Gear form grinding tooth surface topography digitization simulation and contact analysis method

Abstract

The application discloses a gear forming grinding tooth surface appearance digital simulation and contact analysis method, and belongs to the field of gear manufacturing and transmission analysis. The method establishes a grinding wheel abrasive grain model based on grinding wheel parameters, generates theoretical tooth surface discrete points and normal vectors thereof according to gear geometric parameters, determines abrasive grain motion trajectories and undeformed chip thicknesses based on grinding processing parameters and grinding wheel vibration parameters, updates the tooth surface to obtain a micro appearance, and generates a topography error matrix by comparing the theoretical tooth surface; contact discrete points are arranged on the meshing action surface, the topography error is interpolated and mapped to the contact points, and the contact initial gap is constructed by superimposing the system deformation gap correction amount; the contact initial gap is used to solve a bearing contact equation set to obtain a contact analysis result. The application links a complete analysis link from grinding processing parameters to tooth surface contact performance, can establish a quantitative relationship between the two in a simulation stage, and reduces research and development costs.

Description

Technical Field

[0001] This invention belongs to the field of gear manufacturing and gear transmission analysis technology, and specifically relates to a digital simulation and contact analysis method for the morphology of gear forming and grinding tooth surfaces. Background Technology

[0002] Gear forming grinding is one of the important processes for finishing large-module, high-precision gears after heat treatment. The micro-morphology of the gear tooth surface is determined by factors such as the distribution of abrasive grains in the grinding wheel, model parameters, grinding parameters, spatial motion relationship, and machine tool vibration, which directly affect the contact load state and service performance of the gear pair.

[0003] In existing technologies, tooth surface grinding morphology simulation is mainly based on surface grinding or worm wheel generating grinding models. Surface morphology is generated using fractal functions, random functions, or statistical autocorrelation functions. Some methods introduce parameters such as wheel grit size and microstructure to establish an abrasive model and calculate the thickness of undeformed chips. Simulation results are output as discrete coordinate points. Tooth surface load-bearing contact analysis focuses on the macroscopic meshing characteristics of gear pairs. It uses finite element analysis or slicing methods to solve for the influence of transmission system deformation on load distribution and transmission errors. Its tooth surface geometry input comes from theoretical roughness models or standard measurement data, and the input form is a set of contact points on the meshing plane. The data formats and spatial locations of the two types of models are different. Under this current technological state, a quantitative relationship between grinding parameters and tooth surface contact state cannot be established in the simulation stage. In engineering, multiple prototypes and experiments are usually required to evaluate the influence of different processing parameters on the contact state. This significantly increases R&D and time costs for large-module, high-precision gears with high material costs and long processing cycles. Summary of the Invention

[0004] To address the aforementioned problems, the purpose of this invention is to provide a digital simulation and contact analysis method for the tooth surface morphology of gear forming and grinding, which is used to establish a quantitative relationship between grinding parameters and tooth surface contact state during the simulation stage, thereby reducing the number of prototypes and experiments and lowering R&D costs.

[0005] The technical solution of this invention is: a method for digital simulation and contact analysis of gear tooth surface morphology during forming and grinding, comprising the following steps: Obtain gear geometry parameters, grinding wheel parameters, grinding parameters, grinding wheel vibration parameters, transmission system parameters, and load condition parameters.

[0006] A grinding wheel abrasive model is established based on the grinding wheel parameters. Theoretical tooth surface discrete points and their normal vectors are generated according to the gear geometry parameters. The motion trajectory of the abrasive particles relative to the tooth surface is determined based on the grinding parameters and grinding wheel vibration parameters. The undeformed chip thickness at each tooth surface point is determined based on the spatial interference relationship between the motion trajectory and the discrete points on the tooth surface. The coordinates of the discrete points on the tooth surface are updated using the undeformed chip thickness to obtain the microstructure of the shaped ground tooth surface. The microstructure of the shaped ground tooth surface is compared with the theoretical tooth surface to generate a tooth surface morphology error matrix. Since the abrasive particle modeling, motion trajectory calculation, and material removal amount determination are all based on actual grinding parameters and grinding wheel vibration parameters, the obtained tooth surface microstructure can reflect the comprehensive influence of grinding wheel parameters, grinding parameters, and vibration factors.

[0007] Discrete contact points are arranged on the meshing surface to determine the spatial position of each contact point on the tooth surfaces of the driving and driven wheels. The shape error at each contact point is obtained by interpolation based on the tooth surface shape error matrix. The system deformation clearance correction at each contact point is obtained based on the transmission system parameters and the load condition parameters. The initial contact clearance is constructed by superimposing the shape error and the system deformation clearance correction. By mapping the shape error interpolation to the contact points and superimposing it with the system deformation clearance correction, the microscopic shape error and the transmission system deformation response can participate in the load-bearing contact solution within the same analytical framework.

[0008] Based on the initial contact gap, a set of contact equations for tooth surface bearing capacity was established and iteratively solved to obtain the tooth surface contact analysis results. This establishes a complete analytical chain from grinding parameters to tooth surface contact performance.

[0009] Furthermore, the grinding wheel parameters include the grinding wheel grit number and the grinding wheel structure number. Establishing the grinding wheel abrasive model includes: determining the abrasive size distribution based on the grinding wheel grit number, determining the average abrasive spacing based on the grinding wheel structure number, arranging abrasive grains on the working surface of the grinding wheel, and introducing random positional perturbations along the circumference and tooth profile directions of the grinding wheel to characterize the randomness of the abrasive spatial distribution, generating an abrasive identification information table containing the spatial coordinates, diameter, and protrusion height of each abrasive grain. Through refined modeling of the abrasive size and spatial distribution, the grinding wheel abrasive model more closely approximates the actual grinding wheel state, improving the realism of the tooth surface morphology simulation results.

[0010] Furthermore, the grinding parameters include the grinding wheel rotation speed and feed rate; determining the motion trajectory of the abrasive grains relative to the tooth surface includes: determining the instantaneous rotation angle of the grinding wheel based on the grinding wheel rotation speed, determining the instantaneous feed distance of the grinding wheel along the workpiece axis based on the feed rate, and jointly determining the spatial coordinate transformation relationship between the grinding wheel and the workpiece by the instantaneous rotation angle and the instantaneous feed distance; based on the spatial coordinate transformation relationship, and by introducing the grinding wheel vibration parameters in the form of dynamic offset of the grinding wheel center, transforming the position of the abrasive grains on the grinding wheel surface at any moment from the grinding wheel coordinate system to the workpiece coordinate system, determining the instantaneous position sequence of the abrasive grain center in the workpiece coordinate system, and forming the motion trajectory of the abrasive grains relative to the tooth surface. By introducing the grinding wheel vibration parameters in the spatial coordinate transformation, the motion trajectory of the abrasive grains can reflect the dynamic disturbances in actual processing, thereby more accurately characterizing the microscopic peaks and valleys and vibration ripples formed during the form grinding process.

[0011] Further, determining the undeformed chip thickness at each tooth surface point includes: for each discrete point on the tooth surface, traversing the instantaneous spatial positions of all abrasive grains at each discrete time step, determining the instantaneous undeformed chip thickness generated by each abrasive grain at that tooth surface point, and taking the maximum value among all instantaneous values ​​as the undeformed chip thickness at that tooth surface point. By traversing the instantaneous positions of all abrasive grains at each time step and taking the maximum chip thickness, the repeated cutting action of multiple abrasive grains on the same tooth surface point during grinding can be accurately characterized.

[0012] Furthermore, generating the tooth surface topography error matrix includes: calculating the difference between the coordinates of the ground and updated discrete points on the tooth surface and the coordinates of the theoretical discrete points on the tooth surface to obtain the normal deviation at each discrete point, forming a topography error matrix corresponding to the discrete mesh of the tooth surface. This error matrix organizes the micro-topography information using the discrete mesh of the tooth surface as an index, providing quantifiable input data for subsequent load-bearing contact analysis.

[0013] Furthermore, the discrete contact points are arranged by uniformly distributing them along the meshing line, and obtaining the spatial position of each contact point in the driving and driven gear coordinate systems through gear end face coordinate transformation. By uniformly distributing contact points on the meshing surface and establishing a mapping relationship with the driving and driven gear coordinate systems, an accurate spatial positioning basis is provided for subsequent error mapping and contact solution.

[0014] Furthermore, obtaining the morphological errors at each contact discrete point includes: transforming the tooth surface morphological error matrix from the workpiece coordinate system to the gear follower coordinate system of the load-bearing contact analysis model, and then obtaining the morphological errors at each contact discrete point through interpolation. Through coordinate transformation and interpolation operations, the tooth surface morphological errors can be accurately incorporated into the load-bearing contact analysis according to the actual spatial position of the contact discrete points.

[0015] Furthermore, obtaining the system deformation clearance correction includes: establishing and solving the static equilibrium equation of the transmission system using the slice finite element method to obtain the relative displacement between each slice along the tooth width direction; and converting the relative displacement into the system deformation clearance correction at the contact point based on the slice position of the contact discrete point. By solving the transmission system deformation using the slice finite element method, the system deformation response can participate in the load-bearing contact analysis in the form of the contact point clearance correction.

[0016] Furthermore, the tooth surface bearing contact equation set is established and iteratively solved, including: the tooth surface bearing contact equation set is established based on the deformation coordination relationship of the gear pair before and after loading; the equation set includes the contact point compliance matrix, contact deformation vector, rigid body approach vector, contact point remaining clearance vector, contact point initial clearance vector, and contact point load column vector; during the iterative solution process, each iteration first solves the contact equation set to obtain the contact point load and transmission error, then solves the system static equilibrium equation based on the contact point load to update the system deformation clearance correction, and superimposes the updated system deformation clearance correction with the morphology error as the initial clearance for the next iteration, until the convergence tolerance is met. Through the alternating iterative solution of the contact equation set and the system static equation, the coupled analysis of the tooth surface micromorphology error and the overall deformation response of the transmission system is realized, making the contact analysis results closer to the actual service state.

[0017] Compared with existing technologies, the advantages of this invention are as follows: First, this invention performs physical simulation of the morphology of the formed grinding tooth surface based on grinding parameters and grinding wheel vibration parameters, enabling the obtained micro-morphology of the tooth surface to reflect the comprehensive influence of grinding wheel parameters, grinding parameters, and vibration factors. Then, it compares this morphology with the theoretical tooth surface to generate a morphology error matrix, solving the problem of mismatch between simulation results and contact analysis input format. Furthermore, by interpolating the morphology error to discrete contact points and superimposing it with the system deformation gap correction to construct the initial contact gap, the micro-morphology error and the transmission system deformation response can participate in the load-bearing contact solution under the same analytical framework, overcoming the deficiency of separate processing of the two types of errors in existing technologies. Therefore, this invention connects the complete analytical link from grinding parameters to tooth surface contact performance, enabling the quantitative relationship between the two to be established in the simulation stage, thereby reducing the number of trial production iterations, shortening the process development cycle, and providing a basis for optimizing grinding parameters. Attached Figure Description

[0018] Figure 1 This is a flowchart of the present invention; Figure 2 This is a schematic diagram of the position vector of point k on the involute tooth surface of the present invention; Figure 3 This is a schematic diagram of the processing space coordinate system of the present invention; Figure 4This is a schematic diagram of the axial profile of the grinding wheel of the present invention; Figure 5 This is a schematic diagram of the working surface of the grinding wheel of the present invention. Figure 6 This is a schematic diagram showing the position of the abrasive grains in the grinding wheel coordinate system of the present invention; Figure 7 This is a schematic diagram of the grinding motion of the present invention; Figure 8 This is a schematic diagram of the grinding wheel vibration of the present invention; Figure 9 This is a schematic diagram of the undeformed chips of the present invention; Figure 10 This is a static model diagram of the slice gear system of the present invention; Figures 11 to 13 These are comparison images of tooth surface morphology at different feed rates in application examples of this invention; wherein, Figure 11 The feed rate is 5 mm / s. Figure 12 For a feed rate of 10 mm / s, Figure 13 The feed rate is 15 mm / s; Figures 14 to 16 This is a comparison diagram of contact stress at different feed rates in an application example of the present invention; wherein, Figure 14 The feed rate is 5 mm / s. Figure 15 For a feed rate of 10 mm / s, Figure 16 The feed rate is 15 mm / s; Figure 17 , Figure 18 This is a comparison diagram showing the effects of different feed rates on transmission error and meshing stiffness in an application example of the present invention. Detailed Implementation

[0019] The following is combined Figures 1 to 18 The specific embodiments of the present invention will be described in detail below.

[0020] Example like Figure 1 The method for digital simulation and contact analysis of gear tooth surface morphology after forming and grinding, as shown, includes the following steps: S1. Obtain gear geometry parameters, grinding wheel parameters, grinding parameters, grinding wheel vibration parameters, transmission system parameters, and load condition parameters. Among them, the grinding wheel parameters include the grinding wheel grit number and grinding wheel structure number, and the grinding parameters include the grinding wheel speed and feed rate.

[0021] S2. Establish a simulation and error generation model for the morphology of the formed grinding tooth surface, obtain the micro-morphology of the formed grinding tooth surface, and convert it into a tooth surface morphology error matrix.

[0022] S2-1. Establish a spatial coordinate system for the grinding wheel and workpiece by referring to the actual coordinate system of the grinding machine tool. By relating the coordinate system of the actual grinding machine tool, establish a gear follower coordinate system and a grinding wheel tool coordinate system. For example... Figure 3 As shown, let the gear follower coordinate system be... This is a reference coordinate system fixed on the gear workpiece, serving as the datum for the final tooth surface topography data. Regardless of the gear's rotation, this coordinate system always follows the gear's rotation. Its origin... Located at the center of the gear end face axis, The shaft is located within the end face of the gear, along a symmetrical center line pointing from the origin to a certain tooth groove. The shaft and gear axis coincide. The shaft is perpendicular to the end face. and The axis conforms to the right-hand rule.

[0023] Grinding wheel coordinate system This is a tool coordinate system fixed on the grinding wheel, with its origin located at the midpoint of the grinding wheel's axis. The shaft coincides with the axis of the grinding wheel.

[0024] The maximum and average sizes of the corresponding abrasive grains are determined based on the grinding wheel grit number. The average distribution distance of the abrasive grains is determined based on the grinding wheel microstructure number. The number of abrasive grains on the grinding wheel is then determined based on the abrasive grain diameter and the average distribution distance. For example... Figure 5 As shown, the working surface of the grinding wheel is unfolded onto a plane. According to the 3σ principle, the vast majority of abrasive grain sizes are distributed within a 3σ range on both sides of the mean. The largest abrasive grain size is considered as the upper limit deviation of the mean, and the diameter data of each abrasive grain is obtained through random distribution. Figure 6 As shown, it is assumed that abrasive grains are uniformly distributed on the working surface of the grinding wheel, and minute random positional perturbations are introduced along the circumference and tooth profile directions of the grinding wheel to characterize the random characteristics of the spatial distribution of abrasive grains. The perturbation amplitude is related to the average spacing between abrasive grains and is adjusted with changes in grinding wheel grit size, microstructure, and model parameters. The spatial three-dimensional coordinate position of each abrasive grain in the grinding wheel, as well as its diameter and random protrusion height, are stored in an abrasive grain identity information table to complete the establishment of the grinding wheel abrasive grain model.

[0025] S2-2. Generate the theoretical discrete points of the tooth surface and their normal vectors based on the gear geometric parameters.

[0026] Based on the established coordinate system, the position vector expression of any point k on the tooth surface in the workpiece coordinate system is obtained according to the gear parameter calculation formula: ;in, Let k be the position vector of any point k on the tooth surface in the workpiece coordinate system, that is, the position vector of each discrete point on the tooth surface; The base circle radius of the gear; The roll angle of the involute; This represents the tooth width position corresponding to this tooth surface point; The base circle tooth groove half angle.

[0027] Base circle tooth groove half angle According to the formula It is confirmed that, among them, This refers to the number of teeth on the gear. The pressure angle is the pitch circle angle.

[0028] like Figure 2 As shown, based on the differential geometry of the tooth surface, the normal unit vector of any point k on the tooth surface in the workpiece coordinate system is: ;in, It is the unit normal vector of any point k on the tooth surface in the workpiece coordinate system, that is, the normal vector of each discrete point on the tooth surface.

[0029] The tooth surface is discretized along both the tooth profile direction and the tooth width direction. The tooth profile direction is divided into... Each node is divided into several parts in the tooth width direction. Each node discretizes the entire tooth surface into [number] nodes. There are 1 grid point. The coordinates of the discrete tooth surface nodes are: The normal vector at each discrete tooth surface point is always perpendicular to the local tangent plane of the tooth surface and points outward from the tooth surface. The resulting discrete node unit normal vector is... .

[0030] Considering that the actual grinding process usually adopts the method of leaving a grinding allowance, let the grinding allowance in the normal direction of the tooth surface be... Then the position vector of the corresponding discrete point on the tooth surface to be machined can be expressed as: .

[0031] S2-3. Determine the motion trajectory of the abrasive particles relative to the tooth surface.

[0032] like Figure 4 As shown, the axial profile of the grinding wheel is solved based on spatial meshing theory and grinding motion relationships. The wheel-workpiece center distance is corrected based on the actual spatial position during grinding. The corrected center distance is: ;in, The radius of the base circle, Let m be the macroscopic radius of the grinding wheel. This represents the maximum radial protrusion height of the abrasive grains. This represents the radial cutting depth.

[0033] The instantaneous rotation angle of the grinding wheel is determined based on its rotational speed, and the instantaneous feed distance along the workpiece axis is determined based on the feed rate. The spatial coordinate transformation relationship between the grinding wheel and the workpiece is then determined jointly by the instantaneous rotation angle and the instantaneous feed distance. The homogeneous transformation matrix from the workpiece coordinate system to the grinding wheel coordinate system can be expressed as:

[0034] ;in, For the time elapsed The abrasive grains of the rear grinding wheel are around The rotation angle of the shaft; For the time elapsed The abrasive grains of the rear grinding wheel move along The distance the axis moves; , .

[0035] Based on this spatial coordinate transformation relationship, and by introducing grinding wheel vibration parameters in the form of dynamic offset of the grinding wheel center, such as... Figure 7 As shown, the position of any abrasive grain on the grinding wheel surface at any given moment is transformed from the grinding wheel coordinate system to the workpiece coordinate system: .

[0036] By solving for the spatial position of the abrasive grains at different times, the instantaneous position sequence of the abrasive grain center in the workpiece coordinate system is determined, forming the motion trajectory expression of the abrasive grains relative to the tooth surface: ,in, For the first The angular position of each abrasive grain in the circumferential direction of the grinding wheel. This refers to the position of the abrasive grain in the width direction of the grinding wheel. , , It represents a three-dimensional vibration displacement.

[0037] like Figure 8 As shown, the grinding wheel vibration parameters are introduced by using the superposition of multi-order simple harmonic vibration and random noise to simulate the uncertainty of machine vibration. The forming grinding vibration is decomposed into the fundamental frequency vibration of the grinding wheel spindle rotation, the frequency vibration of transmission components or bearing defects, and background noise. The fundamental frequency vibration of the grinding wheel spindle rotation is caused by the residual imbalance of the grinding wheel or spindle eccentricity, and its frequency is... The vibration frequency of transmission components or bearing defects is usually caused by the rotation of the grinding wheel, and its frequency is a multiple of the spindle frequency. Background noise represents the random impact of the cutting fluid and the microscopic fragmentation of abrasive particles, and is simulated using a Gaussian random function. The non-uniform harmonic function simulating machine vibration is: ;in, The amplitude of each order of vibration, For the frequencies of each order of vibration, The initial phase of each order of vibration, This represents a random walk or Gaussian white noise that follows a normal distribution. The vibration is treated as a dynamic bias at the center of the grinding wheel using the vibration matrix, and introduced into the trajectory of the grinding grains.

[0038] S2-4. Determine the thickness of the undeformed chip at each tooth surface point.

[0039] like Figure 9 As shown, for discrete points on the tooth surface Its unit normal vector is ;No. abrasive grains in The coordinates of the center of the sphere at time are abrasive grain radius is The position vector of the abrasive grain center relative to the tooth surface point can be expressed as:

[0040] .

[0041] No. abrasive grains in Constantly on the tooth surface point The instantaneous undeformed chip thickness is: ,in, This is the normal distance between the center of the abrasive grain and a point on the tooth surface; It represents the lateral offset distance of the grinding ball's center relative to the normal of the eating point.

[0042] For each discrete point on the tooth surface, the instantaneous spatial positions of all abrasive grains at each discrete time step are traversed to determine the instantaneous undeformed chip thickness generated by each abrasive grain at that tooth surface point. The maximum value among all instantaneous values ​​is taken as the undeformed chip thickness at that tooth surface point. ,in, The maximum undeformed chip thickness at the tooth surface point; For the first abrasive grains in The instantaneous undeformed chip thickness generated at that point at any given moment.

[0043] S2-5. Obtain the microstructure of the shaped ground tooth surface.

[0044] The tooth surface to be machined is updated based on the maximum undeformed chip thickness at each tooth surface point. The coordinates of the discrete points on the tooth surface after grinding are: ;in, These are the coordinates of discrete points on the tooth surface after grinding; These are the coordinates of discrete points on the tooth surface to be machined; The unit normal vector at the discrete point; This represents the maximum undeformed chip thickness at each discrete tooth surface point.

[0045] S2-6. Generate the tooth surface morphology error matrix.

[0046] The difference between the coordinates of the discrete points on the ground tooth surface after grinding and the coordinates of the discrete points on the theoretical tooth surface is used to obtain the normal deviation at each discrete point: .

[0047] Based on the machined tooth surface and the theoretical tooth surface, a discretized tooth surface shape error height matrix is ​​obtained. The tooth surface shape error height matrix corresponds one-to-one with the spatial position of the tooth surface through the tooth profile and tooth width index.

[0048] S3. Establish a tooth surface bearing contact analysis model that couples the morphology error with the system deformation response, map the tooth surface morphology error and the system deformation error to discrete contact points, and construct the initial contact gap.

[0049] S3-1, Set up discrete contact points.

[0050] Establish a master-slave coordinate system based on gears. and Where the y-axis passes through the center of the gear teeth, and the z-axis is the gear axis. Establish a coordinate system for the meshing surface. Divide the meshing surface evenly into meshing lines, use numbering to determine the meshing lines, and arrange evenly distributed contact points on the meshing lines. The absolute position of each contact point is determined by its number, and its coordinates in the meshing surface coordinate system are expressed as follows: and The contact point is mapped to the mapping point on the end face of the driving wheel and the driven wheel. Represented as and .

[0051] Through The end face of the gear The contact point can be obtained by coordinate transformation. In the absolute spatial position of the master and slave wheel coordinate system, in the formula , The base circle helix angle is the angle between the driving and driven wheels, with right-hand helix being positive and left-hand helix being negative.

[0052] Right now This determines the location of the contact point in the driving and driven wheels.

[0053] S3-2. Obtain the morphological error at each contact discrete point.

[0054] The tooth surface shape error matrix is ​​transformed from the workpiece coordinate system to the gear follower coordinate system of the load-bearing contact analysis model. The coordinate transformation mapping matrix between the form grinding model coordinate system and the load-bearing contact analysis model coordinate system is as follows:

[0055] ;in, The coordinate system rotation matrix is ​​obtained by... Solve the problem. This represents the rotation angle.

[0056] Based on coordinate transformation, the theoretical tooth surface point positions of the ground tooth surface are correlated with the tooth surface positions of the driving and driven gears in the load contact analysis. The absolute positions of the contact points and the absolute positions of the ground tooth surfaces are compared in the same coordinate system. Using the same coordinate points as indexes, the morphological errors of the discretized tooth surfaces are supplemented by interpolation to obtain the corresponding tooth surface morphological errors of each contact point.

[0057] S3-3, Obtain the system deformation gap correction amount at each contact discrete point.

[0058] Based on the mapping of tooth surface morphology errors to contact points, the system deformation clearance correction amount is solved. For example... Figure 10 As shown, the static equilibrium equations of the transmission system are established and solved using the slice finite element method. Specifically, the gear system is discretized into slice meshing elements, shaft segment elements, bearing elements, and coupling elements using generalized finite element theory. The matrix form of the static equilibrium equations of each element is then assembled according to the physical connection relationship of the transmission system to obtain the static equilibrium equations of the system: ;in, For slice meshing stiffness; For slice coupling stiffness; Shaft stiffness; For bearing stiffness; Here is the stiffness matrix of the coupling; The generalized coordinate matrix of the gear pair slice; The load matrix is ​​generated from the load condition parameters obtained from S1.

[0059] The relative displacement between the gear slices along the tooth width direction, i.e., the meshing misalignment, is calculated using the system's static equilibrium equations. According to the definition of meshing misalignment in ISO 6336, the meshing misalignment of a gear pair is the difference in relative displacement between the gear slices along the tooth width direction. The deformation error vector of the meshing line slice system is obtained by solving the problem. , where j represents the contact point number of the meshing line slice.

[0060] The relative displacement is converted into a system deformation gap correction amount at the contact point based on the slice position where the contact discrete point is located.

[0061] S3-4. Construct the initial contact gap.

[0062] The set of load-bearing contact equations for each meshing line established through deformation compatibility relationships is as follows: ,in, This represents the macroscopic deformation compliance matrix of the contact points on the meshing line. The contact deformation vector of the contact point on the meshing line; It is the rigid body proximity vector, and also the static propagation error; The vector representing the remaining gap at the contact point; The initial gap vector at the contact point; This is the column vector of contact point loads.

[0063] The tooth surface topography error obtained by coordinate mapping and the system deformation error obtained by slice statics are superimposed to generate the initial error gap vector for each contact discrete point: .

[0064] S4. Establish the tooth surface bearing contact equation system and solve iteratively to obtain the tooth surface contact analysis results. Set the contact point gap to Superscript The iteration number is given because the contact equations were not solved initially. = At 1 o'clock, .

[0065] Solve the contact analysis model and output the contact point load. and transmission error Based on the obtained data, the static equilibrium equations of the system are constructed and solved. The system deformation error at each contact point is then calculated using the meshing misalignment calculation formula. The system deformation error is added to the initial gap at the contact point for assignment. . judge and Does the relative error satisfy the convergence tolerance? If not, then... As the contact gap, the contact analysis model and system deformation error are re-solved for the next iteration. If the convergence condition is met, the meshing stiffness, transmission error, and load distribution of the gear pair are output.

[0066] Application examples Based on the method proposed in the embodiments, different feed rate machining parameters were selected to examine their effects on tooth surface morphology and contact characteristics, and the effects of different feed rates on overall roughness were obtained as shown in Table 1.

[0067] Table 1: Effect of different feed rates on overall surface roughness 1 60 5 2450 5 1 0.7239 2 60 5 2450 10 1 0.7631 3 60 5 2450 15 1 1.1269 Table 1 shows that when the feed rates are 5, 10, and 15 mm / s, the overall arithmetic mean height Sa of the tooth surface is 0.7239 mm / s. 0.7631 The surface roughness (Sa) generally increases with increasing feed rate, as shown by the values ​​of 1.1269#imgpt134#. When the feed rate increases from 5 mm / s to 10 mm / s, Sa increases by 0.0392#imgpt135#, an increase of approximately 5.42%, indicating that the surface roughness changes relatively little within the lower feed rate range. When the feed rate further increases from 10 mm / s to 15 mm / s, Sa increases by 0.3638#imgpt136#, an increase of 47.67%, indicating a significant deterioration in surface quality. Compared to 5 mm / s, Sa increases by 0.4030#imgpt137# under the 15 mm / s condition, an increase of approximately 55.67%. The quantitative results are consistent with the observations of local and three-dimensional morphology, indicating that the influence of feed rate on surface roughness is more significant within the higher speed range.

[0068] Depend on Figures 11 to 13 It is evident that feed rate has a significant impact on the microstructure of the tooth surface. When the feed rate is 5 mm / s, the grinding texture of the tooth surface is relatively fine, the periodic grooves are relatively regularly distributed, the scale of local peaks and valleys is small, and the surface height distribution is relatively uniform. When the feed rate increases to 10 mm / s, the overall morphology of the tooth surface is similar to that at 5 mm / s, but some strip-like textures are enhanced, and the local peak and valley undulations are slightly increased. When the feed rate is further increased to 15 mm / s, the grinding texture becomes significantly coarser, with an increase in local high peaks, deep valleys, and irregular patches. The spacing and height difference between grooves also increase, and the uniformity of the tooth surface morphology decreases significantly. Therefore, as the feed rate increases, the tooth surface grinding trajectory gradually changes from fine and uniform to coarse and uneven, with the surface fluctuations being most pronounced at 15 mm / s.

[0069] Contact analysis considering deformation and tooth surface errors: such as Figures 14 to 16 As shown, the tooth surface contact stress at different feed rates exhibits similar macroscopic off-center loading characteristics. Along the tooth width direction, the contact stress generally decreases gradually from left to right, with the main load-bearing area concentrated in the tooth width range of 0mm to 60mm, while the stress is relatively low in the 80mm to 100mm region. Along the meshing line direction, the main high-stress zones are located in the range of approximately 11mm to 15mm. This indicates that system deformation remains the main factor determining the macroscopic distribution location of contact stress and the gradient along the tooth width direction, while feed rate mainly modulates the local contact stress by changing the tooth surface grinding texture, residual peaks and valleys, and the continuity of the actual contact area. As the feed rate increases from 5mm / s to 15mm / s, the contact stress distribution gradually changes from relatively continuous and uniform to discrete and concentrated. The maximum contact stress increases from approximately 900MPa to nearly 1000MPa, while the number, area, and local gradient of high-stress spots increase significantly.

[0070] like Figure 17 , Figure 18 As shown, with the feed rate increasing from 5 mm / s to 15 mm / s, the average value of the transmission error does not change significantly overall, but the range of curve fluctuations gradually expands, and the local peak-valley differences become more prominent. At low feed rates, the tooth surface texture is relatively fine, and the actual contact process has good continuity. The multi-tooth meshing area can play a certain role in averaging and weakening local morphological deviations, so the overall transmission error curve is relatively stable. As the feed rate increases, the spatial scale of the grinding texture increases, and the contact phase difference and local clearance changes between different meshing positions intensify, making the actual contact point distribution more discrete. This leads to increased local fluctuations in the transmission error and reduced curve stability.

[0071] Increasing feed rate leads to a general decrease in meshing stiffness, while the amplitude of fluctuations in the stiffness curve gradually increases. At low feed rates, the tooth surface contact area is relatively continuous, the effective load-bearing length is large, and the contact stiffness distribution is relatively uniform, resulting in a high overall stiffness level with gradual changes. As the feed rate increases, the tooth surface texture gradually changes from fine to coarse, the actual contact area becomes discretized, and the effective load-bearing area decreases, leading to a reduction in overall meshing stiffness. Simultaneously, due to the increased unevenness in the distribution of local contact points, the sensitivity of stiffness to changes in meshing position increases, resulting in more pronounced abrupt changes in local stiffness and increased curve fluctuations.

[0072] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and do not limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the protection scope of the present invention.

Claims

1. A method for digital simulation and contact analysis of gear tooth surface morphology during forming and grinding, characterized in that, Includes the following steps: Obtain gear geometry parameters, grinding wheel parameters, grinding parameters, grinding wheel vibration parameters, transmission system parameters, and load condition parameters; A grinding wheel abrasive model is established based on the grinding wheel parameters. The theoretical tooth surface discrete points and their normal vectors are generated according to the gear geometric parameters. The motion trajectory of the abrasive relative to the tooth surface is determined based on the grinding parameters and grinding wheel vibration parameters. The thickness of the undeformed chip at each tooth surface point is determined according to the spatial interference relationship between the motion trajectory and the tooth surface discrete points. The coordinates of the tooth surface discrete points are updated by the undeformed chip thickness to obtain the micro-morphology of the shaped grinding tooth surface. The micro-morphology of the shaped grinding tooth surface is compared with the theoretical tooth surface to generate a tooth surface morphology error matrix. Contact discrete points are arranged on the meshing surface to determine the spatial position of each contact discrete point on the tooth surface of the driving wheel and the driven wheel. The shape error at each contact discrete point is obtained by interpolation according to the tooth surface shape error matrix. The system deformation clearance correction amount at each contact discrete point is obtained based on the transmission system parameters and the load condition parameters. The shape error and the system deformation clearance correction amount are superimposed to construct the initial contact clearance. Based on the initial contact gap, a set of tooth surface bearing contact equations is established and iteratively solved to obtain the tooth surface contact analysis results.

2. The method for digital simulation and contact analysis of gear tooth surface morphology in gear forming and grinding as described in claim 1, characterized in that, The grinding wheel parameters include the grinding wheel grit number and the grinding wheel structure number; Establishing the abrasive model of the grinding wheel includes: determining the abrasive size distribution based on the grinding wheel grit number, determining the average abrasive distribution spacing based on the grinding wheel structure number, arranging abrasives on the working surface of the grinding wheel, and introducing random positional perturbations along the circumferential direction and tooth profile direction of the grinding wheel to characterize the randomness of the spatial distribution of abrasives, and generating an abrasive identification information table containing the spatial coordinates, diameter and protrusion height of each abrasive.

3. The method for digital simulation and contact analysis of gear tooth surface morphology in gear forming and grinding as described in claim 1, characterized in that, The grinding parameters include the grinding wheel speed and feed rate; Determining the motion trajectory of the abrasive grains relative to the tooth surface includes: determining the instantaneous rotation angle of the grinding wheel based on the grinding wheel rotation speed; determining the instantaneous feed distance of the grinding wheel along the workpiece axis based on the feed rate; determining the spatial coordinate transformation relationship between the grinding wheel and the workpiece by combining the instantaneous rotation angle and the instantaneous feed distance; based on the spatial coordinate transformation relationship, and by introducing the grinding wheel vibration parameters in the form of dynamic offset of the grinding wheel center, transforming the position of the abrasive grains on the grinding wheel surface at any moment from the grinding wheel coordinate system to the workpiece coordinate system, determining the instantaneous position sequence of the abrasive grain center in the workpiece coordinate system, and forming the motion trajectory of the abrasive grains relative to the tooth surface.

4. The method for digital simulation and contact analysis of gear tooth surface morphology in gear forming and grinding as described in claim 1, characterized in that, Determining the undeformed chip thickness at each tooth surface point includes: for each discrete point on the tooth surface, traversing the instantaneous spatial positions of all abrasive grains at each discrete time step, determining the instantaneous undeformed chip thickness generated by each abrasive grain at that tooth surface point, and taking the maximum value among all instantaneous values ​​as the undeformed chip thickness at that tooth surface point.

5. The method for digital simulation and contact analysis of gear tooth surface morphology in gear forming and grinding as described in claim 1, characterized in that, Generating the tooth surface topography error matrix includes: calculating the difference between the coordinates of the discrete points on the ground tooth surface after grinding and the coordinates of the discrete points on the theoretical tooth surface to obtain the normal deviation at each discrete point, thus forming a topography error matrix corresponding to the discrete mesh of the tooth surface.

6. The method for digital simulation and contact analysis of gear tooth surface morphology in gear forming grinding as described in claim 1, characterized in that, The arrangement of the discrete contact points includes: uniformly arranging the contact points along the meshing line direction, and obtaining the spatial position of each contact point in the driving gear and driven gear follower coordinate system through gear end face coordinate transformation.

7. The method for digital simulation and contact analysis of gear tooth surface morphology in gear forming and grinding as described in claim 1, characterized in that, Obtaining the topographic error at each contact discrete point includes: transforming the tooth surface topographic error matrix from the workpiece coordinate system to the gear follower coordinate system of the bearing contact analysis model, and then obtaining the topographic error at each contact discrete point through interpolation.

8. The method for digital simulation and contact analysis of gear tooth surface morphology in gear forming and grinding as described in claim 1, characterized in that, Obtaining the system deformation clearance correction amount includes: establishing and solving the static equilibrium equation of the transmission system using the slice finite element method, obtaining the relative displacement between each slice along the tooth width direction, and converting the relative displacement into the system deformation clearance correction amount at the contact point according to the slice position of the contact discrete point.

9. The method for digital simulation and contact analysis of gear tooth surface morphology in gear forming and grinding as described in claim 1, characterized in that, The process of establishing and iteratively solving the tooth surface bearing contact equation set includes: the tooth surface bearing contact equation set is established based on the deformation coordination relationship of the gear pair before and after loading; the equation set includes the contact point compliance matrix, contact deformation vector, rigid body approach vector, contact point remaining clearance vector, contact point initial clearance vector, and contact point load column vector; during the iterative solution process, each iteration first solves the contact equation set to obtain the contact point load and transmission error, then solves the system static equilibrium equation based on the contact point load to update the system deformation clearance correction amount, and superimposes the updated system deformation clearance correction amount with the morphology error as the initial clearance for the next iteration, until the convergence tolerance is met.

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