable hyperbolic arc tooth line cylindrical gear;

[0054] In S1, specifically, the cutter head radius , modulus , number of teeth , tooth width Taking the variable hyperbolic arc tooth line cylindrical gear as an example, the geometric parameters and mesh parameters of the variable hyperbolic arc tooth line cylindrical gear are determined as follows:

[0055] Geometric parameters include but are not limited to: cutter head radius , modulus , number of teeth , tooth addendum coefficient , head clearance coefficient , displacement coefficient , pressure angle , pitch circle radius , tooth root height , base circle radius , tooth tip radius , gear base boundary radius , tooth height , the slope of the transition curve dividing line , tooth width , the distance between the tooth width section and the middle section of the tooth width (Z axis positive direction is positive), straight edge height , tool tip radius , generate the number of gear teeth .

[0056] Among them, the cross-sectional contour lines of the single tooth of the variable hyperbolic arc tooth line cylindrical gear are divided, such as Figure 2 , and establish a plane rectangular coordinate system ,in is the gear axis, the tooth top circle curve , tooth surface working curve , transition curve , root circle transition curve , the straight line of the base part (The line connecting the intersection of the transition curve and the root circle transition curve and the center of the circle, and the line segment from the base boundary to the root circle curve). The center line of a single tooth is the straight line connecting the midpoint of the tooth tip circle curve and the center of the gear circle. , the lower boundary curve of the matrix , where the tooth surface working curve , transition curve , the straight line of the base part The three curves have concave and convex surfaces, and are called concave curves and convex curves respectively.

[0057] The single tooth direction of the middle section is divided into the gear tooth tip circle-working tooth surface area (area I), transition curve area (area II), other areas (area III), and base-tooth root circle transition area (area IV). The segmented expression method is used to construct the middle section node coordinates of the variable hyperbolic arc tooth line cylindrical gear (hereinafter referred to as the gear), as shown in Figure 3 .

[0058] First, the middle cross-section area of ​​a single tooth (hereinafter referred to as the middle cross-section) is divided into two large areas, among which the gear tooth top circle-working tooth surface area (area I), the transition curve area (area II), and the remaining area (area III) are the gear tooth area, and the base-tooth root circle transition area (area IV) is the base transition area. Figure 4 .

[0059] Mesh parameters include but are not limited to: Addendum curve Grid Points , mesh points of tooth surface working curve , transition curve grid points , the number of grid points of the root circle transition curve , the number of linear grid points of the base part , the total number of point clouds of a single tooth section , the total number of nodes on the longitudinal curve , the number of split faces of half tooth width (excluding the middle section) , total number of cross-section point clouds , the total number of single-layer single-tooth grids , single-layer grid number .

[0060] S2. Based on the middle section of the tooth width of a single gear tooth, determine the node coordinates of the tooth profile of a single tooth surface at the middle section;

[0061] In S2, specifically, since the tooth profiles of the variable hyperbolic arc tooth line cylindrical gears (including the area composed of the root circle and part of the base part) have common features, further, the cross-sectional tooth profiles of the variable hyperbolic arc tooth line cylindrical gears cut by any plane perpendicular to the axis and parallel to the cross section in the tooth width still have common features. Therefore, in this step, the node coordinates of the cross section in the tooth width of a single gear tooth (including the area composed of the root circle and part of the base part) are first confirmed.

[0062] One implementation of the step of determining the node coordinates of the tooth profile of a single tooth surface at the middle section (i.e., the section at b=0) based on the middle section of the tooth width of a single gear tooth includes:

[0063] S21. Based on the mid-section of the tooth width of a single gear and the pre-defined key nodes of the single-layer single-tooth area, determine the matrix of the node coordinates of the mid-section gear tooth area and the matrix of the node coordinates of the mid-section matrix transition area;

[0064] S22. Integrate the node coordinates according to the matrix of the node coordinates of the gear tooth area in the middle section and the matrix of the node coordinates of the transition area of ​​the matrix in the middle section to obtain the node coordinates of the tooth profile of a single tooth surface at the middle section.

[0065] In S21, specifically, the predefined key nodes of the single-layer single-tooth area include, but are not limited to: the intersection of the concave root circle transition curve and the transition curve, recorded as node ; The intersection of the concave transition curve and the tooth surface working curve is recorded as the node ; The intersection of the concave tooth tip circle curve and the tooth surface working surface is recorded as the node ; The intersection of the straight line of the concave base part and the base boundary is recorded as the node ; The intersection of the straight line of the convex base part and the base boundary is recorded as the node ; The intersection of the convex root circle transition curve and the transition curve is recorded as the node ; The intersection of the convex transition curve and the tooth surface working curve is recorded as the node ; The intersection of the convex tooth tip circle curve and the tooth surface working surface is denoted as ; The node The node obtained by rotating one tooth angle counterclockwise around the center of the gear along the tooth width direction ; The node The node obtained by rotating one tooth angle counterclockwise around the center of the gear along the tooth width direction ; The node The corresponding position angle is the node obtained by rotating one tooth angle counterclockwise around the center of the gear along the tooth width direction. ; The node The corresponding position angle is the node obtained by rotating one tooth angle counterclockwise around the center of the gear along the tooth width direction. ; Passing node Make the slope The intersection of the straight line and the center line of a single tooth is recorded as the node ; Passing node Make the slope The intersection of the straight line and the center line of a single tooth is recorded as the node ; The midpoint of the tooth tip circle curve is recorded as the node ; The intersection of the lower boundary curve of the matrix and the center line of the single tooth is recorded as the node .

[0066] In some embodiments, based on the middle section of the tooth width of a single gear tooth and predefined key nodes of a single-layer single-tooth area, a matrix of node coordinates of the middle section gear tooth area is determined, specifically including (S211-S212):

[0067] S211. Based on the middle section of the tooth width of a single gear tooth and the predefined key nodes of the single-layer single-tooth area, determine the node coordinates on the longitudinal line segment and the node coordinates on the transverse line segment of the middle section gear tooth area;

[0068] Among them, based on the middle section of the tooth width of a single gear tooth and the pre-defined key nodes of the single-layer single-tooth area, the node coordinates on the longitudinal line segment of the middle section gear tooth area (single-tooth concave curve, single-tooth convex curve, single-tooth center line) are determined, specifically including (S2111-S2114):

[0069] S2111. Based on the middle section of the tooth width of a single gear tooth and the predefined key nodes of the single-layer single-tooth area, determine the node coordinates on the concave curve of the single-tooth in the middle section gear tooth area;

[0070] Specifically, determine that the single tooth concave curve contains the tooth surface working curve , transition curve , the straight line of the base part Three curves. Among them, the tooth surface working curve and the transition curve cannot be evenly divided according to the angle or straight line length in the established plane rectangular coordinates. The equalization method here is: first divide the transition curve (also applicable to the tooth surface working curve) according to the tooth profile equation. ) to generate points on the curve, ensuring that the distance between adjacent discrete points is no greater than a preset value, where the preset value can be any infinitesimal value. In this embodiment, the preset value is 10 -4 mm, the present application is not limited thereto; then the distance between each adjacent discrete point is accumulated to obtain the real total length of the transition curve. Then the real total length of the transition curve is calculated as Divide evenly to get the length distance between two adjacent grid nodes , and then accumulate the adjacent discrete points from the starting point of the curve to get the cumulative length , when the cumulative length achieve , you can get the coordinates of the second grid node on the curve, and then cycle through them to achieve equal distribution of grid nodes. Divide by The length of the segment is divided equally. Radius to the gear body boundary Divide evenly to obtain the straight line of the base part The radius value of each discrete point on the upper segment node is (angle value of point A), obtain the straight line of the base part The polar coordinates of the segment nodes are mathematically transformed to obtain the straight lines of the base part. The rectangular coordinate value of the segment node.

[0071] The mathematical transformation expression is as follows:

[0072]

[0073] in, is the radius from tooth root circle Radius to the gear body boundary Average length, represents the horizontal coordinate of the node on the straight line of the base part, Represents the ordinate of the node on the straight line of the base part.

[0074] In particular: The working tooth profile equation is (the upper symbol represents the convex surface of the gear, and the lower symbol represents the concave surface of the gear):

[0075]

[0076] in: represents the radius of the cutter head, represents the modulus, represents the pressure angle, Indicates the pitch circle radius, Indicates the distance between the tooth width section and the middle section of the tooth width. represents the tooth profile angle position parameter, represents the horizontal coordinate of the tooth profile of the working tooth surface, Represents the ordinate of the tooth profile of the working tooth surface, Indicates the Z-axis coordinate of the tooth profile of the working tooth surface, Represents the position parameters of a point on the tooth profile.

[0077]

[0078] The transition tooth profile equation is (the upper symbol represents the convex surface of the gear, and the lower symbol represents the concave surface of the gear):

[0079]

[0080] in: Indicates the straight edge height, represents the displacement coefficient, Indicates the tool tip radius, The horizontal coordinate of transition tooth profile is shown. represents the ordinate of the transition tooth profile, Represents the Z-axis coordinate of the transition tooth profile, Indicates tool tip radius position parameters.

[0081]

[0082]

[0083]

[0084] Node C and Node The coordinates can be obtained by combining the expression of the working tooth surface profile equation with the following formula:

[0085]

[0086] in: It represents the tooth addendum coefficient;

[0087] Node B and Node The coordinates can be obtained by combining the expression of the working tooth surface profile equation with the following formula:

[0088]

[0089] Node A and Node The coordinates can be obtained by combining the expression of the transition tooth profile equation with the following formula:

[0090]

[0091] in: It represents the head clearance coefficient;

[0092] node The intersection of the straight line with slope k and the center line of the single tooth is made for node A. Its coordinate value is obtained by combining the coordinates of node A with the slope k. Draw a straight line with a slope of -k for node B and the intersection of the center line of the single tooth. Its coordinate value is obtained by combining the coordinates of node B with the slope -k; It is the midpoint of the tooth tip circle curve. Its coordinate value is determined by dividing the left and right end points of the tooth tip circle curve by node C and node The difference in the coordinate values ​​of the node is obtained; It is the intersection of the lower boundary curve of the matrix and the center line of the single tooth. Its coordinate value is determined by the boundary radius of the gear matrix. The coordinates of each node calculated above are obtained as the coordinates of the nodes on the concave surface curve of the single tooth in the mid-section gear tooth area.

[0093] S2112. Determine the node coordinates on the convex surface curve of the single tooth in the middle section of the gear tooth area based on the middle section of the single gear tooth width and the predefined key nodes of the single-layer single tooth area;

[0094] Specifically, the single tooth convex surface curve includes the tooth surface working curve , transition curve , the straight line of the base part The method of dividing the three curves equally is the same as the S2111 operation. The method here is the same as the node discretization method of the concave curve. The only difference is that the symbols in the tooth profile equation are the upper and lower parts. It will not be repeated here. In this way, the node coordinates on the convex curve of a single tooth in the mid-section gear tooth area are obtained.

[0095] S2113. Determine the node coordinates on the midline of the single tooth in the mid-section gear tooth area based on the mid-section of the single gear tooth width and the pre-defined key nodes of the single-layer single tooth area;

[0096] Specifically, the center line of a single tooth is drawn from the tooth tip circle curve To the base lower boundary curve Divide the line segment into three parts evenly according to the length of the radius segment. Section Press The segments are evenly divided. Section Press The segments are evenly divided. Section Press The segments are evenly divided, the same as the straight line of the base part in S2111 Just like the discretization of the nodes on the gear, the rectangular coordinates of each point are obtained, that is, the node coordinates on the midline of a single tooth in the mid-section gear tooth area.

[0097] S2114. Obtain the node coordinates on the longitudinal line segment of the mid-section gear tooth area according to the node coordinates on the concave curve of the single tooth in the mid-section gear tooth area, the node coordinates on the convex curve of the single tooth in the mid-section gear tooth area and the node coordinates on the center line of the single tooth in the mid-section gear tooth area.

[0098] Specifically, the calculated node coordinates on the concave curve of the single tooth in the middle section gear tooth area, the node coordinates on the convex curve of the single tooth in the middle section gear tooth area and the node coordinates on the center line of the single tooth in the middle section gear tooth area are used as the node coordinates on the longitudinal line segment of the middle section gear tooth area.

[0099] Among them, based on the mid-section of the tooth width of a single gear tooth and the pre-defined key nodes of the single-layer single-tooth area, the node coordinates on the transverse line segment (tooth top circle curve, lower matrix boundary curve) of the mid-section gear tooth area are determined, specifically including (S2115-S2117):

[0100] S2115. Tooth tip circle curve use By evenly dividing, we can obtain the tooth top circle curve The angle values ​​of the discrete points on the graph are all , get the tooth tip circle curve The polar coordinates of the segmented nodes are mathematically transformed to obtain the tooth tip circle curve The rectangular coordinate value of the segment node, that is, the node coordinate on the tooth tip circle curve of the mid-section gear tooth area;

[0101] S2116. For the lower boundary curve of the matrix use By averaging, we can obtain the lower boundary curve of the matrix The angle values ​​of the discrete points on the graph are all , get the lower boundary curve of the matrix The polar coordinates of the segmented nodes are mathematically transformed to obtain the lower boundary curve of the matrix The rectangular coordinate value of the segmented node, that is, the node coordinate on the matrix boundary curve under the mid-section gear tooth area.

[0102] S2117. The calculated node coordinates on the tooth top circle curve of the mid-section gear tooth area and the node coordinates on the lower matrix boundary curve of the mid-section gear tooth area are used as the node coordinates on the transverse line segment of the mid-section gear tooth area.

[0103] S212. Obtain a matrix of node coordinates of the mid-section gear tooth area according to the node coordinates on the longitudinal line segments and the node coordinates on the transverse line segments of the mid-section gear tooth area.

[0104] In S212, specifically, the nodes on the concave and convex curves are connected to the corresponding nodes on the single tooth midline, and the horizontal coordinate values ​​of the nodes on the concave and convex curves (calculated asX 1) The horizontal coordinate value of the node at the center line of a single tooth (calculated as X 2) Divide equally into Segment, get the horizontal coordinate value of each node on the line, which is ( X ), according to the formula:

[0105]

[0106] in: Indicates the ordinate value of each node on the line. represents the ordinate of the node on the concave curve, Indicates the ordinate value of the midline node of a single tooth.

[0107] The coordinate values ​​of the discrete points in the gear tooth area on the Y axis can be obtained. Thus, the set of discrete points in the gear tooth area is obtained, and the matrix of the node coordinates of the gear tooth area in the middle section is obtained.

[0108] In some other embodiments, based on the mid-section of the tooth width of a single gear and the predefined key nodes of the single-layer single-tooth area, a matrix of the coordinates of the nodes of the mid-section substrate transition zone is determined, specifically including: the longitudinal line segment of the substrate transition zone is the straight line of the substrate part , as mentioned above S2112, from the root circle radius Radius to the gear body boundary Divided into Segment, the straight line of the base part can be obtained The radius value of each node on the ), same as the straight line of the base part in S2111 The node coordinates on the longitudinal line segment of the matrix transition zone are obtained in the same way as the node discretization on the matrix transition zone. The transverse line segment of the matrix transition zone is the root circle transition curve. , for the root circle transition curve use Divide equally into segments, we can get the angle value of each node (the radius value of each node is ), and then mathematically transform it to obtain the node coordinates on the transverse line segment of the substrate transition zone. Based on the node coordinates on the longitudinal and transverse line segments of the substrate transition zone, the rectangular coordinate values ​​of each node in the substrate transition zone are obtained, thereby obtaining the matrix of the node coordinates of the substrate transition zone.

[0109] In S22, specifically, after obtaining the matrix of the node coordinates of the mid-section gear tooth area and the matrix of the node coordinates of the mid-section matrix transition area, the node coordinates of the tooth profile of a single tooth surface at the mid-section (including the area composed of the root circle and part of the matrix) are integrated to obtain the node coordinates of the tooth profile of a single tooth surface at the mid-section.

[0110] S3. Based on the node coordinates of a single tooth surface at the middle section, the node coordinates of n tooth surfaces at a single layer of the middle section are obtained by copying and rotating;

[0111] In S3, specifically, one implementation of this step includes: a single tooth surface at the middle section is rotated around the center point of the gear circle. , respectively according to the set angle The corresponding tooth spacing angle is rotated in three-dimensional space, and based on the node coordinates of a single tooth surface at the mid-section, the node coordinates of n tooth surfaces at a single layer of the mid-section are copied and obtained.

[0112] In which, the coordinates of each discrete point in the node coordinates of a single layer and a single tooth surface are assumed to be , which can be expressed in polar coordinates as:

[0113]

[0114] in, The coordinates represent the distance from the pole, The coordinates represent the angle of the ray (sometimes called the polar axis) from the 0° ray in the counterclockwise direction. The polar axis is the positive direction of the x-axis in the plane rectangular coordinate system.

[0115] Rotate a set angle in any direction , the coordinates of another tooth surface node can be obtained as ;

[0116] Another tooth surface point cloud can be expressed in polar coordinates as follows:

[0117]

[0118] Combining the above two polar coordinates, we can get the relationship between the required tooth surface point cloud coordinates and the midline single tooth point cloud coordinates:

[0119]

[0120] Set the angle Substituting the value of can obtain another single tooth point cloud set, thereby copying the node coordinates of the single-layer multi-tooth surface.

[0121] S4. Based on the non-mid-section of the tooth width of n gear teeth, determine the node coordinates of the tooth profile of n tooth surfaces at the non-mid-section, and based on the node coordinates of a single tooth surface at the non-mid-section, obtain the node coordinates of n tooth surfaces at the single layer of the non-mid-section by copying and rotating;

[0122] In S4, specifically, the node coordinates of the tooth profiles of n tooth surfaces at different layer depths in the tooth width direction (at b≠0) are obtained with the same idea, the node coordinates of a single tooth surface at the non-mid-section are obtained, and the node coordinates of multiple tooth surfaces at the non-mid-section are obtained by copying and rotating. The calculation method is consistent with the method for obtaining the node coordinates of the mid-section tooth surface in S2 and S3. The function expression of the non-mid-section tooth profile is shown in S2111.

[0123] S5. Based on the calculated node coordinates of the variable hyperbolic arc tooth line cylindrical gear, the nodes of two adjacent layers are connected according to the node connection order rule of the eight-node hexahedral unit to construct the corresponding unit number coordinate matrix;

[0124] In S5, specifically, based on the node coordinates of the variable hyperbolic arc tooth line cylindrical gear calculated in S2-S4 above, the nodes of two adjacent layers are connected according to the node connection order rule of the eight-node hexahedral unit to construct the corresponding unit number coordinate matrix. One implementation method of this step specifically includes:

[0125] S51. Numbering the divided grid nodes of the variable hyperbolic arc tooth line cylindrical gear to obtain grid node numbers;

[0126] In S51, specifically, the mesh nodes of the variable hyperbolic arc tooth line cylindrical gear that have been divided are numbered. Starting from the first tooth of the first layer, the upper left node of the gear tooth area is numbered 1, referring to Figure 4 The gear tooth areas are numbered from left to right. The numbering of the first gear tooth area is completed, followed by the numbering of the first gear base transition area. Figure 4 The basic transition zone is numbered from top to bottom. After the first tooth numbering is completed, multiple teeth and multiple layers are numbered in sequence to obtain the grid node numbering.

[0127] S52. Based on the calculated node coordinates and mesh node numbers of the variable hyperbolic arc tooth line cylindrical gear, the nodes of two adjacent layers are connected according to the eight-node hexahedral unit node connection order rule to construct the corresponding unit number coordinate matrix.

[0128] In S52, specifically, after the grid node numbering is completed in S51, the grid needs to be numbered, and the node coordinates of the gear are connected according to the eight-node hexahedral unit node connection order rule in the finite element software, and the nodes of the two adjacent layers are connected to construct the corresponding unit number coordinate matrix. Among them, the constructed grid unit matrix of the matrix transition zone includes 9 elements, the first one is the unit number, and the last 8 are the 8-node numbers that constitute the grid. The first node number can be found by locating the first node in which layer, tooth, row, and column, and the remaining node numbers can be easily obtained by increasing the number, number of layers, and number of columns. The gear tooth area grid, the matrix transition zone right boundary grid, the matrix transition zone grid, and the matrix transition zone left boundary grid are constructed in sequence to obtain a grid unit matrix.

[0129] The unit number is set to kk (the grid node number has been marked by S51). If the unit belongs to , and is located in the gear tooth area, then kk should satisfy the following formula:

[0130]

[0131] in, , , and substitute them in turn to get the intermediate variables :

[0132]

[0133] Will The remainder of , the business is set as .

[0134] like Can be If it is divisible by , it means that the unit is on the right boundary of the gear tooth area, and the label at this time is The corresponding numbers of the nodes of the cells are:

[0135] Number corresponding to node 1: ;

[0136] Number corresponding to node 2: ;

[0137] The corresponding number of the third node: ;

[0138] Number corresponding to node 4: ;

[0139] Number corresponding to node 5: ;

[0140] Number corresponding to node 6: ;

[0141] Number corresponding to node 7: ;

[0142] Number corresponding to node 8: ;

[0143] like Cannot be If it is divisible by , it means that the unit is on the left boundary and inside of the gear tooth area, then the label at this time is The corresponding numbers of the nodes of the cells are:

[0144] Number corresponding to node 1: ;

[0145] Number corresponding to node 2: ;

[0146] The corresponding number of the third node: ;

[0147] Number corresponding to node 4: ;

[0148] Number corresponding to node 5: ;

[0149] Number corresponding to node 6: ;

[0150] Number corresponding to node 7: ;

[0151] Number corresponding to node 8: ;

[0152] If the unit belongs to the matrix transition zone and belongs to the first column to the right of the matrix transition zone, then kk should satisfy the following formula:

[0153]

[0154] in, , , and substitute them in turn to get the intermediate variables :

[0155]

[0156] Then the label at this time is The corresponding numbers of the nodes of the cells are:

[0157] Number corresponding to node 1: ;

[0158] Number corresponding to node 2: ;

[0159] The corresponding number of the third node: ;

[0160] Number corresponding to node 4: ;

[0161] Number corresponding to node 5: ;

[0162] Number corresponding to node 6: ;

[0163] Number corresponding to node 7: ;

[0164] Number corresponding to node 8: ;

[0165] If the unit belongs to the matrix transition zone and is not the first column on the right, then kk should satisfy the following formula:

[0166]

[0167] in, , , and substitute them in turn to get the intermediate variables :

[0168]

[0169] Will The remainder of , the business is set as .

[0170] like Divisible , it means that the unit is on the right boundary of the first column of the matrix transition area, and the label at this time is The corresponding numbers of the nodes of the cells are:

[0171] Number corresponding to node 1: ;

[0172] Number corresponding to node 2: ;

[0173] The corresponding number of the third node: ;

[0174] Number corresponding to node 4: ;

[0175] Number corresponding to node 5: ;

[0176] Number corresponding to node 6: ;

[0177] Number corresponding to node 7: ;

[0178] Number corresponding to node 8: ;

[0179] like Cannot be If it is divisible by , it means that the unit is on the left boundary and inside of the gear tooth area, then the label at this time is The corresponding numbers of the nodes of the cells are:

[0180] Number corresponding to node 1: ;

[0181] Number corresponding to node 2: ;

[0182] The corresponding number of the third node: ;

[0183] Number corresponding to node 4: ;

[0184] Number corresponding to node 5: ;

[0185] Number corresponding to node 6: ;

[0186] Number corresponding to node 7: ;

[0187] Number corresponding to node 8: ;

[0188] If the unit belongs to the left boundary column of the matrix transition zone, then kk should satisfy the following formula:

[0189]

[0190] in, , , and substitute them in turn to get the intermediate variables :

[0191]

[0192] Then the label at this time is The corresponding numbers of the nodes of the cells are:

[0193] Number corresponding to node 1: ;

[0194] Number corresponding to node 2: ;

[0195] The corresponding number of the third node: ;

[0196] Number corresponding to node 4: ;

[0197] Number corresponding to node 5: ;

[0198] Number corresponding to node 6: ;

[0199] Number corresponding to node 7: ;

[0200] Number corresponding to node 8: ;

[0201] If the grid cell belongs to the Kth tooth, the calculation method is the same as above, only the leftmost column of the matrix transition zone is missing. Through the above calculation, the unit number coordinate matrix can be obtained.

[0202] S6. According to the unit number coordinate matrix, a finite element mesh model of the variable hyperbolic arc tooth line cylindrical gear is established.

[0203] In S6, specifically, one implementation of this step includes: writing the node number, coordinate, unit number and corresponding node number into the inp file according to the fixed format of the inp file and the unit number coordinate matrix; importing the inp file in ABAQUS to obtain the finite element mesh model of the variable hyperbolic arc tooth line cylindrical gear. The format of the inp file can adopt the settings disclosed in the art. After the inp file is generated, open ABAQUS, click File, import, Part in the menu bar, select the input inp file, and obtain the finite element mesh model of the variable hyperbolic arc tooth line cylindrical gear, such as Figure 5 In other embodiments of the present application, the finite element software may also be ANSYS, but the present application is not limited thereto.

[0204] The beneficial effects of this application are:

[0205] 1. This application is to improve the finite element mesh of a variable hyperbolic arc tooth line cylindrical gear, obtain a finite element model of a variable hyperbolic arc tooth line cylindrical gear with better mesh quality, and obtain a more accurate, continuous and smooth stress distribution;

[0206] 2. This application is to parametrically generate a finite element mesh of a variable hyperbolic arc tooth line cylindrical gear. By modifying the geometric parameters, a finite element mesh of a variable hyperbolic arc tooth line cylindrical gear near the tooth profile area can be obtained in a very short time, saving a lot of pre-processing operations;

[0207] 3. This application can set the parameters for controlling the finite element mesh size of the variable hyperbolic arc tooth line cylindrical gear in the program, which is convenient for quickly adjusting and generating finite element models of variable hyperbolic arc tooth line cylindrical gears with different mesh sizes, so it can be reasonably set according to the configuration of the computer used and the required time;

[0208] 4. During the execution of the program in this application, some key intermediate results will be presented in the form of line graphs for quick debugging of the program.

[0209] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A finite element parametric modeling method for a variable hyperbolic arc tooth line cylindrical gear, characterized in that: include: Set the geometric parameters and mesh parameters of the variable hyperbolic arc tooth line cylindrical gear; Based on the middle section of the tooth width of a single gear tooth, determine the node coordinates of the tooth profile of a single tooth surface at the middle section; Based on the node coordinates of a single tooth surface at the middle section, the node coordinates of n tooth surfaces at a single layer of the middle section are obtained by copying and rotating; Based on the non-mid-section of the tooth width of n gear teeth, the node coordinates of the tooth profile of n tooth surfaces at the non-mid-section are determined. Based on the node coordinates of a single tooth surface at the non-mid-section, the node coordinates of n tooth surfaces at the single layer of the non-mid-section are obtained by copying and rotating. Based on the calculated node coordinates of the variable hyperbolic arc tooth line cylindrical gear, the nodes of two adjacent layers are connected according to the node connection order rule of the eight-node hexahedral unit to construct the corresponding unit number coordinate matrix; According to the unit number coordinate matrix, a finite element mesh model of a variable hyperbolic arc tooth line cylindrical gear is established; Wherein, determining the node coordinates of the tooth profile of a single tooth surface at the middle section based on the middle section of the tooth width of a single gear tooth includes: Based on the middle section of the tooth width of a single gear tooth and the predefined key nodes of the single-layer single-tooth area, a matrix of node coordinates of the middle section gear tooth area and a matrix of node coordinates of the middle section matrix transition area are determined; According to the matrix of the node coordinates of the gear tooth area in the middle section and the matrix of the node coordinates of the transition area of ​​the matrix in the middle section, the node coordinates are integrated to obtain the node coordinates of the tooth profile of a single tooth surface at the middle section; The matrix of determining the coordinates of the nodes in the middle section gear tooth area based on the middle section of the tooth width of a single gear tooth and the predefined key nodes of the single-layer single-tooth area includes: Based on the middle section of the tooth width of a single gear tooth and the predefined key nodes of the single-layer single-tooth area, determine the node coordinates on the longitudinal line segment and the node coordinates on the transverse line segment of the middle section gear tooth area; According to the node coordinates on the longitudinal line segment and the node coordinates on the transverse line segment of the mid-section gear tooth area, a matrix of the node coordinates of the mid-section gear tooth area is obtained.

2. The method according to claim 1, characterized in that The geometric parameters include but are not limited to: cutter disc radius, module, number of teeth, tooth top height coefficient, top clearance coefficient, displacement coefficient, pressure angle, pitch circle radius, base circle radius, root height, tooth top circle radius, root circle radius, gear base boundary radius, tooth full height, slope of transition curve dividing line, tooth width, distance of tooth width section from tooth width middle section, straight edge height, tool tip fillet radius, and number of generated gear teeth.

3. The method according to claim 1, characterized in that The grid parameters include but are not limited to: the number of grid points of the tooth top circle curve, the number of grid points of the tooth surface working curve, the number of grid points of the transition curve, the number of grid points of the root circle transition curve, the number of grid points of the base part straight line, the total number of point clouds of a single tooth section, the total number of nodes on the longitudinal curve, the number of dividing surfaces of half the tooth width, the total number of section point clouds, the total number of single-layer single-tooth grids, and the number of single-layer grids.

4. The method according to claim 1, characterized in that The key nodes of the single-layer single-tooth area include but are not limited to: the intersection of the concave root circle transition curve and the transition curve, recorded as the node ; The intersection of the concave transition curve and the tooth surface working curve is recorded as the node ; The intersection of the concave tooth tip circle curve and the tooth surface working surface is recorded as the node ; The intersection of the straight line of the concave base part and the base boundary is recorded as the node ; The intersection of the straight line of the convex base part and the base boundary is recorded as the node ; The intersection of the convex root circle transition curve and the transition curve is recorded as the node ; The intersection of the convex transition curve and the tooth surface working curve is recorded as the node ; The intersection of the convex tooth tip circle curve and the tooth surface working surface is denoted as ; The node The node obtained by rotating one tooth angle counterclockwise around the center of the gear along the tooth width direction ; The node The node obtained by rotating one tooth angle counterclockwise around the center of the gear along the tooth width direction ; The node The corresponding position angle is the node obtained by rotating one tooth angle counterclockwise around the center of the gear along the tooth width direction. ; The node The corresponding position angle is the node obtained by rotating one tooth angle counterclockwise around the center of the gear along the tooth width direction. ; Passing node Make the slope The intersection of the straight line and the center line of a single tooth is recorded as the node ; Passing node Make the slope The intersection of the straight line and the center line of a single tooth is recorded as the node ; The midpoint of the tooth tip circle curve is recorded as the node ; The intersection of the lower boundary curve of the matrix and the center line of the single tooth is recorded as the node .

5. The method according to claim 1, characterized in that The node coordinates of n tooth surfaces at a single layer of the middle section are obtained by copying and rotating the node coordinates of a single tooth surface at the middle section, including: A single tooth surface at the middle section is rotated around the center point of the gear circle at a set angle in three-dimensional space at the corresponding tooth spacing angle, and based on the node coordinates of the single tooth surface at the middle section, the node coordinates of n tooth surfaces at a single layer of the middle section are copied.

6. The method according to claim 1, characterized in that The node coordinates of the variable hyperbolic arc tooth line cylindrical gear calculated based on the node coordinates of the variable hyperbolic arc tooth line are connected according to the eight-node hexahedral unit node connection order rule to construct the corresponding unit number coordinate matrix, including: Number the divided mesh nodes of the variable hyperbolic arc tooth line cylindrical gear to obtain mesh node numbers; Based on the calculated node coordinates and mesh node numbers of the variable hyperbolic arc tooth line cylindrical gear, the nodes of two adjacent layers are connected according to the node connection order rule of the eight-node hexahedral unit to construct the corresponding unit number coordinate matrix.

7. The method as claimed in claim 6, characterized in that The grid cell matrix in the unit number coordinate matrix includes a gear tooth area grid cell matrix, a substrate transition area right boundary grid cell matrix, a substrate transition area grid cell matrix, and a substrate transition area left boundary grid cell matrix.

8. The method as claimed in claim 1, characterized in that The method of establishing a finite element mesh model of a variable hyperbolic arc tooth line cylindrical gear according to the unit number coordinate matrix comprises: According to the fixed format of the inp file and the unit number coordinate matrix, the node number, coordinate, unit number and corresponding node number are written into the inp file; Import the inp file into ABAQUS to obtain the finite element mesh model of the variable hyperbolic arc tooth line cylindrical gear.

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