A tool influence function modeling and prediction method for freeform surface polishing
By designing parabolic test specimens on freeform surfaces and establishing a mapping model of tool influence functions, the problem of unpredictable tool removal characteristics on complex surfaces was solved, achieving high-precision and generalized material removal prediction, and reducing experimental costs and complexity.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- XIAN SANHANG POWER TECH CO LTD
- Filing Date
- 2026-03-25
- Publication Date
- 2026-07-10
AI Technical Summary
Existing technologies struggle to accurately characterize the material removal properties of flexible abrasives on complex free-form surfaces, resulting in insufficient polishing precision. Furthermore, traditional modeling methods are complex and experimental samples are difficult to cover multi-dimensional parameter spaces.
By calculating the K-means clustering analysis and convex hull calculation of the principal curvature parameter pairs, a parabolic test specimen was designed. Combining the surface topography point cloud data and mapping model, the mapping relationship of the tool influence function was established, and prediction was performed using principal component analysis and radial basis function interpolation methods.
It achieves high-precision, generalized prediction of abrasive removal characteristics with limited experimental data, reduces experimental frequency and cost, enhances the robustness and prediction accuracy of the model, and adapts to the multidimensional parameter space of freeform surfaces.
Smart Images
Figure CN122365744A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of surface finishing technology, and particularly relates to a method for modeling and predicting the tool influence function for free-form surface polishing. Background Technology
[0002] In modern manufacturing, key components such as aero-engine blades, high-performance molds, medical implants, and high-end optical elements typically possess complex freeform surface features. The manufacturing precision and surface quality of these parts directly determine the overall dynamic performance, service life, and operational efficiency of the machine. In the process chain for achieving high-precision machining of freeform surfaces, computer-controlled precision polishing technology is a crucial step in controlling surface accuracy. Among these processes, the tool influence function, as a fundamental model describing the material removal distribution characteristics within the contact area between the polishing tool and the workpiece, is a core prerequisite for achieving digital quantitative removal, residence time optimization, and morphology error compensation.
[0003] However, traditional tool influence functions are typically modeled based on planar or simple curved surfaces. When performing high-precision polishing on complex free-form surfaces, the constantly changing local curvature leads to continuous shifts in the instantaneous contact state between the grinding wheel and the workpiece, causing significant geometric distortion in the tool influence function. Secondly, traditional semi-empirical models (such as the Preston equation) heavily rely on accurate calculations of the pressure distribution in the contact area. However, for flexible grinding wheels with complex dynamic characteristics, establishing an accurate physical model of the pressure distribution on free-form surfaces with varying curvature is extremely difficult. Furthermore, while existing experimental characterization methods can obtain high-precision tool influence function data that closely reflects reality, a single fixed-point polishing experiment can only correspond to a specific set of process parameters and curvature characteristics. This makes it difficult to balance modeling efficiency with generalized prediction accuracy for key variables such as contact direction and curvature characteristics within a limited experimental sample. Current technologies struggle to accurately characterize the material removal characteristics of flexible grinding wheels on free-form surfaces, limiting further improvements in polishing accuracy. Summary of the Invention
[0004] The purpose of this invention is to provide a method for modeling and predicting the tool influence function for free-form surface polishing, in order to solve the problems of insufficient prediction accuracy of the tool influence function under the condition of variable curvature of free-form surfaces, complex physical modeling process, and difficulty in covering multi-dimensional parameter space with experimental samples in the prior art.
[0005] This invention adopts the following technical solution: a method for modeling and predicting tool influence functions for freeform surface polishing, comprising: Step 1: Calculate the principal curvature parameter pairs at uniformly discrete points on the freeform surface of the blade to be polished. Perform K-means clustering analysis and convex hull calculation on the principal curvature parameter pairs. Generate M cluster center points as central curvature points based on their distribution characteristics, and extract N dispersed convex hull vertices as boundary curvature points. Then, design a parabolic test piece that approximates the freeform surface of the blade to be polished. Step 2: Measure the surface topography point cloud data of the parabolic test specimen before polishing, then perform fixed-point polishing, and measure the surface topography point cloud data of the parabolic test specimen after polishing; Step 3: Based on the surface topography point cloud data of the parabolic test piece before and after polishing, calculate and obtain the surface deviation distribution of the parabolic test piece relative to the theoretical parabolic surface before and after polishing. Combine coordinate mapping, plane projection and gradient-based region extraction to obtain the material removal distribution data of the contact area. Fit the material removal distribution data of the contact area and then characterize the tool influence function in the form of a curved surface. Step 4: Establish a mapping model between the theoretical surface height vector of the parabolic specimen and the principal components of the tool influence function coefficients using principal component analysis and radial basis function interpolation methods; Step 5: Input the theoretical surface height value vector of the local contact area of the freeform surface to be polished, and use the mapping relationship model to obtain the predicted tool influence function.
[0006] The beneficial effects of this invention are: This invention achieves high-precision and generalized prediction of the grinding wheel removal characteristics during the polishing of free-form surfaces under limited experimental data by effectively constructing sampling logic, mapping mechanism and feedback mechanism; This invention avoids the blindness of traditional exhaustive experiments by combining cluster representative points, boundary feature points and plane reference points; while significantly reducing the frequency and cost of experiments, it ensures that the experimental samples can cover the multidimensional parameter space of free-form surface polishing to the greatest extent, thus enhancing the robustness of the model under the corresponding working conditions. The mapping model established in this invention between the "theoretical surface height value vector" and the "principal component fitting coefficient" breaks away from the dependence of traditional modeling methods on pressure distribution models. It can effectively establish a direct relationship between the shape characteristics of the surface contact area and the tool influence function, effectively ensuring the prediction accuracy of material removal in free-form surface polishing. This invention utilizes a leave-one-out cross-validation strategy combined with adaptive incremental sampling to enable the model to proactively identify "blind spots" and "weak areas" in the feature space. By targeting experimental points in sparse feature regions, closed-loop optimization of model accuracy is achieved, ensuring that the tool's influence function model maintains a high level of generalization prediction across all operating conditions. Attached Figure Description
[0007] Figure 1 This is a schematic diagram of the curvature analysis and experimental point configuration of the present invention; Figure 2 This is a schematic diagram of the point cloud data processing method for fixed-point polishing according to the present invention; Figure 3 This is a schematic diagram of cubic polynomial surface fitting for a set of material point cloud data removed according to the present invention. Figure 4 (a) is a schematic diagram of the local coordinate system for polishing according to the present invention; Figure 4 (b) is a schematic diagram of the discrete points of the theoretical surface contact range height characteristics of the present invention; Figure 5 This is a schematic diagram of the prediction results of the tool influence function in an embodiment of the present invention. Detailed Implementation
[0008] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.
[0009] This invention discloses a method for modeling and predicting the tool influence function for freeform surface polishing, including steps 1-5.
[0010] Step 1: Calculate the principal curvature parameter pairs at uniformly discrete points on the freeform surface of the blade to be polished. Perform K-means clustering analysis and convex hull calculation on the principal curvature parameter pairs. Generate M cluster center points as central curvature points based on their distribution characteristics, and extract N dispersed convex hull vertices as boundary curvature points. Then, design a parabolic test piece that approximates the freeform surface of the blade to be polished. M is preferably 6~10, and N is preferably 5~8.
[0011] Step 1 is as follows: Step 101: Calculate the principal curvature parameters at uniformly discrete points on the freeform surface of the blade to be polished. .in and Let be the minimum principal curvature and the maximum principal curvature at discrete points, respectively, satisfying... .
[0012] Step 102: Perform K-means clustering analysis and convex hull calculation on the principal curvature parameter CP. Based on its distribution characteristics, select 8 cluster center curvature points as representative experimental groups; select 6 scattered convex hull vertices as boundary curvature points.
[0013] Step 103: Based on the principles of differential geometry, design a parabolic test piece that approximates the free-form surface of the blade to be polished, targeting the cluster center curvature points and boundary curvature points. The surface equation is: Where a and b are the shape coefficients of the parabolic surface, and their relationship with the principal curvature parameters of the freeform surface is as follows: Step 104: Surface modeling was performed using UG / NX software. TC17 titanium alloy, consistent with the blade material, was selected as the test material. A test block with the target curvature characteristics was prepared through precision milling. In addition, a plane polishing benchmark experimental group was simultaneously set up to extract standard material removal features of the abrasive blade wheel under zero-curvature plane polishing conditions. The distribution layout of all experimental points is as follows: Figure 1 As shown.
[0014] Based on the parabolic test piece, an abrasive cloth flap wheel with a diameter of 15mm and a width of 12mm was used. The polishing process parameters were set as follows: spindle speed 7000r / min, contact radius 8.3mm, and abrasive grit size P400. The typical contact directions were set as the directions of the maximum and minimum principal curvature of the elliptical point, and the directions of the maximum and minimum principal curvature and asymptotic direction of the hyperbolic point, to ensure that the experimental group covered the typical geometric feature directions of the flattest and most curved surfaces.
[0015] Step 2: Before polishing, measure the surface topography point cloud data of the parabolic test piece, then perform point polishing, and measure the surface topography point cloud data of the parabolic test piece after polishing. Specifically, install the abrasive cloth flap wheel on the machine tool spindle, and perform a point polishing experiment according to preset process parameters and contact posture. The dwell time setting needs to be pre-calibrated to ensure that, under the current process parameters, each experimental point can produce material removal marks with sufficient signal-to-noise ratio and clear boundary features, thereby ensuring the accuracy of subsequent data extraction and fitting. Before and after polishing, a high-precision white light interferometer is used to measure the surface topography point cloud data of the parabolic test piece.
[0016] Step 3: Based on the surface topography point cloud data of the parabolic test piece before and after polishing, calculate and obtain the surface deviation distribution of the parabolic test piece relative to the theoretical parabolic surface before and after polishing. Combine coordinate mapping, plane projection and gradient-based region extraction to obtain the material removal distribution data of the contact area. Fit the material removal distribution data of the contact area and then characterize the tool influence function in the form of a curved surface.
[0017] Step 3 is detailed in the attached document. Figure 2 As shown, it specifically includes steps 301-305.
[0018] Step 301: Eliminate the error between the measurement coordinate system and the machining coordinate system by point cloud registration, that is: drill and scribing the center line on the boundary of the parabolic test piece to form a positioning groove, and achieve accurate matching between the scanned point cloud data and the theoretical surface by positioning the groove of the point cloud data and fine registration of the curved surface.
[0019] Step 302: Calculate the surface deviation distribution before and after polishing; First, calculate the directed distance (i) from the measurement point to the parabolic surface of the parabolic test piece. Where sign is the sign function. For the registered measurement points, This is the closest point on the theoretical surface. Where f(x,y) is the equation of the parabola. ; in, The sign of the curvature is determined by the curvature, and a and b are the shape coefficients of the parabolic surface.
[0020] Step 303: Project the surface deviation distribution onto the plane through coordinate mapping, that is: project the three-dimensional deviation value of each point. According to its planar projection position (x i , y i Mapping The shape of the peeled surface is obtained, with x, y as position coordinates and deviation as... The data is point cloud data with height z.
[0021] Step 304: Perform region extraction based on the gradient change of the removed features. The stripped data is the material removal distribution data of the contact area caused by polishing. That is, according to the material removal depth threshold (e.g., a directional deviation of less than -0.01mm is considered to have produced substantial material removal, otherwise it is considered to be noise error), the point cloud is binarized in the plane, the boundary of the effective removal area is determined by the image edge detection algorithm, and the three-dimensional point cloud data that produced material removal is extracted.
[0022] Step 305: The contact area material removal point cloud data is converted into an analytical representation, thereby obtaining the tool influence function, which is characterized as a feature vector containing surface coefficients and range boundary parameters. In this embodiment, a cubic polynomial function is used to perform surface fitting on the contact area material removal point cloud data. During fitting, the effective boundary of the surface is truncated according to the actual range of the point cloud distribution. Finally, the tool influence function of each experimental sample is characterized as a feature vector containing surface coefficients and range boundary parameters. (See attached...) Figure 3 The image shows a schematic diagram of a data fitting process. The tool influence function is: in, These are the polynomial coefficients.
[0023] In step 3, Gaussian or polynomial functions are used to fit the material removal distribution data in the contact area.
[0024] Step 4: Establish a mapping model between the theoretical surface height vector of the parabolic specimen and the principal components of the tool influence function coefficients using principal component analysis and radial basis function interpolation.
[0025] Step 4 specifically involves: The feature vectors obtained from each set of fixed-point polishing experiments were reorganized into a high-dimensional sample data matrix. (n samples, p variables in each group). First, the data are normalized to eliminate differences in dimensions, and then principal component analysis is used to identify the main direction of variable changes.
[0026] Principal Component Analysis (PCA) is performed using the singular value decomposition (SVD) of the data matrix X: ; in, It is a left singular vector matrix; The main diagonal elements are singular values. ; V is a right singular vector matrix, and the first k principal components are the first k columns of V, corresponding to the largest k singular values.
[0027] Eigenvalues With singular values The relationship is: The number of principal components retained, i.e., the number of variables after dimensionality reduction, is determined by the cumulative variance explained ratio. The cumulative variance explained ratio of the first k principal components is then calculated. for: By setting the cumulative variance explanation rate threshold to 95%, the first k columns of V are extracted, and the original high-dimensional matrix is compressed into a low-dimensional principal component matrix that can represent the core features of morphological distortion removal.
[0028] As attached Figure 4 As shown, a local coordinate system is established with the theoretical contact center of the polishing tool on the curved surface as the origin, where y T Positive axis direction and tool axis direction Conversely, z T The axis is normal to the center of the surface (n) (from the point of contact on the surface to the center of the tool). Tool axis direction. The x-axis (direction of minimum principal curvature d) of the surface coordinate system O-xyz min The positive counterclockwise angle is denoted as This characterizes the contact direction between the grinding wheel and the curved surface. Within the contact area of the planar polishing, 40 feature sampling points are discretely extracted according to a preset regular grid. The height value sequence of the sampling points is then... As an input feature vector characterizing the local shape of a workpiece.
[0029] A radial basis function interpolation method is employed, using the discrete height vector z as the independent variable and the principal components as the dependent variable. An interpolation function is established between the theoretical surface height vector and the principal components of the tool influence function, constructing a nonlinear mapping from the geometric feature space to a space devoid of topographic features. The interpolation function is expressed as follows: in, It is the first The weight coefficients corresponding to each basis function; Represents the relationship between variable x and sample point x i The Euclidean distance; N is the total number of sample points; The radial basis functions are represented using the following Gaussian kernel function: in, It is a shape parameter that controls the width of the radial basis function, and is estimated by the following formula: ; Where, x i For the i-th sample point, x j For the j-th sample point, mean is the mean value; The interpolation function can be written in matrix form as follows: in, ; It is an N×N interpolation matrix, calculated as follows: The solution is: The generalization ability of the mapping relationship model is tested using cross-validation, and experiments are selectively added to update the mapping relationship model based on the evaluation results, thereby ensuring the prediction accuracy of the tool's influence function model. The specific steps are as follows: (1) Leave-one-out cross-validation is used to evaluate the mapping relationship model. Individual sets of experimental data are extracted as test sets, and the remaining data are used to construct the model. The influence function of the prediction tool is then compared with the experimental data. The following metrics are used in this embodiment to quantitatively evaluate the prediction accuracy: Geometric deviation evaluation: Euclidean distance deviation of the location of the maximum valley depth in the influence function calculated by the calculation tool. and the absolute deviation of the maximum valley depth. With relative percentage error ; Global error evaluation: Calculate the root mean square error (RMSE) between the predicted height field and the actual measured field. Morphological similarity evaluation: The structural similarity index (SSIM) was used to assess the consistency between the predicted height field and the experimental height field.
[0030] (2) Error Exceedance Region Identification and Midpoint Interpolation Strategy: Set a preset error threshold (e.g., RMSE > 5% or SSIM < 0.9) to identify target experimental groups whose prediction accuracy does not meet the standard. Based on their distribution characteristics in the parameter space, implement the "midpoint sampling" strategy: Angle dimension encryption: If the prediction accuracy at a certain contact direction angle is not up to standard, then... adjacent experimental directions Between these points, a bisection angle is taken as a new sampling point to perform a supplementary fixed-point polishing experiment. Encryption of curvature dimension: If the prediction accuracy at a certain curvature feature point is not up to standard, a set of midpoint curvature values are interpolated between the target curvature parameter and its nearest curvature parameter in the feature space, and corresponding test pieces are prepared to perform supplementary experiments.
[0031] (3) Model Iteration Update: Introduce the newly added experimental sample data into the original sample set, and re-execute the principal component dimensionality reduction and radial basis function mapping calculation. Repeat the above verification, identification and interpolation update process until all indicators (positional deviation, height deviation, RMSE and SSIM) of the tool influence function on the global experimental group meet the high-precision processing requirements.
[0032] Step 5: Input the theoretical surface height vector of the local contact area of the freeform surface to be polished, and use the mapping relationship model to obtain the predicted tool influence function.
[0033] For the target point on the freeform surface to be predicted, a local coordinate system is established based on the grinding wheel contact direction angle under the current machining conditions. Following the same discrete layout as the mapping relationship model, the theoretical surface height vector within this contact area is extracted. The extracted height feature vector is substituted into the trained mapping relationship model to predict the principal component coefficients of the tool influence function. Subsequently, combined with the feature vector basis, the principal component coefficients are back-projected and reconstructed to increase the dimension to the original dimension represented by the tool influence function. Inverse standardization is then performed to eliminate the scaling effect of the preprocessing stage, yielding the final tool influence function corresponding to the actual working conditions. (See attached...) Figure 5 The figure shows the predicted axial normal curvature k of different surfaces in this embodiment. a The tools below affect the function.
[0034] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for modeling and predicting tool influence functions for freeform surface polishing, characterized in that, include: Step 1: Calculate the principal curvature parameter pairs at uniformly discrete points on the freeform surface of the blade to be polished. Perform K-means clustering analysis and convex hull calculation on the principal curvature parameter pairs. Generate M cluster center points as central curvature points based on their distribution characteristics, and extract N dispersed convex hull vertices as boundary curvature points. Then, design a parabolic test piece that approximates the freeform surface of the blade to be polished. Step 2: Measure the surface topography point cloud data of the parabolic test specimen before polishing, then perform fixed-point polishing, and measure the surface topography point cloud data of the parabolic test specimen after polishing; Step 3: Based on the surface topography point cloud data of the parabolic test piece before and after polishing, calculate and obtain the surface deviation distribution of the parabolic test piece relative to the theoretical parabolic surface before and after polishing. Combine coordinate mapping, plane projection and gradient-based region extraction to obtain the material removal distribution data of the contact area. Fit the material removal distribution data of the contact area and then characterize the tool influence function in the form of a curved surface. Step 4: Establish a mapping model between the theoretical surface height vector of the parabolic specimen and the principal components of the tool influence function coefficients using principal component analysis and radial basis function interpolation methods; Step 5: Input the theoretical surface height value vector of the local contact area of the freeform surface to be polished, and use the mapping relationship model to obtain the predicted tool influence function.
2. The method for modeling and predicting tool influence functions for freeform surface polishing according to claim 1, characterized in that, In step 3, Gaussian or polynomial functions are used to fit the material removal distribution data in the contact area.
3. The method for modeling and predicting tool influence functions for freeform surface polishing according to claim 1, characterized in that, The tool influence function in step 3 is: ， in, These are the polynomial coefficients.
4. The method for modeling and predicting tool influence functions for freeform surface polishing according to claim 1, characterized in that, Step 3 includes: Step 301: Eliminate the error between the measurement coordinate system and the machining coordinate system through point cloud registration; Step 302: Calculate the surface deviation distribution before and after polishing; Step 303: Project the deviation data onto the plane using coordinate mapping; Step 304: Perform region extraction based on the gradient change of the removed features. The stripped data is the material removal distribution data of the contact area caused by polishing. Step 305: Convert the point cloud data of the contact area material into an analytical expression, and then obtain the tool influence function characterized as an eigenvector containing surface coefficients and range boundary parameters.