CN-121997398-A - Modeling method and system for surface of special-shaped polyhedral abrasive grain grinding wheel

CN121997398ACN 121997398 ACN121997398 ACN 121997398ACN-121997398-A

Abstract

The invention belongs to the technical field of grinding wheel surface modeling, and particularly discloses a method and a system for modeling the surface of a special-shaped polyhedral abrasive particle grinding wheel, wherein the method comprises the steps of fitting the side length of the bottom surface of the abrasive particle, the initial height and the rotation angle of the abrasive particle; calculating the number of abrasive particles in unit area and the number of total abrasive particles, presetting the distribution proportion of cutting progression, randomly generating the initial position, the size and the rotation angle of the rectangular pyramid abrasive particles in a cylindrical coordinate system, minimizing a shape evaluation function through a differential evolution algorithm to realize constraint optimization of the positions and the angles of the rectangular pyramid abrasive particles, performing one-stage or multi-stage pyramid cutting treatment on the optimized rectangular pyramid abrasive particles to generate diversified special-shaped polyhedral abrasive particle structures, performing interference judgment on the generated special-shaped polyhedral abrasive particle structures, and constructing a circumferential surface shape model of the grinding wheel. The invention can remarkably improve the geometric and statistical similarity of the morphology while keeping high calculation efficiency, and can flexibly adapt to various abrasive particle grinding wheels such as single crystal corundum, CBN, diamond and the like.

Inventors

ZHANG JINSHENG
ZHANG ZHONGYU
GUO JING
ZHOU JIAN

Assignees

山东大学日照研究院

Dates

Publication Date: 20260508
Application Date: 20260123

Claims (10)

1. The modeling method for the surface of the special-shaped polyhedral abrasive grain grinding wheel is characterized by comprising the following steps of: fitting the bottom side length and the initial height of the abrasive particles by adopting a Gaussian mixture model, and simultaneously fitting the rotation angle of the abrasive particles, calculating the number of abrasive particles in unit area and the total abrasive particles, and presetting the distribution proportion of the cutting progression according to the distribution percentage of the polyhedral number of the actually measured abrasive particles; The initial position, the size and the rotation angle of the square pyramid abrasive particles are randomly generated under a cylindrical coordinate system, and constraint optimization of the positions and the angles of the square pyramid abrasive particles is realized by minimizing a morphology evaluation function through a differential evolution algorithm; Performing primary or multi-stage pyramid cutting treatment on the optimized rectangular pyramid abrasive particles based on a preset cutting progression distribution ratio to generate a diversified special-shaped polyhedral abrasive particle structure; and carrying out interference judgment on the generated special-shaped polyhedral abrasive particle structure, integrating the non-interference abrasive particle parameters into a cylindrical coordinate system, and constructing a circumferential surface morphology model of the grinding wheel.
2. The method for modeling the surface of the irregular polyhedral abrasive grain grinding wheel according to claim 1, wherein geometric parameters and microscopic data of the grinding wheel are collected, a Gaussian mixture model is used for fitting the side length d of the bottom surface of the grinding grain and the initial height h of the grinding grain, and parameters are guaranteed to be subjected to normal distribution, wherein the side length d of the bottom surface is the side length of the square bottom surface of the square abrasive grain of the rectangular pyramid, and the initial height h is the vertical distance from the center to the top point of the bottom surface of the square abrasive grain, and the geometric parameters and the initial height h of the bottom surface are subjected to normal distribution.
3. The modeling method for the surface of the irregular polyhedral abrasive grain grinding wheel according to claim 1, wherein the fitting of the rotation angle of the abrasive grain is specifically as follows: Angle of abrasive particles about x, y and z axes 、、 All obey normal distribution : , , ; Wherein, the Indicating the angle of the abrasive particles about the x-axis, y-axis or z-axis, For the corresponding initial angle of the beam, Representing random perturbations; 、 respectively mean and standard deviation of the corresponding angles.
4. The modeling method for a surface of a shaped polyhedral abrasive wheel according to claim 1, wherein the number of abrasive grains per unit area is calculated And total abrasive particle count The method specifically comprises the following steps: ; ; Wherein, the As the volume fraction of the abrasive particles, Is the bottom surface of the square pyramid abrasive particle the side length of the square is equal to the length of the square, The average initial height of the abrasive particles is R, the radius of the grinding wheel and W, the axial width of the grinding wheel.
5. The modeling method for the surface of the irregular polyhedral abrasive grain grinding wheel according to claim 1, wherein the initial position, the size and the rotation angle of the quadrangular pyramid abrasive grains are randomly generated under a cylindrical coordinate system, specifically: Generating a plurality of initial non-coincident center positions by using random sequence addition, wherein the distance between the positions is at least greater than a preset minimum distance threshold; based on the randomly generated rectangular pyramid bottom surface side length d and the initial height h, combining the central positions to obtain local bottom surface points and vertex coordinates; based on the random fitted rotation angles of the abrasive particles, a rotation matrix around the x axis, the y axis and the z axis is generated, so that the rotated local bottom points are obtained.
6. The modeling method for the surface of the irregular polyhedral abrasive grain grinding wheel according to claim 1, wherein the constraint optimization of the positions and the angles of the quadrangular pyramid abrasive grains is realized by minimizing a morphology evaluation function through a differential evolution algorithm, specifically: Respectively constructing morphology evaluation functions consisting of density matching terms, rejection terms and angle constraint terms, wherein the density matching terms are used for ensuring the number of simulated abrasive particles And the number of abrasive grains per unit area The rejection term is used for preventing adjacent abrasive particles from interfering, and the angle constraint term is used for ensuring that the rotation angle obeys normal distribution; And optimizing the value of the morphology evaluation function by using the minimum morphology evaluation function as a target and adopting a differential evolution algorithm to obtain an optimized simulation position matrix.
7. The modeling method for the surface of the irregular polyhedral abrasive grain grinding wheel according to claim 1, wherein the optimized quadrangular pyramid abrasive grains are subjected to primary or multistage pyramid cutting treatment to generate diversified irregular polyhedral abrasive grain structures, specifically comprising the following steps: Carrying out three-dimensional morphology statistical analysis on the grinding wheel through scanning imaging to obtain the different polyhedron type duty ratios of the grinding wheel abrasive particles, and further determining the distribution proportion of the cutting progression; when primary cutting is carried out, cutting the rectangular pyramid with a preset proportion according to the tangential direction of the circumferential surface of the grinding wheel to form a hexahedron; When the secondary cutting is carried out, abrasive particles with preset proportion are randomly selected from hexahedron to carry out random cutting, so as to form a heptahedron, wherein the random cutting process is specifically as follows: randomly generating a cutting plane through uniform sampling of a normal vector, randomly determining a cutting plane constant in a preset interval according to the protrusion height of the current polyhedron, and determining an actual cutting height based on a cutting proportion coefficient and random disturbance; Determining the normal vector direction of each face of the current polyhedron; when the polyhedron is cut, the cutting surface is limited in that the cutting surface is not perpendicular to the normal vector of any surface to be cut, and at most one edge of all edges of the polyhedron can be positioned on the cutting surface; Respectively carrying out face number verification, bulge height statistical test and self-interference detection, and entering the next round of cutting after the detection is passed; When three-stage cutting is carried out, randomly selecting abrasive particles with preset proportion from the heptahedron to carry out random cutting in the mode so as to form an octahedron; and by analogy, carrying out multistage cutting according to the preset proportion distribution of the abrasive particles, and generating a diversified special-shaped polyhedral abrasive particle structure.
8. The modeling method for the surface of the special-shaped polyhedral abrasive grain grinding wheel according to claim 1, which is characterized by carrying out interference judgment on the generated special-shaped polyhedral abrasive grain structure, and specifically comprises the following steps: Calculating the outer ball receiving radius of the abrasive particles, judging whether the center distance of the outer balls of the two abrasive particles is smaller than the sum of the outer ball receiving radii of the two abrasive particles, if yes, judging that interference possibly exists between the two abrasive particles, removing the abrasive particle parameters possibly existing in interference, and recalling a differential evolution algorithm to optimize the positions of the abrasive particles, otherwise, no interference exists between the two abrasive particles.
9. A shaped polyhedral abrasive wheel surface modeling system, comprising: the cutting progression distribution module is configured to fit the bottom side length and the initial height of the abrasive particles by adopting a Gaussian mixture model, and simultaneously fit the rotation angle of the abrasive particles; The position optimization module is configured to randomly generate initial positions, sizes and rotation angles of the square pyramid abrasive particles under a cylindrical coordinate system, minimize a morphology evaluation function through a differential evolution algorithm and realize constraint optimization of the positions and angles of the square pyramid abrasive particles; The abrasive grain cutting module is configured to perform primary or multistage pyramid cutting treatment on the optimized rectangular pyramid abrasive grains based on a preset cutting progression distribution ratio, so as to generate a diversified special-shaped polyhedral abrasive grain structure; the model construction module is configured to be used for carrying out interference judgment on the generated special-shaped polyhedral abrasive particle structure, integrating the non-interference abrasive particle parameters into a cylindrical coordinate system and constructing a grinding wheel circumferential surface morphology model.
10. A terminal device comprising a processor for implementing instructions and a memory for storing a plurality of instructions, characterized in that the instructions are adapted to be loaded by the processor and to perform the method for modeling the surface of a shaped polyhedral abrasive wheel according to any one of claims 1 to 8.

Description

Modeling method and system for surface of special-shaped polyhedral abrasive grain grinding wheel Technical Field The invention relates to the technical field of grinding wheel surface modeling, in particular to a method and a system for modeling the surface of a special-shaped polyhedral abrasive grain grinding wheel. Background The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art. Grinding is an important process in the field of precision manufacturing. The accurate modeling of the circumferential surface morphology of the grinding wheel is a precondition basis for establishing a microcosmic contact mechanism, grinding force and heat distribution mathematical model, and can provide key support for analyzing the integrity, efficiency and quality influence mechanism of the machined surface. The traditional abrasive particle modeling generally adopts regular geometric bodies such as spheres, ellipsoids, cones, regular octahedrons or truncated octahedrons as model patterns, and the like, and the uniform distribution and ideal shape of abrasive particles are assumed, so that the model precision is insufficient, and the random changes of the bottom diameter, the height and the hardness of the abrasive particles cannot be accurately reflected. Therefore, although the calculation complexity can be reduced and the simulation speed can be increased, the accurate description of the real special-shaped polyhedral structure of the abrasive particles, the height distribution of the random protrusions and the irregular gaps after abrasion is sacrificed, and the problems of obvious deviation between the simulation morphology and the actual grinding wheel, easy interference, insufficient prediction precision and the like are caused. In recent years, although a learner adopts a vibration method, a random deflection method and other means to improve the position randomness and the preliminary wear characteristics of abrasive particles, for example, the vibration method generates random position distribution and spatial orientation of abrasive particles by simulating a vibration process (such as random sampling and high-frequency vibration), so that the assumption of uniform distribution is avoided and the fitting precision of a model to the surface heterogeneity of an actual grinding wheel is improved. But these methods are all modeling paradigms that apply "single fixed geometry prototype + parameter perturbation" and fail to fundamentally break through the characterization bottleneck of highly heterogeneous individual shapes of abrasive particles. The model essentially only realizes 'homomorphism', but not true 'heteromorphism', and has obvious difference from the diversity of the true abrasive particles (the number of faces is six-ten or more, the sharpness of the edge angle and the tip angle are obviously discrete) observed by SEM. Disclosure of Invention Aiming at the key problems, the invention provides a modeling method and a modeling system for the surface of a special-shaped polyhedral abrasive grain grinding wheel, wherein the method takes a simple rectangular pyramid as an initial prototype, realizes independent, real and special-shaped geometric generation of each abrasive grain through multistage random plane cutting and global optimization, remarkably improves the geometric and statistical similarity of the morphology while keeping high calculation efficiency, and can flexibly adapt to various abrasive grain grinding wheels such as single crystal corundum, CBN, diamond and the like. Meanwhile, constraint optimization is carried out on abrasive particle positions and angle distribution by combining a differential evolution algorithm, and random distribution without interference is realized through global search and morphology evaluation functions. In some embodiments, the following technical scheme is adopted: a modeling method for the surface of a special-shaped polyhedral abrasive grain grinding wheel comprises the following steps: fitting the bottom side length and the initial height of the abrasive particles by adopting a Gaussian mixture model, and simultaneously fitting the rotation angle of the abrasive particles, calculating the number of abrasive particles in unit area and the total abrasive particles, and presetting the distribution proportion of the cutting progression according to the distribution percentage of the polyhedral number of the actually measured abrasive particles; The initial position, the size and the rotation angle of the square pyramid abrasive particles are randomly generated under a cylindrical coordinate system, and constraint optimization of the positions and the angles of the square pyramid abrasive particles is realized by minimizing a morphology evaluation function through a differential evolution algorithm; Performing primary or multi-stage pyramid cutting treatment on the optimized