A tooth-meshing transmission matching detection and evaluation method based on hertz contact

Abstract

This invention provides a method and system for detecting and evaluating tooth meshing transmission matching based on Hertzian contact, relating to the field of transmission mechanism design. Addressing the problems of existing physical detection methods being limited by space and unable to accurately measure internal instantaneous meshing forces, and the severe numerical oscillations and inability to identify minute machining errors in traditional discrete mesh simulations, this invention utilizes a surface smoothing fitting algorithm to continuously reconstruct discrete mesh elements. This method is applicable to tooth surfaces of various topologies, including variable transmission ratio gears, cylindrical spur gears, cylindrical helical gears, bevel spur gears, and bevel helical gears. A smooth tooth surface that meets continuity requirements is constructed mathematically, and Hertzian contact theory is applied to this smooth surface to simulate the real material elastic deformation and force transmission process. This allows the simulation results to sensitively capture the unique minute defect characteristics of different types of gears, achieving a refined and quantitative evaluation of the dynamic matching performance of a wide range of tooth meshing transmission mechanisms.

Description

Technical Field

[0001] This invention relates to the field of transmission mechanism design, and specifically to a method for detecting and evaluating tooth meshing transmission matching based on Hertzian contact. Background Technology

[0002] Gear meshing transmission mechanisms, such as spur gears, helical gears, bevel gears, and variable transmission ratio mechanisms, are key mechanical components for realizing motion and power transmission, and are widely used in the transmission systems of vehicles, industrial machine tools, industrial robot joint drives, precision machine tools, construction machinery, and various high-end equipment. To ensure the transmission accuracy and dynamic stability of these mechanisms under high-speed, heavy-load, or precision positioning conditions, rigorous testing of their matching performance is required during the manufacturing and assembly stages. Currently, the industry mainly relies on contact spot coloring, gear measurement center geometric scanning, and mechanical dynamic test benches to test the matching performance of various gear pairs. The contact spot method can only statically and qualitatively assess the contact area distribution; while geometric scanning can obtain the machining deviation of individual tooth profiles, it is difficult to directly reflect the coupling effect during dynamic meshing; and although mechanical bench testing closely resembles actual working conditions, it is limited by the closed and compact internal structure of the transmission mechanism, making it difficult to arrange sensors to directly measure the normal contact force and tangential friction force between the tooth surfaces. Furthermore, the vibration and noise of the external mechanical system easily mask the minute fluctuations in the transmission ratio caused by micron-level machining errors.

[0003] In virtual simulation, whether for standard cylindrical gears or complex curved gears, traditional finite element or multibody dynamics methods typically discretize the tooth profile surface into a mesh. During the simulation of continuous meshing, as the contact point moves across the "rough" surface composed of countless tiny planes, the contact normal vector jumps, causing non-physical numerical oscillations in the calculated contact force and transmission ratio. In high-precision gear transmission analysis, these spurious numerical fluctuations are often larger than those caused by actual machining errors, distorting the simulation results and making them unsuitable for refined evaluation. This makes it difficult to meet the high-fidelity comprehensive testing requirements of various transmission mechanisms, including cylindrical, conical, and variable transmission ratio gears, and it is impossible to accurately and continuously quantitatively evaluate the dynamic performance anomalies of variable transmission ratio mechanisms caused by minor manufacturing defects in a digital environment. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by providing a method and system for detecting and evaluating tooth meshing transmission matching based on Hertzian contact, thereby enabling a refined and quantitative evaluation of the dynamic matching performance of the transmission mechanism under test.

[0005] The first objective of this invention is to provide a method for detecting and evaluating tooth-to-tooth meshing transmission matching based on Hertzian contact, employing the following scheme:

[0006] include: Based on the target transmission ratio function and tooth profile geometric parameters, a three-dimensional geometric model of the transmission mechanism to be tested is constructed; the three-dimensional geometric model includes geometric feature information reflecting the machining quality or assembly state; The meshing tooth surfaces in the three-dimensional geometric model are discretized into a mesh, and the discrete mesh elements are reconstructed into a continuous surface using a surface smoothing fitting algorithm. Dynamic meshing simulation of a three-dimensional geometric model based on Hertzian contact was performed to calculate the contact force and motion transmission based on a continuous surface. The matching performance is evaluated by comparing the actual transmission ratio and meshing force obtained from the simulation with the theoretical benchmark.

[0007] Furthermore, the construction of the three-dimensional geometric model of the transmission mechanism to be tested includes: Based on the preset machining tolerance level, geometric error parameters are actively introduced into the ideal geometric model to construct a three-dimensional geometric model containing preset deviations. Alternatively, a three-dimensional geometric model reflecting the surface morphology of the actual gear can be reconstructed based on reverse scanning data of the gear.

[0008] Furthermore, the introduced geometric error parameters include at least one or more of the following: tooth thickness error, tooth profile error, eccentricity error, axis perpendicularity error, axis intersection angle error, or helix angle error.

[0009] Furthermore, the three-dimensional geometric model of the transmission mechanism to be tested covers at least one of the following types: variable transmission ratio gear and rack meshing model, cylindrical spur gear meshing model, cylindrical helical gear meshing model, bevel spur gear meshing model, or bevel helical gear meshing model.

[0010] Furthermore, the method of reconstructing discrete mesh elements into continuous surfaces using a surface smoothing fitting algorithm includes: The Hermite interpolation algorithm is used to calculate the tangent vectors and curvatures of discrete mesh nodes and construct a continuous interpolation surface covering the discrete mesh to eliminate the abrupt change in the tooth surface normal vector caused by mesh discretization.

[0011] Furthermore, the dynamic meshing simulation of the three-dimensional geometric model based on Hertzian contact includes: Define the tooth surface contact parameters; where the contact parameters include the contact stiffness coefficient determined by the tooth surface material properties and the damping coefficient simulating meshing energy loss; Within the simulation step, the penetration depth of the mesh nodes on the tooth surfaces of the driving and driven components is detected. When penetration is detected, the normal contact force is calculated based on the penetration depth and the contact stiffness coefficient, and the tangential contact force is calculated based on the friction coefficient.

[0012] Furthermore, based on the actual transmission ratio and meshing force obtained from the simulation and compared with the theoretical benchmark, the matching performance is evaluated, including: The ratio of the instantaneous velocity of the driven component to the instantaneous velocity of the driving component in the transmission mechanism is calculated during the simulation, and the actual transmission ratio curve is generated. Calculate the relative error between the actual transmission ratio curve and the target transmission ratio function; if a sudden peak in the transmission ratio is detected in the alternating meshing area of ​​the tooth surface exceeding the preset threshold, it is determined that there is a tooth pitch deviation or tooth profile deviation in the tooth profile.

[0013] Furthermore, based on the comparison between the meshing force obtained from the simulation and the theoretical benchmark, the matching performance is evaluated by including: Calculate the magnitude and direction of the meshing force at the meshing point during meshing, set a threshold for sudden change in meshing force, and when the change in meshing force exceeds the set threshold, it indicates that an impact or transmission interruption has occurred during meshing, and the meshing tooth profile mismatch is defined.

[0014] Furthermore, based on the contact characteristics and phase information obtained from the simulation, the matching performance is evaluated, including: Based on the dynamic meshing simulation results, a contact spot cloud map that changes over time is generated to analyze the distribution of contact spots in the tooth width direction; at the same time, the meshing phase in which the peak contact force occurs is analyzed. If the distribution center of the contact spot deviates from the tooth width centerline and moves towards the tooth tip, or if the peak of the contact force appears in an unexpected meshing phase, it is determined that the transmission mechanism has an axis parallelism error or an assembly eccentricity error.

[0015] A second objective of this invention is to provide a tooth-to-tooth meshing transmission matching detection and evaluation system based on Hertzian contact as described in the first objective, comprising: The modeling module is configured to: construct a three-dimensional geometric model of the transmission mechanism to be tested based on the target transmission ratio function and tooth profile geometric parameters; the three-dimensional geometric model includes geometric feature information reflecting the machining quality or assembly state; The mesh processing module is configured to: discretize the mesh of the meshing tooth surfaces in the three-dimensional geometric model, and reconstruct the discrete mesh elements into continuous surfaces using a surface smoothing fitting algorithm; The simulation calculation module is configured to: perform dynamic meshing simulation on the three-dimensional geometric model based on Hertzian contact theory, and calculate the contact force and motion transmission based on the continuous surface; The evaluation module is configured to evaluate the matching performance based on the comparison between the actual transmission ratio and meshing force obtained from the simulation and the theoretical benchmark.

[0016] Compared with the prior art, the advantages and positive effects of this invention are: To address the limitations of existing physical testing methods, which restrict the accurate measurement of internal instantaneous meshing forces due to space constraints, and the severe numerical oscillations and inability to identify minute machining errors caused by abrupt changes in tooth surface normal vectors in traditional discrete mesh simulations, this paper proposes a method that utilizes a smooth surface fitting algorithm to continuously reconstruct discrete mesh elements. This method is applicable to tooth surfaces of various topologies, including variable transmission ratio gears, cylindrical spur gears, cylindrical helical gears, bevel spur gears, and bevel helical gears. Mathematically, a smooth tooth surface that meets continuity requirements is constructed, fundamentally eliminating non-physical contact force abrupt changes caused by geometric discontinuities when contact points cross mesh boundaries. Furthermore, Hertzian contact theory is applied to this smooth surface to simulate the real elastic deformation and force transmission process of materials. This successfully reproduces a relatively pure meshing signal in a virtual environment, eliminating some numerical computation noise interference. The simulation results can sensitively capture the unique minute defect characteristics of different types of gears, enabling a refined and quantitative evaluation of the dynamic matching performance of a wide range of gear meshing transmission mechanisms.

[0017] By employing the Hermite interpolation algorithm, a continuous interpolation surface covering the discrete mesh is constructed using the tangent vectors and curvature information of the mesh nodes. This mathematically achieves the continuous reconstruction of the geometric features of the tooth surface, enabling the penetration depth and contact force to smoothly transition with the geometric position as the contact point moves across the tooth surface. This effectively filters out numerical noise in the simulation calculation, ensuring that the fluctuations in the output transmission ratio and changes in contact force originate from physical processing errors rather than defects in the calculation model. This improves the reliability of the detection results and the sensitivity to minute defects. Attached Figure Description

[0018] 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.

[0019] Figure 1 This is a graph showing the target transmission ratio function of the variable transmission ratio rack profile in one or more embodiments of the present invention.

[0020] Figure 2 This is a schematic diagram of a variable transmission ratio meshing simulation model in one or more embodiments of the present invention.

[0021] Figure 3 This is a schematic diagram of the mesh division of the tooth surface of a sector gear in one or more embodiments of the present invention.

[0022] Figure 4 This is a schematic diagram of rack tooth surface mesh division in one or more embodiments of the present invention.

[0023] Figure 5 This is a schematic diagram of the discrete tooth surface mesh of a gear rack with variable transmission ratio in one or more embodiments of the present invention.

[0024] Figure 6 This is a schematic diagram of the contact force in the meshing area of ​​the variable transmission ratio gear and rack in one or more embodiments of the present invention.

[0025] Figure 7 This is a schematic diagram of the contact point at which the variable transmission ratio gear and rack will engage in meshing, as shown in one or more embodiments of the present invention.

[0026] Figure 8 This is a schematic diagram of the meshing transmission ratio of a well-matched variable transmission ratio gear and rack model in one or more embodiments of the present invention.

[0027] Figure 9 This is a schematic diagram illustrating the relative error of the meshing transmission ratio of a well-matched variable transmission ratio gear and rack model in one or more embodiments of the present invention.

[0028] Figure 10 This is a schematic diagram illustrating the meshing force of a well-matched variable transmission ratio gear and rack model in one or more embodiments of the present invention.

[0029] Figure 11 This is a schematic diagram of the meshing transition zone of a well-matched variable transmission ratio gear and rack model in one or more embodiments of the present invention.

[0030] Figure 12 This is a schematic diagram of the force on the tooth width of a well-matched variable transmission ratio gear rack model in one or more embodiments of the present invention.

[0031] Figure 13 This is a schematic diagram of the meshing transmission ratio of a variable transmission ratio gear and rack model that incorporates tooth thickness error in one or more embodiments of the present invention.

[0032] Figure 14 This is a schematic diagram of the relative error of the meshing transmission ratio of a variable transmission ratio gear and rack model with introduced tooth thickness error in one or more embodiments of the present invention.

[0033] Figure 15 This is a schematic diagram illustrating the meshing force of a variable transmission ratio gear rack model with introduced tooth thickness error in one or more embodiments of the present invention.

[0034] Figure 16 This is a schematic diagram of the meshing transition zone of a variable transmission ratio gear rack model with introduced tooth thickness error in one or more embodiments of the present invention.

[0035] Figure 17 This is a schematic diagram of the force in the tooth width direction of a variable transmission ratio gear rack model that incorporates tooth thickness error in one or more embodiments of the present invention.

[0036] Figure 18 This is a schematic diagram of a simulation model of variable transmission ratio gear and rack meshing with introduced perpendicularity error in one or more embodiments of the present invention.

[0037] Figure 19 This is a schematic diagram of the meshing transmission ratio of a variable transmission ratio gear and rack model that introduces perpendicularity error in one or more embodiments of the present invention.

[0038] Figure 20 This is a schematic diagram of the meshing transmission ratio of a variable transmission ratio gear and rack model that introduces perpendicularity error in one or more embodiments of the present invention.

[0039] Figure 21 This is a schematic diagram illustrating the meshing force of a variable transmission ratio gear rack model with introduced perpendicularity error in one or more embodiments of the present invention.

[0040] Figure 22 This is a schematic diagram of the tooth width direction offset of a variable transmission ratio gear rack model with introduced perpendicularity error in one or more embodiments of the present invention.

[0041] Figure 23 This is a schematic diagram of a simulation model of cylindrical spur gear meshing in one or more embodiments of the present invention.

[0042] Figure 24 This is a schematic diagram of the meshing of the meshing tooth surface of a cylindrical spur gear in one or more embodiments of the present invention.

[0043] Figure 25 This is a schematic diagram of the meshing transmission ratio of a well-matched cylindrical spur gear model in one or more embodiments of the present invention.

[0044] Figure 26 This is a schematic diagram of the relative error of the meshing transmission ratio of a well-matched cylindrical spur gear model in one or more embodiments of the present invention.

[0045] Figure 27 This is a schematic diagram illustrating the meshing force of a well-matched cylindrical spur gear model in one or more embodiments of the present invention.

[0046] Figure 28 This is a schematic diagram of the force exerted in the tooth width direction on a well-matched cylindrical spur gear model in one or more embodiments of the present invention.

[0047] Figure 29 This is a schematic diagram of a simulation model of cylindrical helical gear meshing in one or more embodiments of the present invention.

[0048] Figure 30 This is a schematic diagram of the meshing of the meshing tooth surface of a cylindrical helical gear in one or more embodiments of the present invention.

[0049] Figure 31 This is a schematic diagram of the meshing transmission ratio of a well-matched cylindrical helical gear model in one or more embodiments of the present invention.

[0050] Figure 32This is a schematic diagram of the relative error of the meshing transmission ratio of a well-matched cylindrical helical gear model in one or more embodiments of the present invention.

[0051] Figure 33 This is a schematic diagram illustrating the meshing force of a well-matched cylindrical helical gear model in one or more embodiments of the present invention.

[0052] Figure 34 This is a schematic diagram of the force exerted in the tooth width direction on a well-matched cylindrical helical gear model in one or more embodiments of the present invention.

[0053] Figure 35 This is a schematic diagram of a simulation model of bevel spur gear meshing in one or more embodiments of the present invention.

[0054] Figure 36 This is a schematic diagram of the meshing of the meshing tooth surface of a bevel spur gear in one or more embodiments of the present invention.

[0055] Figure 37 This is a schematic diagram of the meshing transmission ratio of a well-matched bevel spur gear model in one or more embodiments of the present invention.

[0056] Figure 38 This is a schematic diagram of the relative error of the meshing transmission ratio of a well-matched bevel spur gear model in one or more embodiments of the present invention.

[0057] Figure 39 This is a schematic diagram illustrating the meshing force of a well-matched bevel spur gear model in one or more embodiments of the present invention.

[0058] Figure 40 This is a schematic diagram of the force exerted in the tooth width direction on a well-matched bevel spur gear model in one or more embodiments of the present invention.

[0059] Figure 41 This is a schematic diagram of a simulation model of bevel helical gear meshing in one or more embodiments of the present invention.

[0060] Figure 42 This is a schematic diagram of the meshing of the meshing tooth surface of a bevel helical gear in one or more embodiments of the present invention.

[0061] Figure 43 This is a schematic diagram of the meshing transmission ratio of a well-matched bevel helical gear model in one or more embodiments of the present invention.

[0062] Figure 44 This is a schematic diagram of the relative error of the meshing transmission ratio of a well-matched bevel helical gear model in one or more embodiments of the present invention.

[0063] Figure 45 This is a schematic diagram illustrating the meshing force of a well-matched bevel helical gear model in one or more embodiments of the present invention.

[0064] Figure 46 This is a schematic diagram of the force on the tooth width of a well-matched bevel helical gear model in one or more embodiments of the present invention. Detailed Implementation

[0065] The method of this invention is applicable to both the design verification stage of the transmission mechanism and the quality inspection stage of the finished product.

[0066] During the design verification phase, geometric error parameters (such as tooth thickness error, perpendicularity error, etc.) can be actively introduced into the ideal model to simulate and analyze the impact of different errors on transmission performance, thereby determining the machining tolerance standards.

[0067] During the finished product inspection stage, the point cloud data of the physical object can be obtained through reverse scanning to reconstruct the model, and simulation can be performed directly to evaluate the pass rate of the finished product.

[0068] The following section will use "actively introducing error parameters" as an example to explain in detail the detection sensitivity and evaluation logic of this method.

[0069] Example 1 In a typical embodiment of the present invention, such as Figures 1-12 As shown, a method for detecting and evaluating tooth meshing transmission matching based on Hertzian contact is presented, including: Based on the target transmission ratio function and tooth profile geometric parameters, a three-dimensional geometric model of the transmission mechanism to be tested is constructed; the three-dimensional geometric model includes geometric feature information reflecting the machining quality or assembly state; The meshing tooth surfaces in the three-dimensional geometric model are discretized into a mesh, and the discrete mesh elements are reconstructed into a continuous surface using a surface smoothing fitting algorithm. Dynamic meshing simulation of a three-dimensional geometric model based on Hertzian contact was performed to calculate the contact force and motion transmission based on a continuous surface. The matching performance is evaluated by comparing the actual transmission ratio and meshing force obtained from the simulation with the theoretical benchmark.

[0070] The construction of the three-dimensional geometric model of the transmission mechanism to be tested includes: Based on the preset machining tolerance level, geometric error parameters are actively introduced into the ideal geometric model to construct a three-dimensional geometric model containing preset deviations. Alternatively, a three-dimensional geometric model reflecting the surface morphology of the actual gear can be reconstructed based on reverse scanning data of the gear.

[0071] Among them, the introduced geometric error parameters include at least one or more of the following: tooth thickness error, tooth profile error, eccentricity error, axis perpendicularity error, axis intersection angle error, or helix angle error.

[0072] Reconstructing discrete mesh elements into continuous surfaces using surface smoothing fitting algorithms includes: The Hermite interpolation algorithm is used to calculate the tangent vectors and curvatures of discrete mesh nodes and construct a continuous interpolation surface covering the discrete mesh to eliminate the abrupt change in the tooth surface normal vector caused by mesh discretization.

[0073] The dynamic meshing simulation of the three-dimensional geometric model based on Hertzian contact includes: Define the tooth surface contact parameters; where the contact parameters include the contact stiffness coefficient determined by the tooth surface material properties and the damping coefficient simulating meshing energy loss; Within the simulation step, the penetration depth of the mesh nodes on the tooth surfaces of the driving and driven components is detected. When penetration is detected, the normal contact force is calculated based on the penetration depth and the contact stiffness coefficient, and the tangential contact force is calculated based on the friction coefficient.

[0074] The matching performance is evaluated based on the actual transmission ratio and meshing force obtained from the simulation, compared with the theoretical benchmark, including: The ratio of the instantaneous velocity of the driven component to the instantaneous velocity of the driving component in the transmission mechanism is calculated during the simulation, and the actual transmission ratio curve is generated. Calculate the relative error between the actual transmission ratio curve and the target transmission ratio function; if a sudden peak in the transmission ratio is detected in the alternating meshing area of ​​the tooth surface exceeding the preset threshold, it is determined that there is a tooth pitch deviation or tooth profile deviation in the tooth profile.

[0075] The matching performance is evaluated based on the comparison between the meshing force obtained from the simulation and the theoretical benchmark, including: Calculate the magnitude and direction of the meshing force at the meshing point during meshing, set a threshold for sudden change in meshing force, and when the change in meshing force exceeds the set threshold, it indicates that an impact or transmission interruption has occurred during meshing, and the meshing tooth profile mismatch is defined.

[0076] The matching performance is evaluated based on the contact characteristics and phase information obtained from the simulation, including: Based on the dynamic meshing simulation results, a contact spot cloud map that changes over time is generated to analyze the distribution of contact spots in the tooth width direction; at the same time, the meshing phase in which the peak contact force occurs is analyzed. If the distribution center of the contact spot deviates from the tooth width centerline and moves towards the tooth tip, or if the peak contact force appears in an unexpected meshing phase, then the transmission mechanism is determined to have axial parallelism error or assembly eccentricity error. In this embodiment, taking a variable transmission ratio gear and rack meshing pair as an example, the tooth-to-tooth meshing transmission matching detection and evaluation method based on Hertzian contact first needs to construct a three-dimensional model of the transmission mechanism to be tested. The three-dimensional geometric model includes geometric feature information reflecting the machining quality or assembly state, and the construction method can adopt one of the following two forms: Form 1: Based on the preset machining tolerance level, geometric error parameters (such as tooth thickness error, eccentricity error, etc.) are actively introduced into the ideal CAD geometric model to construct a three-dimensional geometric model containing preset deviations, which is used to simulate meshing performance under different tolerances and formulate inspection standards. Form 2: Based on reverse scanning data (such as point cloud data) of the actual gear, a three-dimensional geometric model reflecting the true shape of the actual surface is reconstructed for direct inspection of the finished product.

[0077] To explain the detection mechanism of this method in detail, this embodiment and subsequent embodiments mainly use the active introduction of error in Form 1 as an example.

[0078] Based on the target transmission ratio function, the tooth profile coordinate point data of the variable transmission ratio sector gear rack are accurately collected. A high-fidelity meshing simulation calculation model consistent with the actual physical model is established using the tooth profile coordinate point data, i.e., the meshing model of the variable transmission ratio sector gear rack to be tested. For the meshing pair of the variable transmission ratio sector gear rack, the tooth surface involved in meshing is divided into discrete planar mesh elements, and Hermite interpolation is used to fit the discrete planar elements into continuous curved surface elements to accurately describe the tooth surface morphology. Specifically, the tangent vector and curvature information of the discrete mesh nodes are used to construct a continuous interpolation surface covering the discrete mesh, so that the contact normal vector and penetration depth can smoothly transition when the contact point moves on the tooth surface, avoiding non-physical numerical oscillations.

[0079] Hertzian contact theory describes the contact between two objects. It assumes that penetration occurs when the two objects come into contact and calculates the contact force based on the amount of penetration and the elastic coefficient. Based on Hertzian contact theory, the elastic coefficient and damping parameter of the meshing tooth surfaces are defined. Specifically, the elastic coefficient is determined by the material properties and the radius of curvature, while the damping coefficient is used to simulate the energy loss during the meshing process. The rack is defined as the driving component that moves at a constant linear velocity, and the sector gear is the driven component that can rotate freely around the center of rotation. The rack and sector gear make Hertzian contact through the tooth surfaces. The rack mesh nodes penetrate the driven component mesh surface, generating contact force and transmitting motion and force to the sector gear. The linear velocity of the rack and the rotational speed of the sector gear must satisfy a predetermined target transmission ratio function. The magnitude of the contact force should change smoothly to avoid abrupt changes. At the same time, the transition between teeth should be smooth to avoid collisions and jamming. Set several time points, record the linear velocity of the rack and the angular velocity of the sector gear at each time point, and the ratio of the two is the transmission ratio. Fit the discrete data points to the transmission ratio curve, and compare it with the ideal transmission ratio to analyze the changes in transmission ratio and relative error. As the two mesh, the position of the meshing point changes, the position and size of the penetration area also change, and the direction and magnitude of the meshing force also change accordingly. By recording the position of the penetration area and the changes in the direction and magnitude of the meshing force during the meshing process, the meshing force can be detected and analyzed.

[0080] Specifically, in combination Figures 1-12 This paper provides a detailed explanation of the matching detection and evaluation method for tooth meshing transmission based on Hertzian contact.

[0081] This implementation first obtains the coordinate points of the rack tooth profile that meshes with the standard sector gear, based on the known target transmission ratio function and the geometric parameters of the standard sector gear. The transmission ratio function is as follows: Figure 1 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): (1); 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.

[0082] 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 Based on the target transmission ratio function and the geometric parameters of the sector gear, a rack tooth profile that meshes with the sector gear and meets the variable transmission ratio requirement is designed, and a variable transmission ratio meshing simulation model is built, such as... Figure 2 As shown.

[0083] The meshing tooth surfaces in the model are divided into discrete planar elements. For example, the mesh of a sector gear tooth surface is shown below. Figure 3 As shown, the rack tooth surface mesh is as follows Figure 4 As shown, because the transition between planar micro-element meshes is not smooth after dividing the tooth surface, this unevenness causes fluctuations in the transmission ratio and meshing force at the meshing point during the simulation of a sector gear meshing transmission model. Therefore, in this embodiment, the Hermite interpolation algorithm is used to fit the discrete planar micro-element meshes into continuous curved surface micro-element meshes, as shown in the figure. Figure 5 As shown, the curve represents discrete planar micro-elements, while the solid line represents continuous curved surface micro-elements after fitting. After fitting, the transition between each grid micro-elements is smooth, avoiding fluctuations and abrupt changes in the transmission ratio and meshing force during the detection process.

[0084] As the rack moves, the grid nodes on the rack tooth surface will contact and penetrate the grid surface of the sector gear tooth surface, and the contact force in the meshing area will be as follows: Figure 6 As shown, when the sector gear is rotated, the meshing position is not a line, but a region. The contact force in this region is calculated based on the elastic stiffness and penetration depth, as shown below. Figure 7 As shown, the rack transmits motion and force to the sector gear through the contact force generated by this contact, and the load torque of the sector gear is set to 2600 N•m.

[0085] During the transmission meshing process, several recording time points are set to record the rack linear velocity, sector gear speed, and meshing force in the meshing area at each time point. In this embodiment, the matching is relatively good, and the transmission ratio detection results are as follows: Figure 8 , Figure 9 As shown, the transmission ratio variation curve roughly fits the target transmission ratio, with a maximum relative error of 0.975%. The meshing force detection results are as follows. Figure 10 As shown, the meshing force changes smoothly. Under a load torque of 2600 N•m, the meshing force at the meshing point fluctuates between 61000 N and 62000 N. Simultaneously, the transition in the meshing area is smooth, and there is no jamming or impact when the teeth engage. Figure 11 As shown. During transmission, the force is uniform in the tooth width direction, and no eccentric load phenomenon occurs, as shown. Figure 12 As shown.

[0086] Example 2 In this embodiment, as Figures 13-17 As shown, the difference between the Hertzian contact-based variable transmission ratio gear rack matching detection and evaluation method provided in this embodiment and Embodiment 1 is that tooth thickness error is introduced into the variable transmission ratio sector gear rack pair.

[0087] In this embodiment, the transmission ratio function is the same as that in Embodiment 1, for comparative analysis, as shown in equation (1) and Figure 1 As shown.

[0088] The geometric parameters of the sector gear include module, pressure angle, total number of teeth, addendum coefficient, clearance coefficient, displacement coefficient, and installation eccentricity, which are consistent with the geometric parameters of the sector gear selected in Example 1, as shown in Table 1. At the same time, an artificial error of +0.1mm is introduced in the tooth thickness direction of the sector gear to simulate the meshing situation when the tooth thickness error exists.

[0089] Based on the target transmission ratio function and the geometric parameters of the sector gear after introducing artificial errors, a sector gear model is established. At the same time, based on the rack model established in Example 1 without introducing artificial errors, a variable transmission ratio meshing simulation model is built according to the same backlash meshing assembly.

[0090] The meshing tooth surfaces in the model are divided into discrete planar micro-elements. The same meshing method is used for the sector gear and rack as in Example 1. Then, the Hermite interpolation algorithm is used to fit the discrete planar micro-elements into continuous curved surface micro-elements.

[0091] Similar to Example 1, as the rack moves, the grid nodes on the rack tooth surface will contact and penetrate the grid curved surface on the sector gear tooth surface. At this time, the meshing position is not a line, but a region. The contact force in this region is calculated by the elastic coefficient and the penetration depth. The rack transmits motion and force to the sector gear through the contact force generated by this contact, causing the sector gear to rotate. The load torque of the sector gear is set to 2600 N•m.

[0092] During the transmission meshing process, several recording time points are set to record the rack linear velocity, sector gear speed, and meshing force in the meshing area at each time point. In this embodiment with poor matching, the transmission ratio detection results are as follows: Figure 13 , Figure 14 As shown, when the intermediate teeth are engaged, the transmission ratio change curve roughly matches the target transmission ratio. However, during the transition from the first tooth to the second tooth, due to the increased tooth thickness, the second tooth forces the first tooth to disengage during engagement, causing a sudden increase in the sector gear's speed and resulting in a sudden change in the transmission ratio. At this point, the maximum relative error of the transmission ratio reaches 8.3%, exceeding the transmission ratio error threshold. Simultaneously, the meshing force detection results are as follows... Figure 15 As shown, the change is stable when the first tooth engages, with the meshing force fluctuating between 61000N and 62000N. However, during the transition from the first tooth to the second tooth, the increased tooth thickness of the second tooth causes an impact upon entering engagement, resulting in a sudden increase in the magnitude and a shift in the direction of the meshing force. This exceeds the threshold for sudden changes in meshing force, and in severe cases, it can lead to jamming and failure of the transmission mechanism. Figure 16 As shown. During transmission, the force is uniform in the tooth width direction, and no eccentric load phenomenon occurs, as shown. Figure 17 As shown.

[0093] Example 3 In this embodiment, as Figures 18-22 As shown, the difference between the variable transmission ratio gear rack matching detection and evaluation method based on Hertzian contact provided in this embodiment and Embodiment 1 is that a perpendicularity error is introduced into the variable transmission ratio sector gear rack pair.

[0094] In this embodiment, the transmission ratio function is the same as that in Embodiment 1, for comparative analysis, as shown in equation (1) and Figure 1 As shown.

[0095] The geometric parameters of the sector gear include module, pressure angle, total number of teeth, addendum coefficient, clearance coefficient, displacement coefficient, and installation eccentricity, which are consistent with the geometric parameters of the sector gear selected in Example 1, as shown in Table 1. At the same time, a perpendicularity error of 0.09 mm is introduced between the end face of the sector gear and the axis of rotation to simulate the meshing situation with poor matching performance caused by the perpendicularity error.

[0096] Based on the target transmission ratio function and the geometric parameters of the sector gear, a sector gear-ratio rack meshing model is established. Following the same backlash meshing assembly as in Example 1, the sector gear is rotated around its axis. The sector gear has a tooth width of 55mm. Calculations show that the end face of the sector gear rotates by 0.094 degrees. Rotating the sector gear around any straight line passing through the center of rotation within its end face by this angle introduces a perpendicularity error into the model. In this example, the sector gear is rotated around a straight line passing through the center of rotation. Figure 18 The X-axis is rotated by 0.094 degrees.

[0097] The meshing tooth surfaces in the model are divided into discrete planar micro-elements. The same meshing method is used for the sector gear and rack as in Example 1. Then, the Hermite interpolation algorithm is used to fit the discrete planar micro-elements into continuous curved surface micro-elements.

[0098] Similar to Example 1, as the rack moves, the grid nodes on the rack tooth surface will contact and penetrate the grid curved surface on the sector gear tooth surface. At this time, the meshing position is not a line, but a region. The contact force in this region is calculated by the elastic coefficient and the penetration depth. The rack transmits motion and force to the sector gear through the contact force generated by this contact, causing the sector gear to rotate. The load torque of the sector gear is set to 2600 N•m.

[0099] During the transmission meshing process, several recording time points are set to record the rack linear velocity, sector gear speed, and meshing force in the meshing area at each time point. In this embodiment that introduces perpendicularity error, the transmission ratio detection results are as follows: Figure 19 , Figure 20 As shown, during the transmission process, the transmission ratio change curve roughly fits the target transmission ratio, with a maximum relative error of 1.4%, which does not exceed the transmission ratio error threshold. Meanwhile, the meshing force detection results are as follows... Figure 21 As shown, the transmission process is relatively smooth, with the meshing force fluctuating between 61000N and 62000N, not exceeding the threshold for sudden change in meshing force. However, due to the introduction of perpendicularity error, the sector gear and rack experience off-center loading in the tooth width direction during meshing. The center of the meshing part shifts relative to the tooth width centerline, exceeding the offset threshold. Only one side participates in meshing and bears force in the tooth width direction, as shown in the figure. Figure 22As shown, this leads to localized stress concentration, making high-stress areas prone to uneven wear, tooth surface spalling, pitting, and in severe cases, root cracks, shortening tooth life. Figure 22 As shown, after introducing perpendicularity error, not only does the distribution center of the contact spot deviate from the tooth width centerline (i.e., off-center loading occurs in the tooth width direction), but also, by comparing the curves of contact force changing over time (such as...), Figure 21 As shown, and with reference Figure 10 Based on the theoretical benchmark, it can be observed that the timing of the peak contact force (i.e., the engagement phase) has shifted relative to the theoretical benchmark. For example, in the phase range that should theoretically be in a stable engagement state, the actual simulation results show the peak contact force occurring earlier (phase leading) or later. This phenomenon of the peak contact force appearing at an unexpected engagement phase, combined with the spatial offset of the contact spots, is an important basis for determining whether there is an axis parallelism error or assembly eccentricity error in the transmission mechanism. Example 4 In this embodiment, as Figures 23-28 As shown, the difference between the tooth meshing transmission matching detection and evaluation method based on Hertzian contact provided in this embodiment and the first embodiment is that the tooth meshing pair is a cylindrical spur gear meshing pair, and the three-dimensional geometric model of the transmission mechanism to be tested is a cylindrical spur gear meshing model.

[0100] The geometric parameters of a cylindrical spur gear include module, pressure angle, number of teeth, addendum coefficient, and clearance coefficient. The geometric parameters of the cylindrical spur gear selected in this embodiment are shown in Table 2 below.

[0101] Table 2 Geometric parameters of cylindrical spur gears Modulus 10mm pressure angle 20° Number of teeth 10 Tooth tip height coefficient 1 porosity 0.25 Based on the aforementioned gear geometric parameters, the gear tooth profile was designed, and a simulation model of cylindrical spur gear meshing was built, as follows: Figure 23 As shown.

[0102] The meshing tooth surfaces in the model are divided into discrete planar elements. For the cylindrical spur gear, the mesh is then created, and the Hermite interpolation algorithm is used to fit the discrete planar elements into continuous surface elements, such as... Figure 24 As shown.

[0103] As the driving gear rotates, the mesh nodes on the driving gear tooth surface will contact and penetrate the mesh surface on the driven gear tooth surface. At this time, the meshing position is not a line, but a region. The contact force in this region is calculated by the elastic coefficient and the penetration depth. The driving gear transmits motion and force to the driven gear through the contact force generated by this contact, causing the driven gear to rotate. The driving gear speed is set to 60 rpm, and the driven gear load torque is 1000 N•m.

[0104] During the transmission engagement process, several recording time points are set to record the rotational speed of the driving and driven gears and the magnitude of the meshing force in the meshing area at each time point. In this embodiment, the detection result of the transmission ratio is as follows: Figure 25 , Figure 26 As shown, the transmission ratio fluctuates significantly during the transition between adjacent teeth meshing, indicating a transmission error in the cylindrical spur gear during meshing. The average relative transmission error is 0.50%, and the maximum relative transmission error reaches 2.95%, which does not exceed the transmission ratio error threshold. Meanwhile, the meshing force test results are as follows... Figure 27 As shown, the average meshing force is 21755 N. During the transition between adjacent teeth, there is an impact in the meshing force, with the maximum impact force reaching 23296 N, exceeding the average meshing force by 7% and exceeding the threshold for sudden changes in meshing force. This impact occurs in the transition region between adjacent teeth. During transmission, the force is uniform in the tooth width direction, and no eccentric loading phenomenon occurs. Figure 28 As shown.

[0105] Example 5 In this embodiment, as Figures 29-34 As shown, the difference between the tooth meshing transmission matching detection and evaluation method based on Hertzian contact provided in this embodiment and that in embodiment four is that the tooth meshing pair is a cylindrical helical gear meshing pair, and the three-dimensional geometric model of the transmission mechanism to be tested is a cylindrical helical gear meshing model.

[0106] In the error analysis of this embodiment, in addition to tooth thickness error, "helix angle error" can also be introduced (for example, adjusting the helix angle from 8° to 8.05°) to detect its influence on the axial contact position.

[0107] In this embodiment, the geometric parameters include module, pressure angle, number of teeth, tooth tip height coefficient, tip clearance coefficient, and helix angle. Except for the newly added helix angle parameter, the other parameters are the same as those in Embodiment 2, as shown in Table 3.

[0108] Table 3 Geometric parameters of cylindrical helical gears Modulus 10mm pressure angle 20° Number of teeth 10 Tooth tip height coefficient 1 porosity 0.25 helix angle 8° dextrorotatory Based on the aforementioned gear geometric parameters, the gear tooth profile was designed, and a simulation model of cylindrical helical gear meshing was built, as follows: Figure 29 As shown.

[0109] The meshing tooth surfaces in the model are divided into discrete planar elements. For the cylindrical spur gear, the mesh is then created, and the Hermite interpolation algorithm is used to fit the discrete planar elements into continuous surface elements, such as... Figure 30 As shown.

[0110] As the driving gear rotates, the mesh nodes on the driving gear tooth surface will contact and penetrate the mesh surface on the driven gear tooth surface. At this time, the meshing position is not a line, but a region. The contact force in this region is calculated by the elastic coefficient and the penetration depth. The driving gear transmits motion and force to the driven gear through the contact force generated by this contact, causing the driven gear to rotate. The driving gear speed is set to 60 rpm, and the driven gear load torque is 1000 N•m.

[0111] During the transmission engagement process, several recording time points are set to record the rotational speed of the driving and driven gears and the magnitude of the meshing force in the meshing area at each time point. In this embodiment, the detection result of the transmission ratio is as follows: Figure 31 , Figure 32 As shown, compared to the cylindrical spur gear in Example 2, the cylindrical helical gear provides smoother transmission during meshing, with an average transmission error of 0.22% and a maximum relative transmission error of 1.00%, both within the transmission ratio error threshold. Meanwhile, the meshing force detection results are as follows... Figure 33 As shown, the average meshing force is 21552 N, and the maximum meshing force is 21830 N. The transition between adjacent teeth is smoother and does not exceed the threshold for sudden changes in meshing force. Due to the meshing characteristics of helical gears in the tooth width direction, the tooth surface begins to engage at one end face, and during meshing, the meshing part moves towards the other end face until it disengages at the other end face, as shown. Figure 34 As shown.

[0112] Example 6 In this embodiment, as Figures 35-40 As shown, the difference between the tooth meshing transmission matching detection and evaluation method based on Hertzian contact provided in this embodiment and the first embodiment is that the tooth meshing pair is a bevel spur gear meshing pair, and the three-dimensional geometric model of the transmission mechanism to be tested is a bevel spur gear meshing model.

[0113] Similarly, for bevel gears, an "axis intersection error" can be introduced during modeling (e.g., adjusting the axis intersection angle from 90° to 89.9°) to simulate the contact area offset caused by the non-perpendicularity of the axis during assembly.

[0114] The geometric parameters of a bevel spur gear include module, pressure angle, number of teeth, addendum coefficient, and clearance coefficient. The geometric parameters of the bevel spur gear selected in this embodiment are shown in Table 4 below.

[0115] Table 4 Geometric parameters of bevel spur gears Modulus 5mm pressure angle 20° Number of teeth 17、34 Tooth tip height coefficient 1 porosity 0.25 Axial angle 90° cone angle 45°、45° Based on the aforementioned gear geometric parameters, the gear tooth profile was designed, and a simulation model of bevel spur gear meshing was built, as follows: Figure 35 As shown.

[0116] The meshing tooth surfaces in the model are divided into discrete planar elements. For the cylindrical spur gear, the mesh is then created, and the Hermite interpolation algorithm is used to fit the discrete planar elements into continuous surface elements, such as... Figure 36 As shown.

[0117] Define the small bevel gear as the driving gear and the large bevel gear as the driven gear. As the driving gear rotates, the mesh nodes on the tooth surface of the driving gear will contact and penetrate the mesh surface on the tooth surface of the driven gear. At this time, the meshing position is not a line, but a region. The contact force in this region is calculated by the elastic coefficient and the penetration depth. The driving gear transmits motion and force to the driven gear through the contact force generated by this contact, causing the driven gear to rotate. Set the speed of the driving gear to 120 rpm and the load torque of the driven gear to 500 N•m.

[0118] During the transmission engagement process, several recording time points are set to record the rotational speed of the driving and driven gears and the magnitude of the meshing force in the meshing area at each time point. In this embodiment, the detection result of the transmission ratio is as follows: Figure 37 , Figure 38 As shown, the transmission ratio fluctuates during the transition between adjacent teeth meshing, indicating a transmission error in the bevel spur gear during meshing. The average transmission error is 0.40%, and the maximum relative transmission error reaches 1.02%, which does not exceed the transmission ratio error threshold. Meanwhile, the meshing force detection results are as follows... Figure 39 As shown, the average meshing force is 7317 N. During the transition between adjacent teeth meshing, there is an impact in the meshing force, with the maximum impact meshing force reaching 8059 N, exceeding the average meshing force by 10.14% and exceeding the threshold for sudden changes in meshing force, indicating an impact during transmission. During transmission, no off-center loading phenomenon occurs in the tooth width direction. Figure 40 As shown.

[0119] Example 7 In this embodiment, as Figures 41-46 As shown, the difference between the tooth meshing transmission matching detection and evaluation method based on Hertzian contact provided in this embodiment and Embodiment Six is ​​that the tooth meshing pair is a bevel helical gear meshing pair, and the three-dimensional geometric model of the transmission mechanism to be tested is a bevel helical gear meshing model.

[0120] In this embodiment, the geometric parameters include module, pressure angle, number of teeth, tooth addendum coefficient, clearance coefficient, and helix angle. Except for the newly added helix angle parameter, the other parameters are the same as those in Embodiment 4, as shown in Table 5.

[0121] Table 5 Geometric parameters of bevel helical gears Modulus 5mm pressure angle 20° Number of teeth 17、34 Tooth tip height coefficient 1 porosity 0.25 Axial angle 90° cone angle 45°、45° helix angle 8° Left-handed Based on the aforementioned gear geometric parameters, the gear tooth profile was designed, and a simulation model of bevel helical gear meshing was built, as follows: Figure 41 As shown.

[0122] The meshing tooth surfaces in the model are divided into discrete planar elements. For the cylindrical spur gear, the mesh is then created, and the Hermite interpolation algorithm is used to fit the discrete planar elements into continuous surface elements, such as... Figure 42 As shown.

[0123] As the driving gear rotates, the mesh nodes on the driving gear tooth surface will contact and penetrate the mesh surface on the driven gear tooth surface. At this time, the meshing position is not a line, but a region. The contact force in this region is calculated by the elastic coefficient and the penetration depth. The driving gear transmits motion and force to the driven gear through the contact force generated by this contact, causing the driven gear to rotate. The driving gear speed is set to 120 rpm, and the driven gear load torque is 500 N•m.

[0124] During the transmission engagement process, several recording time points are set to record the rotational speed of the driving and driven gears and the magnitude of the meshing force in the meshing area at each time point. In this embodiment, the detection result of the transmission ratio is as follows: Figure 43 , Figure 44 As shown, compared to the spur gear in Example 2, the helical gear exhibits smoother transmission during meshing, with an average transmission error of 0.38% and a maximum relative transmission error of 1.14%, both within the transmission ratio error threshold. Meanwhile, the meshing force detection results are as follows... Figure 45 As shown, the average meshing force is 6611 N, and the maximum meshing force is 6709 N. The impact of meshing force is smaller during the transition between adjacent teeth, and it does not exceed the threshold for sudden change in meshing force, resulting in a smooth transmission process. Due to the meshing characteristics of helical gears in the tooth width direction, the tooth surface begins to participate in meshing at the large end of the bevel gear. During meshing, the meshing part moves towards the small end until it disengages at the small end. In this embodiment, the meshing tooth surface disengages at approximately 20% of the tooth width from the small end, indicating that the tooth surface within 20% of the tooth width length from the small end in the tooth width direction does not participate in meshing. There is a shift in the center of the meshing part in the tooth width direction towards the large end by approximately 10% compared to the tooth width center, i.e., off-center loading occurs in the tooth width direction. Figure 46 As shown.

[0125] Example 7 In another typical embodiment of the present invention, such as Figures 1-12 As shown, a tooth meshing transmission matching detection and evaluation system based on Hertzian contact is presented, including: The modeling module is configured to: construct a three-dimensional geometric model of the transmission mechanism to be tested based on the target transmission ratio function and tooth profile geometric parameters; the three-dimensional geometric model includes geometric feature information reflecting the machining quality or assembly state; The mesh processing module is configured to: discretize the mesh of the meshing tooth surfaces in the three-dimensional geometric model, and reconstruct the discrete mesh elements into continuous surfaces using a surface smoothing fitting algorithm; The simulation calculation module is configured to: perform dynamic meshing simulation on the three-dimensional geometric model based on Hertzian contact theory, and calculate the contact force and motion transmission based on the continuous surface; The evaluation module is configured to evaluate the matching performance based on the comparison between the actual transmission ratio and meshing force obtained from the simulation and the theoretical benchmark.

[0126] The working method of the tooth meshing transmission matching detection and evaluation system based on Hertz contact is the same as that in Example 1, and will not be repeated here.

[0127] 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 method for detecting and evaluating tooth-to-tooth meshing transmission matching based on Hertzian contact, characterized in that, include: Based on the target transmission ratio function and tooth profile geometric parameters, a three-dimensional geometric model of the transmission mechanism to be tested is constructed; the three-dimensional geometric model includes geometric feature information reflecting the machining quality or assembly state; The meshing tooth surfaces in the three-dimensional geometric model are discretized into a mesh, and the discrete mesh elements are reconstructed into a continuous surface using a surface smoothing fitting algorithm. Dynamic meshing simulation of a three-dimensional geometric model based on Hertzian contact was performed to calculate the contact force and motion transmission based on a continuous surface. The matching performance is evaluated by comparing the actual transmission ratio and meshing force obtained from the simulation with the theoretical benchmark.

2. The tooth-to-tooth meshing transmission matching detection and evaluation method based on Hertzian contact as described in claim 1, characterized in that, The construction of the three-dimensional geometric model of the transmission mechanism to be tested includes: Based on the preset machining tolerance level, geometric error parameters are actively introduced into the ideal geometric model to construct a three-dimensional geometric model containing preset deviations. Alternatively, a three-dimensional geometric model reflecting the surface morphology of the actual gear can be reconstructed based on reverse scanning data of the gear.

3. The tooth-to-tooth meshing transmission matching detection and evaluation method based on Hertzian contact as described in claim 2, characterized in that, The introduced geometric error parameters include at least one or more of the following: tooth thickness error, tooth profile error, eccentricity error, axis perpendicularity error, axis intersection angle error, or helix angle error.

4. The tooth-to-tooth meshing transmission matching detection and evaluation method based on Hertzian contact as described in claim 1, characterized in that, The three-dimensional geometric model of the transmission mechanism to be tested includes at least one of the following types: variable transmission ratio gear and rack meshing model, cylindrical spur gear meshing model, cylindrical helical gear meshing model, bevel spur gear meshing model, or bevel helical gear meshing model.

5. The tooth-to-tooth meshing transmission matching detection and evaluation method based on Hertzian contact as described in claim 1, characterized in that, The method of reconstructing discrete mesh elements into continuous surfaces using a surface smoothing fitting algorithm includes: The Hermite interpolation algorithm is used to calculate the tangent vectors and curvatures of discrete mesh nodes and construct a continuous interpolation surface covering the discrete mesh to eliminate the abrupt change in the tooth surface normal vector caused by mesh discretization.

6. The tooth-to-tooth meshing transmission matching detection and evaluation method based on Hertzian contact as described in claim 1, characterized in that, The dynamic meshing simulation of the three-dimensional geometric model based on Hertzian contact includes: Define the tooth surface contact parameters; where the contact parameters include the contact stiffness coefficient determined by the tooth surface material properties and the damping coefficient simulating meshing energy loss; Within the simulation step, the penetration depth of the mesh nodes on the tooth surfaces of the driving and driven components is detected. When penetration is detected, the normal contact force is calculated based on the penetration depth and the contact stiffness coefficient, and the tangential contact force is calculated based on the friction coefficient.

7. The tooth-to-tooth meshing transmission matching detection and evaluation method based on Hertzian contact as described in claim 6, characterized in that, The matching performance is evaluated based on the actual transmission ratio and meshing force obtained from the simulation, compared with the theoretical benchmark, including: The ratio of the instantaneous velocity of the driven component to the instantaneous velocity of the driving component in the transmission mechanism is calculated during the simulation, and the actual transmission ratio curve is generated. Calculate the relative error between the actual transmission ratio curve and the target transmission ratio function; if a sudden peak in the transmission ratio is detected in the alternating meshing area of ​​the tooth surface exceeding the preset threshold, it is determined that there is a tooth pitch deviation or tooth profile deviation in the tooth profile.

8. The tooth-to-tooth meshing transmission matching detection and evaluation method based on Hertzian contact as described in claim 6, characterized in that, The matching performance is evaluated based on the comparison between the meshing force obtained from the simulation and the theoretical benchmark, including: Calculate the magnitude and direction of the meshing force at the meshing point during meshing, set a threshold for sudden change in meshing force, and when the change in meshing force exceeds the set threshold, it indicates that an impact or transmission interruption has occurred during meshing, and the meshing tooth profile mismatch is defined.

9. The tooth-to-tooth meshing transmission matching detection and evaluation method based on Hertzian contact as described in claim 6, characterized in that, The matching performance is evaluated based on the contact characteristics and phase information obtained from the simulation, including: Based on the dynamic meshing simulation results, a contact spot cloud map that changes over time is generated to analyze the distribution of contact spots in the tooth width direction; at the same time, the meshing phase in which the peak contact force occurs is analyzed. If the distribution center of the contact spot deviates from the tooth width centerline and moves towards the tooth tip, or if the peak of the contact force appears in an unexpected meshing phase, it is determined that the transmission mechanism has an axis parallelism error or an assembly eccentricity error.

10. A tooth-to-tooth meshing transmission matching detection and evaluation system based on Hertzian contact, characterized in that, include: The modeling module is configured to: construct a three-dimensional geometric model of the transmission mechanism to be tested based on the target transmission ratio function and tooth profile geometric parameters; the three-dimensional geometric model includes geometric feature information reflecting the machining quality or assembly state; The mesh processing module is configured to: discretize the mesh of the meshing tooth surfaces in the three-dimensional geometric model, and reconstruct the discrete mesh elements into continuous surfaces using a surface smoothing fitting algorithm; The simulation calculation module is configured to: perform dynamic meshing simulation on the three-dimensional geometric model based on Hertzian contact theory, and calculate the contact force and motion transmission based on the continuous surface; The evaluation module is configured to evaluate the matching performance based on the comparison between the actual transmission ratio and meshing force obtained from the simulation and the theoretical benchmark.

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