Parametric modeling method of variable-ratio rack and pinion tooth profile considering machining errors

Abstract

The application provides a variable transmission ratio rack and pinion tooth profile parameterization modeling method considering machining errors, relates to the technical field of mechanical transmission design, and aims at the problem that the actual meshing track deviation is caused by the fact that the traditional variable transmission ratio transmission mechanism ignores the errors in the machining and assembling processes; the error variable is introduced at the source of the parameterization modeling; the inevitable tooth pitch deviation and eccentricity error are superimposed into the theoretical tooth profile coordinate equation when the mathematical model of the sector gear is constructed, the non-ideal sector gear tooth profile reflecting the actual manufacturing state is generated, the motion law defined by the target transmission ratio is combined, the variable transmission ratio rack tooth profile coordinate point in conjugate engagement is reversely solved, the simulation model containing the error is built to perform comparison and analysis, the nonlinear influence of the sector gear machining error on the final meshing performance is analyzed, and thus the design stage is guided to optimize the tolerance distribution or correct the tooth profile, and the stability and reliability of the variable transmission ratio transmission mechanism in the actual operation are improved.

Description

Technical Field

[0001] This invention relates to the field of mechanical transmission design technology, and specifically to a parametric modeling method for the tooth profile of a rack / gear with variable transmission ratio that takes into account machining errors. Background Technology

[0002] Variable ratio gear and rack transmission mechanisms, as key mechanical components enabling nonlinear motion control, are widely used in industrial automation equipment, precision engineering machinery, robot joint drives, and vehicle steering systems. These mechanisms, through special tooth profile designs, allow the meshing radius between the gear and rack to change according to a predetermined law during rotation, thereby achieving nonlinear adjustment of output speed or output force. For example, providing high thrust at the ends of the stroke and high speed in the middle. Currently, the industry mainly employs methods such as the envelope-based generating method, Boolean reduction algorithm, and numerical calculation methods based on meshing equations for the design of variable ratio gear and rack pairs. These methods typically use a preset target transmission ratio function and standard driving component parameters to construct a mathematical model to solve for the theoretical tooth profile point cloud of the driven component that satisfies the conjugate meshing condition, and then fit and generate a solid model, thus solving the problem of digital generation and parametric design of variable ratio tooth profiles.

[0003] However, the existing parametric modeling methods still have significant technical limitations when facing the demands of high-precision and high-reliability mechanical transmissions. Existing modeling theories are all based on the assumption of "ideal rigid geometry," meaning that the geometric dimensions, pitch distribution, and rotation center of gears and racks are assumed to be absolutely precise. However, in actual machining and assembly processes, tool wear, machine tool indexing errors causing pitch deviations, and eccentricity errors generated during installation are unavoidable. For fixed-ratio gears, these can be corrected using standard tolerance grades; however, for variable-ratio gear pairs, due to the continuous change in tooth profile curvature, they are highly sensitive to errors. Small pitch or eccentricity errors are amplified during nonlinear meshing, causing the actual meshing trajectory to deviate from the theoretical design, leading to sudden changes in transmission ratio, instantaneous jamming, and increased impact vibration or wear due to abnormal backlash. Summary of the Invention

[0004] In view of this, the present invention provides a parametric modeling method and system for the tooth profile of a variable transmission ratio rack / gear that takes into account machining errors. In the parametric modeling stage, the pitch error of the sector gear, the eccentricity error, and the pitch error of the rack are directly introduced to solve the problem of significant degradation in meshing performance caused by manufacturing tolerances.

[0005] The first objective of this invention is to provide a parametric modeling method for the tooth profile of a variable transmission ratio rack that takes into account machining errors, using the following approach: include: Obtain the target transmission ratio function of the transmission mechanism and the geometric parameters of the sector gear; the target transmission ratio function is the correspondence between the rotation angle of the sector gear and the transmission ratio of the transmission mechanism. Based on the target transmission ratio function and the geometric parameters of the sector gear, a gear and rack meshing coordinate system is established, and the correspondence between rack displacement and sector gear rotation angle is calculated. Error parameters from the machining process are introduced into the theoretical tooth profile model of the sector gear, and the tooth profile coordinates of the sector gear after introducing the errors are calculated and obtained. Based on the correspondence between rack displacement and sector gear rotation angle, and the sector gear tooth profile coordinates after introducing errors, the coordinate points of the variable transmission ratio rack tooth profile are solved. A three-dimensional model of a rack with a variable transmission ratio is generated by fitting the coordinate points of the rack tooth profile. A gear-rack meshing simulation model including the machining error of the sector gear is built, and the transmission ratio fluctuation and meshing performance are compared and analyzed under ideal conditions and under error conditions.

[0006] Furthermore, the process of solving for the coordinate points of the variable transmission ratio rack tooth profile includes: Define a calculation line for the random rack displacement. At each position of the calculation line, traverse all rack displacements and solve for the intersection points of the calculation line and the sector gear tooth profile after introducing errors. Select the intersection point with the largest coordinate value in the tooth height direction as the meshing point. The set of meshing points obtained by traversing all positions of the calculation line is the coordinate of the rack tooth profile point.

[0007] Furthermore, establishing the gear-rack meshing coordinate system includes: Establish a local coordinate system for the gear with the geometric center of the sector gear as the origin, and a global fixed coordinate system with the center of the tooth root line of the standard rack as the origin; The local coordinate system of the gear can rotate around its origin, and the calculation line corresponding to the rack tooth profile is parallel to the vertical axis of the global fixed coordinate system and moves along the horizontal axis with the rack.

[0008] Furthermore, the introduction of error parameters from the machining process into the theoretical tooth profile model of the sector gear includes: The pitch error and installation eccentricity error of the sector gear are introduced; the pitch error is superimposed on the reference angle parameter of the sector gear tooth profile, and the installation eccentricity error is superimposed on the eccentricity parameter of the sector gear, thereby correcting the sector gear tooth profile coordinates.

[0009] A second objective of this invention is to provide a parametric modeling system for the profile of a variable transmission ratio rack as described in the first objective, taking into account machining errors, comprising: The parameter acquisition module is configured to: acquire the target transmission ratio function of the transmission mechanism and the geometric parameters of the sector gear; the target transmission ratio function is the correspondence between the rotation angle of the sector gear and the transmission ratio of the transmission mechanism. The relationship derivation module is configured to: establish a gear and rack meshing coordinate system based on the target transmission ratio function and the geometric parameters of the sector gear, and calculate the correspondence between the rack displacement and the sector gear rotation angle; The error introduction module is configured to: introduce error parameters from the machining process into the theoretical tooth profile model of the sector gear, and calculate and obtain the tooth profile coordinates of the sector gear after introducing the error; The tooth profile generation module is configured to: solve for the coordinate points of the variable transmission ratio rack tooth profile based on the correspondence between the rack displacement and the sector gear rotation angle, and the sector gear tooth profile coordinates after introducing errors; The model generation module is configured to: generate a 3D model of a rack with a variable transmission ratio using the coordinate points of the rack tooth profile; build a gear and rack meshing simulation model that includes the machining error of the sector gear; and compare and analyze the transmission ratio fluctuation and meshing force changes under ideal and error conditions.

[0010] The third objective of this invention is to provide a parametric modeling method for the tooth profile of variable transmission ratio gears that takes into account machining errors, employing the following scheme: Obtain the target transmission ratio function of the transmission mechanism and the geometric parameters of the standard rack; Based on the target transmission ratio function and the geometric parameters of the standard rack, a gear-rack meshing coordinate system is established, and the correspondence between the standard rack displacement and the sector gear rotation angle is calculated. Error parameters from the machining process are introduced into the theoretical tooth profile model of a standard rack, and the rack tooth profile coordinates after introducing the errors are calculated and obtained. Based on the correspondence between the standard rack displacement and the sector gear rotation angle, and the rack tooth profile coordinates after introducing errors, the coordinate points of the variable transmission ratio sector gear tooth profile are solved. A three-dimensional model of a sector gear with variable transmission ratio is generated by fitting the coordinate points of the tooth profile of the sector gear. A gear-rack meshing simulation model including rack machining errors is built, and the transmission ratio fluctuation and meshing performance under ideal and error conditions are compared and analyzed.

[0011] Furthermore, the process of solving for the coordinate points of the variable transmission ratio sector gear tooth profile includes: Define a line segment that rotates around the rotation center of the gear. At each initial angle, traverse all rotation angles and solve for the intersection points of the line segment and the rack tooth profile after introducing errors. Select the intersection point that is closest to the rotation center and determine the coordinates of the tooth profile points of the sector gear based on the distance from the nearest intersection point to the rotation center.

[0012] Further, determining the tooth profile point coordinates of the sector gear based on the distance from the nearest intersection point to the center of rotation includes: The distance from the nearest intersection point to the center of rotation is taken as the polar radius. The cosine and sine values ​​of the initial angle of the rotation segment corresponding to this distance are multiplied by the polar radius to obtain the coordinates of the tooth profile point of the sector gear in the rectangular coordinate system.

[0013] Furthermore, the introduction of error parameters from the machining process into the theoretical tooth profile model of the standard rack includes: Introduce the pitch error of the rack; superimpose the pitch error into the formula for calculating the abscissa of the rack tooth profile point, thereby correcting the formula for calculating the coordinate of the rack tooth profile point.

[0014] A fourth objective of this invention is to provide a parametric modeling system for the tooth profile of a variable transmission ratio gear, as described in the first objective, taking into account machining errors, comprising: The parameter acquisition module is configured to: acquire the target transmission ratio function of the transmission mechanism and the geometric parameters of the sector gear; the target transmission ratio function is the correspondence between the rotation angle of the sector gear and the transmission ratio of the transmission mechanism. The relationship derivation module is configured to: establish a gear and rack meshing coordinate system based on the target transmission ratio function and the geometric parameters of the sector gear, and calculate the correspondence between the rack displacement and the sector gear rotation angle; The error introduction module is configured to: introduce error parameters from the machining process into the theoretical tooth profile model of the sector gear, and calculate and obtain the tooth profile coordinates of the sector gear after introducing the error; The tooth profile generation module is configured to: solve for the coordinate points of the variable transmission ratio rack tooth profile based on the correspondence between the rack displacement and the sector gear rotation angle, and the sector gear tooth profile coordinates after introducing errors; The model generation module is configured to: generate a 3D model of a rack with a variable transmission ratio using the coordinate points of the rack tooth profile; build a gear and rack meshing simulation model that includes the machining error of the sector gear; and compare and analyze the transmission ratio fluctuation and meshing force changes under ideal and error conditions.

[0015] Compared with the prior art, the advantages and positive effects of this invention are: To address the issue that traditional variable ratio transmission mechanisms neglect errors in machining and assembly that lead to deviations in the actual meshing trajectory, this invention introduces error variables at the source of parametric modeling. When constructing the mathematical model of the sector gear, unavoidable pitch and eccentricity errors are superimposed on the theoretical tooth profile coordinate equation, generating a non-ideal sector gear tooth profile that reflects the actual manufacturing state. Based on this, and combined with the motion law defined by the target transmission ratio, the coordinate points of the variable ratio rack tooth profile that meshes with it are solved in reverse. This realizes the pre-production inspection of manufacturing tolerances to the design stage. By building a simulation model that includes errors for comparative analysis, the nonlinear impact of sector gear machining errors on the final meshing performance can be accurately quantified. This guides the optimization of tolerance allocation or correction of tooth profile during the design stage, significantly reducing trial production costs and improving the stability and reliability of the variable ratio transmission mechanism in actual operation.

[0016] When constructing the mathematical model of a standard rack, the tooth pitch error parameter is introduced to correct the theoretical tooth profile coordinates, generating a rack model that includes machining deviations. Using this as a boundary condition, and combined with the preset variable transmission ratio motion law, the coordinate points of the matching variable transmission ratio sector gear tooth profile are derived in reverse using a conjugate solution algorithm. This realizes the design transformation from ideal rigid matching to real error matching. By constructing a simulation model that includes rack errors for quantitative analysis, the specific influence mechanism of rack machining accuracy on the meshing performance of variable transmission ratio gear pairs can be effectively revealed. This guides the error-resistant optimization design of sector gear tooth profiles or in reverse determines the reasonable machining tolerance level of racks, improving the accuracy retention and operational stability of transmission mechanisms in nonlinear speed change processes.

[0017] In terms of coordinate system establishment, by constructing a local coordinate system for rotating gears and a globally fixed coordinate system for horizontal movement, the complex relative motion of the variable transmission ratio mechanism is decoupled into a rigorous geometric mapping, ensuring the synchronous evolution of the calculated straight line and the gear rotation angle under the constraint of the target transmission ratio function. Regarding the error introduction mechanism, by directly superimposing the pitch error onto the tooth profile reference angle and the eccentricity error onto the geometric offset, a high-fidelity mathematical description of machining defects is achieved, enabling the model to realistically simulate tooth profile distortion caused by production deviations. By defining a "calculation straight line" that varies with displacement and selecting the coordinate extreme points in the tooth height direction, this method numerically simulates the "sweeping" process of the gear on the rack space, thereby accurately capturing the actual contact trajectory that still satisfies the conjugate meshing condition under error interference. This not only reduces the fundamental errors in traditional generating method modeling but also enables the designed rack tooth profile to achieve precise matching with the sector gear with manufacturing defects under "non-ideal conditions," fundamentally predicting and solving meshing interference caused by pitch deviation and installation eccentricity, and improving the motion stability of the variable transmission ratio transmission pair under complex working conditions.

[0018] This invention provides two inverse modeling paths: "inverse rack calculation including gear error" and "inverse gear calculation including rack error". It is applicable to gear and rack transmission mechanisms that require transmission accuracy and variable transmission ratio characteristics, such as industrial automation equipment, precision engineering machinery, robot joint drive, and vehicle steering systems, and has broad engineering application value. Attached Figure Description

[0019] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0020] Figure 1 This is a schematic diagram of the process for parametric modeling of the tooth profile of the variable transmission ratio rack considering machining errors in Embodiments 1 and 2 of the present invention.

[0021] Figure 2 The graphs show the target transmission ratio function curves of the variable transmission ratio rack tooth profile in Embodiments 1 and 2 of the present invention.

[0022] Figure 3 This is a schematic diagram of the coordinate system for calculating the tooth profile of the variable transmission ratio rack in Embodiments 1 and 2 of the present invention.

[0023] Figure 4 This is a schematic diagram illustrating the solution of the meshing point of the variable transmission ratio rack tooth profile in Embodiments 1 and 2 of the present invention.

[0024] Figure 5 This is a schematic diagram of the tooth profile of the variable transmission ratio rack in Embodiments 1 and 2 of the present invention.

[0025] Figure 6 This is a comparative schematic diagram of the tooth profile of the variable transmission ratio rack with the introduction of sector gear eccentricity error in Embodiments 1 and 2 of the present invention.

[0026] Figure 7 This is a comparative schematic diagram of the tooth profile of the variable transmission ratio rack with the introduction of sector gear tooth thickness error in Embodiments 1 and 2 of the present invention.

[0027] Figure 8 This is a comparative schematic diagram of the tooth profile of the variable transmission ratio rack with the introduction of sector gear eccentricity and tooth thickness error in Embodiments 1 and 2 of the present invention.

[0028] Figure 9 This is a schematic diagram of the simulation model of variable transmission ratio gear rack meshing with sector gear machining error in Embodiments 1 and 2 of the present invention.

[0029] Figure 10 This is a schematic diagram of the process for parametric modeling of the tooth profile of a variable transmission ratio sector gear considering machining errors in Embodiments 3 and 4 of the present invention.

[0030] Figure 11 The graphs show the target transmission ratio function curves of the variable transmission ratio sector gear tooth profile in Embodiments 3 and 4 of the present invention.

[0031] Figure 12 This is a schematic diagram of the coordinate system for calculating the tooth profile of the variable transmission ratio sector gear in Embodiments 3 and 4 of the present invention.

[0032] Figure 13 This is a schematic diagram illustrating the solution of the meshing point of the variable transmission ratio sector gear tooth profile in Embodiments 3 and 4 of the present invention.

[0033] Figure 14 This is a schematic diagram of the tooth profile of the variable transmission ratio sector gear in Embodiments 3 and 4 of the present invention.

[0034] Figure 15 This is a comparative schematic diagram of the tooth profile of the variable transmission ratio sector gear with rack pitch error introduced in Embodiments 3 and 4 of the present invention.

[0035] Figure 16 This is a schematic diagram of the simulation model of variable transmission ratio gear and rack meshing with rack machining error in Embodiments 3 and 4 of the present invention. Detailed Implementation

[0036] Example 1 In a typical embodiment of the present invention, such as Figures 1-9 As shown, a parametric modeling method for the tooth profile of a variable transmission ratio rack considering machining errors is presented, including: Obtain the target transmission ratio function of the transmission mechanism and the geometric parameters of the sector gear; the target transmission ratio function is the correspondence between the rotation angle of the sector gear and the transmission ratio of the transmission mechanism. Based on the target transmission ratio function and the geometric parameters of the sector gear, a gear and rack meshing coordinate system is established, and the correspondence between rack displacement and sector gear rotation angle is calculated. Error parameters from the machining process are introduced into the theoretical tooth profile model of the sector gear, and the tooth profile coordinates of the sector gear after introducing the errors are calculated and obtained. Based on the correspondence between rack displacement and sector gear rotation angle, and the sector gear tooth profile coordinates after introducing errors, the coordinate points of the variable transmission ratio rack tooth profile are solved. A three-dimensional model of a rack with a variable transmission ratio is generated by fitting the coordinate points of the rack tooth profile. A gear-rack meshing simulation model including the machining error of the sector gear is built, and the transmission ratio fluctuation and meshing performance are compared and analyzed under ideal conditions and under error conditions.

[0037] Solving for the coordinate points of the variable transmission ratio rack tooth profile includes: Define a calculation line for the random rack displacement. At each position of the calculation line, traverse all rack displacements and solve for the intersection points of the calculation line and the sector gear tooth profile after introducing errors. Select the intersection point with the largest coordinate value in the tooth height direction as the meshing point. The set of meshing points obtained by traversing all positions of the calculation line is the coordinate of the rack tooth profile point.

[0038] Establishing the gear and rack meshing coordinate system includes: Establish a local coordinate system for the gear with the geometric center of the sector gear as the origin, and a global fixed coordinate system with the center of the tooth root line of the standard rack as the origin; The local coordinate system of the gear can rotate around its origin, and the calculation line corresponding to the rack tooth profile is parallel to the vertical axis of the global fixed coordinate system and moves along the horizontal axis with the rack.

[0039] Error parameters from the machining process are introduced into the theoretical tooth profile model of the sector gear, including: The pitch error and installation eccentricity error of the sector gear are introduced; the pitch error is superimposed on the reference angle parameter of the sector gear tooth profile, and the installation eccentricity error is superimposed on the eccentricity parameter of the sector gear, thereby correcting the sector gear tooth profile coordinates.

[0040] Specifically, in this embodiment, the target transmission ratio function of the steering gear and the geometric parameters of the sector gear are obtained. The target transmission ratio function specifically refers to the correspondence between the rotation angle of the sector gear in the steering gear and the transmission ratio. The geometric parameters of the sector gear include module, pressure angle, total number of teeth, tooth tip height coefficient, clearance coefficient, displacement coefficient, installation eccentricity, etc. Based on the target transmission ratio function and the geometric parameters of the sector gear, the coordinate points of the tooth profile of the variable transmission ratio rack are calculated and obtained; The specific steps for calculating the coordinates of the tooth profile points of the variable transmission ratio rack include: Construct a gear and rack meshing coordinate system, with the geometric center of the gear as the origin. Establish a local coordinate system for the gear and a global fixed coordinate system. The local coordinate system can rotate around the origin; define this rotation angle as... Define the rack coordinate system line as a straight line parallel to the y-axis of the global fixed coordinate system, fixedly connected to the rack, and capable of displacement with the rack. Define the coordinates of this line as x=x i The rack displacement is s; Based on the relationship between the transmission ratio and the gear shaft rotation angle in the target transmission ratio function, the rotation angle is solved according to the rack displacement s. Thus, the rack displacement s and the sector gear rotation angle are obtained. The correspondence; By introducing pitch and eccentricity errors during gear machining, the gear tooth profile coordinates after introducing the errors are calculated, and the gear tooth profile curves after introducing the errors that participate in meshing are obtained. Calculate the coordinates of the intersection point between the straight line in the rack coordinate system and the gear tooth profile after introducing errors, at x=x i Iterate through all displacements s, solve for the coordinates of the intersection points of the rack coordinate system line and the gear tooth profile after introducing errors under all displacements s, and take the largest ordinate y. imax The coordinates of the intersection point are the meshing points of the gear tooth profile and rack tooth profile after introducing errors. This is determined by traversing all rack coordinates X. i The result (x) i ,y imax The coordinate set is the coordinate of the tooth profile point of the rack.

[0041] Based on the calculated coordinates of the rack tooth profile points, fit the variable transmission ratio rack tooth profile curve, generate a three-dimensional model of the variable transmission ratio rack, and build a simulation model of the variable transmission ratio gear rack meshing that includes the machining error of the sector gear. Based on a simulation model of gear and rack meshing with variable transmission ratio that includes sector gear machining errors, this study analyzes the gear and rack meshing performance under the influence of errors, analyzes the transmission ratio and meshing force, and compares the differences in meshing performance under ideal conditions and under conditions with errors, thereby exploring the influence of gear machining and assembly errors on meshing performance.

[0042] Combination Figures 1-9 This paper provides a detailed explanation of the parametric modeling method for the tooth profile of a variable transmission ratio rack that takes into account machining errors.

[0043] like Figure 1 As shown, based on the known target transmission ratio function and standard gear geometric parameters, a rack tooth profile that meshes with a standard gear and satisfies the target transmission ratio function is designed. Gear machining errors are introduced during the design process to achieve parametric design and modeling of a variable transmission ratio rack tooth profile that includes sector gear machining errors.

[0044] Step 1: Obtain the target transmission ratio function of the steering gear and the geometric parameters of the sector gear.

[0045] 1.1 Obtain the target gear ratio function of the steering gear.

[0046] (1); In this embodiment, the target transmission ratio function is selected as follows: Figure 2 As shown, the transmission ratio function is a piecewise function, and the sector gear rotation angle... Between ±48°, the transmission ratio i increases from 46 to 54, and a linear transition is adopted in the transition section. The transmission ratio function is shown in Formula 1.

[0047] 1.2 Obtain the geometric parameters of the sector gear.

[0048] The geometric parameters of a sector gear include module, pressure angle, total number of teeth, addendum coefficient, clearance coefficient, displacement coefficient, and mounting eccentricity. The geometric parameters of the sector gear selected in this embodiment are shown in Table 1 below.

[0049] Table 1 Geometric parameters of sector gears Modulus 11.5mm pressure angle 25° Total number of teeth 8 Tooth tip height coefficient 1 porosity 0.25 displacement coefficient 0.406087 Installation eccentricity 0.6mm Step 2: Calculate and obtain the coordinate points of the rack tooth profile with variable transmission ratio.

[0050] 2.1 Establish the gear and rack meshing coordinate system.

[0051] like Figure 3 As shown, with the geometric center of the sector gear as the origin, a local coordinate system x0o0y0 and a global fixed coordinate system xoy are established. The local coordinate system can rotate around the origin, and this rotation angle is defined as... Define the rack coordinate system line as a straight line parallel to the y-axis of the global fixed coordinate system, fixedly connected to the rack, and capable of displacement with the rack. Define the coordinates of this line as x=x i The rack displacement is s. Tooth profiles a, b, and c are the tooth profiles on the sector gear that participate in the variable transmission ratio meshing. Points 1, 2, 4, 3, 5, and 6 are defined as the tooth root and tooth vertex of tooth profiles a, b, and c, respectively. Let be the reference angle at any point t on the gear tooth profile. R is the pressure angle at point t. t Let t be the distance from point t to the geometric center of the gear, and p be the eccentricity between the geometric center and the center of rotation of the gear.

[0052] 2.2 Solving for the rack displacement s and sector gear rotation angle Correspondence.

[0053] The transmission ratio of the gear rack pair varies with the rotation angle of the involute gear. It changes with the rotation angle of the involute gear. The formula for calculating the gear rotation angle is derived from the relationship between the gear ratio rack displacement s and the gear rotation angle. The specific formulas are shown in (2) to (5).

[0054] (2); (3); (4); (5).

[0055] 2.3 Calculate the coordinates of the gear tooth profile points and introduce machining errors. (s-loop) The coordinates of the gear tooth profiles a, b, and c involved in meshing are represented in the coordinate system established above. The coordinate value of any point on the tooth profile satisfies equation (6). (6); in, Let t be the distance from point t on the tooth profile to the geometric center of the gear. Let be the reference angle at any point t on the gear tooth profile, and p be the eccentricity between the gear's geometric center and its center of rotation. and Satisfying equations (7) and (8), This refers to the gear rotation angle.

[0056] (7); (8); in, The base circle radius of the gear. This is the reference angle at point 1 on the gear tooth profile. Let t be the pressure angle at any point t on the gear tooth profile.

[0057] Therefore, the coordinates of the tooth profiles a, b, and c involved in the meshing of the gear can be obtained as shown in equations (9), (10), and (11), respectively. (9); (10); (11); in, , , The reference angles are at points 1, 3, and 5. The pressure angle at point i (i=1,2,...,6), and the gear rotation angle. The displacement s and rotation angle can be obtained from equations (2) to (5) based on the transmission ratio function and the rack displacement s. One-to-one correspondence, when the displacement s is 0, the rotation angle Since the value is also 0, by iterating through the displacement s from the maximum value of the deviation from the center position to the center position, the corresponding rotation angle can be calculated. Range, based on the obtained turning angle The gear tooth profile position corresponding to each rack displacement s can then be calculated.

[0058] Introducing gear pitch error Eccentricity error The reference angle and eccentricity after introducing the error are denoted as... and They are represented by equations (12) and (13) respectively.

[0059] (12); (13); Therefore, the coordinates of the tooth profile points a, b, and c of the gear after introducing errors can be represented by equations (14), (15), and (16).

[0060] (14); (15); (16).

[0061] 2.4 Calculate the coordinates of the intersection point between the straight line in the rack coordinate system and the gear tooth profile. (x-loop) Define a straight line x = x passing through point t. i A straight line fixed to the rack tooth profile and displaced with the rack displacement is called the calculation line. At each instant during the transmission process, the calculation line intersects the corresponding gear tooth profile after introducing the error. The change in the ordinate value of the intersection point between the calculation line and the gear tooth profile after introducing the error follows a certain pattern: the ordinate value of the intersection point increases from small to large, reaching a maximum value y at the moment when the tooth profile point t engages in meshing. imax ,like Figure 4 As shown, the coordinate value of the tooth profile point t is equal to the coordinate value of the intersection point where the extreme value is obtained during the transmission process. Therefore, by finding the extreme value of the intersection point of the calculation line passing through the tooth profile point and the gear tooth profile, the coordinate value of the tooth profile point of the variable ratio rack can be obtained.

[0062] By traversing the horizontal coordinates of the rack tooth profile points from the left end to the right end of the meshing part of the rack, and solving for the maximum value of the vertical coordinate under each horizontal coordinate, the combination of these coordinates is the set of coordinate points of the variable transmission ratio rack tooth profile.

[0063] Step 3: Modeling the tooth profile of the rack with variable transmission ratio, including the machining error of the sector gear, based on the mathematical model of variable transmission ratio meshing.

[0064] The variable transmission ratio rack tooth profile designed based on the above-mentioned variable transmission ratio rack tooth profile design theory is as follows: Figure 5 As shown.

[0065] For recirculating ball steering systems, due to their critical function in vehicle steering, the gear precision grade is typically required to be no lower than grade 8. This corresponds to a gear shaft eccentricity error controlled within 0.03mm. When the eccentricity error exceeds ±0.03mm, the wear rate of the eccentric shaft bearing increases by 30%~50%, and the tooth surface contact stress increases, leading to premature pitting. Simultaneously, the gear tooth thickness error must be within ±0.04mm, as this directly determines the meshing backlash. This invention provides a parametric modeling difference for variable transmission ratio racks, incorporating machining errors in the sector gear. The eccentricity error and tooth thickness error of the sector gear are both taken as 0.02mm, and this error is introduced into the parametric modeling process of the variable transmission ratio rack. The tooth profile difference is as follows: Figure 6 , Figure 7 as well as Figure 8 As shown. In the tooth profile of a variable transmission ratio rack that includes the eccentricity error of the sector gear, tooth profile a shifts inward towards the original tooth profile, while tooth profiles b and c shift outward towards the original tooth profile; in the tooth profile of a variable transmission ratio rack that includes the tooth thickness error of the sector gear, tooth profiles a and c shift inward towards the original tooth profile, while tooth profile b shifts outward towards the original tooth profile; in the tooth profile of a variable transmission ratio rack that includes both the eccentricity error and the tooth thickness error of the sector gear, tooth profiles a and c shift inward towards the original tooth profile, while tooth profile b shifts outward towards the original tooth profile.

[0066] A three-dimensional model was established based on the tooth profile of the variable transmission ratio rack, and a variable transmission ratio meshing simulation model incorporating the machining error of the sector gear was built, such as... Figure 9 As shown, the gear and rack meshing performance under the influence of error is analyzed based on the simulation model. The transmission ratio and meshing force are analyzed, and the difference in meshing performance under ideal conditions and under the condition of error is compared, so as to explore the influence of gear machining error on meshing performance.

[0067] Example 2 In another typical embodiment of the present invention, such as Figures 1-9 As shown, a parametric modeling system for the tooth profile of a variable transmission ratio rack considering machining errors is presented, including: The parameter acquisition module is configured to: acquire the target transmission ratio function of the transmission mechanism and the geometric parameters of the sector gear; the target transmission ratio function is the correspondence between the rotation angle of the sector gear and the transmission ratio of the transmission mechanism. The relationship derivation module is configured to: establish a gear and rack meshing coordinate system based on the target transmission ratio function and the geometric parameters of the sector gear, and calculate the correspondence between the rack displacement and the sector gear rotation angle; The error introduction module is configured to: introduce error parameters from the machining process into the theoretical tooth profile model of the sector gear, and calculate and obtain the tooth profile coordinates of the sector gear after introducing the error; The tooth profile generation module is configured to: solve for the coordinate points of the variable transmission ratio rack tooth profile based on the correspondence between the rack displacement and the sector gear rotation angle, and the sector gear tooth profile coordinates after introducing errors; The model generation module is configured to: generate a 3D model of a rack with a variable transmission ratio using the coordinate points of the rack tooth profile; build a gear and rack meshing simulation model that includes the machining error of the sector gear; and compare and analyze the transmission ratio fluctuation and meshing force changes under ideal and error conditions.

[0068] The working method of the variable transmission ratio rack tooth profile parametric modeling system that takes into account machining errors is the same as that in Example 1, and will not be repeated here.

[0069] Example 3 In a typical embodiment of the present invention, such as Figures 10-15 As shown, a parametric modeling method for the tooth profile of variable transmission ratio gears considering machining errors is presented, including: Obtain the target transmission ratio function of the transmission mechanism and the geometric parameters of the standard rack; Based on the target transmission ratio function and the geometric parameters of the standard rack, a gear-rack meshing coordinate system is established, and the correspondence between the standard rack displacement and the sector gear rotation angle is calculated. Error parameters from the machining process are introduced into the theoretical tooth profile model of a standard rack, and the rack tooth profile coordinates after introducing the errors are calculated and obtained. Based on the correspondence between the standard rack displacement and the sector gear rotation angle, and the rack tooth profile coordinates after introducing errors, the coordinate points of the variable transmission ratio sector gear tooth profile are solved. A three-dimensional model of a sector gear with variable transmission ratio is generated by fitting the coordinate points of the tooth profile of the sector gear. A gear-rack meshing simulation model including rack machining errors is built, and the transmission ratio fluctuation and meshing performance under ideal and error conditions are compared and analyzed.

[0070] Solving for the coordinate points of the tooth profile of the variable transmission ratio sector gear includes: Define a line segment of rotation about the gear's rotation center. At each initial angle, traverse all rotation angles and solve for the intersection points of the line segment of rotation with the rack tooth profile after introducing errors. Select the intersection point that is closest to the rotation center, and determine the coordinates of the tooth profile points of the sector gear based on the distance from this closest intersection point to the rotation center. The coordinates of the tooth profile points of the sector gear are determined based on the distance from the nearest intersection point to the center of rotation, including: The distance from the nearest intersection point to the center of rotation is taken as the polar radius. The cosine and sine values ​​of the initial angle of the rotation segment corresponding to this distance are multiplied by the polar radius to obtain the coordinates of the tooth profile point of the sector gear in the rectangular coordinate system.

[0071] Error parameters from the machining process are introduced into the theoretical tooth profile model of a standard rack, including: Introduce the pitch error of the rack; superimpose the pitch error into the formula for calculating the abscissa of the rack tooth profile point, thereby correcting the formula for calculating the coordinate of the rack tooth profile point.

[0072] Specifically, in this embodiment, the target transmission ratio function of the steering gear and the geometric parameters of the standard rack are obtained. The target transmission ratio function specifically refers to the correspondence between the rotation angle of the sector gear in the steering gear and the transmission ratio. The geometric parameters of the standard rack include the module, pressure angle, tooth tip height coefficient, and tip clearance coefficient. Based on the target transmission ratio function and the geometric parameters of the standard rack, the coordinate points of the tooth profile of the variable transmission ratio sector gear are calculated and obtained; The steps for calculating the coordinates of the tooth profile points of a sector gear with a variable transmission ratio include the following: Establish a gear-rack meshing coordinate system. Using the midpoint of the standard rack tooth pitch root line as the origin, establish a global fixed coordinate system with the rack tooth pitch direction as the positive x-axis and the rack tooth direction as the positive y-axis. Establish a local gear coordinate system with the gear's rotation center as the origin. This local coordinate system can rotate around the origin. Define a rotational line segment with a length equal to the gear's addendum circle radius. This rotational line segment can rotate around the rotation center, with a rotation angle of θ. Define the angle as 0° when the rotating line segment is in the same direction as the positive x-axis, and the initial angle is... Define the rack as capable of displacement along the x-axis of the global fixed coordinate system, and define this displacement as s; Based on the relationship between the transmission ratio and the gear shaft rotation angle in the target transmission ratio function, according to the rotation angle Solve for the rack displacement s to obtain the relationship between the rack displacement s and the sector gear rotation angle. The correspondence; By introducing the pitch error during rack machining, the rack tooth profile coordinates after introducing the error are calculated to obtain the rack tooth profile lines that participate in meshing after introducing the error; Calculate the coordinates of the intersection point of the rotated line segment and the rack tooth profile after introducing the error. = i Iterate through all corners. Solve for all corners The coordinates of the intersection points of the lower rotating line segment and the rack tooth profile after introducing the error are taken. The intersection point with the smallest distance from the rotation center is selected. The product of the distance from this point to the rotation center and the cosine and sine of the initial angle is the coordinate of the meshing point of the rack tooth profile and the sector gear tooth profile after introducing the error. This process is repeated for all initial angles of the sector gears. The set of intersection points with the minimum distance to the rotation center obtained at each initial angle is the coordinate of the tooth profile point of the sector gear.

[0073] Based on the calculated coordinates of the sector gear tooth profile points, the tooth profile curve of the variable transmission ratio sector gear is fitted, a three-dimensional model of the variable transmission ratio sector gear is generated, and a simulation model of variable transmission ratio gear and rack meshing including rack machining errors is built. Based on a simulation model of gear and rack meshing with variable transmission ratio that includes rack machining errors, this paper analyzes the gear and rack meshing performance under the influence of errors, analyzes the transmission ratio and meshing force, and compares the difference in meshing performance under ideal conditions and under conditions with errors, thereby exploring the influence of different errors on meshing performance.

[0074] Combination Figures 10-15 This paper provides a detailed explanation of the parametric modeling method for the tooth profile of variable transmission ratio sector gears, taking into account machining errors.

[0075] like Figure 10 As shown, this embodiment designs a sector gear tooth profile that meshes with a standard rack, based on the known target transmission ratio function, standard rack geometric parameters, and the total number of teeth and displacement coefficient of the designed variable transmission ratio sector gear. In the design process, the machining error of the standard rack is introduced to achieve parametric design and modeling of the variable transmission ratio sector gear tooth profile that includes the machining error of the rack.

[0076] Step 1: Obtain the target gear ratio function of the steering gear and the geometric parameters of the standard rack.

[0077] 1.1 Obtain the target gear ratio function of the steering gear.

[0078] In this embodiment, the target transmission ratio function is selected as follows: Figure 11 As shown, the transmission ratio function is a piecewise function, and the sector gear rotation angle... Between ±48°, the gear ratio i increases from 46 to 54, and the transition section uses a cosine function transition, as shown in Formula 17: (17); 1.2 Obtain the geometric parameters of the standard rack and the total number of teeth and displacement coefficient of the designed variable transmission ratio sector gear. The standard rack geometry parameters include module, pressure angle, addendum coefficient, and clearance coefficient. The required geometry parameters are selected in this embodiment as shown in Table 2 below.

[0079] Table 2 Required Geometric Parameters Modulus 10mm pressure angle 25° Tooth tip height coefficient 1 porosity 0.25 Step 2: Calculate and obtain the coordinate points of the tooth profile of the variable transmission ratio sector gear.

[0080] 2.1 Establish the gear and rack meshing coordinate system.

[0081] like Figure 12 As shown, a global fixed coordinate system xoy is established with the midpoint of the standard rack tooth pitch root line as the origin, and the rack tooth pitch direction as the positive x-axis and the rack tooth direction as the positive y-axis. A local coordinate system x1o1y1 is established with the gear rotation center as the origin. This local coordinate system can rotate around o1. A rotation segment o1t with a length equal to the radius of the gear addendum circle is defined. This rotation segment can rotate around the rotation center with a rotation angle of θ. x1'o1'y1' and o1't' are the local coordinate system and rotation segment of the rotated gear. The rotation segment is defined as 0° when it is in the same direction as the positive x-axis, and the initial angle is... Define the rack as capable of displacement along the x-axis of the global fixed coordinate system, and define this displacement as s.

[0082] 2.2 Solving for the standard rack displacement s and the sector gear rotation angle Correspondence.

[0083] The transmission ratio of the gear rack pair varies with the rotation angle of the involute gear. It changes according to the rotation angle of the sector gear. The relationship with rack displacement s is used to derive the formula for calculating rack displacement, and the specific formulas are shown in equations (2) to (4).

[0084] 2.3 Calculate the coordinates of the rack tooth profile points and introduce machining errors. (s-loop) Represent the meshing rack tooth profiles a, b, and c in the coordinate system established above. Define the x-coordinates of the tooth apex and tooth root on tooth profiles a, b, and c as x_top_a, x_root_a, x_top_b, x_root_b, x_top_c, and x_root_c, respectively, when the rack displacement is 0. The y-coordinate of the tooth apex is the total tooth height h, and the y-coordinate of the tooth root is 0. Then, any point on the rack tooth profiles a, b, and c satisfies the following equations (18), (19), and (20). (18); (19); (20); Where (x_a, y_a) is any point on rack tooth profile a, (x_b, y_b) is any point on rack tooth profile b, (x_c, y_c) is any point on rack tooth profile c, and s is the rack displacement value, which can be obtained from equations (2) to (5) based on the transmission ratio function and gear rotation angle. What we need is the displacement s and the rotation angle. One-to-one correspondence, corner When the value is 0, the displacement s is also 0, and the rotation angle is... By iterating from the maximum value deviating from the center position back to the center position, the corresponding displacement s can be calculated. Based on the obtained displacement s, each rotation angle can be calculated. The corresponding rack tooth profile position.

[0085] Introducing rack pitch error After introducing the error into the calculation formula of the rack tooth profile point, we can obtain equations (21), (22), and (23).

[0086] (twenty one); (twenty two); (twenty three).

[0087] 2.4 Calculate the coordinates of the intersection point between the rotating line segment and the rack tooth profile. (x-loop) Define a line segment of rotation passing through the center of rotation, with a length equal to the radius of the gear's addendum circle, which rotates with the gear. At each instant during the transmission process, this rotating line segment intersects the corresponding rack tooth profile after the introduction of error. The distance between the intersection point of the rotating line segment and the rack tooth profile after the introduction of error and the center of rotation follows a certain pattern, decreasing from a large value to a minimum value r at the moment when the tooth profile point t engages in meshing. imax ,like Figure 13 As shown, the coordinate value of the tooth profile point t is equal to the product of the minimum distance and the initial angle cosine and sine of the rotating line. Therefore, by obtaining the distance from the intersection of the rotating line segment and the rack tooth profile to the center of rotation, the coordinate value of the tooth profile point of the gear with the variable ratio can be obtained.

[0088] By traversing the rotating line segment from the left limit position to the right limit position of the meshing part of the gear, the minimum distance between the intersection point of the rotating line segment and the rack tooth profile at each initial angle is solved. Multiplying this minimum value by the cosine of the initial angle, the resulting coordinate set is the coordinate point set of the gear tooth profile of the variable transmission ratio gear.

[0089] Step 3: Modeling the tooth profile of the variable transmission ratio sector gear of the steering gear, including rack machining errors, based on the variable transmission ratio meshing mathematical model.

[0090] The variable transmission ratio rack tooth profile designed based on the above-mentioned variable transmission ratio rack tooth profile design theory is as follows: Figure 14 As shown.

[0091] Typically, the pitch error of the rack is required to be kept within ±0.02mm. This invention addresses the differences in parametric modeling of variable transmission ratio sector gears that include rack error. Taking the rack pitch error as 0.02mm, this error is introduced into the parametric modeling process of the sector gear, and the tooth profile differences are as follows: Figure 15 As shown, tooth profile a shifts outward from the original tooth profile, tooth profile b shifts inward from the original tooth profile, and tooth profile c coincides with the original tooth profile. This is due to the increased pitch of the rack meshing with it.

[0092] A three-dimensional model was established based on the tooth profile of the variable transmission ratio sector gear, and a variable transmission ratio meshing simulation model incorporating the machining error of the sector rack was built, such as... Figure 16 As shown, the gear and rack meshing performance under the influence of error is analyzed based on the simulation model. The transmission ratio and meshing force are analyzed, and the difference in meshing performance under ideal conditions and under the condition of error is compared, so as to explore the influence of rack machining error on meshing performance.

[0093] Example 4 In another typical embodiment of the present invention, such as Figures 10-15 As shown, a rack and pinion variable transmission ratio tooth profile parametric modeling system considering machining errors is presented, including: The parameter acquisition module is configured to: acquire the target transmission ratio function of the transmission mechanism and the geometric parameters of the sector gear; the target transmission ratio function is the correspondence between the rotation angle of the sector gear and the transmission ratio of the transmission mechanism. The relationship derivation module is configured to: establish a gear and rack meshing coordinate system based on the target transmission ratio function and the geometric parameters of the sector gear, and calculate the correspondence between the rack displacement and the sector gear rotation angle; The error introduction module is configured to: introduce error parameters from the machining process into the theoretical tooth profile model of the sector gear, and calculate and obtain the tooth profile coordinates of the sector gear after introducing the error; The tooth profile generation module is configured to: solve for the coordinate points of the variable transmission ratio rack tooth profile based on the correspondence between the rack displacement and the sector gear rotation angle, and the sector gear tooth profile coordinates after introducing errors; The model generation module is configured to: generate a 3D model of a rack with a variable transmission ratio using the coordinate points of the rack tooth profile; build a gear and rack meshing simulation model that includes the machining error of the sector gear; and compare and analyze the transmission ratio fluctuation and meshing force changes under ideal and error conditions.

[0094] The working method of the rack and pinion gear tooth profile parametric modeling system that takes into account machining errors is the same as that of the gear tooth profile parametric modeling method that takes into account machining errors in Example 3, and will not be repeated here.

[0095] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A parametric modeling method for the tooth profile of a rack with variable transmission ratio considering machining errors, characterized in that, include: Obtain the target transmission ratio function of the transmission mechanism and the geometric parameters of the sector gear; The target transmission ratio function is the relationship between the rotation angle of the sector gear in the transmission mechanism and the transmission ratio. Based on the target transmission ratio function and the geometric parameters of the sector gear, a gear and rack meshing coordinate system is established, and the correspondence between rack displacement and sector gear rotation angle is calculated. Error parameters from the machining process are introduced into the theoretical tooth profile model of the sector gear, and the tooth profile coordinates of the sector gear after introducing the errors are calculated and obtained. Based on the correspondence between rack displacement and sector gear rotation angle, and the sector gear tooth profile coordinates after introducing errors, the coordinate points of the variable transmission ratio rack tooth profile are solved. A three-dimensional model of a rack with a variable transmission ratio is generated by fitting the coordinate points of the rack tooth profile. A gear-rack meshing simulation model including the machining error of the sector gear is built, and the transmission ratio fluctuation and meshing performance are compared and analyzed under ideal conditions and under error conditions.

2. The parametric modeling method for the tooth profile of a variable transmission ratio rack considering machining errors as described in claim 1, characterized in that, The coordinate points for solving the variable transmission ratio rack tooth profile include: Define a calculation line for the random rack displacement. At each position of the calculation line, traverse all rack displacements and solve for the intersection points of the calculation line and the sector gear tooth profile after introducing errors. Select the intersection point with the largest coordinate value in the tooth height direction as the meshing point. The set of meshing points obtained by traversing all positions of the calculation line is the coordinate of the rack tooth profile point.

3. The parametric modeling method for the tooth profile of a variable transmission ratio rack considering machining errors as described in claim 2, characterized in that, Establishing the gear and rack meshing coordinate system includes: Establish a local coordinate system for the gear with the geometric center of the sector gear as the origin, and a global fixed coordinate system with the center of the tooth root line of the standard rack as the origin; The local coordinate system of the gear can rotate around its origin, and the calculation line corresponding to the rack tooth profile is parallel to the vertical axis of the global fixed coordinate system and moves along the horizontal axis with the rack.

4. The parametric modeling method for the tooth profile of a variable transmission ratio rack considering machining errors as described in claim 1, characterized in that, The introduction of error parameters from the machining process into the theoretical tooth profile model of the sector gear includes: The pitch error and installation eccentricity error of the sector gear are introduced; the pitch error is superimposed on the reference angle parameter of the sector gear tooth profile, and the installation eccentricity error is superimposed on the eccentricity parameter of the sector gear, thereby correcting the sector gear tooth profile coordinates.

5. A parametric modeling system for the tooth profile of a variable transmission ratio rack considering machining errors, characterized in that, include: The parameter acquisition module is configured to: acquire the target transmission ratio function of the transmission mechanism and the geometric parameters of the sector gear; the target transmission ratio function is the correspondence between the rotation angle of the sector gear and the transmission ratio of the transmission mechanism. The relationship derivation module is configured to: establish a gear and rack meshing coordinate system based on the target transmission ratio function and the geometric parameters of the sector gear, and calculate the correspondence between the rack displacement and the sector gear rotation angle; The error introduction module is configured to: introduce error parameters from the machining process into the theoretical tooth profile model of the sector gear, and calculate and obtain the tooth profile coordinates of the sector gear after introducing the error; The tooth profile generation module is configured to: solve for the coordinate points of the variable transmission ratio rack tooth profile based on the correspondence between the rack displacement and the sector gear rotation angle, and the sector gear tooth profile coordinates after introducing errors; The model generation module is configured to: generate a 3D model of a rack with a variable transmission ratio using the coordinate points of the rack tooth profile; build a gear and rack meshing simulation model that includes the machining error of the sector gear; and compare and analyze the transmission ratio fluctuation and meshing force changes under ideal and error conditions.

6. A parametric modeling method for the tooth profile of variable transmission ratio gears considering machining errors, characterized in that, include: Obtain the target transmission ratio function of the transmission mechanism and the geometric parameters of the standard rack; Based on the target transmission ratio function and the geometric parameters of the standard rack, a gear-rack meshing coordinate system is established, and the correspondence between the standard rack displacement and the sector gear rotation angle is calculated. Error parameters from the machining process are introduced into the theoretical tooth profile model of a standard rack, and the rack tooth profile coordinates after introducing the errors are calculated and obtained. Based on the correspondence between the standard rack displacement and the sector gear rotation angle, and the rack tooth profile coordinates after introducing errors, the coordinate points of the variable transmission ratio sector gear tooth profile are solved. A three-dimensional model of a sector gear with variable transmission ratio is generated by fitting the coordinate points of the tooth profile of the sector gear. A gear-rack meshing simulation model including rack machining errors is built, and the transmission ratio fluctuation and meshing performance under ideal and error conditions are compared and analyzed.

7. The parametric modeling method for the tooth profile of a variable transmission ratio gear considering machining errors as described in claim 1, characterized in that, The coordinate points for solving the tooth profile of the variable transmission ratio sector gear include: Define a line segment that rotates around the rotation center of the gear. At each initial angle, traverse all rotation angles and solve for the intersection points of the line segment and the rack tooth profile after introducing errors. Select the intersection point that is closest to the rotation center and determine the coordinates of the tooth profile points of the sector gear based on the distance from the nearest intersection point to the rotation center.

8. The parametric modeling method for the tooth profile of a variable transmission ratio gear considering machining errors as described in claim 7, characterized in that, The determination of the tooth profile point coordinates of the sector gear based on the distance from the nearest intersection point to the center of rotation includes: The distance from the nearest intersection point to the center of rotation is taken as the polar radius. The cosine and sine values ​​of the initial angle of the rotation segment corresponding to this distance are multiplied by the polar radius to obtain the coordinates of the tooth profile point of the sector gear in the rectangular coordinate system.

9. The parametric modeling method for the tooth profile of a variable transmission ratio gear considering machining errors as described in claim 1, characterized in that, The introduction of error parameters from the machining process into the theoretical tooth profile model of the standard rack includes: Introduce the pitch error of the rack; superimpose the pitch error into the formula for calculating the abscissa of the rack tooth profile point, thereby correcting the formula for calculating the coordinate of the rack tooth profile point.

10. A rack and pinion variable transmission ratio tooth profile parametric modeling system considering machining errors, characterized in that, include: The parameter acquisition module is configured to acquire the target transmission ratio function of the transmission mechanism and the geometric parameters of the standard rack. The relationship derivation module is configured to: establish a gear and rack meshing coordinate system based on the target transmission ratio function and the geometric parameters of the standard rack, and calculate the correspondence between the standard rack displacement and the sector gear rotation angle; The error introduction module is configured to: introduce error parameters from the machining process into the theoretical tooth profile model of the standard rack, and calculate and obtain the rack tooth profile coordinates after introducing the error; The tooth profile generation module is configured to: solve for the coordinate points of the variable transmission ratio sector gear tooth profile based on the correspondence between the standard rack displacement and the sector gear rotation angle, as well as the rack tooth profile coordinates after introducing errors; The model generation module is configured to: use the coordinate points of the tooth profile of the variable transmission ratio sector gear to fit and generate a three-dimensional model of the variable transmission ratio sector gear, build a gear and rack meshing simulation model including rack machining errors, and compare and analyze the transmission ratio fluctuation and meshing performance under ideal conditions and under error conditions.

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