Coordinated tool servo diamond turning method and system based on trajectory pre-filtering

Abstract

The application provides a kind of trajectory pre-filtering-based cooperative tool servo diamond turning method and system, comprising: step S1: by fast tool shaft is integrated to the machine tool axis along the cutting depth direction, construct master-slave cooperative tool servo system;Wherein, the machine tool axis is as the master-slave cooperative tool servo system main servo axis, the low-frequency tool trajectory obtained after reference tool trajectory pre-filtering is executed;The fast tool shaft is as the master-slave cooperative tool servo system slave servo axis, real-time compensation is carried out to the deviation of actual displacement of main servo axis and reference tool trajectory;Step S2: based on master-slave cooperative tool servo system implements cooperative tool servo machining process;Step S3: after processing, surface profile data is obtained, and the processing result is quantitatively evaluated by surface roughness index and surface error.

Description

Technical Field

[0001] This invention relates to the field of precision manufacturing technology, and more specifically, to a collaborative tool servo diamond turning method and system based on trajectory pre-filtering. Background Technology

[0002] The collaborative tool servo system executes the reference tool path through the master servo axis and simultaneously uses the slave servo axis to compensate for the tracking error of the master servo axis in real time. It combines the advantages of the long stroke of the master servo axis and the high bandwidth of the slave servo axis, effectively improving machining accuracy and adaptability. However, due to the kinematic and dynamic characteristics of the master servo axis, the high-frequency components in the reference tool path can easily lead to an increase in the motion error and vibration of the master servo axis, which in turn exceeds the effective compensation range of the slave servo axis. This means that the method can only achieve stable machining at lower spindle speeds, limiting further improvement in machining efficiency. At the same time, the slave servo axis uses a single proportional-integral controller, whose dynamic compensation capability is limited by the controller bandwidth and nonlinear characteristics, making it difficult to meet the requirements of high-precision and high-speed machining.

[0003] Patent document CN113495527A (application number: 202010262963.4) discloses a fast-slow tool servo master-slave cooperative cutting method, including the following steps: Step 1: Calculate the tool trajectory Z(t) based on the geometry of the workpiece surface to be machined; Step 2: Input the tool trajectory Z(t) command to the machine tool, and the slow tool servo system drives the Z-axis slow tool servo slide (6) to reciprocate; Step 3: The fast tool servo system compensates for the error of the slow tool servo system in real time, and the final tool tip motion is the sum of the fast and slow tool servo motions. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the purpose of this invention is to provide a collaborative tool servo diamond turning method and system based on trajectory pre-filtering.

[0005] A collaborative tool servo diamond turning method based on trajectory pre-filtering according to the present invention includes:

[0006] Step S1: By integrating the fast tool axis into the machine tool axis along the depth of cut, a master-slave cooperative tool servo system is constructed; wherein, the machine tool axis serves as the master servo axis of the master-slave cooperative tool servo system, executing the low-frequency tool trajectory obtained after pre-filtering the reference tool trajectory; the fast tool axis serves as the slave servo axis of the master-slave cooperative tool servo system, compensating in real time for the deviation between the actual displacement of the master servo axis and the reference tool trajectory.

[0007] Step S2: Implement collaborative tool servo machining process based on master-slave collaborative tool servo system;

[0008] Step S3: After processing, obtain surface contour data and quantitatively evaluate the processing results through surface shape error and surface roughness index.

[0009] Preferably, the master-slave cooperative tool servo system includes: machine tool axes C-axis, X-axis, Z-axis, and a fast tool axis W-axis; wherein, the C-axis is responsible for the main rotational motion of the workpiece; the X-axis is used to realize the radial feed of the tool; the Z-axis and W-axis are used to jointly complete the feed of the tool along the depth of cut; the machine tool axes C-axis, X-axis, and Z-axis are synchronously controlled by the machine tool's multi-axis motion controller, and the fast tool axis W-axis moves in coordination with the machine tool axes through a dedicated controller.

[0010] Preferably, the online data-driven control strategy adopted by the fast tool axis W-axis includes: a high-bandwidth feedback controller and a feedforward controller;

[0011] The high-bandwidth feedback controller includes: employing a notch filter to suppress the resonant mode of the W-axis for the servo axis dynamic characteristics, and compensating for the nonlinear error caused by the W-axis hysteresis through a high-gain proportional-integral controller;

[0012] The feedforward controller includes: applying the Koopman operator to perform dynamic modeling of the feedback control loop of the slave axis, using real-time data to predict the tracking error, and adjusting the input signal of the slave axis online according to the prediction results to achieve tracking with near-zero phase lag of the slave axis.

[0013] Preferably, the transfer function of the notch filter in the high-bandwidth feedback controller is as follows:

[0014]

[0015] Among them, w n ξ1 and ξ2 are the center angular frequency of the notch filter, and the damping coefficients affect its attenuation depth and notch bandwidth. These parameters together determine the resonance suppression effect and frequency response characteristics of the notch filter.

[0016] Preferably, the transfer function of the high-gain proportional-integral controller in the high-bandwidth feedback controller is as follows:

[0017]

[0018] Where, k p and k i These are the proportional gain and integral gain, respectively.

[0019] Preferably, in order to obtain a high-bandwidth feedback controller with optimal control performance, a parameter optimization model based on frequency response data is constructed, and the optimal parameter configuration of the high-bandwidth feedback controller is obtained by solving the parameter optimization model;

[0020] With controller parameters N = [ξ1, ξ2, w n ,k p ,k i As an optimization variable, the objective function is to flatten the frequency response of the feedback controller within the desired bandwidth.

[0021]

[0022] Among them, w d w is the highest angular frequency of the desired bandwidth. k Let D(·) be a series of fixed angular frequency points within the desired bandwidth, and let D(·) be the closed-loop transfer function of the feedback controller.

[0023] The optimal parameter configuration of the high-bandwidth feedback controller is obtained by solving the objective function using an optimization algorithm.

[0024] Preferably, the feedforward controller includes:

[0025] By using real-time data, the tracking error caused by the nonlinear phase lag of the high-bandwidth feedback controller is predicted in each sampling period. Based on the prediction results, the input signal of the W-axis is adjusted online to achieve near-zero phase lag accurate tracking of the W-axis. The future output of the W-axis is represented as:

[0026]

[0027] in, To characterize the unknown nonlinear function y of the high-bandwidth feedback controller's dynamic behavior, k+1 For the future output of the high-bandwidth feedback controller, y k and r k These represent the current output and input of the high-bandwidth feedback controller, respectively; for constructing... The nonlinear mapping relationship is represented using data-driven Koopman operator theory. By transforming the finite-dimensional nonlinear system into an infinite-dimensional linear space, the dynamics of the system are modeled. Specifically, the extended dynamic mode decomposition algorithm is used to approximate the solution of the infinite-dimensional operator within a finite high-dimensional linear space, thereby reducing computational complexity while preserving the original dynamic information of the system to the greatest extent. Based on this modeling method, the future prediction output of the W-axis is shown below:

[0028]

[0029] in, This represents the predicted output of the W-axis at the (k+1)th sampling point in the future. This is a finite-dimensional approximation of the Koopman operator. After obtaining the approximate parameters of the Koopman operator through offline training and identification, the future tracking error is predicted online. This error will serve as a reference for adjusting the W-axis input trajectory.

[0030]

[0031] in, This represents the prediction tracking error at the (k+1)th sampling point in the future.

[0032] Preferably, the method for cooperative tool servo diamond turning based on trajectory pre-filtering according to claim 1, wherein step S2 includes:

[0033] Step S2.1: Generate a reference tool path based on the target surface features and tool parameters;

[0034] Step S2.2: Based on the reference tool path planning, which is constrained by the kinematic and dynamic characteristics along the Z-axis in the depth of cut direction, a low-frequency tool path that meets the preset constraints is obtained after pre-filtering its component along this direction using a zero-phase low-pass filter. The machine tool axis is then driven to move based on the low-frequency tool path that meets the constraints.

[0035] Step S2.3: Real-time acquisition of the actual Z-axis displacement and comparison with the reference tool path to obtain the deviation between the actual displacement of the main servo axis and the reference tool path, and compensation for the deviation between the two through the W-axis.

[0036] Preferably, step S2.2 includes:

[0037] The servo axis components (θ(n), ρ(n), y) corresponding to the reference tool path in polar coordinates d (n) is represented as:

[0038]

[0039] Among them, y d (n) represents the position coordinates of the reference tool path along the depth of cut, w C R is the C-axis rotational speed, n is the index of the discrete point of the reference toolpath, Δt is the time interval between adjacent points, and R W f is the workpiece radius. t This refers to the X-axis feed rate. This is a stable X-axis tool radius compensation function based on tool geometry parameters and target surface features;

[0040] The pre-filtering process includes: performing frequency domain decomposition on the components of the reference tool trajectory along the depth of cut using a zero-phase low-pass filter to obtain the low-frequency tool trajectory, expressed as:

[0041]

[0042] Among them, z d The low-frequency tool trajectory points are used to control the Z-axis motion, and h is the impulse response of the filter. This indicates that the sequence is reversed. To effectively suppress high-frequency interference components in the tool path, a high-order filter is used to process the reference tool path.

[0043] To ensure that the low-frequency tool path conforms to the kinematic and dynamic constraints of the Z-axis, a suitable cutoff frequency needs to be selected for the zero-phase low-pass filter. The kinematic constraints of the Z-axis require that the Z-axis motion meet the maximum speed and acceleration limits of the machine tool axis, as shown below:

[0044]

[0045] in, Z-axis velocity, v is the acceleration along the Z-axis. max,z a is the maximum permissible speed along the Z-axis. max,z This represents the maximum permissible acceleration along the Z-axis.

[0046] The Z-axis dynamic constraints require that the cutoff frequency of the zero-phase low-pass filter be within the Z-axis operating bandwidth to avoid the Z-axis being in undesirable motion modes or experiencing instability, and that the motion error of the Z-axis should not exceed the maximum permissible error, as shown below:

[0047]

[0048] Among them, f cut f is the cutoff frequency of the zero-phase low-pass filter. max,z e represents the highest frequency of the Z-axis operating bandwidth. z e represents the motion error along the Z-axis. max,z This represents the maximum permissible error along the Z-axis.

[0049] A collaborative tool servo diamond turning system based on trajectory pre-filtering, according to the present invention, includes:

[0050] Module M1: By integrating the fast tool axis into the machine tool axis along the depth of cut, a master-slave collaborative tool servo system is constructed; wherein, the machine tool axis serves as the master servo axis of the master-slave collaborative tool servo system, executing the low-frequency tool trajectory obtained after pre-filtering the reference tool trajectory; the fast tool axis serves as the slave servo axis of the master-slave collaborative tool servo system, compensating in real time for the deviation between the actual displacement of the master servo axis and the reference tool trajectory;

[0051] Module M2: Implements collaborative tool servo machining process based on master-slave collaborative tool servo system;

[0052] Module M3: After processing, it acquires surface contour data and quantifies the processing results through surface shape error and surface roughness indicators.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] 1. This invention solves the problems of kinematic and dynamic constraints of the master servo axis limiting the improvement of machining efficiency and insufficient tracking accuracy of the slave servo axis when diamond turning of complex optical components with traditional collaborative tool servo systems by constructing a master-slave collaborative tool servo system, pre-filtering the reference tool trajectory, and designing an online data-driven control strategy for the slave servo axis.

[0055] 2. This invention meets the requirements of high-precision and high-speed machining. The master-slave collaborative tool servo system constructed utilizes the master servo axis to extend the system stroke, improving machining adaptability. At the same time, the slave servo axis, with its high bandwidth characteristics and near-zero phase tracking capability, can quickly respond to adjust the tool position, significantly improving machining speed and ensuring machining accuracy, fully meeting the industry's demand for high-precision and high-speed machining of complex optical components.

[0056] 3. The system operation stability is enhanced in this invention. By pre-filtering the reference tool path, a low-frequency tool path is obtained to drive the main servo axis motion. This effectively bypasses the limitations of the kinematic and dynamic characteristics of the main servo axis on the planning of the reference tool path, so that the main servo axis can still run stably according to the planned path at higher spindle speeds. This effectively suppresses its motion error and vibration, laying a solid foundation for the stable operation of the entire collaborative tool servo system. Experimental results show that the machining efficiency can be improved by 2.5 times compared with the traditional CTS, while maintaining high machining accuracy and surface quality.

[0057] 4. In this invention, the tracking accuracy of the servo axis is improved by designing an online data-driven control strategy that combines a feedforward controller based on the Koopman operator with a high-bandwidth feedback controller. The feedforward controller uses real-time data to predict the tracking error and adjust the input trajectory in advance, while the high-bandwidth feedback controller effectively suppresses the resonant mode and compensates for the nonlinear hysteresis effect, enabling the servo axis to achieve near-zero phase accurate tracking. By optimizing the control performance of the servo axis, the processing accuracy of complex optical components is guaranteed, thereby enhancing the system's adaptability to complex processing tasks. Attached Figure Description

[0058] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0059] Figure 1 This is a schematic diagram of the hardware integration of a collaborative tool servo diamond turning system based on trajectory pre-filtering.

[0060] Figure 2 This is a schematic diagram of a collaborative tool servo diamond turning system based on trajectory pre-filtering.

[0061] Figure 3 This is a schematic diagram of the W-axis online drive control strategy.

[0062] Figure 4 This is a flowchart of a collaborative tool servo diamond turning method based on trajectory pre-filtering.

[0063] Figures 5a to 5c This is a schematic diagram illustrating the implementation of the W-axis online drive control strategy.

[0064] Figure 6 This is a schematic diagram of the W-axis trajectory tracking results.

[0065] Figures 7a to 7c This is a schematic diagram of the controller integration.

[0066] Figures 8a to 8c This is a schematic diagram of the target surface.

[0067] Figures 9a to 9b This is a schematic diagram of the dynamics and kinematics analysis of the tool trajectory.

[0068] Figure 10 a to Figure 10 Figure d shows the performance of collaborative tool servo tracking based on trajectory pre-filtering at different rotational speeds.

[0069] Figures 11a to 11d This diagram illustrates the collaborative tool servo cutting performance based on trajectory pre-filtering at different speeds.

[0070] Figure 12 This is a schematic diagram of the performance of traditional collaborative tool servo tracking when the C-axis speed is 10 RPM.

[0071] Figures 13a to 13c This is a schematic diagram showing the machining results of a microlens array using different collaborative tool servo modes. Detailed Implementation

[0072] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0073] Example 1

[0074] This invention provides a method and system for collaborative tool servo diamond turning based on trajectory pre-filtering. Addressing the kinematic and dynamic characteristics of the master servo axis (long stroke, low bandwidth) and slave servo axis (short stroke, high bandwidth) in a collaborative tool servo system, the invention pre-filters the tool trajectory and drives the master servo axis. The slave servo axis is used to compensate for the deviation between the actual displacement of the master servo axis and the reference tool trajectory in real time. Simultaneously, an online data-driven control strategy combining a feedforward controller based on the Koopman operator and a high-bandwidth feedback controller is designed for the slave servo axis, achieving near-zero phase tracking. This invention effectively bypasses the limitations imposed by the kinematic and dynamic characteristics of the master servo axis on the planning of the reference tool trajectory and solves the problem of insufficient tracking accuracy when using single feedback control for the slave servo axis, enabling high-precision, high-speed machining of complex optical components.

[0075] The cooperative tool servo diamond turning method based on trajectory pre-filtering includes:

[0076] Step 1: Construct a master-slave collaborative tool servo system: By integrating the fast tool axis into the machine tool axis along the depth of cut, a master-slave collaborative tool servo system is constructed; the machine tool axis acts as the master servo axis, executing the low-frequency tool trajectory obtained after pre-filtering the reference tool trajectory; the fast tool axis acts as the slave servo axis, compensating in real time for the deviation between the actual displacement of the master servo axis and the reference tool trajectory, thus realizing the hardware integration and control coordination of the collaborative tool servo system.

[0077] Step 2: Design a high-bandwidth feedback controller for the servo axis: For the dynamic characteristics of the servo axis, a notch filter is used to suppress its resonant mode, and a high-gain proportional-integral controller is used to compensate for the nonlinear hysteresis effect; with the optimization objective of making the frequency response of the feedback controller tend to be flat within the desired bandwidth, the controller parameters are selected as optimization variables, and a parameter optimization model based on frequency response data is established. The optimal parameter configuration of the high-bandwidth feedback controller is obtained by solving the model.

[0078] Step 3: Establish a feedforward controller for the servo axis based on the Koopman operator: Apply the Koopman operator to perform dynamic modeling of the feedback control loop of the servo axis, use real-time data to predict the tracking error, and adjust the input signal of the servo axis online according to the prediction results to achieve accurate tracking with near-zero phase lag of the servo axis.

[0079] Step four, implement collaborative tool servo machining process: Based on the tool geometry parameters and surface features of complex optical components, plan a reference tool trajectory; perform frequency domain decomposition of the reference tool trajectory in the depth of cut direction through pre-filtering to extract a low-frequency tool trajectory that conforms to the kinematic and dynamic constraints of the main servo axis; drive the main servo axis to execute the low-frequency tool trajectory, and simultaneously acquire the real-time deviation of the main servo axis for compensation by the slave servo axis to achieve collaborative machining of complex optical components; after machining is completed, use precision measuring equipment to acquire surface contour data and evaluate the machining results.

[0080] Specifically, in step one, the master-slave cooperative tool servo system includes machine tool axes C-axis, X-axis, Z-axis and fast tool axis W-axis. The C-axis is responsible for the main rotational motion of the workpiece, the X-axis realizes the radial feed of the tool, and the master servo axis Z-axis and the slave servo axis W-axis jointly complete the feed of the tool along the depth of cut. The machine tool axes C-axis, X-axis and Z-axis are synchronously controlled by the machine tool's multi-axis motion controller, while the W-axis moves in coordination with the machine tool axes through a dedicated controller.

[0081] The reference tool trajectory is generated by combining equal-angle sampling with a stable X-axis tool radius compensation algorithm to ensure smooth C-axis rotation and uniform X-axis feed during synchronous machine tool axis motion; the servo axis components (θ(n), ρ(n), y) corresponding to the reference tool trajectory in polar coordinates are... d (n) can be represented as:

[0082]

[0083] Among them, y d (n) represents the position coordinates of the reference tool path along the depth of cut, w C R is the C-axis rotational speed, n is the index of the discrete point of the reference toolpath, Δt is the time interval between adjacent points, and R W f is the workpiece radius. t This refers to the X-axis feed rate. This is a stable X-axis tool radius compensation function based on tool geometry parameters and target surface features. Since the tool feed rate along the depth of cut needs to be adjusted in real time to ensure that the tool can accurately track the target surface, the acceleration fluctuation of the reference tool trajectory along the depth of cut will be more severe, making the kinematic and dynamic characteristics of the Z-axis a key limiting factor affecting the planning of the reference tool trajectory.

[0084] The pre-filtering process uses a zero-phase low-pass filter to perform frequency domain decomposition on the components of the reference tool trajectory along the depth of cut. The resulting low-frequency tool trajectory can be expressed as:

[0085]

[0086] Among them, z dThe low-frequency tool trajectory points are used to control the Z-axis motion, and h is the impulse response of the filter. This indicates that the sequence is reversed. To effectively suppress high-frequency interference components in the tool path, a high-order filter is used to process the reference tool path.

[0087] To ensure that the low-frequency tool path conforms to the kinematic and dynamic constraints of the Z-axis, a suitable cutoff frequency needs to be selected for the zero-phase low-pass filter; the kinematic constraints of the Z-axis require that the Z-axis motion meet the maximum speed and acceleration limits of the machine tool axis, as shown in equation (3):

[0088]

[0089] in, Z-axis velocity, v is the acceleration along the Z-axis. max,z a is the maximum permissible speed along the Z-axis. max,z This represents the maximum permissible acceleration along the Z-axis.

[0090] The Z-axis dynamic constraints require that the cutoff frequency of the zero-phase low-pass filter be within the Z-axis operating bandwidth to avoid the Z-axis being in an undesirable motion mode or experiencing instability, and that the motion error of the Z-axis should not exceed the maximum permissible error, as shown in equation (4):

[0091]

[0092] Among them, f cut f is the cutoff frequency of the zero-phase low-pass filter. max,z e represents the highest frequency of the Z-axis operating bandwidth. z e represents the motion error along the Z-axis. max,z This represents the maximum permissible error along the Z-axis.

[0093] The obtained low-frequency tool path is used to control the Z-axis motion, ensuring that the deviation between the actual Z-axis displacement and the reference tool path remains within the W-axis travel range. This method fully utilizes the dynamic performance of the Z-axis while effectively bypassing the influence of Z-axis characteristics on the reference tool path planning. The actual Z-axis displacement is collected in real time by a linear grating displacement sensor and compared with the corresponding interpolation result of the reference tool path. The obtained deviation is used as the input signal of the W-axis, thereby utilizing the W-axis and Z-axis to complete the feed along the depth of cut.

[0094] In step two, the high-bandwidth feedback controller includes a notch filter and a high-gain proportional-integral controller. The notch filter is used to effectively suppress the resonant mode of the W-axis to improve the stability margin of the system. Its transfer function is shown in equation (5).

[0095]

[0096] Among them, w n ξ1 and ξ2 are the center angular frequency of the notch filter, and the damping coefficients affect its attenuation depth and notch bandwidth. These parameters together determine the resonance suppression effect and frequency response characteristics of the notch filter.

[0097] The high-gain proportional-integral controller is used to compensate for the residual nonlinear error caused by W-axis hysteresis, and its transfer function is shown in equation (6):

[0098]

[0099] Where, k p and k i These are proportional gain and integral gain, respectively.

[0100] To obtain a high-bandwidth feedback controller with optimal control performance, a parameter optimization model based on frequency response data is constructed: The controller parameters N = [ξ1, ξ2, w] are used. n ,k p ,k i As the optimization variable, the optimization objective is to make the frequency response of the feedback controller tend to be flat within the desired bandwidth. The objective function is shown in equation (7):

[0101]

[0102] Among them, w d w is the highest angular frequency of the desired bandwidth. k Let D(·) be a series of fixed angular frequency points within the desired bandwidth, and let D(·) be the closed-loop transfer function of the feedback controller. By using an optimization algorithm to solve the objective function, the optimal parameter configuration of the high-bandwidth feedback controller can be obtained.

[0103] In step three, the feedforward controller predicts the tracking error caused by the nonlinear phase lag of the feedback controller in each sampling period using real-time data, and adjusts the input signal of the W-axis online according to the prediction results to achieve near-zero phase lag accurate tracking of the W-axis. The future output of the W-axis can be represented by equation (8):

[0104]

[0105] in, To characterize the unknown nonlinear function y of the feedback controller's dynamic behavior k+1 For the future output of the feedback controller, y k and r k These represent the current output and input of the feedback controller, respectively; for constructing... The nonlinear mapping relationship is represented by the data-driven Koopman operator theory. By transforming the finite-dimensional nonlinear system into an infinite-dimensional linear space, the dynamic model of the system is realized. Specifically, the extended dynamic mode decomposition algorithm is used to approximate the solution of the infinite-dimensional operator in a finite high-dimensional linear space, thereby reducing the computational complexity while preserving the original dynamic information of the system to the maximum extent. Based on the modeling method, the future prediction output of the W axis is shown in Equation (9):

[0106]

[0107] in, This represents the predicted output of the W-axis at the (k+1)th sampling point in the future. This is a finite-dimensional approximation of the Koopman operator. After obtaining the approximate parameters of the Koopman operator through offline training and identification, the future tracking error can be predicted online. This error will serve as a reference for adjusting the W-axis input trajectory.

[0108]

[0109] in, This represents the prediction tracking error at the (k+1)th sampling point in the future;

[0110] In step four, a reference tool path is generated based on the target surface features and tool parameters. Considering that the planning of the reference tool path is limited by the kinematic and dynamic characteristics of the Z-axis along the depth of cut, a zero-phase low-pass filter is used to pre-filter its component along this direction to obtain a low-frequency tool path that meets the constraints, and a corresponding CNC program is generated to drive the machine tool axis motion. At the same time, the actual displacement of the Z-axis is collected in real time and compared with the reference tool path. The deviation between the two is compensated by using online data-driven control of the W-axis. After machining, surface contour data is obtained using precision measuring equipment to verify the effectiveness of the collaborative tool servo diamond turning based on trajectory pre-filtering.

[0111] The present invention also provides a collaborative tool servo diamond turning system based on trajectory pre-filtering. The collaborative tool servo diamond turning system based on trajectory pre-filtering can be implemented by executing the process steps of the collaborative tool servo diamond turning method based on trajectory pre-filtering. That is, those skilled in the art can understand the collaborative tool servo diamond turning method based on trajectory pre-filtering as a preferred embodiment of the collaborative tool servo diamond turning system based on trajectory pre-filtering.

[0112] Example 2

[0113] Example 2 is a preferred example of Example 1.

[0114] This invention provides a collaborative tool servo diamond turning system based on trajectory pre-filtering, comprising: pre-filtering the component of the reference tool trajectory along the depth of cut to generate a low-frequency tool trajectory that adapts to the kinematic and dynamic characteristics of the master servo axis, so as to reduce the limitation of the corresponding constraints of the master servo axis on the planning of the reference tool trajectory; and configuring the slave servo axis to compensate the deviation between the actual displacement of the master servo axis and the reference tool trajectory online, so as to realize the collaborative control of the master and slave servo axes in the machining of complex optical components and meet the requirements of high-precision and high-efficiency ultra-precision machining.

[0115] Specifically, such as Figure 1 As shown, the collaborative tool servo diamond turning system based on trajectory pre-filtering includes: a base, machine tool axis Z-axis 1, machine tool axis X-axis 2, machine tool axis C-axis 3, workpiece fixture 4, fast tool axis W-axis 5, worktable 51, stacked piezoelectric ceramics 52, end effector 53, diamond tool 54, and reading head 55. Machine tool axis Z-axis 1 and machine tool axis X-axis 2 are mounted on the base in a T-shape to achieve reciprocating translational motion along a straight line, and the movement directions of machine tool axis Z-axis 1 and machine tool axis X-axis 2 are perpendicular to each other. Machine tool axis C-axis 3 is mounted on the slide surface of machine tool axis X-axis 2 to achieve rotational motion around its central axis, and the central axis of machine tool axis C-axis 3 is parallel to the movement direction of machine tool axis Z-axis 1. Workpiece fixture 4 is fixed on machine tool axis C-axis 3 for positioning and clamping the workpiece. Fast tool axis W-axis 5 is located on machine tool axis Z-axis 1. The machine tool axis Z-axis 1 is parallel to the machine tool axis Z-axis 1 and is used to achieve high-frequency reciprocating oscillation motion with a small amplitude along the cutting depth direction to compensate for the deviation between the actual displacement of the machine tool axis Z-axis 1 and the reference tool trajectory. The worktable 51 is fixed on the slide surface of the machine tool axis Z-axis 1 and has stacked piezoelectric ceramics 52 installed inside. The two end faces of the stacked piezoelectric ceramics 52 are in contact with the worktable 51 and the end effector 53 respectively, and are used to convert electrical energy into mechanical energy. It can be controlled to extend and retract along the W-axis direction by inputting a changing electrical signal. The end effector 53 is connected to the worktable 51 through a flexible hinge and outputs displacement in the W-axis direction through the drive of the stacked piezoelectric ceramics 52 and the guiding effect of the flexible hinge. The diamond tool 54 is mounted on the end effector 53 and is used to complete the cutting. The reading head 55 is used to obtain the actual displacement of the fast tool axis W-axis 5 in real time.

[0116] like Figure 2 As shown, control coordination is achieved on the basis of the hardware system, including pre-filtering of the reference tool path and real-time compensation of the fast tool axis W-axis 5.

[0117] The reference toolpath is generated by combining equal-angle sampling with a stable X-axis tool radius compensation algorithm, and the corresponding servo axis components (θ(n), ρ(n), y) in polar coordinates are shown. d (n) can be represented as:

[0118]

[0119] Among them, y d (n) represents the position coordinates of the reference tool path along the depth of cut, w C R is the C-axis rotational speed, n is the index of the discrete point of the reference toolpath, Δt is the time interval between adjacent points, and R W f is the workpiece radius. t This refers to the X-axis feed rate. This is a stable X-axis tool radius compensation function based on tool geometry parameters and target surface features. Since the machine tool Z-axis 1 needs to adjust the height of the diamond tool 54 along the depth of cut in real time to accurately track the target surface, its kinematic and dynamic characteristics become key factors affecting the planning of the reference tool trajectory.

[0120] To circumvent the aforementioned limitations, a zero-phase low-pass filter is used to perform frequency domain decomposition on the components of the reference tool trajectory in the depth of cut, thereby obtaining a low-frequency tool trajectory for controlling the movement of the machine tool axis Z-axis 1.

[0121]

[0122] Among them, y d The low-frequency tool trajectory point is used to control the movement of the machine tool's Z-axis 1. h represents the impulse response of the filter. This indicates that the sequence is reversed. To effectively suppress high-frequency interference components in the tool path, a high-order filter is used to process the reference tool path.

[0123] By selecting an appropriate cutoff frequency, the low-frequency tool trajectory is made to conform to the kinematic and dynamic constraints of the machine tool axis Z-axis 1. The kinematic constraints require that the motion of the machine tool axis Z-axis 1 must meet the maximum speed and acceleration limits.

[0124]

[0125] in, Z-axis velocity, v is the acceleration along the Z-axis. max,z a is the maximum permissible speed along the Z-axis. max,z This represents the maximum allowable acceleration along the Z-axis.

[0126] The dynamic constraints require that the cutoff frequency of the zero-phase low-pass filter should be within the operating bandwidth of machine tool axis Z-axis 1 to avoid machine tool axis Z-axis 1 being in undesirable motion modes or experiencing instability, and the motion error of machine tool axis Z-axis 1 should be less than the maximum permissible error.

[0127]

[0128] Among them, f cut f is the cutoff frequency of the zero-phase low-pass filter. max,ze represents the highest frequency of the working bandwidth of the machine tool's Z-axis 1. z e represents the motion error of the machine tool axis Z-axis 1. max,z This represents the maximum permissible error of the machine tool's Z-axis 1.

[0129] The fast tool axis W-axis 5 is used to compensate for the deviation between the actual displacement of the machine tool axis Z-axis 1 and the reference tool path in real time. It works in conjunction with the machine tool axis Z-axis 1 to achieve accurate tracking of the reference tool path component along the depth of cut. By reading the output signals of the machine tool's linear and angular gratings in real time, the actual displacements of the machine tool axis Z-axis 1 and machine tool axis C-axis 3 can be obtained. The components of the reference tool path at the corresponding moment can be obtained through the spline interpolation function y. d =f(c) is used for calculation, where c is the actual displacement of machine tool axis C-axis 3. By comparing the actual displacement of machine tool axis Z-axis 1 with the interpolation results of the reference tool trajectory along the depth of cut component, the input signal of fast tool axis W-axis 5 is obtained; fast tool axis W-axis 5 adopts as follows Figure 3 The online data-driven control strategy shown combines a high-bandwidth feedback controller with a feedforward controller based on the Koopman operator to ensure that the W-axis 5 of the fast tool axis can effectively track the input deviation.

[0130] The high-bandwidth feedback controller includes a notch filter and a high-gain proportional-integral controller, which are used to suppress the resonant mode of the fast tool axis W-axis 5 and to compensate for the residual nonlinear error caused by hysteresis, respectively. The transfer function of the notch filter can be expressed as:

[0131]

[0132] Among them, w n ξ1 and ξ2 are the center angular frequency of the notch filter, and the damping coefficients affect its attenuation depth and notch bandwidth. These parameters together determine the resonance suppression effect and frequency response characteristics of the notch filter.

[0133] The transfer function of a high-gain proportional-integral controller can be expressed as:

[0134]

[0135] Where, k p and k i These are proportional gain and integral gain, respectively.

[0136] To obtain a high-bandwidth feedback controller with optimal control performance, a parameter optimization model based on frequency response data is constructed: The controller parameters N = [ξ1, ξ2, w] are used. n ,k p ,k i As an optimization variable, with the goal of flattening the frequency response of the feedback controller within the desired bandwidth, the objective function can be expressed as:

[0137]

[0138] Among them, w d w is the highest angular frequency of the desired bandwidth. k Let D(·) be a series of fixed angular frequency points within the desired bandwidth, and let D(·) be the closed-loop transfer function of the feedback controller. By using an optimization algorithm to solve the objective function, the optimal parameter configuration of the high-bandwidth feedback controller can be obtained.

[0139] The feedforward controller based on the Koopman operator can predict the tracking error caused by the nonlinear phase lag of the feedback controller in real time within each sampling period, and adjust the input signal of the W-axis 5 of the fast tool axis online according to the prediction results, so as to achieve near-zero phase lag accurate tracking of the W-axis 5 of the fast tool axis; the future output of the W-axis 5 of the fast tool axis can be expressed as:

[0140]

[0141] in, To characterize the unknown nonlinear function y of the feedback controller's dynamic behavior k+1 For the future output of the feedback controller, y k and r k These represent the current output and input of the feedback controller, respectively; for constructing... The nonlinear mapping relationship is represented by the data-driven Koopman operator theory. By transforming the finite-dimensional nonlinear system into an infinite-dimensional linear space, the dynamics of the system are modeled. Specifically, the extended dynamic mode decomposition algorithm is used to approximate the solution of the infinite-dimensional operator in a finite high-dimensional linear space, thereby reducing computational complexity while preserving the original dynamic information of the system to the maximum extent. Based on this modeling method, the future prediction output of the fast-tool axis W-axis 5 can be expressed as:

[0142]

[0143] in, This represents the predicted output of the fast blade axis W-axis 5 at the (k+1)th sampling point in the future. This is a finite-dimensional approximation of the Koopman operator. After obtaining the approximate parameters of the Koopman operator through offline training and identification, the future tracking error can be predicted online. This error will serve as a reference for adjusting the input trajectory of the W-axis of the fast-track axis.

[0144]

[0145] in, This represents the prediction tracking error at the (k+1)th sampling point in the future.

[0146] Example 3

[0147] Example 3 is a preferred example of Example 1.

[0148] like Figure 4 As shown, this invention provides a cooperative tool servo diamond turning method based on trajectory pre-filtering, which includes the following steps:

[0149] Step 1: Based on the target surface features and tool geometry parameters, plan the reference tool trajectory using equal-angle sampling and a stable X-axis tool radius compensation algorithm;

[0150] Step 2: Implement an online data-driven control strategy for the W-axis, including optimizing the parameters of the high-bandwidth feedback controller and offline training to build a feedforward controller based on the Koopman operator;

[0151] Step 3: Determine the parameters of the zero-phase low-pass filter based on the kinematic and dynamic constraints of the Z-axis, and filter the reference tool path along the depth of cut to obtain the low-frequency tool path;

[0152] Step 4: Use low-frequency toolpath to control the Z-axis movement, and use the W-axis to compensate online for the deviation between the actual Z-axis displacement and the reference toolpath;

[0153] Step 5: Evaluate the collaborative tool servo performance based on trajectory pre-filtering by comprehensively considering surface topography error, surface roughness, and machining efficiency.

[0154] More specifically, based on the target surface features and tool geometry parameters, a reference tool trajectory is planned using equal-angle sampling and a stable X-axis tool radius compensation algorithm; the fast tool axis W-axis 5 is controlled using the NI prototype system; the tools and cutting parameters used, as well as the performance parameters of the machine tool axis Z-axis 1 and fast tool axis W-axis 5, are shown in Tables 1 and 2, respectively:

[0155] Table 1 Tool and Cutting Parameters

[0156]

[0157]

[0158] Table 2 Performance parameters of Z-axis and W-axis

[0159] ultra-precision lathe control system sampling frequency 6000Hz Maximum permissible speed along the Z-axis 10mm / s Maximum permissible acceleration along the Z-axis <![CDATA[1000mm / s 2 ]]> Maximum permissible tracking error along the Z-axis 1μm NI prototype system sampling frequency 20kHz W-axis travel 10μm

[0160] like Figures 5a to 5c As shown, Figure 5a The implementation process of the W-axis controller Figure 5b This is the open-loop frequency response along the W-axis; Figure 5cThis is the training set for the Koopman operator; more specifically, to obtain the open-loop frequency response data of the W-axis 5 of the fast tool axis, a sweep frequency signal with an amplitude of 20V and a frequency range of 1 to 10000Hz is applied to the W-axis 5 to excite its motion. The reference trajectory and the actual displacement of the end effector 53 are acquired through the NI prototype system, and the results are obtained after FFT transformation as shown below. Figure 5b The results show a significant resonance peak in the open-loop frequency response curve, resulting in a small gain margin for the W-axis 5 controller. A parameter optimization model for the feedback controller is established using the obtained open-loop frequency response data, and the optimal parameter combination for the feedback controller is obtained by solving the optimization model using the differential evolution algorithm. The notch filter and proportional-integral controller used can be expressed as follows:

[0161]

[0162] After determining the feedback controller parameters, a sweep frequency signal with an amplitude of 0.5 μm is applied to the feedback control system to excite its motion. The reference trajectory and the actual displacement of the end effector 53 are acquired through the NI prototype system, such as... Figure 5c As shown, the dataset is used as the training dataset for the Koopman operator. After training, the near-zero phase lag of the W-axis of the fast tool is accurately tracked by integrating a high-bandwidth feedback controller with a feedforward controller based on the Koopman operator.

[0163] Specifically, the controller performance of the W-axis 5 of the fast tool axis was tracked and tested using single-frequency and multi-frequency reference trajectories. Table 3 compares the tracking results of different reference trajectories with and without a feedforward controller. The tracking results of the single-frequency reference trajectory with a frequency component of 200Hz and the multi-frequency reference trajectory composed of 60, 120, and 180Hz frequency components are plotted in Table 3. Figure 6 middle;

[0164] Table 3 W-axis controller trajectory tracking results

[0165]

[0166] According to the results shown in Table 3, the PV and RMS values ​​of the tracking error are significantly reduced when using a feedforward controller compared to not using one. For a single-frequency reference trajectory of 200Hz, the PV and RMS values ​​of the tracking error are reduced by 66.7% when using a feedforward controller. For a multi-frequency reference trajectory with frequency components of 60, 120, and 180Hz, the PV value of the tracking error is reduced by 75.3%, and the RMS value is reduced by 75.9%. The results indicate that using a feedforward controller can effectively compensate for the tracking error caused by phase lag, enabling the W-axis 5 of the fast tool to accurately track the input signal.

[0167] A linear sweep frequency signal with an amplitude of 0.5 μm, a maximum frequency of 100 Hz, and a duration of 10 s is applied to the Z-axis 1 of the machine tool to excite its motion. The reference trajectory and actual displacement are synchronously acquired by a multi-axis motion controller to obtain, for example... Figure 7a The Z-axis closed-loop frequency response curve shown shows that the working bandwidth of the machine tool axis Z-axis 1 corresponds to a frequency of 62.3Hz at 3dB. Within this bandwidth range, there are amplitude variations and phase lags, which makes the Z-axis prone to large tracking errors when machining complex optical components. To ensure machining accuracy, it is necessary to reduce the speed of the machine tool axis C-axis 3, thereby affecting the improvement of machining efficiency.

[0168] When applying a linear sweep frequency signal to the W-axis (5) of the fast tool axis, set the maximum frequency to 2000Hz, and keep other parameters the same as the linear sweep frequency signal for the Z-axis (1) of the machine tool, as shown below. Figure 7b The closed-loop frequency response curve of the W-axis shown shows that the working bandwidth of the fast tool axis W-axis 5 at -3dB corresponds to a frequency of 1450.0Hz, which is much higher than the working bandwidth of the machine tool axis Z-axis 1. This indicates that the fast tool axis W-axis 5 has the ability to accurately track the input high-frequency deviation signal.

[0169] Figure 7c In the process of selecting a machining strategy, when the depth of cut of the target surface is less than the travel of the fast tool axis W5, machining is completed solely by using the fast tool axis W5; while when the depth of cut of the target surface is greater than the travel of the fast tool axis W5, machining is completed using the aforementioned collaborative tool servo based on trajectory pre-filtering.

[0170] Specifically, the options are as follows: Figure 8a The 5×5 microlens array shown is used as the target surface to verify the effectiveness of the collaborative tool servo method based on trajectory pre-filtering. The lens unit is designed with a diameter of 1 mm, a depth of 25 μm, and a spacing of 1.1 mm between adjacent lenses. Figure 7c The standard shown requires the use of collaborative tool servo based on trajectory pre-filtering for machining; Figure 8b The distribution of the reference tool path is shown. Under the condition of constant spindle speed, the tool oscillates more significantly in the outer region of the workpiece and has a higher linear velocity. Figure 8c The reference tool trajectory segment along the NN direction has a steep transition at the connection between the structure and the plane, which causes the diamond tool to undergo a sudden position change at the edge of the lens, which can easily lead to tracking errors along the cutting depth direction.

[0171] Figure 9a The cumulative energy frequency, maximum speed, and maximum acceleration corresponding to different C-axis rotation speeds are shown, illustrating the correspondence between the cumulative energy frequency, maximum speed, and maximum acceleration of the reference trajectory along the cutting depth direction and the rotation speed of the C-axis 3 of the machine tool. The cumulative energy frequency is defined as the frequency component corresponding to 98% of the total energy of the trajectory. Figure 9a This indicates that for the same reference tool path, the cumulative energy frequency is directly proportional to the rotational speed of machine tool axis C-axis 3, and that as the rotational speed of machine tool axis C-axis 3 increases, the instantaneous velocity and acceleration also show an increasing trend; for example... Figure 9b For the spectrum, velocity, and acceleration analysis of the C-axis at a speed of 100 RPM, the maximum absolute acceleration is 18252.0 mm / s² when the machine tool axis C-axis 3 speed is 100 RPM. 2 The acceleration has exceeded the maximum allowable acceleration of the machine tool's Z-axis (axis 1), which may lead to insufficient drive capability. According to the proposed method, a zero-phase low-pass filter with a cutoff frequency of 20Hz and an order of 50 is used to pre-filter the original reference trajectory to obtain a low-frequency reference tool trajectory, reducing the maximum absolute acceleration to 436.9 mm / s². 2 It satisfies the maximum acceleration constraint of the machine tool axis Z-axis 1, and compensates the deviation between the actual displacement of the machine tool axis Z-axis 1 and the reference tool trajectory online through the fast tool axis W-axis 5;

[0172] While keeping the filter parameters constant, changing the rotational speed of machine tool axis C3 yields... Figure 10 The tracking results are shown; among them, Figure 10 (a) is 25 RPM; (b) is 50 RPM; (c) is 75 RPM; (d) is 100 RPM. At speeds of 25 and 50 RPM, the tracking error of the fast tool axis W-axis 5 remains within the normal error range of ±20 nm. As the speed increases to 75 RPM, the RMS and PV values ​​of the tracking error are 28 nm and 367 nm, respectively. When the speed reaches 100 RPM, the RMS and PV values ​​of the tracking error are 38 nm and 418 nm, respectively, which are significantly higher than the tracking errors at speeds of 25 and 50 RPM. This indicates that as the speed of the machine tool axis C-axis 3 increases, the tracking error of the fast tool axis W-axis 5 gradually increases. At speeds of 25 and 50 RPM, the fast tool axis W-axis 5 exhibits good tracking performance.

[0173] Figures 11a to 11d The processing results of the lens units in four regions (A, B, C, and D) are shown, demonstrating that the lenses possess excellent shape accuracy; among them, Figure 11a For surface shape error analysis; Figure 11b For surface roughness analysis; Figure 11c A two-dimensional diagram of surface shape error; Figure 11dThe surface roughness is shown in a two-dimensional diagram. When the machine tool axis C3 rotates at 25, 50, and 75 RPM, the PV value of the shape error of the lens unit in region B remains within 1 μm, and the RMS value remains within 100 nm. At the same time, the trend of the surface shape error is consistent with the result of the tracking error, further verifying the influence of rotation speed on machining accuracy. The surface roughness of the machined surface is evaluated by using the root mean square height Sq and the arithmetic mean height Sa. At each rotation speed, the Sq value is less than 6 nm and the Sa value is less than 5 nm. The measured surface roughness of the machined surface is within the ideal range.

[0174] Specifically, the proposed method (TP-CTS) is compared with the traditional Cooperative Tool Servo Technology (CTS). In CTS, the fast tool axis W-axis 5 is controlled by the same controller to compensate for the motion error of the machine tool axis Z-axis 1, but the reference tool trajectory is not pre-filtered. To ensure that the acceleration of the machine tool axis Z-axis 1 does not exceed the threshold specified in Table 2, the spindle speed needs to be reduced to below 10 RPM during CTS machining. Figure 12 The tracking results of CTS are shown. In the region of abrupt tool position change, the tracking error of machine tool axis Z-axis 1 is more obvious. The tracking error of machine tool axis Z-axis 1, which is assigned to fast tool axis W-axis 5, is kept within ±0.5μm. The RMS value and PV value of the tracking error of fast tool axis W-axis 5 are 14nm and 276nm, respectively, which are similar to the results of TP-CTS. However, TP-CTS bypasses the kinematic and dynamic constraints of machine tool axis Z-axis 1 by pre-filtering. Its execution speed is 2.5 times that of CTS, which significantly improves the machining efficiency and reduces the machining time from 4560s to 1824s.

[0175] Figures 13a to 13c The processing results of traditional CTS and TP-CTS were compared, among which, Figure 13a For the overall surface morphology; Figure 13b For surface shape error; Figure 13c For surface roughness, it can be seen that the shape accuracy and surface roughness indicators of the parts processed by CTS and TP-CTS are almost the same. The surface shape error results show that the PV value and RMS value of the surface shape error of lens D processed by CTS are 749nm and 81nm, respectively, while the PV value and RMS value of the surface shape error of lens D processed by TP-CTS are 710nm and 83nm, respectively. The surface roughness results show that the Sa value and Sq value of CTS and TP-CTS are approximately 4nm and 5nm, respectively. This further illustrates that TP-CTS can maintain high processing accuracy and surface quality while improving processing efficiency.

[0176] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0177] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A cooperative tool servo diamond turning method based on trajectory pre-filtering, characterized in that, include: Step S1: By integrating the fast tool axis into the machine tool axis along the depth of cut, a master-slave cooperative tool servo system is constructed; wherein, the machine tool axis serves as the master servo axis of the master-slave cooperative tool servo system, executing the low-frequency tool trajectory obtained after pre-filtering the reference tool trajectory; the fast tool axis serves as the slave servo axis of the master-slave cooperative tool servo system, compensating in real time for the deviation between the actual displacement of the master servo axis and the reference tool trajectory. Step S2: Implement collaborative tool servo machining process based on master-slave collaborative tool servo system; Step S3: After processing, obtain surface contour data and quantitatively evaluate the processing results through surface shape error and surface roughness index; The master-slave cooperative tool servo system includes: machine tool axes C-axis, X-axis, Z-axis, and a fast tool axis W-axis; wherein, the C-axis is responsible for the main rotational motion of the workpiece; the X-axis is used to realize the radial feed of the tool; the Z-axis and W-axis are used to jointly complete the feed of the tool along the depth of cut; the machine tool axes C-axis, X-axis, and Z-axis are synchronously controlled by the machine tool's multi-axis motion controller, and the fast tool axis W-axis moves in coordination with the machine tool axes through a dedicated controller; The online data-driven control strategy adopted by the fast tool axis W-axis includes: a high-bandwidth feedback controller and a feedforward controller; The high-bandwidth feedback controller includes: employing a notch filter to suppress the resonant mode of the W-axis for the servo axis dynamic characteristics, and compensating for the nonlinear error caused by the W-axis hysteresis through a high-gain proportional-integral controller; The feedforward controller includes: applying the Koopman operator to perform dynamic modeling of the feedback control loop of the slave axis, using real-time data to predict the tracking error, and adjusting the input signal of the slave axis online according to the prediction result to achieve tracking with near-zero phase lag of the slave axis; The transfer function of the notch filter in the high-bandwidth feedback controller is shown below: in, The center angular frequency of the notch filter. and The damping coefficient affects the attenuation depth and notch bandwidth; these parameters together determine the resonance suppression effect and frequency response characteristics of the notch filter. To obtain a high-bandwidth feedback controller with optimal control performance, a parameter optimization model based on frequency response data is constructed, and the optimal parameter configuration of the high-bandwidth feedback controller is obtained by solving the parameter optimization model. With controller parameters As the optimization variable, the objective is to make the frequency response of the feedback controller tend to flatten within the desired bandwidth. The objective function is as follows: in, The highest angular frequency of the desired bandwidth. For a series of fixed angular frequency points within the desired bandwidth, This is the closed-loop transfer function of the feedback controller; The optimal parameter configuration of the high-bandwidth feedback controller is obtained by solving the objective function using an optimization algorithm.

2. The collaborative tool servo diamond turning method based on trajectory pre-filtering according to claim 1, characterized in that, The transfer function of the high-gain proportional-integral controller in the high-bandwidth feedback controller is shown below: in, and These are the proportional gain and integral gain, respectively.

3. The collaborative tool servo diamond turning method based on trajectory pre-filtering according to claim 1, characterized in that, The feedforward controller includes: By using real-time data, the tracking error caused by the nonlinear phase lag of the high-bandwidth feedback controller is predicted in each sampling period. Based on the prediction results, the input signal of the W-axis is adjusted online to achieve near-zero phase lag accurate tracking of the W-axis. The future output of the W-axis is represented as: in, An unknown nonlinear function characterizing the dynamic behavior of a high-bandwidth feedback controller. For the future output of the high-bandwidth feedback controller, and These represent the current output and input of the high-bandwidth feedback controller, respectively; for constructing... The nonlinear mapping relationship is represented using data-driven Koopman operator theory. By transforming the finite-dimensional nonlinear system into an infinite-dimensional linear space, the dynamics of the system are modeled. Specifically, the extended dynamic mode decomposition algorithm is used to approximate the solution of the infinite-dimensional operator within a finite high-dimensional linear space, thereby reducing computational complexity while preserving the original dynamic information of the system to the greatest extent. Based on this modeling method, the future prediction output of the W-axis is shown below: in, This represents the predicted output of the W-axis at the (k+1)th sampling point in the future. This is a finite-dimensional approximation of the Koopman operator. After obtaining the approximate parameters of the Koopman operator through offline training and identification, the future tracking error is predicted online. This error will serve as a reference for adjusting the W-axis input trajectory. ； in, This represents the prediction tracking error at the (k+1)th sampling point in the future.

4. The collaborative tool servo diamond turning method based on trajectory pre-filtering according to claim 1, characterized in that, Step S2 includes: Step S2.1: Generate a reference tool path based on the target surface features and tool parameters; Step S2.2: Based on the reference tool path planning, which is constrained by the kinematic and dynamic characteristics along the Z-axis in the depth of cut direction, a low-frequency tool path that meets the preset constraints is obtained after pre-filtering its component along this direction using a zero-phase low-pass filter. The machine tool axis is then driven to move based on the low-frequency tool path that meets the constraints. Step S2.3: Real-time acquisition of the actual Z-axis displacement and comparison with the reference tool path to obtain the deviation between the actual displacement of the main servo axis and the reference tool path, and compensation for the deviation between the two through the W-axis.

5. The collaborative tool servo diamond turning method based on trajectory pre-filtering according to claim 4, characterized in that, Step S2.2 includes: The servo axis components corresponding to the reference tool path in polar coordinates Represented as: in, For reference, the position coordinates of the tool path along the depth of cut, Where n is the C-axis rotational speed, and n is the index of the discrete point of the reference toolpath. The time interval between adjacent points Let the workpiece radius be 1. This refers to the X-axis feed rate. This is a stable X-axis tool radius compensation function based on tool geometry parameters and target surface features; The pre-filtering process includes: performing frequency domain decomposition on the components of the reference tool trajectory along the depth of cut using a zero-phase low-pass filter to obtain the low-frequency tool trajectory, expressed as: in, To control the low-frequency tool trajectory points of the Z-axis motion, The impulse response of the filter. This indicates that the sequence is reversed. To effectively suppress high-frequency interference components in the tool path, a high-order filter is used to process the reference tool path. To ensure that the low-frequency tool path conforms to the kinematic and dynamic constraints of the Z-axis, a suitable cutoff frequency needs to be selected for the zero-phase low-pass filter. The kinematic constraints of the Z-axis require that the Z-axis motion meet the maximum speed and acceleration limits of the machine tool axis, as shown below: in, Z-axis velocity, Z-axis acceleration The maximum permissible speed along the Z-axis. This represents the maximum permissible acceleration along the Z-axis. The Z-axis dynamic constraints require that the cutoff frequency of the zero-phase low-pass filter be within the Z-axis operating bandwidth to avoid the Z-axis being in undesirable motion modes or experiencing instability, and that the motion error of the Z-axis should not exceed the maximum permissible error, as shown below: in, The cutoff frequency of the zero-phase low-pass filter is [the cutoff frequency of the filter]. The highest frequency of the Z-axis operating bandwidth. The motion error along the Z-axis, This represents the maximum permissible error along the Z-axis.

6. A cooperative tool servo diamond turning system based on trajectory pre-filtering, characterized in that, The method for cooperative tool servo diamond turning based on trajectory pre-filtering, as described in any one of claims 1 to 5, includes: Module M1: By integrating the fast tool axis into the machine tool axis along the depth of cut, a master-slave collaborative tool servo system is constructed; wherein, the machine tool axis serves as the master servo axis of the master-slave collaborative tool servo system, executing the low-frequency tool trajectory obtained after pre-filtering the reference tool trajectory; the fast tool axis serves as the slave servo axis of the master-slave collaborative tool servo system, compensating in real time for the deviation between the actual displacement of the master servo axis and the reference tool trajectory; Module M2: Implements collaborative tool servo machining process based on master-slave collaborative tool servo system; Module M3: After processing, it acquires surface contour data and quantifies the processing results through surface shape error and surface roughness indicators.

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