A turning tool path post-processing method, electronic device and storage medium

Abstract

The application provides a turning tool path post-processing method, an electronic device and a storage medium. The method comprises the following steps: determining a predicted tracking error of a servo shaft in a cutting depth direction according to a reference instruction corresponding to an initial tool path of a workpiece; predicting a surface topography in a machining area to obtain a predicted surface shape error; sampling the predicted surface shape error along a spiral scanning path and obtaining a sampling result by using a high-order low-pass filter combined with phase compensation; adjusting a coordinate value of a target surface shape in a workpiece coordinate system with the sampling result as a correction amount, and re-implementing tool radius compensation to obtain a corrected tool path; controlling a spindle and a radial servo shaft of a super-precision lathe to operate according to an original reference instruction, controlling the servo shaft in the cutting depth direction to operate according to a corrected instruction, and cutting the workpiece to obtain a target surface shape, so as to improve the surface shape precision of single turning of a complex curved surface and reduce the dependence on repeated compensation machining.

Description

Technical Field

[0001] This invention relates to the field of turning, and in particular to a method for post-processing turning toolpaths, an electronic device, and a storage medium. Background Technology

[0002] Currently, freeform surface topography prediction models for turning toolpath planning exist, using grid points to discretize the machined surface and calculate grid point coordinates based on the geometric relationship between the grid points and tool contacts. Through surface reconstruction, the machined surface can be predicted and toolpath accuracy verified without cutting experiments. However, this method only considers the trimming effect of the cutting edge at adjacent tool contacts within the radial section when calculating grid point coordinates, neglecting the influence of other tool contacts caused by the undulations of the target surface profile. Furthermore, this method does not consider the impact of servo axis tracking performance on the machining results, making it difficult to accurately reflect the surface topography at higher cutting speeds. Moreover, its simulation process uses a point-by-point calculation method, which is inconsistent with the continuous dynamic evolution of the actual cutting process, thus reducing the intuitiveness of the results. Therefore, the application scope of existing methods is mainly limited to verifying machining results, with limited guidance for toolpath correction and further optimization. Summary of the Invention

[0003] To address the aforementioned technical problems, the technical solution adopted by this invention is as follows:

[0004] According to one aspect of this application, a post-processing method for turning toolpaths is provided, comprising:

[0005] Step S100: Generate an initial toolpath based on the geometric features of the target surface of the workpiece;

[0006] Step S200: Determine the predicted tracking error of the servo axis along the depth of cut of the ultra-precision lathe based on the reference instruction corresponding to the initial tool path;

[0007] Step S300: In the workpiece coordinate system corresponding to the workpiece The machining area of ​​the workpiece is discretized into a uniform grid in the plane, and the grid points are used to characterize the surface morphology within the machining area. The plane is the plane containing the horizontal coordinate axis, the origin, and the vertical coordinate axis of the workpiece coordinate system;

[0008] Step S400: Based on the prediction of the surface morphology, the predicted surface shape error is obtained;

[0009] Step S500: Sample the predicted surface error along the spiral scanning path used when planning the initial tool path, and obtain the sampling result by combining a high-order low-pass filter with phase compensation, so that the sampling result is limited to the desired frequency band that the servo axis can track along the depth of cut.

[0010] Step S600: Using the filtered sampling result as a correction amount, adjust the driving path corresponding to the target surface shape in the workpiece coordinate system. The coordinate values ​​of the direction are determined, and tool radius compensation is re-implemented to obtain the corrected toolpath; The direction is the vertical coordinate axis of the workpiece coordinate system;

[0011] Step S700: According to the corrected tool path, control the spindle and radial servo axis of the ultra-precision lathe to run according to the original reference command, and control the servo axis along the depth of cut of the ultra-precision lathe to run according to the corrected command to cut the workpiece to obtain the target surface shape.

[0012] According to another aspect of this application, a non-transitory computer-readable storage medium is provided, wherein at least one instruction or at least one program is stored therein, the at least one instruction or the at least one program being loaded and executed by a processor to implement the aforementioned turning toolpath post-processing method.

[0013] According to another aspect of this application, an electronic device is provided, including a processor and the aforementioned non-transitory computer-readable storage medium.

[0014] The present invention has at least the following beneficial effects:

[0015] The post-processing method for turning toolpaths of this invention predicts the tracking status of the servo axis to the reference command by utilizing the identification results of the servo axis dynamic response model of an ultra-precision lathe. It then simulates the impact of tracking errors on the surface morphology of the machined surface through sequential material removal simulation. Based on this, the reference command is corrected offline according to the surface error distribution characteristics to achieve feedforward compensation. This method can dynamically display the formation process of the target surface before machining, intuitively reflecting the influence of various error factors on the machined surface. It has high computational efficiency, is suitable for rapid prediction of complex curved surfaces, and provides a reliable basis for subsequent toolpath correction. The corrected toolpath can better match the dynamic performance of the machine tool, meeting the surface accuracy requirements in the first machining, effectively reducing the dependence on repeated compensation machining, thereby reducing machining costs and improving production efficiency. The toolpath correction process is completed offline before actual machining, and the corrected toolpath maintains the same number of discrete points as the initial path, without increasing machining time. It can be directly used for CNC program generation and cutting execution. Furthermore, relying on the general principles of servo axis dynamic characteristic modeling and surface morphology prediction, this method can adapt to the ultra-precision turning needs of various complex curved surfaces, possessing good engineering feasibility and application value. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A flowchart illustrating the steps of the post-processing method for turning toolpaths provided in this embodiment of the invention;

[0018] Figure 2 A schematic diagram of an ultra-precision turning system provided in an embodiment of the present invention;

[0019] Figure 3 A schematic flowchart of the turning toolpath post-processing method provided in an embodiment of the present invention;

[0020] Figure 4 A schematic diagram of the initial toolpath planning provided in an embodiment of the present invention;

[0021] Figure 5 This is a schematic diagram illustrating the process of predicting the morphology of the machined surface of a workpiece according to an embodiment of the present invention.

[0022] Figure 6 This is a schematic diagram of the target surface shape and the Z-axis frequency response of the servo axis provided in an embodiment of the present invention;

[0023] Figure 7 A schematic diagram of the prediction results of the reference command for servo axis Z-axis tracking corresponding to the mesh plane provided in an embodiment of the present invention;

[0024] Figure 8 This is a schematic diagram of the grid surface prediction results provided in an embodiment of the present invention;

[0025] Figure 9 This is a schematic diagram of the sinusoidal surface prediction results provided in an embodiment of the present invention;

[0026] Figure 10 A schematic diagram comparing the predicted trajectory and tracking error of the servo axis Z-axis corresponding to the mesh before and after toolpath correction, as provided in an embodiment of the present invention.

[0027] Figure 11 This is a schematic diagram of the predicted surface shape error after toolpath correction provided in an embodiment of the present invention;

[0028] Figure 12 A schematic diagram comparing the predicted trajectory and the actual trajectory of the grid plane corresponding to the servo axis Z-axis, provided in an embodiment of the present invention;

[0029] Figure 13A schematic diagram comparing the surface morphology and cross-sectional profile of a mesh surface obtained using a white light interferometer, as provided in an embodiment of the present invention.

[0030] Figure 14 This is a schematic diagram of the surface contour measurement results for a sinusoidal surface machining process provided in an embodiment of the present invention.

[0031] In the diagram: 1. Servo axis Z-axis; 2. Servo axis X-axis; 3. Servo axis C-axis; 4. Workpiece; 5. Tool. Detailed Implementation

[0032] 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.

[0033] This application proposes a toolpath post-processing method for turning, which is applied to an ultra-precision turning system with an integrated toolpath post-processor. The ultra-precision turning system consists of a host computer and an ultra-precision lathe. The toolpath post-processor is integrated into the host computer and communicates bidirectionally with the multi-axis motion controller inside the ultra-precision lathe through a data interface.

[0034] The toolpath post-processor is responsible for identifying the dynamic characteristics of the servo axis, predicting the surface morphology of the machined surface, and correcting the toolpath. The generated prediction and correction results can be directly transmitted to the machining process and converted into a CNC program to drive the ultra-precision lathe to perform machining.

[0035] By introducing feedforward compensation based on the dynamic characteristics of servo axes into the CNC program, the ultra-precision turning system can improve the surface accuracy of complex curved surfaces in a single turning operation at higher cutting speeds, thereby reducing the reliance on repeated compensation machining.

[0036] Specifically, such as Figure 2 As shown, the ultra-precision turning system with integrated toolpath post-processor includes: a base, servo axis Z-axis 1, servo axis X-axis 2, servo axis C-axis 3, workpiece 4, and tool 5 (which can be a cutting tool).

[0037] Both the X-axis (servo axis 2) and Z-axis (servo axis 1) are linear axes, orthogonally arranged in a T-shape on the base, to achieve radial feed and feed along the depth of cut, respectively.

[0038] Servo axis C-axis 3 is a rotary axis, mounted on the slide of servo axis X-axis 2. Its rotation axis is parallel to the movement direction of servo axis Z-axis 1, and it is used to drive the workpiece to achieve the main rotational motion.

[0039] The workpiece 4 is fixed on the vacuum chuck of the servo axis C-axis 3 by a fixture, and the tool 5 is mounted on the servo axis Z-axis 1. By adjusting the relative positions of the two, the center of the workpiece coincides with the rotation axis of the servo axis C-axis 3. When the servo axes are all at zero position, the tip of the tool 5 is located at the center of the machined surface of the workpiece 4, and the rake face of the tool 5 is perpendicular to the machined surface of the workpiece 4, thereby determining the position and orientation of the tool 5 relative to the workpiece 4.

[0040] Establish a workpiece coordinate system on the machining surface of workpiece 4. ,in The axis coincides with the rotation axis of servo axis C-axis 3.

[0041] Ultra-precision lathes use multi-axis motion controllers to coordinate and control each servo axis in order to complete ultra-precision turning of complex curved surfaces. The corresponding machining planning process is mainly implemented in the host computer.

[0042] This application proposes a post-processing method for turning toolpaths that considers tracking errors, such as... Figure 3 As shown, this method predicts the tracking status of the servo axis to the reference command based on the identification results of the servo axis dynamic response model, and removes the influence of the tracking error on the surface morphology of the machined surface by sequential material removal simulation. On this basis, the reference command is corrected offline according to the surface error distribution characteristics, a corrected tool path is generated, and the post-processor outputs it for actual machining, thereby improving the surface accuracy of a single turning operation and reducing the number of repeated compensation machining operations.

[0043] Specifically, the specific implementation steps of a turning toolpath post-processing method according to this application are as follows: Figure 1 As shown, it includes:

[0044] Step S100: Generate an initial toolpath based on the geometric features of the target surface of the workpiece;

[0045] Based on the geometric features of the target surface, appropriate tool parameters and process parameters are selected, and the initial tool path is generated using CAM (Computer-Aided Manufacturing) software based on geometric principles.

[0046] Furthermore, step S100 includes steps S110-S130:

[0047] Step S110: Determine the tool parameters and process parameters for ultra-precision turning based on the geometric features of the target surface of the workpiece.

[0048] The ultra-precision turning is performed on the aforementioned ultra-precision lathe.

[0049] Step S120: Input the feature data of the target surface, tool parameters and process parameters into the preset computer-aided manufacturing software, and the computer-aided manufacturing software generates the drive path;

[0050] The method for planning the driving path includes step S121:

[0051] Step S121: Establish a workpiece coordinate system on the machined surface of the workpiece. ;

[0052] in, The axis of rotation coincides with the C-axis of the servo axis;

[0053] like Figure 4 As shown in (a), the driving path passes through a coordinate system parallel to the workpiece coordinate system. The spiral scan path along the plane Target surface shape projected onto the workpiece in the axial direction Obtained from above.

[0054] The center of the spiral scan path and The axes coincide, and their discrete points are obtained by a preset angle sampling strategy.

[0055] Discrete points on the driving path This can be represented in polar coordinates as:

[0056]

[0057] In the formula, , and These represent the radial position, rotation angle, and position along the depth of cut, respectively, of the i-th discrete point along the driving path; i is the index of the discrete point on the driving path. The radius of the machined surface of the workpiece; This represents the feed per revolution of the servo axis X. This represents the rotation angle increment of the servo axis C-axis;

[0058] Step S130: Perform tool radius compensation on the drive path to obtain the initial tool path output by the computer-aided manufacturing software;

[0059] The initial toolpath planning method includes step S131:

[0060] Step S131: The drive path is adjusted along the preset stable X-axis tool radius compensation algorithm. The axial direction is offset so that the cutting edge of the tool is tangent to the contour of the target surface in the radial section;

[0061] Among them, such as Figure 4As shown in (b), after the tool is compensated, the center of the tool tip arc is located on an equidistant curve from the contour of the target surface.

[0062] The tool tip radius; the tool tip point corresponds to a discrete point on the initial toolpath. Its position along the cutting depth direction for:

[0063]

[0064] In the formula, Represented as an equidistant curve within the j-th radial section The height value at the location; j is the index of the radial section;

[0065] Components of the initial toolpath , and These serve as reference commands for the C-axis, X-axis, and Z-axis of the servo axis, respectively. The high-frequency trajectory component is assigned to the reference command for the Z-axis, making the tracking error of this axis the main factor restricting the improvement of surface accuracy. Therefore, the impact of the tracking error of the Z-axis on surface accuracy is considered.

[0066] Step S200: Determine the predicted tracking error of the servo axis along the depth of cut of the ultra-precision lathe based on the reference instruction corresponding to the initial tool path;

[0067] The servo axis along the depth of cut is driven by an excitation signal, and its command position information and actual position information are collected simultaneously. The transfer function of the servo axis along the depth of cut is calculated, the corresponding reference command is extracted from the initial toolpath, and the tracking situation of the servo axis along the depth of cut is predicted by combining the identified transfer function.

[0068] Furthermore, step S200 includes steps S210-S240:

[0069] Step S210: When the ultra-precision lathe drives each servo axis to move along the reference command under the unified coordination of the multi-axis motion controller, the tool traverses the machining surface of the workpiece along the initial tool path, and ensures that the cutting edge of the tool is always tangent to the target surface of the workpiece.

[0070] Step S220: Under given operating conditions, the servo axis Z-axis is equivalent to a linear time-invariant system, and its response characteristics to reference commands are characterized by the transfer function.

[0071] The steps for determining the transfer function are as follows:

[0072] To obtain the transfer function of the servo axis Z, an excitation signal covering the desired frequency band is designed, and a corresponding CNC program is generated to drive the servo axis Z. Simultaneously, the reference position signal and the actual position signal of the servo axis Z are acquired. After performing a z-transform on the acquired data, the input-output relationship is fitted using a rational function to obtain the following:

[0073]

[0074] In the formula, The transfer function for the servo axis Z-axis; and These are the coefficients of the numerator and denominator polynomials, respectively, which are related to the system's frequency response characteristics; K and M are the orders of the numerator and denominator polynomials, respectively.

[0075] Step S230, Record as reference instructions ;

[0076] Where n is the index of the discrete sampling point; based on the transfer function of the servo axis Z-axis in equation (3), its output can be calculated to obtain the predicted trajectory of the servo axis Z-axis:

[0077]

[0078] In the formula, refer to the instructions. and predicted trajectory All are discrete-time signals; and These are their representations in the z-domain; N is the length of the reference instruction signal.

[0079] Step S240: Compare the reference command and the predicted trajectory to obtain the predicted tracking error of the servo axis Z-axis. :

[0080] .

[0081] Step S300: In the workpiece coordinate system corresponding to the workpiece The machining area of ​​the workpiece is discretized into a uniform grid in the plane, and the grid points are used to characterize the surface morphology within the machining area.

[0082] The plane is the plane containing the horizontal coordinate axis, the origin, and the vertical coordinate axis of the workpiece coordinate system.

[0083] Furthermore, step S300 includes step S310:

[0084] Step S310: Use a uniform mesh to cover the corresponding machining surface of the workpiece to uniformly discretize the machining area of ​​the workpiece.

[0085] Among them, such as Figure 5 As shown, Figure 5 (a) is a 3D diagram of the simulation process of a single path segment; Figure 5 (b) is a top view of the area affected by the path segment along direction B; Figure 5 (c) is a front view of the cutting edge of the tool along the C direction; the morphology of the machined surface is discretely sampled using uniformly distributed grid points, and the height value of the grid point is used to characterize the discrete sampling of the morphology of the machined surface at the location of the grid point.

[0086] Grid points The representation in a rectangular coordinate system is:

[0087]

[0088] In the formula, , and Representing grid points respectively The three-dimensional coordinates in the workpiece coordinate system; r and c are the grid points, respectively. Row indexes and column indexes; and The coordinates of the bottom left grid point; For along Grid resolution in the direction; For along Grid resolution in the direction; W represents the initial height of the machined surface; W is the mesh edge. Width along the direction; L is the grid width along the direction. The length of the direction.

[0089] Step S400: Based on the prediction of the surface morphology, the predicted surface shape error is obtained;

[0090] Furthermore, step S400 includes steps S410-S450:

[0091] Step S410: Divide the predicted tool path corresponding to the target surface shape into several path segments along the cutting direction to determine the working area of ​​the tool cutting edge corresponding to each path segment.

[0092] The predicted toolpath is synthesized from the reference commands of the servo axis C and servo axis X and the predicted trajectory of the servo axis Z, and is used to perform subsequent surface topography prediction.

[0093] The predicted tool path is divided into multiple path segments along the cutting direction. The height of the grid points in each path segment after being trimmed by the tool cutting edge is calculated in turn to reflect the dynamic evolution of the machined surface morphology. At the same time, the trimming effect that may be generated by the profile of all tool cutting edges on the same radial section is also considered.

[0094] To reduce the computational cost per step, for each path segment, only the mesh points located within the cutting edge's action area are considered to be affected by the cutting edge trimming action. The action area is the swept surface formed by the cutting edge along the path segment. Direction to The projection onto the plane can be represented as an equivalent sector ring. When the path segment is far from the workpiece center, the sector ring does not intersect with the workpiece center, and the grid points within the effective area... The following conditions must be met:

[0095]

[0096] In the formula, This indicates the path segment from its starting point to the point along the cutting direction. The angle of rotation of the radial section; Indicates from Radial distance to the center of the workpiece; and These are the rotation angles of the servo axis C-axis corresponding to the start and end points of the path segment, respectively. This represents the X-axis displacement of the servo axis corresponding to the starting point of the path segment. The wrap angle of the cutting tool;

[0097] When the condition is met At this point, the area of ​​action intersects with the center of the workpiece, forming two fan-shaped regions; further conditions need to be introduced to determine... Is it located within a sector-shaped area on the other side of the workpiece center?

[0098]

[0099] when When equation (7) or equation (8) is satisfied, it is considered that Located within the effective area of ​​the path segment; within this path segment, interpolation is further used to calculate the path taken by the tool cutting edge. The servo axis displacement corresponding to the radial section:

[0100]

[0101] In the formula, , and These represent the cutting edges of the tool passing through... The displacements of the servo axis C-axis, servo axis X-axis, and servo axis Z-axis at the radial section; and These are the interpolation functions for the servo axis X and servo axis Z, respectively. Their outputs are derived from the adjacent discrete points on both sides of the radial section along the predicted toolpath. , and servo axis C-axis displacement Joint decision;

[0102] Step S420: Within the radial section, calculate based on geometric relationships to obtain... Height value of the cutting edge profile of the tool :

[0103]

[0104]

[0105] In the formula, d represents the interpolation point on the predicted toolpath and Radial distance between; select and Update the height value of the corresponding grid point with the smaller value.

[0106] The decrease in grid point height reflects the material removal process, in which the area of ​​the workpiece's machined surface above the tool's cutting edge is trimmed, while the area below the tool's cutting edge remains unchanged.

[0107] Step S430: By sequentially determining the effective area of ​​each path segment and updating the height values ​​of the grid points therein, the predicted morphology of the entire processed surface can be obtained.

[0108] Step S440: Obtain the predicted surface shape error by comparing the target surface shape with the predicted surface topography.

[0109]

[0110] In the formula, This represents the predicted surface shape error of the grid point in the r-th row and c-th column; and These represent the height values ​​of the target surface shape and the predicted surface morphology at the corresponding grid points, respectively.

[0111] Step S450: Evaluate the predicted surface shape error using the error peak-to-valley value (PV) and the root mean square value (RMS).

[0112]

[0113]

[0114] In the formula, This is the set of predicted surface shape error values ​​for each grid point in the evaluation area. This represents the total number of grid points within the region.

[0115] Step S500: Sample the predicted surface error along the spiral scanning path used when planning the initial tool path, and obtain the sampling result by combining a high-order low-pass filter with phase compensation, so that the sampling result is limited to the desired frequency band that the servo axis can track along the depth of cut.

[0116] Furthermore, step S500 includes steps S510-S530:

[0117] Step S510: Move the spiral scanning path along... The axial direction is projected onto the predicted surface shape error to obtain the initial sampling results of the predicted surface shape error;

[0118] Step S520: Use a high-order low-pass filter to suppress high-frequency components that exceed the bandwidth in the initial sampling result to obtain the filtering result;

[0119] Step S530: Perform phase compensation on the filtering result to obtain the sampling result.

[0120] Step S600: Using the filtered sampling result as a correction amount, adjust the driving path corresponding to the target surface shape in the workpiece coordinate system. The coordinate values ​​of the direction are determined, and tool radius compensation is re-implemented to obtain the corrected toolpath;

[0121] The direction is the vertical coordinate axis of the workpiece coordinate system;

[0122] Furthermore, step S600 includes steps S610-S620:

[0123] Step S610: Adjust the height of the drive path based on the sampling results to obtain the corrected drive path:

[0124]

[0125] In the formula, and These are the corrected driving path and the height value of the driving path at the i-th discrete point, respectively. Let be the value of the sampling result at the i-th discrete point; i is the index of the discrete point along the driving path.

[0126] Step S620: Re-compensate the tool radius on the corrected drive path to obtain the corrected tool path.

[0127] The initial toolpath is corrected offline before actual machining to ensure that the corrected toolpath can be directly applied to machining. Since the number of discrete points in the toolpath before and after correction remains the same, this correction process does not increase machining time.

[0128] Step S700: According to the corrected tool path, control the spindle and radial servo axis of the ultra-precision lathe to run according to the original reference command, and control the servo axis along the depth of cut of the ultra-precision lathe to run according to the corrected command to cut the workpiece to obtain the target surface shape.

[0129] Furthermore, step S700 includes steps S710-S720:

[0130] Step S710: Generate a CNC program based on the modified toolpath to control the spindle and radial servo axis of the ultra-precision lathe to run according to the original reference instructions, and control the servo axis of the ultra-precision lathe along the depth of cut to run according to the modified instructions to cut the workpiece to obtain the target surface shape.

[0131] Step S720: After processing is completed, the contour data of the processed surface of the workpiece is obtained using a precision measuring device, and the effectiveness of the processed target surface is verified according to the preset surface accuracy evaluation.

[0132] Specifically, to demonstrate the effectiveness of the turning toolpath post-processing method of this application, the following will be implemented: Figure 6 (a) and Figure 6 The mesh surface and sinusoidal surface shown in (b) are used as the target surface shape, and their expression is as follows:

[0133]

[0134] in, and These are the target surface shape functions.

[0135] By setting different tool parameters and machining parameters for two types of target surface shapes, the universality of the turning toolpath post-processing method of this application is verified. The specific parameters are shown in Table 1.

[0136] Table 1 CAM Toolpath Planning and Surface Topography Prediction Setting Parameters

[0137]

[0138] The initial toolpaths of the mesh surface and the sinusoidal surface generated according to the given parameters contain 1,188,001 and 742,501 discrete points, respectively, corresponding to machining times of 1,188 and 742.5 seconds.

[0139] The dynamic characteristics of the servo axis Z were altered by adjusting the slide load mass, and two different operating conditions were set for it. To identify the transfer function model of the servo axis Z under the two conditions, a linear sweep frequency signal in the range of 0.001Hz to 60Hz was selected as a reference command and applied to the servo axis Z. The amplitude of this signal was 4μm and the duration was 250s; the sampling frequency during the operation of the ultra-precision lathe was set to 1000Hz.

[0140] Figure 6 (c) and Figure 6 (d) compares the identified results of the servo axis Z-axis frequency response with the experimental results under two conditions. The two results are basically consistent within the desired frequency band (0 to 60 Hz), indicating that the identified transfer function can accurately characterize the dynamic characteristics of the servo axis Z-axis. Under both conditions, there is a slight amplitude amplification and phase shift in the high-frequency band, which reduces the system tracking performance and ultimately leads to a deviation between the machined surface and the target surface shape. Under closed-loop conditions, the discrete transfer functions of the servo axis Z-axis under conditions I and II are given by equations (18) and (19), respectively.

[0141]

[0142]

[0143] Taking a mesh surface as an example, such as Figure 7 As shown, the analysis focuses on the area 2.95 mm from the center of the grid surface (corresponding to times 126 to 126.9 s). Figure 7 (The instruction segment shown in (a)) and 1.175mm (corresponding to time 765 to 765.9s) Figure 7 (See instruction snippet shown in (b)) Servo axis Z-axis reference instruction snippet.

[0144] The results show that the peaks and troughs of the tracking error correspond to the high valleys and peaks of the reference command acceleration, indicating that the tracking error of the servo axis Z-axis is affected by both its dynamic characteristics and closely related to the trajectory characteristics. In command segments farther from the center of the grid surface, the fluctuations of the reference command are more significant. Furthermore, due to the sparse distribution of discrete points of the initial toolpath in the peripheral region caused by equal-angle sampling, the fluctuations in velocity and acceleration are more severe, resulting in a higher tracking error amplitude in the peripheral region than in the central region. FFT analysis of the command segments reveals that, compared to the peripheral region segments, the frequency components of the central region segments are mainly concentrated in the low-frequency range, with the dominant frequency decreasing from 48.8Hz to 17.8Hz. This indicates that in the central region, the tracking error caused by insufficient high-frequency response of the servo axis Z-axis (such as amplitude changes and phase shifts) is no longer the main factor affecting machining accuracy.

[0145] like Figure 8 As shown, Figure 8 (a) is a schematic diagram of the predicted surface morphology of the mesh surface. Figure 8 (b) is a schematic diagram of the predicted surface shape error of the grid surface. Figure 8Figure (c) shows a schematic diagram of the predicted tracking error of the mesh surface. The predicted surface morphology height ranges from -3.125 to 3.14 μm, while the target surface design height ranges from -3 to 3 μm. The prediction results indicate that the surface shape error is at the sub-micron level. Taking the target mesh surface shown in purple as a reference, the predicted surface morphology exhibits a striped distribution, with the stripes extending outward from the center along the structural periodic direction, corresponding to the alternating distribution of material residue and overcut areas on the machined surface. This phenomenon originates from the dynamic response limitation of the servo axis Z-axis when the motion direction is reversed, causing the tool to overshoot along the original direction and gradually converge to the reference command. Comparing the predicted surface shape error and the tracking error reveals that their PV and RMS values ​​are quite similar, and both show a symmetrical increasing trend with the center distance. This non-uniformity of error distribution disrupts the shape consistency of the periodic structure, limiting the improvement of the accuracy of complex curved surfaces.

[0146] The height variation of the sinusoidal surface morphology exhibits a clear directionality; the height remains consistent when parallel to the structural arrangement direction, but shows significant fluctuations in the vertical direction. For example... Figure 9 As shown, the servo axis Z-axis exhibits significant oscillation overshoot in the predicted trajectory segment near the periphery, corresponding to a corresponding increase in tracking error. Both the predicted surface shape error and the tracking error show a comb-like distribution, with their amplitudes gradually increasing from the center to both ends, and the fluctuations are more pronounced in the direction perpendicular to the structure arrangement. Although the predicted surface shape error varies depending on the target surface shape, its amplitude is usually larger in areas where the surface morphology fluctuates significantly along the cutting direction. The fundamental reason is that the severe oscillation of the servo axis Z-axis leads to an increase in tracking error. For a set workpiece radius and mesh resolution, the time required to complete the surface morphology prediction in the host computer is approximately 2 minutes, significantly less than the actual machining time. The high computational efficiency ensures that prediction results can be obtained quickly before machining, facilitating the comparison and optimization of different process schemes during the machining planning stage, ultimately reducing overall costs and improving machining efficiency.

[0147] Taking a mesh surface as an example, such as Figure 10 As shown, the tracking results of the predicted servo axis Z-axis are compared when the initial toolpath and the modified toolpath are used as inputs, respectively. Without toolpath correction, the predicted trajectory deviates significantly from the reference command due to the high dynamic response requirements of the servo axis Z-axis in the peak-valley region of the reference command, and the extreme points of the tracking error are also located nearby. In contrast, when the modified toolpath is used as input, the consistency between the predicted trajectory and the reference command is significantly improved, and the tracking error amplitude is significantly reduced.

[0148] like Figure 11As shown, after toolpath correction, the PV value of the predicted surface shape error for the mesh surface decreased from 311 nm to 52 nm, and the RMS value decreased from 36 nm to 5 nm; the PV value of the predicted surface shape error for the sinusoidal surface decreased from 405 nm to 129 nm, and the RMS value decreased from 38 nm to 6 nm. The prediction results indicate that toolpath correction not only significantly reduces the amplitude of the surface shape error but also improves the uniformity of the error distribution.

[0149] To verify the effectiveness of the post-processing method in surface topography prediction and toolpath correction, cutting experiments were conducted on the target mesh surface and the sinusoidal surface. Two workpieces were machined for each target surface shape using both the initial toolpath and the corrected toolpath. The workpiece machined using the initial toolpath was used to verify the impact of servo axis Z-axis tracking error on surface shape error, while the workpiece machined using the corrected toolpath was used to demonstrate the effect of the post-processing method in improving surface shape accuracy. When generating the corrected toolpath, the cutoff frequency and order of the low-pass FIR filter were set to 60Hz and 100th order, respectively.

[0150] For mesh surfaces, such as Figure 12 As shown, the predicted trajectory of the servo axis Z-axis largely coincides with the actual trajectory throughout the machining process, with only a slight amplitude deviation in the outer region. This deviation may be caused by modeling errors introduced by system identification. The envelopes of both the predicted and actual trajectories gradually converge from a relatively large amplitude to the designed amplitude of 3 μm, indicating that the dynamic performance of the servo axis Z-axis has a significant impact on the uniformity of the periodic structure height of the machined surface. These results verify that the obtained transfer function can effectively characterize the dynamic response of the servo axis Z-axis, providing a reliable basis for subsequent surface morphology prediction and toolpath correction.

[0151] The surface morphology of the mesh surface measured using a white light interferometer is as follows: Figure 13 As shown. Figure 13 (a) is a schematic diagram of the machined surface morphology without toolpath correction. Figure 13 (b) Schematic diagram of the machined surface morphology after toolpath correction. After toolpath correction, the maximum height difference of the periodic structure in the measurement area decreased from 6.55 μm to 6.23 μm; at the same time, the profiles of sections AA and BB were extracted and analyzed, and their profile error RMS values ​​decreased from 98 nm and 76 nm to 41 nm and 39 nm, respectively, with a reduction of more than 48%; the deviation between the measured profile and the target profile is mainly concentrated at the turning point near the edge area. By correcting the toolpath based on the predicted surface shape error, such deviations can be effectively reduced.

[0152] The surface contour measurement results of the sinusoidal surface machining are as follows Figure 14 As shown, Figure 14 (a) is a schematic diagram of the measurement area of ​​the sinusoidal surface obtained after processing. Figure 14Figure (b) shows a comparison of the cross-sectional profile before and after toolpath correction. Without toolpath correction, the cross-sectional measured profile deviates significantly from the target profile, and the profile height is noticeably tilted from the center to the periphery, resulting in a large profile error RMS value. After toolpath correction, the tilt of the measured profile is significantly reduced, the deviation from the target profile is reduced, and the profile error RMS value is also significantly reduced, verifying the effectiveness of the post-processing method in improving servo axis tracking performance and enhancing surface accuracy.

[0153] This invention proposes a post-processing method for ultra-precision turning toolpaths that combines surface topography prediction and toolpath correction. This method optimizes the initial toolpaths generated by CAM software based on geometric principles, addressing the issue of surface shape errors caused by the failure to consider the dynamic characteristics of servo axes. The method utilizes the identification results of the servo axis dynamic response model to predict the servo axis's tracking of reference commands. It then uses sequential material removal to simulate the impact of tracking errors on the machined surface topography. Based on this, it performs offline correction of the reference commands according to the surface shape error distribution characteristics, achieving feedforward compensation. This improves the surface shape accuracy of single-pass turning of complex curved surfaces, reduces reliance on repetitive compensation machining, and effectively suppresses surface shape errors caused by the failure to consider the dynamic characteristics of servo axes in the machining planning.

[0154] By establishing a surface morphology prediction model based on tool path and material removal mechanism, the formation process of the target surface shape can be dynamically displayed before machining, and the influence of various error factors on the machined surface can be intuitively reflected. This method has high computational efficiency, is suitable for rapid prediction of complex curved surfaces, and provides a reliable basis for subsequent tool path correction, thereby improving the accuracy of ultra-precision turning machining planning and realizing efficient prediction of machined surface morphology.

[0155] By combining the dynamic response characteristics of servo axes, the surface error distribution of reference commands in actual execution is predicted, and the initial toolpath is corrected offline before machining to achieve feedforward compensation. The corrected toolpath can better match the dynamic performance of the machine tool and meet the surface accuracy requirements in the first machining, effectively reducing the dependence on repeated compensation machining, thereby reducing machining costs and improving production efficiency, improving the surface accuracy of single turning and reducing repeated compensation.

[0156] The toolpath correction process is completed offline before actual machining, and the corrected toolpath maintains the same number of discrete points as the initial path, without increasing machining time. It can be directly used for CNC program generation and cutting execution. At the same time, this method relies on the general principles of servo axis dynamic characteristic modeling and surface morphology prediction, which can adapt to the ultra-precision turning requirements of various complex surfaces. It has good engineering feasibility and promotion and application value, ensuring the feasibility and versatility of the corrected toolpath.

[0157] Embodiments of the present invention also provide a computer program product including program code, which, when the program product is run on an electronic device, causes the electronic device to perform the steps of the methods described above in various exemplary embodiments of the present invention.

[0158] Furthermore, although the steps of the method in this disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result. Additional or alternative steps may be omitted, multiple steps may be combined into one step, and / or a step may be broken down into multiple steps.

[0159] From the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, mobile terminal, or network device, etc.) to execute the methods according to the embodiments of this disclosure.

[0160] In an exemplary embodiment of this disclosure, an electronic device capable of implementing the above-described method is also provided.

[0161] Those skilled in the art will understand that various aspects of the present invention can be implemented as systems, methods, or program products. Therefore, various aspects of the present invention can be specifically implemented in the following forms: entirely in hardware, entirely in software (including firmware, microcode, etc.), or in a combination of hardware and software, collectively referred to herein as “circuit,” “module,” or “system.”

[0162] An electronic device according to this embodiment of the invention. The electronic device is merely an example and should not be construed as limiting the functionality or scope of the embodiments of the invention.

[0163] Electronic devices are manifested in the form of general-purpose computing devices. Components of an electronic device may include, but are not limited to: at least one processor, at least one memory, and buses connecting different system components (including memory and processor).

[0164] The storage device stores program code that can be executed by the processor to perform the steps described in the "Exemplary Methods" section above, according to various exemplary embodiments of the present invention.

[0165] The storage may include readable media in the form of volatile storage, such as random access memory (RAM) and / or cache memory, and may further include read-only memory (ROM).

[0166] The storage may also include programs / utilities having a set (at least one) of program modules, including but not limited to: an operating system, one or more applications, other program modules, and program data, each or some combination of these examples may include an implementation of a network environment.

[0167] A bus can represent one or more of several bus architectures, including a memory bus or memory controller, a peripheral bus, a graphics acceleration port, a processor, or a local bus that uses any of the various bus architectures.

[0168] Electronic devices can also communicate with one or more external devices (such as keyboards, pointing devices, Bluetooth devices, etc.), one or more devices that enable users to interact with the electronic device, and / or any device that enables the electronic device to communicate with one or more other computing devices (such as routers, modems, etc.). This communication can be performed through input / output (I / O) interfaces. Furthermore, electronic devices can also communicate with one or more networks (such as local area networks (LANs), wide area networks (WANs), and / or public networks, such as the Internet) via network adapters.

[0169] From the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, terminal device, or network device, etc.) to execute the methods according to the embodiments of this disclosure.

[0170] In exemplary embodiments of this disclosure, a computer-readable storage medium is also provided, on which a program product capable of implementing the methods described above is stored. In some possible embodiments, various aspects of the invention may also be implemented as a program product comprising program code that, when the program product is run on a terminal device, causes the terminal device to perform the steps of the various exemplary embodiments of the invention described in the "Exemplary Methods" section of this specification.

[0171] The program product may employ any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0172] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable signal medium may also be any readable medium other than a readable storage medium, capable of sending, propagating, or transmitting programs for use by or in conjunction with an instruction execution system, apparatus, or device.

[0173] The program code contained on the readable medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0174] Program code for performing the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0175] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention, and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0176] It should be noted that although several modules or units for the device used to perform actions have been mentioned in the detailed description above, this division is not mandatory. In fact, according to embodiments of this disclosure, the features and functions of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units.

[0177] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for post-processing turning toolpaths, characterized in that, include: Step S100: Generate an initial toolpath based on the geometric features of the target surface of the workpiece; Step S200: Determine the predicted tracking error of the servo axis along the depth of cut of the ultra-precision lathe according to the reference instruction corresponding to the initial tool path; Step S300: In the workpiece coordinate system corresponding to the workpiece The machining area of ​​the workpiece is discretized into a uniform grid within a plane, and the grid points are used to characterize the surface morphology within the machining area; The plane is the plane containing the horizontal coordinate axis, the origin, and the vertical coordinate axis of the workpiece coordinate system; Step S400: Based on the prediction of the surface morphology, a predicted surface shape error is obtained; Step S500: Sample the predicted surface error along the spiral scanning path used when planning the initial tool path, and obtain the sampling result by combining a high-order low-pass filter with phase compensation, so that the sampling result is limited to the desired frequency band that the servo axis can track along the depth of cut direction; Step S600: Using the filtered sampling result as a correction amount, adjust the driving path corresponding to the target surface shape in the workpiece coordinate system. The coordinate values ​​of the direction are determined, and tool radius compensation is re-implemented to obtain a corrected toolpath; The direction is the vertical coordinate axis of the workpiece coordinate system; Step S700: According to the corrected tool path, control the spindle and radial servo axis of the ultra-precision lathe to run according to the original reference command, and control the servo axis along the depth of cut of the ultra-precision lathe to run according to the corrected command to cut the workpiece to obtain the target surface shape; Step S100 includes: Step S110: Determine the tool parameters and process parameters for ultra-precision turning based on the geometric features of the target surface of the workpiece. The ultra-precision turning is performed on an ultra-precision lathe, wherein the servo axes X and Z of the ultra-precision lathe are both linear axes, arranged orthogonally in a T-shape on the base, to realize radial feed and feed along the depth of cut, respectively. The servo axis C of the ultra-precision lathe is a rotary axis, which is mounted on the slide of the servo axis X. Its rotation axis is parallel to the movement direction of the servo axis Z, and is used to drive the workpiece to achieve the main rotational motion. The workpiece is mounted on the servo axis C, and the tool is mounted on the servo axis Z. By adjusting their relative positions, the center of the workpiece coincides with the rotation axis of the servo axis C. When the servo axis C and the servo axis Z are at their zero positions, the tip of the tool is located at the center of the machined surface of the workpiece, and the rake face of the tool is perpendicular to the machined surface of the workpiece, thereby determining the position and orientation of the tool relative to the workpiece. Step S120: Input the feature data of the target surface shape, the tool parameters and the process parameters into the preset computer-aided manufacturing software, and the computer-aided manufacturing software generates the drive path; The method for planning the driving path is as follows: Establish a workpiece coordinate system on the machined surface of the workpiece. ; The axis coincides with the rotation axis of the servo axis C; The driving path is parallel to the workpiece coordinate system. The spiral scan path along the plane Target surface shape of the workpiece projected along the axial direction Obtained from above; The center of the spiral scanning path and The axes coincide, and their discrete points are obtained by a preset angle sampling strategy; Discrete points on the driving path In polar coordinates, this is represented as: ； In the formula, , and These represent the radial position, rotation angle, and position along the depth of cut of the i-th discrete point along the driving path, respectively; i is the index of the discrete point on the driving path. The radius of the machined surface of the workpiece; The feed per revolution of the servo axis X; This is the rotation angle increment of the servo axis C; Step S130: Perform tool radius compensation on the drive path to obtain the initial tool path output by the computer-aided manufacturing software; The method for planning the initial toolpath is as follows: The drive path is then processed by a preset stable X-axis tool radius compensation algorithm along... The cutting edge of the tool is offset in the axial direction so that it is tangent to the contour of the target surface in the radial section; the center of the tool tip arc after compensation is located on an equidistant curve from the contour of the target surface. The radius of the tool tip arc; the tool tip point corresponds to a discrete point on the initial tool path. Its position along the cutting depth direction for: ； In the formula, Represented as an equidistant curve within the j-th radial section The height value at the location; j is the index of the radial section; the components of the initial toolpath. , and These serve as reference commands for the servo axis C, the servo axis X, and the servo axis Z, respectively.

2. The method according to claim 1, characterized in that, Step S200 includes: Step S210: When the ultra-precision lathe drives each servo axis to move along the reference command under the unified coordination of the multi-axis motion controller, the tool traverses the machining surface of the workpiece along the initial tool path, and ensures that the cutting edge of the tool is always tangent to the target surface shape of the workpiece. Step S220: Under given operating conditions, the servo axis Z-axis is equivalent to a linear time-invariant system, and its response characteristics to reference commands are characterized by the transfer function. The steps for determining the transfer function are as follows: Design an excitation signal covering the desired frequency band and generate a corresponding CNC program to drive the servo axis Z-axis. Simultaneously acquire the reference position signal and actual position signal of the servo axis Z-axis. After performing a z-transform on the acquired data, fit the input and output relationship using a rational function to obtain: ； In the formula, The transfer function of the servo axis Z-axis is represented; and These are the coefficients of the numerator and denominator polynomials, respectively, which are related to the system's frequency response characteristics; K and M are the orders of the numerator and denominator polynomials, respectively. Step S230, Record as reference instructions ; Where n is the index of the discrete sampling point; the output is calculated based on the transfer function of the servo axis Z-axis described in equation (3) to obtain the predicted trajectory of the servo axis Z-axis: ； In the formula, the reference instruction and the predicted trajectory All are discrete-time signals; and These are their representations in the z-domain; N is the length of the reference command signal. Step S240: Compare the reference command and the predicted trajectory to obtain the predicted tracking error of the servo axis Z-axis. : 。 3. The method according to claim 2, characterized in that, Step S300 includes: Step S310: Cover the corresponding machining surface of the workpiece with a uniform grid to uniformly discretize the machining area of ​​the workpiece. The height value of the grid point is used to characterize the discrete sampling of the surface morphology at the location of the grid point. Grid points The representation in a rectangular coordinate system is: ； In the formula, , and Representing grid points respectively The three-dimensional coordinates in the workpiece coordinate system; r and c are the grid points respectively. Row indexes and column indexes; and The coordinates of the bottom left grid point; For along Grid resolution in the direction; For along Grid resolution in the direction; W represents the initial height value of the machined surface; W represents the mesh edge. Width along the direction; L is the width of the grid along the direction. The length of the direction.

4. The method according to claim 3, characterized in that, Step S400 includes: Step S410: Divide the predicted tool path corresponding to the target surface shape into several path segments along the cutting direction to determine the working area of ​​the tool cutting edge corresponding to each path segment. The predicted toolpath is synthesized from the reference commands of the servo axis C-axis and the servo axis X-axis and the predicted trajectory of the servo axis Z-axis, and is used to perform subsequent surface topography prediction. The area of ​​action is the swept surface formed by the cutting edge of the tool along the path segment. Direction to Projection of a plane; When the path segment is far from the workpiece center, the corresponding area of ​​action of the path segment does not intersect with the workpiece center, and the grid points within the area of ​​action... The following conditions must be met: ； In the formula, This indicates the distance along the cutting direction from the starting point of the path segment to... The angle of rotation of the radial section; Indicates from Radial distance to the center of the workpiece; and These are the rotation angles of the servo axis C-axis corresponding to the starting and ending points of the path segment, respectively. The servo axis X-axis displacement corresponding to the starting point of the path segment; The wrap angle of the cutting tool; When the condition is met At that time, the area of ​​action intersects with the center of the workpiece and forms two fan-shaped areas; ； when When equation (7) or equation (8) is satisfied, Located within the effective area of ​​the path segment; within this path segment, the path traveled by the tool cutting edge is calculated using interpolation. The servo axis displacement corresponding to the radial section: ； In the formula, , and These represent the cutting edges of the tool passing through... The displacements of the servo axis C-axis, the servo axis X-axis, and the servo axis Z-axis at the radial section; and These are the interpolation functions for the servo axis X and the servo axis Z, respectively, and their outputs are derived from adjacent discrete points on both sides of the radial cross-section along the predicted toolpath. , and the C-axis displacement of the servo axis Joint decision; Step S420: Within the radial section, calculate based on geometric relationships to obtain... Height value of the cutting edge profile of the tool : ； ； In the formula, d represents the interpolation point on the predicted toolpath and Radial distance between; select and Update the height value of the corresponding grid point with the smaller value. Step S430: By sequentially determining the effective area of ​​each path segment and updating the height values ​​of the grid points therein, the predicted morphology of the entire processed surface is obtained. Step S440: By comparing the target surface shape with the predicted surface topography, the predicted surface shape error is obtained. ； In the formula, This represents the predicted surface shape error of the grid point in the r-th row and c-th column; and These represent the height values ​​of the target surface shape and the predicted surface morphology at the corresponding grid points, respectively. Step S450: Evaluate the predicted surface shape error using the error peak-to-valley value (PV) and the root mean square value (RMS). ； ； In the formula, This is the set of predicted surface shape error values ​​for each grid point in the evaluation area. This represents the total number of grid points within the region.

5. The method according to claim 4, characterized in that, Step S500 includes: Step S510: Move the spiral scanning path along... The axial direction is projected onto the predicted surface shape error to obtain the initial sampling result of the predicted surface shape error; Step S520: Use a high-order low-pass filter to suppress high-frequency components that exceed the bandwidth in the initial sampling result to obtain the filtering result; Step S530: Perform phase compensation on the filtering result to obtain the sampling result.

6. The method according to claim 5, characterized in that, Step S600 includes: Step S610: Adjust the height of the drive path according to the sampling results to obtain the corrected drive path: ； In the formula, and These are the corrected driving path and the height value of the driving path at the i-th discrete point, respectively. The value of the sampling result at the i-th discrete point; i is the index of the discrete point along the driving path; Step S620: Re-compensate the tool radius of the corrected drive path to obtain the corrected tool path.

7. The method according to claim 6, characterized in that, Step S700 includes: Step S710: Generate a CNC program based on the corrected toolpath to control the spindle and radial servo axis of the ultra-precision lathe to run according to the original reference instructions, and control the servo axis of the ultra-precision lathe along the depth of cut to run according to the corrected instructions to cut the workpiece to obtain the target surface shape. Step S720: After processing is completed, the contour data of the processed surface of the workpiece is obtained using a precision measuring device, and the effectiveness of the processed target surface is verified according to the preset surface accuracy evaluation.

8. A non-transitory computer-readable storage medium, characterized in that, The storage medium stores at least one instruction or at least one program segment, which is loaded and executed by a processor to implement the method as described in any one of claims 1-7.

9. An electronic device, characterized in that, Includes a processor and the non-transitory computer-readable storage medium as described in claim 8.

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