Method and device for determining tooth root transition curve, electronic equipment and storage medium

Abstract

The application discloses a method and device for determining a dedendum transition curve, electronic equipment and a storage medium. The method comprises the following steps: receiving gear configuration parameters and multiple sets of control parameters, and generating a tooth profile curve of the gear based on the gear configuration parameters and a preset involute equation; for each set of control parameters, generating a candidate dedendum transition curve from the tooth profile curve to the dedendum based on the tooth profile curve and the set of control parameters, and splicing the candidate dedendum transition curve with the tooth profile curve to obtain a single-tooth slot profile; generating a region to be analyzed based on the single-tooth slot profile, and performing grid division on the region to be analyzed; performing finite element solving on the grid region to be analyzed to obtain a stress value of the dedendum corresponding to the candidate dedendum transition curve; and determining a target dedendum transition curve from the candidate dedendum transition curves based on the stress values of the dedenda corresponding to the candidate dedendum transition curves. The application avoids the loss of precision caused by multiple format conversions when data is transmitted between multiple software, and improves the determination efficiency.

Description

Technical Field

[0001] This application generally relates to the field of gear analysis technology. More specifically, this application relates to a method, apparatus, electronic device, and storage medium for determining a tooth root transition curve. Background Technology

[0002] As a core component in mechanical transmission systems, the bending strength of the gear tooth root directly affects the overall load-bearing capacity, reliability, and lifespan of the machine. The geometry of the tooth root transition curve determines the degree of stress concentration at the tooth root. Therefore, accurately analyzing and optimizing the tooth root transition line to obtain the final tooth root transition line is crucial for gear design.

[0003] Currently, the method for analyzing and optimizing tooth root transition curves generally involves using multiple software programs (CAD software, CAE software, etc.), and each step of the optimization process requires manual intervention. This results in accuracy loss due to multiple format conversions during data transfer between software programs, and the time-consuming manual intervention makes batch processing difficult.

[0004] In view of this, there is an urgent need to provide a method, apparatus, electronic device and storage medium for determining the tooth root transition curve, so that the tooth root transition curve can be optimized in one process, avoiding the loss of accuracy caused by multiple format conversions when data is transferred between multiple software programs, and improving the determination efficiency without manual intervention. Summary of the Invention

[0005] In order to at least solve one or more of the technical problems mentioned above, this application proposes a method, apparatus, electronic device and storage medium for determining the tooth root transition curve in several aspects.

[0006] In a first aspect, this application provides a method for determining a tooth root transition curve, comprising: receiving gear construction parameters and multiple sets of control parameters, and generating a tooth profile curve of the gear based on the gear construction parameters and a preset involute equation; wherein, the multiple sets of control parameters are used to generate multiple different candidate tooth root transition curves; for each set of control parameters, generating a candidate tooth root transition curve from the tooth profile curve to the tooth root based on the tooth profile curve and the set of control parameters, and splicing the candidate tooth root transition curve with the tooth profile curve to obtain a single tooth groove profile; generating a region to be analyzed based on the single tooth groove profile, and meshing the region to be analyzed to obtain a mesh region to be analyzed; performing finite element analysis on the mesh region to be analyzed to obtain the stress value of the tooth root corresponding to the candidate tooth root transition curve; and determining a target tooth root transition curve from each candidate tooth root transition curve based on the stress value of the tooth root corresponding to each candidate tooth root transition curve.

[0007] In some embodiments, the gear construction parameters include at least one of the following: number of teeth, pressure angle, helix angle, displacement coefficient, gear addendum circle radius, profile circle radius, dedendum circle radius, and normal module.

[0008] In some embodiments, generating the gear tooth profile curve based on the gear construction parameters and a preset involute equation includes: calculating the base circle radius based on the number of teeth, the normal module, the helix angle, and the pressure angle; calculating the maximum roll angle of the involute based on the base circle radius and the gear tip circle radius, and calculating the minimum roll angle of the involute based on the base circle radius and the profile circle radius; and generating the gear tooth profile curve based on the base circle radius, the maximum roll angle, the minimum roll angle, and the preset involute equation.

[0009] In some embodiments, the control parameters include: a first offset distance, a second offset distance, a convex angle, a first curve control parameter, and a second curve control parameter; at least one control parameter includes a set value range and a set number of sample points, and multiple sets of control parameters are determined based on the set value range and the set number of sample points.

[0010] In some embodiments, generating a candidate tooth root transition curve from the tooth profile curve to the tooth root based on the tooth profile curve and the set of control parameters includes: offsetting the tooth profile curve based on a first offset distance in the set of control parameters to obtain a first offset curve, wherein the first offset curve and a preset circular curve intersect at point A; and offsetting the first offset curve based on a second offset distance in the set of control parameters to obtain a second offset curve; drawing a vertical baseline through point A, and drawing a construction line through point A based on the convex angle in the set of control parameters, wherein the angle between the construction line and the baseline is the convex angle. The construction line intersects the second offset curve at point B; a first curve segment is drawn between the intersection point A and the intersection point B based on the first curve control parameter in the set of control parameters; the first offset curve, the second offset curve, the construction line, and the first curve segment are symmetrically mapped along a set symmetry axis; wherein the set symmetry axis intersects the root circle of the gear at point C; a second sub-curve segment is drawn between the intersection point B and the intersection point C based on the second curve control parameter in the set of control parameters, and the two second sub-curve segments located on both sides of the set symmetry axis form the second curve segment; the first curve segment and the second curve segment form the candidate root transition curve.

[0011] In some embodiments, generating the region to be analyzed based on the single tooth groove contour includes: copying the single tooth groove contour to generate a target region including at least three tooth grooves; and supplementing the boundary of the target region to obtain the region to be analyzed.

[0012] In some embodiments, the supplementary boundaries include: the tooth tip boundary of the gear, the inner hole boundary of the gear, and the side cut-off boundary of the target region.

[0013] In some embodiments, the meshing of the region to be analyzed includes: obtaining the global mesh size and the mesh size range; performing uniform meshing on the non-root region of the region to be analyzed based on the global mesh size; and performing non-uniform meshing on the root region of the region to be analyzed based on the mesh size range.

[0014] In some embodiments, the step of performing finite element analysis on the mesh region to be analyzed to obtain the stress value of the tooth root corresponding to the candidate tooth root transition curve includes: for each mesh in the mesh region to be analyzed, calculating the geometric matrix and elastic matrix of the mesh; calculating the assembly element stiffness matrix of the mesh based on the geometric matrix and elastic matrix of the mesh; mapping the assembly element stiffness matrix to a global sparse stiffness matrix; calculating the nodal force of each node on the tooth profile curve according to the pre-set load parameters; calculating the displacement vector of each node based on the nodal force, the global sparse stiffness matrix and the pre-set formula, and obtaining the mesh stress of each mesh based on the displacement vector; and taking the maximum value of the mesh stress as the stress value of the tooth root corresponding to the candidate tooth root transition curve.

[0015] In some embodiments, determining the target tooth root transition curve from the candidate tooth root transition curves based on the stress value of the tooth root corresponding to each candidate tooth root transition curve includes: using the candidate tooth root transition curve generated by the control parameter group corresponding to the minimum stress value as the target tooth root transition curve.

[0016] In a second aspect, this application provides a device for determining a tooth root transition curve, comprising: a parameter receiving module, used to receive gear construction parameters and multiple sets of control parameters, and generate a tooth profile curve of the gear based on the gear construction parameters and a preset involute equation; wherein, the multiple sets of control parameters are used to generate multiple different candidate tooth root transition curves; a single tooth groove profile obtaining module, used to generate a candidate tooth root transition curve from the tooth profile curve to the tooth root based on the tooth profile curve and the set of control parameters for each set of control parameters, and splice the candidate tooth root transition curve with the tooth profile curve to obtain a single tooth groove profile; a mesh generation module, used to generate an analysis region based on the single tooth groove profile, and perform mesh generation on the analysis region; a finite element analysis module, used to perform finite element solution on the analysis region after mesh generation to obtain the stress value of the tooth root corresponding to the candidate tooth root transition curve; and a target tooth root transition curve determining module, used to determine the target tooth root transition curve from each candidate tooth root transition curve based on the stress value of the tooth root corresponding to each candidate tooth root transition curve.

[0017] In a third aspect, this application provides an electronic device, comprising: a processor; and a memory storing program instructions that, when executed by the processor, implement the method according to the first aspect or any of the embodiments of the first aspect.

[0018] In a fourth aspect, this application provides a computer-readable storage medium storing computer program instructions that, when executed by a processor, implement the method according to the first aspect or any of the embodiments of the first aspect.

[0019] Using the method, apparatus, electronic device, and storage medium for determining the tooth root transition curve provided above, the embodiments of this application receive gear construction parameters and multiple sets of control parameters, and generate the gear tooth profile curve based on the gear construction parameters and a preset involute equation. For each set of control parameters, a candidate tooth root transition curve from the tooth profile curve to the tooth root is generated based on the tooth profile curve and the set of control parameters. The candidate tooth root transition curve is then spliced ​​with the tooth profile curve to obtain a single tooth groove profile. An area to be analyzed is generated based on the single tooth groove profile, and the area to be analyzed is meshed to obtain an area to be analyzed mesh. Finite element analysis is performed on the area to be analyzed mesh to obtain the stress value of the tooth root corresponding to the candidate tooth root transition curve. The candidate tooth root transition curve generated by the control parameter set corresponding to the minimum stress value is used as the target tooth root transition curve. The optimization of the tooth root transition curve can be achieved through a single process, realizing a fully automated closed loop. There is no need to manually switch between multiple software programs, avoiding the accuracy loss caused by multiple format conversions when data is transferred between multiple software programs. At the same time, the absence of manual intervention also improves the determination efficiency. Attached Figure Description

[0020] The above and other objects, features, and advantages of exemplary embodiments of this application will become readily understood by reading the following detailed description with reference to the accompanying drawings. In the drawings, several embodiments of this application are illustrated by way of example and not limitation, and the same or corresponding reference numerals denote the same or corresponding parts, wherein:

[0021] Figure 1 An exemplary flowchart of a method for determining the tooth root transition curve according to some embodiments of this application is shown; Figure 2 Exemplary structural diagrams of gears according to some embodiments of this application are shown; Figure 3 Example diagrams of tooth profile curves and offset curves of some embodiments of this application are shown; Figure 4 Example diagrams illustrating the generation of tooth root transition curves according to some embodiments of this application are shown; Figure 5 Example diagrams of mirror mapping of some embodiments of this application are shown; Figure 6 Example diagrams of the regions to be analyzed in some embodiments of this application are shown; Figure 7 The diagram shows the mesh setting input interface of the gear tooth root stress synthesis system according to some embodiments of this application; Figure 8 The diagram shows the load parameter input interface of the gear tooth root stress synthesis system according to some embodiments of this application; Figure 9 An exemplary structural block diagram of a device for determining the tooth root transition curve according to some embodiments of this application is shown; Figure 10 An exemplary structural block diagram of an electronic device according to some embodiments of this application is shown. Detailed Implementation

[0022] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0023] It should be understood that the terms "comprising" and "including" used in the specification and claims of this application indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0024] It should also be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the application. As used in this specification and claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used in this specification and claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations.

[0025] As used in this specification and claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if [described condition or event] is detected" may be interpreted, depending on the context, as "once determined," "in response to determination," "once [described condition or event] is detected," or "in response to detection of [described condition or event]."

[0026] The specific embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0027] Exemplary application scenarios As a core component in mechanical transmission systems, the bending strength of the gear tooth root directly affects the overall load-bearing capacity, reliability, and lifespan of the machine. The geometry of the tooth root transition curve determines the degree of stress concentration at the tooth root. Therefore, accurately analyzing and optimizing the tooth root transition line to obtain the final tooth root transition line is crucial for gear design.

[0028] Currently, the common method for analyzing and optimizing tooth root transition curves involves using multiple software programs (including CAD and CAE software). This includes modeling the gear in CAD software (e.g., SolidWorks, NX), exporting the intermediate format file, importing it into CAE software (e.g., Ansys, Abaqus) for mesh generation, boundary condition setting, and solving, then exporting the results to post-processing software for data analysis. The input parameters are then modified based on the analysis results, and the process is repeated until the optimal tooth root transition curve is obtained. However, each step in the optimization process requires manual intervention; for example, each step requires manual operation of the software GUI. This results in multiple format conversions during data transfer between multiple software programs, leading to accuracy loss, and the manual intervention is time-consuming, making batch processing difficult.

[0029] In view of this, there is an urgent need to provide a method for determining the tooth root transition curve, so that the tooth root transition curve can be optimized in one process, avoiding the loss of accuracy caused by multiple format conversions when data is transferred between multiple software programs, and improving the efficiency of determining the tooth root transition curve without manual intervention.

[0030] Figure 1 An exemplary flowchart of a method 100 for determining the tooth root transition curve according to some embodiments of this application is shown. It is understood that the above-described method 100 for determining the tooth root transition curve can be executed by any suitable device with data processing capabilities, such as, but not limited to, terminal devices, processors, and servers. The aforementioned device integrates software for determining the tooth root transition curve (i.e.,... Figure 7 The gear tooth root stress comprehensive analysis system A6 can automatically determine the tooth root transition curve.

[0031] The following is combined with Figure 2 Explain the basic concepts of gears, such as... Figure 2 As shown, a gear (i.e., a complete gear geometry) includes multiple teeth (tooth 1, tooth 2, tooth 3, tooth 4, etc.), and the space between any two adjacent teeth is the tooth groove ( Figure 2 The area indicated by the red arrow between tooth 1 and tooth 2). In this embodiment of the application, a single tooth groove includes two tooth profile curves ( Figure 2 The blue working involute on the left and the green involute on the right) and a tooth root transition curve ( Figure 2 (The red curve in the image). This root transition curve connects to the two tooth profile curves respectively.

[0032] like Figure 1 As shown, the method 100 for determining the tooth root transition curve includes: Step S110: receiving gear construction parameters and multiple sets of control parameters, and generating the gear tooth profile curve based on the gear construction parameters and a preset involute equation; wherein, the multiple sets of control parameters are used to generate multiple different candidate tooth root transition curves; Step S120: for each set of control parameters, generating a candidate tooth root transition curve from the tooth profile curve to the tooth root based on the tooth profile curve and the set of control parameters, and splicing the candidate tooth root transition curve with the tooth profile curve to obtain a single tooth groove profile; Step S130: generating the region to be analyzed based on the single tooth groove profile, and dividing the region to be analyzed into a mesh region to obtain the mesh region to be analyzed; Step S140: performing finite element analysis on the mesh region to be analyzed to obtain the stress value of the tooth root corresponding to the candidate tooth root transition curve; Step S150: determining the target tooth root transition curve from each candidate tooth root transition curve based on the stress value of the tooth root corresponding to each candidate tooth root transition curve.

[0033] For example, the gear construction parameters in step S110 above refer to the basic design parameters used to uniquely determine the gear geometry. In the embodiments of this application, the gear construction parameters may include at least one of the following: number of teeth, pressure angle, helix angle, displacement coefficient, gear addendum circle radius, profile circle radius, dedendum circle radius, and normal module.

[0034] Among them, the number of teeth (denoted as z) is the total number of teeth on the gear, which determines the diameter of the pitch circle and the transmission ratio; the pressure angle (denoted as α, in degrees) refers to the angle of the tooth profile curve on the pitch circle, affecting the curvature of the tooth profile and the contact strength; the helix angle (denoted as β) refers to the inclination angle of the gear teeth relative to the gear axis, used to measure the degree of tooth inclination; the displacement coefficient (denoted as x) refers to the ratio of the distance (denoted as Δm) that the gear cutter moves relative to the gear pitch circle to the module (denoted as m), used to adjust the center distance of the gear or improve the root strength; the addendum circle radius (denoted as r_a) refers to the radius of the outermost edge of the gear; the profile circle radius (denoted as r_f) refers to the radius of an auxiliary geometric circle introduced in the process of generating the root transition line, which can be used to determine the boundary position between the gear tooth profile curve and the root transition curve; the root circle radius (denoted as r_r) refers to the radius of the bottom of the tooth space of the gear; and the normal module (i.e., the above m) refers to the module in the normal direction of the gear, which is the basic unit for calculating gear dimensions.

[0035] In this embodiment of the application, the gear construction parameters are input through the geometric parameter display interface of the software.

[0036] For example, the aforementioned control parameters refer to variables used to regulate the geometric shape of the tooth root transition curve. In this embodiment, each set of control parameters includes: a first offset distance (denoted as d1_offset, in mm), a second offset distance (denoted as d2_offset, in mm), a convex angle (denoted as γ, in degrees), a first curve control parameter (denoted as W1, in mm), and a second curve control parameter (denoted as W2, in mm).

[0037] Here, both the first offset distance and the second offset distance refer to the distance values ​​used in the offset processing. See also Figure 3 , Figure 3 The black dashed line represents the tooth profile curve; the black solid line C1 is the offset curve obtained based on the first offset distance; and the purple curve C2 is the offset curve obtained based on the second offset distance. The convex angle is used to determine the extension direction of the starting segment of the tooth root transition curve; both the first curve control parameter and the second curve control parameter are used to control the curvature of the tooth root transition curve. The specific method for generating the tooth root transition curve based on each set of control parameters is illustrated in the following examples and will not be elaborated upon here.

[0038] In this embodiment of the application, similar to the gear construction parameters described above, the control parameters are also input through the geometric parameter display interface of the software.

[0039] In this embodiment of the application, at least one of the above-mentioned control parameters includes a set value range and a set number of sample points. For example, one of the above five control parameters includes a set value range and a set number of sample points (for example, the set value range of W2 is 3~7, and the number of sample points is 2, such as...). Figure 7 For example, two of the above five control parameters include their respective set value range and set sample number; for example, all five control parameters include their respective set value range and set sample number.

[0040] The aforementioned sets of control parameters are used to generate multiple different candidate tooth root transition curves. In this embodiment, the aforementioned sets of control parameters are determined based on a set value range and a set number of sample points. Specifically, for each control parameter, if the parameter has a set value range and a set number of sample points, then all values ​​of the parameter are determined according to the set value range and the set number of sample points; if the parameter does not have a set value range and a set number of sample points, then the parameter has only one value; then the values ​​of each control parameter are combined to obtain multiple sets of control parameters. Each set of control parameters includes each of the aforementioned parameters.

[0041] For example, if only one of the control parameters includes a set value range and a set number of sample points, and the parameter has three possible values ​​based on the set value range and the set number of sample points, then there are a total of 3 sets of control parameters after combination.

[0042] This application embodiment uses five control parameters—first offset distance, second offset distance, convex angle, first curve control parameter, and second curve control parameter—to control the generation of the tooth profile curve. Compared with the traditional method of manually drawing and annotating dimensions one by one in CAD, it realizes the parameterized control of the tooth root transition curve, providing a foundation for multi-parameter automated optimization.

[0043] For example, the preset involute equation in step S110 above refers to the standard mathematical curve used for the working segment of the gear tooth profile. In this embodiment, the standard involute parametric equation can be used to generate the tooth profile curve (i.e., the tooth profile lattice). Here, the gear curve refers to the profile of a single working tooth surface of a single tooth space (e.g., Figure 2 (The blue working involute in the middle).

[0044] In this embodiment, the gear tooth profile curve is generated based on gear construction parameters and a preset involute equation, including: calculating the base circle radius based on the number of teeth, normal module, helix angle, and pressure angle; calculating the maximum roll angle of the involute based on the base circle radius and the gear tip circle radius, and calculating the minimum roll angle of the involute based on the base circle radius and the profile circle radius; and generating the gear tooth profile curve based on the base circle radius, the maximum roll angle, the minimum roll angle, and the preset involute equation.

[0045] Specifically, the base circle radius can be calculated based on the number of teeth, normal module, helix angle, and pressure angle. First, the pitch circle radius (denoted as r) can be calculated based on the number of teeth, normal module, and helix angle, for example, using the following formula:

[0046] Then, the base circle radius is calculated based on the pitch circle radius and the pressure angle, as shown in the following formula: rb =r cosα In this embodiment of the application, the maximum angle (θmax) for calculating the involute roll angle based on the base circle radius and the gear addendum circle radius can be: θmax=

[0047] In this embodiment, the minimum angle for calculating the roll angle of the involute based on the base circle radius and the shape circle radius can be: if r_f is greater than or equal to rb If r_f is less than 0, then the minimum rolling angle (θmin) is 0; rb Then θmin= .

[0048] In this embodiment of the application, after determining the maximum and minimum roll angles, multiple roll angles can be determined within the range of the minimum and maximum roll angles, for example, 50.

[0049] The above-mentioned pre-defined involute equation can be expressed by the following formula: x = rb (cos θ + θ sin θ ) y = rb (sin θ θ cos θ ) In this embodiment of the application, the base circle radius and multiple rolling angles are input into the preset involute equation to obtain multiple discrete points, and the tooth profile curve of the gear is formed by the multiple discrete points.

[0050] In this embodiment, each set of control parameters can generate a candidate tooth root transition curve. Based on the multiple sets of control parameters obtained above, multiple candidate tooth root transition curves can be obtained. Specifically, for each set of control parameters, a step is performed to generate a candidate tooth root transition curve from the tooth profile curve to the tooth root based on the tooth profile curve and the set of control parameters, and then splice the candidate tooth root transition curve with the tooth profile curve to obtain a single tooth groove profile.

[0051] As an optional embodiment of this application, generating a candidate tooth root transition curve from the tooth profile curve to the tooth root based on the tooth profile curve and the set of control parameters can specifically be as follows: The tooth profile curve is offset based on a first offset distance in the set of control parameters to obtain a first offset curve, which intersects with a preset circular curve at point A; the first offset curve is offset based on a second offset distance in the set of control parameters to obtain a second offset curve; a vertical baseline is drawn through intersection point A, and a construction line is drawn through intersection point A based on the convex angle in the set of control parameters, wherein the angle between the construction line and the baseline is... The angle is a convex angle; the construction line intersects the second offset curve at point B; based on the first curve control parameter in this set of control parameters, a first curve segment is drawn between intersection point A and intersection point B; the first offset curve, the second offset curve, the construction line, and the first curve segment are symmetrically mapped along a set symmetry axis; wherein, the set symmetry axis intersects the root circle of the gear at point C; based on the second curve control parameter in this set of control parameters, a second sub-curve segment is drawn between intersection point B and intersection point C, and the two second sub-curve segments located on both sides of the set symmetry axis form the second curve segment; the first curve segment and the second curve segment form the candidate root transition curve.

[0052] Figure 3 Example diagrams of tooth profile curves and offset curves of some embodiments of this application are shown; Figure 4 Example diagrams illustrating the generation of tooth root transition curves according to some embodiments of this application are shown; Figure 5 Example diagrams illustrating mirror mapping of some embodiments of this application are shown below. Figures 3-5 The process of generating the tooth root transition curve is described as follows: For each set of control parameters, such as Figure 3 As shown, the tooth profile curve (black curve) is biased based on the first offset distance in the set of control parameters to obtain the first offset curve (i.e., C1); then the first offset curve (i.e., C1) is biased based on the second offset distance in the set of control parameters to obtain the second offset curve (i.e., C2).

[0053] See Figure 4 The first offset curve C1 and the preset circular curve (auxiliary feature circle) Figure 4 The red curve located at the top of the line intersects with point A (i.e., the feature control point). Then, draw a vertical baseline through point A (i.e.,...). Figure 4 The vertical baseline is drawn, and a construction line passing through the intersection point A is drawn based on the convex angle in the control parameters. The angle between the drawn construction line and the baseline is the convex angle (i.e., γ). The drawn construction line intersects the second offset curve (i.e., C2, purple dashed line) at point B.

[0054] Then, a quadratic rational curve segment (i.e., the first curve segment) is introduced between the construction line and the second bias curve C2. Figure 3 The purple solid line segment in the diagram represents the two endpoints of the first curve segment, which are intersection point A and intersection point B, respectively. The curvature of the first curve segment is controlled by the first curve control parameter in the aforementioned control parameters.

[0055] Specifically, the first curve segment mentioned above can be constructed using the following formula:

[0056] Wherein, w0 and w2 are both fixed weights, and in this embodiment, w0 and w2 are both set to 1; w1 represents the first curve control parameter; t represents the normalized curve parameter, with a value range of 0≤t≤1, used to characterize the position progress of the current drawing point on the first curve; P(t) represents the coordinates of the drawing point corresponding to parameter t on the first curve segment; P0, P1, and P2 represent the starting control point, intermediate control point, and ending control point of the first curve segment, respectively, and the three together define the shape and direction of the curve segment.

[0057] In this embodiment, the aforementioned axis of symmetry is defined as a vertical line along the center of the tooth groove (see...). Figure 5 The vertical black dashed line in the diagram represents the axis of symmetry, which intersects the root circle of the gear at point C. Based on this, the first offset curve, the second offset curve, the construction line, and the first curve segment are mirror-symmetrically mapped along this axis of symmetry to generate a line on the other side of the tooth groove that is completely symmetrical to the first offset curve, the second offset curve, the construction line, and the first curve segment (see [reference]). Figure 5 ).

[0058] In this embodiment of the application, based on the above description, a quadratic rational curve segment (i.e., the second curve segment) symmetrical about a set axis of symmetry is introduced at the bottom of the tooth groove. Figure 4(The green solid line curve in the diagram). This second curve segment connects the two first curve segments located on both sides of the tooth groove. The two endpoints of the second curve segment are the two intersection points B on both sides of the tooth groove. The curvature of the sub-curve segment between intersection points B and C is controlled by the second curve control parameter mentioned above. For details, please refer to the description of the first curve segment, which will not be repeated here.

[0059] In this embodiment of the application, after obtaining the first curve segment and the second curve segment, the first curve segment and the second curve segment can form a candidate tooth root transition curve. Then, the candidate tooth root transition curve is spliced ​​with the above tooth profile curve to obtain a single tooth groove profile. The above single tooth groove profile can be stored in the software memory in the form of an array.

[0060] For example, the region to be analyzed mentioned above refers to the complete computational domain for which finite element stress analysis is required. It is understood that while a single tooth groove profile includes the geometric information of the tooth root transition line region, a computational domain containing multiple tooth groove profiles needs to be constructed to more accurately simulate the stress state of the gear during actual meshing. Using a multi-tooth groove model can effectively eliminate the influence of boundary effects on the stress calculation results.

[0061] Specifically, the single tooth groove contour is copied to generate a target region including at least three tooth grooves; the boundary of the target region is supplemented to obtain the region to be analyzed.

[0062] In practice, a target region containing at least three adjacent tooth slots is generated by rotating and copying the profile of a single tooth slot along the circumference of the gear. Figure 6 (Taking 3 as an example). Then, the target area is supplemented by boundary addition to form a complete closed curve loop, thus obtaining the area to be analyzed. Here, the supplemented boundary includes, but is not limited to: the tooth tip boundary of the gear, the inner hole boundary of the gear ( Figure 6 The lower circular sawtooth boundary and the side (left and right) cut-off boundaries of the target area ( Figure 6 (The jagged edges on the left and right sides of the middle).

[0063] In this embodiment, after obtaining the region to be analyzed, a mesh generation library is loaded in the same process, and the region to be analyzed is meshed to obtain the mesh region to be analyzed. In this embodiment, there are many methods for meshing the region to be analyzed. For example, the region to be analyzed can be uniformly divided according to a set size; another example is a non-uniform gradient division of the region to be analyzed according to a set size range. Of course, other meshing methods are also possible, and this embodiment does not specifically limit these methods; they can be determined according to the actual situation.

[0064] The data of each mesh after division is stored in the software's memory in the form of node coordinates and mesh connection table. No intermediate files are required throughout the process. It can be used as input for the finite element analysis and can be directly called during the finite element analysis.

[0065] It should be noted that the above-mentioned dimensions and size ranges can be entered through the grid settings display interface of the software.

[0066] In this embodiment of the application, the grid in the grid area to be analyzed can be a triangular grid, a quadrilateral grid, or a polygonal grid. This embodiment of the application does not specifically limit this.

[0067] For example, the above-mentioned finite element solution is a process of solving the partial differential equations of elasticity using numerical methods based on a discrete mesh (i.e., the mesh region to be analyzed). In this embodiment, in the same process, the above-mentioned mesh data, including node coordinates and mesh connection tables, are acquired. The finite element solver is used to perform finite element solutions on the mesh region to be analyzed obtained from each set of control parameters, obtaining the stress value of the tooth root corresponding to each candidate tooth root transition curve. Finite element analysis can be completed without relying on external CAE software. Then, the candidate tooth root transition curve generated by the control parameter set corresponding to the minimum stress value among the stress values ​​is used as the target tooth root transition curve.

[0068] The specific finite element solution process is illustrated in the following examples, and will not be repeated here.

[0069] In this embodiment, after obtaining the stress value of the tooth root corresponding to each candidate tooth root transition curve, the target tooth root transition curve is determined from the candidate tooth root transition curves based on the stress value of the tooth root corresponding to each candidate tooth root transition curve. In this embodiment, there are many methods for determining the target tooth root transition curve. For example, the candidate tooth root transition curve generated by the control parameter group corresponding to the stress value closest to the average value of each stress value can be used as the target tooth root transition curve; another example is using the candidate tooth root transition curve generated by the control parameter group corresponding to the minimum stress value as the target tooth root transition curve. This embodiment does not specifically limit this method, but preferably uses the candidate tooth root transition curve generated by the control parameter group corresponding to the minimum stress value as the target tooth root transition curve.

[0070] This application embodiment receives gear construction parameters and multiple sets of control parameters, and generates the gear tooth profile curve based on the gear construction parameters and a preset involute equation. For each set of control parameters, a candidate tooth root transition curve from the tooth profile curve to the tooth root is generated based on the tooth profile curve and the set of control parameters. The candidate tooth root transition curve is then spliced ​​with the tooth profile curve to obtain a single tooth groove profile. Based on the single tooth groove profile, an analysis region is generated, and the analysis region is meshed to obtain the analysis mesh region. Finite element analysis is performed on the analysis mesh region to obtain the stress value of the tooth root corresponding to the candidate tooth root transition curve. The candidate tooth root transition curve generated by the control parameter set corresponding to the minimum stress value is used as the target tooth root transition curve. The entire process of geometric construction, mesh generation, finite element analysis, and parameter optimization can be automated through a single process, achieving optimization of the tooth root transition curve. Data is transferred between processes via memory, eliminating the need for manual switching between multiple software programs. This avoids the accuracy loss caused by multiple format conversions when data is transferred between multiple software programs. At the same time, the elimination of manual intervention also improves the determination efficiency, reducing the time from several days to several seconds or minutes. Furthermore, there is no need to purchase CAD and CAE software, thus reducing costs.

[0071] As an optional embodiment of this application, the meshing of the region to be analyzed in step S130 above includes: obtaining the global mesh size and the mesh size range; performing uniform meshing on the non-root region of the region to be analyzed based on the global mesh size; and performing non-uniform meshing on the root region of the region to be analyzed based on the mesh size range.

[0072] For example, the aforementioned global mesh size (i.e. Figure 7 The overall size (in the text) refers to the standard element size used in regions of the analysis area where stress changes are gradual; the mesh size range mentioned above refers to the minimum size used to divide the root region (i.e., Figure 7 The local encryption size and the maximum size (i.e., the size of the local encryption) and the maximum size (i.e., Figure 7 The maximum size in the grid). In this embodiment, the global grid size and grid size range are both displayed through the grid settings interface of the software (see...). Figure 7 (Input by )

[0073] The aforementioned non-tooth root region refers to the area far from the tooth root transition curve, where the stress gradient is relatively small. For this region, a uniform mesh is generated based on the global mesh size, meaning that the resulting meshes all have the same size, which is the global mesh size.

[0074] The aforementioned tooth root region refers to the area around the tooth root transition line where the stress gradient is significant. For this region, a non-uniform gradient mesh is generated based on the mesh size range. After meshing, the closer the region is to the tooth root transition line, the smaller the mesh size; conversely, the farther the region is from the tooth root transition line, the larger the mesh size (see [reference]). Figure 6 ).

[0075] This application embodiment uses different mesh divisions for different regions of the analysis area. High-density mesh division can be performed in areas with severe stress concentration (i.e., the tooth root region) to capture strong changes in stress gradient and determine the accuracy of finite element analysis results. Low-density mesh division is used in areas with less severe stress concentration (i.e., non-tooth root regions) to avoid unnecessary waste of computational resources. Furthermore, non-uniform gradient mesh division is performed by using a range of mesh sizes to avoid abrupt changes in mesh size, ensuring mesh quality and improving the numerical stability of finite element solutions.

[0076] As an optional embodiment of this application, the step S140 above, which involves performing a finite element solution on the mesh region to be analyzed to obtain the stress value of the tooth root corresponding to the candidate tooth root transition curve, includes: calculating the geometric matrix and elastic matrix of each mesh in the mesh region to be analyzed; calculating the assembly element stiffness matrix of the mesh based on the geometric matrix and elastic matrix; mapping the assembly element stiffness matrix to the global sparse stiffness matrix; calculating the nodal force of each node on the tooth profile curve according to the pre-set load parameters; calculating the displacement vector of each node based on the nodal force, the global sparse stiffness matrix, and the set formula, and obtaining the mesh stress of each mesh based on the displacement vector; and taking the maximum value of the mesh stress as the stress value of the tooth root corresponding to the candidate tooth root transition curve.

[0077] For example, the geometric matrix (denoted as B) refers to the transformation matrix between mesh nodes and mesh strain, which can be calculated from the coordinates of the mesh nodes. The elastic matrix (denoted as D) refers to the transformation relationship between stress and strain within the mesh, which can be calculated from the elastic modulus and Poisson's ratio of the gear material.

[0078] As for the specific calculation methods of the geometric matrix and the elasticity matrix, they are all conventional calculation methods and are not the protection points of this application. Please refer to the descriptions in relevant materials, and they will not be elaborated here.

[0079] For example, the stiffness matrix of the assembly element (denoted as K_e) refers to the matrix describing the mesh's resistance to deformation. In this embodiment, it can be calculated using the geometric matrix and the elasticity matrix, specifically, using the following formula: Ke=A B T DB Here, A is a constant.

[0080] For example, the aforementioned global sparse stiffness matrix (denoted as K) refers to the total stiffness matrix after merging all meshes in the mesh region to be analyzed. In this embodiment, after calculating the assembly element stiffness matrix of all meshes, all assembly element stiffness matrices are numbered according to the nodal degrees of freedom and assembled to form an overall matrix, i.e., the global sparse stiffness matrix. This global sparse stiffness matrix can be stored in a compressed sparse format to reduce memory usage.

[0081] For example, the aforementioned load parameters refer to a set of quantitative indicators used in the finite element method (FE) solution process to accurately simulate the actual stress on the tooth surface (i.e., tooth profile curve) during gear meshing. These parameters may include the loading radius, Gaussian half-width, load direction angle, etc. The loading radius refers to the position where the load is applied to the tooth surface, typically at a certain height on the tooth profile curve; the Gaussian half-width controls the range of load distribution along and on the tooth profile curve of the gear; and the load direction angle refers to the components of the load along the horizontal and vertical directions.

[0082] The above load parameters are preset; specifically, they can be set via... Figure 8 The software's load parameter display interface is shown for input.

[0083] In practical implementation, the distance from the center point corresponding to the loading radius to each node on the tooth profile curve (denoted as di) is calculated. The larger the distance, the farther the node is from the meshing contact area, and the smaller the assigned load. Then, the load weight of each node on the tooth profile curve is calculated using a Gaussian decay function. After calculating the load weight of each node, all load weights are normalized. After normalization, the load directional components are applied to each node on the tooth profile curve to form the equivalent node force F. Here, the equivalent node force is the concentrated force of the meshing distributed load distributed to each node of the tooth profile curve through Gaussian weighting.

[0084] For example, after obtaining the nodal force of each node on the tooth profile curve, displacement constraints can be applied to the added boundaries (i.e., the inner hole boundary and the left and right truncation boundaries mentioned above) to prevent the nodes from displacing. Then, based on the nodal forces, the global sparse stiffness matrix mentioned above, and the set formula, the sparse direct method is called to directly calculate the displacement vector of each node, and the mesh stress of each mesh is obtained based on the displacement vector.

[0085] The formula here can be, for example: K u=F Where F represents nodal force, K represents global sparse stiffness matrix, and u represents displacement vector.

[0086] In this embodiment, after calculating the displacement vector of each node based on the above-mentioned formula, the strain components of each mesh are calculated back-substituted based on the displacement vector of each node and the geometric matrix (denoted as...). εx , εy , γxy Then, the stress components of each mesh are calculated using the strain components and the elasticity matrix (denoted as ). σx , σy , τxy Then, the stress value of each grid is calculated based on the stress components. After calculating the stress value of all grids, the maximum stress value is taken as the stress value of the tooth root corresponding to the candidate tooth root transition curve.

[0087] Figure 9 An exemplary structural block diagram of a tooth root transition curve determination device 900 according to some embodiments of this application is shown.

[0088] like Figure 9 As shown, the aforementioned tooth root transition curve determination device 900 includes: a parameter receiving module 910, used to receive gear construction parameters and multiple sets of control parameters, and generate a gear tooth profile curve based on the gear construction parameters and a preset involute equation; wherein, the multiple sets of control parameters are used to generate multiple different candidate tooth root transition curves; a single tooth groove profile acquisition module 920, used to generate a candidate tooth root transition curve from the tooth profile curve to the tooth root based on the tooth profile curve and the set of control parameters for each set of control parameters, and splice the candidate tooth root transition curve with the tooth profile curve to obtain a single tooth groove profile; a mesh generation module 930, used to generate an analysis area based on the single tooth groove profile, and perform mesh generation on the analysis area; a finite element analysis module 940, used to perform finite element solution on the analysis area after mesh generation to obtain the stress value of the tooth root corresponding to the candidate tooth root transition curve; and a target tooth root transition curve determination module 950, used to determine the target tooth root transition curve from each candidate tooth root transition curve based on the stress value of the tooth root corresponding to each candidate tooth root transition curve.

[0089] As an optional embodiment of this application, the gear construction parameters include at least one of the following: number of teeth, pressure angle, helix angle, displacement coefficient, gear addendum circle radius, profile circle radius, dedendum circle radius, and normal module.

[0090] As an optional embodiment of this application, the gear tooth profile curve generated by the receiving module 910 based on gear construction parameters and a preset involute equation includes: calculating the base circle radius based on the number of teeth, normal module, helix angle, and pressure angle; calculating the maximum roll angle of the involute based on the base circle radius and the gear tip circle radius, and calculating the minimum roll angle of the involute based on the base circle radius and the profile circle radius; and generating the gear tooth profile curve based on the base circle radius, the maximum roll angle, the minimum roll angle, and the preset involute equation.

[0091] As an optional embodiment of this application, the control parameters include: a first offset distance, a second offset distance, a convex angle, a first curve control parameter, and a second curve control parameter; at least one control parameter includes a set value range and a set number of sample points, and multiple sets of control parameters are determined based on the set value range and the set number of sample points.

[0092] As an optional embodiment of this application, the single tooth profile acquisition module 920 is specifically used for: offsetting the tooth profile curve based on a first offset distance in the set of control parameters to obtain a first offset curve, wherein the first offset curve and a preset circular curve intersect at point A; and offsetting the first offset curve based on a second offset distance in the set of control parameters to obtain a second offset curve; drawing a vertical baseline through point A, and drawing a construction line through point A based on the convex angle in the set of control parameters, wherein the angle between the construction line and the baseline is the convex angle; The construction line intersects with the second offset curve at point B; based on the first curve control parameter in this set of control parameters, a first curve segment is drawn between intersection point A and intersection point B; the first offset curve, the second offset curve, the construction line, and the first curve segment are symmetrically mapped along a set axis of symmetry; wherein, the set axis of symmetry intersects with the root circle of the gear at point C; based on the second curve control parameter in this set of control parameters, a second sub-curve segment is drawn between intersection point B and intersection point C, and the two second sub-curve segments located on both sides of the set axis of symmetry form the second curve segment; the first curve segment and the second curve segment form the candidate root transition curve.

[0093] As an optional embodiment of this application, the above-mentioned mesh division module 930 is specifically used to: copy the single tooth groove contour to generate a target region including at least three tooth grooves; and supplement the boundary of the target region to obtain the region to be analyzed.

[0094] As an optional embodiment of this application, the additional boundaries include: the tooth tip boundary of the gear, the inner hole boundary of the gear, and the side cut-off boundary of the target area.

[0095] As an optional embodiment of this application, the mesh generation module 930 is further configured to: obtain the global mesh size and the mesh size range; perform uniform mesh generation on the non-root region of the region to be analyzed based on the global mesh size; and perform non-uniform mesh generation on the root region of the region to be analyzed based on the mesh size range.

[0096] As an optional embodiment of this application, the finite element analysis module 940 is specifically used for: calculating the geometric matrix and elastic matrix of each mesh in the mesh region to be analyzed; calculating the assembly element stiffness matrix of the mesh based on the geometric matrix and elastic matrix; mapping the assembly element stiffness matrix to the global sparse stiffness matrix; calculating the nodal force of each node on the tooth profile curve according to the pre-set load parameters; calculating the displacement vector of each node based on the nodal force, the global sparse stiffness matrix and the set formula, and obtaining the mesh stress of each mesh based on the displacement vector; and using the maximum value of the mesh stress as the stress value of the tooth root corresponding to the candidate tooth root transition curve.

[0097] As an optional embodiment of this application, the target tooth root transition curve determination module 950 is specifically used to: use the candidate tooth root transition curve generated by the control parameter group corresponding to the minimum stress value as the target tooth root transition curve.

[0098] For details on the specific implementation methods and beneficial effects, please refer to the description of the method 100 for determining the tooth root transition curve above, which will not be repeated here.

[0099] Correspondingly, embodiments of this application also provide Figure 9 The hardware structure diagram of the device shown is as follows: Figure 10 As shown, the electronic device 1000 can be a device for implementing the above-described method 100 for determining the tooth root transition curve. For example... Figure 10 As shown, the electronic device 1000 includes a processor 1010 and a memory 1020. The memory 1020 is configured to store program instructions; the processor 1010 is configured to load and execute the program instructions stored in the memory 1020 to implement an embodiment of the tooth root transition curve determination method 100 shown above.

[0100] As one embodiment, memory 1020 can be any electronic, magnetic, optical, or other physical storage device that can contain or store information such as program instructions, data, etc. For example, memory 1020 can be volatile memory, non-volatile memory, or similar storage media. Specifically, memory 1020 can be RAM (Random Access Memory), flash memory, storage drive (such as hard disk drive), solid-state drive, any type of storage disk (such as optical disc, DVD, etc.), or similar storage media, or combinations thereof.

[0101] This concludes the process. Figure 10 Description of the electronic device shown.

[0102] While numerous embodiments of this application have been shown and described herein, it will be apparent to those skilled in the art that such embodiments are provided by way of example only. Many modifications, alterations, and alternatives will arise for those skilled in the art without departing from the spirit and intent of this application. It should be understood that various alternatives to the embodiments of this application described herein may be employed in the practice of this application. The appended claims are intended to define the scope of protection of this application and therefore cover equivalents or alternatives within the scope of these claims.

Claims

1. A method for determining a tooth root transition curve, characterized in that, include: The system receives gear construction parameters and multiple sets of control parameters, and generates the tooth profile curve of the gear based on the gear construction parameters and a preset involute equation; wherein, the multiple sets of control parameters are used to generate multiple different candidate tooth root transition curves. For each set of control parameters, a candidate tooth root transition curve from the tooth profile curve to the tooth root is generated based on the tooth profile curve and the set of control parameters, and the candidate tooth root transition curve is spliced ​​with the tooth profile curve to obtain a single tooth groove profile. The region to be analyzed is generated based on the single tooth groove contour, and the region to be analyzed is meshed to obtain the mesh region to be analyzed. The finite element method is used to solve the mesh region to be analyzed, and the stress value of the tooth root corresponding to the candidate tooth root transition curve is obtained. The target tooth root transition curve is determined from the tooth root transition curves based on the stress value of the tooth root corresponding to each candidate tooth root transition curve.

2. The method according to claim 1, characterized in that, The gear construction parameters include at least one of the following: number of teeth, pressure angle, helix angle, displacement coefficient, gear addendum circle radius, profile circle radius, dedendum circle radius, and normal module.

3. The method according to claim 2, characterized in that, The process of generating the tooth profile curve of the gear based on the gear construction parameters and the preset involute equation includes: The base circle radius is calculated based on the number of teeth, the normal module, the helix angle, and the pressure angle. The maximum roll angle of the involute is calculated based on the base circle radius and the gear tip circle radius, and the minimum roll angle of the involute is calculated based on the base circle radius and the profile circle radius. The tooth profile curve of the gear is generated based on the base circle radius, the maximum rolling angle, the minimum rolling angle, and the preset involute equation.

4. The method according to claim 1, characterized in that, The control parameters include: a first offset distance, a second offset distance, a convex angle, a first curve control parameter, and a second curve control parameter; at least one control parameter includes a set value range and a set number of sample points, and multiple sets of control parameters are determined based on the set value range and the set number of sample points.

5. The method according to claim 4, characterized in that, The generation of candidate tooth root transition curves from the tooth profile curve to the tooth root based on the tooth profile curve and the set of control parameters includes: The tooth profile curve is offset based on the first offset distance in this set of control parameters to obtain a first offset curve, which intersects with a preset circular curve at point A; and The first bias curve is biased based on the second bias distance in the set of control parameters to obtain the second bias curve; Draw a vertical baseline through the intersection point A, and draw a construction line through the intersection point A based on the convex angle in the set of control parameters, wherein the angle between the construction line and the baseline is the convex angle; the construction line intersects the second offset curve at point B; A first curve segment is drawn between intersection point A and intersection point B based on the first curve control parameter in this set of control parameters; The first offset curve, the second offset curve, the construction line, and the first curve segment are symmetrically mapped along a set symmetry axis; wherein the set symmetry axis intersects the root circle of the gear at a point C; Based on the second curve control parameter in the set of control parameters, a second sub-curve segment is drawn between the intersection point B and the intersection point C. The two second sub-curve segments located on both sides of the set axis of symmetry form the second curve segment; the first curve segment and the second curve segment form the candidate tooth root transition curve.

6. The method according to claim 1, characterized in that, The process of generating the region to be analyzed based on the single tooth groove contour includes: The single tooth groove contour is copied to generate a target region including at least three tooth grooves; The target region is then supplemented with boundary information to obtain the region to be analyzed.

7. The method according to claim 6, characterized in that, The additional boundaries include: the tooth tip boundary of the gear, the inner hole boundary of the gear, and the side cut-off boundary of the target area.

8. The method according to claim 1, characterized in that, The process of dividing the region to be analyzed into a grid includes: Get the global grid size and grid size range; For the non-root region of the region to be analyzed, a uniform mesh is generated based on the global mesh size; For the tooth root region of the region to be analyzed, a non-uniform mesh is generated based on the mesh size range.

9. The method according to claim 1, characterized in that, The step of performing finite element analysis on the mesh region to be analyzed to obtain the stress value of the tooth root corresponding to the candidate tooth root transition curve includes: For each grid in the grid region to be analyzed, calculate the geometric matrix and elasticity matrix of that grid; The stiffness matrix of the assembled elements of the mesh is calculated based on the geometric matrix and elasticity matrix of the mesh. The stiffness matrix of the assembly unit is mapped to the global sparse stiffness matrix; Calculate the nodal force at each node on the tooth profile curve based on the pre-set load parameters; The displacement vector of each node is calculated based on the nodal forces, the global sparse stiffness matrix, and the set formula, and the mesh stress of each mesh is obtained based on the displacement vector. The maximum value of the mesh stress is taken as the stress value of the tooth root corresponding to the candidate tooth root transition curve.

10. The method according to claim 1, characterized in that, The determination of the target tooth root transition curve from the candidate tooth root transition curves based on the stress value of the tooth root corresponding to each candidate tooth root transition curve includes: The candidate tooth root transition curve generated by the control parameter set corresponding to the minimum stress value is used as the target tooth root transition curve.

11. A device for determining a tooth root transition curve, characterized in that, include: The parameter receiving module is used to receive gear construction parameters and multiple sets of control parameters, and generate the tooth profile curve of the gear based on the gear construction parameters and the preset involute equation; wherein, the multiple sets of control parameters are used to generate multiple different candidate tooth root transition curves. The single tooth groove profile acquisition module is used to generate a candidate tooth root transition curve from the tooth profile curve to the tooth root based on the tooth profile curve and the set of control parameters for each set of control parameters, and to splice the candidate tooth root transition curve with the tooth profile curve to obtain the single tooth groove profile. The mesh generation module is used to generate the region to be analyzed based on the single tooth groove contour, and to perform mesh generation on the region to be analyzed. The finite element analysis module is used to perform finite element solutions on the meshed region to be analyzed, and obtain the stress value of the tooth root corresponding to the candidate tooth root transition curve. The target tooth root transition curve determination module is used to determine the target tooth root transition curve from each candidate tooth root transition curve based on the stress value of the tooth root corresponding to each candidate tooth root transition curve.

12. An electronic device, characterized in that, include: processor; A memory storing program instructions that, when executed by the processor, implement the method according to any one of claims 1-10.

13. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer program instructions that, when executed by a processor, implement the method according to any one of claims 1-10.

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