Special-shaped polyhedral abrasive particle grinding wheel surface modeling method and system

Abstract

The invention belongs to the technical field of grinding wheel surface modeling, and particularly discloses a special-shaped polyhedral abrasive particle grinding wheel surface modeling method and system.The method comprises the steps that the bottom face side length, the initial height and the abrasive particle rotation angle of abrasive particles are fitted; calculating the number of abrasive particles per unit area and the total number of abrasive particles; presetting a cutting stage number distribution proportion; randomly generating an initial position, a size and a rotation angle of the rectangular pyramid abrasive particle under a cylindrical coordinate system; the morphology evaluation function is minimized through a differential evolution algorithm, and constraint optimization of the positions and angles of the rectangular pyramid abrasive particles is achieved; the optimized rectangular pyramid abrasive particles are subjected to one-stage or multi-stage pyramid cutting treatment, and diversified special-shaped polyhedral abrasive particle structures are generated; and interference judgment is conducted on the generated special-shaped polyhedral abrasive particle structure, and a grinding wheel circumferential surface appearance model is constructed. According to the method, the geometric and statistical similarity of the morphology is remarkably improved while efficient calculation is kept, and the method can be flexibly matched with various abrasive particle grinding wheels such as single crystal corundum, CBN and diamond.

Description

Technical Field

[0001] This invention relates to the field of grinding wheel surface modeling technology, and in particular to a method and system for modeling the surface of irregularly shaped polyhedral abrasive grinding wheels. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Grinding is a crucial process in precision manufacturing. Accurate modeling of the circumferential surface morphology of the grinding wheel is a prerequisite for establishing mathematical models of microscopic contact mechanisms, grinding forces, and heat distribution, providing key support for analyzing the mechanisms affecting the integrity, efficiency, and quality of the machined surface.

[0004] Traditional abrasive modeling typically uses regular geometric shapes such as spheres, ellipsoids, cones, regular octahedrons, or truncated octahedrons as model styles, often assuming uniform distribution and ideal shapes of abrasive grains. This results in insufficient model accuracy, failing to accurately reflect the random variations in abrasive grain diameter, height, and hardness. While this reduces computational complexity and speeds up simulation, it sacrifices accurate descriptions of the true irregular polyhedral structure of worn abrasive grains, the random distribution of protrusion heights, and irregular gaps. This leads to significant deviations between the simulated morphology and the actual grinding wheel, susceptibility to interference, and insufficient prediction accuracy.

[0005] In recent years, some scholars have used methods such as vibration methods and random deflection methods to improve the randomness of abrasive grain positions and initial wear characteristics. For example, the vibration method generates the random position distribution and spatial orientation of abrasive grains by simulating vibration processes (such as random sampling and high-frequency vibration), thereby avoiding the assumption of uniform distribution and improving the model's fitting accuracy to the heterogeneity of actual grinding wheel surfaces. However, these methods all apply the modeling paradigm of "single fixed geometric prototype + parameter perturbation," failing to fundamentally overcome the bottleneck of representing the highly heterogeneous shape of individual abrasive grains. The model essentially only achieves "isomorphic displacement," rather than true "heterogeneous displacement," and there is still a significant gap compared to the real abrasive grain diversity observed by SEM (number of facets varies from six to more than ten, and the sharpness of edges and the apex cone angle are significantly discrete). Summary of the Invention

[0006] To address the aforementioned key issues, this invention proposes a method and system for modeling the surface of irregularly shaped polyhedral abrasive grinding wheels. This method uses a simple square pyramid as an initial prototype and achieves independent, realistic, and irregular geometric generation of each abrasive grain through multi-level random planar cutting and global optimization. While maintaining computational efficiency, it significantly improves the geometric and statistical similarity of the morphology and can flexibly adapt to various abrasive grinding wheels such as single-crystal corundum, CBN, and diamond. Simultaneously, it combines a differential evolution algorithm to constrain and optimize the position and angle distribution of abrasive grains, achieving interference-free random distribution through global search and a morphology evaluation function.

[0007] In some implementations, the following technical solutions are adopted: A method for modeling the surface of an irregularly shaped polyhedral abrasive grinding wheel includes: A Gaussian mixture model is used to fit the bottom edge length and initial height of the abrasive grains, and the rotation angle of the abrasive grains is also fitted. The number of abrasive grains per unit area and the total number of abrasive grains are calculated. Based on the percentage distribution of polyhedral numbers of the measured abrasive grains, the distribution ratio of the cutting level is preset. The initial position, size, and rotation angle of the pyramidal abrasive grains are randomly generated in cylindrical coordinates. The position and angle of the pyramidal abrasive grains are optimized by minimizing the morphology evaluation function through a differential evolution algorithm. Based on the preset cutting level distribution ratio, the optimized square pyramid abrasive grains are subjected to one or more levels of pyramid cutting to generate diverse irregular polyhedral abrasive grain structures. Interference judgment is performed on the generated irregular polyhedral abrasive grain structure, and the non-interference abrasive grain parameters are integrated into the cylindrical coordinate system to construct the surface morphology model of the grinding wheel circumference.

[0008] As a further step, the geometric parameters of the grinding wheel and microscopic data were collected, and the bottom side length d and initial height h of the abrasive grain were fitted using a Gaussian mixture model to ensure that the parameters follow a normal distribution. Here, the bottom side length d is the side length of the square bottom surface of the pyramidal abrasive grain, and the initial height h is the vertical distance from the center of the bottom surface to the vertex of the pyramidal abrasive grain. Both of them follow a standard normal distribution.

[0009] As a further approach, the rotation angle of the abrasive grains is fitted, specifically as follows: Angles of abrasive grains around the x, y, and z axes , , All follow a normal distribution : , , ; in, This indicates the angle of the abrasive grains around the x-axis, y-axis, or z-axis. For the corresponding initial angle, Indicates random perturbation; , These represent the mean and standard deviation of the corresponding angles, respectively.

[0010] As a further approach, the number of abrasive particles per unit area is calculated. Total number of abrasive particles Specifically: ; ; in, This represents the volume fraction of abrasive particles. Let be the side length of the square base of the pyramidal abrasive grain. R is the average initial height of the abrasive grains, R is the radius of the grinding wheel, and W is the axial width of the grinding wheel.

[0011] As a further approach, the initial position, size, and rotation angle of the pyramidal abrasive grains are randomly generated in cylindrical coordinates, specifically as follows: Multiple initial non-overlapping center positions are generated by adding them in a random order, and the distance between each position is at least greater than a preset minimum distance threshold. Based on the randomly generated side length d of the base of the square pyramid and the initial height h, combined with the center position, the coordinates of the local base point and the vertex are obtained; Based on the randomly fitted abrasive grain rotation angle, a rotation matrix around the x-axis, y-axis, and z-axis is generated, thereby obtaining the local bottom surface point after rotation.

[0012] As a further approach, the morphology evaluation function is minimized using a differential evolution algorithm to achieve constrained optimization of the position and angle of the pyramidal abrasive grains, specifically: Construct morphology evaluation functions consisting of density matching terms, exclusion terms, and angle constraint terms; the density matching term is used to ensure the simulated abrasive grain count. Number of abrasive particles per unit area Matching; the exclusion term is used to prevent interference between adjacent abrasive grains; the angle constraint term is used to ensure that the rotation angle follows a normal distribution; With the goal of minimizing the morphology evaluation function, the differential evolution algorithm is used to optimize the value of the morphology evaluation function, resulting in an optimized simulated position matrix.

[0013] As a further approach, the optimized pyramidal abrasive grains are subjected to one-stage or multi-stage pyramidal cutting to generate diverse irregular polyhedral abrasive grain structures, specifically: By performing three-dimensional morphological statistical analysis on the grinding wheel through scanning imaging, the proportion of different polyhedral types of grinding wheel abrasive grains is obtained, thereby determining the distribution ratio of cutting levels; During the first-level cutting, the quadrangular pyramid of a preset proportion is cut in the direction of the tangent of the grinding wheel's circumference to form a hexahedron; During secondary cutting, a pre-defined proportion of abrasive grains are randomly selected from the hexahedron for random cutting to form a heptahedron; the specific process of random cutting is as follows: The cutting plane is randomly generated by uniform sampling of the normal vector. The cutting plane constant is randomly determined within a preset range based on the current convex height of the polyhedron. The actual cutting height is determined based on the cutting ratio coefficient and random perturbation. For each face of the current polyhedron, determine its normal vector direction; when cutting the polyhedron, impose the following restrictions on the cutting face: the cutting face is not perpendicular to the normal vector of any face being cut, and at most one edge of the polyhedron can be located on the cutting face; after the cutting is completed, add the new face formed by the intersection of the cutting face and each edge of the polyhedron to the face set of the polyhedron, and update the protrusion height; delete the volume part on the side pointing to the cutting plane; The number of faces, the statistical test of the protrusion height, and the self-interference test are performed respectively. After passing the test, the next round of cutting is carried out. When performing three-stage cutting, a pre-defined proportion of abrasive grains are randomly selected from the heptahedron and randomly cut in the manner described above to form an octahedron. Similarly, multi-stage cutting is performed according to the preset proportion of abrasive grains to generate diverse irregular polyhedral abrasive grain structures.

[0014] As a further approach, interference analysis is performed on the generated irregular polyhedral abrasive grain structure, specifically as follows: Calculate the circumscribed sphere radius of the abrasive grains, and determine whether the center distance between the two circumscribed spheres is less than the sum of their radii. If so, it is determined that there may be interference between the two abrasive grains, and the abrasive grain parameters that may cause interference are removed. The differential evolution algorithm is then called again to optimize the abrasive grain position. Otherwise, there is no interference between the two abrasive grains.

[0015] In other embodiments, the following technical solutions are adopted: A surface modeling system for irregularly shaped polyhedral abrasive grinding wheels includes: The cutting level allocation module is configured to fit the bottom edge length and initial height of the abrasive grains using a Gaussian mixture model, while also fitting the rotation angle of the abrasive grains; calculate the number of abrasive grains per unit area and the total number of abrasive grains; and preset the cutting level distribution ratio based on the measured percentage of polyhedral quantity distribution of the abrasive grains. The position optimization module is configured to randomly generate the initial position, size, and rotation angle of the pyramidal abrasive grains in cylindrical coordinates; and to achieve constrained optimization of the position and angle of the pyramidal abrasive grains by minimizing the morphology evaluation function through a differential evolution algorithm. The abrasive cutting module is configured to perform one-level or multi-level pyramidal cutting on optimized quadrangular pyramidal abrasive grains based on a preset cutting level distribution ratio, generating diverse irregular polyhedral abrasive grain structures. The model building module is configured to perform interference judgment on the generated irregular polyhedral abrasive structure, integrate the non-interference abrasive parameters into the cylindrical coordinate system, and construct the surface morphology model of the grinding wheel circumference.

[0016] In other embodiments, the following technical solutions are adopted: A terminal device includes a processor and a memory, the processor being used to implement instructions; the memory being used to store multiple instructions adapted to be loaded and executed by the processor for the above-described method for modeling the surface of an irregularly shaped polyhedral abrasive wheel.

[0017] Compared with the prior art, the beneficial effects of the present invention are: (1) This invention not only effectively simulates the complex geometry and random distribution of abrasive particles, but also accurately captures the evolution of irregular polyhedrons (such as hexahedrons, heptahedrons, octahedrons, nonahedrons, decahedrons and other diverse structures) and irregular gap regions during the wear process, avoiding the limitations of traditional methods in terms of uniformity assumptions and static modeling.

[0018] Meanwhile, the grinding wheel parameter input and fitting module, differential evolution optimization module, and cutting module constructed in this invention together constitute a complete and efficient modeling system. By adjusting the polyhedron distribution ratio (which decreases as the number of faces increases), the computational efficiency and simulation speed are optimized, providing strong technical support for grinding wheel performance optimization and grinding mechanism research. This solves the current problems of insufficient accuracy, parameter neglect, and low interference detection efficiency in grinding wheel modeling.

[0019] (2) This invention breaks through the limitations of traditional models in terms of idealizing abrasive grain shape, assuming uniform distribution and interference post-processing, significantly improves the consistency with SEM measured data, and can truly reproduce abrasive grain heterogeneity, negative rake angle cutting characteristics and complex irregular gap regions, providing a high-precision and robust numerical simulation tool for accurate prediction of grinding force / heat, surface integrity analysis and intelligent optimization of grinding wheel process parameters.

[0020] Other features and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0021] Figure 1 This is a flowchart of the method for modeling the surface of an irregularly shaped polyhedral abrasive grinding wheel in an embodiment of the present invention; Figure 2 Image of abrasive grain shape extracted from a single-crystal corundum resin grinding wheel using an EM-30 Plus scanning electron microscope; Figure 3 This is a schematic diagram illustrating the generation of random abrasive grains on the circumferential surface of the grinding wheel in an embodiment of the present invention; Figure 4 This is a schematic diagram of the process of introducing and generating pyramidal abrasive particles in an embodiment of the present invention; Figure 5 This is a schematic diagram of the irregular hexahedral abrasive particles generated by pyramid cutting and the output of surface morphology in an embodiment of the present invention; Figure 6This is a schematic diagram of the final generation of irregular polyhedral abrasive particles in an embodiment of the present invention. Detailed Implementation

[0022] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0023] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0024] Example 1 In one or more embodiments, a method for modeling the surface of an irregularly shaped polyhedral abrasive grinding wheel is disclosed, combined with Figure 1 Specifically, it includes the following processes: S101: The bottom edge length and initial height of the abrasive grains are fitted using a Gaussian mixture model (GMM), and the rotation angle of the abrasive grains is also fitted; the number of abrasive grains per unit area and the total number of abrasive grains are calculated; and the distribution ratio of the cutting level is preset based on the percentage of polyhedral quantity distribution of the measured abrasive grains.

[0025] In this embodiment, the geometric parameters of the grinding wheel and microscope data are collected, and the bottom side length d and initial height h of the abrasive grain are fitted using a Gaussian mixture model to ensure that the parameters follow a normal distribution. The bottom side length d is the side length of the square bottom surface of the pyramidal abrasive grain, and the initial height h is the vertical distance from the center of the bottom surface to the vertex of the pyramidal abrasive grain. Both of them follow a standard normal distribution.

[0026] Specifically, the geometric parameters of a grinding wheel refer to its macroscopic physical dimensions and structural characteristics; in a specific embodiment, these parameters include: grinding wheel diameter (e.g., 400 mm, therefore radius R = 200 mm), grinding wheel width (e.g., W = 40 mm), and abrasive ratio (e.g., ...). ), organization number (e.g., S=10), abrasive grain size (e.g., F46, corresponding to a standard particle diameter range of ), , ).

[0027] Microscopic data refers to the microscopic information obtained by observing the actual surface of the grinding wheel through a microscope. This data is primarily used to fit the statistical distribution characteristics of the abrasive grains, ensuring that the model reflects the randomness and heterogeneity of the real grinding wheel. It mainly includes: samples of the bottom edge length of the abrasive grains (e.g., sample mean 0.35 mm, standard deviation 0.05 mm) and samples of the initial height of the abrasive grains (e.g., average height). Standard deviation of height ) and abrasive grain rotation angle samples (e.g., standard rotation angle values) Rotation angle variance ).

[0028] Using a single-crystal corundum resin grinding wheel as the experimental object, the grinding wheel was imaged from multiple angles and at high resolution using an EM-30 Plus scanning electron microscope. Figure 2 The image shows the shape extraction of abrasive particles from a single-crystal corundum resin grinding wheel using an EM-30 Plus scanning electron microscope. Figure 2 (a) and (b) in the image are images of abrasive grains taken from the surface of the grinding wheel. Figure 2 (c) and (d) are images of abrasive particles taken from inside the grinding wheel.

[0029] Three-dimensional morphology statistical analysis was performed on 1000 randomly selected abrasive grains (including abrasive grains on the surface of the grinding wheel and abrasive grains inside the wheel). The proportion of each type of abrasive grain was obtained according to the polyhedral characteristics of the abrasive grains, as shown in Table 1.

[0030] Table 1. Statistical distribution of polyhedral types of abrasive grains in single-crystal corundum resin grinding wheels

[0031] In this embodiment, the fitting process for the bottom edge length and initial height of the abrasive grain is as follows: (1) Fitting the bottom edge length of the abrasive grain: The base side length *d* refers to the side length of the base of the pyramidal abrasive grain (usually assumed to be a square base), that is, the length of each side of the quadrilateral base (e.g., a sample mean of 0.35 mm), used to define the base size of the abrasive grain. The base side length *d* follows a standard normal distribution, and its probability density function is: (1) Where d represents the side length of the base. , These represent the sample mean and standard deviation of the base side length, respectively.

[0032] Considering the heterogeneous characteristics of grinding wheel abrasive grains (such as random dimensional variations and SEM data bias), the measured standard deviation fitted from the sample is used. Sample mean The minimum difference in the length of the base side is 0.01 mm, which is the step size of the base side length; substituting into formula (1) yields: ; For a specific abrasive sample, assuming the measured value d = 0.37 mm, substituting it into formula (1) yields the probability: ; (2) Fitting of initial height distribution of abrasive particles: The initial height *h* refers to the vertical distance from the center of the base to the vertex of the pyramidal abrasive grain, i.e., the full height of the cone (before cutting), used to simulate the initial geometric characteristics of the abrasive grain. The initial height *h* follows a standard normal distribution, and its probability density function is: (2) Where h represents the initial height, , These represent the sample mean and standard deviation of the initial height, respectively.

[0033] Based on the extracted height samples, the average height Standard deviation of height The minimum difference in abrasive grain height is 0.01 mm, which is the step size of the bottom edge length. For a specific abrasive grain sample, assuming the height h = 0.21, substituting it into formula (2) yields the probability: % In this embodiment, the bottom edge length d and the original height h of the abrasive grains follow a normal distribution, which can more accurately capture heterogeneity and improve model accuracy.

[0034] (3) Fitting of abrasive grain rotation angle distribution: Define the angles of the abrasive grains around the x, y, and z axes as follows: , , Extract abrasive grain rotation angle samples from microscopic data, conforming to... , This is the standard value for the rotation angle. Let be the variance of the rotation angle.

[0035] Iterative equations: , , (3) in, This indicates the angle of the abrasive grains around the x-axis, y-axis, or z-axis. For the corresponding initial angle, Indicates random perturbation; , These represent the mean and standard deviation of the corresponding angles, respectively.

[0036] For example: Initial random disturbance ,but Similar calculations , This yields an N x 6 matrix of rotation angle distribution, where N is the total number of abrasive grains. An example of each column is shown below: (4) x, y, and z represent the Cartesian coordinates (in mm) of the abrasive grain center in a cylindrical coordinate system, used to define the spatial position of the abrasive grain on the grinding wheel surface. For example, x = 180 mm represents the x-coordinate position, y = 0 mm represents the y-coordinate position, and z = 10 mm represents the z-coordinate position (z is along the width of the grinding wheel, from -20 mm to 20 mm). These coordinates are generated by adding them in a random order to ensure no overlap, and are combined with the rotation angle. , , To simulate the orientation of abrasive particles.

[0037] The spatial orientation of abrasive grains on the actual grinding wheel surface is affected by manufacturing process and random factors. Their distribution is often close to a normal form, which can accurately capture the heterogeneity of orientation and improve the accuracy of the model for interference optimization.

[0038] In this embodiment, the calculation of the number of abrasive particles per unit area and the total number of abrasive particles is carried out as follows: Number of abrasive particles per unit area : (5) in, The abrasive volume fraction represents the proportion of abrasive material in the total volume of the grinding wheel (usually expressed as a percentage or decimal, such as 0.45 = 45%). It is a key parameter for grinding wheel specifications and is affected by the microstructure number S (e.g., ...). This value is used to calculate abrasive grain density. It reflects the density of the grinding wheel and grinding efficiency. This means more abrasive grains, but potentially more hardness. It is the side length of the square base of the pyramidal abrasive grain, derived from the grain size specification (e.g., F46 corresponds to the range of 0.315~0.425mm) and the statistical fitting of measured sample data (e.g., measuring multiple abrasive grain samples using a SEM microscope). The average initial height represents the average height by which the abrasive grains protrude from the binder surface. In modeling, this is the average value before cutting.

[0039] for example: ; Total number of abrasive grains: (6) for example: (indivual) Where R represents the radius of the grinding wheel (unit: mm, e.g., 200 mm corresponds to a diameter of 400 mm), used to calculate the circumferential surface area; W represents the axial width of the grinding wheel (unit: mm, e.g., 40 mm), which, together with R, determines the surface area.

[0040] The final output is the fitted distribution parameters (including the mean of the base side length d). and standard deviation The mean of the initial height h and standard deviation The parameters, such as the mean μ and standard deviation σ of the rotation angle, are used to describe the statistical characteristics of the abrasive grain distribution (e.g., the mean and variance of the normal distribution). These parameters are used to randomly generate specific abrasive grain instances in subsequent steps (e.g., by generating d, h, and angle for each abrasive grain through sampling), thereby accurately capturing the randomness and heterogeneity of abrasive grains and adapting to the diversity of actual SEM observations.

[0041] This embodiment lays the data foundation for subsequent modeling by calculating the number of abrasive grains per unit area and the total number of abrasive grains; at the same time, based on the percentage distribution of the number of polyhedra of the measured abrasive grains, the distribution ratio of the cutting levels is preset to provide guidance for multi-level cutting.

[0042] S102: Randomly generate the initial position, size, and rotation angle of the pyramidal abrasive grains in cylindrical coordinates; minimize the morphology evaluation function through a differential evolution algorithm to achieve constrained optimization of the position (abrasive grain number density matching, no interference repulsion) and angle distribution of the pyramidal abrasive grains.

[0043] In this embodiment, a cylindrical coordinate system is established with the center of the grinding wheel as the origin (0,0,0). The height of the grinding wheel z ranges from -20mm to 20mm, and the z coordinate varies along the width of the grinding wheel (from -20mm to 20mm). The radial coordinate r of the grinding wheel is a radius R = 200mm to simulate the outer circular surface morphology of the grinding wheel. The angle θ is used to describe the circumferential distribution.

[0044] Combination Figure 3 The initial position, size, and rotation angle of the pyramidal abrasive grains are randomly generated in cylindrical coordinates, as follows: (1) Generate multiple initial non-overlapping center positions by adding them in a random order: The Random Sequential Addition (RSA) algorithm is used to generate non-overlapping center positions for abrasive grains. This algorithm is an iterative particle placement method used to simulate the random distribution of abrasive grains on the circumferential surface of a grinding wheel. The specific process is as follows: Initialize an empty surface; repeatedly generate candidate positions; check the Euclidean distance between the candidate position and all existing positions; if all distances are greater than a minimum distance threshold, the position is accepted and added; otherwise, it is rejected and a new candidate position is generated; the iteration continues until the total number of abrasive grains N is reached. This method ensures that the position distribution is uniform, random, and non-overlapping, simulating the heterogeneity of abrasive grain deposition in actual grinding wheel manufacturing.

[0045] Specifically, in cylindrical coordinates, the candidate position is represented as (r, θ, z), where r is fixed as the grinding wheel radius (a constant used to define the surface modeling); θ is the circumferential angle (unit: radians, uniformly and randomly distributed in [0, 2π] to cover the entire circumference); and z is the axial coordinate (unit: mm, uniformly and randomly distributed in [-W / 2, W / 2] = [-20mm, 20mm], corresponding to the grinding wheel width W = 40mm).

[0046] Convert the cylindrical coordinates (r, θ, z) to Cartesian coordinates (x, y, z) for subsequent geometric calculations (such as rotation matrices and interference determination); the conversion formula is: , , z=z. As a specific example: x≈-200mm (cos(θ)≈-1 when θ≈π); y≈0mm (sin(θ)≈0 when θ≈π); z=-8 mm (directly inherited from cylindrical coordinate z).

[0047] A minimum allowable Euclidean distance threshold (in mm) is set between the centers of abrasive grains to prevent positional overlap or initial interference. This threshold can be obtained through statistical fitting based on actual abrasive grain gap measurements using SEM (Scanning Electron Microscopy). As a specific example, the minimum Euclidean distance threshold is set to 0.4 mm, slightly larger than 1.14 times the average bottom side length d = 0.35 mm, as a safety margin.

[0048] The total number of abrasive grains N is the number of effective abrasive grain center positions generated on the circumferential surface of the grinding wheel; the total number of abrasive grains N is calculated according to the aforementioned formulas (5) and (6).

[0049] Calculate the Euclidean distance between the centers of each abrasive grain. : (7) in, Cartesian coordinates (unit: mm) representing the center point of the first abrasive grain; The Cartesian coordinates (unit: mm) represent the center point of the second abrasive grain.

[0050] Ensure that the Euclidean distance between all abrasive grain center points is >0.4mm; this constraint is achieved through a distance check loop of the RSA algorithm: when adding each candidate position, calculate its Euclidean distance with all existing center points, and reject any pair if they are ≤0.4mm; this mechanism performs a global check (not just adjacent points) to prevent interference and match the measured morphology.

[0051] (2) Based on the randomly generated side length d of the base of the square pyramid and the initial height h, combined with the center position, the coordinates of the local base point and the vertex are obtained: Define the base of the square pyramid as a square, and randomly generate the side lengths based on a normal distribution. .

[0052] Local base points are used to describe the coordinates of the four corner points of the base of a pyramidal abrasive grain. These coordinates are defined relative to the center position of the abrasive grain (denoted as [0,0,0]) and are used to construct the geometry of the abrasive grain. For example, taking the base side length d as an example, the four local base points can be represented as: [d / 2,d / 2,0], [d / 2,-d / 2,0], [-d / 2,d / 2,0], and [-d / 2,-d / 2,0]; these points are located in the z=0 plane (base) and are centrally symmetrically distributed, which facilitates subsequent rotation and optimization calculations.

[0053] The vertex refers to the coordinates of the top of the square pyramid, which is defined relative to the center position as [0,0,h], where h is the initial height of the abrasive grain, the vertical distance from the bottom surface to the vertex.

[0054] (3) Based on the randomly fitted abrasive grain rotation angle, generate rotation matrices around the x-axis, y-axis and z-axis, thereby obtaining the local bottom surface points after rotation.

[0055] As an example, suppose the local bottom point is Angles are randomly generated based on a normal distribution. Then the rotation matrix for: ; Similarly, calculation , ,complex .

[0056] Then the local bottom point 1 after rotation is: .

[0057] The square pyramidal abrasive grains randomly generated in this step, such as Figure 4 As shown.

[0058] In this embodiment, a morphology evaluation function F is constructed, and the morphology evaluation function is minimized by a differential evolution algorithm to achieve optimization of abrasive particle number density matching, interference-free repulsion, and angular distribution constraints.

[0059] The morphology evaluation function F is as follows: (8) in, , , These represent the weights of each item. Typically, they are all set to 1 to treat them as equal weights.

[0060] This is a density matching term used to ensure the simulated abrasive grain count. Matching the number of abrasive particles per unit area; ,in This indicates the current number of simulated abrasive particles. This represents the number of abrasive grains per unit area, and A represents the surface area of ​​the grinding wheel. Minimizing this term ensures that the model density matches the actual SEM data (relative error <5%).

[0061] This is an exclusion term, used to prevent interference between adjacent abrasive grains; ;in, This indicates the minimum permissible distance (e.g., 0.4 mm). This refers to the distance between the centers of adjacent abrasive grains; for example, if the distance between two adjacent abrasive grains... ,but .

[0062] This is an angle constraint term used to ensure that the rotation angle follows a normal distribution; , , , , respectively, represent the rotation angles of the abrasive grains around the x, y, and z axes; σ represents the standard deviation of the rotation angles; minimizing this term ensures that the angular heterogeneity conforms to the fitted distribution; σ comes from the statistical fitting of the microscopic data (samples of abrasive grain rotation angles observed under a microscope), and is used to describe the random perturbation distribution of the rotation angles of the abrasive grains around the x, y, or z axes.

[0063] The process of minimizing the morphology evaluation function using the differential evolution algorithm is as follows: Define the optimization objective as: minimize F(x), where x is the vector of an individual in the population, and the dimension D≈N×6 (N is the total number of abrasive grains, and 6 is the position of each abrasive grain + angle of 3).

[0064] Initialize the population: Randomly generate M individuals each The initial values ​​are generated by adding non-overlapping center positions in a random order (distance between each position > minimum distance). The local bottom points and vertices are obtained by combining the fitted bottom side length d and the initial height h. The rotated points are obtained by using rotation matrices around the x, y, and z axes (the positions are uniformly distributed on the grinding wheel surface, and the angles are normally distributed N(μ,σ)).

[0065] Calculate the fitness of each individual: .

[0066] Where: M represents the population size, and F represents the number of candidate configurations for parallel optimization, which is related to F and used to evaluate multiple morphological schemes; D represents the vector of the i-th individual; D represents the vector dimension. This represents the morphology evaluation function value for this configuration (the smaller the value, the better).

[0067] Mutation operation: For each parent individual Randomly select three distinct individuals from the population that are not equal to i. , , ( ).

[0068] Generate mutation vectors : F is the scaling factor, which is set to 0.7 here. This formula is derived through difference... Introduce diversity.

[0069] Crossover operation: mutates the vector With father The experiment vector is obtained by mixing according to dimensions. .

[0070] For each dimension j=1,...,D: (1) Generate uniform random numbers ; (2) Randomly select a dimension (It is guaranteed that at least one dimension comes from the mutation vector).

[0071] Cross rules: ; CR is the crossover probability (usually taken as 0.9), which determines the proportion of mutation information retained.

[0072] Select operation: Calculate the test vector Fitness (morphological evaluation function) and with the father generation Compare: ; This refers to the i-th individual in the g+1th generation. Only individuals with improved fitness (lower fitness) are retained to achieve intergenerational progression.

[0073] Iteration and Termination Conditions: Number of iterations: up to 500 generations (g=1,...,500).

[0074] Termination threshold: If the fitness of the best individual in the current population satisfies: If it stops early, then it will stop early; otherwise, it will end at the 500th generation.

[0075] The optimized position matrix ensures random distribution of abrasive grains, no interference between abrasive grains, and a simulated number of abrasive grains. Matches the calculated density.

[0076] S103: Based on the preset cutting level distribution ratio, the optimized square pyramid abrasive grains are subjected to one or more levels of pyramid cutting to generate diverse irregular polyhedral abrasive grain structures.

[0077] Specifically, taking the distribution of polyhedral types of abrasive grains in single-crystal corundum resin grinding wheels shown in Table 1 as an example, assuming the total number of abrasive grains is... The specific cutting process is as follows: First generate all 2.3% of the four-sided pyramids are simplified to four-sided pyramids; then, 97.7% of the four-sided pyramids are randomly selected from the 1,175,610 four-sided pyramids, and the selected four-sided pyramids are cut in the direction of the tangent of the grinding wheel circumference to form hexahedrons. Figure 5 A schematic diagram is provided showing the generation of irregular hexahedral abrasive grains and the output of surface morphology from pyramid cutting.

[0078] During the first-stage cutting process, the direction of the tangential direction (i.e., the normal vector) of the grinding wheel's circumferential surface is determined based on the principle of global uniformity of the tangential direction of the grinding wheel's circumferential surface. Specifically, the calculation is defined as follows: First, based on the grinding wheel's geometric parameters (e.g., radius R = 200 mm) and rotation direction (assuming tangential along the yz plane), the normal vector is set to a unit vector perpendicular to the radial direction, for example, n = [-1, 0, 0] (corresponding to negative x-axis cutting). The normalization function `normalize([-1, 0, 0])` ensures that ||n|| = 1. This normal vector simulates the uniform cutting effect of the stable wear stage, ensuring that the cutting plane is parallel to the grinding wheel's tangential direction, avoiding radial deviations that could cause the morphology to deviate from the measured data. All abrasive grains use the same normal vector, rather than varying according to their position, because the first-stage cutting uses a globally uniform depth and direction to achieve overall consistency and synchronous constraint of the grinding wheel surface; if each abrasive grain has a different normal vector, it will lead to increased morphological deviation, violating the uniformity of simulating the initial wear. From the second-stage cutting onwards, the normal vector is randomly generated, and each cut is independent and different.

[0079] Two-pole cutting: Randomly selecting from a hexahedron The abrasive grains are randomly cut to form a heptahedron.

[0080] The specific proportions are calculated as follows: ; Starting from the second-level cutting (cutting a hexahedron into a heptahedron, and subsequent levels generating octahedrons, nonahedrons, decihedrons, etc.), the tangential direction is no longer limited; instead, a random cutting method is adopted to increase the diversity and heterogeneity of abrasive grain shapes, simulating irregular fracture and spalling in complex wear processes. The specific method of this random cutting is as follows, ensuring that a corresponding number of new faces are added at each level.

[0081] The specific implementation method of random cutting is as follows: (1) The cutting plane is randomly generated by uniform sampling of the normal vector. The cutting plane constant is randomly determined within a preset range based on the current convex height of the polyhedron. The actual cutting height is determined based on the cutting ratio coefficient and random disturbance.

[0082] Specifically, two spherical coordinate angles are uniformly sampled on a unit sphere (radius = 1): , The unit normal vector is obtained from spherical coordinates: ; ; ; ; Thus guarantee This means that the normal vector is uniformly distributed in three-dimensional space; U is an abbreviation for uniform distribution, for example, when uniformly sampling two spherical coordinate angles. and ,mean A value is randomly selected within the interval [0, π], with each value having an equal probability of appearing; similarly... exist Values ​​are randomly selected within the interval, with each value having an equal probability of occurrence. This uniform sampling ensures randomness on a unit sphere, and then the spherical coordinates are converted into unit normal vectors, thereby generating uniformly distributed cutting plane directions in three-dimensional space.

[0083] Let the current convex height of the polyhedron be... Let the cutting plane constant This interval prevents both cutting too shallowly (which would prevent the creation of new surfaces) and cutting too deeply (which would lead to geometric self-interference or excessively low convexity).

[0084] Cutting ratio coefficient When calculating the cutting height, the proportional control used to characterize the cutting depth during wear reflects the relative cutting degree of the abrasive grains (a percentage relative to the initial height) to simulate the random variability and heterogeneity of the abrasive grain protrusion height. Specifically, The basic cutting depth is determined by multiplying by the initial height, thereby controlling the distribution of the protrusion height after cutting.

[0085] Actual cutting height for: (9) in, This is the cutting ratio coefficient. Here, d is the shape correction factor, and d is the side length of the base. The average side length of the base. It is a random perturbation used to simulate wear effects.

[0086] Cutting ratio coefficient The value follows a uniform distribution U[0.75, 0.80], meaning it is randomly selected within the range of 0.75 to 0.80. This range is selected based on statistical analysis of actual grinding wheel wear conditions: when k < 0.75, the cut is too shallow, making it difficult to form a distinct hexahedral structure and the bulge height distribution is too high; when k > 0.80, the cut is too deep, the abrasive grain bulge height is too low, resulting in a significant reduction in the number of effective cutting edges, which does not match the morphological characteristics of the actual grinding wheel's "stable wear" stage.

[0087] In this embodiment, the selected =0.77 (this value is within the interval and is randomly generated from a uniform distribution), shape correction factor β=0.1 (the influence coefficient of the base dimensions on the height based on the GMM fitting), and random perturbation standard deviation. Disturbance term (It follows the N(0,0.01) rule; Substitute the example value ( =0.2mm, d=0.37mm), resulting in: .

[0088] This embodiment introduces a cutting ratio coefficient, a shape correction factor, and a random perturbation term to determine the actual cutting height, which can ensure that the protrusion height conforms to a normal distribution and can simulate the random wear effect.

[0089] (2) For each face of the current polyhedron, determine the direction of its normal vector; when cutting the polyhedron, the following restrictions are imposed on the cutting plane: the cutting plane is not perpendicular to the normal vector of any of the cut faces, and at most one edge of the polyhedron can lie on the cutting plane; after the cutting is completed, add the new face formed by the intersection points of the cutting plane and the edges of the polyhedron to the face set of the polyhedron, update the protrusion height; delete the volume part on the side pointed to by the cutting plane.

[0090] The direction vector dir represents the vector difference from the bottom point coordinates of the edge to the vertex coordinates, and is used to calculate the intersection parameter t of the line segment and the cutting plane. This vector not only ensures the accuracy of the intersection calculation, but also characterizes the direction and length of the edge; specifically, for each edge of the current polyhedron (such as a hexahedron) , calculate the direction vector as: dir = q - p; The intersection parameter t is used to characterize the position ratio (parameter value) of the intersection point on the edge line segment, where t = 0 represents the bottom point, t = 1 represents the vertex, and 0 < t < 1 represents that the valid intersection point is inside the edge; it is used to determine the coordinates of the new top face points after cutting, ensure the cutting depth is accurate, and avoid boundary coincidence (t < 0.99 is the threshold judgment); the intersection parameter t of each edge and the cutting plane is specifically: ; where, represents the dot product of vectors, p represents the starting coordinate of the edge (usually called the bottom point or base point), which is a three-dimensional vector , used to define the starting position of the line segment. q represents the ending coordinate of the edge (usually called the vertex or end point), which is a three-dimensional vector , used to define the ending position of the line segment. dir = q - p is the direction vector from p to q, used to calculate the intersection parameter t.

[0091] The criterion for the intersection to be valid is (to avoid the intersection point exactly falling on the end point resulting in boundary coincidence or numerical errors).

[0092] Based on the above parameters, determine the intersection coordinates as: .

[0093] Subsequently, perform geometric structure update: add the new face composed of the intersection points to the face set of the polyhedron; delete the volume part on the side pointed to by the cutting plane (i.e., the direction pointed to by n).

[0094] Update the protrusion height: ; where, is the updated protrusion height.

[0095] (3) Perform face count verification, protrusion height statistical test and self-interference test respectively. After passing the test, proceed to the next round of cutting.

[0096] Specifically, the face count verification involves counting the number of faces of the polyhedron after cutting to ensure it meets expectations (e.g., it should have seven faces after two-stage cutting).

[0097] The statistical test for protrusion height is as follows: Calculate the mean height of all bumps after the update. with standard deviation We then examine whether it still follows a normal distribution (consistent with the distribution after the first-order cut).

[0098] Self-interference detection specifically refers to: Calculate the distance from each test point x on the new surface to the existing surface: ; If any threshold If self-interference occurs or the number of faces does not increase as expected, the plane is resampled and randomly cut, with a maximum of 3 retries to control the computational load.

[0099] After completing a valid cut, with a new protrusion height Based on this, proceed to the next round of random cutting.

[0100] Each level can add 1-3 new faces until the required number of faces (e.g., 8, 9, 10 faces) is reached or the protrusion height is lower than the set threshold.

[0101] This random cutting method achieves abrasive grain shape diversification through a globally random plane, significantly improving the statistical similarity of morphology, and can be flexibly extended to higher-order cutting. While maintaining computational efficiency, it matches the actual abrasive grain diversity (6 to more than 10 faces) observed by SEM.

[0102] (4) When performing a three-level cut, randomly select from the heptahedron. The abrasive grains are randomly cut in the manner described above to form an octahedron.

[0103] The method for calculating the ratio is as follows: ; When performing a fourth-order cut, randomly select from the octahedron. The abrasive grains are randomly cut in the manner described above to form a nonahedron.

[0104] When performing a five-level cut, a nonahedron is cut into a decihedron or higher. Here, all decihedrons and higher are classified as decihedrons to simplify the modeling steps, just as pentahedrons are all categorized as square pyramids for simplification.

[0105] ; Randomly select from the nonahedron The abrasive grains are randomly cut in the manner described above to form a decahedron; the method of random cutting is the same as described above and will not be described in detail hereafter.

[0106] Similarly, multi-stage cutting is performed according to the preset ratio distribution of abrasive grains to generate diverse irregular polyhedral abrasive grain structures; Figure 6 An example of generating irregularly shaped polyhedral abrasive grains is given. In the figure, red represents a square pyramid, dark green represents a hexahedron, blue represents a heptahedron, cyan represents an octahedron, magenta represents a nonahedron, and black represents a decahedron.

[0107] S104: Interference judgment is performed on the generated irregular polyhedral abrasive grain structure, and the non-interference abrasive grain parameters are integrated into the cylindrical coordinate system to construct the surface morphology model of the grinding wheel circumference.

[0108] In this embodiment, the circumscribed sphere radius of the abrasive grain is calculated, and it is determined whether the center distance between the two abrasive grains is less than the sum of the circumscribed sphere radii of the two abrasive grains. If so, there may be interference between the two abrasive grains. The abrasive grain parameters that may cause interference are removed, and the differential evolution algorithm is called again to optimize the position of the abrasive grains. Otherwise, there is no interference between the two abrasive grains.

[0109] Among them, the circumscribed sphere radius of the abrasive grain The calculation method is as follows: (10) Where d is the side length of the base. The updated protrusion height, This indicates a safety margin (which can generally be set between 0.01 and 0.03 mm).

[0110] Integrating non-interference parameters, a cylindrical coordinate model is constructed. The output matrix (position, size, height, angle) is used to compare the similarity between the simulated grinding wheel circumferential surface morphology model and the actual SEM (scanning electron microscope) observation data. Specifically, it verifies the degree of agreement between the output parameters of the simulated model and the measured parameters of SEM to ensure the accuracy and reliability of the model; if the relative error is less than 5%, the verification is considered successful.

[0111] As a specific example, statistical methods are used to verify similarity, and the specific process is as follows: (1) Data preparation: Extract the parameters of all abrasive particles from the output matrix of the simulation model, and calculate the simulated abrasive particle number density ( ,in To simulate the total number of abrasive grains, A represents the circumferential surface area of ​​the grinding wheel (πDW) and the average height distribution (all). (average).

[0112] (2) Calculation of relative error: For each parameter, use the formula: relative error = |simulated value - measured value| / measured value × 100%. For example, density error = |simulated density - 23.39| / 23.39 × 100%; height error = |simulated mean - 0.165| / 0.165 × 100%. If both errors are < 5%, the similarity verification is passed.

[0113] (3) Iterative adjustment: If the similarity is >5%, the differential evolution algorithm is called again or the cutting parameters (such as k, β) are adjusted, and iterative optimization is performed until the target is met. This validation ensures the practicality of the model for applications such as grinding force / heat prediction.

[0114] The method in this embodiment overcomes the limitations of traditional models in terms of idealizing abrasive grain shape, assuming uniform distribution, and post-processing interference. It significantly improves the consistency with SEM measured data, and can realistically reproduce abrasive grain heterogeneity, negative rake angle cutting characteristics, and complex irregular gap regions, thereby improving modeling accuracy.

[0115] Example 2 In one or more embodiments, a surface modeling system for irregularly shaped polyhedral abrasive grinding wheels is disclosed, comprising: The cutting level allocation module is configured to fit the bottom edge length and initial height of the abrasive grains using a Gaussian mixture model, while also fitting the rotation angle of the abrasive grains; calculate the number of abrasive grains per unit area and the total number of abrasive grains; and preset the cutting level distribution ratio based on the measured percentage of polyhedral quantity distribution of the abrasive grains. The position optimization module is configured to randomly generate the initial position, size, and rotation angle of the pyramidal abrasive grains in cylindrical coordinates; and to achieve constrained optimization of the position and angle of the pyramidal abrasive grains by minimizing the morphology evaluation function through a differential evolution algorithm. The abrasive cutting module is configured to perform one-level or multi-level pyramidal cutting on optimized quadrangular pyramidal abrasive grains based on a preset cutting level distribution ratio, generating diverse irregular polyhedral abrasive grain structures. The model building module is configured to perform interference judgment on the generated irregular polyhedral abrasive structure, integrate the non-interference abrasive parameters into the cylindrical coordinate system, and construct the surface morphology model of the grinding wheel circumference.

[0116] It should be noted that the specific implementation methods of the above modules are exactly the same as those in Example 1, and will not be described in detail again.

[0117] Example 3 In one or more embodiments, a terminal device is disclosed, comprising a processor and a memory, wherein the processor is used to implement instructions; and the memory is used to store multiple instructions adapted to be loaded by the processor and executed by the processor to model the surface of the irregular polyhedral abrasive wheel in Embodiment 1.

[0118] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for modeling the surface of an irregularly shaped polyhedral abrasive grinding wheel, characterized in that, include: A Gaussian mixture model was used to fit the bottom edge length and initial height of the abrasive grain, and the rotation angle of the abrasive grain was also fitted. Calculate the number of abrasive particles per unit area and the total number of abrasive particles; Based on the measured percentage distribution of polyhedral abrasive particles, the distribution ratio of cutting levels is preset; The initial position, size, and rotation angle of the pyramidal abrasive grains are randomly generated in cylindrical coordinates. The position and angle of the pyramidal abrasive grains are optimized by minimizing the morphology evaluation function through a differential evolution algorithm. Based on the preset cutting level distribution ratio, the optimized square pyramid abrasive grains are subjected to one or more levels of pyramid cutting to generate diverse irregular polyhedral abrasive grain structures. Interference judgment is performed on the generated irregular polyhedral abrasive grain structure, and the non-interference abrasive grain parameters are integrated into the cylindrical coordinate system to construct the surface morphology model of the grinding wheel circumference.

2. The method for modeling the surface of an irregularly shaped polyhedral abrasive grinding wheel as described in claim 1, characterized in that, Collect grinding wheel geometry parameters and microscope data, and use a Gaussian mixture model to fit the bottom side length d and initial height h of the abrasive grain to ensure that the parameters follow a normal distribution. Here, the bottom side length d is the side length of the square bottom surface of the pyramidal abrasive grain, and the initial height h is the vertical distance from the center of the bottom surface to the vertex of the pyramidal abrasive grain. Both of them follow a standard normal distribution.

3. The method for modeling the surface of an irregularly shaped polyhedral abrasive grinding wheel as described in claim 1, characterized in that, The fitting abrasive grain rotation angle is as follows: Angles of abrasive grains around the x, y, and z axes , , All follow a normal distribution : ， ， ； in, This indicates the angle of the abrasive grains around the x-axis, y-axis, or z-axis. For the corresponding initial angle, Indicates random perturbation; , These represent the mean and standard deviation of the corresponding angles, respectively.

4. The method for modeling the surface of an irregularly shaped polyhedral abrasive grinding wheel as described in claim 1, characterized in that, Calculate the number of abrasive particles per unit area Total number of abrasive particles Specifically: ； ； in, This represents the volume fraction of abrasive particles. Let be the side length of the square base of the pyramidal abrasive grain. R is the average initial height of the abrasive grains, R is the radius of the grinding wheel, and W is the axial width of the grinding wheel.

5. The method for modeling the surface of an irregularly shaped polyhedral abrasive grinding wheel as described in claim 1, characterized in that, The initial position, size, and rotation angle of the pyramidal abrasive grains are randomly generated in cylindrical coordinates, specifically as follows: Multiple initial non-overlapping center positions are generated by adding them in a random order, and the distance between each position is at least greater than a preset minimum distance threshold. Based on the randomly generated side length d of the base of the square pyramid and the initial height h, combined with the center position, the coordinates of the local base point and the vertex are obtained; Based on the randomly fitted abrasive grain rotation angle, a rotation matrix around the x-axis, y-axis, and z-axis is generated, thereby obtaining the local bottom surface point after rotation.

6. The method for modeling the surface of an irregularly shaped polyhedral abrasive grinding wheel as described in claim 1, characterized in that, By minimizing the morphology evaluation function using a differential evolution algorithm, the position and angle of the pyramidal abrasive grains are optimized under constraints. Specifically: Construct morphology evaluation functions consisting of density matching terms, exclusion terms, and angle constraint terms; the density matching term is used to ensure the simulated abrasive grain count. Number of abrasive particles per unit area Matching; the exclusion term is used to prevent interference between adjacent abrasive grains; the angle constraint term is used to ensure that the rotation angle follows a normal distribution; With the goal of minimizing the morphology evaluation function, the differential evolution algorithm is used to optimize the value of the morphology evaluation function, resulting in an optimized simulated position matrix.

7. The method for modeling the surface of an irregularly shaped polyhedral abrasive grinding wheel as described in claim 1, characterized in that, The optimized square pyramid abrasive grains are subjected to one-stage or multi-stage pyramid cutting to generate diverse irregular polyhedral abrasive grain structures, specifically: By performing three-dimensional morphological statistical analysis on the grinding wheel through scanning imaging, the proportion of different polyhedral types of grinding wheel abrasive grains is obtained, thereby determining the distribution ratio of cutting levels; During the first-level cutting, the quadrangular pyramid of a preset proportion is cut in the direction of the tangent of the grinding wheel's circumference to form a hexahedron; During secondary cutting, a pre-defined proportion of abrasive grains are randomly selected from the hexahedron for random cutting to form a heptahedron; the specific process of random cutting is as follows: The cutting plane is randomly generated by uniform sampling of the normal vector. The cutting plane constant is randomly determined within a preset range based on the current convex height of the polyhedron. The actual cutting height is determined based on the cutting ratio coefficient and random perturbation. For each face of the current polyhedron, determine its normal vector direction; when cutting the polyhedron, impose the following restrictions on the cutting face: the cutting face is not perpendicular to the normal vector of any face being cut, and at most one edge of the polyhedron can be located on the cutting face; after the cutting is completed, add the new face formed by the intersection of the cutting face and each edge of the polyhedron to the face set of the polyhedron, and update the protrusion height; Delete the volume portion pointing to the side of the cutting plane; The number of faces, the statistical test of the protrusion height, and the self-interference test are performed respectively. After passing the test, the next round of cutting is carried out. When performing three-stage cutting, a pre-defined proportion of abrasive grains are randomly selected from the heptahedron and randomly cut in the manner described above to form an octahedron. Similarly, multi-stage cutting is performed according to the preset proportion of abrasive grains to generate diverse irregular polyhedral abrasive grain structures.

8. The method for modeling the surface of an irregularly shaped polyhedral abrasive grinding wheel as described in claim 1, characterized in that, Interference analysis is performed on the generated irregular polyhedral abrasive grain structure, specifically as follows: Calculate the circumscribed sphere radius of the abrasive grains, and determine whether the center distance between the two circumscribed spheres is less than the sum of their radii. If so, it is determined that there may be interference between the two abrasive grains, and the abrasive grain parameters that may cause interference are removed. The differential evolution algorithm is then called again to optimize the abrasive grain position. Otherwise, there is no interference between the two abrasive grains.

9. A surface modeling system for irregularly shaped polyhedral abrasive grinding wheels, characterized in that, include: The cutting level assignment module is configured to fit the bottom edge length and initial height of the abrasive grains using a Gaussian mixture model, while also fitting the rotation angle of the abrasive grains. Calculate the number of abrasive particles per unit area and the total number of abrasive particles; based on the measured percentage distribution of the polyhedral number of abrasive particles, preset the distribution ratio of the cutting level; The position optimization module is configured to randomly generate the initial position, size, and rotation angle of the pyramidal abrasive grains in cylindrical coordinates; and to achieve constrained optimization of the position and angle of the pyramidal abrasive grains by minimizing the morphology evaluation function through a differential evolution algorithm. The abrasive cutting module is configured to perform one-level or multi-level pyramidal cutting on optimized quadrangular pyramidal abrasive grains based on a preset cutting level distribution ratio, generating diverse irregular polyhedral abrasive grain structures. The model building module is configured to perform interference judgment on the generated irregular polyhedral abrasive structure, integrate the non-interference abrasive parameters into the cylindrical coordinate system, and construct the surface morphology model of the grinding wheel circumference.

10. A terminal device comprising a processor and a memory, the processor for implementing instructions; the memory for storing multiple instructions, characterized in that, The instructions are adapted to be loaded by a processor and executed as described in any one of claims 1-8, the method for modeling the surface of an irregularly shaped polyhedral abrasive wheel.

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