A method, medium, and equipment for controlling the motion of a fast tool axis based on dynamic imbalance.

Abstract

This invention relates to the field of precision machining tool control technology, and in particular to a method, medium, and device for controlling the motion of a fast tool axis based on dynamic unbalance. The method is applied to a dynamic rotary tool cutting system. The method includes: acquiring machining trajectory characteristics in real time; predicting tracking errors using a dynamic unbalance disturbance prediction model; superimposing the errors onto the original trajectory to generate a compensated trajectory; and using the compensated trajectory as a control input. The prediction model is obtained by acquiring data through a frequency sweep signal applied to the U-axis during B-axis rotation, and using Gaussian process regression to learn the mapping relationship between the reference trajectory and the error. This invention predicts and cancels disturbances through a feedforward compensation mechanism, avoiding phase lag, improving trajectory tracking accuracy, solving the problem of dynamic centroid shift caused by U-axis displacement, and improving the machining quality of microlens arrays.

Description

Technical Field

[0001] This invention relates to the field of precision machining tool control technology, and in particular to a method, medium, and device for controlling the motion of a fast tool axis based on dynamic imbalance. Background Technology

[0002] In the field of precision optical component manufacturing, the surface morphology accuracy of microlens arrays is closely related to their optical performance. Currently, Fast Tool Servo (FTS) systems are widely used for the precision machining of freeform microlens arrays. A typical system configuration includes the machine tool's B-axis as the main rotary axis and a two-dimensional fast tool device integrated into the rotating end of the B-axis. This fast tool device typically consists of orthogonally arranged fast tool U-axis (workpiece radial) and fast tool V-axis (depth of cut direction), with the V-axis end used to mount a single-crystal diamond cutting tool. During machining, the machine tool's B-axis provides continuous main rotary motion, while the fast tool U-axis and V-axis perform micro-displacement adjustments according to the target surface shape. The coordinated motion of these three axes forms the helical tool trajectory corresponding to each microlens unit in the large-scale microlens array, achieving precise shaping of the freeform surface.

[0003] However, in the above system configuration, the trajectory tracking accuracy of the fast tool's U-axis is significantly affected by dynamic imbalance disturbances. Since the fast tool device is directly fixed to the end of the B-axis of the rotary machine tool, any unevenness in the system's mass distribution will generate centrifugal force and torque when the machine tool's B-axis is rotating at high speed, causing vibration and resulting in trajectory deviation. In the above-mentioned rotary fast tool servo cutting system, such dynamic imbalance disturbances mainly originate from the following two aspects: First, the system struggles to achieve an ideal static equilibrium. Although counterweights can be used for balancing during assembly, the combined effects of machining tolerances, assembly errors, and uneven material density distribution mean the system can only achieve static balance with limited precision. As the machine tool's B-axis speed increases, the centrifugal torque generated by the initial residual imbalance grows proportionally to the square of the angular velocity. At high speeds (e.g., 800 rpm), the amplitude of this disturbance can be hundreds of times greater than at low speeds (e.g., 80 rpm), severely degrading machining accuracy.

[0004] Secondly, during the fabrication of microlens arrays, to ensure precise alignment between the geometric center of each microlens unit and the tool's trajectory, the U-axis of the fast tool needs to be repositioned when machining different units. This process characteristic causes the centroid position of the fast tool assembly to change in real time with the displacement of the U-axis, resulting in a dynamic eccentricity effect. It is worth noting that even if ideal static balance is achieved during initial assembly, any displacement of the U-axis will disrupt the original balance, causing the tool to deviate from its rotation axis. This dynamic centroid offset caused by the active movement of the U-axis has time-varying characteristics, and traditional one-time static balancing techniques cannot effectively suppress it.

[0005] The two types of dynamic imbalance disturbances mentioned above are coupled together under high-speed rotation conditions, severely restricting the trajectory tracking performance of the fast-tool U-axis. Especially when machining irregularly shaped microlenses with sharp edges (such as triangles and quadrilaterals), the fast-tool U-axis needs to accurately track high-frequency changing trajectory commands. However, the periodic disturbances caused by dynamic imbalance lead to system response lag, resulting in rounded edges and surface distortion, significantly reducing optical surface quality. Existing technologies typically use a proportional-integral (PI) controller to form a single closed-loop control system. This method can only correct existing trajectory errors and cannot predict or actively suppress periodic disturbances related to rotation. Therefore, there is an urgent need to develop an advanced control method that can effectively identify and compensate for dynamic imbalance disturbances to improve the trajectory tracking accuracy of the system under high-speed rotation conditions and meet the manufacturing requirements of high-precision freeform surface microlens arrays. Summary of the Invention

[0006] To address one of the aforementioned technical problems, the present invention adopts the following technical solution: According to one aspect of the present invention, a method for controlling the motion of a fast tool axis based on dynamic imbalance is provided, applied to a dynamic rotary tool cutting system. The system includes a machine tool B-axis and a fast tool device fixedly mounted on the rotating end of the machine tool B-axis. The fast tool device includes a fast tool U-axis arranged radially along the workpiece and a fast tool V-axis arranged along the depth of cut. The method is characterized by comprising the following steps: Real-time acquisition of reference signal characteristics of the current processing trajectory; The tracking error is predicted by a pre-trained dynamic imbalance perturbation prediction model. The predicted tracking error is superimposed on the original reference trajectory to generate a compensated reference trajectory signal; The compensated reference trajectory signal is used as the initial control input for the U-axis of the fast tool; The dynamic imbalance disturbance prediction model is obtained through the following methods: Under the condition that the B-axis of the machine tool rotates at a preset speed, a sweep frequency signal is applied to the U-axis of the fast tool to collect the reference trajectory of the U-axis and its corresponding actual output trajectory, and a training dataset is constructed; the frequency range of the sweep frequency signal covers the spectral characteristics required for the machining trajectory; Based on the training dataset, a Gaussian process regression model is used to learn the nonlinear mapping relationship between the reference trajectory features and the tracking error, thereby obtaining a dynamic imbalance disturbance prediction model.

[0007] According to a second aspect of the present invention, a non-transitory computer-readable storage medium is provided, which stores a computer program that, when executed by a processor, implements the above-described method for controlling the motion of a fast tool axis based on dynamic imbalance.

[0008] According to a third aspect of the present invention, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described method for controlling the motion of a fast tool axis based on dynamic imbalance.

[0009] This invention has at least one of the following beneficial effects: This invention constructs a dynamic imbalance disturbance prediction mechanism using a Gaussian process regression model, fundamentally changing the passive response mode of traditional PI control. In this technical solution, the system pre-collects the U-axis sweep frequency response data of the fast tool at a specific B-axis speed. The trained Gaussian process model can accurately establish the nonlinear mapping relationship between the reference trajectory characteristics and the tracking error. During actual machining, the system acquires the current trajectory characteristics in real time and predicts the corresponding error, directly superimposing the compensation amount onto the original reference trajectory to form a feedforward control signal. This "prediction-compensation" mechanism cancels out the disturbance before it actually affects the trajectory, avoiding the inherent phase lag problem of traditional feedback control. Especially when machining microlens units with sharp edges, this method can accurately reproduce the trajectory turning characteristics, significantly improving the edge rounding phenomenon commonly found in traditional methods, making the optical surface morphology closer to the theoretical design, and greatly improving the consistency of the optical performance of the microlens array.

[0010] This invention effectively solves the problem of dynamic centroid shift caused by the displacement of the U-axis of a rotary cutting tool, a problem that existing static balancing techniques cannot overcome. In this technical solution, a swept-frequency signal covering the required spectral characteristics for machining is used during training data acquisition, enabling the Gaussian process model to learn the disturbance characteristics of the U-axis at different positions. In practical applications, the system uses the current position of the U-axis as a key input feature to predict the resulting imbalance disturbance in real time. This design directly addresses the process characteristics of microlens array machining: when the U-axis of the cutting tool shifts to align with the centers of different microlens units, traditional methods cause significant vibrations due to the change in centroid, often requiring a reduction in rotational speed or rebalancing; however, this invention, through a feedforward compensation mechanism, adapts to real-time changes in centroid without interrupting the machining process. This dynamic adaptability allows the system to maintain stable trajectory tracking accuracy throughout the entire machining stroke, ensuring consistency between microlens units at different positions and solving a core process challenge in rotary cutting tool servo systems.

[0011] This invention achieves full-frequency adaptability to various microlens shapes through a data-driven control strategy. In this technical solution, the swept-frequency signal covers the spectral characteristics required for the processing trajectory, enabling the trained Gaussian process model to accurately predict tracking errors at different frequency components. Combined with a dual closed-loop control architecture of "feedforward + feedback," the system can accurately track various trajectory characteristics from low-frequency spherical surfaces to high-frequency sharp edges while maintaining high-speed rotation. Especially under high-speed conditions, since dynamic imbalance disturbances increase proportionally to the square of the rotational speed, traditional PI controllers struggle to effectively suppress them; however, this method, by learning the disturbance characteristics at specific rotational speeds during offline training, can accurately predict and compensate for these disturbances in advance during actual processing, avoiding bandwidth limitations of the control system. This control strategy enables the system to overcome the contradiction between speed and precision, achieving a balance between high speed and high precision. This provides technical support for the high-efficiency, high-quality manufacturing of large-scale microlens arrays, significantly improving the production efficiency and product performance of precision optical components. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 This is an overall structural diagram of a dynamic rotary tool turning system driven by dual piezoelectric ceramics provided in an embodiment of the present invention; Figure 2 This is an overall structural diagram of the dual piezoelectric ceramic driven fast knife device provided in an embodiment of the present invention; Figure 3for Figure 2 A magnified view of the V-axis section of the medium-fast cutting tool; Figure 4 Schematic diagrams of the U-direction flexible hinge structure and the V-direction flexible hinge structure provided in the embodiments of the present invention; Figure 5 The finite element simulation results of the structural stiffness and first-order resonant frequency of the fast tool U-axis and fast tool V-axis provided in the embodiments of the present invention are shown. Figure 6 A comparative schematic diagram of microlens array cutting processes: (a) dynamic rotary tool cutting, (b) fast tool servo cutting, (c) dynamic rotary tool cutting driven by dual piezoelectric ceramics in this invention; Figure 7 A schematic diagram of the harmonic response of the U-axis and V-axis of the fast cutter along the motion direction and the corresponding parasitic motion results provided in an embodiment of the present invention; Figure 8 A flowchart illustrating a method for controlling the motion of a fast tool axis based on dynamic imbalance, provided in an embodiment of the present invention; Figure 9 The following is a schematic diagram of the motion control of the U-axis of the fast cutter provided in the embodiment of the present invention: (a) schematic diagram of the U-axis controller of the fast cutter; (b) trajectory tracking result of the V-axis of the fast cutter. Figure 10 A schematic diagram illustrating the influence of the position and rotation speed of the microlens unit on the processing results provided in this embodiment of the invention: (a) surface roughness and (b) cross-sectional profile error of microlens units with different radial distances, and (c) surface roughness and (d) cross-sectional profile error at different rotation speeds of the machine tool B-axis (including the standard deviation obtained from 5 repeated measurements). Figure 11 A schematic diagram of the processing results of the freeform surface microlens array provided in the embodiments of the present invention: (a) the overall surface shape of the microlens array; (b) the surface shape error of the microlens unit; (c) the cross-sectional profile of the microlens unit; (d) the surface shape of the randomly distributed freeform surface microlens array and the microlens with special shapes.

[0014] Figure Labels 1. Machine tool X-axis; 2. Machine tool Y-axis; 3. Machine tool Z-axis; 4. Machine tool B-axis; 5. Machine tool C-axis; 6. Flexible tool holder; 7. Fast tool U-axis; 71. U-axis support plate; 72. U-axis piezoelectric ceramic actuator; 73. U-axis flexible hinge; 74. U-axis actuator; 8. Fast tool V-axis; 81. V-axis piezoelectric ceramic actuator; 82. V-axis flexible hinge; 83. V-axis actuator; 9. Diamond cutting tool; 10. Workpiece fixture; 11. Mass balance block. Detailed Implementation

[0015] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] As one possible embodiment of the present invention, such as Figure 1-3 As shown, a dual piezoelectric ceramic driven dynamic rotary tool turning system is provided, comprising: The B-axis 4 of the machine tool serves as the main rotary motion axis, used to drive the diamond tool 9 to achieve the main rotary motion.

[0017] The dual piezoelectric ceramic driven high-speed tool device is directly and fixedly mounted on the rotating end of the B-axis 4 of the machine tool, rotating synchronously with the B-axis 4. The device includes a high-speed tool U-axis 7 and a high-speed tool V-axis 8. The high-speed tool U-axis 7 is arranged radially along the workpiece, and the high-speed tool V-axis 8 is orthogonally positioned on the actuator of the high-speed tool U-axis 7 along the depth of cut direction. Both the high-speed tool U-axis 7 and the high-speed tool V-axis 8 drive the actuator via piezoelectric ceramic actuators. The high-speed tool V-axis 8 is used to mount the cutting tool.

[0018] In this process, the rotational motion of the machine tool's B-axis 4 is linked with the micro-displacement motions of the fast tool's U-axis 7 and V-axis 8 to form a realistic helical tool path for machining freeform surface microlens arrays. A dual piezoelectric ceramic driven fast tool device is integrated on the B-axis of an ultra-precision lathe to achieve dynamic rotary tool cutting. During machining, the machine tool's X-axis 1 and Z-axis 3 are controlled to precisely position the tool's rotation axis, driving the B-axis 4, fast tool's U-axis 7, and fast tool's V-axis 8 in conjunction to complete the cutting motion. Each freeform surface microlens unit is machined sequentially using an independent, realistic helical tool path, thus improving the problem of insufficient tool path continuity in traditional slow / fast tool servo turning technology, achieving efficient and highly consistent machining of large-scale freeform surface microlens arrays at higher cutting speeds.

[0019] Specifically, such as Figure 2 and 3 As shown, the V-axis 8 of the fast cutter is completely embedded inside the actuator of the U-axis 7 of the fast cutter, forming an orthogonal series nested structure.

[0020] The QuickTool U-axis 7 includes: The U-axis support plate 71 is fixed to the flexible tool holder 6 and serves as the fixed reference for the U-axis.

[0021] The U-axis piezoelectric ceramic actuator 72 has one end in contact with the U-axis support plate 71 and the other end in contact with the U-axis actuator 74. It achieves extension and contraction along the U-axis by using the inverse piezoelectric effect through the input of an electrical signal.

[0022] A U-axis flexible hinge 73 connects the U-axis support plate 71 and the U-axis actuator 74. The U-axis flexible hinge 73 consists of four identical links, each link including one leaf spring flexible hinge (LSFH) and two right circular flexible hinges (RCFH). The two ends of the leaf spring flexible hinge are respectively connected to the right circular flexible hinges, which are located between the U-axis support plate 71 and the U-axis actuator 74.

[0023] The four links are arranged in pairs, respectively within the gaps on both sides formed by the U-axis support plate 71 and the U-axis actuator 74. Two links in any pair are arranged parallel to each other along the U-axis, and the four links form a symmetrical dual-parallelogram mechanism (DPM). This mechanism converts the axial extension and retraction of the U-axis piezoelectric ceramic actuator 72 into the linear displacement of the U-axis actuator 74, while suppressing non-U-axis parasitic motion and providing elastic restoring force, so that the U-axis can maintain stable motion even under high-frequency vibration.

[0024] A U-axis displacement sensor is used to detect the displacement of the U-axis actuator 74, thereby achieving closed-loop control of the fast-moving tool's U-axis 7. A high-resolution capacitive sensor may also be used.

[0025] like Figure 2 and 3 As shown, the fast tool V-axis 8 includes: The V-axis piezoelectric ceramic actuator 81 has one end in contact with the U-axis actuator 74 and the other end in contact with the V-axis actuator. Extension and contraction along the V-axis are achieved by utilizing the inverse piezoelectric effect through an input electrical signal.

[0026] The V-axis flexible hinge 82 is fixed at one end to the surface of the U-axis actuator 74 and connected to the V-axis actuator at the other end.

[0027] The V-axis flexible hinge 82 consists of eight identical leaf springs, arranged in four groups of two parallel leaf springs per group. Each leaf spring's ends contact the U-axis actuator 74 and connect to the V-axis actuator. The four groups of leaf springs are arranged circumferentially opposite each other around the V-axis actuator, forming a crossed dual-parallelogram mechanism (CDPM). This mechanism converts the axial extension and retraction of the V-axis piezoelectric ceramic actuator 81 into linear displacement of the V-axis actuator, while simultaneously suppressing non-V-axis parasitic motion and providing elastic restoring force.

[0028] A V-axis displacement sensor is used to detect the displacement of the V-axis actuator, thereby enabling closed-loop control of the V-axis 8 of the fast cutter.

[0029] Single-objective optimization models were established for the U-axis 7 and V-axis 8 of the fast cutting tool, respectively, and the parameters corresponding to the U-axis flexible hinge 73 and V-axis flexible hinge 82 were obtained. This ensures that the U-axis 7 and V-axis 8 of the fast cutting tool meet the travel requirements and first-order resonant frequency requirements in the cutting process.

[0030] Specifically, such as Figure 4 As shown, for the U-axis 7 of the fast tool, its coordinate system O xy DPM The following is the representation of the compliance matrix: Among them, To i C is the coordinate transformation matrix. R and C L Let be the compliance matrices of the circular flexible hinge and the leaf spring flexible hinge, respectively. Let l, h, and w be the length, thickness, and width of the leaf spring flexible hinge, respectively, and let R, t, and b be the radius, width, and thickness of the circular flexible hinge, respectively. From this, the U-axis of the fast cutter relative to the reference point o can be further calculated. D Stiffness matrix: Where Ty is a rotation matrix of π radians about the y-axis.

[0031] For the Quick Tool V-axis 8, such as Figure 4 As shown, it is in coordinate system O zx CDPM Relative to reference point O C The stiffness matrix can be expressed as: The first resonant frequency f between the U-axis 7 and V-axis 8 of the fast cutter DPM and f CDPM It can be represented as: Among them, M U and M V These are the equivalent motion masses of the fast cutter's U-axis 7 and V-axis 8, respectively.

[0032] Without considering the preload of the piezoelectric ceramic actuator, the strokes of the fast cutter U-axis 7 and fast cutter V-axis 8 can be obtained according to Newton's second law: Among them, X nom-U and X nom-V The nominal strokes of the U-axis piezoelectric ceramic actuator 72 and the V-axis piezoelectric ceramic actuator 81 are respectively, K nom-U and K nom-VThese are the nominal stiffnesses of the U-axis piezoelectric ceramic actuator 72 and the V-axis piezoelectric ceramic actuator 81, respectively.

[0033] To ensure that the travel and first-order resonant frequency of the fast tool's U-axis 7 and V-axis 8 meet the cutting requirements, corresponding single-objective optimization models are established: Where w1, w2, w3, and w4 are weighting coefficients, and X is... obj-U and X obj-V The target travel distances for the U-axis 7 and V-axis 8 of the fast tool are respectively determined. The model is solved using an optimization algorithm to obtain the flexible hinge parameters that meet the performance requirements.

[0034] In this embodiment, the nominal parameter X of the piezoelectric ceramic actuator used is... nom-U X nom-V K nom-U and K nom-V The target travel X of the fast tool axis are 80μm, 16μm, 91 N / μm and 281 N / μm, respectively. obj-U and X obj-V The values ​​are 60 μm and 15 μm, respectively; the optimization results of the flexible hinge parameters are obtained by solving the model shown in equation (7) using the differential evolution algorithm, as shown in Table 1: Table 1 Based on the optimized parameters of the flexible hinge, the structural stiffness of the U-axis 7 of the fast tool was calculated using a theoretical model to be 30.04 N / μm, with a first-order resonant frequency of 2677 Hz; the structural stiffness of the V-axis 8 of the fast tool was 16.70 N / μm, with a first-order resonant frequency of 11644 Hz. For details, please refer to... Figure 5 The finite element simulation results shown in the figure are the structural deformation simulation results of each flexible hinge under a stress state (100N). The colors in the figure, from blue to red, indicate that the deformation increases. Among them, the displacement data under this stress state (e.g., 3.464×10) -3 The structural stiffness data can be calculated using μm. The calculation results show that the simulation results are basically consistent with the calculation results of the above-mentioned optimization model, indicating that the above-mentioned optimization model has high accuracy and is usable.

[0035] The dual piezoelectric ceramic driven high-speed tool device uses piezoelectric ceramic actuators as inputs for the high-speed tool's U-axis 7 and V-axis 8, enabling the diamond tool 9 to achieve high-frequency micro-displacement along the U-axis and V-axis directions. By optimizing the flexible hinge parameters, both axes exhibit high dynamic response characteristics along the feed direction, and the stroke meets machining requirements. A matching high-speed tool device was developed for the surface features of freeform microlens units, and combined with a feedforward feedback control algorithm to ensure its bandwidth and stability, significantly improving the system's response speed and forming accuracy in the machining of freeform microlens arrays.

[0036] The fast tool U-axis 7 and fast tool V-axis 8 of the dual piezoelectric ceramic driven fast tool device are arranged in orthogonal series, with a compact structure and decoupled from each other along the direction of motion. The moving parts of the fast tool device have small inertia, which can reduce the impact of the device's dynamic imbalance on machining accuracy during the rotation of the machine tool B-axis 4. The requirement for an active dynamic balancing device is small, and the system control is relatively simple.

[0037] like Figure 7 As shown, a trajectory tracking experiment was conducted on the U-axis 7 and V-axis 8 of the fast-actuator. In the experiment, a simple harmonic signal was used as input to measure the output displacement of the U-axis actuator 74 and the V-axis actuator 83. The results show that the output displacement waveforms of the two axes are consistent with the input signals, and the parasitic displacement along the orthogonal directions is negligible. This indicates that the orthogonal series structure of the fast-actuator U-axis 7 and V-axis 8 can effectively achieve displacement decoupling and can be regarded as two independent single-input single-output systems.

[0038] like Figure 1 As shown, the dual piezoelectric ceramic driven dynamic rotary tool turning system also includes: A flexible tool holder 6 is located at the rotating end of the B-axis 4 of the machine tool. The dual piezoelectric ceramic driven high-speed tool device is connected to the B-axis 4 of the machine tool through the flexible tool holder 6. The flexible tool holder 6 is used to adjust the installation position of the dual piezoelectric ceramic driven high-speed tool device on the plane of the B-axis 4 of the machine tool, to perform test cuts and observe the surface processing of the workpiece, until the surface at the axis of rotation is flat and free of residual cutting marks; the flexible tool holder 6 is then locked, at which point the tip of the diamond tool 9 coincides with the axis of rotation of the B-axis 4 of the machine tool, thereby determining the position and orientation of the diamond tool 9 relative to the workpiece.

[0039] A mass balance block 11 is located at the rotating end of the B-axis 4 of the machine tool, on opposite sides of the dual piezoelectric ceramic driven high-speed tool device. It compensates for the weight of the dual piezoelectric ceramic driven high-speed tool device, achieving static balance of the cutting system. This design effectively reduces the initial imbalance of the system and decreases the initial amplitude of dynamic imbalance disturbances.

[0040] A slip ring, mounted on the B-axis 4 of the machine tool, is used to transmit electrical signals between the dual piezoelectric ceramic driven high-speed cutter device and external equipment during rotation, ensuring real-time transmission of control signals and displacement feedback signals for the high-speed cutter U-axis 7 and V-axis 8. If the slip ring is electrically connected to an external industrial control computer, the computer generates control commands based on the real-time rotation angle signal of the B-axis 4 of the machine tool, driving the high-speed cutter U-axis 7 and V-axis 8 to complete radial and depth-of-cut feed movements respectively, and reads the displacement signals of the high-speed cutter axes to achieve closed-loop control.

[0041] In addition, the dual piezoelectric ceramic driven dynamic rotary tool turning system also includes: The machine tool's X-axis 1 and Z-axis 3 are mounted on the base in a T-shape.

[0042] The Y-axis 2 of the machine tool is mounted on the slide of the X-axis 1 of the machine tool.

[0043] The C-axis 5 of the machine tool is mounted on the slide of the Y-axis 2 of the machine tool.

[0044] The workpiece fixture 10 is fixed on the C-axis 5 of the machine tool and is used to hold the workpiece to be processed so that the surface of the workpiece is perpendicular to the rotation axis of the B-axis 4 of the machine tool.

[0045] The B-axis 4 of the machine tool is mounted on the slide of the Z-axis 3 of the machine tool, and the rotation axis of the B-axis 4 is parallel to the movement direction of the Y-axis 2 of the machine tool.

[0046] Specific examples Figure 1As shown, the structure of the dual piezoelectric ceramic driven dynamic rotary tool turning system is detailed below: The machine tool X-axis 1 and Z-axis 3 are mounted on the base in a T-shape. The machine tool Y-axis 2 is mounted on the slide of the machine tool X-axis 1, and the movement directions of the machine tool X-axis 1, Y-axis 2, and Z-axis 3 are perpendicular to each other, used to achieve reciprocating translational motion along a straight line. The machine tool B-axis 4 and C-axis 5 are respectively mounted on the slides of the machine tool Z-axis 3 and Y-axis 2. The rotation axis of the machine tool B-axis 4 is parallel to the movement direction of the machine tool Y-axis 2, used to achieve rotational motion around the axis. The fast tool U-axis 7 and fast tool V-axis 8 are orthogonally connected in series to form... The dual piezoelectric ceramic driven fast tool device has a diamond tool 9 mounted on the actuator end. The device support plate has mounting holes for fixed connection to a flexible tool holder 6. The flexible tool holder 6 is positioned within the B-axis 4 plane of the machine tool and is used to adjust the position of the dual piezoelectric ceramic driven fast tool device, ensuring the tip of the diamond tool 9 is aligned with the rotation axis of the B-axis 4. The workpiece is fixed to the C-axis 5 of the machine tool by a workpiece clamp 10, ensuring the surface to be machined is perpendicular to the rotation axis of the B-axis 4. A mass balance block 11 is installed on the B-axis 4 to compensate for the centrifugal force generated during high-speed rotation, improving the system's dynamic balance performance. The dual piezoelectric ceramic driven fast tool device is electrically connected to an external industrial control computer via a slip ring 12. It can receive control signals from the fast tool U-axis 7 and fast tool V-axis 8 in real time and feed back their displacement detection signals to achieve precise motion control of the fast tool axes.

[0047] In actual machining, the target surface is composed of multiple freeform surface microlens units. An equal-angle sampling strategy combined with a tool radius compensation algorithm is used to generate independent helical tool paths for each microlens unit. To ensure that the machine tool B-axis 4 rotates smoothly and the fast tool U-axis 7 feeds radially at a constant speed while the diamond tool 9 moves along the helical tool path, the reciprocating oscillation motion of the diamond tool 9 is concentrated in the depth of cut direction. Therefore, the tracking accuracy of the fast tool V-axis 8 directly affects the machining accuracy and efficiency of each unit. After determining the machining sequence of each microlens unit, the machine tool X-axis 1 and Z-axis 3 displacements are adjusted before cutting to align the tool rotation axis sequentially with the target center position of each microlens unit. A corresponding CNC program is generated based on the independent helical tool paths and machining sequence to control the dynamic rotary tool cutting system to complete the machining of the freeform surface microlens array.

[0048] like Figure 6As shown, the machining method of microlens arrays using a dual piezoelectric ceramic driven dynamic rotary tool in this invention is compared with the characteristics of existing dynamic rotary tool cutting and fast-tool servo cutting methods for microlens arrays. Based on the structural characteristics of the freeform surface microlens array, the method of this invention generates an independent helical toolpath for each microlens unit and sequentially completes the machining of each unit. Compared with the traditional machining method using a single helical toolpath, this method avoids toolpath differences caused by the different positions of microlens units in the array, thus ensuring consistent cutting states for each unit. Furthermore, this method overcomes the discontinuity limitation of a single helical toolpath in microlens array machining, focusing the machining target on the surface features of a single microlens unit. Through the coordinated linkage of the high-dynamic-response fast-tool axis and the machine tool rotary axis, the precise forming of complex unit structures is achieved, thereby realizing high-precision and high-consistency machining of freeform surface microlens arrays.

[0049] When the fast tool device in the above embodiment is installed at the end of the B-axis 4 of a high-speed rotating machine tool, the centrifugal force generated by the uneven mass distribution of the system increases proportionally to the square of the rotational speed. Traditional PI controllers can only provide feedback correction for existing errors and cannot actively suppress periodic disturbances. Simultaneously, the frequent displacement of the fast tool U-axis 7 during microlens array machining causes real-time changes in the center of mass, resulting in a dynamic eccentricity effect that traditional static balancing techniques cannot resolve. To meet the machining requirements of high-precision freeform surfaces, especially irregularly shaped microlenses, as another possible embodiment of the present invention, such as... Figure 8 As shown, a method for controlling the motion of a fast tool axis based on dynamic unbalance is also provided to solve the above-mentioned technical problems. This method is applied to dynamic rotary tool cutting systems (such as the dual piezoelectric ceramic driven dynamic rotary tool turning system described in the above embodiments). The method includes the following steps: S1: Real-time acquisition of reference signal features of the current machining trajectory. Reference signal features include at least: position, velocity, acceleration, and frequency characteristics of the reference trajectory. They may also include the current position of the fast tool's U-axis 7, the machine tool's B-axis 4 rotational speed, and the machine tool's B-axis 4 phase angle. Acquiring these feature parameters allows the system to comprehensively understand the current machining state, providing necessary input for predicting dynamic imbalance disturbances. Especially when U-axis displacement causes centroid shift, the current position of the fast tool's U-axis 7 serves as a key input feature, enabling the system to accurately predict the resulting dynamic imbalance disturbances.

[0050] By acquiring the reference signal characteristics of the current machining trajectory in real time, and combining them with key parameters such as the current position of the fast tool's U-axis 7, the machine tool's B-axis 4 speed and phase angle, the system can comprehensively grasp the current machining status. In particular, for the centroid shift caused by U-axis displacement, it can accurately predict the resulting dynamic imbalance disturbance, thereby achieving effective prediction and compensation for trajectory tracking errors and improving the system's trajectory tracking accuracy.

[0051] S2: Predict the corresponding tracking error using a pre-trained dynamic imbalance perturbation prediction model.

[0052] By employing a pre-trained dynamic imbalance disturbance prediction model, tracking errors under different frequency, speed, and position conditions can be predicted. This feedforward compensation mechanism enables the system to compensate for errors before they occur, actively suppressing rotation-related periodic disturbances, breaking through the bandwidth limitations of traditional feedback control, and significantly improving the system's anti-interference capability.

[0053] The dynamic imbalance disturbance prediction model is obtained through the following methods: S2.1: Under the condition that the machine tool's B-axis 4 rotates at a preset speed, a sweep frequency signal is applied to the fast tool's U-axis 7 to collect the reference trajectory of the fast tool's U-axis 7 and its corresponding actual output trajectory, thus constructing a training dataset. The frequency range of the sweep frequency signal covers the spectral characteristics required for the machining trajectory. Specifically, the actual machining speed of the machine tool's B-axis 4 is usually set to a constant value. The preset speed is consistent with the actual machining speed of the machine tool's B-axis 4, making the trained dynamic imbalance disturbance prediction model applicable to compensation control under specific speed conditions. Through this data acquisition process, the system can capture the mapping relationship between U-axis motion and tracking error at a specific speed, providing high-quality data for Gaussian process model training.

[0054] If the machine tool B-axis 4 is kept rotating at a fixed speed (e.g., 80 rpm), the fast tool U-axis 7 executes a frequency sweep signal, i.e., reciprocating linear motion, to collect position, speed, and acceleration data of the fast tool U-axis 7 at different frequencies. When collecting data, the frequency sweep signal must cover all frequencies, speeds, accelerations, and position characteristics required for the actual machining trajectory.

[0055] Based on the aforementioned dataset, the following features are constructed: Input features: position, velocity, acceleration, and frequency of the reference trajectory on the U-axis of the fast-tracking device. Output features: corresponding tracking error (the difference between the actual trajectory and the reference trajectory). Then, a Gaussian process regression (GPR) model is trained to establish a nonlinear mapping relationship between the input features and the tracking error.

[0056] S2.2: Based on the training dataset, a Gaussian process regression model is used to learn the nonlinear mapping relationship between the reference trajectory features and the tracking error, thereby obtaining a dynamic imbalance disturbance prediction model.

[0057] Specifically, the Gaussian process regression model can use automatic correlation to determine the kernel function and optimize the hyperparameters by maximizing marginal likelihood estimation. During model training, a sparse Gaussian process algorithm is employed, selecting no more than 100 induced points to reduce computational complexity while meeting real-time control requirements. This model can accurately predict tracking errors under different frequency, speed, and position conditions, providing a reliable basis for feedforward compensation.

[0058] S3: The predicted tracking error is superimposed on the original reference trajectory to generate the compensated reference trajectory signal.

[0059] S4: Use the compensated reference trajectory signal as the initial control input for the U-axis 7 of the fast tool.

[0060] By superimposing the prediction error onto the original reference trajectory, the system compensates for the error before it occurs, effectively avoiding the impact of dynamic imbalance disturbances on trajectory tracking. This feedforward compensation mechanism enables the system to actively suppress rotation-related periodic disturbances, overcoming the bandwidth limitations of traditional feedback control. The initial control input already includes predictive compensation for dynamic imbalance disturbances, making the motion trajectory of the U-axis 7 of the fast tool more accurate.

[0061] S5: Obtain the residual error between the actual output position of the U-axis 7 of the fast tool and the initial control input.

[0062] S6: A proportional-integral (PI) controller is used to adjust the residual error and generate a feedback control signal.

[0063] Regarding the radial motion characteristics of the U-axis 7 of the fast tool, such as Figure 9 As shown in (a), a feedforward feedback control method is used to improve trajectory tracking accuracy. Based on feedforward compensation, the traditional PI controller C(s) is retained as a feedback loop to handle residual errors not fully captured by the feedforward model, external disturbances, and system parameter drift. Where Y... r (t) Reference trajectory of the microlens unit to be processed, Y out (t) represents the actual output trajectory, and the controlled object G(s) represents the dynamic characteristics of the U-axis, including the electromechanical coupling behavior of the piezoelectric ceramic actuator, flexible hinge, and actuator; the predicted tracking error is e(t); the compensated input signal Y is generated. r '(t)=Y r (t)+e(t); The feedback control loop inputs Y after comparison and compensation. r '(t) and actual output Y out The deviation of (t) is adjusted in real time to ensure system stability and robustness. The feedback controller is optimized based on the characteristics of the controlled object, and dynamic compensation is achieved in the feedforward stage using a Gaussian process model. This effectively suppresses the trajectory tracking error of the fast tool U-axis 7 while maintaining system bandwidth and stability. Figure 9 As shown in (b) in the figure, the experimental results show that after feedforward compensation, the actual trajectory of the U-axis 7 of the fast tool is significantly improved in terms of its consistency with the target trajectory.

[0064] S7: The feedback control signal and the feedforward compensation signal are superimposed to jointly control the movement of the U-axis 7 of the fast cutter, forming a feedforward + feedback dual closed-loop control structure. Alternatively, existing conventional high-bandwidth control strategies can be used for the motion control of the U-axis 7 of the fast cutter.

[0065] By superimposing the feedforward compensation signal and the feedback control signal to jointly control the movement of the U-axis 7 of the fast tool, a feedforward + feedback dual closed-loop control structure is formed. This structure utilizes feedforward compensation to actively suppress predictable dynamic imbalance disturbances and feedback control to handle residual errors, ensuring that the system maintains high-precision trajectory tracking even under high-speed rotation conditions. Simultaneously, the use of a PI controller further enhances the system's stability and robustness, reducing the impact of external factors on machining quality.

[0066] This control method can be implemented simply by upgrading the control algorithm through software, without requiring additional mechanical modifications to existing equipment, thus significantly reducing implementation costs. Simultaneously, this method improves the system's adaptability to different microlens shapes, increases production flexibility, and helps enhance the company's market competitiveness.

[0067] Based on the dynamic imbalance-based fast tool axis motion control method proposed in this invention, a dual piezoelectric ceramic driven dynamic rotary tool system is controlled to perform cutting. A white light interferometer is used to measure the surface of the workpiece cut by the dual piezoelectric ceramic driven dynamic rotary tool, to evaluate the influence of the microlens unit position and the machine tool B-axis 4 rotation speed on the machined surface quality. Figure 10 As shown in (a) and (b), the radial position variation of the microlens unit has a relatively small impact on the surface roughness and contour error of the machined surface. Compared with the large surface quality differences of microlens units at different radial positions in traditional fast-tool servo cutting, the method proposed in this invention can significantly improve the consistency of microlens array machining and is beneficial for obtaining uniform surface quality. Figure 10 As shown in (c) and (d), with the increase of the B-axis speed of the machine tool, the surface roughness and contour error of the microlens unit slightly increase, but the overall surface roughness and submicron surface shape error can still be maintained at the nanometer level. This phenomenon may be due to the increase in centrifugal force caused by the increase in speed, which leads to a slight increase in the steady-state error of the system. The comprehensive analysis results show that the technical solution proposed in this invention can still maintain excellent dynamic stability and machining repeatability under high-speed machining conditions.

[0068] like Figure 11As shown in (a) and (b) of this paper, a freeform surface microlens array was machined using the dual piezoelectric ceramic driven dynamic rotary tool cutting technology proposed in this invention. The average surface roughness Sa of the 16 microlens units was measured to be 4.5 nm, with a standard deviation of 0.2 nm, indicating that this method can achieve high-quality and high-repeatability cutting of freeform surface microlens arrays. To evaluate the surface accuracy of the microlens units, as shown in (a) and (b) of this paper, a dynamic rotary tool cutting technology proposed in this invention was used to machine a freeform surface microlens array. Figure 11 As shown in (c), the cross-sectional profiles along the major axis (AA) and minor axis (BB) directions passing through the lens center were extracted and measured. The results show that the measured profiles match the design target profile well, with a profile error PV value of 126 nm along the major axis and 119 nm along the minor axis. Furthermore, as... Figure 11 As shown in (d), the randomly distributed freeform surface microlens array and the freeform surface microlens with special shapes (such as triangular and quadrangular microlens units) were further processed, and good surface quality was obtained. This shows that the method proposed in this invention can make full use of the high dynamic response characteristics of the fast tool axis to achieve the precise forming of complex microlens units, and has good process adaptability and stability.

[0069] Furthermore, although the steps of the method in this disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result. Additional or alternative steps may be omitted, multiple steps may be combined into one step, and / or a step may be broken down into multiple steps.

[0070] From the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, mobile terminal, or network device, etc.) to execute the methods according to the embodiments of this disclosure.

[0071] In an exemplary embodiment of this disclosure, an electronic device capable of implementing the above-described method is also provided.

[0072] Those skilled in the art will understand that various aspects of the present invention can be implemented as systems, methods, or program products. Therefore, various aspects of the present invention can be specifically implemented in the following forms: entirely in hardware, entirely in software (including firmware, microcode, etc.), or in a combination of hardware and software, collectively referred to herein as “circuit,” “module,” or “system.”

[0073] An electronic device according to this embodiment of the invention. The electronic device is merely an example and should not be construed as limiting the functionality or scope of the embodiments of the invention.

[0074] Electronic devices are manifested in the form of general-purpose computing devices. The components of an electronic device may include, but are not limited to: at least one processor, at least one memory, and a bus connecting different system components (including memory and processor).

[0075] The memory stores program code that can be executed by a processor, causing the processor to perform the steps described in the "Exemplary Methods" section above, according to various exemplary embodiments of the present invention.

[0076] The storage may include readable media in the form of volatile storage, such as random access memory (RAM) and / or cache memory, and may further include read-only memory (ROM).

[0077] The storage may also include programs / utilities having a set (at least one) of program modules, including but not limited to: an operating system, one or more applications, other program modules, and program data, each or some combination of these examples may include an implementation of a network environment.

[0078] A bus can represent one or more of several bus architectures, including a memory bus or memory controller, a peripheral bus, a graphics acceleration port, a processor, or a local bus that uses any of the various bus architectures.

[0079] The electronic device can also communicate with one or more external devices (e.g., keyboards, pointing devices, Bluetooth devices, etc.), one or more devices that enable a user to interact with the electronic device, and / or any device that enables the electronic device to communicate with one or more other computing devices (e.g., routers, modems, etc.). This communication can be performed via input / output (I / O) interfaces. Furthermore, the electronic device can communicate with one or more networks (e.g., local area networks (LANs), wide area networks (WANs), and / or public networks, such as the Internet) via a network adapter. The network adapter communicates with other modules of the electronic device via a bus. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with the electronic device, including but not limited to: microcode, device drivers, redundant processors, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0080] In exemplary embodiments of this disclosure, a computer-readable storage medium is also provided, on which a program product capable of implementing the methods described above is stored. In some possible embodiments, various aspects of the present invention may also be implemented as a program product comprising program code that, when the program product is run on a terminal device, causes the terminal device to perform the steps of the various exemplary embodiments of the present invention described in the "Exemplary Methods" section above.

[0081] The program product may employ any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: electrical connections having one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0082] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable signal medium may also be any readable medium other than a readable storage medium, capable of sending, propagating, or transmitting programs for use by or in conjunction with an instruction execution system, apparatus, or device.

[0083] The program code contained on the readable medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0084] Program code for performing the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0085] Furthermore, the accompanying drawings are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention and are not intended to be limiting. It is readily understood that the processes shown in the above drawings do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0086] It should be noted that although several modules or units for the device used to perform actions have been mentioned in the detailed description above, this division is not mandatory. In fact, according to embodiments of this disclosure, the features and functions of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units.

[0087] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for controlling the motion of a fast tool axis based on dynamic unbalance, characterized in that, An application to a dynamic rotary tool cutting system, the system comprising a machine tool B-axis and a high-speed tool device fixedly mounted on the rotating end of the machine tool B-axis, the high-speed tool device comprising a high-speed tool U-axis arranged radially along the workpiece and a high-speed tool V-axis arranged along the depth of cut, characterized in that the method comprises the following steps: Real-time acquisition of reference signal characteristics of the current processing trajectory; The tracking error is predicted by a pre-trained dynamic imbalance perturbation prediction model. The predicted tracking error is superimposed on the original reference trajectory to generate a compensated reference trajectory signal; The compensated reference trajectory signal is used as the initial control input for the U-axis of the fast tool; The dynamic imbalance disturbance prediction model is obtained through the following method: Under the condition that the B-axis of the machine tool rotates at a preset speed, a sweep frequency signal is applied to the U-axis of the fast tool to collect the reference trajectory of the U-axis and its corresponding actual output trajectory, and a training dataset is constructed; the frequency range of the sweep frequency signal covers the spectral characteristics required for the machining trajectory; Based on the training dataset, a Gaussian process regression model is used to learn the nonlinear mapping relationship between the reference trajectory features and the tracking error, thereby obtaining the dynamic imbalance disturbance prediction model.

2. The method according to claim 1, characterized in that, The method further includes: Obtain the residual error between the actual output position of the U-axis of the fast cutter and the initial control input; A proportional-integral controller is used to adjust the residual error to generate a feedback control signal. The feedback control signal and the feedforward compensation signal are superimposed to jointly control the U-axis movement of the fast cutter, forming a feedforward + feedback dual closed-loop control structure.

3. The method according to claim 1, characterized in that, The reference signal features include at least the position, velocity, acceleration, and frequency characteristics of the reference trajectory.

4. The method according to claim 3, characterized in that, The reference signal features also include the current position of the fast tool's U-axis, the machine tool's B-axis speed, and the machine tool's B-axis phase angle.

5. The method according to claim 1, characterized in that, The preset speed is consistent with the actual B-axis speed of the machine tool during processing, so that the dynamic imbalance disturbance prediction model obtained from the training is applicable to compensation control under specific speed conditions.

6. The method according to claim 1, characterized in that, The fast cutting device is a dual piezoelectric ceramic driven fast cutting device, including a fast cutting U-axis and a fast cutting V-axis. The fast cutting U-axis is arranged radially along the workpiece, and the fast cutting V-axis is orthogonally arranged on the actuator of the fast cutting U-axis along the depth of cut direction. Both the fast cutting U-axis and the fast cutting V-axis drive the actuator to move through piezoelectric ceramic actuators. The fast cutting V-axis is used to mount the cutting tool. The rotational motion of the machine tool's B-axis is linked with the micro-displacement motions of the fast tool's U-axis and V-axis to form a real helical tool path, which is used to process free-form surface microlens arrays.

7. The method according to claim 6, characterized in that, The fast cutter V-axis is completely embedded inside the actuator of the fast cutter U-axis, forming an orthogonal series nested structure.

8. The method according to claim 6, characterized in that, The dynamic rotary tool cutting system also includes: A mass balance block is located at the rotating end of the B-axis of the machine tool, on opposite sides of the dual piezoelectric ceramic driven fast tool device, to compensate for the weight of the dual piezoelectric ceramic driven fast tool device and achieve static balance of the tool cutting system.

9. A non-transitory computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements a fast tool axis motion control method based on dynamic imbalance as described in any one of claims 1 to 8.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements a fast tool axis motion control method based on dynamic imbalance as described in any one of claims 1 to 8.

Images