Full-band surface error collaborative control method based on composite structure polishing tool

Abstract

The present invention belongs to the field of ultra-precision machining technology, and specifically discloses a full-band surface error collaborative control method based on a composite structure polishing tool, including: obtaining initial low, medium and high frequency error distribution models. Analyzing the error distribution characteristics of each frequency band on the workpiece surface, and establishing a full-band surface error collaborative control model. Obtaining the material removal depth, and setting the maximum value of the surface error distribution of each frequency band. Adopting the optimal combination algorithm to obtain the optimal driving voltage value, the optimal trajectory and the related parameter combination. According to the optimal parameter combination, a judgment matrix is established to evaluate the execution effect under the parameter combination. According to the judgment matrix, the coefficient value in the collaborative control model is calculated, combined with the external constraints, and substituted into the full-band surface error collaborative control model to obtain the optimal solution and obtain the optimal collaborative control strategy. The present invention can ensure the structural stability of the entire tool, and ensure that the low-frequency surface shape is not damaged while suppressing the medium-frequency PSD1 error.

Description

Technical Field

[0001] The present invention belongs to the field of ultra-precision machining, and in particular relates to a full-band surface error collaborative control method based on a composite structure polishing tool. Background Art

[0002] Ultra-precision processing technology for laser optical components is a core technology in the fields of high-power lasers, ultra-short-intensity lasers, and laser countermeasures. To ensure that laser devices achieve ideal laser beam quality and stable operation under high-throughput conditions, laser optical components are subject to stringent full-band precision control indicators, extreme low-defect control requirements, and high-efficiency, mass-produced, and engineered manufacturing goals. Currently, the main evaluation indicators for the surface accuracy of optical components focus on low- and high-frequency surface error parameters such as PV value, RMS value, and roughness. However, there is no corresponding systematic evaluation of surface errors in the mid-frequency band. Therefore, the control method of full-band surface errors, especially mid-frequency errors, still needs further exploration.

[0003] Among the currently available methods for controlling mid-frequency errors, the most typical is polishing disc optimization for smoothing. Currently, a non-Newtonian fluid polishing disc machining technique has been proposed, based on flexible polishing discs. By actively designing the disc's pressure gradient and studying its matching conditions with aspheric surfaces, this technique has been shown to effectively suppress mid-frequency errors during the grinding and polishing stages while achieving a stable removal function. However, this technique still suffers from weak local polishing correction capabilities, loss of low-frequency surface shape, edge effects, and high equipment costs. Sources of mid-frequency errors also include convolution effects introduced by excessively repeatable machining paths. Controlling mid-frequency errors through trajectory optimization is also a key technology. The airbag polishing technique, developed in the 1990s by the Optical Science Laboratory of the University of London and Zeeko, improves the randomness of the machining path while ensuring good tool-workpiece fit, effectively eliminating low-frequency errors while achieving reasonable control of mid-frequency errors. However, continuous machining can easily increase the mid-frequency errors in the original frequency band, and the airbag is prone to deformation under continuous inflation pressure, making continuous machining unsuitable.

[0004] Furthermore, CCOS industrial robot machining systems are prone to end-of-line jitter during actual machining due to forced vibration or chatter, which can introduce new mid-frequency surface errors during the polishing process. Therefore, suppressing the mid-frequency errors in optical components introduced by industrial robot vibration is a pressing technical challenge.

[0005] However, there is currently no processing method for the above-mentioned technical problems at home and abroad. The present invention suppresses the vibration of the processing system to ensure the low-frequency surface shape during the processing, uses reasonable trajectory planning to reduce the medium-frequency error introduced by continuous processing, and improves the high-frequency surface shape error, thereby realizing coordinated control of the full-band surface shape error. Therefore, the applicant proposes a full-band surface shape error coordinated control method based on a composite structure polishing tool. Summary of the Invention

[0006] In order to make up for the deficiencies of the prior art, the present invention provides a technical solution for a full-band surface error collaborative control method based on a composite structure polishing tool.

[0007] A full-band surface error collaborative control method based on a composite structure polishing tool comprises the following steps:

[0008] Step 1: using a laser interferometer to collect the initial surface error distribution characteristics of the workpiece to be processed, separating the surface error distribution characteristics according to the DT-CWT adaptive theory, and obtaining the initial low, medium, and high frequency error distribution models;

[0009] Step 2: Analyze the error distribution characteristics of each frequency band on the workpiece surface, establish a full-band surface error collaborative control model, and obtain the optimal processing parameter combination;

[0010] Step 3: Obtain the material removal depth and set the maximum value of the surface error distribution in each frequency band;

[0011] Step 4: Combined with the layered correction method, the optimal trajectory control strategy is obtained by suppressing the surface shape error in the high-frequency band and the mid-frequency error in the PSD2 band;

[0012] Step 5: For the surface shape error in the low frequency band and the mid-frequency error in the PSD1 band, study the influence of the grinding and polishing tool mode on the vibration modes of the system, and use the Bayesian algorithm to optimize the optimal processing parameter combination.

[0013] Step 6: To suppress surface errors in the high-frequency band, based on the principle of electroosmosis, the contact stress between the tool and the workpiece is micro-controlled to achieve deterministic material removal. Simulation analysis and machining tests are used to verify the optimal driving voltage range to ensure workpiece surface machining accuracy.

[0014] Step 7: Use the decision matrix to obtain the optimal processing parameter combination decision solution and evaluate the execution effect under the parameter combination;

[0015] Step 8: Calculate the coefficient values in the full-band surface error collaborative control model according to the decision matrix;

[0016] In step 9, the external constraints are combined and substituted into the full-band surface error collaborative control model to obtain the optimal solution and the best collaborative control strategy.

[0017] Furthermore, the process of establishing the full-band surface error collaborative control model in step 2 includes:

[0018] Step 2.1, use Zernike terms to simulate surface irregularities, that is:

[0019]

[0020] Where z is the surface sagittal height, Z i is the aberration of the i-th aspheric surface, r is the polar coordinate radial length in lens units, c is the curvature, k is the conic coefficient, α i The coefficient of the i-th aspheric surface, N is the number of Zernike coefficients, A i The coefficient of the i-th Zernike Standard polynomial, ρ is the normalized radial coordinate of the light, is the angular coordinate of the light, A is the amplitude of the periodic term, ω0 is the frequency of the periodic term, is the phase shift;

[0021] Analyze the surface properties of the workpiece to be processed and determine r, α i , c, k these surface characteristic coefficients;

[0022] Step 2.2: To ensure effective control of the errors in each frequency band, the following problems need to be solved:

[0023]

[0024] The optimal combination of machining parameters that minimizes surface irregularity is obtained by the optimization method, and the judgment matrix is established accordingly:

[0025]

[0026] Where U is the optimal electroosmosis control parameter combination, G is the optimal trajectory parameter combination, F is the optimal vibration suppression related parameter combination, K1, K2, and K3 refer to the determination coefficients of the optimal electroosmosis control parameter combination, the optimal trajectory parameter combination, and the optimal vibration suppression related parameter combination, respectively. P is the determination matrix, P1 is the electroosmosis control parameter determination matrix, P2 is the trajectory parameter determination matrix, and P3 is the vibration suppression parameter determination matrix.

[0027] Step 2.3: Based on the calculation results of step 2.2 and the load constraint conditions of the machining system when machining the workpiece, the optimal machining parameter combination for the coordinated control of the full-band surface error is obtained as shown in formula (4):

[0028]

[0029] Where f is the vibration frequency of the machining system, f min is the minimum vibration frequency of the machining system, f max is the maximum vibration frequency of the machining system, Z min is the minimum irregular sag height of the surface, Z e is the optimal irregular sag height, Z max is the maximum surface irregularity sag, c is the element surface curvature, c0 is the minimum curvature of the element surface, and c1 is the maximum curvature of the element surface;

[0030] In step 2.4, the optimal parameter combination for collaborative control of full-band surface errors is obtained based on the constraints, and a collaborative control model for full-band surface errors is established.

[0031] Furthermore, step 4 includes: using a layered shaping method to quantitatively divide the single removal depth, reasonably designing single-layer processing parameters based on the actual removal depth of each layer after cutting, combining trajectory planning, and quantitatively removing material as needed, specifically including:

[0032] Step 4.1: Use a layered reshaping method to reduce the feed rate, reduce the single-pass material removal depth, and simultaneously reduce the peak-to-valley values of the removal profile during a single removal pass. This allows for mid-frequency error suppression by superimposing removal profiles with lower peak-to-valley values. Because the peak-to-valley values of the material removal profile are positively correlated with the single-pass material removal depth, the single-pass material removal depth is calculated based on the Preston equation, and a material removal model and a surface residual error analysis model are constructed.

[0033] Step 4.2, reasonably plan the spacing of single-layer tracks to control the waviness of the single material removal profile, such as Figure 3 As shown, the number of layers and the single-layer track spacing conditions are input into the material removal model, and then the corresponding simulation experiments are carried out based on the variable combination of the inter-layer position relationship and the track type. The inter-layer position relationship refers to the offset of each single-layer track. The track types include conventional Peano track and Hilbert track. The corresponding material removal profile is obtained, and the variation curve of the two peak values of the material removal profile within the spacing range is plotted. The fitting equation of the two curves and the intersection of the two curves are obtained. The spacing value corresponding to the intersection is the optimal single-layer track spacing. The single-layer track spacing conditions are updated to obtain the optimal single-layer track spacing processing parameters.

[0034] Step 4.3, optimize the dwell time:

[0035] Assuming the optical processing system to be a linear shift-invariant system, we have:

[0036]

[0037] Where e(x,y) is the residual surface error, s(x,y) is the initial surface error, r(x,y) is the material removal function, and d(x,y) is the dwell time function;

[0038] The dwell time must meet the non-negative requirement and the difference between the dwell times of two adjacent points must be less than its upper limit, that is:

[0039]

[0040] Where d(x i ,y i ) and d(x i+1 ,y i+1 ) is the dwell time between two adjacent points, d(x d ,y d ) is the upper limit of the difference in dwell time between two adjacent points;

[0041] Will Perform Fourier transform to get

[0042] E(u,v)=S(u,v)-R(u,v)D(uv) (6)

[0043] Where E(u,v), S(u,v), R(u,v), and D(u,v) are the Fourier transform spectrum functions of e(x,y), s(x,y), r(x,y), and d(x,y), respectively;

[0044] Minimize the residence time, that is, solve

[0045] max||E-S+RD||2 (7)

[0046] Step 4.4, conduct simulation test verification:

[0047] Through simulation software, the material removal depth image is obtained according to pseudo-random paths such as Peano trajectory and Hilbert trajectory. The influence of trajectory spacing, dwell time and pressure-related parameters on the contour removal depth and contour waviness in the material removal model is analyzed, and a time-related smoothing prediction model is established.

[0048] This process primarily controls high-frequency and mid-frequency PSD2 errors. Experimental results reveal the influence of dwell time, trajectory spacing, number of layers, inter-layer positional relationships, and trajectory type on the peak-to-valley values of the material removal profile and trajectory randomness. The impact of the convolution effect introduced by trajectory stacking on mid-frequency errors is also investigated. Combined with a surface residual error analysis model, the DT-CWT adaptive theory is used to separate the surface error distribution characteristics, obtaining trajectory-optimized low-, mid-, and high-frequency error distribution models. These are then compared with the initial surface error distribution characteristics, verifying the time-dependent smoothing prediction model, and obtaining the optimized parameter combination for trajectory planning and layered reshaping coupled with the layered reshaping process.

[0049] Furthermore, the step 5 includes: (verification test) fixing the workpiece to be processed on the work platform, using a polishing device with a gradient lattice composite structure polishing tool as the execution end, setting the external drive voltage, different rotation speeds, feed rate, track spacing, dwell time, single material removal depth and number of layers and other track-related process parameter combinations according to the optimal processing parameter combination requirements obtained in step 2.2, and carrying out process tests. Since the natural frequencies of the various components in the optical processing system are different when they are in operation, it will cause the entire system to produce different modes of vibration, so it is necessary to collect the vibration mode signals of the processing system separately and obtain the modal parameters, re-detect the surface shape error of the workpiece after processing, analyze the suppression effect of the polishing tool on the vibration mode of the processing system, repeat the separation of the surface shape error distribution characteristics in step 1, and establish low, medium and high frequency surface shape error distribution difference models respectively; establish a processing test table. Analyze processing results:

[0050] 1) Analyze the influence of the above-mentioned process parameters and vibration suppression effects on the surface error of each frequency band;

[0051] 2) Using the Bayesian algorithm to study the influence of various processing parameters and vibration modes of each processing system on the surface error in each frequency band;

[0052] 3) Calculate the evaluation index (PV, RMS) as the output objective function c(x);

[0053] 4) Construct a proxy function G(x) to replace the initial objective function c(x) and establish the acquisition function PI;

[0054] 5) Initialize the prior distribution of the surrogate function, select data points so that the acquisition function reaches its maximum value, evaluate the data points in the objective function and obtain their results, use the new data to update the surrogate function, and obtain a posterior distribution (which serves as the prior distribution for the next step);

[0055] 6) Repeat the process in step 5) until the maximum number of iterations is reached; optimize the optimal parameter combination based on the numerical calculation results, and modify the full-band surface error collaborative control model established in step 2.4.

[0056] Furthermore, the step 6 includes:

[0057] Under the goal of achieving coordinated control of full-band surface errors, the polishing tool mode used is a grid structure with a gradient elastic modulus distribution along the radial direction. The tool's rigidity and flexibility cannot be accurately switched, which will cause a certain loss of low-frequency surface shape and affect the deterministic removal of materials. Therefore, the deterministic removal of materials is micro-regulated based on the electroosmosis principle: simulation software is used to establish the tool-workpiece dynamic and static contact stress distribution model under different working conditions, and the influence of various parameters on the dynamic and static contact stress distribution differences is analyzed. The uniformity of the contact stress distribution model is used as an evaluation indicator. For example, the voltage regulation process includes:

[0058] Theoretical calculation process: The electroosmosis control voltage range is preset to 100-1000V, and the electroosmosis drive control equation is established. The electroosmosis drive control equation is substituted into the contact stress distribution model, and the influence of voltage on the contact stress distribution difference is obtained using numerical calculation methods;

[0059] Experimental verification process: Carry out machining tests within 100-1000V, use an online detection system composed of strain gauges and acceleration sensors to detect the tool-workpiece contact stress distribution under different voltages, compare the dynamic and static contact stress distribution models of the tool-workpiece, analyze the fluctuations within 5% of the actual error, and prove the effectiveness of the established model; analyze the uniformity of the actual contact stress distribution, and compare the evaluation indicators to verify the reasonable range of voltage-driven regulation; after the evaluation of each parameter is completed, adjust and optimize the combination of parameters related to electroosmosis regulation.

[0060] Furthermore, the online monitoring system includes a strain gauge and an acceleration sensor. The strain gauge is provided on the rigid layer of the polishing tool to realize real-time monitoring of the contact stress during the processing. The acceleration sensor is provided on the spindle of the polishing tool to realize the rotation speed detection of the polishing tool. Figure 6 As shown, the online detection system converts the collected signals into digital signals and performs filtering and amplification processing, and uses MATLAB software to perform linear fitting on the collected signals to obtain contact stress distribution images and velocity field distribution images during the actual processing process.

[0061] Compared with the prior art, the present invention has the following beneficial effects:

[0062] The present invention is based on a gradient lattice composite structure polishing tool, which adopts a gradient lattice structure as the flexible support of the tool to provide a basis for surface adaptation. At the same time, a homogeneous layer is used to provide a smooth transition for the gradient change of the tool contact stress while ensuring the structural stability of the entire tool, thereby suppressing the medium-frequency PSD1 error while ensuring that the low-frequency surface shape is not damaged. Based on this, the layered shaping and trajectory planning methods are combined, and the single material removal depth, inter-layer position relationship, trajectory type, trajectory spacing and other parameters are reasonably designed through the processing path design combined with the layered shaping method to obtain a parameter combination that effectively controls the high-frequency and medium-frequency PSD2 errors, thereby obtaining an effective control strategy for the surface shape error of the entire frequency band. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 The control method and control effect diagram corresponding to the surface error of each frequency band of the present invention;

[0064] Figure 2 To establish the basic flow chart of the optimal collaborative control strategy;

[0065] Figure 3 Material removal profile curve for obtaining the optimal single-layer track spacing;

[0066] Figure 4 This is a diagram of the specific implementation process of the collaborative control strategy;

[0067] Figure 5 The macroscopic and microscopic diagrams of the tool of the present invention flexibly fitting workpieces with different curvatures;

[0068] Figure 6 Flowchart for processing, analyzing and applying dynamic and static contact stress distribution signals collected by online detection system between tool and workpiece. DETAILED DESCRIPTION

[0069] The present invention will be further described below with reference to the accompanying drawings.

[0070] See also Figures 1-6 A method for collaboratively controlling full-band surface errors based on a composite structure polishing tool is provided, characterized in that it comprises the following steps:

[0071] Step 1: Use a laser interferometer to collect the initial surface error distribution characteristics of the workpiece to be processed, separate the surface error distribution characteristics according to the DT-CWT adaptive theory, and obtain the initial low, medium and high frequency error distribution models.

[0072] Step 2: Analyze the error distribution characteristics of each frequency band on the workpiece surface, such as Figure 2 As shown in FIG, a full-band surface error collaborative control model is established, wherein the establishment process of the full-band surface error collaborative control model includes:

[0073] Step 2.1, use Zernike terms to simulate surface irregularities, that is:

[0074]

[0075] Where z is the surface sagittal height, Z i is the aberration of the i-th aspheric surface, r is the polar coordinate radial length in lens units, c is the curvature, k is the conic coefficient, α i The coefficient of the i-th aspheric surface, N is the number of Zernike coefficients, A i The coefficient of the i-th Zernike Standard polynomial, ρ is the normalized radial coordinate of the light, is the angular coordinate of the light, A is the amplitude of the periodic term, ω0 is the frequency of the periodic term, is the phase shift;

[0076] Analyze the surface properties of the workpiece to be processed and determine r, α i , c, k surface characteristic coefficients;

[0077] Step 2.2: To ensure effective control of the errors in each frequency band, the following problems need to be solved:

[0078]

[0079] The optimal combination of machining parameters that minimizes surface irregularity is obtained by the optimization method, and the judgment matrix is established accordingly:

[0080]

[0081] Where U is the optimal electroosmosis control parameter combination, G is the optimal trajectory parameter combination, F is the optimal vibration suppression related parameter combination, K1, K2, and K3 refer to the determination coefficients of the optimal electroosmosis control parameter combination, the optimal trajectory parameter combination, and the optimal vibration suppression related parameter combination, respectively. P is the determination matrix, P1 is the electroosmosis control parameter determination matrix, P2 is the trajectory parameter determination matrix, and P3 is the vibration suppression parameter determination matrix.

[0082] Step 2.3: Based on the calculation results of step 2.2 and the load constraint conditions of the machining system when machining the workpiece, the optimal machining parameter combination for the coordinated control of the full-band surface error is obtained as shown in formula (4):

[0083]

[0084] Where f is the vibration frequency of the machining system, f min is the minimum vibration frequency of the machining system, f max is the maximum vibration frequency of the machining system, Z min is the minimum irregular sag height of the surface, Ze is the optimal irregular sag height, Z max is the maximum surface irregularity sag, c is the element surface curvature, c0 is the minimum curvature of the element surface, and c1 is the maximum curvature of the element surface;

[0085] In step 2.4, the optimal parameter combination for collaborative control of full-band surface errors is obtained based on the constraints, and a collaborative control model for full-band surface errors is established.

[0086] Step 3: Obtain the material removal depth and set the maximum value of the surface error distribution in each frequency band.

[0087] Step 4: Combined layered shaping method is used, such as Figure 4 As shown in the simulation module, Figure 1 The mid-frequency error of the PSD2 segment introduced by trajectory planning is used to optimize the process parameters of the optical processing system to obtain the optimal trajectory control strategy, including: using a layered shaping method to quantitatively divide the single removal depth, reasonably designing the single-layer processing parameters based on the actual removal depth of each layer after cutting, and combining trajectory planning to quantitatively remove materials as needed, specifically including:

[0088] Step 4.1: Use a layered reshaping method to reduce the feed rate, reduce the single-pass material removal depth, and simultaneously reduce the peak-to-valley values of the removal profile during a single removal pass. This allows for mid-frequency error suppression by superimposing removal profiles with lower peak-to-valley values. Because the peak-to-valley values of the material removal profile are positively correlated with the single-pass material removal depth, the single-pass material removal depth is calculated based on the Preston equation, and a material removal model and a surface residual error analysis model are constructed.

[0089] Step 4.2, reasonably plan the spacing of single-layer tracks to control the waviness of the single material removal profile, such as Figure 3 As shown, the number of layers and the single-layer track spacing conditions are input into the material removal model, and then the corresponding simulation experiments are carried out based on the variable combination of the inter-layer position relationship and the track type. The inter-layer position relationship refers to the offset of each single-layer track. The track types include conventional Peano track and Hilbert track. The corresponding material removal profile is obtained, and the variation curve of the two peak values of the material removal profile within the spacing range is plotted. The fitting equation of the two curves and the intersection of the two curves are obtained. The spacing value corresponding to the intersection is the optimal single-layer track spacing. The single-layer track spacing conditions are updated to obtain the optimal single-layer track spacing processing parameters.

[0090] Step 4.3, optimize the dwell time:

[0091] Assuming the optical processing system to be a linear shift-invariant system, we have:

[0092]

[0093] Where e(x,y) is the residual surface error, s(x,y) is the initial surface error, r(x,y) is the material removal function, and d(x,y) is the dwell time function;

[0094] The dwell time must meet the non-negative requirement and the difference between the dwell times of two adjacent points must be less than its upper limit, that is:

[0095]

[0096] Where d(x i ,y i ) and d(x i+1 ,y i+1 ) is the dwell time between two adjacent points, d(x d ,y d ) is the upper limit of the difference in dwell time between two adjacent points;

[0097] Will Perform Fourier transform to get

[0098] E(u,v)=S(u,v)-R(u,v)D(uv) (6)

[0099] Where E(u,v), S(u,v), R(u,v), and D(u,v) are the Fourier transform spectrum functions of e(x,y), s(x,y), r(x,y), and d(x,y), respectively;

[0100] Minimize the residence time, that is, solve

[0101] max||E-S+RD||2 (7)

[0102] Step 4.4, conduct simulation test verification:

[0103] Through Matlab simulation software, the material removal depth image is obtained according to pseudo-random paths such as Peano trajectory and Hilbert trajectory. The influence of relevant parameters such as trajectory spacing, dwell time and downward pressure on the contour removal depth and contour waviness is analyzed, and a time-related smoothing prediction model is established.

[0104] This process primarily controls high-frequency and mid-frequency PSD2 errors. Experimental results reveal the influence of dwell time, trajectory spacing, number of layers, inter-layer positional relationships, and trajectory type on the peak-to-valley values of the material removal profile and trajectory randomness. The impact of the convolution effect introduced by trajectory stacking on mid-frequency errors is also investigated. Combined with a surface residual error analysis model, the DT-CWT adaptive theory is used to separate the surface error distribution characteristics, obtaining trajectory-optimized low-, mid-, and high-frequency error distribution models. These are then compared with the initial surface error distribution characteristics, verifying the time-dependent smoothing prediction model, and obtaining the optimized parameter combination for trajectory planning and layered reshaping coupled with the layered reshaping process.

[0105] Step 5, such as Figure 4 As shown in the processing test verification module, for the surface error in the low-frequency band and the medium-frequency error in the PSD1 segment, the influence of the grinding and polishing tool mode on the various vibration modes of the system is studied, and the Bayesian algorithm is used to optimize the optimal processing parameter combination, specifically including: (verification test) The workpiece to be processed is fixed on the work platform, and a grinding and polishing device with a gradient lattice composite structure grinding and polishing tool as the execution end is used. According to the requirements of the collaborative control optimal parameter combination, the external driving voltage, different speeds, feed rates, track spacing, dwell time, single material removal depth and number of layers and other trajectory-related process parameter combinations are set to carry out process tests. Due to the different natural frequencies between the various components when the optical processing system is in operation, it will cause the entire system to produce different modes of vibration. Therefore, it is necessary to collect the vibration mode signals of the processing system separately and obtain the modal parameters. The surface surface error of the workpiece after processing is re-detected, and the suppression effect of the grinding and polishing tool on the vibration mode of the processing system is analyzed. The separation of the surface error distribution characteristics in step 1 is repeated to establish low, medium and high frequency surface error distribution difference models respectively; and a processing test table is established. Analyze the processing results: 1) Analyze the influence of the above-mentioned process parameters and vibration suppression effects on the surface errors of each frequency band; 2) Use the Bayesian algorithm to study the influence of each processing parameter and each processing system vibration mode on the surface errors of each frequency band; 3) Calculate the evaluation index (PV, RMS) as the output objective function c(x); 4) Construct the proxy function G(x) to replace the initial objective function c(x), and establish the acquisition function PI; 5) Initialize the prior distribution of the proxy function, select data points so that the acquisition function takes the maximum value, evaluate the data points in the objective function and obtain their results, use the new data to update the proxy function, and obtain a posterior distribution (as the prior distribution for the next step) and repeat the process 5) until the maximum number of iterations is reached; optimize the optimal parameter combination according to the numerical calculation results, and modify the full-band surface error collaborative control model established in step 2.4.

[0106] Among them, the above tool mode refers to: using the active design of the internal structure of the tool, since the tool base is made of transparent resin material and has elastic deformation characteristics, it responds to the change of contact stress in the tool-workpiece contact area to adapt to the surface characteristics of the workpiece, such as Figure 5 As shown in the figure, the shear thickening characteristics of the non-Newtonian fluid filled in the tool are combined to suppress the vibration of the machining system, so that the stress distribution at the high points of the workpiece surface corrugation characteristics is higher than that at the low points, and the material removal at the high points is higher than that at the low points, thereby effectively suppressing the low-frequency surface error of the component and the mid-frequency PSD1 error.

[0107] Step 6, for Figure 1 The high-frequency surface shape error introduced by trajectory planning is suppressed. Based on the principle of electroosmosis, the contact stress between the tool and the workpiece is micro-controlled to achieve deterministic material removal. The optimal driving voltage range is obtained through simulation analysis and machining test verification to ensure the surface machining accuracy of the workpiece. Specifically, the following are included:

[0108] To achieve coordinated control of surface errors across the entire frequency band, deterministic material removal is micro-regulated based on the principle of electroosmosis. ANSYS simulation is used to establish dynamic and static contact stress distribution models between the tool and workpiece under different working conditions. The relationship between various parameters and the differences in dynamic and static contact stress distributions is analyzed, and the uniformity of the contact stress distribution model is used as an evaluation indicator. For example, the voltage regulation process includes:

[0109] Theoretical calculation process: The electroosmosis control voltage range is preset to 100-1000V, and the electroosmosis drive control equation is established. The electroosmosis drive control equation is substituted into the contact stress distribution model, and the influence of voltage on the contact stress distribution difference is obtained using numerical calculation methods;

[0110] Experimental verification process: Carry out machining tests within 100-1000V, use an online detection system composed of strain gauges and acceleration sensors to detect the tool-workpiece contact stress distribution under different voltages, compare the dynamic and static contact stress distribution models of the tool-workpiece, analyze the fluctuations within 5% of the actual error, and prove the effectiveness of the established model; analyze the uniformity of the actual contact stress distribution, and compare the evaluation indicators to verify the reasonable range of voltage-driven regulation; after the evaluation of each parameter is completed, adjust and optimize the combination of parameters related to electroosmosis regulation.

[0111] Step 7: Establish a judgment matrix based on the optimal processing parameter combination and evaluate the execution effect under the parameter combination;

[0112] Step 8: Calculate the coefficient values in the full-band surface error collaborative control model according to the decision matrix;

[0113] In step 9, the external constraints are combined and substituted into the full-band surface error collaborative control model to obtain the optimal solution and the best collaborative control strategy.

[0114] The above-mentioned online monitoring system includes a strain gauge and an acceleration sensor. The strain gauge is arranged on the rigid layer of the polishing tool to realize real-time monitoring of the contact stress during the processing process. The acceleration sensor is arranged on the main shaft of the polishing tool to realize the rotation speed detection of the polishing tool; the online detection system converts the collected signal into a digital signal and performs filtering and amplification processing, and uses MATLAB software to perform linear fitting on the collected signal to obtain the contact stress distribution image and velocity field distribution image during the actual processing process.

[0115] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A full-band surface error collaborative control method based on a composite structure polishing tool, characterized in that: The steps include: Step 1: using a laser interferometer to collect the initial surface error distribution characteristics of the workpiece to be processed, separating the surface error distribution characteristics according to the DT-CWT adaptive theory, and obtaining the initial low, medium, and high frequency error distribution models; Step 2: Analyze the error distribution characteristics of each frequency band on the workpiece surface, establish a full-band surface error collaborative control model, and obtain the optimal processing parameter combination. The establishment process of the full-band surface error collaborative control model includes: Step 2.1, use Zernike terms to simulate surface irregularities, that is: Where z is the surface sagittal height, Z i is the aberration of the i-th aspheric surface, r is the polar coordinate radial length in lens units, c is the curvature, k is the conic coefficient, α i The coefficient of the i-th aspheric surface, N is the number of Zernike coefficients, A i The coefficient of the i-th Zernike Standard polynomial, ρ is the normalized radial coordinate of the light, is the angular coordinate of the light, A is the amplitude of the periodic term, ω0 is the frequency of the periodic term, is the phase shift; Analyze the surface properties of the workpiece to be processed and determine r, α i , c, k these surface characteristic coefficients; Step 2.2: To ensure effective control of the errors in each frequency band, the following problems need to be solved: The optimal combination of machining parameters that minimizes surface irregularity is obtained by the optimization method, and the judgment matrix is established accordingly: Where U is the optimal electroosmosis control parameter combination, G is the optimal trajectory parameter combination, F is the optimal vibration suppression related parameter combination, K1, K2, and K3 refer to the determination coefficients of the optimal electroosmosis control parameter combination, the optimal trajectory parameter combination, and the optimal vibration suppression related parameter combination, respectively. P is the determination matrix, P1 is the electroosmosis control parameter determination matrix, P2 is the trajectory parameter determination matrix, and P3 is the vibration suppression parameter determination matrix. Step 2.3: Based on the calculation results of step 2.2 and the load constraint conditions of the machining system when machining the workpiece, the optimal machining parameter combination for the coordinated control of the full-band surface error is obtained as shown in formula (4): Where f is the vibration frequency of the machining system, f min is the minimum vibration frequency of the machining system, f max is the maximum vibration frequency of the machining system, Z min is the minimum irregular sag height of the surface, Z e is the optimal irregular sag height, Z max is the maximum surface irregularity sagittal height, c is the curvature, c0 is the minimum curvature of the component surface, and c1 is the maximum curvature of the component surface; Step 2.4: Obtain the optimal parameter combination for the coordinated control of full-band surface errors based on the constraints, and establish a coordinated control model for the full-band surface errors. Step 3: Obtain the material removal depth and set the maximum value of the surface error distribution in each frequency band; Step 4: Combined with the layered correction method, the optimal trajectory control strategy is obtained by suppressing the surface shape error in the high-frequency band and the mid-frequency error in the PSD2 band; Step 5: For the surface shape error in the low-frequency band and the mid-frequency error in the PSD1 band, the influence of the polishing tool mode on the vibration modes of the system is studied, and the Bayesian algorithm is used to optimize the optimal processing parameter combination; Step 6: To suppress surface errors in the high-frequency band, based on the principle of electroosmosis, the contact stress between the tool and the workpiece is micro-controlled to achieve deterministic material removal. Simulation analysis and machining tests are used to verify the optimal driving voltage range to ensure workpiece surface machining accuracy. Step 7: Use the decision matrix to obtain the optimal processing parameter combination decision solution and evaluate the execution effect under the parameter combination; Step 8: Calculate the coefficient values in the full-band surface error collaborative control model according to the decision matrix; In step 9, the external constraints are combined and substituted into the full-band surface error collaborative control model to obtain the optimal solution and the best collaborative control strategy.

2. The method for collaboratively controlling full-band surface errors based on a composite structure polishing tool according to claim 1, characterized in that: The step 4 includes: using a layered shaping method to quantitatively divide the single removal depth, reasonably designing single-layer processing parameters based on the actual removal depth of each layer after cutting, combining trajectory planning, and quantitatively removing material as needed, specifically including: Step 4.1: Use a layered reshaping method to reduce the feed rate, reduce the single-pass material removal depth, and simultaneously reduce the peak-to-valley values of the removal profile during a single removal. Intermediate-frequency error suppression is achieved by superimposing removal profiles with low peak-to-valley values. Since the peak-to-valley values of the material removal profile are positively correlated with the single-pass material removal depth, the single-pass material removal depth is calculated according to the Preston equation, and a material removal model and a surface residual error analysis model are constructed. Step 4.2: Rationally plan the spacing between single-layer tracks to control the waviness of the single-layer material removal profile. Input the number of layers and the single-layer track spacing conditions into the material removal model. Then, conduct corresponding simulation experiments based on the variable combination of the inter-layer position relationship and the track type to obtain the corresponding material removal profile. Plot the variation curve of the two peak values of the material removal profile within the spacing range, obtain the fitting equation of the two curves and the intersection of the two curves. The spacing value corresponding to the intersection is the optimal single-layer track spacing. Update the single-layer track spacing conditions to obtain the optimal single-layer track spacing processing parameters. Step 4.3, optimize the dwell time: Assuming the optical processing system to be a linear shift-invariant system, we have: Where e(x,y) is the residual surface error, s(x,y) is the initial surface error, r(x,y) is the material removal function, and d(x,y) is the dwell time function; The dwell time must meet the non-negative requirement and the difference between the dwell times of two adjacent points must be less than its upper limit, that is: Where d(x i ,y i ) and d(x i+1 ,y i+1 ) is the dwell time between two adjacent points, d(x d ,y d ) is the upper limit of the difference in dwell time between two adjacent points; Will Perform Fourier transform to get E(u,v)=S(u,v)-R(u,v)D(uv) (6) Where E(u,v), S(u,v), R(u,v), and D(u,v) are the Fourier transform spectrum functions of e(x,y), s(x,y), r(x,y), and d(x,y), respectively; Minimize the residence time, that is, solve max||E-S+RD||2 (7) Step 4.4, conduct simulation test verification: Through simulation software, material removal depth images are obtained based on pseudo-random paths. The influence of trajectory spacing, dwell time, and pressure on the profile removal depth and profile waviness in the material removal model is analyzed, and a time-dependent smoothing prediction model is established. Combined with the surface residual error analysis model, the above surface error distribution characteristics are separated according to the DT-CWT adaptive theory, and the low, medium and high frequency error distribution models after trajectory optimization are obtained. By comparing the initial surface error distribution characteristics, the time-dependent smoothing prediction model is verified, and the parameter combination under the coupled relationship of optimized trajectory planning and layered correction is obtained.

3. The method for collaboratively controlling full-band surface errors based on a composite structure polishing tool according to claim 1, characterized in that: The step 5 includes: fixing the workpiece to be processed on a work platform, using a polishing device with a gradient lattice composite structure polishing tool as the execution end, setting a trajectory-related process parameter combination according to the optimal processing parameter combination requirements obtained in step 2.2, conducting a process test, respectively collecting vibration modal signals of the processing system and obtaining modal parameters, re-detecting the surface shape error of the processed workpiece, analyzing the suppression effect of the polishing tool on the vibration mode of the processing system, repeating the separation of the surface shape error distribution characteristics in step 1, and establishing low, medium, and high frequency surface shape error distribution difference models respectively; establishing a processing test table; and analyzing the processing results: 1) Analyze the influence of various process parameters and vibration suppression effects on the surface error of each frequency band; 2) Using the Bayesian algorithm to study the influence of various processing parameters and vibration modes of each processing system on the surface error in each frequency band; 3) Calculate the evaluation index as the output objective function c(x); 4) Construct a proxy function G(x) to replace the initial objective function c(x) and establish the acquisition function PI; 5) Initialize the prior distribution of the surrogate function, select data points so that the acquisition function reaches its maximum value, evaluate the data points in the objective function and obtain their results, and use the new data to update the surrogate function to obtain a posterior distribution; 6) Repeat the process in step 5) until the maximum number of iterations is reached; optimize the optimal processing parameter combination based on the numerical calculation results, and modify the full-band surface error collaborative control model established in step 2.

4.

4. The method for collaboratively controlling full-band surface errors based on a composite structure polishing tool according to claim 1, characterized in that: The step 6 comprises: To achieve coordinated control of surface errors across the entire frequency band, deterministic material removal is micro-regulated based on the principle of electroosmosis. Simulation software is used to establish dynamic and static contact stress distribution models between the tool and workpiece under different working conditions. The relationship between various parameters and the differences in dynamic and static contact stress distributions is analyzed. The uniformity of the contact stress distribution model is used as an evaluation indicator. The voltage regulation process includes the following: Theoretical calculation process: The electroosmosis control voltage range is preset to 100-1000V, and the electroosmosis drive control equation is established. The electroosmosis drive control equation is substituted into the contact stress distribution model, and the influence of voltage on the contact stress distribution difference is obtained using numerical calculation methods; Experimental verification process: Carry out machining tests within 100-1000V, use an online detection system composed of strain gauges and acceleration sensors to detect the tool-workpiece contact stress distribution under different voltages, compare the dynamic and static contact stress distribution models of the tool-workpiece, analyze the fluctuations within 5% of the actual error, and prove the effectiveness of the established model; analyze the uniformity of the actual contact stress distribution, and compare the evaluation indicators to verify the reasonable range of voltage-driven regulation; after the evaluation of each parameter is completed, adjust and optimize the combination of parameters related to electroosmosis regulation.

5. The method for collaboratively controlling full-band surface errors based on a composite structure polishing tool according to claim 4, characterized in that: The online monitoring system includes a strain gauge and an acceleration sensor. The strain gauge is arranged on the rigid layer of the polishing tool to realize real-time monitoring of the contact stress during the processing process. The acceleration sensor is arranged on the main shaft of the polishing tool to realize the rotation speed detection of the polishing tool. The online detection system converts the collected signal into a digital signal and performs filtering and amplification processing. The collected signal is linearly fitted using MATLAB software to obtain the contact stress distribution image and velocity field distribution image during the actual processing process.

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