CN111823418B - Ultra-precise fly-cutting machining tool surface shape error compensation and control method - Google Patents
Ultra-precise fly-cutting machining tool surface shape error compensation and control method Download PDFInfo
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Abstract
A surface shape error compensation and control method for an ultra-precise fly-cutting processing machine tool solves the problems that the surface shape error is large, particularly the intermediate frequency error is prominent and the like in the existing ultra-precise fly-cutting processing machine tool. According to an angle signal measured by a spindle angle encoder of the fly-cutting machine tool in real time and a forming rule of the relative vibration of a cutter and a workpiece on the ripple error of the fly-cutting machining surface, the vibration signal measured in real time is input in a reversed phase mode, and the ripple error of the machining surface of the ultra-precise fly-cutting machine tool is restrained by regulating and controlling the position and the posture of a piezoelectric driving nano feeding compensation platform.
Description
Technical Field
The invention relates to the technical field of ultra-precision machining, in particular to a method for compensating and controlling the machining surface shape error of an ultra-precision fly cutting machine tool based on a piezoelectric driving nano feeding platform.
Background
Potassium dihydrogen phosphate (KDP) crystals are widely applied to national major scientific engineering such as laser inertial confinement fusion, laser weapons and the like due to high laser damage threshold, good light transmittance and other excellent optical properties, and are important optical materials for realizing photoelectric switches and frequency doubling conversion. The use performance of the KDP crystal optical element is closely related to the surface topography precision thereof, for example, laser inertial confinement fusion respectively puts different extremely high manufacturing precision requirements on low-frequency surface shape error, medium-frequency ripple error and high-frequency roughness error of the KDP crystal optical element. The KDP crystal is recognized as one of the most difficult optical materials to process due to the characteristics of soft quality, frangibility, easy deliquescence, anisotropy and the like, the traditional grinding and polishing processing technology is difficult to meet the precision requirement required by the KDP crystal optical element, and ultra-precise single-point diamond fly-cutting is the most effective and most widely used technology for processing the KDP crystal optical element at present. A layer of extremely thin material on the surface of a part is removed through a fly cutter, the nanoscale surface quality and the shape precision are directly obtained, but the machined surface of the part generally has obvious waviness errors. The spatial frequency of the waviness error is between that of the surface shape error and the roughness, the wavelength is from tens of micrometers to hundreds of micrometers, and the amplitude is generally lower than 100 nanometers. The medium-frequency micro-wave errors on the processing surface of the KDP crystal can directly influence the optical performance and the quality of a focusing light spot, and the periodic micro-wave can scatter or diffract laser, even cause abnormal focusing of the laser to damage an optical element, so that the laser damage threshold is greatly reduced.
Disclosure of Invention
Aiming at the problem that the machined surface of the existing ultra-precise fly-cutting machine tool generally has obvious waviness errors, the invention provides a compensation and control method for the surface shape errors of the ultra-precise fly-cutting machine tool, which solves the problems, and solves the problems that the existing ultra-precise fly-cutting machine tool has large surface shape errors, particularly has prominent intermediate frequency ripple errors and the like.
The invention is realized by the following technical scheme:
a surface shape error compensation and control method for an ultra-precise fly-cutting processing machine tool comprises the following steps:
s1, establishing a forming rule of a cutter-workpiece relative vibration on a fly-cutting machining surface waviness error;
s2, combining an angle signal measured in real time by a spindle angle encoder of a fly-cutting machine tool based on a forming rule of a waviness error of a fly-cutting processing surface by tool-workpiece relative vibration;
and S3, inputting the vibration signal measured in real time in a reverse phase manner, and realizing real-time compensation of the processed surface shape waviness error by regulating and controlling the position and the posture of the piezoelectric driving nano feeding compensation platform.
Further preferably, in the step S1, the specific operation includes the following steps: establishing a mapping relation between the relative vibration of the cutter and the workpiece and the waviness of the fly-cutting machining surface of the cutter and the workpiece, and obtaining a surface shape simulation model through simulation analysis; obtaining full-band surface shape information of the fly-cutting simulation surface shape through a surface shape simulation model; and effectively decomposing the full-frequency-band surface shape information according to high frequency, medium frequency and low frequency bands, and selecting medium frequency surface shape information to obtain medium frequency surface shape information and a formation rule.
Further preferably, the surface shape simulation model is obtained by the following method:
s11, simulating and analyzing a workpiece-cutter relative vibration rule caused by different amplitudes of intermittent cutting force and frequency domain distribution by using a single-point diamond fly-cutting machine tool overall dynamics model, simultaneously carrying out a process cutting test, detecting vibration signals of a cutter and a workpiece, and verifying a simulation result;
s12, analyzing a spatial motion track of the cutter according to the structural characteristics of the fly-cutting machine tool by combining the rotating speed of the main shaft, the feeding speed and the relative vibration of the cutter and the workpiece;
s13, considering the geometric shape of the diamond cutter, setting the diamond cutter to reflect the cutting edge profile of the diamond cutter to the surface of the workpiece through the relative motion between the cutter and the workpiece to form the surface shape of the workpiece, and establishing a simulation mapping model from the cutter-workpiece relative vibration track to the surface shape by utilizing a three-dimensional shape simulation technology.
In addition, an improved two-dimensional empirical mode decomposition method can be adopted to carry out multi-scale adaptive mode decomposition on the simulation surface shape data, and the local detail information of the surface shape data is extracted; constructing a monogenic surface shape signal based on Riesz technology transformation, calculating the integral frequency of the surface shape, and obtaining a two-dimensional empirical mode decomposition circulation termination condition; extracting a contour curve of the simulated surface shape; combining a single-channel information source separation method for generating a pseudo information source by an optimal matching tracking algorithm, and performing pseudo information source removal separation on the extracted contour curve; during each step of calculation of the optimal matching tracking algorithm, selecting the optimal atoms by using a genetic algorithm, then further performing power spectral density analysis on the separated characteristic profile curve by adopting a space Power Spectral Density (PSD) technology, and calculating the waviness error of the simulated surface shape; and forming a complete simulation analysis prediction algorithm of the error from interrupted cutting to waviness, and researching the change rule of the waviness error of the fly-cutting surface caused by the dynamic behavior of the machine tool by using the algorithm.
Further preferably, the method further comprises performing model identification and optimization control operation on the piezoelectric driving nano-feeding compensation platform, wherein the model identification and optimization control operation comprises at least one or a combination of the following steps:
A. for hysteresis nonlinearity, adopting a genetic algorithm to identify a nonlinear model based on a Bouc-Wen model to obtain hysteresis inverse model parameters;
B. obtaining system linear link model parameters by using a frequency domain identification method;
C. an improved zero-phase feedforward is adopted to eliminate phase errors, and the tracking performance of the piezoelectric driving nano-feed compensation platform is improved;
D. a delay position feedback controller is introduced to increase the damping of the platform, reduce the oscillation generated in the actual operation of the piezoelectric driving nano-feeding compensation platform and improve the bandwidth of the system.
Further preferably, in the step a, the specific operation includes the following steps:
SA1. construction of a system model: a Hammerstein model is adopted to represent a dynamic system of a nanometer feeding compensation platform containing a linear link and a nonlinear link, and the dynamic system is formed by cascading a hysteresis link H (-) and a linear link G (-) in a cascading manner; as shown in formula (1):
wherein u and x are respectively the voltage input of the piezoelectric ceramic and the displacement output of the platform, and m, k and b are linear link parameters respectively representing mass, damping coefficient and rigidity;
SA2, establishing a coupling relation between a hysteresis link and a linear link: the Bouc-Wen model is adopted to describe the piezoelectric voltage-displacement hysteresis phenomenon; for the hysteresis link in the piezoelectric ceramic, according to the formula (1), a dynamic model of a design model system is shown as the formula (2):
wherein d is the dielectric constant of the piezoelectric ceramic, c1And c2Reduced identification parameters for sorting and replacing;
SA3. decoupling operation of coupling relationship between hysteresis link and linear link: the model shown in equation (2 has 8 unknown parameters to be identified as parameter sets { m, b, k, α, β, γ, c }1,c2}; the parameter sets are divided into 2 groups: linear link parameter Kl{ m, b, K } and a non-linear Bouc-Wen model parameter Kbw＝{α,β,γ,c1,c2}; separately identifying non-linear Bouc-Wen model parameters KbwAnd then identifying the linear link parameter Kl。
Further preferably, the coupling relationship between the hysteresis link and the linear link is decoupled:
selecting a low-frequency sinusoidal signal excitation system with the frequency of 1Hz, and measuring the actual displacement of the platform; modeling the hysteresis link by adopting a Bouc-Wen model, identifying the hysteresis link H (-) and obtaining a hysteresis link parameter Kbw(ii) a A small-amplitude sine frequency sweeping signal is selected as an input to excite the system, a linear link G (-) is identified, and a linear link parameter K is obtainedl。
The invention has the following advantages and beneficial effects:
1. the method is based on the change rule of the waviness error of the fly-cutting surface, and combines the angle signal measured by the angle encoder of the main shaft of the fly-cutting machine tool in real time, the vibration signal measured in real time is input in a reverse phase manner, and the real-time compensation of the waviness error of the machined surface is realized by regulating and controlling the position and the posture of the piezoelectric driving nanometer feeding compensation platform. The invention effectively solves the problem that the machining surface of the existing ultra-precise fly-cutting machining tool generally has obvious waviness errors, can improve the cutting machining efficiency of the machine tool, reduces the oscillation generated in the actual operation of the piezoelectric driving nano-feeding compensation platform, improves the system bandwidth, and ensures the performance use requirement of the ultra-precise machining surface shape.
2. According to the invention, through identification and optimization control of the system model, a series of problems of hysteresis nonlinearity, low bandwidth, phase lag when tracking periodic sawtooth waves and the like existing in the piezoelectric driving nano-feed compensation platform are solved, so that the fly-cutting nano-feed compensation platform can accurately track input signals, and the tracking performance of the piezoelectric driving nano-feed compensation platform is improved.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is a schematic diagram of the calculation of the surface shape according to the present invention; FIG. 1(a) shows a mesh partitioning diagram; FIG. 1(b) shows the determination of coordinate node K (x)k,yk) A schematic diagram;
FIG. 2 is a flow chart of a surface mapping algorithm of the present invention;
FIG. 3 is a surface shape simulation result with a vibration frequency of 0 Hz;
FIG. 4 is a result of surface simulation with a vibration frequency of 585 Hz;
FIG. 5 is a schematic diagram of the surface profile compensation of the present invention;
FIG. 6 is a piezoelectric driven nano-feed compensation device;
FIG. 7 is an integrated view of a surface profile compensator and a fly-cutting machine;
FIG. 8 is a diagram of a Hammerstein model architecture for a nano-feed compensation platform;
FIG. 9 is a structural diagram of a Hammerstein platform of a nano-feed compensation platform based on a B-W model;
FIG. 10 is a flowchart of nano-feed compensation stage identification.
The sequence numbers in the figures illustrate: 1-a working platform, 2-a supporting part, 3-a flexible hinge, 4-a micro-displacement driver, 5-a displacement sensor, 6-a base, 7-a supporting bulge, 8-an adsorption hole, 9-a round flexible hinge, 10-a motor, 11-an air static pressure spindle, 12-a liquid static pressure guide rail, 13-a base and 14-a working platform.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to examples and accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not meant to limit the present invention.
Examples
The embodiment provides a surface shape error compensation and control method for an ultra-precise fly-cutting processing machine tool, which comprises the following specific steps:
s1, establishing a forming rule of a cutter-workpiece relative vibration on a fly-cutting machining surface waviness error;
s2, combining an angle signal measured in real time by a spindle angle encoder of a fly-cutting machine tool based on a forming rule of a waviness error of a fly-cutting processing surface by tool-workpiece relative vibration;
and S3, inputting the vibration signal measured in real time in a reverse phase manner, and realizing real-time compensation of the processed surface shape waviness error by regulating and controlling the position and the posture of the piezoelectric driving nano feeding compensation platform.
1. In the step S1, a mapping relation between the relative vibration of the tool and the workpiece and the waviness of the fly-cutting machining surface needs to be established, and a surface-shaped simulation model is obtained through simulation analysis; obtaining full-band surface shape information of the fly-cutting simulation surface shape through a surface shape simulation model; and effectively decomposing the full-frequency-band surface shape information according to high frequency, medium frequency and low frequency bands, and selecting medium frequency surface shape information to obtain medium frequency surface shape information and a formation rule. The specific operation is as follows:
firstly, the mapping algorithm comprises the following calculation steps:
1) performing mesh division on the surface of the workpiece, and determining a node coordinate K (x)k，yk) As shown in fig. 1;
2) calculating the serial number [ i-c, i + c ] of the tool nose track drawn in the distance of the radius of the tool nose before and after the node (screening an interference path);
3) calculating a main shaft rotation angle theta when the ith path track is cut to the position of the K point;
4) calculating the distance d from the point K to the center of the tool nose;
5) obtaining a depth vector of the node K under the 2c blade point tracks, and selecting a maximum value as the depth of the point;
6) and generating a three-dimensional topography of the workpiece, and calculating the surface shape precision.
In the step 3, the accurate position of the spindle rotation angle Θ when the ith track is cut to the position of the point K, that is, the accurate time when the ith track is cut to the point K needs to be calculated, and the time t is calculatedkiThe following transcendental equation needs to be solved:
to solve the equation, the intersection characteristic time of the ith track is determined, and the time constraint condition [ t ] before and after the track is calculatedki -，tki +]And finally, calculating the special solution of the transcendental equation at the point by using a derivative-free optimal algorithm, thereby obtaining the accurate time for the fly-cutting track to cut to the corresponding grid point.
A software algorithm flow chart based on the mapping model described above is shown in fig. 2.
According to the algorithm flow chart (as shown in figure 2), a corresponding surface shape mapping algorithm is developed based on MATLAB, relevant surface shape simulation analysis is carried out, and figure 3 is the surface shape of the cutter-workpiece with vibration of 0Hz and 585Hz respectively obtained by adopting the algorithm. A surface shape simulation model is established aiming at the surface shape simulation algorithm, and full-band surface shape information of the fly-cutting simulation surface shape can be obtained by adding simulation conditions such as geometric parameters of a cutter, cutting parameters, relative vibration between the cutter and a workpiece and the like in the simulation model.
Then, the obtained fly-cutting simulation surface shape full-frequency-band surface shape information is effectively decomposed by adopting a two-dimensional empirical mode decomposition method according to high frequency, medium frequency and low frequency bands, medium frequency surface shape information which is particularly concerned by the invention is selected, and the surface shape decomposition comprises the following specific steps:
1) recording full-frequency-band surface shape information data established based on a surface shape simulation algorithm designed by the invention as F (x, y), wherein x and y are sampling points of rows and columns respectively, recording new surface shape data after boundary data extension as F (x, y), and x and y are sampling points of rows and columns of corresponding surface shape data respectively;
2) for margin internal initialization ri(x, y) ═ f (x, y), i ═ 1; initialize the margin hij(x,y)＝ri(x,y),j＝1；
3) Calculate hij(x, y) local maxima and forming a maximum spectrum, denoted Jij(ii) a For maximum value spectrum JijThe maximum value point in the intermediate value is interpolated to obtain hijUpper envelope surface of (x, y), denoted Bmax(x,y)；
4) Calculate hijLocal minima of (x, y) and forming a spectrum of minima, denoted Sij(ii) a For minimum value spectrum SijThe minimum value point in the intermediate value is interpolated to obtain hijLower envelope surface of (x, y), denoted Bmin(x,y)；
5) Calculate hijAverage envelope surface of (x, y)
6) Extraction ofLocal detail information h of surface shape datai(j+1)(x,y)，hi(j+1)(x,y)＝hij(x,y)-Pij(x,y)；
7) To hi(j+1)(x, y) performing Riesz transformation, wherein the spatial domain expression of the Riesz transformation is as follows:
8) local detail information h for surface shape datai(j+1)(x, y) with a singleton signal of: h isM(x,y)＝(h,Rx*,RyH) is convolution operation, so that local amplitude l of two-dimensional surface data frequency spectrum informationA：
Local phase l of two-dimensional surface data spectrum informationp，
9) The local phase is further calculated to obtain the local frequency l of the two-dimensional surface shape data frequency spectrum informationf：
From a local frequency lfThe overall frequency can be obtained:
10) the end-of-cycle condition is calculated,
if it is
If the wavelength is less than the given cutoff wavelength, returning to the step 5) to carry out the calculation again in a circulating way; if it is
Above a given cutoff wavelength, there is an ith intrinsic mode function BIMFi＝hi(j+1)And updating the margin r of the decompositioni(x,y)＝ri1(x,y)-BIMFi(x,y)。
Finally, based on the result obtained by decomposing the face shape data, the original face shape data of the workpiece after fly-cutting processing can be composed of a plurality of sets of BIMF components and a set of margin data, and the requirement of the BIMF components and the margin data is met
And selecting the intermediate frequency error frequency band after the surface shape is decomposed through a two-dimensional empirical mode to obtain intermediate frequency surface shape information and a forming rule.
2. In step S3, the present embodiment performs model identification and optimization control for a series of problems of non-linearity of hysteresis, low bandwidth, and phase lag when tracking a periodic saw wave existing in the piezoelectric-driven nano-feed compensation platform. For hysteresis nonlinearity, adopting a genetic algorithm to identify a nonlinear model based on a Bouc-Wen model to obtain hysteresis inverse model parameters; and obtaining system linear link model parameters by using a frequency domain identification method. And the improved zero-phase feedforward is adopted to eliminate the phase error, and the tracking performance of the piezoelectric driving nano-feed compensation platform is improved. A delay position feedback controller is introduced to increase the damping of the platform, reduce the oscillation generated in the actual operation of the piezoelectric driving nano feeding compensation platform, improve the system bandwidth and ensure the reliability of a prototype of the piezoelectric driving nano feeding compensation platform. The specific steps are as follows:
a Hammerstein model is adopted to represent a dynamic system of the nano-feed compensation platform containing a linear link and a nonlinear link, and is shown in FIG. 8. Wherein u and x are respectively voltage input and displacement output; the system is composed of a hysteresis link H (-) and a linear link G (-) in cascade connection. According to the figure, the system model of the nanometer positioning platform containing the nonlinear hysteresis link is as follows:
wherein u and x are respectively the voltage input of the piezoelectric ceramic and the displacement output of the platform, and m, k and b are linear link parameters respectively representing the mass \ damping coefficient and the rigidity. For the system such as the formula (2), besides the linear link parameters m, b and k, a suitable model is selected to identify the nonlinear link h (u).
For the dynamic models described in formula (2) and fig. 8, the difficulty of identification is not only the complexity of the hysteresis link model, but also the coupling phenomenon between the two links that is not negligible. However, the only experimental data available for identification are the system voltage input u (t) and the measured displacement output x (t). The intermediate variables w (t), etc. are not measurable. Either link lacks direct input or output data for individual recognition. Therefore, it is necessary to analyze the coupling relationship between the ring segments and adopt an appropriate means to perform decoupling.
A Bouc-Wen model is selected to describe the piezoelectric voltage-displacement hysteresis phenomenon. For the hysteresis element in the piezoelectric ceramic, the dynamic model of the system is written as:
wherein d is the dielectric constant of the piezoelectric ceramic, c1And c2To sort out and replace the reduced identification parameters. The Hammerstein model corresponding to equation (3) is shown in FIG. 9.
Thus, the dynamics in the nano-feed compensation platform analyzed herein can be described by equation (3). There are 8 unknown parameters { m, b, k, alpha, beta, gamma, c to be identified in the model1,c2}. From the above analysis, it is difficult to identify these 8 parameters at the same time. Thus, the parameter set is divided into 2 groups: linear link parameter Kl{ m, b, K } and a non-linear Bouc-Wen model parameter Kbw＝{α,β,γ,c1,c2And respectively adopting different means to identify. This embodiment first identifies non-linear Bouc-Wen model parametersNumber KbwAnd then identifying the linear link parameter Kl。
A model decoupling identification strategy of a nanometer feeding compensation platform is adopted, and basic steps are shown in FIG. 10. Firstly, selecting a low-frequency sinusoidal signal excitation system with the frequency of 1Hz, and measuring the actual displacement of the platform. And modeling the hysteresis link by adopting a Bouc-Wen model. Providing an accurate and rapid identification method to obtain a hysteresis link parameter Kbw. Secondly, selecting a sine sweep frequency signal with small enough amplitude as an input to excite the system, and identifying a linear link G (-) to obtain a linear link parameter Kl。
3. The piezoelectric driving nano-feeding platform surface shape compensation device adopted by the invention adopts a nano-feeding component for an ultra-precise fly-cutting machine tool, which is provided by a published patent (publication number: CN110815613A), and is shown in figure 6. The integrated figure of the surface shape compensation device and the fly-cutting machine is shown in figure 7. The compensation device in the embodiment adopts a piezoelectric driving fly-cutting micro-feeding compensation platform, and adopts a parallel flexible hinge mechanism with a piezoelectric ceramic driver as a driving element and a 4-point driving mode. Each branched chain of the parallel mechanism comprises a flexible hinge mechanism, and the flexible hinge mechanism is formed by combining two round flexible hinges, and the structural schematic diagram is shown in fig. 6. The nanometer feeding compensation mechanism for the ultra-precise fly-cutting processing machine tool can rotate around any rotating shaft in an xy plane, meanwhile, the position of the center is kept unchanged, real-time compensation of the processed surface waviness error is achieved by regulating and controlling the posture of the three-degree-of-freedom piezoelectric driving nanometer feeding compensation platform according to an angle signal fed back by the main shaft angle encoder in real time and in combination with the change rule of the fly-cutting surface waviness error, and the advantages of good decoupling performance, strong bearing capacity, high compensation precision and the like are achieved.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (4)
1. A surface shape error compensation and control method for an ultraprecise fly-cutting processing machine tool is characterized by comprising the following steps:
s1, establishing a forming rule of a cutter-workpiece relative vibration on a fly-cutting machining surface waviness error;
s2, combining an angle signal measured in real time by a spindle angle encoder of a fly-cutting machine tool based on a forming rule of a waviness error of a fly-cutting processing surface by tool-workpiece relative vibration;
s3, inputting the vibration signal measured in real time in a reverse phase manner, and realizing real-time compensation of the processed surface shape waviness error by regulating and controlling the position and the posture of the piezoelectric driving nano feeding compensation platform;
in the step S1, the specific operation includes the following steps: establishing a mapping relation between the relative vibration of the cutter and the workpiece and the waviness of the fly-cutting machining surface of the cutter and the workpiece, and obtaining a surface shape simulation model through simulation analysis; obtaining full-band surface shape information of the fly-cutting simulation surface shape through a surface shape simulation model; effectively decomposing the full-frequency-band surface shape information according to high frequency, medium frequency and low frequency bands, selecting medium frequency surface shape information, and obtaining medium frequency surface shape information and a forming rule;
obtaining a surface shape simulation model by the following method:
s11, simulating and analyzing a workpiece-cutter relative vibration rule caused by different amplitudes of intermittent cutting force and frequency domain distribution by using a single-point diamond fly-cutting machine tool overall dynamics model, simultaneously carrying out a process cutting test, detecting vibration signals of a cutter and a workpiece, and verifying a simulation result;
s12, analyzing a spatial motion track of the cutter according to the structural characteristics of the fly-cutting machine tool by combining the rotating speed of the main shaft, the feeding speed and the relative vibration of the cutter and the workpiece;
s13, considering the geometric shape of the diamond cutter, setting the diamond cutter to reflect the cutting edge profile of the diamond cutter to the surface of the workpiece through the relative motion between the cutter and the workpiece to form the surface shape of the workpiece, and establishing a simulation mapping model from the cutter-workpiece relative vibration track to the surface shape by utilizing a three-dimensional shape simulation technology.
2. The method for compensating and controlling the surface shape error of the ultra-precise fly-cutting machine tool according to claim 1, further comprising performing model identification and optimal control operation on the piezoelectric driven nano-feeding compensation platform, wherein the model identification and optimal control operation comprises at least one or a combination of the following steps:
A. for hysteresis nonlinearity, adopting a genetic algorithm to identify a nonlinear model based on a Bouc-Wen model to obtain hysteresis inverse model parameters;
B. obtaining system linear link model parameters by using a frequency domain identification method;
C. an improved zero-phase feedforward is adopted to eliminate phase errors, and the tracking performance of the piezoelectric driving nano-feed compensation platform is improved;
D. a delay position feedback controller is introduced to increase the damping of the platform, reduce the oscillation generated in the actual operation of the piezoelectric driving nano-feeding compensation platform and improve the bandwidth of the system.
3. The method as claimed in claim 2, wherein the operations in step a include the following steps:
SA1, constructing a system model: a Hammerstein model is adopted to represent a dynamic system of a nanometer feeding compensation platform containing a linear link and a nonlinear link, and the dynamic system is formed by cascading a hysteresis link H (-) and a linear link G (-) in a cascading manner; as shown in formula (1):
wherein u and x are respectively the voltage input of the piezoelectric ceramic and the displacement output of the platform, and m, k and b are linear link parameters respectively representing mass, damping coefficient and rigidity;
SA2, establishing a coupling relation between a hysteresis link and a linear link: the Bouc-Wen model is adopted to describe the piezoelectric voltage-displacement hysteresis phenomenon; for the hysteresis link in the piezoelectric ceramic, according to the formula (1), a dynamic model of a design model system is shown as the formula (2):
wherein d is the dielectric constant of the piezoelectric ceramic, c1And c2Reduced identification parameters for sorting and replacing;
SA3. decoupling operation of coupling relationship between hysteresis link and linear link: the model shown in formula (2) has 8 unknown parameters to be identified as parameter sets { m, b, k, α, β, γ, c1,c2}; the parameter sets are divided into 2 groups: linear link parameter Kl{ m, b, K } and a non-linear Bouc-Wen model parameter Kbw＝{α,β,γ,c1,c2}; separately identifying non-linear Bouc-Wen model parameters KbwAnd then identifying the linear link parameter Kl。
4. The method for compensating and controlling the surface shape error of the ultra-precise fly-cutting machine tool according to claim 3, wherein the coupling relationship between the hysteresis link and the linear link is decoupled:
selecting a low-frequency sinusoidal signal excitation system with the frequency of 1Hz, and measuring the actual displacement of the platform; modeling the hysteresis link by adopting a Bouc-Wen model, identifying the hysteresis link H (-), and obtaining a hysteresis link parameter Kbw；
A small-amplitude sine sweep frequency signal is selected as an input to excite the system, a linear link G (-) is identified, and a linear link parameter K is obtainedl。
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| CN105171521B (en) * | 2015-10-13 | 2017-06-27 | 北京卫星制造厂 | A kind of high accuracy Machining of Shaft-type Parts method based on repeated detection and compensation |
| CN105666711B (en) * | 2016-01-27 | 2017-08-25 | 北京工业大学 | A kind of KDP crystalline materials single-point diamond fly cutting device |
| CN111144193B (en) * | 2019-10-31 | 2023-04-07 | 中国工程物理研究院机械制造工艺研究所 | Relative vibration identification method based on ultra-precise fly-cutting machining surface shape |
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