Linear grating processing apparatus and method

Abstract

The application discloses a linear grating processing device and method, and relates to the field of precise optical processing. The device comprises a continuously rotating workbench, a multi-axis driven cutter module, a measuring unit and a control system. The control system establishes a time-sharing and partition error compensation model based on the measuring data; in the continuous rotation processing process, the system identifies the current workpiece identity according to the real-time angle feedback, calls the corresponding offset and drives the cutter module to perform high-frequency lifting and swing correction, so as to independently eliminate the clamping height difference and tilt error for each workpiece. The application solves the technical problems of poor processing consistency and low yield rate caused by the clamping height difference and tilt error between workpieces during the parallel processing of multiple workpieces on the continuously rotating workbench, and significantly improves the consistency and yield rate of the parallel processing of multiple workpieces.

Description

Technical Field

[0001] This invention relates to the field of ultra-precision optical processing technology, and in particular to a linear grating processing apparatus and method for manufacturing components such as Fresnel lenses and microstructure molds. Background Technology

[0002] Linear gratings and linear Fresnel lenses are widely used in optical fields such as concentrated photovoltaics, laser shaping, and 3D displays. Traditional linear grating processing often employs planing or fly cutter cutting processes, which can produce high-precision straight grooves, but their processing efficiency is relatively low and they are difficult to adapt to the needs of mass production.

[0003] To improve machining efficiency, rotary cutting using ultra-precision single-point diamond lathes has become a trend. Especially when multiple workpieces are simultaneously clamped on a large-diameter rotary table for parallel machining, the cost per workpiece can be significantly reduced. However, parallel machining of linear gratings on a continuous rotary table faces significant technical challenges:

[0004] 1. When multiple workpieces are discretely distributed across various stations on a rotary table, the height of the upper surface and the spatial orientation (tilt) of each workpiece will inevitably differ by micrometers or even sub-micrometers due to limitations in the workpiece's thickness tolerance, the machining accuracy of the fixture, and random errors in manual assembly. Traditional CNC systems typically generate machining codes based on an "ideal single plane." If the tool moves strictly along a fixed ideal trajectory, it can lead to excessive cutting depths for some protruding workpieces (damaging the grating groove structure), while insufficient cutting depths or even "cutting empty" phenomena may occur for some recessed workpieces.

[0005] 2. While simple height differences can be partially mitigated by overall translation, minute tilts on the workpiece surface are more detrimental. In grating machining, tilts on the workpiece surface cause periodic changes in the actual cutting angle of the tool relative to the workpiece surface, resulting in gradual changes in grating groove depth or asymmetry in groove shape (such as blaze angle deviation). This will severely reduce the diffraction efficiency or focusing performance of the Fresnel lens.

[0006] 3. Under conditions of high-speed rotation of the worktable, the time window for the tool to transition from one workpiece to the next is extremely short (typically on the order of milliseconds). Existing machine tool servo systems struggle to detect and respond to such abrupt error changes within such a short time, resulting in an inability to perform precise error compensation for each individual workpiece.

[0007] Therefore, there is an urgent need to develop a linear grating parallel processing device and method that can sense the morphological differences of workpieces at each station online and has high-frequency dynamic adjustment capabilities to solve the above-mentioned technical problems. Summary of the Invention

[0008] The purpose of this invention is to provide a linear grating processing apparatus and method to solve the technical problems of poor processing consistency and low yield caused by the clamping height difference and tilting error between the workpieces when performing parallel processing of multiple workpieces on a continuously rotating worktable in the prior art.

[0009] To achieve the above objectives, the present invention provides a linear grating processing apparatus, comprising:

[0010] The worktable is configured to rotate continuously about a vertical central axis, and its surface has multiple stations for mounting workpieces along the circumferential direction.

[0011] A tool module, suspended above a worktable, includes a tool holder for mounting a tool and a multi-axis drive mechanism for driving the tool holder; the multi-axis drive mechanism is configured to give the tool holder multi-dimensional motion freedom relative to the worktable, the multi-dimensional motion freedom including at least a lifting motion freedom along a direction perpendicular to the worktable surface and a swing motion freedom for adjusting the tool posture.

[0012] A measuring unit is set above the worktable and is used to scan the surface morphology of the workpiece at each station before or during processing.

[0013] The control system is connected to the worktable, tool module, and measurement unit via signals.

[0014] The control system is configured to execute the following control logic:

[0015] Based on the circumferential indexing of the worktable surface, establish the mapping relationship between the rotation angle of the worktable and the spatial coordinates of the workpieces at each station.

[0016] Receive surface topography data from the measurement unit and calculate the height deviation and tilt angle of each workpiece relative to the ideal machining plane to generate a time-sharing and zone-based error compensation model.

[0017] During the continuous rotation of the worktable, the workpiece identity is identified based on the real-time angle feedback of the worktable, and the corresponding error data is retrieved from the time-division and zone error compensation model. This data is then converted into dynamic compensation commands and superimposed on the motion control of the multi-axis drive mechanism in real time, thereby driving the tool holder to perform corresponding lifting and swing compensation movements to independently eliminate clamping height difference and tilt error for each workpiece.

[0018] Preferably, the multi-axis drive mechanism includes:

[0019] The first linear drive unit is configured to drive the tool holder to move radially parallel to the worktable surface;

[0020] The second linear drive unit is configured to execute the lifting motion degrees of freedom;

[0021] A swing drive unit is configured to execute the swing motion degree of freedom, and the rotation axis of the swing drive unit is parallel to the motion direction of the second linear drive unit;

[0022] The motion control strategy of the swing drive unit is configured as follows: based on the real-time position of the tool holder on the first linear drive unit, the tangential direction of the current tool cutting trajectory is calculated, and the swing angle of the tool holder is adjusted in real time so that the rake face of the tool always maintains a predetermined constant angle with the tangential direction of the current cutting trajectory.

[0023] Preferably, the second linear drive unit in the multi-axis drive mechanism includes a coarse motion module that provides large stroke motion, and a high-frequency micro-motion stage connected in series at the end of the coarse motion module and connected to the tool holder;

[0024] The control system is configured to decompose the dynamic compensation command into low-frequency and high-frequency components, assign the low-frequency components to the coarse motion module for execution, and assign the high-frequency components to the high-frequency micro-motion stage for execution, so as to achieve superimposed control of large stroke and micron-level high-frequency response in a coordinated manner.

[0025] Preferably, the measurement unit is a spectral confocal sensor or a laser displacement sensor;

[0026] The control system is configured to use the pulse signal output by the rotary encoder of the worktable as a hard trigger source to control the measurement unit to collect the surface morphology data of the workpiece at each station at equal angular intervals, thereby establishing a correspondence between the collected surface morphology data and the rotation angle position of the worktable.

[0027] Preferably, the method for generating a time-sharing and zone-based error compensation model in the control system includes:

[0028] The discrete point cloud data collected by the measurement unit is fitted using the least squares method to construct the best fitting plane for each workpiece processing surface;

[0029] Based on the best-fit plane, the height difference between the geometric center of the workpiece's machined surface and the ideal machined plane is calculated as the height compensation amount, and the angle between the normal vector of the best-fit plane and the normal of the ideal machined plane is calculated as the tilt compensation amount.

[0030] Preferably, the control system is also configured to perform constant linear velocity cutting control:

[0031] As the tool holder moves radially along the worktable, the cutting radius of the tool relative to the central axis changes. The control system adjusts the rotational angular velocity of the worktable in real time to keep the linear velocity of the cutting point of the tool relative to the workpiece surface constant.

[0032] Meanwhile, the calling frequency of the time-sharing and partitioning error compensation model is automatically and synchronously adjusted according to the change of the rotational angular velocity of the worktable, so that the dynamic compensation command is output at equal rotational angle intervals of the worktable.

[0033] Preferably, the measuring unit is configured to scan the cutting edge profile of the tool during the machining gap; when the tool's cutting edge wear is detected, the control system adds the wear amount to the control command of the lifting motion degree of freedom to maintain a constant cutting depth of the tool.

[0034] The present invention also provides a linear grating fabrication method, comprising the following steps:

[0035] S1. Install multiple workpieces at various stations on the worktable, drive the worktable to rotate and use the measuring unit to scan the surface morphology of the workpieces at each station, control the system to calculate and establish a time-sharing and partition error compensation model that includes the height and tilt offset of the workpieces at each station.

[0036] S2. Drive the worktable to rotate continuously at the working speed and control the tool holder to feed radially along the worktable; during this process, the control system identifies the workpiece to which the current cutting point of the tool belongs based on the real-time angle feedback of the worktable, and retrieves the corresponding offset from the time-sharing and partitioning error compensation model.

[0037] S3. The control system converts the offset amount into a drive command in real time, driving the multi-axis drive mechanism to perform high-frequency lifting and swing correction of the tool holder, so that the tool can automatically adapt to the independent positional error of each workpiece during continuous cutting.

[0038] One or more technical solutions provided in this invention have at least the following technical effects or advantages:

[0039] 1. Unlike traditional CNC systems that control based on a single ideal plane, the control system of this invention utilizes a time-sharing and zone-based error compensation model established by a measurement unit. This model can accurately describe the height deviation and tilt angle of each workpiece relative to the ideal machining plane. During machining, the system identifies the workpiece in real time and drives the tool holder to perform high-frequency lifting and oscillating compensation movements. This effectively eliminates coplanarity differences caused by workpiece thickness tolerances or fixture installation errors, preventing "overcutting" of protruding workpieces and "cutting empty" of concave workpieces. This ensures that all workpieces produced in a batch during a single setup can achieve the precision level of single-piece ultra-precision machining.

[0040] 2. Addressing the characteristic of the cutting direction changing constantly with the trajectory in linear grating machining, the oscillating drive unit of this invention can adjust the oscillation angle of the tool in real time according to the radial position of the tool holder. Combined with compensation for the tilt angle, this achieves two effects: first, it ensures that the rake face of the tool always maintains a predetermined constant angle with the tangent of the current cutting trajectory, avoiding rake angle fluctuations; second, it corrects the entry angle deviation caused by workpiece surface tilt. This fundamentally solves the problems of grating groove asymmetry and blaze angle deviation caused by inaccurate cutting posture, ensuring the diffraction efficiency of optical components such as Fresnel lenses.

[0041] 3. To address the step error jumps encountered when the tool rapidly switches between different workpieces, this invention decomposes the dynamic compensation command into low-frequency and high-frequency components. The coarse motion module is responsible for the large-stroke contour motion, while the high-frequency micro-motion stage (such as piezoelectric ceramic) is responsible for performing high-frequency, small-amplitude error compensation. This frequency-domain splitting design gives the second linear drive unit extremely high dynamic response bandwidth, enabling it to follow shape changes within a millisecond-level time window without lag, overcoming the technical bottleneck of sluggish response in traditional servo systems under high-speed rotation conditions.

[0042] 4. This invention utilizes the rotary encoder pulses of the worktable as a hard trigger source, forcing the measurement unit to perform constant angular interval acquisition. This design eliminates phase misalignment caused by software communication delays or system clock drift. Especially when the rotational speed changes in real time due to constant linear velocity cutting control, the system can automatically and synchronously adjust the model call frequency to ensure that error compensation commands are always output at constant rotational angular intervals of the worktable. This guarantees that the spatial resolution of error compensation remains constant regardless of changes in the cutting radius and rotational speed, further ensuring machining accuracy across the entire diameter range. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the overall structure of the linear grating processing device provided in an embodiment of the present invention;

[0044] Figure 2 This is a schematic diagram of the tool module structure in an embodiment of the present invention;

[0045] Figure 3 This is a flowchart of the linear grating fabrication method provided in an embodiment of the present invention.

[0046] Explanation of reference numerals in the attached drawings: 10, worktable; C1, central axis; W, workpiece; 20, tool module; 21, tool holder; 22, tool; 23, first linear drive unit; 24, second linear drive unit; 241, coarse motion module; 242, high-frequency micro-motion stage; 25, oscillation drive unit; C2, oscillation axis; 30, measuring unit; 40, base; 50, mounting bracket. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0048] Please see Figure 1 and Figure 2 This embodiment provides a high-precision linear grating processing device, which is based on the design concept of ultra-precision machine tools and adopts a high-rigidity gantry layout.

[0049] like Figure 1 As shown, the basic support structure of the linear grating processing device consists of a base 40 and a gantry-type mounting frame 50 spanning it. To isolate external environmental vibrations and ensure thermal stability during processing, the base 40 is preferably made of natural granite. The worktable 10 is rotatably mounted in the center of the base 40. The core function of the worktable 10 is to support the workpiece W for high-speed, stable, and continuous rotation. In specific engineering implementation, the worktable 10 is supported by an air hydrostatic bearing. High-pressure gas forms a micron-level air film between the worktable 10 and the base 40, achieving frictionless and wear-free suspension support, thereby ensuring extremely high rotational accuracy of the worktable 10. For drive, the worktable 10 is directly driven by a built-in torque motor, eliminating backlash caused by gear or belt drives and enabling smooth stepless speed regulation from low to high speeds. In addition, a high-resolution circular encoder is integrated at the rotation axis of the worktable 10. This encoder is not only used for servo closed-loop control of the speed and angle of the worktable 10, but is also configured to output an independent physical pulse signal to the control system as a hard trigger source for subsequent measurement.

[0050] Regarding workpiece clamping and fixing, to avoid workpiece deformation caused by clamping stress from traditional mechanical fixtures, the worktable 10 in this embodiment preferably employs a vacuum adsorption method. Specifically, the worktable 10 has several independent vacuum channels inside, which are connected to various workstations on the table surface. Each workstation surface is inlaid with microporous ceramic suction cups or machined with evenly distributed negative pressure grooves to provide uniform adsorption force. An external vacuum source (such as a vacuum pump) is connected to the vacuum channels inside the worktable 10 through a gas path rotary joint installed at the bottom of the central axis C1. During processing, turning on the negative pressure firmly adsorbs the workpiece W onto the table surface; after processing, turning off the negative pressure or introducing positive pressure gas allows for quick removal of the workpiece. In addition, considering safety during high-speed rotation, auxiliary mechanical limit blocks can preferably be set on the radial outer side of each workstation to prevent the workpiece from flying out in case of accidental gas interruption or overspeed.

[0051] Below the crossbeam of the mounting bracket 50, a first linear drive unit 23 responsible for X-axis feed is installed. This first linear drive unit 23, as the X-axis moving component, uses a hydrostatic guide rail or an air-bearing guide rail as the guiding mechanism to ensure the straightness and rigidity of the movement. The drive element is preferably a coreless linear motor, which directly drives the slide plate equipped with the second linear drive unit 24 to move radially (X-direction) parallel to the surface of the worktable 10. In conjunction with a nanometer-resolution linear grating ruler mounted on the side of the mounting bracket 50, the first linear drive unit 23 can achieve high-precision position control with a fully closed loop.

[0052] like Figure 2 As shown, the second linear drive unit 24 is vertically mounted below the sliding plate of the first linear drive unit 23, serving as a Z-axis motion component. To resolve the contradiction between large-stroke feed and micron-level high-frequency error compensation in grating machining, the second linear drive unit 24 in this embodiment creatively employs a macro-micro composite drive structure. Specifically, the second linear drive unit 24 includes a coarse motion module 241 and a high-frequency micro-motion stage 242. The coarse motion module 241, acting as the "macro-motion stage," uses a linear motor in conjunction with a pneumatic gravity balance cylinder to counteract the gravity of the slide block and lower components. It is primarily responsible for tool setting, feed, and large-stroke movement of the tool 22 following the low-frequency contour changes of the workpiece W. The high-frequency micro-motion stage 242 is connected in series at the end of the coarse motion module 241, acting as the "micro-motion stage." It is a flexible hinge mechanism driven by a piezoelectric ceramic or voice coil motor. The high-frequency micro-motion stage 242 possesses extremely high rigidity and dynamic response frequency, specifically responsible for executing the high-frequency error compensation commands decomposed from the control system, performing micron-level rapid lifting and lowering corrections on the tool 22.

[0053] In terms of tool attitude control, the oscillating drive unit 25 is connected below the high-frequency micro-motion stage 242 to adjust the deflection attitude of the tool 22. This oscillating drive unit 25 is a precision direct-drive rotary table, with its rotation axis C2 parallel to the Z-axis (i.e., parallel to the movement direction of the second linear drive unit 24). The tool holder 21 is rigidly connected to the lower end of the rotor of the oscillating drive unit 25, and the tool 22 is mounted at the center of the tool holder 21. When the first linear drive unit 23 drives the second linear drive unit 24 to move along the X-direction, causing a change in the cutting radius, the tangent direction of the cutting trajectory relative to the tool 22 will change. At this time, the control system calculates this angle change in real time based on geometric relationships and drives the oscillating drive unit 25 to synchronously rotate the tool 22, thereby ensuring that the rake face of the tool 22 is always perpendicular to the cutting pattern or maintains a predetermined optimal cutting angle, thus achieving tangent-following control.

[0054] Furthermore, the measuring unit 30 is fixed to one side of the mounting bracket 50, located above the worktable 10. In this embodiment, the measuring unit 30 preferably employs a spectral confocal displacement sensor. This spectral confocal displacement sensor transmits optical signals through optical fibers, enabling non-contact ranging of the surface of a high-speed rotating workpiece with nanometer-level precision, and is unaffected by the reflective properties of the workpiece surface material.

[0055] Please see Figure 3 This invention also provides a method for high-precision parallel processing of linear gratings using the aforementioned device. This method effectively solves the consistency problem of multiple workpieces by establishing a time-sharing and partitioning error compensation model. The specific process is as follows:

[0056] 1. Perform step S1, namely scanning modeling and error decoupling. Multiple workpieces W (such as Fresnel lens molds) to be processed are attached to various stations of the worktable 10. The worktable 10 is started to rotate, at which time the circular grating encoder inside the worktable 10 outputs pulse signals at equal angular intervals (e.g., every 0.1 degrees of rotation). This pulse signal directly serves as a hard trigger source, triggering the measurement unit 30 to collect surface morphology data of the workpiece W at each station. This hard trigger mode avoids the time delay of the operating system, ensuring that each collected data point strictly corresponds to a certain absolute angular position of the worktable 10. After collecting discrete point cloud data, the control system uses the least squares algorithm to fit the data of each independent workpiece region, constructing the best-fit plane characterizing the actual posture of the workpiece. Based on this, the system calculates the height difference (Z-axis offset) of each workpiece center relative to the ideal processing plane and the tilt normal vector of the plane (tilt error), generating a time-division and partition error compensation model containing the error parameters of the workpieces at all stations.

[0057] 2. Proceed to step S2, namely parallel machining and real-time identification. The first linear drive unit 23 drives the second linear drive unit 24 to move to the machining starting point and accelerates the worktable 10 to its operating speed. To ensure consistent surface quality of the grating groove, the system implements constant linear velocity control: as the X-axis feed causes the cutting radius to decrease, the system automatically increases the speed of the worktable 10 to maintain a constant cutting linear velocity. During this speed change, the system uses the error model and real-time rotational angle feedback to determine in real-time which workpiece is being passed beneath the current tool 22. Once the workpiece is identified, the system immediately retrieves the corresponding height offset and tilt offset from the time-sharing and partitioning error compensation model. It is worth noting that as the rotational speed changes, the system automatically adjusts the calling frequency of the time-sharing and partitioning error compensation model synchronously to ensure that compensation commands are always output at equal rotational angle intervals of the worktable 10.

[0058] 3. Execute step S3, namely multi-axis linkage dynamic correction. The control system converts the retrieved offset amount into specific axis motion commands and sends them to each drive unit. For height correction in the Z direction, the system uses a frequency domain filter to decompose the command: low-frequency large contour signals are sent to the coarse motion module 241, while high-frequency small error signals (such as micron-level runout on the workpiece surface) are sent to the high-frequency micro-motion stage 242. The high-frequency micro-motion stage 242 utilizes the fast response characteristics of piezoelectric ceramics to drive the tool 22 to perform high-frequency reciprocating motion, eliminating the workpiece clamping height difference in real time. For attitude correction, the system superimposes the tilt offset amount with the rotation angle required for tangent following and sends it to the oscillating drive unit 25. The oscillating drive unit 25 drives the tool 22 to rotate slightly around the C2 axis, correcting the entry angle error caused by workpiece tilt on the one hand, and keeping the tool aligned with the tangent on the other hand to prevent edge chipping.

[0059] Furthermore, as a preferred embodiment, the measuring unit 30 is also configured to scan the cutting edge profile of the tool 22 during the machining gap. When cutting edge wear is detected on the tool 22, the control system automatically adds the wear amount to the control command of the second linear drive unit 24 to maintain a constant cutting depth of the tool 22.

[0060] By combining the aforementioned precise mechanical structure with advanced control algorithms, this invention enables the independent and precise processing of multiple workpieces with individual differences in a single clamping operation, effectively solving the consistency problem of parallel processing of multiple workpieces.

[0061] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A linear grating processing apparatus characterized by comprising: The utility model relates to a kind of multi-axis machining center, comprising: Workbench (10) is configured to be able to continuously rotate around the central axis (C1) of vertical direction, and a plurality of workstations for mounting workpieces are provided on the table surface in the circumferential direction; Tool module (20) is suspended above the workbench (10), including tool holder (21) for installing tool (22) and multi-axis drive mechanism for driving the tool holder (21);The multi-axis drive mechanism is configured to give the tool holder (21) a multi-dimensional motion freedom relative to the workbench (10), which includes at least a lifting motion freedom in the direction perpendicular to the workbench (10) table surface and a swing motion freedom for adjusting the attitude of the tool (22); Measurement unit (30) is arranged above the workbench (10) for scanning the surface topography of the workpiece in each workstation before or during processing; Control system is signal connected with workbench (10), tool module (20) and measurement unit (30); Wherein, the control system is configured to execute the following control logic: Based on the circumferential division of the workbench (10) table surface, the rotation angle of the workbench (10) and the spatial coordinate mapping relationship of the workpiece in each workstation are established; Receive surface topography data from measurement unit (30), and calculate the height deviation value and inclination angle value of each workpiece relative to the ideal machining plane to generate a time-zoned error compensation model; During the continuous rotation of the workbench (10) in the processing process, the workpiece identity currently entering the processing area is identified according to the real-time angle feedback of the workbench (10), and the corresponding error data is called from the time-zoned error compensation model, which is converted into dynamic compensation instructions and superimposed into the motion control of the multi-axis drive mechanism in real time, so as to drive the tool holder (21) to execute corresponding lifting and swing compensation motion, so as to eliminate the clamping height difference and inclination error for each workpiece independently.

2. The apparatus of claim 1, wherein, The multi-axis drive mechanism includes: First linear drive unit (23) is configured to drive the tool holder (21) to move along the radial direction parallel to the workbench (10) table surface; Second linear drive unit (24) is configured to execute the lifting motion freedom; Swing drive unit (25) is configured to execute the swing motion freedom, and the rotation axis of the swing drive unit (25) is parallel to the motion direction of the second linear drive unit (24); Wherein, the motion control strategy of the swing drive unit (25) is configured to calculate the tangent direction of the current tool (22) cutting trajectory according to the real-time position of the tool holder (21) on the first linear drive unit (23), and adjust the swing angle of the tool holder (21) in real time, so that the rake face of the tool (22) always maintains a predetermined constant angle with the tangent direction of the current cutting trajectory.

3. The apparatus of claim 2, wherein, The second linear drive unit (24) in the multi-axis drive mechanism includes coarse motion module (241) for providing large stroke motion, and high-frequency fine motion table (242) connected with the tool holder (21) in series at the end of the coarse motion module; The control system is configured to decompose the dynamic compensation instruction into a low-frequency component and a high-frequency component, assign the low-frequency component to the coarse motion module (241) for execution, and assign the high-frequency component to the high-frequency micro-motion stage (242) for execution, to cooperatively achieve superimposed control of large stroke and micron-level high-frequency response.

4. The apparatus of claim 1, wherein, The measurement unit (30) is a spectral confocal sensor or a laser displacement sensor; The control system is configured to use pulse signals output by a rotary encoder of the worktable (10) as a hard trigger source to control the measurement unit (30) to collect surface topography data of workpieces at each station at equal angular intervals, so that the collected surface topography data is in correspondence with the rotational angular position of the worktable (10).

5. The apparatus of claim 1, wherein, The method for generating the time-and-zone division error compensation model by the control system comprises: The least square method is used to fit the discrete point cloud data collected by the measurement unit (30) to construct an optimal fitting plane for each workpiece machining surface; Based on the optimal fitting plane, the height difference of the geometric center of the workpiece machining surface relative to the ideal machining plane is calculated as a height compensation amount, and the included angle of the normal vector of the optimal fitting plane relative to the normal of the ideal machining plane is calculated as a tilt compensation amount.

6. The apparatus of claim 1, wherein, The control system is also configured to perform constant linear velocity cutting control: As the tool holder (21) moves along the radial direction of the worktable (10) to change the cutting radius of the tool (22) relative to the center axis (C1), the control system adjusts the rotational angular velocity of the worktable (10) in real time to keep the linear velocity of the cutting point of the tool (22) relative to the workpiece machining surface constant; At the same time, the calling frequency of the time-and-zone division error compensation model is automatically adjusted synchronously with the change of the rotational angular velocity of the worktable (10), so that the dynamic compensation instruction is output at equal rotational angular intervals of the worktable (10).

7. The apparatus of claim 1, wherein, The measurement unit (30) is configured to scan the edge profile of the tool (22) in the machining gap; when the tool wear of the tool (22) is detected, the control system superimposes the wear into the control instruction of the lifting motion degree of freedom to maintain the constant cutting depth of the tool (22).

8. A method for linear grating processing using the apparatus according to any one of claims 1 to 7, characterized by, The method comprises the following steps: S1, a plurality of workpieces are respectively installed on each station of the worktable (10), the worktable (10) is driven to rotate, and the measurement unit (30) is used to traverse and scan the surface topography of the workpieces at each station, and the control system calculates and establishes a time-and-zone division error compensation model containing the height and tilt bias of the workpieces at each station; S2, the worktable (10) is continuously rotated at a working rotational speed, and the tool holder (21) is fed along the radial direction of the worktable (10); during this process, the control system identifies the workpiece identity to which the current cutting point of the tool (22) belongs according to the real-time angular feedback of the worktable (10), and retrieves the corresponding bias from the time-and-zone division error compensation model. S3. The control system converts the offset amount into a driving command in real time, and drives the multi-axis drive mechanism to perform high-frequency lifting and swing correction on the tool holder (21), so that the tool (22) can automatically adapt to the independent position error of each workpiece during continuous cutting.

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