A variable-tooth-fan variable-ratio tooth-fan-rack-pair tooth surface point cloud reconstruction method
By constructing the involute rack tooth profile transformation equation and calculating the intersection point, the tooth surface point cloud of the variable transmission ratio gear sector is reconstructed. This solves the problem of low accuracy of tooth surface point cloud in the analytical method of meshing principle, realizes the tooth surface boundary point cloud with equidistant and uniform distribution, and improves the machining accuracy and the accuracy of finite element analysis.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHANDONG AGRICULTURAL UNIVERSITY
- Filing Date
- 2023-11-10
- Publication Date
- 2026-07-21
AI Technical Summary
In the design of variable transmission ratio gear sector rack pairs, the tooth surface point cloud calculated by the meshing principle analytical method is not accurate and cannot obtain equidistant and uniformly distributed tooth surface boundary points. This results in a mismatch between the finite element analysis results and the actual service conditions, and it cannot be used as a benchmark for machining accuracy testing.
By constructing the involute rack tooth profile transformation equation and calculating the circle intersection solution equation, the tooth surface point cloud of the variable transmission ratio gear sector is reconstructed. Using equal spacing settings and numerical solution methods, tooth surface point clouds with equal axial distance and equal radial spacing are obtained.
High-precision point cloud reconstruction of tooth surface with variable transmission ratio was achieved, obtaining equidistant and uniformly distributed tooth surface boundary points, meeting the requirements of high-precision modeling and finite element analysis, and improving the accuracy of machining precision detection.
Smart Images
Figure CN117494342B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of gear transmission technology, specifically to a method for reconstructing the point cloud of the tooth surface of a variable gear sector-variable transmission ratio gear sector rack pair. Background Technology
[0002] In recent years, variable ratio steering systems have gradually become a standard core component of commercial vehicle steering systems. They achieve real-time changes in the transmission ratio during steering through variable ratio gear sector rack pairs, thus achieving a balance between easy and responsive steering. Variable gear sector technology, exemplified by Isuzu of Japan, uses a specially shaped gear sector to achieve variable transmission ratio in the steering gear rack pair, while variable rack technology, exemplified by ZF of Germany, uses a specially shaped rack to achieve the same. How to design and optimize variable ratio gear sector rack pairs and ensure that manufacturing meets design requirements is a crucial engineering theoretical problem in the automotive industry.
[0003] While the analytical method based on the meshing principle yields highly accurate point clouds of the variable transmission ratio tooth surface, the distribution of these point clouds along the instantaneous contact line is non-equidistant and non-uniform. Furthermore, point clouds at the boundary between the working and transition tooth surfaces exhibit mixing and overlap. Additionally, the equidistant dispersion method based on the meshing principle cannot obtain the tooth surface points at the boundary of the variable transmission ratio tooth surface. Therefore, the solid model of the variable transmission ratio tooth surface fitted with these point clouds lacks accuracy, and the finite element analysis results cannot match the actual service conditions. Moreover, the disordered point clouds cannot serve as a benchmark for detecting the accuracy of the machined variable transmission ratio tooth surface. Summary of the Invention To address the shortcomings of existing technologies, this invention provides a method for reconstructing the point cloud of the tooth surface of a variable gear sector-variable transmission ratio gear sector rack pair. This method overcomes the various drawbacks of traditional meshing principle-based calculations of point clouds on the tooth surface of variable transmission ratio gears, and obtains point clouds of variable transmission ratio gears with equidistant and uniform distribution and accurate tooth surface boundary points.
[0004] This invention is achieved through the following technical solution, providing a method for reconstructing the point cloud of the tooth surface of a variable-gear sector / variable-transmission-ratio gear sector rack pair, comprising the following steps: S1: Within the radial section of the variable transmission ratio gear sector with equal spacing, based on the spatial transformation relationship of the tooth profile of the involute rack end face in the radial section of the variable transmission ratio gear sector, the transformation tooth profile equation of the involute rack is constructed. Under the constrained motion of the variable transmission ratio curve and the shovel-shaped relationship, the tooth profile equation of the radial section of the variable transmission ratio gear sector with the transformation tooth profile shovel shape of the involute rack is obtained. Through spacing setting and numerical solution, the tooth profile point cloud of the variable transmission ratio gear sector with equal axial distance can be obtained. S2: Within the tooth profile range of the variable transmission ratio gear sector with equal axial spacing, set up a calculation circle with equal radial spacing, and construct a set of equations for the intersection of the calculation circle and the radial section tooth profile of the variable transmission ratio gear sector. The intersection point is the point cloud of the radial tooth profile of the variable transmission ratio gear sector with equal radial spacing.
[0005] As an optimization, in step S1, the transformed tooth profile equation of the involute rack is shown in formulas (1) and (2): (1) (2) Wherein, formulas (1) and (2) are respectively the transformation tooth profile equation and the transformation tooth vertex equation of the involute rack end face tooth profile; , These represent the coordinates of the transformed tooth profile point and the coordinates of the transformed tooth vertex of the involute rack, respectively. This represents the distance between the origin of the coordinate system and the involute tooth profile. This represents the distance between the tooth vertex and the perpendicular line passing through the origin of the tooth profile. This represents the distance between the tooth profile point and the tooth vertex. For assembly corner, For the width of the rack teeth, For tooth tip height, For tooth root height, For top gap, For pressure angle, These are the parameters of the rack tooth profile.
[0006] As an optimization, in step S1, the tooth profile equation of the radial section of the variable thickness and variable transmission ratio tooth sector is shown in formulas (3) and (4): (3) (4) Among them, formulas (3) and (4) are the working tooth profile equation and the transition tooth profile equation of the radial section of the variable thickness and variable transmission ratio tooth sector, respectively; , These are the coordinates of the working tooth profile point and the transition tooth profile point of the radial section of the variable thickness and variable transmission ratio gear sector, respectively. For the gear sector rotation angle; The rack displacement is calculated by integrating the gear sector rotation angle onto the variable transmission ratio curve function of the gear sector rack pair. Center distance; , These are the unit normal vectors of the tooth profile points of the sector tooth and the relative velocities of the tooth profiles at the meshing points, respectively. The meshing equation represents the variable transmission ratio gear sector profile of the involute rack with a different tooth profile envelope.
[0007] As an optimization, in step S2, the solution equations for the intersection of the calculation circle and the radial section tooth profile of the variable transmission ratio gear sector are shown in equations (5) and (6): (5) (6) Among them, formulas (5) and (6) are respectively the solution equations for the radial working tooth profile and the transition tooth profile of the variable transmission ratio gear sector. To calculate the circular coordinates, To calculate the radius of a circle, To calculate the parameters of a circle, let represent the polar angle corresponding to any point on the circle; To calculate the tooth profile parameters at the intersection of the circle and the tooth profile of the variable transmission ratio gear sector, the solution set obtained by the calculation model (5) and (6) is substituted into the tooth profile equations (3) and (4) of the variable transmission ratio gear sector to obtain the tooth profile point cloud with equal radial spacing of the tooth profile of the variable transmission ratio gear sector.
[0008] The beneficial effects of this invention are as follows: The method for reconstructing the point cloud of the tooth surface of the variable gear sector-variable transmission ratio gear sector rack pair addresses the various shortcomings of current variable transmission ratio tooth surface design methods. Taking the variable transmission ratio gear sector rack pair with variable gear sector design as the research object, and aiming at the needs of high-precision modeling and finite element analysis, this invention studies the method for reconstructing the point cloud of the tooth surface of the variable transmission ratio, overcomes the various drawbacks of the point cloud of the tooth surface of the variable transmission ratio generated by the traditional meshing principle, and obtains the point cloud of the tooth surface of the variable transmission ratio with equidistant and uniform distribution and accurate tooth surface boundary points. Attached Figure Description
[0009] Figure 1 This is a variable transmission ratio curve diagram of the variable transmission ratio gear sector rack pair in a specific embodiment of the present invention; Figure 2 This is a geometric relationship diagram of the initial assembly moment of the gear sector rack pair within the radial zero displacement section of the variable transmission ratio gear sector in a specific embodiment of the present invention; Figure 3 This is a point cloud diagram of the equidistant tooth surface of the variable transmission ratio gear sector calculated in a specific embodiment of the present invention. Detailed Implementation
[0010] To clearly illustrate the technical features of this solution, the following detailed implementation method will be used to explain the solution.
[0011] like Figures 1-3 As shown, the present invention provides a method for reconstructing the point cloud of the tooth surface of a variable-gear sector / variable-ratio gear sector rack pair, comprising the following steps: S1: Within the radial section of the variable transmission ratio gear sector with equal spacing, based on the spatial transformation relationship of the tooth profile of the involute rack end face in the radial section of the variable transmission ratio gear sector, the transformation tooth profile equation of the involute rack is constructed. Under the constrained motion of the variable transmission ratio curve and the shovel-shaped relationship, the tooth profile equation of the radial section of the variable transmission ratio gear sector with the transformation tooth profile shovel shape of the involute rack is obtained. Through spacing setting and numerical solution, the tooth profile point cloud of the variable transmission ratio gear sector with equal axial distance can be obtained. The transformation tooth profile equations of the involute rack are shown in formulas (1) and (2): (1) (2) Wherein, formulas (1) and (2) are respectively the transformation tooth profile equation and the transformation tooth vertex equation of the involute rack end face tooth profile; , These represent the coordinates of the transformed tooth profile point and the coordinates of the transformed tooth vertex of the involute rack, respectively. This represents the distance between the origin of the coordinate system and the involute tooth profile. This represents the distance between the tooth vertex and the perpendicular line passing through the origin of the tooth profile. This represents the distance between the tooth profile point and the tooth vertex. For assembly corner, For the width of the rack teeth, For tooth tip height, For tooth root height, For top gap, For pressure angle, These are the parameters of the rack tooth profile.
[0012] The tooth profile equations for the radial section of the variable-thickness, variable-ratio gear sector are shown in formulas (3) and (4): (3) (4) Among them, formulas (3) and (4) are the working tooth profile equation and the transition tooth profile equation of the radial section of the variable thickness and variable transmission ratio tooth sector, respectively; , These are the coordinates of the working tooth profile point and the transition tooth profile point of the radial section of the variable thickness and variable transmission ratio gear sector, respectively. For the gear sector rotation angle; The rack displacement is calculated by integrating the gear sector rotation angle onto the variable transmission ratio curve function of the gear sector rack pair. Center distance; , These are the unit normal vectors of the tooth profile points of the sector tooth and the relative velocities of the tooth profiles at the meshing points, respectively. The meshing equation represents the variable transmission ratio gear sector profile of the involute rack with a different tooth profile envelope.
[0013] S2: Within the tooth profile range of the variable transmission ratio gear sector with equal axial spacing, set up a calculation circle with equal radial spacing, and construct a set of equations for the intersection of the calculation circle and the radial section tooth profile of the variable transmission ratio gear sector. The intersection point is the point cloud of the radial tooth profile of the variable transmission ratio gear sector with equal radial spacing.
[0014] The equations for solving the intersection of the calculation circle and the radial section of the variable transmission ratio gear sector are shown in formulas (5) and (6): (5) (6) Among them, formulas (5) and (6) are respectively the solution equations for the radial working tooth profile and the transition tooth profile of the variable transmission ratio gear sector. To calculate the circular coordinates, To calculate the radius of a circle, To calculate the parameters of a circle, let represent the polar angle corresponding to any point on the circle; To calculate the tooth profile parameters at the intersection of the circle and the tooth profile of the variable transmission ratio gear sector, the solution set obtained by the calculation model (5) and (6) is substituted into the tooth profile equations (3) and (4) of the variable transmission ratio gear sector to obtain the tooth profile point cloud with equal radial spacing of the tooth profile of the variable transmission ratio gear sector.
[0015] The method for reconstructing the point cloud of the tooth surface of the variable gear ratio sector rack pair for commercial vehicle steering was tested in practice, such as... Figure 1 The transmission ratio curve of the variable transmission ratio gear sector rack pair shown in the design is as follows: In the formula, The transmission ratio of the variable transmission ratio gear sector rack pair.
[0016] In this experiment, the variable transmission ratio gear sector is designed with 3 teeth, and the design parameters are: module is... The involute pressure angle is The cone angle is The top gap is Tooth tip height is The root height is Tooth width is The center distance is The distance between the origin of the coordinate system and the involute tooth profile is The distance between the large end face of the gear sector and the radial zero-displacement section of the gear sector is The distance between the small end face of the gear sector and the radial zero-displacement section of the gear sector is .
[0017] In this experiment, the geometric relationship of the gear sector and rack pair at the initial assembly moment within the radial zero-displacement section of the variable transmission ratio gear sector is as follows: Figure 2 As shown, the range of values for the radius of the calculated circle within the cross-sectional plane containing the large end of the variable transmission ratio gear sector is: The unit is " The radial distance between two adjacent calculation circles is... .
[0018] In this experiment, the coordinates of each tooth profile point of the variable transmission ratio gear sector were obtained through an equidistant point cloud computing model between the tooth tip circle and the tooth root circle within the radial zero displacement section. and As shown in Table 1, the unit is " ".
[0019] Table 1 In this experiment, the spacing between adjacent radial sections was set to be... The point cloud reconstruction operation is performed on the non-zero displacement radial section of the variable transmission ratio gear sector as described above.
[0020] This experiment ultimately yielded point clouds of equiaxial and equiradial spacing on the tooth surface of the variable transmission ratio sector gear, as shown in the figure. Figure 3 As shown.
[0021] This invention is not limited to the above-described variable transmission ratio gear sector rack and pinion implementation method, but is also applicable to the numerical solution of equidistant point cloud of gear tooth surfaces for various gear pairs designed based on meshing principles.
[0022] Of course, the above description is not limited to the examples above. Technical features not described in this invention can be implemented by or using existing technology, and will not be repeated here. The above embodiments and drawings are only used to illustrate the technical solutions of this invention and are not intended to limit this invention. This invention has been described in detail with reference to preferred embodiments. Those skilled in the art should understand that any changes, modifications, additions or substitutions made by those skilled in the art within the scope of this invention do not depart from the spirit of this invention and should also fall within the scope of protection of the claims of this invention.
Claims
1. A method for reconstructing point clouds of the tooth surface of a variable-gear sector rack and pinion, characterized in that, Includes the following steps: S1: Within the radial section of the variable transmission ratio gear sector with equal spacing, based on the spatial transformation relationship of the tooth profile of the involute rack end face in the radial section of the variable transmission ratio gear sector, the transformation tooth profile equation of the involute rack is constructed. Under the constraint motion of the variable transmission ratio curve and the shovel-shaped relationship, the tooth profile equation of the radial section of the variable transmission ratio gear sector with the transformation tooth profile shovel shape of the involute rack is obtained. Through spacing setting and numerical solution, the tooth profile point cloud of the variable transmission ratio gear sector with equal axial distance can be obtained. S2: Within the tooth profile range of the variable transmission ratio gear sector with equal axial spacing, set up a calculation circle with equal radial spacing, and construct a set of equations for the intersection of the calculation circle and the radial section tooth profile of the variable transmission ratio gear sector. The intersection is the point cloud of the radial tooth profile of the variable transmission ratio gear sector with equal radial spacing. In step S1, the transformation tooth profile equation of the involute rack is shown in formulas (1) and (2): （1） （2） Wherein, formulas (1) and (2) are respectively the transformation tooth profile equation and the transformation tooth vertex equation of the involute rack end face tooth profile; , These represent the coordinates of the transformed tooth profile point and the coordinates of the transformed tooth vertex of the involute rack, respectively. This represents the distance between the origin of the coordinate system and the involute tooth profile. This represents the distance between the tooth vertex and the perpendicular line passing through the origin of the tooth profile. This represents the distance between the tooth profile point and the tooth vertex. For assembly corner, For the width of the rack teeth, For tooth tip height, For tooth root height, For top gap, For pressure angle, These are the rack tooth profile parameters; In step S1, the tooth profile equations of the radial section of the variable thickness and variable transmission ratio tooth sector are shown in formulas (3) and (4): （3） （4） Among them, formulas (3) and (4) are the working tooth profile equation and the transition tooth profile equation of the radial section of the variable thickness and variable transmission ratio tooth sector, respectively; , These are the coordinates of the working tooth profile point and the transition tooth profile point of the radial section of the variable thickness and variable transmission ratio gear sector, respectively. For the gear sector rotation angle; The rack displacement is calculated by integrating the gear sector rotation angle onto the variable transmission ratio curve function of the gear sector rack pair. Center distance; , These are the unit normal vectors of the tooth profile points of the sector tooth and the relative velocities of the tooth profiles at the meshing points, respectively. The meshing equation represents the variable transmission ratio gear sector profile of the involute rack with a different tooth profile envelope.
2. The method for reconstructing point cloud of tooth surface of variable gear sector-variable transmission ratio gear sector rack pair according to claim 1, characterized in that: In step S2, the solution equations for the intersection of the calculation circle and the radial section of the variable transmission ratio gear sector are shown in equations (5) and (6): （5） （6） Among them, formulas (5) and (6) are respectively the solution equations for the radial working tooth profile and the transition tooth profile of the variable transmission ratio gear sector. To calculate the circular coordinates, To calculate the radius of a circle, To calculate the parameters of a circle, let represent the polar angle corresponding to any point on the circle; To calculate the tooth profile parameters at the intersection of the circle and the tooth profile of the variable transmission ratio gear sector, the solution set obtained by the calculation model (5) and (6) is substituted into the tooth profile equations (3) and (4) of the variable transmission ratio gear sector to obtain the tooth profile point cloud with equal radial spacing of the tooth profile of the variable transmission ratio gear sector.