A geometric error prediction method based on the microstructure of the mating surface of the translational axis guideway in high-end CNC machine tools

Abstract

This invention discloses a geometric error prediction method based on the microscopic morphology of the guide rail mating surface of a high-end CNC machine tool, belonging to the field of machine tool precision analysis technology. The method includes: acquiring three-dimensional point cloud data of the guide rail mating surface; performing coordinate unification and preprocessing on the point cloud data to construct a motion reference plane and generate a normal error field; extracting low-frequency shape error components from the normal error; constructing a surface model of the guide rail mating surface using B-spline surface fitting; and establishing an error propagation model to map the surface model normal error into five geometric errors. This invention, through a complete innovation process of "point cloud acquisition—error field construction—multi-scale decomposition—surface modeling—error mapping," constructs a systematic modeling framework of "guide rail surface geometry—motion behavior—geometric error," realizing quantitative prediction of translational axis geometric errors during the design phase. It solves the problem of existing technologies relying on post-assembly measurement and is applicable to geometric error analysis of various guide rail structures.

Description

Technical Field

[0001] This invention relates to the field of precision analysis technology for high-end CNC machine tools, specifically to a geometric error prediction method based on the microstructure of the mating surface of the translational shaft guide rail. Background Technology

[0002] High-end CNC machine tools, as an important component of advanced manufacturing equipment, directly determine the forming quality and assembly precision of complex parts through their machining accuracy. High-end CNC machine tools, such as... Figure 1 As shown, the errors generated by machine tools during operation mainly include geometric errors, thermal errors, force errors, and control errors. Among these, geometric errors originate from the manufacturing precision, assembly quality, and structural characteristics of key machine tool components. They possess relative stability and repeatability, and are the fundamental error source affecting the machining accuracy of machine tools. Therefore, analyzing and controlling geometric errors during the machine tool design phase is of great significance for improving the overall accuracy of the machine.

[0003] In the machine tool geometric error system, the motion accuracy of the translational axis is a crucial factor determining the machining accuracy. A translational axis typically consists of a guideway pair and a ball screw pair. The guideway pair provides guidance and load-bearing functions, and the microscopic morphology of its mating surface directly affects the straightness and angular errors of the translational axis. When the guideway mating surface has a non-ideal microscopic morphology, this non-ideal morphology will be transmitted with the motion during the feed motion and transformed into a deviation in the motion trajectory, thus forming machine tool geometric errors. Therefore, the actual microscopic morphology of the guideway mating surface is a significant source of translational axis errors.

[0004] In existing technologies, the acquisition of machine tool geometric errors mainly relies on high-precision measuring equipment such as laser interferometers and ballbars. Errors are measured on each motion axis after the entire machine is assembled, and a geometric error model is established using error identification methods. This type of method belongs to the post-processing detection and compensation approach, making it difficult to predict errors during the machine tool design and manufacturing stages. Furthermore, some studies rely on tolerance analysis methods to estimate the overall machine geometric error through the dimensional and geometrical tolerances of components. However, such methods are usually based on ideal geometric assumptions and fail to fully consider the spatial distribution characteristics of the actual non-ideal surface morphology of the guide rail mating surfaces, making it difficult to accurately reflect the influence of the guide rail surface microstructure on motion accuracy.

[0005] Meanwhile, existing geometric error modeling methods mostly start from the shaft level or the whole machine level, lacking a modeling approach that constructs error transmission relationships based on the actual surface morphology of components. A systematic modeling method reflecting the intrinsic relationship between "guide rail surface geometry—motion behavior—geometric error" has not yet been formed. Specifically, existing technologies have the following shortcomings: 1. Limitations in measurement methods and difficulty in guaranteeing the quality of raw data: Traditional geometric error acquisition relies on equipment such as laser interferometers and ballbars for measurement after the entire machine is assembled, which is a post-assembly inspection path and cannot provide data support during the design stage. Contact measurement may cause damage to the guide rail surface, and the measurement efficiency is low with sparse sampling points, making it difficult to obtain complete microscopic morphological information of the guide rail mating surface. The lack of a unified reference frame during multi-coordinate system transformation easily introduces cumulative errors, affecting the accuracy and consistency of the raw data. 2. Human error exists in estimation based on experience: At the beginning of machine tool design, the geometric error of the whole machine is estimated by the dimensions and geometric tolerances of the parts. Such methods are usually based on ideal geometric assumptions and fail to fully consider the spatial distribution characteristics of the actual non-ideal surface morphology of the guide rail mating surface, making it difficult to truly reflect the influence of the microscopic morphology of the guide rail surface on motion accuracy. 3. Unclear error propagation relationship and difficulty in uniformly predicting the five geometric errors: Existing technology has not established a quantitative mapping relationship between the microscopic morphology of the guide rail mating surface and the five geometric errors of the translational axis. The mechanisms underlying straightness errors and pitch errors in the vertical plane, straightness errors and yaw errors in the horizontal plane, and tilt errors caused by parallelism errors between two guide rails are unclear, and explicit calculation formulas are lacking. The multi-point contact characteristics of the slide and guide rails are not accurately characterized, leading to significant deviations between error prediction results and actual conditions. 4. Lack of an end-to-end systematic approach, with fragmented processes: Existing research often focuses on improving single aspects, failing to develop a comprehensive systematic approach encompassing the entire process from obtaining the true morphology of the guide rail mating surface to error mapping. Measurement, processing, modeling, and analysis are fragmented, resulting in significant information loss during data transmission, making it difficult to construct a complete technical chain of "guide rail surface geometry—motion behavior—geometric error." The method lacks versatility and is difficult to extend to the prediction of geometric errors in different types of guide rail structures.

[0006] Therefore, how to establish a modeling method that can realistically characterize the non-ideal geometric shape of the guide rail mating surface and reveal its transformation into machine tool geometric errors during the feed motion, and realize the predictive analysis of geometric errors, has become a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0007] The purpose of this invention is to propose a geometric error prediction method based on the microscopic morphology of the guide rail mating surface of a high-end CNC machine tool translation axis. This method solves the problem that existing technologies rely on measurement to obtain geometric errors after the entire machine is assembled, making it difficult to predict errors during the design stage. It enables quantitative mapping and prediction between the non-ideal geometric morphology of the guide rail mating surface and the geometric error of the translation axis.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: A geometric error prediction method based on the microstructure of the mating surface of the translational axis guideway in a high-end CNC machine tool includes the following steps: S1: Obtain the 3D point cloud data of the guide rail mating surface to form a point cloud matrix. A line laser stereo camera is used to acquire 3D point cloud data of the guide rail mating surface. Based on the principle of laser triangulation, a line laser is projected onto the guide rail surface at a fixed angle. By extracting the change information of the center position of the laser stripes, the spatial height distribution of the guide rail surface is obtained. The camera's intrinsic and extrinsic parameters and the laser plane parameters are jointly calibrated to achieve accurate conversion from image pixel coordinates to spatial 3D coordinates. A scanning layout of "fixed camera and moving guide rail" is adopted. The guide rail moves at a uniform linear speed along the feed direction. The spatial spacing between adjacent scan frames is strictly controlled by the slider encoder pulses. All point cloud data are uniformly expressed in the experimental platform motion coordinate system.

[0009] S2: Perform coordinate unification and preprocessing on the point cloud data, construct a motion reference plane, and generate a normal error field. First, the point cloud data is coordinate unified. A geometric mapping relationship between the camera coordinate system and the world coordinate system is established through system-level calibration. Furthermore, the rigid transformation relationship between the world coordinate system and the test platform motion coordinate system is determined. Point clouds from each scan frame are stitched together in the feed sequence to reconstruct the complete 3D point cloud data of the guide rail mating surface. Second, the point cloud data is cropped, filtered, and smoothed. A 3D cropping method is used to extract the functional area surface. Mean filtering and weighted smoothing are used to remove outliers and noise, preserving low-frequency geometric features. Then, a guide rail motion reference plane is constructed. The plane's spatial position is determined in the least squares sense, minimizing the sum of squares of the normal deviations of all measurement points on the effective functional surface of the guide rail relative to this plane. Finally, the normal deviation is defined, and the normal projection deviation of each sampling point relative to the ideal translational reference plane is calculated to construct the guide rail surface normal error field.

[0010] S3: Extract low-frequency shape error components from the normal error. A two-dimensional parametric coordinate system is introduced within the tangential plane of the guide rail to map discrete measurement points to the parameter space. The normal error field is meshed and edge-processed, and the discrete point cloud is interpolated into a regular two-dimensional grid. A mirror expansion method is used to suppress boundary effects. Two-dimensional discrete wavelet decomposition is employed to perform multi-scale analysis of the normal error field, extracting low-frequency detail components as the shape error of the guide rail mating surface, while discarding the mid-to-high-frequency components corresponding to waviness and roughness.

[0011] S4: Construct a guide rail interface surface model using B-spline surface fitting. B-spline surfaces are used to fit the extracted low-frequency shape errors, generating a continuous, smooth, and differentiable surface mathematical model from the discrete error field. This surface model geometrically approximates the actual surface morphology of the guide rail, and motion behavior consistency constraints are introduced during the modeling stage, serving as the mathematical carrier connecting the geometric morphology of the guide rail mating surface with its translational motion behavior.

[0012] S5: Establish an error propagation model, mapping the surface model normal error to five geometric errors. By combining the surface model of the guide rail mating surface of the translational axis, a mapping relationship is established between the microscopic morphology of the guide rail mating surface and the straightness and rotation errors. Based on the geometric relationship of the slide moving along the guide rail surface, calculation formulas are derived for the straightness and pitch errors in the vertical plane, the straightness and yaw errors in the horizontal plane, and the tilt error caused by the parallelism error between the two guide rails. Substituting the surface model into the above formulas, a direct mapping and prediction of the five geometric errors of the translational axis from the non-ideal microscopic morphology of the guide rail mating surface is achieved.

[0013] Compared with the prior art, the present invention has the following beneficial effects: 1. Non-contact high-precision measurement ensures the quality of raw data. A line laser stereo camera is used to acquire 3D point cloud data of the guide rail mating surface. Based on the principle of laser triangulation, non-contact, high-precision measurement is achieved, avoiding surface damage that may occur with contact measurements. Through joint calibration of camera intrinsic and extrinsic parameters and laser plane parameters, accurate conversion from image pixel coordinates to spatial 3D coordinates is achieved, with measurement accuracy reaching the micrometer level, providing high-fidelity raw data for subsequent error analysis. A scanning layout of "fixed camera, moving guide rail" is adopted. The spatial spacing between adjacent scan frames is strictly controlled by the slide table encoder pulses, ensuring the sampling uniformity and spatial consistency of the point cloud data in the feed direction, eliminating measurement errors introduced by motion speed fluctuations. All point cloud data are uniformly expressed in the experimental platform's motion coordinate system, completing point cloud stitching. This ensures that subsequent point cloud data processing is performed under the same reference frame, guaranteeing the authenticity and continuity of the data.

[0014] 2. Effectively perform point cloud preprocessing to construct the normal error field of the guide rail surface. A rigid transformation relationship between the camera coordinate system, world coordinate system, and test platform motion coordinate system is established through system-level calibration, achieving spatial consistency of multi-frame data during the point cloud generation stage, eliminating the need for post-processing registration and avoiding additional errors introduced by registration algorithms. A 3D clipping method is used to accurately extract the functional area surface, focusing the analysis on the effective working area of ​​the guide rail mating surface. A combination of mean filtering and weighted smoothing, with a smoothing coefficient optimized to 0.5, effectively preserves low-frequency geometric features while removing outliers and noise, achieving a balance between data smoothing and feature fidelity. The spatial position of the motion reference plane is determined in the least squares sense, minimizing the sum of squares of the normal deviations of all measurement points on the effective functional surface of the guide rail relative to this plane, providing a unified benchmark for quantifying the overall geometric deviation of the guide rail mating surface relative to the ideal translational state. The normal error field is defined as the deviation of the normal projection of each sampling point relative to the ideal translational reference plane, comprehensively characterizing the overall deviation of the guide rail mating surface relative to the ideal translational reference from a geometric perspective, providing core input data for subsequent multi-scale decomposition and surface modeling.

[0015] 3. Multi-scale decomposition separates error components, revealing the influence mechanism of errors at different scales. Discrete point clouds are interpolated into regular two-dimensional grids, and uniform sampling step sizes are defined along the length and width directions of the guide rail to make the discrete error data continuous, facilitating subsequent mathematical processing. A mirror extension method is used to symmetrically extend the error field at the parameter domain boundary, effectively suppressing boundary effects caused by finite support regions and ensuring the accuracy of error analysis in the boundary region. Two-dimensional discrete wavelet decomposition is used to perform multi-scale analysis of the normal error field, decomposing the geometric error of the guide rail mating surface into components of different spatial scales: high-frequency roughness, mid-frequency waviness, and low-frequency shape error. The sym4 wavelet basis is used as the decomposition basis function, which takes into account compact support, approximate symmetry, and smoothness, making the low-frequency shape error continuous and stable in two-dimensional space. This decomposition method achieves the separation of geometric errors at different scales on the guide rail surface and clarifies their respective influence mechanisms on motion behavior: high-frequency roughness mainly affects local contact state and friction behavior, mid-frequency waviness affects the smoothness and vibration characteristics of slider motion, and low-frequency shape error directly determines the overall geometric consistency and macroscopic motion deviation of the component, providing a new technical path for error tracing and accuracy optimization.

[0016] 4. B-spline surface fitting is used to construct a skin model, realizing a continuous mathematical representation of the morphology. B-spline surfaces are used to fit the extracted low-frequency shape errors, transforming discrete error data into a continuous, smooth, and differentiable mathematical expression. The local support properties of the B-spline basis functions allow the surface to accurately approximate local geometric features, and the number of control points can be flexibly adjusted according to the complexity of the error, balancing fitting accuracy and computational efficiency. The generated surface model not only geometrically approximates the actual surface morphology of the guide rail but also introduces motion behavior consistency constraints during the modeling stage, making it a mathematical carrier connecting the geometric morphology of the guide rail mating surface with its translational motion behavior. This model has first-order continuous differentiability, supporting the accurate calculation of the surface slope in the subsequent error propagation model, laying the mathematical foundation for the quantitative mapping of the five geometric errors.

[0017] 5. The error propagation model reveals the mapping pattern, enabling unified prediction of five geometric errors. Based on the actual geometric relationship of the slide's movement along the guide rail surface, the correspondence between different error components and the micro-morphology of the guide rail surface is clarified: In the vertical plane, straightness error is affected by the micro-morphology of the guide rail's vertical surface; pitch error is affected by the straightness error in the vertical plane and the slide length. In the horizontal plane, straightness error is affected by the micro-morphology of the guide rail's horizontal surface; yaw error is affected by the straightness error in the horizontal plane and the slide length. Tilt error is affected by the parallelism error of the two guide rail pairs and the slide width. This mapping relationship reveals the transformation law of the guide rail mating surface micro-morphology into machine tool geometric errors, realizing the transparency of the error generation mechanism. Explicit calculation formulas for five geometric errors are derived, and error prediction results can be obtained by directly substituting the surface model. For the straightness error and pitch error in the vertical plane, the geometric relationship between the height difference of the front and rear contact points of the slide and the slide length is used for calculation; for the straightness error and yaw error in the horizontal plane, a similar method is used for derivation in the horizontal plane; for the tilt error, the geometric relationship between the height difference of the left and right guide rails and the slide width is used for calculation. In the formula derivation, the bivariate function is averaged at different y values ​​to accurately characterize the multi-point contact characteristics between the slide and the guide rail. This method achieves a direct mapping from the non-ideal microscopic morphology of the guide rail mating surface to the five geometric errors of the translational axis, enabling error prediction during the machine tool design stage and providing a preliminary evaluation method for machine tool precision design and error compensation.

[0018] 6. End-to-end process innovation to build a systematic prediction system. This invention constructs an innovative end-to-end method from "point cloud acquisition" to "error mapping," forming a systematic modeling framework of "guide rail surface geometry—motion behavior—geometric error," and for the first time achieving geometric error prediction based on the actual surface morphology of components. The systematic advantages of this system are specifically reflected in: Error prediction during the design phase breaks through the limitations of post-production inspection: without waiting for the complete machine assembly, the geometric error of the translation axis can be predicted during the design and manufacturing stages, providing a pre-assessment method for machine tool precision design, greatly shortening the R&D cycle and reducing manufacturing costs; Accurately reflects the microscopic morphology and improves the accuracy of error modeling: Starting from the actual non-ideal surface morphology of the guide rail mating surface, it overcomes the limitations of traditional tolerance analysis methods based on ideal geometric assumptions, and significantly improves the authenticity and accuracy of error prediction; Revealing the error generation mechanism and connecting the morphology-motion-error transmission chain: It reveals the inherent law of the transformation of the micro-morphology of the guide rail mating surface into machine tool geometric errors during the feed motion, providing a theoretical basis for error tracing and accuracy optimization; Unified prediction of five geometric errors to meet engineering application needs: The micro-morphology of the guide rail mating surface is mapped to five geometric errors of the translation axis, and the prediction results can be directly used for machine tool accuracy analysis and error compensation. It is highly versatile and adaptable to various guide rail structures: the point cloud acquisition, error field construction, surface modeling and error propagation methods are not dependent on specific guide rail types and can be widely applied to various translational axis guide rail mating surfaces, with strong versatility and scalability. Attached Figure Description

[0019] Figure 1 Schematic diagram of a high-end CNC machine tool; Figure 2 Flowchart for predicting geometric errors of translational axis guideways in high-end CNC machine tools; Figure 3 Experimental schematic diagram; Figure 4 Schematic diagram of the normal error field; Figure 5 Schematic diagram of skin surface model; Figure 6 Schematic diagram of the actual motion structure of the slide; Figure 7 A schematic diagram of the error morphology of the slide moving along the guide rail on the vertical plane; Figure 8 Parallelism error morphology and side view of the guide rail surface. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] like Figure 2 As shown, this embodiment provides a geometric error prediction method based on the microstructure of the mating surface of the translational axis guideway of a high-end CNC machine tool, including the following steps: S1: Obtain the three-dimensional point cloud data of the guide rail mating surface and form a point cloud matrix; To establish a digital model of the microscopic morphology of the guide rail mating surface, this invention employs a line laser stereo camera to acquire three-dimensional point cloud data of the guide rail mating surface. This technology is based on the principle of laser triangulation: a line laser is projected onto the guide rail surface at a fixed angle, and changes in surface height cause the laser stripes to shift in position on the camera's imaging plane. By extracting the information on the change in the center position of the stripes, the spatial height distribution of the guide rail surface can be obtained inversely.

[0022] To achieve accurate conversion from image pixel coordinates to three-dimensional spatial coordinates, joint calibration of camera intrinsic and extrinsic parameters, as well as laser plane parameters, is required. This paper uses a standard calibration block to acquire calibration images under multiple poses and extract the sub-pixel center positions of the calibration points. And solve the camera intrinsic parameters External reference and the laser plane equation L: Pixel coordinates The corresponding normalized camera coordinates are:

[0023] Normalized camera coordinates Spatial point cloud coordinates Geometric mapping relationship between them:

[0024] in Using depth as a factor, a series of spatial point cloud coordinates are obtained. This enables high-precision three-dimensional reconstruction of the guide rail mating surface.

[0025] This method employs a scanning layout of "fixed camera and moving guide rail," such as... Figure 3 As shown. After system calibration, all point cloud data are uniformly represented in the motion coordinate system of the test bench. In the middle. Among them, The direction is consistent with the feed direction of the guide rail. Corresponding to the width direction of the guide rail, This is the normal direction of the guide rail mating surface. The guide rail moves along... The direction is uniform linear motion, and the spatial spacing between adjacent scan frames is... It is strictly controlled by the pulse of the slide encoder.

[0026] S2: Perform coordinate unification, filtering and smoothing on the point cloud data, construct a motion reference plane, calculate the normal deviation, and form a normal error field; S2.1: Unify the coordinates of the point cloud data; Real-time data transmission is performed between the line laser stereo camera and the computer, and a camera coordinate system is established through system-level calibration. With world coordinate system The geometric mapping relationship between them was determined, and the world coordinate system and the test platform motion coordinate system were further defined. The rigid transformation relationship between them. Based on this coordinate unification model, the laser stripe pixels of each scanning frame are first reconstructed as three-dimensional points in the world coordinate system, and then transformed to the motion coordinate system of the test platform for unified expression, thereby achieving spatial consistency of multi-frame data in the point cloud generation stage.

[0027] Let the number of points obtained from the first frame scan be... Then the point cloud of that frame can be represented as:

[0028] in This indicates that the i-th laser stripe point in the first frame is in the motion coordinate system of the test platform. The three-dimensional coordinates are determined. Since the trajectory of the guide rail is known, the point clouds of each frame can be aligned during the generation process through prior motion displacement, eliminating the need for post-processing registration. The point clouds of each frame are stitched together in the feed sequence to gradually reconstruct the complete three-dimensional point cloud data of the guide rail mating surface. .

[0029] S2.2: Perform cropping, filtering, and smoothing on the guide rail combined surface point cloud data; After unifying the point cloud coordinates and stitching them together, a complete 3D point cloud of the guide rail mating surface was obtained. To remove ambient noise and extract the functional area surface, a 3D clipping method is used to confine the point cloud to a specific area. The cropped functional area point cloud is denoted as... This serves as the point cloud input for subsequent preprocessing.

[0030] For the cropped point cloud Preprocessing is performed. First, the average height is obtained through mean filtering:

[0031] in It is defined as a point cloud after cropping. The neighborhood point set, Average point cloud height Represents the original point cloud. This represents the number of neighborhood points. The filtered point cloud is then weighted.

[0032] in The smoothing coefficient is taken after debugging. To achieve a balance between smoothing and preserving original features, the final result is a preprocessed smooth point cloud:

[0033] After cropping and preprocessing, the point cloud of the guide rail interface remains continuous along its length and exhibits good spatial consistency. Outliers and noise are mainly distributed in the edge regions or at locations with localized reflection anomalies, and have been removed through preprocessing. The processed point cloud data retains low-frequency geometric features, and its overall continuity and geometric consistency meet the requirements for subsequent surface model construction and guide rail motion analysis.

[0034] S2.3: Construct a reference plane for the guide rail motion; To quantify the overall geometric deviation of the guide rail mating surface relative to the ideal translational state and to uniformly characterize the motion behavior of the guide rail, a motion reference plane needs to be introduced during the surface model construction process. This invention represents this reference plane as a function. Its normal vector direction is perpendicular to the theoretical feed direction of the machine tool translation axis, and its spatial position is determined in the least squares sense, so that the sum of the squares of the normal deviations of all measuring points on the effective functional surface of the guide rail relative to the plane is minimized.

[0035] S2.4: Define the normal deviation and construct the normal error field of the guide rail surface. Based on the reference plane, the preprocessed point cloud of the guide rail bonding surface is mapped onto the coordinate system of that plane to quantify the geometric deviation of each point relative to the ideal translational state. The preprocessed point cloud can be represented as a discrete set of sampling points. , Figure 4 The ideal translational reference plane of the guide rail is given. The construction and normal error field are illustrated, showing the point cloud of the guide rail interface, the ideal translational datum and their relative geometric relationships.

[0036] Further calculate the deviation of each sampling point from the normal projection relative to the ideal translational reference plane, and define the normal error field as: .in, Indicates the first guide rail mating surface Point cloud measurement points , Let it be its orthogonal projection point on the ideal translational reference plane. Let be the unit normal vector of this ideal translational reference plane, defined as follows: The point indicates that it is located on the positive side of the normal direction of the reference plane.

[0037] The normal error field geometrically describes the overall deviation of the guide rail mating surface from the ideal translational reference, and is an important geometric source of deviation in the guide rail motion behavior.

[0038] S3: Extract low-frequency shape errors from normal errors. Geometric errors at guide rail mating surfaces have different physical sources and functional impacts at different spatial scales. High-frequency roughness mainly affects local contact states and frictional behavior, mid-frequency waviness is related to periodic errors in machining and assembly processes, and low-frequency shape errors directly determine the overall geometric consistency and macroscopic motion deviation of the component. Table 1 summarizes the characteristics and functions of errors at different scales.

[0039] Table 1 Spatial Scale and Physical Influence of Geometric Errors at Guide Rail Mating Surface

[0040] To facilitate the description of the spatial distribution of guide rail mating surface errors in the length and width directions, this invention introduces a two-dimensional parametric coordinate system in the tangential plane of the guide rail. Where u represents the guide rail length direction parameter and v represents the guide rail width direction parameter. Discrete measurement points are then parameterized using point cloud methods. Mapped to the corresponding position in the parameter space Thus, the discrete normal error can be expressed as:

[0041] S3.1: Mesh generation and edge processing of the normal error field Discrete point cloud Interpolation is a regular two-dimensional grid. First, define the parameters of the regular two-dimensional mesh:

[0042] in These represent the uniform sampling step sizes along the length and width directions of the guide rail, respectively. A two-dimensional interpolation operator is used. By mapping the discrete point cloud onto a regular grid, a discrete representation of the continuous error field is obtained:

[0043] This leads to the construction of the normal error field matrix defined on a regular two-dimensional mesh:

[0044] To suppress the boundary effects caused by the finite support region, a mirror expansion method is used to adjust the error field. Symmetric extension is performed at the boundary of the parameter domain to obtain a boundary-continuous extended error field. .

[0045] S3.2: Perform multi-scale decomposition on the normal error field to extract low-frequency shape error components. Two-dimensional discrete wavelet decomposition is used to analyze the normal error field. Multiscale analysis can be performed, and its decomposition form can be expressed as: .

[0046] in, For the first The low-frequency approximation component after layer decomposition corresponds to the shape error of the guide rail mating surface; and These represent the mid-to-high frequency detail components in different directions, corresponding to waviness and roughness components. The sym4 wavelet basis is used as the wavelet decomposition basis function, which takes into account compact support, approximate symmetry, and smoothness, making the low-frequency shape error continuous and stable in two-dimensional space; within a reasonable range of decomposition levels, the low-frequency components are not sensitive to parameter changes.

[0047] S4: Construct a guide rail interface surface model using B-spline surface fitting. S4.1: Using B-spline surfaces to fit low-frequency shape errors Obtaining the shape error of the guide rail mating surface Afterwards, this article will As the geometric support for motion behavior, the surface of the guide rail mating surface is modeled using B-spline surfaces, and its mathematical expression is:

[0048] in, As control points, and They are respectively Rank and Step spline basis functions and These represent the number of control points in the two parameter directions, respectively. In the specific implementation, the parameter directions... and These correspond to the direction of movement and the lateral direction of the guide rail, respectively.

[0049] S4.2: Generating a Mathematical Model of a Continuous Skin Surface Discrete error field A continuous, smooth, and differentiable skin model is generated by B-spline surface fitting. Skin model such as Figure 5 As shown. Guide rail It not only geometrically approximates the actual surface morphology of the guide rail, but also introduces motion behavior consistency constraints in the modeling stage, making it a mathematical carrier connecting the geometric morphology of the guide rail mating surface with the translational motion behavior.

[0050] S5: Establish an error propagation model, mapping the surface model normal error to five geometric errors. S5.1: Based on the structural parameters of the translational shaft guide rail, establish the mapping relationship between normal error and straightness and rotational error. As the slide moves along the guide rail surface, it is affected by the micro-morphological curve of the guide rail surface. To establish the relationship between the surface model of the guide rail and geometric errors, the following assumptions are made: First, the slide is considered a rigid point; second, the contact point between the guide rail and the slide is considered as two infinitesimally small rigid wheels; third, the guide rail offset error caused by the mass of the slide and the load is ignored; fourth, the surface model representing the shape error is considered as the microscopic morphology curve of the guide rail surface. Figure 6 As shown in the schematic diagram of the actual motion structure, with the X-axis as the reference direction, the straightness error in the vertical plane is... The pitch error is affected by the surface micromorphology on the vertical surface of the guide rail. The straightness error is affected by the straightness error in the vertical plane of the guide rail and the length of the slide. The straightness error in the horizontal plane... The runout error is affected by the surface micromorphology of the guide rail horizontal surface. The tilt error is affected by the straightness error of the guide rail in the horizontal plane and the length of the slide. It is affected by the parallelism error of the two guide rail pairs and the width of the slide.

[0051] S5.2: Calculate the five geometric errors.

[0052] Derivation of the vertical plane and Calculation formula, such as Figure 7 The diagram shows the error morphology of the slide along the guide rail in the vertical plane, where L is the length of the slide. This is the error morphology curve on the vertical plane. Figure 7 The geometric relationship can be obtained The pitch is caused by the uneven height of the slide at the front and rear. The difference in height between the front and rear forms an angle with the length of the slide. This angle is defined as... The calculation formula is: .

[0053] Similarly, the movement of the slide along the guide rail on the horizontal plane generates... and They are respectively: and

[0054] The slide plate slides on the two guide rails as follows Figure 8 As shown, when the slide slides along the guide rails, due to the parallelism error between the left and right guide rails, F(X) represents the inconsistent height of the slide on the left and right guide rails. In the Y direction, F(X) represents the position of the rigid small wheel on the left and right guide rails at a certain moment, and D represents the width of the slide. The height difference of the slide on the left and right guide rails forms an angle with the slide width D, denoted as F(X). Based on mathematical relationships, the derivation is... The calculation formula is: ,in This indicates the height value at the left or right center line of the slide.

[0055] Point cloud data of the guide rail surface is obtained by scanning with a vision camera. Shape errors in the point cloud are extracted, and a surface model representing the microstructure of the guide rail surface is obtained by B-spline surface fitting. For ease of representation, we use to replace . It is a bivariate function, where x and y both correspond to a single z, where z represents the height of the skin surface. Now, using the skin surface model... To predict the geometric errors of the guide rail surface.

[0056] For the vertical plane and skin model Substituting the values, we get the following calculation formulas: and

[0057] for ,because It is a bivariate function, where one x corresponds to multiple y values, and the average of these multiple y values ​​is obtained. , As a symbol, it can represent any value of y. Since there are two guide rails, we need to find the two values ​​corresponding to x at a given moment. ,right The average value is taken to obtain the y value corresponding to x at this moment. This indicates the position of the slide center at a given moment. and This represents the average of the y-values ​​of two points before and after the center of the slide, indicating the position of the center of the slide at that moment. value.

[0058] for At the midline of the slide, y=0, This indicates the position of the corresponding slide on the left and right guide rails. This represents the pitch error, where the slide is either higher at the front and lower at the back, or vice versa. It is obtained by quotienting the height difference with the slide length L. The pitch angle at any given moment.

[0059] and and and The derivation method is similar, and we can directly obtain the result. and The calculation formulas are as follows: and

[0060] The parallelism error between the two guide rails caused skin model Substituting the values, we obtain the formula for calculating the tilt error:

[0061] for D represents the width of the slide. Indicates the front and rear center lines of the slide. At that point, the y-coordinates on the two guide rails respectively correspond to and The average of the two values ​​for z is taken to represent the height of the z-value at the center of the slide.

[0062] This method enables direct mapping from the non-ideal microstructure of the guide rail mating surface to the geometric error of the translational axis, allowing error prediction to be completed during the machine tool design stage.

[0063] The method provided by this invention has been described in detail above. It should be noted that those skilled in the art can make various improvements and modifications to this invention without departing from its principles, and these improvements and modifications should also fall within the protection scope of this invention.

Claims

1. A geometric error prediction method based on the micro-topography of the joint surface of the translational axis guide of a high-end CNC machine tool, characterized in that, Includes the following steps: Step 1: Obtain the 3D point cloud data of the guide rail mating surface to form a point cloud matrix; Step 2: Perform coordinate unification, filtering and smoothing on the point cloud data, construct a motion reference plane, calculate the normal deviation, and form the normal error field of the guide rail surface; Step 3: Extract the low-frequency shape error components from the normal error; Step 4: Construct the guide rail bonding surface model using B-spline surface fitting; Step 5: Based on the structural parameters of the translational shaft guide rail, establish an error propagation model and map the surface model normal error into five geometric errors; The five geometric errors include straightness error along the x-axis direction y, straightness error along the x-axis direction z, pitch error, yaw error, and tilt error.

2. The geometric error prediction method based on the micro-topography of the combination surface of the translational axis guide rail of a high-end CNC machine tool according to claim 1, characterized in that, In step one, a line laser stereo camera is used to acquire three-dimensional point cloud data of the guide rail mating surface, and the spatial height distribution of the guide rail surface is inverted based on the laser triangulation principle; the camera intrinsic parameters, extrinsic parameters and laser plane parameters are jointly calibrated to realize the conversion from image pixel coordinates to spatial three-dimensional coordinates; a scanning layout of "fixed camera and moving guide rail" is adopted, the guide rail moves at a uniform linear speed along the feed direction, the spatial spacing between adjacent scanning frames is controlled by the pulse of the slide table encoder, and all point cloud data are uniformly expressed in the motion coordinate system of the test platform.

3. The geometric error prediction method based on the micro-topography of the combination surface of the translational axis guide rail of a high-end CNC machine tool according to claim 1, characterized in that, Step two specifically includes: S2.1 Unify the coordinates of the point cloud data: Establish the geometric mapping relationship between the camera coordinate system and the world coordinate system through system-level calibration, determine the rigid transformation relationship between the world coordinate system and the test platform motion coordinate system, and stitch the point clouds of each scan frame in the feed order to reconstruct the three-dimensional point cloud data of the complete guide rail mating surface. S2.

2. Trimming, filtering and smoothing the point cloud data of the guide rail: The surface of the functional area is extracted by three-dimensional trimming method, and outliers and noise are removed by mean filtering and weighted smoothing, while retaining low-frequency geometric features. S2.3 Constructing a reference plane for guide rail motion: Determine the spatial position of the plane in the least squares sense, so that the sum of squares of the normal deviations of all measuring points on the effective functional surface of the guide rail relative to this plane is minimized; S2.4 Define normal deviation and construct the normal error field of the guide rail surface: Calculate the deviation of the normal projection of each sampling point relative to the ideal translational reference plane, and define it as the normal error field.

4. The geometric error prediction method based on the micro-topography of the guideway joint surface of the translational axis of the high-end CNC machine tool according to claim 3, characterized in that, In step S2.2, the smoothing coefficient is adjusted to 0.5 to achieve a balance between data smoothing and feature fidelity.

5. The geometric error prediction method based on the micro-topography of the guideway joint surface of the translational axis of the high-end CNC machine tool according to claim 1, characterized in that, Step three specifically includes: S3.

1. Mesh generation and edge processing of the normal error field: Interpolate the discrete point cloud into a regular two-dimensional mesh, define a uniform sampling step size along the length and width directions of the guide rail, and use a mirror extension method to symmetrically extend the error field at the parameter domain boundary to suppress boundary effects. S3.

2. Perform multi-scale decomposition on the normal error field and extract low-frequency shape error components: Use two-dimensional discrete wavelet decomposition to perform multi-scale analysis on the normal error field, extract low-frequency approximation components as the shape error of the guide rail mating surface, and mid-to-high frequency detail components correspond to waviness and roughness components.

6. The geometric error prediction method based on the micro-topography of the guideway joint surface of the translational axis of the high-end CNC machine tool according to claim 5, characterized in that, In S3.2, the sym4 wavelet basis is used as the wavelet decomposition basis function.

7. The geometric error prediction method based on the micro-topography of the guideway joint surface of the translational axis of a high-end CNC machine tool according to claim 1, characterized in that, Step four specifically includes: S4.1 Fitting low-frequency shape errors using B-spline surfaces: Using B-spline surfaces to fit the extracted low-frequency shape errors to generate a continuous, smooth, and differentiable surface mathematical model. S4.2 Generate a continuous surface mathematical model: This surface model geometrically approximates the actual surface morphology of the guide rail, and introduces motion behavior consistency constraints in the modeling stage, becoming a mathematical carrier connecting the geometric morphology of the guide rail mating surface with the translational motion behavior.

8. The geometric error prediction method based on the micro-topography of the guideway joint surface of the translational axis of a high-end CNC machine tool according to claim 1, characterized in that, Step five specifically includes: S5.

1. Based on the structural parameters of the translational shaft guide rail, establish the mapping relationship between normal error and straightness and rotation angle error: Based on the geometric relationship of the slide moving along the guide rail surface, clarify the calculation formulas for straightness error and pitch error in the vertical plane, straightness error and yaw error in the horizontal plane, and tilt error caused by parallelism error between the two guide rails. S5.2 Calculate the five geometric errors: Substitute the surface model into the above formula to realize the direct mapping and prediction of the five geometric errors of the translation axis from the non-ideal micro-morphology of the guide rail mating surface.

9. The geometric error prediction method based on the microstructure of the mating surface of the translational axis guideway of a high-end CNC machine tool according to claim 8, characterized in that, In S5.2, the calculation formulas for straightness error and pitch error in the vertical plane are derived based on the geometric relationship between the height difference between the front and rear contact points of the slide and the length of the slide. The formulas for calculating straightness error and yaw error in the horizontal plane are derived in the horizontal plane using a similar method; the formula for calculating tilt error is derived based on the geometric relationship between the height difference between the left and right guide rails and the width of the slide.

10. The geometric error prediction method based on the microstructure of the mating surface of the translational axis guideway of a high-end CNC machine tool according to claim 8, characterized in that, In S5.2, the bivariate function is averaged at different y values ​​to accurately characterize the multi-point contact characteristics between the slide and the guide rail.

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