A dynamic compensation measurement method for straightness of a laser collimation guide rail

Abstract

The application belongs to the technical field of high-end measuring equipment, and particularly discloses a laser collimation guide rail straightness dynamic compensation measurement method, which comprises the following steps: forcibly synchronizing the initial optical two-dimensional displacement signal, the inertial transient angular velocity signal, the inertial transient acceleration signal and the orthogonal temperature field signal output by a multi-sensor integrated measurement head through a global hardware clock bus based on a field programmable gate array in a central synchronous processing unit; and calculating the light path transverse refractive index spatial gradient based on the orthogonal temperature field signal and deducing the false light spot transverse displacement compensation amount vector. The application aims to solve the technical problems that the existing pure optical straightness measurement technology is difficult to strip the light beam transverse thermal bending false image, difficult to decouple high-frequency mechanical vibration and low-frequency geometric deformation under complex dynamic working conditions, thereby affecting the dynamic closed-loop compensation precision and possibly causing system mechanical resonance.

Description

Technical Field

[0001] This invention relates to the technical field of high-end measurement equipment, specifically to a method for dynamic compensation measurement of the straightness of a laser collimation guide rail. Background Technology

[0002] In the fields of modern ultra-precision manufacturing and large-size measurement, high-precision guideways serve as the core physical reference components for achieving linear motion and spatial positioning. Their geometric motion accuracy in three-dimensional space (especially the straightness errors in the horizontal and vertical directions) directly determines the final operational performance of large, high-end equipment. As industrial manufacturing continues to evolve towards extremely long strokes (greater than 10 meters), high dynamics (high acceleration / deceleration feed), and nanometer-level precision, how to achieve real-time perception and precise compensation of the guideway's true straightness error during operation has become a key technical focus of continuous attention and extremely difficult to overcome in the field of precision engineering.

[0003] Existing methods for measuring the straightness and multi-degree-of-freedom errors of linear guideways typically employ a combination of purely optical laser collimation and laser interferometry. Typical high-precision linear guideway error measurement systems generally follow a design paradigm of "isomorphic optical redundancy."

[0004] Specifically, such systems typically place a laser and multiple beam-splitting prisms at the fixed end of the machine tool, and a cornerstone prism at the moving slider end. A large number of quadrant detectors or position-sensitive detectors are used to receive the beam displacements cut into multiple paths by the beam splitters. The core logic is: assuming the beam propagates in an ideal straight line in the air, by analyzing the geometric projection relationship of the beam displacement captured by photodetectors at different physical positions, a complex system of multivariate linear mathematical equations is established, attempting to decouple and separate errors in straightness, yaw angle, pitch angle, and roll angle through purely mathematical means. To overcome the thermal drift of the light source itself, existing technologies typically include a monitoring detector bypassing the light source's emission end to subtract the initial pointing drift of the laser.

[0005] In summary, how to effectively separate transverse refractive index disturbances and high-frequency mechanical vibrations in complex dynamic environments, and to extract the true straightness error of the guide rail and achieve safe closed-loop compensation, is a technical problem faced by those skilled in the art. Summary of the Invention

[0006] This invention provides a dynamic compensation measurement method for the straightness of a laser collimation guide rail. The purpose is to solve the technical problems of existing pure optical straightness measurement technology under complex dynamic conditions, which is difficult to remove the lateral thermal bending artifact of the beam and difficult to decouple high-frequency mechanical vibration and low-frequency geometric deformation, thereby affecting the accuracy of dynamic closed-loop compensation and potentially causing mechanical resonance of the system.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A method for dynamic compensation measurement of the straightness of a laser collimation guide rail includes: The initial optical two-dimensional displacement signal, inertial transient angular velocity signal, inertial transient acceleration signal, and orthogonal temperature field signal output by the multi-sensor integrated measurement head are forcibly and synchronously acquired through the global hardware clock bus based on the field-programmable gate array inside the central synchronization processing unit. Based on the orthogonal temperature field signal, the spatial gradient of the optical path refractive index is calculated, the lateral displacement compensation vector of the false spot is derived, and it is subtracted from the initial two-dimensional optical displacement signal to obtain the first corrected displacement signal. The inertial transient angular velocity signal is integrated over time to obtain the true angular displacement. The first corrected displacement signal is then corrected by three-dimensional spatial coordinate transformation in combination with the physical eccentric installation vector to obtain the second corrected displacement signal. The time-domain integral step size is used to establish the spatiotemporal mapping between the inertial transient acceleration signal and the second corrected displacement signal, and the low-frequency straightness geometric deviation and high-frequency structural vibration term are separated by the Kalman filter algorithm; The low-frequency straightness geometric deviation is physically canceled by driving the piezoelectric ceramic micro-displacement compensation mechanism; the command transmission link from the high-frequency structural vibration term to the piezoelectric ceramic micro-displacement compensation mechanism is cut off, and it is used only for feedforward interpolation calculation.

[0008] In one aspect of the invention, the forced synchronous acquisition of the initial optical two-dimensional displacement signal, inertial transient angular velocity signal, inertial transient acceleration signal, and orthogonal temperature field signal output by the multi-sensor integrated measurement head via the global hardware clock bus based on a field-programmable gate array within the central synchronization processing unit includes: A laser emitting unit is arranged on the guide rail base to provide a parallel reference beam. The multi-sensor integrated measuring head, which integrates a four-quadrant detector, a three-axis microelectromechanical system accelerometer, a three-axis microelectromechanical system gyroscope, and an orthogonal high-precision platinum resistance temperature sensor array, is fixed on the slider of the guide rail to be tested. Using the internal sampling clock of the triaxial microelectromechanical system accelerometer as the sole reference source, a global synchronization trigger pulse is generated by frequency division through a phase-locked loop; By using the global synchronization trigger pulse to simultaneously trigger the analog-to-digital converter and the environmental sensor interface, it is ensured that the acquired initial optical two-dimensional displacement signal, inertial transient angular velocity and acceleration signal, and orthogonal temperature field signal strictly point to the same transient moment on the physical timeline.

[0009] In one aspect of the present invention, the step of calculating the spatial gradient of the optical path refractive index based on the orthogonal temperature field signal, deriving the spurious spot lateral displacement compensation vector, and subtracting it from the initial two-dimensional optical displacement signal to obtain the first corrected displacement signal includes: Obtain the current atmospheric pressure value and part of the water vapor pressure value, and combine them with the improved Edren mathematical model to calculate the absolute correction value of the air refractive index; The absolute correction value is added to the baseline air refractive index under undisturbed conditions to obtain the true air refractive index parameter for the current environment; Multiply the spatial gradient of the optical path's lateral refractive index by the reciprocal of the real air refractive index parameter, and perform the first-order spatial integration and the second-order spatial integration sequentially along the physical propagation direction of the beam to obtain the lateral displacement compensation vector of the false spot in the horizontal axis direction and the vertical axis direction. By subtracting the spurious spot lateral displacement compensation vector from the initial optical two-dimensional displacement signal using vector subtraction, the first corrected displacement signal, stripped of environmental thermodynamic interference, is output.

[0010] In one aspect of the invention, the step of time-integrating the inertial transient angular velocity signal to obtain the true angular displacement, and then performing three-dimensional spatial coordinate transformation correction on the first corrected displacement signal in conjunction with the physical eccentric installation vector to obtain the second corrected displacement signal includes: Establish the physical eccentricity mounting vector between the actual rotation center of the slider and the geometric center of the four-quadrant detector in the multi-sensor integrated measuring head; The spatial cross product of the physical eccentric installation vector and the angular displacement vector formed by the actual angular displacement is performed to obtain the translational error component induced by the slider attitude deflection coupling. The first corrected displacement signal is expanded to a three-dimensional homogeneous coordinate system, multiplied by the three-dimensional direction cosine rotation transformation matrix, and then superimposed with the translation error component to complete the complete compensation of the Abbe error and output the second corrected displacement signal.

[0011] In one aspect of the invention, the step of establishing a spatiotemporal mapping between the inertial transient acceleration signal and the second corrected displacement signal using a time-domain integration step size, and separating the low-frequency straightness geometric deviation and high-frequency structural vibration term using a Kalman filter algorithm includes: Initialize a five-dimensional state vector, which is strictly composed of the low-frequency straightness geometric deviation, high-frequency vibration velocity, high-frequency vibration acceleration, low-frequency environmental drift residual of the laser beam, and the high-frequency structural vibration term; Establish a state transition equation containing a state transition matrix. In the discrete iterative operation, multiply the inertial transient acceleration signal of the previous moment by the time domain integration step size and superimpose it onto the high-frequency vibration velocity of the previous moment to force an update of the current velocity state. An observation equation is established, and the second corrected displacement signal is defined in the mathematical model as a linear superposition of the low-frequency straightness geometric deviation and the high-frequency structural vibration term; Trust weights are assigned online using the Kalman gain matrix to isolate high-frequency fluctuation characteristics into the high-frequency structural vibration term, and the low-frequency straightness geometric deviation after removing the mechanical high-frequency resonance component is output.

[0012] In one aspect of the invention, the step of physically canceling the low-frequency straightness geometric deviation driven by the piezoelectric ceramic micro-displacement compensation mechanism; and cutting off the command transmission link from the high-frequency structural vibration term to the piezoelectric ceramic micro-displacement compensation mechanism, using it only for feedforward interpolation calculations, includes: The low-frequency straightness geometric deviation is sent to the servo control system of the guide rail in the form of digital signal packets via fieldbus. The servo control system converts digital signal packets into analog voltage signals, which physically drive the piezoelectric ceramic micro-displacement compensation mechanism to generate equal-amplitude and opposite-axis mechanical displacements, thereby offsetting the static and low-frequency deformation errors of the guide rail profile in real time. The physical execution authority of the high-frequency structural vibration item is intercepted at the bottom layer of the control architecture, and it is fed back to the host computer CNC system as an independent compensation residual data stream, which only participates in the tool trajectory advance interpolation prediction of the machining program.

[0013] In one aspect of the invention, before calculating the spatial gradient of the optical path's transverse refractive index based on the orthogonal temperature field signal, deriving the spurious spot transverse displacement compensation vector, and subtracting it from the initial two-dimensional optical displacement signal to obtain the first corrected displacement signal, a dynamic displacement gain compensation stage is further included, specifically comprising: The system receives real-time feedback signals of the absolute position of the slider from an external grating ruler to obtain the current measurement distance. Combining the current measurement distance, the basic beam waist radius of the laser beam, the beam quality factor, and the center wavelength, the evolution proportional constant of the beam diameter is calculated using a nonlinear correction model for the beam shape. The coordinate gain of the initial optical two-dimensional displacement signal is dynamically adjusted nonlinearly using the evolution proportional constant to eliminate the detection sensitivity attenuation caused by beam divergence under long stroke.

[0014] In one aspect of the invention, the internal processing architecture configuration for executing the central synchronization processing unit includes: The field-programmable gate array is configured to process multi-channel high-speed raw data streams, execute low-level digital filtering logic, and control the global hardware clock bus. A high-performance digital signal processor is configured to perform double-precision floating-point matrix operations of the first-order spatial integration, the second-order spatial integration, the three-dimensional spatial coordinate transformation, and the Kalman filter algorithm. A high-speed on-chip bus is constructed to connect the two types of processors for direct memory access and data exchange, ensuring that the overall physical delay from the data acquisition end to the control output end used to output the low-frequency straightness geometric deviation is controlled within a preset millisecond limit.

[0015] Compared with the prior art, the present invention has the following beneficial effects: First, existing pure optical technologies have a blind spot in sensing the aerodynamic bending of long-path beams. This invention introduces an orthogonal high-precision platinum resistance temperature sensor array to calculate the spatial gradient of the transverse refractive index of the optical path by acquiring the orthogonal temperature field of the optical path cross section. Starting from the underlying thermodynamic physical mechanism, this scheme derives and removes the spurious transverse displacement compensation vector from the initial two-dimensional optical displacement signal, outputting a corrected first displacement signal to reduce measurement errors caused by air convection in harsh workshop environments.

[0016] Secondly, addressing the issues of optical path bulkiness and secondary interference caused by the reliance on complex beam-splitting prism arrays for decoupling angles in existing technologies, this invention employs an angle measurement path based on inertial sensors. The system directly utilizes the integration of the inertial transient angular velocity signal from a three-axis microelectromechanical system gyroscope to obtain angular displacement, and combines this with a physically eccentric mounting vector to perform three-dimensional spatial coordinate transformation. This correction method based on a rigid body kinematics model outputs a second corrected displacement signal at a lower hardware cost and reduces the cross-coupling effects between multiple optical signals.

[0017] Furthermore, existing technologies treat the tested guide rail as a quasi-static rigid body, leading to an overlap of geometric deformation and manufacturing vibration. This invention utilizes the global hardware clock bus of a field-programmable gate array (FPGA) to achieve nanosecond-level synchronization of heterogeneous data and introduces a time-domain integration step into the Kalman state-space model to establish a spatiotemporal mapping between the inertial transient acceleration signal and the second corrected displacement signal. This mechanism achieves dynamic-static separation within the mathematical model, decomposing the total displacement into low-frequency straightness geometric deviation and high-frequency structural vibration terms.

[0018] Finally, addressing the issue that existing systems may cause high-frequency whistling in machine tools due to the piezoelectric actuator's feedback of the total error, this invention implements physical shunting at the control output. The system only sends the calculated low-frequency straightness geometric deviation to the piezoelectric ceramic micro-displacement compensation mechanism for physical spatial cancellation; simultaneously, in the underlying logic, the physical execution permission of the high-frequency structural vibration term is cut off, and it is only transmitted to the CNC system for feedforward interpolation calculations. This asymmetric design, while ensuring static compensation accuracy, helps reduce the risk of phase lag and resonance in dynamic compensation. Attached Figure Description

[0019] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.

[0020] Figure 1 This is a flowchart illustrating the steps of a dynamic compensation measurement method for the straightness of a laser collimation guide rail according to the present invention.

[0021] Figure 2 This is a step-by-step flowchart of step 1 of the laser collimation guide rail straightness dynamic compensation measurement method of the present invention.

[0022] Figure 3 This is a step-by-step flowchart of step 2 of the laser collimation guide rail straightness dynamic compensation measurement method of the present invention. Detailed Implementation

[0023] The present invention will be further described below with reference to embodiments. These embodiments are merely some, not all, of the embodiments of the present invention. Other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are all within the protection scope of the present invention.

[0024] Please see Figures 1-3 As shown, this embodiment discloses a method for dynamic compensation measurement of the straightness of a laser collimation guide. To make the purpose, technical solution, and physical implementation mechanism of this invention clearer and more explicit, the various steps of the method described in this invention are explained in detail: The macroscopic system architecture of this invention consists of three main parts: a laser emitting unit, a multi-sensor integrated measuring head, and a central synchronization processing unit. The laser emitting unit is fixed to one end of the guide rail base, the multi-sensor integrated measuring head is mounted on a slider that moves with the guide rail, and the central synchronization processing unit is responsible for data acquisition, fusion calculation, and command distribution throughout the entire process. In practical operation, this method strictly follows these steps in a progressive manner: Step 1: Since the system must establish a unified data reference on a physical time scale before any error decoupling is performed, this step establishes a measurement system that includes a laser emission unit, a multi-sensor integrated measurement head, and a central synchronization processing unit. The global hardware clock bus in the central synchronization processing unit is used to force the synchronous acquisition of the initial optical two-dimensional displacement signal, inertial transient angular velocity signal, inertial transient acceleration signal, and orthogonal temperature field signal output by the multi-sensor integrated measurement head.

[0025] Step 1-1: Physical Deployment of Multi-Source Heterogeneous Reference Hardware The laser emitting unit is arranged on the guide rail base to provide an absolutely parallel physical optical reference beam; the multi-sensor integrated measuring head, which integrates a four-quadrant detector, a three-axis microelectromechanical system accelerometer, a three-axis microelectromechanical system gyroscope, and an orthogonal high-precision platinum resistance temperature sensor array, is fixed on the slider of the guide rail to be tested.

[0026] In this embodiment, the laser emitting unit is not only a light source but also a linear physical anchor point in space. This embodiment employs a dual-longitudinal-mode helium-neon laser with active frequency stabilization, locking the center wavelength at 632.991 nm. To eliminate high-frequency spatial noise caused by long-distance transmission, the emitting unit is equipped with a Fourier-based spatial filter (including a microscope objective and a pinhole) to force the transverse mode of the laser beam into an ideal fundamental Gaussian beam, thereby ensuring the absolute symmetry of the energy center distribution at the measurement end.

[0027] The multi-sensor integrated measuring head is the physical carrier of the sensing end; in order to prevent the deformation of the sensor integrated measuring head itself from introducing secondary errors, its shell material must be made of Invar alloy with an extremely low coefficient of thermal expansion.

[0028] The four-quadrant detector replaces the traditional position-sensitive detector for outputting the initial optical two-dimensional displacement signal. The four-quadrant detector consists of four independent photodiode quadrants with extremely small dead zones. Because it is based on the integral conversion of photon energy, it has extremely high time response bandwidth and sub-micron spatial resolution.

[0029] The triaxial microelectromechanical system (MEMS) accelerometer and gyroscope are key to overcoming the blind zone of pure optics in this solution. The MEMS accelerometer measures the forced transient specific force (acceleration) of the slider in three orthogonal directions in space according to Newton's second law. The gyroscope measures the transient angular velocity of the slider based on the Coriolis effect. The inertial sensor outputs a time-domain signal, which is not affected by external optical path obstruction or changes in the refractive index of the medium.

[0030] The orthogonal high-precision platinum resistance temperature sensor array differs from traditional single-point temperature measurement, which only acquires scalar values. This array aims to acquire the vector gradient of the field. The array consists of multiple platinum resistance sensors, orthogonally distributed in a cross shape along the upper, lower, left, and right edges of the optical path aperture at the receiving end. The platinum resistance utilizes the physical property of the changing probability of free electron scattering in metallic platinum at different temperatures to provide temperature sampling accurate to 0.005℃.

[0031] Steps 1-2: Using the internal master sampling clock of the triaxial microelectromechanical system accelerometer as the sole physical reference source, a jitter-free global synchronization trigger pulse is generated through the phase-locked loop frequency division and multiplication network inside the central synchronization processing unit.

[0032] The heterogeneous data phase misalignment trap refers to the fact that the photoelectric conversion of a quadrant detector is instantaneous (nanosecond level), the sampling of an analog-to-digital converter is microsecond level, while the microelectromechanical system (MEMS) accelerometer typically contains a low-pass mechanical filter, resulting in an inherent group delay; and the thermal conductivity response of a temperature sensor is in the millisecond range. If these sensors are simply polled using host computer software, a 1-millisecond reading time difference during high-speed slider movement (e.g., 1000 mm / s) can lead to a 1-millisecond spatial misalignment.

[0033] The single reference source means that, in order to eliminate misalignment, the system must abandon the multi-clock source structure; since the resonant frequency of the internal micromechanical structure of the microelectromechanical system accelerometer is fixed, its internal sampling clock is the most rigid. Therefore, this scheme configures the clock pin of the microelectromechanical system accelerometer in master clock output mode, and all other electronic links' analog-to-digital conversions are passively triggered as slave devices.

[0034] A phase-locked loop (PLL) is a feedback control circuit that uses a phase detector to compare the phase difference between a reference clock and an internal voltage-controlled oscillator (VCO) to generate a control voltage that ensures the phase of the output clock is absolutely locked to the reference clock. Using a PLL, a system can multiply the master clock of a microelectromechanical system (MEMS) accelerometer, for example, from 4kHz to 40kHz or 100kHz without phase jitter, in order to generate a sufficiently high-resolution global synchronization trigger pulse.

[0035] Steps 1-3: Using the global synchronization trigger pulse, at the physical level, through parallel hardware routing, simultaneously trigger the analog-to-digital converter, microelectromechanical system data bus reading interface, and environmental sensor multiplexer interface of the four-quadrant detector link, ensuring that the acquired initial optical two-dimensional displacement signal, inertial transient angular velocity and acceleration signal, and orthogonal temperature field signal strictly point to the same transient physical moment of the guide rail motion on the physical timeline.

[0036] The global hardware clock bus is not a software concept, but a dedicated low-latency wiring network deployed within the field-programmable gate array of the central synchronization processing unit. This bus has strictly equal-length physical wiring characteristics to ensure that the electrical signal transmission delay of the synchronization trigger pulse to different functional modules (optical conversion, inertial readout, thermodynamic acquisition) is completely consistent.

[0037] Timestamp alignment refers to the process where, upon the rising edge of the global synchronization trigger pulse, the four-channel synchronous analog-to-digital converter at the back end of the four-quadrant detector simultaneously holds and quantizes the charge within the same nanosecond; the field-programmable gate array synchronously latches the latest frame of acceleration and angular velocity data in the microelectromechanical system output register; and simultaneously latches the latest digital value from the temperature transmitter. Ultimately, these three types of data, with distinct physical sources and varying frequency responses, are stamped with the same absolute timestamp and packaged into the subsequent decoupling algorithm. This ensures that the mathematical model's fusion is absolutely self-consistent in both physical space and time.

[0038] Specifically, in the measurement and modification of a certain ultra-precision aerospace aluminum alloy structural component processing machine tool, the X-axis guide rail travel of the machine tool reached 12 meters, and the maximum rapid traverse speed was 600 mm / s.

[0039] To implement step 1, this solution adopts the following hardware configuration and quantization control strategy: The laser emitting unit uses a frequency-stabilized 1.5mW helium-neon laser, mounted on an independent vibration-isolated base. The base for the multi-sensor integrated measuring head is integrally machined from Invar alloy using slow wire cutting on the slider.

[0040] In terms of hardware circuit design, the central synchronization processing unit uses a Xilinx Zynq-7000 series heterogeneous chip. The field-programmable gate array (FPGA) handles the hard synchronization task. The system extracts the internal 4kHz data readiness interrupt signal from the triaxial microelectromechanical system accelerometer (noise density controlled below 20μg / Hz) and inputs it to the phase-locked loop (PLL) inside the FPGA. The PLL multiplies the signal to 100kHz without jitter, generating an ultra-high frequency global synchronization trigger pulse.

[0041] The 100kHz sampling frequency setting here is based on the following considerations: taking into account the system control cycle requirement (less than 1ms), the original output frequency of the MEMS accelerometer (4kHz), and the Nyquist sampling theorem's requirement for sampling high-frequency vibration components (up to approximately 350Hz). Setting the sampling frequency to 100kHz ensures sufficient sampling of high-frequency vibration signals while meeting real-time control requirements. This frequency is achieved through phase-locked loop frequency multiplication, requiring no manual setting; in the actual system, it is automatically generated by the field-programmable gate array based on the MEMS accelerometer's reference clock.

[0042] The 100kHz pulse is directly hardwired to the conversion start pin (CONVST) of the 24-bit fully differential synchronous analog-to-digital converter (ADC) at the back end of the four-quadrant detector via an equal-length routing line. Precise measurements using an oscilloscope show that the physical time skew between the trigger pulse arriving at the optical ADC link and the inertial digital communication link is strictly limited to within 3.5 nanoseconds.

[0043] At the extreme speed of 600 mm / s, even with the maximum time skew of 3.5 nanoseconds, the introduced spatial position misalignment of the slider is only 600 mm / s × 3.5 ns = 0.0021 μm. This effectively reduces the phase misalignment error caused by software polling in existing technologies, providing a foundation for underlying data consistency for subsequent complex decoupling algorithms.

[0044] The aforementioned nonlinear correction model for the beam spot shape is based on Gaussian beam propagation theory, and the beam spot diameter... With propagation distance The relationship of change is as follows:

[0045] in, Based on the waist radius, The center wavelength. Evolutionary proportionality constant. This is used for nonlinear dynamic adjustment of the coordinate gain of the initial two-dimensional optical displacement signal, i.e.:

[0046] Step 2: After completing the nanosecond-level synchronous acquisition of heterogeneous data in Step 1, the system acquired the initial optical two-dimensional displacement signal and the orthogonal temperature field signal pointing to the same physical time.

[0047] The core physical objective of this step is to address the aerodynamic bending blind spot in pure optical measurement techniques. According to Fermat's principle, light always travels along the shortest path when propagating in a non-uniform medium. When there are localized heat sources (such as motor heating or human radiation) or air convection in the workshop, the air density along the laser beam propagation path undergoes a lateral gradient change, leading to uneven distribution of the air refractive index across the spatial cross-section perpendicular to the optical axis. The beam will inevitably bend and deflect towards regions with higher refractive indices; this phenomenon is called aerodynamic beam deflection in physical optics. This step uses a rigorous thermodynamic mathematical model and ray trajectory equations to directly calculate this bending amount from a physical level and completely eliminates it from the total displacement of the optical measurement.

[0048] Step 2-1: Absolute Refractive Index Correction Based on the Improved Edren Model The current atmospheric pressure and partial water vapor pressure values ​​are obtained, and combined with the temperature values ​​obtained by an orthogonal high-precision platinum resistance temperature sensor array, an improved Edren mathematical model is introduced to calculate the absolute correction value of the air refractive index.

[0049] The partial water vapor pressure refers to the fact that air is a mixture of multiple components, including nitrogen, oxygen, and water vapor. According to Dalton's law of partial pressures, the independent pressure contributed by water vapor to the total atmospheric pressure is the partial water vapor pressure. Because water molecules are polar, their polarization response to electromagnetic fields of light waves is quite different from that of non-polar nitrogen and oxygen; therefore, it must be included as an independent variable in the refractive index calculation.

[0050] The improved Edren mathematical model, based on the classic Lorentz-Lorentz equations, reveals the relationship between the macroscopic refractive index of a medium and the microscopic molecular polarizability and number density. The Edren model represents an empirical advancement of this theory in the field of engineering metrology. The improved model used in this invention further corrects for fluctuations in carbon dioxide concentration and dispersion characteristics in the near-infrared / visible light bands. Its specific mathematical expression is as follows:

[0051] This formula is used to calculate the correction amount of the air refractive index relative to the standard state under current environmental conditions. Since the optical path length of a laser beam propagating in air is directly related to the refractive index, and the refractive index varies with temperature, pressure, and water vapor partial pressure, without correction, optical measurement results will contain displacement errors caused by non-geometric factors. The purpose of introducing this formula is to quantify the impact of refractive index changes on the optical path length using real-time acquired environmental parameters, providing fundamental physical parameters for subsequent environmental compensation of the laser spot displacement.

[0052] in, : Represents the absolute correction value of the air refractive index calculated at the current measurement moment, dimensionless; : Represents the current absolute atmospheric pressure value collected in real time by a piezoresistive atmospheric pressure sensor, in Pascals (Pa). This indicates that the helium-neon laser with a center wavelength of 632.991 nm operates under standard atmospheric conditions. , , The refractive index constant under humidity (usually taken as 1) ); This indicates the current transient air temperature in degrees Celsius, measured by an orthogonal high-precision platinum resistance temperature sensor array. : This represents the current partial water vapor pressure value calculated by combining the capacitive humidity sensor and the local temperature, in Pascals (Pa). in, Standard atmospheric pressure; , , , , These are all empirical constants determined by experimental fitting of the improved Edren formula near the 633nm band, and are used to correct the effects of air pressure, temperature, and water vapor on the refractive index, respectively.

[0053] Step 2-2: Establish the reference parameters of the real medium. Add the absolute correction value calculated in step 2-1 to the base air refractive index under undisturbed conditions to obtain the real air refractive index parameters of the current environment.

[0054] The mathematical form of this step is extremely concise, namely... .in, The refractive index of basic air under vacuum or absolutely ideal conditions (usually set to an ideal constant value), while This is the actual air refractive index parameter at the current spatial point. This parameter serves as the absolute physical scale for the phase velocity of light waves propagating in this local spatial medium, and will be used as the denominator benchmark for the next step of the ray integral equation, reducing the risk of divergence or singular values ​​in the calculation.

[0055] Step 2-3: Solving the aerodynamic bending vector by spatial differentiation and double integration. Multiply the spatial gradient of the lateral refractive index of the optical path by the reciprocal of the real air refractive index parameter, and perform the first-order spatial integration and the second-order spatial integration along the physical propagation direction of the beam to obtain the lateral displacement compensation vector of the false spot in the horizontal axis direction and the vertical axis direction.

[0056] Among them, the spatial gradient of the lateral refractive index of the optical path ( This is the core physical parameter of the invention. The laser beam propagates along the Z-axis, and the mechanical cause of beam bending lies in the non-uniform density of the medium in the XY plane perpendicular to the Z-axis. The system uses the temperature difference measured by orthogonal temperature sensors arranged on the top, bottom, left, and right sides of the optical path cross-section, combined with the finite difference algorithm, to calculate the refractive index gradient in the horizontal X-axis direction. and the refractive index gradient in the direction perpendicular to the Y-axis .

[0057] Light ray trajectory equation: Under the paraxial approximation, the bending of light rays in a non-uniform medium is described by the paraxial ray equation: . Its length along the propagation path By performing two Riemann space integrals, the spot displacement deviation at the endpoint can be obtained, and its rigorous mathematical expression is:

[0058] This formula originates from the ray propagation equation under the paraxial approximation and describes the bending trajectory of a light beam in a transverse refractive index gradient field. Its physical meaning lies in the fact that when there is a transverse temperature distribution in the air medium, the uneven refractive index distribution causes the light beam to bend towards regions with higher refractive indices, thus generating spurious displacement signals on the detector. The purpose of introducing this double integral formula is to quantitatively calculate the spurious spot displacement caused by this environmental disturbance by spatially integrating the transverse refractive index gradient along the beam propagation path, so as to eliminate it from the measurement results.

[0059] in, : This represents the amount of false displacement compensation of the light spot in the horizontal X-axis direction caused by environmental disturbances such as lateral air convection, and the unit is meters; : This represents the amount of spurious displacement compensation of the light spot in the direction perpendicular to the Y-axis caused by environmental disturbance, in meters; : This indicates the absolute physical propagation distance between the current multi-sensor integrated measuring head (receiving end) and the laser emitting unit. This value is provided in real time by the external grating ruler. This represents the first-order spatial integral variable along the direction of beam propagation. The inner integration variables represent the second-order spatial integral; both are continuous spatial position coordinates along the laser beam propagation axis (Z-axis), and the integration interval starts from the laser emitter (…). ) to the current sensor integrated measurement head position ( ).

[0060] : Represents the true air refractive index parameter of the current spatial location obtained in step 2-2; and : Represents the orthogonal transverse refractive index spatial gradients along the X and Y axes, respectively, in units of .

[0061] Steps 2-4: Physical stripping and purification output. Using vector subtraction, the initial optical two-dimensional displacement signal obtained in step 1 is subtracted from the false spot lateral displacement compensation vector obtained by the double integral above, and the first corrected displacement signal stripped of environmental thermodynamic interference is output.

[0062] This step, mathematically speaking, is represented by the subtraction of linear vectors: .

[0063] In this step, through this subtraction, the system forcibly straightens the laser beam bent by hot air in digital space. The first corrected displacement signal is then output. This is completely equivalent to the spot displacement measured in an ideal environment of absolute vacuum and zero temperature gradient, thus improving the impact of environmental drift on the measurement results in pure optical measurement technology.

[0064] Specifically, in the actual measurement of the aforementioned 12-meter stroke aerospace aluminum alloy component processing machine tool, a high-power spindle coolant pump was present in the workshop, causing the local air temperature on the left side of the guide rail to be approximately higher than that on the right side. As the slider moves to... At a distance of meters, the piezoresistive atmospheric pressure sensor measures the absolute ambient pressure. The capacitive humidity sensor provides feedback to calculate part of the water vapor pressure. An orthogonal high-precision platinum resistance temperature sensor array (four PT1000 sensors arranged in a cross shape, spaced 10 mm apart), mounted at the light inlet of the sensor integrated measuring head, captured the lateral temperature difference in real time. The high-performance digital signal processor (DSP) of the central synchronization processing unit immediately substituted the improved Edren formula upon receiving the synchronization data. Because the left side has a higher temperature (lower density) and the right side has a lower temperature (higher density), the DSP calculated the extremely small horizontal lateral refractive index spatial gradient. For continuous double-space integration, the DSP internally employs a discretized fourth-order Runge-Kutta numerical integration algorithm for fast approximation. Over a propagation distance of meters, the beam actually underwent a physical bend to the right (the cold air side), invisible to the naked eye but extremely sensitive to the instrument. After floating-point matrix operations, the DSP calculated the horizontal spurious displacement compensation. (Deflected to the right), vertical spurious displacement compensation amount (Vertical temperature difference is extremely small). At this point, the initial two-dimensional optical displacement signal actually measured by the four-quadrant detector is horizontal. Without compensation, the system will mistakenly assume that the guide rail has malfunctioned. The geometric deformation. After executing steps 2-4, the system will... This is output as the first corrected displacement signal. This calculation process, accelerated by the DSP hardware floating-point unit (FPU), takes only [time missing]. With extremely low computational latency, the system successfully and precisely removed the thermodynamic artifacts hidden in the geometric deformation of the guide rail, providing pure optical projection coordinates for the next step of kinematic Abbe error compensation.

[0065] Step 3: Compensate for Abbe error and reconstruct the motion trajectory After completing the thermodynamic decoupling in step 2 and outputting the first corrected displacement signal, the system has eliminated the interference from changes in air refractive index. However, due to the physical limitations of the measuring instrument, the geometric center of the photosensitive surface of the four-quadrant detector (the measurement point) cannot be completely aligned with the actual rotation center of the guide rail slider (the measured spatial point). There must be a physical eccentricity between them. According to Abbe's principle in precision measurement, when the slider moves on the guide rail and is accompanied by small pitch, yaw, or roll angular displacements, this eccentricity acts like a "lever arm," amplifying the angular displacement and converting it into a translational error at the measurement point.

[0066] Existing technologies (such as CN117073587A) attempt to solve these angles by adding beam splitters and multi-path photodetectors, using a system of linear equations with multiple variables in pure optics. This not only leads to complex optical structures, but also results in severe error coupling between optical paths.

[0067] The effect of this step is that it no longer relies on the optical angle measurement path, but directly uses the inertial transient angular velocity signal synchronously acquired in step 1. In the pure mathematical rigid body kinematic space, the Abbe error is completely removed through three-dimensional homogeneous coordinate transformation, thereby reconstructing the true motion trajectory of the slider's geometric center (the second corrected displacement signal).

[0068] Step 3-1: Time Domain Integration to Obtain True Angular Displacement. Perform high-precision time domain Riemann integration on the inertial transient angular velocity signal obtained in Step 1 (i.e., the output of the triaxial microelectromechanical system gyroscope) to obtain the true angular displacement of the slider in three-dimensional space.

[0069] Among them, the inertial transient angular velocity signal ( : Output in real time by a triaxial microelectromechanical system (MEMS) gyroscope. Its underlying physics relies on the Coriolis effect—when a vibrating mass moves in a rotating reference frame, it experiences a lateral Coriolis force proportional to its rotational angular velocity. This force causes a change in the distance between the capacitor plates, from which the angular velocity can be calculated. The unit is typically degrees per second (°C / s). ) or radians / second ( ).

[0070] The time-domain Riemann integral is the angular velocity, which is the time derivative. ), must be done through time Only by integrating can the angular displacement be restored. In discrete digital control systems, the high-performance digital signal processor of the central synchronous processing unit uses the trapezoidal integration method or the fourth-order Runge-Kutta numerical algorithm for high-precision accumulation.

[0071] This formula, based on the integral relationship between angular velocity and angular displacement in kinematics, is used to convert the angular velocity signal measured by the inertial gyroscope into angular displacement. Since the gyroscope output is a transient angular velocity, and the Abbe error caused by changes in the guide rail attitude depends on the absolute angular displacement, the angular information must be reconstructed through time-domain integration. The purpose of introducing this integral formula is to provide accurate attitude input for subsequent three-dimensional coordinate transformations and Abbe error compensation.

[0072] in, : These represent the calculated actual angular displacements of the slider around the X-axis (pitch), Y-axis (yaw), and Z-axis (roll), respectively, in radians; : These represent the three-axis transient angular velocities synchronously sampled by the gyroscope of the three-axis microelectromechanical system; : Represents the cumulative time variable since the system started running from the initial calibration point.

[0073] Step 3-2: Establish the physical eccentricity installation vector and cross-coupled translation error component. Establish the physical eccentricity installation vector between the actual rotation center of the slider and the geometric center of the four-quadrant detector in the multi-sensor integrated measuring head; perform a spatial cross product operation on the angular displacement vector formed by the physical eccentricity installation vector and the actual angular displacement to obtain the translation error component induced by the slider attitude deflection coupling.

[0074] Among them, the physical eccentric installation vector ( The definition of is the physical distance between the center of the photosensitive surface of the four-quadrant detector and the theoretical center of motion of the slider, precisely calibrated by a coordinate measuring machine during the initial assembly stage of the system. It is a three-dimensional spatial vector. .

[0075] The spatial cross product and the definition of the translation error component are as follows: According to the kinematic principle of rigid body infinitesimal displacement in theoretical mechanics, the translational displacement of any point on a rigid body not at the center of rotation due to a tiny rotation is strictly equal to the cross product of the rotation vector and the position vector of that point. That is: Abbe translation error = This calculation thoroughly explains how angles contaminate linear displacement.

[0076] The expansion of the cross product operation is: ; The first two components correspond to the horizontal (X-direction) and vertical (Y-direction) translation errors caused by Abbe errors, respectively.

[0077] This formula is used to map the spatial coordinates from the measurement point (center of the four-quadrant detector) to the actual motion center of the slider. The rotation transformation matrix is ​​used to achieve this. This describes the attitude deflection of the sensor integrated measuring head coordinate system relative to the guide rail reference coordinate system, and the cross product term. Based on the principles of rigid body kinematics, the additional translational error caused by eccentric installation is calculated. The purpose of introducing this formula is to convert the sensor measurement value to the true geometric center of the measured object, according to Abbe's principle, thereby eliminating the influence of attitude deflection on straightness measurement.

[0078] Step 3-3: Three-dimensional homogeneous coordinate transformation and reconstruction of the second corrected displacement signal. The first corrected displacement signal output in step 2 is expanded from the two-dimensional coordinate system to the three-dimensional homogeneous coordinate system. After multiplying with the three-dimensional direction cosine rotation transformation matrix, the translation error component is superimposed to complete the complete compensation of the Abbe error and output the second corrected displacement signal.

[0079] In this context, the extended dimension of the three-dimensional homogeneous coordinate system is represented by the fact that a four-quadrant detector can only measure the two-dimensional coordinates of the light spot within the photosensitive plane (XY plane). However, when performing real 3D rigid body kinematics compensation, the dimensions of the matrix must match. Therefore, this method forcibly expands it into a 3D column vector in digital space. The third element This means that, in the detector's local coordinate system, the depth of the light spot relative to the normal (Z-direction) of the photosensitive plane is zero.

[0080] Direction cosine rotation transformation matrix ( A large number of rotation matrices obtained by multiplying three basic rotation matrices (about the X, Y, and Z axes) together. The matrix contains sine and cosine terms of all angular displacements, representing the overall attitude tilt of the local coordinate system relative to the global reference coordinate system.

[0081] Absolute compensation formula:

[0082] in, This is the second corrected displacement signal (i.e., the pure X and Y displacements) that is finally output in this step. It has eliminated all the contamination from thermodynamics and the Abbe effect and is strictly mapped to the ideal geometric center of the slider. : Represents the small coupling sway in the Z direction, which is used as an internal state variable and is usually not used for straightness compensation. : Calculated based on actual angular displacement Spatial direction cosine rotation transformation matrix; : The first corrected displacement signal output in step 2 (two-dimensional displacement with thermodynamic artifacts removed); This refers to the translation error component calculated in step 3-2.

[0083] Specifically, under the actual operating conditions of an ultra-precision machine tool, due to the periodic installation error of the ball screw, the slider will... At a distance of meters, a pitch angle displacement about the X-axis occurs. This is achieved through analysis of the gyroscope in the three-axis microelectromechanical system. The ultra-high frequency angular velocity data stream is digitally integrated, and the DSP calculates the current transient true angular displacement: pitch angle. arcsecond (approximately equal to) radians), yaw angle Arcseconds, roll angle Arcseconds. In the system's factory calibration, the physical off-center mounting vector written to the non-volatile memory is... (That is, the center of the detector is 65mm higher than the actual rotation center of the slider). Now, we focus on the displacement measurement in the vertical direction (Y direction). According to rigid body mechanics, the slider undergoes a pitch angle about the X-axis. It will be due to vertical height eccentricity This produces a false vertical displacement on the detector plane. Substituting the Y-component into the cross product formula above: the false vertical translation caused by the Abbe error. .

[0084] A more accurate deduction: Due to the excessively high installation height of the four-quadrant detector ( When the slider rolls around the Z-axis... arc seconds ( When the radius is radians, it will induce an Abbe translation error in the horizontal X direction: Simultaneously, the pitch angle around the X-axis radian, combined with Z-axis eccentricity This will induce Abbe translation error in the Y direction: Assume that the first corrected displacement signal input in step 2 is at this point. The DSP's internal hardware floating-point unit substitutes these parameters into a massive three-dimensional homogeneous coordinate transformation matrix for instantaneous solution. The final output second-corrected displacement signal will discard these parameters. and The Abbe error interferes with the measurement results, and the output is extremely close to the true geometric coordinates: By performing rigid body kinematic mapping in pure digital space, this invention reduces the physical volume and hardware cost of beam splitters and detector arrays in existing technologies, achieves sub-micron level decoupling accuracy for multi-degree-of-freedom errors, and reduces secondary reflection interference within the optical system.

[0085] Step 4: Separate static and dynamic data to extract purity error After completing the Abbe error reconstruction in step 3, the second corrected displacement signal output by the system is absolutely accurate at the geometric and thermodynamic levels. However, from the physical essence of machine tool machining dynamics, this displacement signal is actually a superposition of two completely different physical sources: one is the extremely low-frequency spatial geometric deformation caused by the guide rail's self-weight deformation and assembly tolerances, which is the actual straightness deviation; the other is the high-frequency forced mechanical vibration caused by the motor cutting force and the ball screw commutation impact, which is the transient displacement. Traditional pure optical systems can only measure the total displacement. If the total displacement is directly used to judge the quality of the guide rail, it will inevitably lead to misjudgment.

[0086] The core of this step is to break the limitations of optical signals, forcibly introduce the inertial transient acceleration signal obtained in step 1, and use Kalman filtering to establish the spatiotemporal integral mapping of Newton's second law of motion in the state space model, thereby accurately tearing the aliased displacement signal into low-frequency straightness geometric deviation and high-frequency structural vibration terms.

[0087] Step 4-1: Initialize the five-dimensional state vector. Within the central synchronization processing unit, an initial five-dimensional state vector containing the full physical operating state of the guide rail is constructed. The five-dimensional state vector is strictly composed of low-frequency straightness geometric deviation, high-frequency vibration velocity, high-frequency vibration acceleration, low-frequency environmental drift residual of the laser beam, and high-frequency structural vibration term.

[0088] Among them, the state vector ( The meaning of ) is that, in modern control theory, the state vector is the smallest set of variables sufficient to completely describe the dynamic behavior of a system. The five-dimensional state vector of this invention is defined as follows:

[0089] This state vector is used to establish the system model of the Kalman filter. Its construction is based on the fact that in guide rail straightness measurement, the total displacement signal is composed of multiple physical components, including geometric deformation, high-frequency vibration, and sensor drift, which cannot be directly observed and separated. The purpose of introducing the five-dimensional state vector is to incorporate each physical component as an independent state variable into a unified state-space model, providing a mathematical foundation for subsequent dynamic-static separation through Kalman filtering.

[0090] in, Low-frequency straightness geometric deviation represents the deformation of the pure guide rail geometry that we ultimately want to extract. Its physical characteristics are extremely low-frequency signals that change slowly with spatial position (rather than time).

[0091] These represent the transient high-frequency vibration velocity and high-frequency vibration acceleration of the slider in the direction perpendicular to the guide rail (provided by the microelectromechanical system accelerometer).

[0092] The low-frequency environmental drift residual of the laser beam refers to the extremely small white noise drift that remains after thermodynamic compensation in step 2 and changes very slowly over time.

[0093] This is the high-frequency structural vibration term, representing the acceleration due to high-frequency vibration. The transient high-frequency displacement component generated by quadratic integration in the time domain.

[0094] State vector at system startup The initial values ​​are set as follows: Set to 0 (assuming no geometric deviation at the initial position). and Set it to 0 (assuming it is initially at rest). Set to 0 (assuming the initial drift residual is zero). Set to 0 (initially no vibration component).

[0095] Step 4-2: Establish the state transition equation containing the spatiotemporal mapping matrix. In the discrete iterative operation, the inertial transient acceleration signal of the previous moment is multiplied by the time domain integration step size and superimposed on the high-frequency vibration velocity of the previous moment to force an update of the current velocity and displacement state.

[0096] The state transition equation describes the change in system state from state to state. Always towards The differential physical equations that evolve naturally over time. Their discrete form is: .

[0097] State transition matrix ( ) and time-domain integration step size ( ) is one of the core patented features of this invention, matrix It is not an empirical parameter, but an integral matrix strictly constructed based on Newton's laws of motion.

[0098] Where the state transition matrix The specific form is as follows:

[0099] The state transition matrix is ​​constructed based on Newton's laws of kinematics, where the updates of velocity and displacement strictly follow the time integral relationship of acceleration. The purpose of introducing this matrix is ​​to use the acceleration measurement results of the inertial sensor as a physical constraint on the system state evolution, thereby maintaining spatiotemporal consistency between optical displacement estimation and inertial measurement during the filtering process and improving the ability to distinguish between high-frequency vibrations and low-frequency geometric deformations.

[0100] in, This represents the discrete-time integration step size, in seconds.

[0101] Because the sampling frequency of the control system is Then the integration step size The integral step size The value of is determined by the system's global synchronization trigger pulse frequency, which is 100kHz. The selection of this frequency is based on two criteria: firstly, it must meet the Nyquist sampling requirements for high-frequency vibration components (up to approximately 500Hz); secondly, it must match the response bandwidth of the piezoelectric ceramic compensation mechanism (approximately 1kHz), while ensuring that the DSP completes all matrix operations within one control cycle (the measured DSP operation time is approximately 60μs, which can be completed within a cycle of less than 10μs; a parallel pipeline architecture is actually used for implementation). This parameter is the system's inherent sampling period and does not require manual setting.

[0102] According to kinematic equations, displacement equals the integral of velocity, and velocity equals the integral of acceleration; therefore, the matrix... The following physical coupling was established internally:

[0103]

[0104] Through the aforementioned matrix structure, this invention, for the first time, applies the physical constraint of inertial time integration to a simple optical spatial displacement within the mathematical model.

[0105] Step 4-3: Establish observation equations to achieve heterogeneous data fusion. Establish observation equations and define the second corrected displacement signal output in step 3 as a linear superposition of the low-frequency straightness geometric deviation and the high-frequency structural vibration term in the mathematical model; at the same time, use the acceleration output of the microelectromechanical system as the second dimension of the observation vector.

[0106] The observation equation describes the invisible state within the system. How is it mapped to external readings that the sensor can measure? The equation is in the form of... .

[0107] Among them, the observation matrix The specific form is as follows:

[0108] The first row represents the optical second correction displacement signal. The second line represents the acceleration signal. .

[0109] In this invention, the observation vector is represented as .

[0110] This observation equation describes the mapping relationship between the system's internal state and the sensor output. Among them, the optical second-correction displacement signal... Modeled as low-frequency geometric deviation High-frequency structural vibration The linear superposition of acceleration signals Acceleration components in directly observed states The purpose of introducing this equation is to unify the heterogeneous measurement data from optical and inertial sensors into the same state space framework, providing an input-output relationship for data fusion and state estimation by the Kalman filter.

[0111] in, This is the second corrected displacement signal output from step 3 (absolute coordinates measured purely optically). In the observation matrix... Under the definition, That is, the movement of the light spot is a macroscopic superposition of the geometric deformation of the guide rail and the high-frequency vibration of the slider.

[0112] This refers to the inertial transient acceleration signal of the microelectromechanical system synchronously acquired in step 1, and its directly observed state vector contains... .

[0113] Among them, the noise covariance matrix of the Kalman filtering process The method for determining the value is as follows: The matrix is ​​in diagonal form, with its diagonal elements corresponding to the process noise variance of the five-dimensional state variables. The values ​​are based on the following criteria: and The change is slow, and the process noise variance is set to a small value. ; and The noise variance was calculated based on the noise density parameter and sampling frequency (100kHz) in the datasheet of the microelectromechanical system accelerometer, and is approximately ; The noise variance is taken as an empirical value of the acceleration integral error. In actual system operation, after static data acquisition, the Q matrix can be adaptively adjusted using the maximum likelihood estimation method to optimize the filtering convergence performance.

[0114] Among them, the Kalman filter observation noise covariance matrix The method for determining the value is as follows: for The diagonal matrix, with diagonal elements corresponding to the variance of optical displacement observation noise and the variance of microelectromechanical system accelerometer observation noise, respectively. The variance of optical displacement observation noise is obtained through statistical analysis of the residuals after calibration in step 6-1, and the measured variance is approximately... The variance of the observation noise of the microelectromechanical system (MEMS) accelerometer was calculated based on the noise density (20 μg / √Hz) and sampling frequency (100 kHz) in the MEMS accelerometer datasheet, and is approximately... In practical applications, after the system calibration is completed, a period of static data (lasting 10 seconds) can be collected to calculate the variance of the sensor output as the initial value of the R matrix, and then adjusted online based on the actual residuals during operation.

[0115] For the low-frequency environmental drift residual of the laser beam in the state vector It is not directly mapped to the sensor output in the observation equation, but rather through the system process noise covariance matrix. The corresponding terms in the model are constrained, assuming they satisfy a zero-mean, slowly varying Gaussian random walk model, thereby achieving indirect estimation and suppression of the filter.

[0116] Step 4-4: Online Iteration of Kalman Gain Matrix and Frequency Domain Isolation. Trust weights are assigned through online iteration of the Kalman gain matrix to isolate high-frequency fluctuation characteristics into the high-frequency structural vibration term, and output the pure low-frequency straightness geometric deviation after removing the mechanical high-frequency resonance component.

[0117] The method for determining the initial covariance matrix of the Kalman filter is as follows: After the system completes offline calibration, a set of sensor data under static conditions (duration not less than 10 seconds) is collected, and the variances of the optical displacement signal and the microelectromechanical system accelerometer signal are calculated respectively, which are used as the initial values ​​of the diagonal elements of the initial state covariance matrix. Specifically, let the initial state covariance matrix be... ,in The variance of the optical displacement signal in static condition (measured to be approximately) ), Take the static variance of the integral of the acceleration signal. Take the static noise variance of the microelectromechanical system accelerometer (based on the microelectromechanical system accelerometer datasheet, approximately...). ), Get experience points , Take the variance of the static vibration amplitude (measured to be approximately...). In practical engineering applications, the above parameters can be automatically calculated from 10 seconds of static data after the first power-on.

[0118] Among them, Kalman gain ( The purpose of Kalman filtering is to arbitrate heterogeneous data fusion. Optical sensors are extremely accurate at low frequencies but suffer from ambiguity at high frequencies, while inertial microelectromechanical system (MEMS) accelerometers respond very quickly at high frequencies but exhibit severe integration drift at low frequencies. Kalman filtering automatically assigns weights in the frequency domain by calculating and predicting the covariance matrix in real time: for transient high-frequency displacement jumps, the system will absolutely trust the result obtained from the integration by the MEMS accelerometer. And remove it from the total displacement; for slow, low-frequency displacement changes, the system will trust the optical displacement and classify it as such. .

[0119] Specifically, in high-speed cutting tests on machine tools, the cutting tool generates high-frequency cutting motions as it enters the material. The flutter. At this time, the second corrected displacement signal output in step 3. It manifests as a On the DC reference surface, a peak-to-peak value of High-frequency burrs (total displacement reaches) The synchronously sampled microelectromechanical system accelerometer instantaneously captured a value as high as... (about The transient forced acceleration of the DSP in the central synchronous processing unit. Within the computation cycle, Kalman prediction and update logic is executed. Through By integrating forward, the system immediately calculates this. The acceleration will trigger in the current instant High-frequency structural vibration terms The Kalman gain matrix reveals the total optical displacement. A sudden change occurred, but because the microelectromechanical system (MEMS) accelerometer provided a clear high-frequency interpretation, the system immediately determined that this change was due to vibration rather than guide rail bending. Therefore, the system will... Into The variables are isolated and imprisoned; while the output exhibits pure low-frequency linearity geometric deviation. Still stable This achieves effective separation of low-frequency geometric deviations from high-frequency vibrations.

[0120] Step 5: Isolate resonance to perform asymmetric closed loop After the rigorous screening process of the first four steps, the system finally obtains the low-frequency straightness geometric deviation after filtering out high-frequency interference and the isolated high-frequency structural vibration term. This step addresses the problem of how to safely perform physical compensation. The shortcoming of existing technologies lies in their symmetrical rigid closed-loop design; that is, whatever error is measured, the compensation mechanism is commanded to move in the opposite direction by that amount. However, the micro-displacement compensation mechanism itself has mechanical mass and stiffness, and its physical response bandwidth has a limit (usually lower than...). If you force it to track what was just measured... High-frequency cutting vibration inevitably leads to severe phase hysteresis. When the hysteresis exceeds... At this time, the original negative feedback cancellation will turn into positive feedback excitation, instantly triggering severe resonance in the machine tool spindle. This invention provides an asymmetric closed-loop control strategy that implements strict traffic control at the intersection of physical and software, reducing the risk of resonance.

[0121] Step 5-1: Low-frequency geometric error data transmission. Based on real-time industrial fieldbuses such as EtherCAT, the calculated extremely low-frequency straightness geometric deviation is sent to the underlying servo control system of the machine tool guideway with microsecond-level time determinism.

[0122] Step 5-2: The safe physical space cancellation servo control system converts the received digital signal packets into analog voltage drive signals through a high-precision digital-to-analog converter (DAC). This physically drives the piezoelectric ceramic micro-displacement compensation mechanism to generate equal-amplitude and opposite mechanical displacements, thereby canceling the static and low-frequency deformation errors of the guide rail profile in real time.

[0123] The piezoelectric ceramic micro-displacement compensation mechanism refers to a solid-state actuator that operates using the inverse piezoelectric effect. When a voltage is applied, its internal lattice deforms, producing a physical displacement with nanometer-level resolution. It is embedded in the intermediate connecting layer between the slider and the stage.

[0124] The meaning of the physical offset safety boundary is that, since what is issued at this time is the product purified in step 4... (Low-frequency straightness geometric deviation, frequency usually) The forces generated by the piezoelectric ceramic mechanism, such as thermal expansion and deformation of the guide rail and sagging due to its own weight, are far below the natural frequency of the piezoelectric ceramic mechanism (typically in the hundreds of hertz). Therefore, the piezoelectric ceramic can generate reverse thrust smoothly and easily, achieving safe and overshoot-free physical negative feedback compensation.

[0125] Step 5-3: Physical cut-off and feedforward interpolation of high-frequency vibration terms. In the underlying logic of the control architecture, the physical execution authority of high-frequency structural vibration terms is forcibly intercepted, and the command transmission link to the piezoelectric ceramic micro-displacement compensation mechanism is cut off. At the same time, it is sent to the host computer CNC system as an independent compensation residual data stream via Ethernet, and only participates in the tool trajectory advance interpolation prediction of the machining program.

[0126] The physical execution cutoff frequency threshold for the high-frequency structural vibration term is set to 100Hz. This value is based on the fact that the mechanical resonant frequency of the piezoelectric ceramic micro-displacement compensation mechanism is typically 300Hz-500Hz, with an effective control bandwidth of approximately 100Hz. Therefore, if vibration components with frequencies higher than 100Hz are forcibly driven by the piezoelectric ceramic, a phase lag exceeding 90° will occur, potentially leading to positive feedback resonance. This threshold is determined during system design based on the frequency response characteristic curve of the selected piezoelectric ceramic actuator and verified through actual frequency sweep testing (i.e., applying sinusoidal signals of different frequencies to the piezoelectric ceramic and observing its amplitude-frequency response; the frequency corresponding to the amplitude decaying to -3dB is the upper limit of the bandwidth, and this value is taken as the cutoff threshold).

[0127] Among them, physical disconnection: in the output routing of the central synchronization processing unit, variables A hardware mask is set to disable physical output. The servo driver will never receive these high-frequency switching commands, thus avoiding resonant excitation from a physical causal chain perspective.

[0128] Feedforward interpolation means that this high-frequency vibration is not wasted. It is sent to the CNC system on the host computer. The digital twin model in the CNC system knows that the tool is vibrating. After vibration, it will not attempt to resist it with a slow physical slider, but will use high-frequency means such as controlling the high-speed magnetic levitation bearing of the tool spindle or adjusting the spindle speed for soft compensation, or for early warning, such as indicating that the tool is about to break.

[0129] Specifically, based on the measured data from step 4, the system extracted... Low-frequency straightness geometric deviation and (frequency The high-frequency structural vibration term. Under asymmetric closed-loop control, the field-programmable gate array of the central synchronization processing unit immediately... Convert to Position commands are sent to the piezoelectric amplifier via a real-time bus. The piezoelectric ceramic actuator uses... The physical delay caused a smooth elongation, pushing the worktable back onto the preset linear reference surface. The entire lifting process was smooth. Meanwhile, that section... The high-frequency vibration data was confined to the digital domain and transmitted to the host computer via a high-speed network port. Upon receiving the alarm, the machine tool's main controller determined that the cutting chatter exceeded the limit and automatically adjusted the spindle feed rate from... Instantly downgraded to The chatter (high-frequency structural vibration term) automatically decayed and disappeared within the following 2 seconds. Finally, after blind testing with a third-party laser interferometer, the 12-meter ultra-precision machine tool using this invention, under extremely harsh conditions of full-speed heavy-load cutting, maintained a stable dynamic straightness error within [value missing]. Within the limits of performance, it eliminates the servo whine and overshoot oscillation commonly found in traditional pure optical systems.

[0130] Step 6: System offline calibration and zero-point initialization mechanism In any precision sensing system, machining tolerances, temperature drift of electronic components, and non-orthogonality errors between the sensor coordinate system and the machine coordinate system are inevitably introduced during the physical manufacturing and assembly process. If these fundamental system errors are not measured, solidified, and eliminated in advance, even the most perfect mathematical decoupling model used in steps 2 to 4 will lead to serious inaccuracies in the final compensation accuracy due to the fundamental contamination of the input parameters.

[0131] The core physical objective of this step is to establish a zero-point reference and nonlinear sensitivity mapping matrix for the entire system by least-squares fitting calibration of various native errors of the multi-sensor integrated measuring head in a controlled laboratory or constant-temperature workshop environment before the system is officially put into dynamic closed-loop measurement.

[0132] Step 6-1: Nonlinear and nonorthogonal calibration of optical sensors. Using a controlled nanoscale two-dimensional high-precision displacement stage, the multi-sensor integrated measuring head is driven to perform gridded scanning movement in the plane to calibrate the actual photoelectric conversion coefficient matrix of the four-quadrant detector.

[0133] The non-orthogonality error means that, ideally, the X-axis and Y-axis of a four-quadrant detector are perfectly perpendicular. However, in microelectronic etching fabrication, the electrode dividing lines may have a slight angular deviation. If we were to forcibly assume it to be... Displacement in the X direction will cause crosstalk in the Y direction.

[0134] Nonlinear photoelectric conversion sensitivity refers to the fact that the energy of the light spot follows a Gaussian distribution, which determines that the light spot center moves similarly when it is near the cross-shaped dead zone (center) and far away from the dead zone (edge). The rate of change of photocurrent output in the four quadrants is different (non-linear).

[0135] Calibration matrix construction refers to the process by which the nanoscale displacement stage provides the actual physical displacement input vector during the calibration phase. The four-quadrant detector outputs the original electrical signal vector. By sampling thousands of points in a gridded manner, the system internally uses the least squares method to fit a high-dimensional calibration matrix that includes first-order sensitivity, second-order nonlinearity, and cross-coupling coefficients. In subsequent actual measurements, the original voltage can be multiplied by the inverse of this matrix to recover the absolutely accurate spatial displacement.

[0136] Step 6-2: Zero bias and installation alignment calibration of the microelectromechanical system inertial sensor. Using a high-precision three-axis tilt turntable, the attitude deflection of the slider in all directions is simulated to calibrate the zero bias instability, scale factor error and cross axis sensitivity of the three-axis microelectromechanical system accelerometer and gyroscope.

[0137] Zero-bias instability refers to the fact that, when a microelectromechanical system is absolutely at rest, its output is not absolutely zero due to internal electronic noise and the thermal motion of its micromechanical structure; instead, it exhibits a slowly drifting noise floor. If zero-bias is not subtracted before integration, because... The velocity error will diverge linearly with time; while the displacement error... It will diverge significantly in a quadratic manner over time.

[0138] Cross-axis sensitivity refers to the fact that, due to installation tolerances, the internal microscopic X-axis of the microelectromechanical system (MEMS) accelerometer may not be parallel to the macroscopic X-axis of the sensor's integrated measuring head housing. When the turntable rotates along one axis, the system records the parasitic outputs of the other two axes and calculates... The mounting alignment matrix is ​​used to force the microscopic coordinate system to align with the macroscopic shell by rotating the matrix at the firmware level.

[0139] Step 6-3: Precise three-coordinate measurement of the spatial physical eccentricity installation vector. Using a high-precision three-coordinate measuring machine, the physical eccentricity installation vector between the actual rotation center of the slider and the geometric center of the four-quadrant detector is obtained during the machine tool assembly stage.

[0140] Among them, the physical eccentric installation vector ( The meaning of ) is that the key static parameters necessary for Abbe error compensation in step 3 are... The true rotation center of the slider is determined by the force envelope of the ball or roller on the machine tool guideway, while the optical detector is usually installed on the side or above the slider. The coordinate measuring machine uses a probe to mark points to determine the geometric center line equation of the guideway, and then probes the positioning reference hole of the sensor-integrated measuring head. The difference between the two is used to obtain the three-dimensional vector, which is permanently burned into the read-only memory (ROM) of the central synchronous processing unit.

[0141] Specifically, in a temperature-controlled cleanroom before the system leaves the factory ( Calibration was performed within the system. The multi-sensor integrated measuring head was fixed onto a piezoelectric nano-positioning stage from a German company. The nano-stage... The step size, in Within the scope The array moves in a serpentine grid. The central synchronous processing unit collects all photoelectric coordinates and calculates a high-order fitting polynomial. Tests show that, before calibration, the four-quadrant detector has good performance at the edge range ( The nonlinear error at (location) is as high as After the calibration matrix mapping in step 6-1, the spatial residuals across the entire range are controlled within... Within [a certain range]. Simultaneously, the inertial components were calibrated using a six-degree-of-freedom turntable. The gyroscope's zero bias was measured to be [a certain value]. The zero bias of the accelerometer in the microelectromechanical system is These factory-set zero bias values ​​serve as the state vector. The constant initial offset value is injected into the Kalman filter, which effectively suppresses integral divergence.

[0142] Step 7: Heterogeneous Kernel Parallel Computation and Anti-interference Physical Layer Implementation Industrial environments are filled with interference from spindle motor inverter PWM choppers, induced magnetic fields, and grounding loop noise, reaching thousands of volts. If the underlying hardware architecture for measuring weak physical signals is not robust enough, any decoupling algorithm will be drowned out by the intense electromagnetic background noise of electromagnetic pulses.

[0143] This step details the system's end-to-end anti-interference physical isolation and heterogeneous parallel computing timing mechanisms from the analog front-end to the digital back-end, which ensures that the control delay is less than [a certain value]. The soul of hardware with demanding requirements.

[0144] Step 7-1: The weak analog photocurrent signal output by the multi-sensor integrated measurement head is converted into a fully differential voltage signal after being amplified by a pre-amplifier and transmitted to the receiving end of the central synchronization processing unit through a shielded twisted pair cable. At the receiving end, common-mode suppression is performed by a high-performance instrumentation amplifier.

[0145] The meaning of fully differential transmission is that, unlike traditional single-ended transmission (which uses one signal line and one ground line) where electromagnetic interference is directly superimposed on the signal line, causing voltage jumps, differential transmission uses two lines (…). and Transmit a pair of phase differences of The inverted signal. Common-mode rejection ratio (CMRR): When an electromagnetic pulse radiates from the workshop onto the twisted pair, it will... and The same polarity and amplitude of interference voltage (common-mode noise) are induced in the upper part. The instrumentation amplifier at the back end only amplifies... and The difference between them (the useful signal) is used to physically cancel out the common-mode noise that is the same for both.

[0146] The instrumentation amplifier in this solution has a CMRR configuration of up to [missing information]. This means that electromagnetic interference before entering the analog-to-digital converter is effectively suppressed.

[0147] Step 7-2: The high-speed parallel pipeline of the field-programmable gate array (FPGA) processes the digitized data packets into the FPGA, performs hardware-level multi-stage filtering, and processes massive amounts of raw sensor byte streams in parallel.

[0148] Parallel pipelines refer to the ability of field-programmable gate arrays (FPGAs) to perform independent and parallel addition and multiplication operations on four photoelectric channels, six inertial channels, and fifteen temperature channels within the same nanosecond clock cycle, by directly configuring the underlying logic gate circuits, compared to the serial queuing mechanism of traditional CPU instruction execution.

[0149] Median filtering refers to a method in the digital domain specifically designed to handle transient high-energy electromagnetic pulses (which manifest as isolated extreme points in the data stream) caused by the closing of power grid switches. Field-programmable gate arrays (FPGAs) perform real-time sorting of five consecutive sampling points at the hardware level, outputting the median value, thus directly eliminating electromagnetic spikes at the cost of zero phase delay.

[0150] Step 7-3: Double-precision floating-point matrix computation of digital signal processor. The field-programmable gate array and digital signal processor realize direct memory access level data exchange through high-speed on-chip bus. The DSP focuses on performing large-scale double-precision floating-point matrix operations, including Kalman filtering.

[0151] Among them, heterogeneous kernels refer to the fact that field-programmable gate arrays are good at simple but massive parallel computing, while DSPs have multiply-accumulators and hard-core floating-point units that are optimized for matrix multiplication and are good at complex mathematical algorithms.

[0152] Double-precision floating-point refers to the fact that when inverting the five-dimensional state covariance matrix of a Kalman filter, using single-precision calculations can lead to ill-conditioned divergence of the matrix due to tiny truncation errors over tens of thousands of iterations. By forcibly adopting the 64-bit double-precision format of the IEEE 754 standard, the mathematical convergence stability of the system during indefinite continuous operation is ensured.

[0153] Specifically, at the equipment site, the central synchronous processing unit is installed next to the machine tool's power control cabinet. The measurement signal transmission line is 15 meters long and is connected to... The inverter's power lines are routed in parallel. In such a harsh electromagnetic compatibility (EMC) environment, the differential driver and instrumentation amplifier in step 7-1 play a decisive role, achieving a reading as high as [missing information - likely a value] under oscilloscope monitoring. Inductive common-mode interference is suppressed to The following does not result in any loss of true optical submicron displacement resolution.

[0154] Within a heterogeneous processing architecture, the field-programmable gate array (FPGA) receives... After the data bus request, only consuming This completes the digital median filtering and packaging of all channels. Then, it is transmitted via the AXI4 bus... The bandwidth pushes clean data blocks into the DSP's internal memory. The DSP employs a deep pipeline architecture, completing all core algorithm floating-point matrix operations within the next sampling cycle (10μs) after receiving the data block for the current sampling cycle. The measured maximum single-cycle computation time is approximately 8.5μs. Ultimately, from photon incidence to compensation command output, the total closed-loop physical delay of the entire link is controlled within two sampling cycles (20μs), ensuring the system's real-time dynamic response at a 100kHz sampling rate. This perfectly satisfies the requirement that the control cycle be absolutely shorter than... Requirements in the field of ultra-precision machining.

[0155] Step 8: Guide rail full life cycle health monitoring mechanism based on multi-physics field fusion data In traditional purely optical measurement systems, the measurement data is usually discarded after use because it is impossible to distinguish between guide rail bending and machine tool vibration, and cannot be used to assess the health status of the machine tool itself.

[0156] The present invention, through the Kalman spatiotemporal decoupling in step 4, not only obtains the low-frequency straightness geometric deviation for closed-loop control, but also accurately captures the pure high-frequency structural vibration term in the digital domain. Wear of the machine tool guideways, drying of lubricating oil, or breakage of ball bearings inevitably leads to physical changes in its operating friction and forced vibration frequency. The core objective of this step is to leverage the decoupled historical data accumulated over a long period by the central synchronous processing unit to establish a data-driven model based on physical phenomena, thereby enabling a shift from passive maintenance to predictive maintenance for ultra-precision equipment.

[0157] Step 8-1: Construction of a multi-dimensional physical state benchmark fingerprint database. Under the absolutely healthy state after the initial assembly or overhaul of the machine tool, the central synchronous processing unit records the low-frequency straightness geometric deviation and high-frequency structural vibration terms at different feed speeds throughout the entire stroke range to construct the initial health state physical fingerprint database.

[0158] The physical fingerprint refers to the fact that, like a human fingerprint, each machine tool, even brand new ones, will have a unique set of mechanical resonant frequencies and basic geometric profiles when running at a specific speed due to slight differences in assembly tolerances. The system uses Fast Fourier Transform to convert the high-frequency structural vibration terms in the time domain into a frequency domain spectrum; it records the low-frequency straightness geometric deviations in the spatial domain as the basic envelope surface; these data are stored long-term in non-volatile memory as a health status benchmark for subsequent comparisons.

[0159] Step 8-2: Extraction of Time-Frequency Feature Degradation Evolution Law During the subsequent long-term operation of the equipment, the central synchronous processing unit continuously runs the feature extraction algorithm in the background, and performs differential comparison between the current vibration spectrum and geometric deviation and the physical fingerprint database in real time to extract feature variables representing mechanical degradation.

[0160] Feature degradation refers to the fact that the wear and tear of a physical entity is always gradual. For example, when a section of a guide rail is depleted of its lubricating grease due to long-term reciprocating motion, the coefficient of friction of the slider passing through that area will undergo a physical abrupt change.

[0161] The evolution law mapping refers to the physical mapping of low-frequency straightness geometric deviation to slow unidirectional drift at a specific location over a long period, which is physically mapped to machine tool foundation settlement or long-term stress release deformation of the cast iron bed. When the energy density of high-frequency structural vibration terms in a specific frequency band (such as a specific passing frequency caused by pitting of the ball screw) increases exponentially with the number of months of operation, it is physically mapped to mechanical fatigue spalling of the rolling elements.

[0162] Step 8-3: Trend prediction and predictive maintenance early warning issuance. Using time series-based machine learning algorithms to fit the extracted feature variables to trends, when it is predicted that a certain physical state residual will exceed the safety threshold within a specific time in the future, a predictive maintenance early warning is issued to the CNC system or manufacturing execution system through the industrial Ethernet interface.

[0163] Predictive maintenance, as the name suggests, differs from traditional corrective and preventative maintenance. It is based on the actual physical wear rate of the machine tool and provides intervention suggestions in advance before a fatal failure occurs that leads to scrap or downtime.

[0164] Time series algorithms, such as LSTM networks or the autoregressive moving average model ARIMA, are used to analyze degraded data with strong time memory and calculate the remaining service life of the guide rail.

[0165] The method for determining the aforementioned predictive maintenance early warning safety threshold is as follows: Based on statistical analysis of a limited number of historical operation data of the same model machine tool guideway throughout its entire life cycle, the extreme values ​​of the frequency domain energy density of the high-frequency structural vibration term that led to the surface roughness of the machined workpiece exceeding the standard are extracted; these extreme values ​​form a historical sample set, and the sample set is fitted with a Gaussian distribution to calculate its mean. with standard deviation According to the Raida Criterion ( (Guidelines), combined with the actual machining accuracy allowance requirements of the machine tool, select This serves as the safety threshold. For example, in the analysis of historical data from 10 test machine tools, it was found that the average extreme value of the vibration energy density in the 210Hz frequency band that caused the surface roughness to exceed the standard was... The standard deviation is To preserve sufficient lead time for early warnings, take This serves as the final set safety threshold.

[0166] Specifically, after a certain ultra-precision machine tool had run continuously for 5000 hours, the background health monitoring process of the central synchronous processing unit detected a hidden physical anomaly. This anomaly occurred during each high-speed feed of the slider to... At a specific location, the frequency domain characteristics of the high-frequency structural vibration terms extracted by the Kalman filter underwent significant changes: The vibrational energy near the frequency point is higher than the baseline value in the factory physical fingerprint database. Meanwhile, the low-frequency straightness geometric deviation remained unchanged at that location. The system algorithm made a precise diagnosis: since only the high-frequency excitation force increased while the geometric profile remained unchanged, this was not due to guide rail bending, but rather... Early micro-fatigue spalling (pitting) appeared on the ball bearings of the lead screw raceway or guide rail slider at a distance of meters. As the ball rolled over the spalling pits, it produced… The high-frequency impact caused the guide rail to continue processing, and the anomaly would be undetectable by traditional manual experience. However, the central synchronous processing unit, through data fitting, predicted that the high-frequency impact would cause a sharp deterioration in the vibration amplitude after 150 hours, leading to excessive surface roughness of the processed workpiece.

[0167] The system then sent a high-level data packet to the workshop MES system via industrial Ethernet: "Warning: Early contact fatigue exists at 3.5m on the Z-axis. It is recommended to schedule a shutdown for inspection and replenish high-viscosity grease or replace the slider within 100 hours." This mechanism helps to detect potential faults in advance and reduce the risk of losses caused by abnormal processing quality.

[0168] In some alternative embodiments, in the application scenario of dynamic compensation measurement of the straightness of the guide rail of a high-speed vertical passenger elevator in a 120-meter super high-rise building, the laser emitting unit is firmly installed at the absolute bottom of the vertical elevator shaft, providing an absolutely parallel physical optical reference beam upwards. The multi-sensor integrated measuring head is fixed to the inspection robot (slider) that climbs along the vertical elevator guide rail.

[0169] When the detection robot moves upwards to the current measurement distance At a certain time, the system receives an absolute position feedback signal from an external grating ruler. The basic beam waist radius of the laser emitting unit is known. meters, center wavelength rice The system calculates the evolution of the spot diameter using a nonlinear correction model of the spot morphology, applying the formula:

[0170] The radius of the light spot at that height is obtained. Meters. From this, the proportionality constant of the light spot diameter evolution is derived. Subsequently, the initial two-dimensional optical displacement signal captured by the four-quadrant detector (assuming lateral displacement) was analyzed. Vertical The system uses an evolution proportional constant to dynamically adjust its coordinate gain nonlinearly, and substitutes it into the formula. Output dynamically adjusted signal and This successfully eliminated the decrease in detection sensitivity caused by beam divergence over an 80-meter long path.

[0171] Due to the significant chimney effect within the vertical elevator shaft and the unilateral solar radiation from the building's exterior walls, complex localized thermodynamic convection phenomena exist within the shaft space. At a height of 80 meters, an orthogonal high-precision platinum resistance temperature sensor array captures the current transient air temperature in Celsius in real time. The absolute atmospheric pressure value is measured by a piezoresistive atmospheric pressure sensor. Pa, a partial water vapor pressure value is calculated using a capacitive humidity sensor. Pa. To eliminate the artifact of transverse thermal bending of the beam, the high-performance digital signal processor of the central synchronization processing unit introduces an improved Edren mathematical model to calculate the absolute correction value of the air refractive index: The refractive index constant of a helium-neon laser under standard atmospheric conditions. Input the following and calculate: The system then adds the absolute correction value to the base air refractive index using the formula... Establish the true air refractive index parameters of the current wellbore environment. It serves as the absolute physical measure of the phase velocity of light waves propagating in that local spatial medium.

[0172] By measuring the minute temperature difference using orthogonal temperature sensors positioned at the edge of the optical path cross-section, the system further calculates the spatial gradient of the transverse refractive index of the optical path within the horizontal plane of the vertical elevator shaft at this moment, along the horizontal X-axis. perpendicular to the Y-axis direction To solve for the aerodynamic curvature of an upwardly emitted reference beam, the system performs a Riemann space integral along the physical propagation direction of the beam, applying the ray trajectory equation: After quadratic spatial integration over a propagation distance of 80 meters, the lateral displacement compensation vector of the false light spot is determined to be a horizontal offset. Vertical offset Finally, using vector subtraction, the system completely eliminates the error caused by environmental convection from the initially acquired displacement signal: The final output is the first corrected displacement signal, stripped of environmental thermodynamic interference. and .

[0173] During the climbing process, the tiny steps at the guide rail joints and the robot's own mechanical vibrations cause high-frequency structural vibrations and attitude deflections. The triaxial microelectromechanical system gyroscope inside the multi-sensor integrated measurement head synchronously outputs transient angular velocity signals. For a cycle The system performs a high-precision time-domain Riemann integral on the transient angular velocity signals over a cumulative running time of seconds, strictly following the formula: Calculations are performed. By accumulating the numbers, the absolute angular displacement of the robot in three-dimensional space is accurately reconstructed, and the pitch angle around the X-axis is calculated. radians, yaw angle about the Y-axis radians, roll angle around the Z-axis Radius. This rigid body kinematics reduction, a purely mathematical concept, completely avoids the secondary interference problems caused by introducing beam splitters for angle measurement in optical measurement frameworks.

[0174] Because there is an inherent physical eccentricity between the actual rotation center of the detection robot and the geometric center of the four-quadrant detector, the system calls upon the physical eccentricity installation vector that was previously precisely calibrated using a coordinate measuring machine. ,in mm, mm, mm. The system uses spatial cross product operations to derive the translational error components induced by slider attitude deflection coupling: The additional Abbe translation error in the horizontal X direction is thus calculated. Additional Abbe translation error in the vertical Y direction Next, the system expands the two-dimensional first corrected displacement signal to a three-dimensional homogeneous coordinate system, multiplies it by the three-dimensional direction cosine rotation transformation matrix, and adds the translation error, applying the absolute compensation formula: The calculation yields a second corrected displacement signal that approximates the robot's geometric center extremely closely. and .

[0175] To safely isolate high-frequency structural vibration terms during dynamic processes, and thus extract only low-frequency straightness geometric deviations to feed back to the compensation mechanism, the system initializes a five-dimensional state vector containing the entire system state:

[0176] This state evolves naturally at an ultra-high sampling frequency of 100kHz, and its discretized state transition equation is: The equations incorporate a state transition matrix based on Newton's laws:

[0177] In the iterative computation of this model, the integration step size is strictly locked to 1. Seconds [cite:203,204][cite_start]. The system forces a spatiotemporal mapping between the high-frequency acceleration provided by the microelectromechanical accelerometer and the optical displacement, ensuring that the forced velocity updates strictly follow [the specified parameters]. The evolution of high-frequency vibration displacement follows Through the aforementioned matrix structure, simple optical spatial displacement is subjected to the physical constraint of inertial time integral.

[0178] In the final Kalman heterogeneous data fusion arbitration stage, the system establishes the observation equations. Using observation matrix An observation vector containing the optical second-corrected displacement signal and the MEMS acceleration signal was constructed. When the robot passes over a microscopic protrusion on the guide rail, it triggers a transient acceleration extreme value. At that time, the Kalman gain matrix automatically adjusts the trust weights in the frequency domain. The model will It is considered as a linear superposition of low-frequency straightness and high-frequency vibration [cite:215,216][cite_start], and the vibration caused by the bumps is precisely separated. High-frequency structural vibration terms To be placed in isolation and imprisonment [cite:224][cite_start]. The final purified product... Low-frequency straightness geometric deviation The piezoelectric ceramic micro-displacement compensation mechanism is sent to cancel out the physical space with equal amplitude and opposite direction. The asymmetric control strategy completely cuts off the risk of main shaft resonance caused by high frequency vibration and realizes nanometer-level safety closed-loop compensation in the full-speed operation state of the vertical elevator guide rail.

[0179] In summary, the laser collimation guide rail straightness dynamic compensation measurement method disclosed in this invention completely abandons the purely optical isomorphic patch design of traditional precision measurement. Starting from the first physical principles of precision measurement, this invention precisely deconstructs complex guide rail errors into three fundamental physical fields: spatial optical geometric projection, time-domain rigid body inertial kinematics, and spatial thermodynamic medium gradient.

[0180] Physical synchronization of heterogeneous data is achieved through a global nanosecond-level hardware clock bus; thermodynamic separation of aerodynamic bending is achieved through orthogonal temperature arrays and quadratic spatial integration; pure kinematic compensation of Abbe error is achieved through gyroscope integration; spatiotemporal mapping is established through Kalman state-space equations to separate the dynamic and static characteristics of extremely low-frequency geometric deformation and high-frequency mechanical vibration; and finally, compensation resonance is eliminated at the physical level through asymmetric closed-loop control.

[0181] This invention can achieve sub-micron level dynamic measurement and compensation accuracy in industrial environments, providing technical support for the accuracy maintenance and health monitoring of high-end CNC machine tools, extreme ultraviolet lithography machines and other equipment, and has engineering application value and industrialization prospects.

[0182] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A dynamic compensation measurement method for straightness of a laser collimation guide rail, characterized in that, include: The initial optical two-dimensional displacement signal, inertial transient angular velocity signal, inertial transient acceleration signal, and orthogonal temperature field signal output by the multi-sensor integrated measurement head are forcibly and synchronously acquired through the global hardware clock bus based on the field-programmable gate array inside the central synchronization processing unit. Based on the orthogonal temperature field signal, the spatial gradient of the optical path refractive index is calculated, the lateral displacement compensation vector of the false spot is derived, and it is subtracted from the initial two-dimensional optical displacement signal to obtain the first corrected displacement signal. The inertial transient angular velocity signal is integrated over time to obtain the true angular displacement. The first corrected displacement signal is then corrected by three-dimensional spatial coordinate transformation in combination with the physical eccentric installation vector to obtain the second corrected displacement signal. The time-domain integral step size is used to establish the spatiotemporal mapping between the inertial transient acceleration signal and the second corrected displacement signal, and the low-frequency straightness geometric deviation and high-frequency structural vibration term are separated by the Kalman filter algorithm; The low-frequency straightness geometric deviation is physically canceled by driving the piezoelectric ceramic micro-displacement compensation mechanism; the command transmission link from the high-frequency structural vibration term to the piezoelectric ceramic micro-displacement compensation mechanism is cut off, and it is used only for feedforward interpolation calculation.

2. The dynamic compensation method for straightness error of a laser collimation guide rail according to claim 1, wherein, The forced synchronous acquisition of the initial optical two-dimensional displacement signal, inertial transient angular velocity signal, inertial transient acceleration signal, and orthogonal temperature field signal output by the multi-sensor integrated measurement head via the global hardware clock bus based on a field-programmable gate array within the central synchronization processing unit includes: A laser emitting unit is arranged on the guide rail base to provide a parallel reference beam. The multi-sensor integrated measuring head, which integrates a four-quadrant detector, a three-axis microelectromechanical system accelerometer, a three-axis microelectromechanical system gyroscope, and an orthogonal high-precision platinum resistance temperature sensor array, is fixed on the slider of the guide rail to be tested. Using the internal sampling clock of the triaxial microelectromechanical system accelerometer as the sole reference source, a global synchronization trigger pulse is generated by frequency division through a phase-locked loop; By using the global synchronization trigger pulse to simultaneously trigger the analog-to-digital converter and the environmental sensor interface, it is ensured that the acquired initial optical two-dimensional displacement signal, inertial transient angular velocity and acceleration signal, and orthogonal temperature field signal strictly point to the same transient moment on the physical timeline.

3. The method for dynamic compensation measurement of the straightness of a laser collimation guide rail according to claim 1, characterized in that, The step of calculating the transverse refractive index spatial gradient of the optical path based on the orthogonal temperature field signal, deriving the spurious spot transverse displacement compensation vector, and subtracting it from the initial two-dimensional optical displacement signal to obtain the first corrected displacement signal includes: Obtain the current atmospheric pressure value and part of the water vapor pressure value, and combine them with the improved Edren mathematical model to calculate the absolute correction value of the air refractive index; The absolute correction value is added to the baseline air refractive index under undisturbed conditions to obtain the true air refractive index parameter for the current environment; Multiply the spatial gradient of the optical path's lateral refractive index by the reciprocal of the real air refractive index parameter, and perform the first-order spatial integration and the second-order spatial integration sequentially along the physical propagation direction of the beam to obtain the lateral displacement compensation vector of the false spot in the horizontal axis direction and the vertical axis direction. By subtracting the spurious spot lateral displacement compensation vector from the initial optical two-dimensional displacement signal using vector subtraction, the first corrected displacement signal, stripped of environmental thermodynamic interference, is output.

4. The method for dynamic compensation measurement of the straightness of a laser collimation guide rail according to claim 1, characterized in that, The step of integrating the inertial transient angular velocity signal over time to obtain the true angular displacement, and then performing a three-dimensional spatial coordinate transformation correction on the first corrected displacement signal using the physical eccentric installation vector, yields the second corrected displacement signal, which includes: Establish the physical eccentricity mounting vector between the actual rotation center of the slider and the geometric center of the four-quadrant detector in the multi-sensor integrated measuring head; The spatial cross product of the physical eccentric installation vector and the angular displacement vector formed by the actual angular displacement is performed to obtain the translational error component induced by the slider attitude deflection coupling. The first corrected displacement signal is expanded to a three-dimensional homogeneous coordinate system, multiplied by the three-dimensional direction cosine rotation transformation matrix, and then superimposed with the translation error component to complete the complete compensation of the Abbe error and output the second corrected displacement signal.

5. The method for dynamic compensation measurement of the straightness of a laser collimation guide rail according to claim 1, characterized in that, The step of establishing a spatiotemporal mapping between the inertial transient acceleration signal and the second corrected displacement signal using a time-domain integration step, and separating the low-frequency straightness geometric deviation and high-frequency structural vibration terms using a Kalman filter algorithm, includes: Initialize a five-dimensional state vector, which is strictly composed of the low-frequency straightness geometric deviation, high-frequency vibration velocity, high-frequency vibration acceleration, low-frequency environmental drift residual of the laser beam, and the high-frequency structural vibration term; Establish a state transition equation containing a state transition matrix. In the discrete iterative operation, multiply the inertial transient acceleration signal of the previous moment by the time domain integration step size and superimpose it onto the high-frequency vibration velocity of the previous moment to force an update of the current velocity state. An observation equation is established, and the second corrected displacement signal is defined in the mathematical model as a linear superposition of the low-frequency straightness geometric deviation and the high-frequency structural vibration term; Trust weights are assigned online using the Kalman gain matrix to isolate high-frequency fluctuation characteristics into the high-frequency structural vibration term, and the low-frequency straightness geometric deviation after removing the mechanical high-frequency resonance component is output.

6. The method for dynamic compensation measurement of the straightness of a laser collimation guide rail according to claim 1, characterized in that, The low-frequency straightness geometric deviation is physically offset by the piezoelectric ceramic micro-displacement compensation mechanism. Disconnecting the command transmission link from the high-frequency structural vibration term to the piezoelectric ceramic micro-displacement compensation mechanism, and using it only for feedforward interpolation calculations includes: The low-frequency straightness geometric deviation is sent to the servo control system of the guide rail in the form of digital signal packets via fieldbus. The servo control system converts digital signal packets into analog voltage signals, which physically drive the piezoelectric ceramic micro-displacement compensation mechanism to generate equal-amplitude and opposite-axis mechanical displacements, thereby offsetting the static and low-frequency deformation errors of the guide rail profile in real time. The physical execution authority of the high-frequency structural vibration item is intercepted at the bottom layer of the control architecture, and it is fed back to the host computer CNC system as an independent compensation residual data stream, which only participates in the tool trajectory advance interpolation prediction of the machining program.

7. The method for dynamic compensation measurement of the straightness of a laser collimation guide rail according to claim 1, characterized in that, Before calculating the spatial gradient of the optical path's transverse refractive index based on the orthogonal temperature field signal, deriving the spurious spot transverse displacement compensation vector, and subtracting it from the initial two-dimensional optical displacement signal to obtain the first corrected displacement signal, a dynamic displacement gain compensation stage is also included, specifically comprising: The system receives real-time feedback signals of the absolute position of the slider from an external grating ruler to obtain the current measurement distance. Combining the current measurement distance, the basic beam waist radius of the laser beam, the beam quality factor, and the center wavelength, the evolution proportional constant of the beam diameter is calculated using a nonlinear correction model for the beam shape. The coordinate gain of the initial optical two-dimensional displacement signal is dynamically adjusted nonlinearly using the evolution proportional constant to eliminate the detection sensitivity attenuation caused by beam divergence under long stroke.

8. The method for dynamic compensation measurement of the straightness of a laser collimation guide rail according to claim 3, characterized in that, The internal processing architecture configuration of the central synchronization processing unit includes: The field-programmable gate array is configured to process multi-channel high-speed raw data streams, execute low-level digital filtering logic, and control the global hardware clock bus. A high-performance digital signal processor is configured to perform double-precision floating-point matrix operations of the first-order spatial integration, the second-order spatial integration, the three-dimensional spatial coordinate transformation, and the Kalman filter algorithm. A high-speed on-chip bus is constructed to connect the two types of processors for direct memory access and data exchange, ensuring that the overall physical delay from the data acquisition end to the control output end used to output the low-frequency straightness geometric deviation is controlled within a preset millisecond limit.

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