CN-122023954-A - Ball end mill wear characterization method integrating geometric features and Gaussian kernel functions

CN122023954ACN 122023954 ACN122023954 ACN 122023954ACN-122023954-A

Abstract

The invention relates to the field of cutting processing of numerical control machine tools, and provides a ball end mill wear characterization method integrating geometric features and Gaussian kernel functions, which comprises the steps of introducing a Gaussian-polynomial model containing boundary correction, the characterization function conforming to the physical abrasion mechanism is constructed, the precise characterization of the uneven abrasion distribution of the cutting edge in the complex curved surface processing is realized, and the technical problem that the interference of uneven abrasion to the cutting force is difficult to quantify in the prior art is solved. Compared with the traditional single index characterization method which only depends on the maximum wear width, the method can construct the wear distribution function which has clear physical meaning and is mathematically continuous, thereby more accurately reflecting the actual geometric state of the contact of the cutter and the workpiece in the cutting process.

Inventors

SHI XUDONG
SHI KAINING
REN JUNXUE
YAN SHUAI
SHI RUOCHEN
HU ZONGJUN
DU YANZHAO
SHI YAOYAO

Assignees

西北工业大学

Dates

Publication Date: 20260512
Application Date: 20260410

Claims (8)

1. The ball end mill wear characterization method integrating the geometric features and the Gaussian kernel function is characterized by comprising the following steps of: shooting and obtaining the surface morphology images of the rear cutter face abrasion of all cutting edges of the ball end mill by using an electron microscope; drawing a cutting edge fitting curve and marking a cutter point in a rear cutter surface abrasion surface morphology image based on geometric features of a ball end mill, selecting a plurality of sampling points on the cutting edge fitting curve at equal intervals, and determining an actual abrasion width VB corresponding to each sampling point; Step three, taking a two-dimensional vector distance between a cutter point and each sampling point on an electron microscope shooting plane, and combining the Euclidean distance between a cutter point and each sampling point under a spherical coordinate system taking a cutter center of a ball end milling cutter as an origin, and calculating an axial immersion angle kappa corresponding to each sampling point; Establishing a parameterized wear model integrating a Gaussian kernel function and a polynomial boundary correction term by taking an axial immersion angle kappa as an independent variable, wherein the parameterized wear model is used for describing the peak value and the distribution width of an actual wear area of a rear tool face of a cutting edge; And fifthly, extracting the average wear morphology feature value of the rear cutter face of each cutting edge by an arithmetic average method based on a nonlinear fitting curve, and carrying out parameterized regression analysis on the average wear morphology feature, thereby constructing and obtaining a rear cutter face wear rule regression model for describing all the cutting edges of the ball end mill, and realizing the wear characterization of the ball end mill.
2. The method for characterizing wear of a ball nose milling cutter by combining geometric features and a Gaussian kernel function according to claim 1, wherein in the step one, when the image of the wear surface topography of the relief surface is acquired, the relief surface of the cutting edge involved in cutting is kept perpendicular to the shooting view angle of an electron microscope, so as to ensure that the geometric dimension of the image of the wear surface topography of the relief surface is not distorted in projection.
3. The method for characterizing wear of a ball end mill by fusing geometric features and Gaussian kernel functions according to claim 1, wherein in the second step, the cutting edge fitting curve is obtained by taking two endpoints in the length direction of an actual wear area of a rear tool face of a cutting edge as curve endpoints, combining discrete points at any position in the actual wear area and fitting by a curve generation mode of three-point circular arcs, and further obtaining a target number of sampling points on the cutting edge fitting curve by a pitch calculation mode of equal arc length; The marked tool tip point is the midpoint of a connecting line between two end points of the chisel edge of the ball end mill; The sampling point is taken as the starting end point of the straight line, the tail end of the actual abrasion area is taken as the cut-off end point of the straight line in the direction of the inner normal vector of the fitting curve of the cutting edge at the sampling point, and at the moment, the determined straight line length is the actual abrasion width VB corresponding to the sampling point.
4. The method for characterizing wear of a ball nose milling cutter by combining geometric features and gaussian kernel functions according to claim 1, wherein in the step three, the step of calculating the axial immersion angle κ is: First, the two-dimensional vector distance d 1 of the knife point O (x 0 ,y 0 ) and the sampling point P i (x i ,y i is expressed as: , Secondly, based on the cosine theorem, under a spherical coordinate system with the center of the ball end mill with the radius of R as an origin, the Euclidean distance d 2 between the cutter point O and the sampling point P i is calculated as follows: , Wherein, beta is the included angle between the shooting plane of the electron microscope and the cutter shaft of the ball end mill, d 3 is the projection distance of the shooting plane relative to the cutter point O after the sampling point P i is equivalently mapped into the meridian plane of the ball end mill perpendicular to the shooting plane; Wherein d 3 is calculated based on the two-dimensional vector distance d 1 , and d 3 has the expression: , Finally, the axial immersion angle κ of the sampling point P i is calculated by the euclidean distance d 2 and the ball nose milling cutter radius R, and is: 。
5. the method for characterizing wear of a ball nose milling cutter by combining geometric features and gaussian kernel functions according to claim 1, wherein said step four is specifically: step 41, taking the axial immersion angle kappa as an independent variable, wherein the definition domain of the axial immersion angle kappa is: κ min =min(κ data ),κ max =max(κ data ); wherein κ data is the data set of all axial immersion angles in the measurement data set; Constructing a Gaussian kernel function containing the distribution parameters a, b, c, in which case the Gaussian kernel function The expression of (2) is: ; Step 42, constructing a straight line connecting two end points of the Gaussian kernel function The method comprises the following steps: , step 43, constructing a quadratic polynomial correction term containing a quadratic term parameter d The method comprises the following steps: , step 44, gaussian kernel function Straight line Second order polynomial correction term Adding to obtain a parameterized wear model F VB , wherein the parameterized wear model F VB is: , Step 45, for the N sampling points of the trailing face of any cutting edge, solving the parameter vector x j = (a, b, c, d) contained in the parameterized wear model F VB by the least square method of the residuals of the actual measured value and the theoretical calculated value, and solving the calculation formula The method comprises the following steps: , In the formula, Is the actual wear width of any sampling point; further, fitting calculation is performed based on the least square method, thereby obtaining a nonlinear fitting curve.
6. The method for characterizing wear of a ball nose milling cutter by combining geometric features and Gaussian kernel functions according to claim 1, In the fifth step, the step of extracting the average wear morphology feature value of the rear face of each cutting edge by an arithmetic average method refers to respectively calculating parameterized wear models F VB,j (W) of measurement data sets W of M cutting edges for M cutting edges of a ball-end milling cutter, wherein W is each sampling point in the measurement data sets W, and then averaging the parameterized wear models F VB,j (W) of the M cutting edges to obtain an average parameterized wear model The method comprises the following steps: , Then, for the average parameterized wear model Performing parameterized regression analysis, and performing least square method on the residual error of the average value and the theoretical calculation value on the average parameterized wear model Fitting and solving are carried out, and the obtained parameter vector x final of the average parameterized wear model is as follows: x final =(a’,b’,c’,d’), wherein a ', b', c 'are distribution parameters of a Gaussian kernel function of the average parameterized wear model, and d' are quadratic term parameters of a quadratic polynomial correction term of the average parameterized wear model; Thereby substituting the parameter x final into the parameterized wear model F VB to construct the wear law regression model The method comprises the following steps: 。
7. The method for characterizing wear of a ball end mill by combining geometric features and gaussian kernel functions according to any of claims 1 to 6, wherein the wear of the rear faces of all cutting edges of the ball end mill characterizes the wear state of a tool during the cutting process of the ball end mill.
8. A ball nose milling cutter wear characterization method according to any of claims 1 to 6 wherein the relief surface wear surface topography image is a two-dimensional gray scale image.

Description

Ball end mill wear characterization method integrating geometric features and Gaussian kernel functions Technical Field The invention relates to the field of cutting machining of numerical control machine tools. Background The ball end milling cutter cutting technology is a key technological means for realizing precise manufacturing of complex curved surface parts such as aero-engine blades, blisks and the like. In the cutting process, cutting force is an important physical parameter for evaluating the stability of a machining system, predicting the deformation of the surface of a workpiece and evaluating the residual life of a cutter. However, as the cutting process continues, the cutting edge of the tool inevitably wears, and this degradation of the microscopic geometry will significantly alter the contact topology of the tool with the workpiece, resulting in the cutting forces exhibiting highly complex nonlinear evolution characteristics. Therefore, how to accurately represent the wear state of the cutter and accordingly realize real-time and high-fidelity prediction of cutting force is a common technical problem to be broken through in the current high-end precision manufacturing field. At present, methods for tool wear characterization and cutting force prediction are mainly divided into two types, namely an indirect monitoring method based on a multisource sensor (such as vibration, acoustic emission, current and the like), wherein the method has good real-time performance, but because the industrial processing site environment is severe, sensor signals are extremely easy to be impacted by high-pressure cutting fluid and interfered by high-temperature metal chips, the mapping relation between signal characteristics and a wear physical mechanism is difficult to accurately construct, the signal-to-noise ratio is low, the generalization capability is limited, and the other type is an empirical or semi-empirical formula method based on an analytical model, namely inversion or prediction of cutting force is realized by establishing mathematical correlation between cutting force coefficients and wear amounts. However, existing analytical models have significant technical limitations when applied to five-axis milling scenarios, primarily in that, first, existing wear characterization models are mostly based on "homogeneity" assumptions. In the five-axis machining process, the cutter axis vector is dynamically changed in real time, so that the region of the cutting edge of the cutter involved in cutting presents a sharp dynamic fluctuation characteristic. In the prior art, complex tool wear is generally reduced to the maximum wear zone width of the flank surface measured along the cutting edge, and the gradient effect of the change of the cutting speed and the effective cutting radius along the edge line of the ball end mill is ignored, so that the non-uniform distribution characteristic of the wear along the edge direction cannot be accurately described. Secondly, the existing evolution model is difficult to capture the localized and random characteristics of abrasion, a fixed linear degradation function is often adopted to describe the abrasion process, and the cutting depth and the contact position in five-axis machining are changed at any time, so that the abrasion rates of different parts of the cutter are obviously different. The linear assumption cannot effectively characterize Gaussian distribution features or local concentration features presented by a wear region under variable working conditions, so that the cutting force prediction accuracy under a cross-working condition or long-term processing scene is severely distorted. Therefore, a method which not only can adapt to the dynamic geometric contact characteristics of five-axis machining, but also can realize the fine description of the local abrasion evolution rule of the cutting edge is needed. Disclosure of Invention The invention aims to overcome the defects of the prior art and provides a ball-end mill wear characterization method which is used for constructing a characterization function conforming to a physical wear mechanism by introducing a Gaussian-polynomial model containing boundary correction and realizing accurate reconstruction of wear spatial distribution, thereby remarkably improving the accuracy and robustness of five-axis milling force prediction and integrating geometric features and Gaussian kernel functions. In order to achieve the purpose, the technical scheme adopted by the invention is that the ball end mill wear characterization method integrating geometric features and Gaussian kernel functions comprises the following steps: shooting and obtaining the surface morphology images of the rear cutter face abrasion of all cutting edges of the ball end mill by using an electron microscope; drawing a cutting edge fitting curve and marking a cutter point in a rear cutter surface abrasion surface morphology image based on geometr