High-precision dynamic error real-time compensation method based on five-axis linkage

Abstract

The invention discloses a high-precision dynamic error real-time compensation method based on five-axis linkage, and relates to the technical field of machine manufacturing, and the method comprises the following steps: multi-source dynamic error perception: collecting geometric errors of a machine tool through a grating ruler, collecting temperature field distribution through an infrared thermal imager, and collecting cutting force disturbance through a piezoelectric force sensor; the method comprises the steps of constructing a grating ruler, constructing a thermal infrared imager, constructing a multi-source data acquisition system, carrying out nonlinear coupling modeling, and establishing a dynamic error model based on improved Volterra series, and has the advantages that the multi-source data acquisition system is constructed through the grating ruler, the thermal infrared imager and the piezoelectric force sensor, geometric, thermal and force multi-source dynamic errors are sensed synchronously, and the dynamic error detection accuracy is improved. The nonlinear coupling characteristic of the thermal-force-geometric error is accurately quantified by combining an improved Volterra series model and Lyapunov exponent analysis, the problem that a traditional single-source error model cannot accurately describe a complex error field is solved, and the accuracy of error prediction is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical manufacturing, and in particular to a high-precision dynamic error real-time compensation method based on five-axis linkage. Background Art

[0002] Five-axis machining technology, as a core support in high-end manufacturing, is widely used in the production of key components in aerospace, automotive molds, precision electronics, and other fields. Its machining accuracy directly affects equipment performance and reliability. However, during the high-speed, high-precision machining process of five-axis machine tools, multiple sources of dynamic errors, such as geometric errors, thermal deformation errors, and cutting force disturbance errors, couple with each other, forming a complex nonlinear error field. Traditional single-source error compensation methods are unable to effectively suppress error transmission, resulting in key indicators such as machining profile and surface quality failing to meet precision manufacturing requirements. In the existing technology, most compensation methods have problems such as insufficient real-time performance and weak adaptability: on the one hand, traditional compensation models do not fully consider the chaotic characteristics of thermal-mechanical-geometric errors, and the quantification of nonlinear cross-coupling effects is not accurate; on the other hand, the compensation rule base is fixed and cannot be dynamically optimized according to the actual processing effect. In addition, there is a lack of reliable fault-tolerant mechanism when sensor data is abnormal, which can easily lead to compensation failure or accuracy fluctuations, restricting the application expansion of five-axis machine tools in ultra-precision machining scenarios. To this end, we propose a high-precision dynamic error real-time compensation method based on five-axis linkage. Summary of the Invention

[0003] The purpose of the present invention is to provide a high-precision dynamic error real-time compensation method based on five-axis linkage.

[0004] To achieve the above object, the present invention provides the following technical solution: a high-precision dynamic error real-time compensation method based on five-axis linkage, the compensation method comprising the following steps: S1. Use the grating ruler to collect the machine tool geometric error, the infrared thermal imager to collect the temperature field distribution, and the piezoelectric force sensor to collect the cutting force disturbance. The data from the grating ruler, infrared thermal imager, and piezoelectric force sensor are used to build a multi-source data acquisition system. S2, the data is transmitted to the Volterra series through the multi-source data acquisition system to establish the dynamic error model, whose state equation is: ; in, is the state vector The instantaneous rate of change over time, is the system state vector, is the control input, is the thermal error, For force error, the dynamic error model introduces Lyapunov exponent to analyze the chaotic characteristics of thermal-mechanical-geometric errors and quantify the nonlinear cross-coupling effect; S3. After establishing the dynamic error model, the sliding window recursive least squares method is used to update the model parameters, and the fuzzy adaptive compensator is combined to output the dynamic gain , the dynamic gain It is the real-time adjustment coefficient output by the fuzzy adaptive compensator, which is used to dynamically optimize the compensation intensity; S4, setting up a field programmable gate array, also known as FPGA, wherein the FPGA adopts a field programmable gate array hardware platform with a parallel pipeline architecture to generate a feedforward pre-compensation amount and feedback compensation , the total compensation , controlling the piezoelectric ceramic micro-displacement platform to perform nanometer-level corrections based on dynamic gain Generate total compensation amount; S5. Analyze the compensation effect evaluation index through the multi-source data acquisition system. The compensation effect evaluation index measures the compensation accuracy index, and trigger the rule base optimization based on the evaluated compensation effect; S6. When sensor data in the multi-source data acquisition system is abnormal, a Kalman filter is triggered to estimate a replacement value; S7. The actual machining error of the machine tool after correction by the compensation algorithm is measured by the grating ruler, and the error spectrum and contour error after compensation are detected to determine whether the machining accuracy requirements are met.

[0005] As a further solution of the present invention, the multi-source data acquisition system described in S1 is specifically: the grating ruler is used to obtain the position error data of the five axes of the machine tool X, Y, Z, A and C in real time, the infrared thermal imager collects the temperature field distribution of the key components of the spindle, guide rail and screw at a frequency of ≤10Hz, and the piezoelectric force sensor monitors the cutting force disturbance in the three directions of X, Y and Z during the cutting process at a sampling rate of ≥1kHz.

[0006] As a further solution of the present invention, the nonlinear coupling modeling in S2 further includes: S21. Perform ISO230-2 geometric error calibration in cold state and establish the basic geometric error parameter library of machine tools; S22. Obtaining the heat conduction matrix through temperature rise experiment ,in is the heat source location, For the affected parts, For the Heat source for the The thermal conductivity of each component, the axial expansion of the main shaft ,in, is the thermal conductivity coefficient, is the spindle temperature variation; S23. Force Error Quantification: Validating Cutting Force Using Cointegration Analysis and position error The coupling relationship is to collect 100 sets of historical processing data, among which Respectively hour and To ensure the cutting force, the data is directly related to the multi-source data acquisition system of S1, and the position error is obtained by fitting the cointegration equation using the least squares method. The specific formula is as follows: ; in, For the hour Position error, is the initial error, for The force influence coefficient, for The force influence coefficient, It is a stationary residual series, verified by ADF test stability.

[0007] As a further solution of the present invention, the parameter update formula of the sliding window recursive least squares method in S3 is: ; in, For the The model parameter vector of the iteration, is the parameter vector of the previous iteration, is the gain matrix, For the The actual error value of the observation, is the regression vector, is the transpose of the matrix, and the formula of the gain matrix is ,in is the covariance matrix, and the formula of the covariance matrix is ,in, For the forgetting factor.

[0008] As a further solution of the present invention, the rule base of the fuzzy adaptive compensator is designed as follows: Calculate the error fluctuation range and the error standard deviation using the formula: ; ; in, is the error fluctuation amplitude, is the current error, For the The deviation between the actual error of the machine tool and the ideal position within a cycle, is the last error, is the standard error, is the mean error of the first 100 periods; when When the error change rate is 0 o'clock, then , and adjust the gain according to the upper limit of the piezoelectric ceramic; when When ,in, as well as are the gain voltages applied to the piezoelectric ceramics; when When , the Gaussian membership function is used to calculate , the specific function is ,in, is the base of natural logarithms, is the mean error.

[0009] As a further solution of the present invention, in S4, the feedforward precompensation amount The generation method is: analyze the trajectory of the next three interpolation cycles, and calculate the rotation axis compensation by quaternion interpolation method. The interpolation formula is: ; in, and is the attitude quaternion of the adjacent interpolation points, for and The angle of is the interpolation parameter.

[0010] As a further solution of the present invention: the compensation effect evaluation index is calculated in each processing cycle in S5 ,in, The actual error after compensation is measured by the grating ruler. is the target error, when , then the fuzzy rule base is updated through genetic algorithm.

[0011] As a further solution of the present invention: the FPGA hardware implementation in S4 adopts a parallel pipeline architecture, and the timing satisfies: ; in, is the analog-to-digital conversion time, is the compensation calculation time, The time for digital-to-analog conversion is used. At the same time, the high-frequency oscillation is suppressed by the magnetorheological damper. The damping force in, is the damping force, The damping coefficient is adjusted in real time. The damping coefficient is dynamically calculated by FPGA according to the vibration frequency. is the vibration velocity, which is obtained by integrating the acceleration sensor.

[0012] As a further solution of the present invention, the specific formula for the Kalman filter estimation substitute value in S6 is as follows: ; in, For the step-predicted state vector, is the estimated state of the previous step, is the previous step control input, is the forecast error covariance matrix, is the prediction error covariance matrix of the previous step, is the state transition matrix, is the control input matrix, is the process noise covariance matrix.

[0013] By adopting the above technical solution, compared with the prior art, the beneficial effects of the present invention are: 1. This invention constructs a multi-source data acquisition system using a grating ruler, an infrared thermal imager, and a piezoelectric force sensor to simultaneously sense geometric, thermal, and force multi-source dynamic errors. Combining an improved Volterra series model with Lyapunov exponent analysis, this system accurately quantifies the nonlinear coupling characteristics of thermal, force, and geometric errors. This solves the problem of inaccurate description of complex error fields by traditional single-source error models and significantly improves the accuracy of error prediction. 2. This invention uses a sliding window recursive least squares method to update model parameters in real time. Combining a fuzzy adaptive compensator with a genetic algorithm dynamic optimization rule base, the system can automatically adjust compensation strategies (such as dynamic gain parameters) based on machining results. This overcomes the limitations of poor adaptability of traditional fixed rule bases, effectively suppresses error fluctuations, and ensures long-term machining accuracy consistency. 3. The present invention achieves a compensation cycle of ≤50μs through an FPGA-based parallel pipeline architecture, combined with the nanometer-level correction capability of the piezoelectric ceramic micro-displacement platform to meet the real-time requirements of high-speed machining. At the same time, the Kalman filter fault-tolerant mechanism processes abnormal sensor data to avoid compensation interruptions, significantly improving the reliability and stability of five-axis machine tools in ultra-precision machining scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 This is a flow chart of nonlinear coupling modeling in an embodiment of the present invention; Figure 2This is a flow chart of the sliding window recursive least squares method in an embodiment of the present invention; Figure 3 This is a flow chart of fuzzy adaptive compensator rules in an embodiment of the present invention; Figure 4 A flow chart for generating a feedforward pre-compensation amount in an embodiment of the present invention; Figure 5 This is a flow chart of dynamic rule base optimization in an embodiment of the present invention; Figure 6 This is a flow chart of the fault tolerance mechanism in an embodiment of the present invention; Figure 7 This is a flow chart of FPGA hardware accelerated closed-loop control in an embodiment of the present invention. DETAILED DESCRIPTION

[0015] The specific embodiments of the present invention will be further described below in conjunction with the accompanying drawings. It should be noted that the description of these embodiments is used to help understand the present invention, but does not constitute a limitation of the present invention.

[0016] In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0017] Please see the attached Figure 1 -Attached Figure 7 The present invention is based on a high-precision dynamic error real-time compensation method for five-axis linkage, and the compensation method includes the following steps: S1. Use the grating ruler to collect the machine tool geometric error, the infrared thermal imager to collect the temperature field distribution, and the piezoelectric force sensor to collect the cutting force disturbance. The data from the grating ruler, infrared thermal imager, and piezoelectric force sensor are used to build a multi-source data acquisition system. S2, the data is transmitted to the Volterra series through the multi-source data acquisition system to establish the dynamic error model, whose state equation is: ; in, is the state vector The instantaneous rate of change over time, is the system state vector, is the control input, is the thermal error, For force error, the dynamic error model introduces Lyapunov exponent to analyze the chaotic characteristics of thermal-mechanical-geometric errors and quantify the nonlinear cross-coupling effect; S3. After establishing the dynamic error model, the sliding window recursive least squares method is used to update the model parameters, and the fuzzy adaptive compensator is combined to output the dynamic gain , the dynamic gain It is the real-time adjustment coefficient output by the fuzzy adaptive compensator, which is used to dynamically optimize the compensation intensity; S4, setting up a field programmable gate array, also known as FPGA, wherein the FPGA adopts a field programmable gate array hardware platform with a parallel pipeline architecture to generate a feedforward pre-compensation amount and feedback compensation , the total compensation , controlling the piezoelectric ceramic micro-displacement platform to perform nanometer-level corrections based on dynamic gain Generate total compensation amount; S5. Analyze the compensation effect evaluation index through the multi-source data acquisition system. The compensation effect evaluation index measures the compensation accuracy index, and trigger the rule base optimization based on the evaluated compensation effect; S6. When sensor data in the multi-source data acquisition system is abnormal, a Kalman filter is triggered to estimate a replacement value; S7. The actual machining error of the machine tool after correction by the compensation algorithm is measured by the grating ruler, and the error spectrum and contour error after compensation are detected to determine whether the machining accuracy requirements are met.

[0018] In one embodiment of the present invention, the multi-source data acquisition system in S1 is specifically as follows: the grating ruler is used to obtain the position error data of the five axes of the machine tool X, Y, Z, A and C in real time, the infrared thermal imager collects the temperature field distribution of the key components of the spindle, guide rail and screw at a frequency of ≤10Hz (the sampling frequency is determined based on the thermal error response time constant of 30s, satisfying the Nyquist sampling theorem), and the piezoelectric force sensor monitors the cutting force disturbances in the three directions of X, Y and Z during the cutting process at a sampling rate of ≥1kHz (covering the main frequency components of the cutting force 10~500Hz).

[0019] In one embodiment of the present invention, the nonlinear coupling modeling in S2 further includes: S21. Perform ISO230-2 geometric error calibration in cold state and establish the basic geometric error parameter library of machine tools; S22. Obtaining the heat conduction matrix through temperature rise experiment ,in is the heat source location, For the affected parts, For the Heat source for the The thermal conductivity of each component, the axial expansion of the main shaft ,in, is the thermal conductivity coefficient, Spindle temperature variation is the linear expansion coefficient of the spindle material (40Cr); S23. Force Error Quantification: Validating Cutting Force Using Cointegration Analysis and position error The coupling relationship is to collect 100 sets of historical processing data, among which Respectively hour and To ensure the cutting force, the data is directly related to the multi-source data acquisition system of S1, and the position error is obtained by fitting the cointegration equation using the least squares method. The specific formula is as follows: ; in, For the hour Position error, is the initial error, for The force influence coefficient, for The force influence coefficient, It is a stationary residual series, verified by ADF test stability.

[0020] In one embodiment of the present invention, the parameter update formula of the sliding window recursive least squares method in S3 is: ; in, For the The model parameter vector of the iteration (including the kernel function coefficients of the Volterra series), is the parameter vector of the previous iteration, is the gain matrix (adjustment parameter update rate), For the The actual error value of the observation (measured by the grating ruler), is the regression vector (including historical errors cutting force temperature input variables), is the transpose of the matrix, and the formula of the gain matrix is ,in is the covariance matrix, and the formula of the covariance matrix is ,in, is the forgetting factor (set according to the historical data weight attenuation requirement so that each period, the weight of historical data decays to , balancing real-time performance and data utilization).

[0021] In one embodiment of the present invention, the rule base of the fuzzy adaptive compensator is designed as follows: Calculate the error fluctuation range and the error standard deviation using the formula: ; ; in, is the error fluctuation amplitude, is the current error, is the index variable for summation, is the last error, is the standard error, is the mean error of the first 100 periods; when When the error change rate is When , and adjust the gain according to the upper limit of the piezoelectric ceramic; when hour, ,in, as well as are the gain voltages applied to the piezoelectric ceramics; At that time, the Gaussian membership function is used to calculate , the specific function is ,in, is the base of natural logarithms, is the mean error.

[0022] In one embodiment of the present invention, the feedforward precompensation amount in S4 is The method for generating is to analyze the trajectory of the next three interpolation cycles (the interpolation cycle is set to 16.7 μs by the CNC system) and calculate the rotation axis compensation using quaternion interpolation (a mathematical method for three-dimensional rotation interpolation that can avoid universal joint lock compared to Euler angle interpolation). The interpolation formula is: ; in, and is the attitude quaternion of the adjacent interpolation points (output by the trajectory planning module of the CNC system in the form of , is the scalar part, is the vector part), for and The angle (calculated by dot product ), is the interpolation parameter (determined by the interpolation time ratio, correspond correspond ).

[0023] In one embodiment of the present invention: In S5, the compensation effect evaluation index is calculated for each processing cycle (about 10ms). ,in, The actual error after compensation is measured by the grating ruler. is the target error, set to 0.5μm, when , then the fuzzy rule base is updated by genetic algorithm (adjust and other parameters).

[0024] In one embodiment of the present invention, the FPGA hardware implementation in S4 adopts a parallel pipeline architecture, and the timing satisfies: ; in, is the analog-to-digital conversion time, , is the compensation calculation time, is the digital-to-analog conversion time, , while suppressing high frequency oscillations through magnetorheological dampers, the damping force in, is the damping force, The damping coefficient is adjusted in real time. The damping coefficient is dynamically calculated by FPGA according to the vibration frequency. is the vibration velocity, which is obtained by integrating the acceleration sensor.

[0025] In one embodiment of the present invention, the specific formula for estimating the replacement value by Kalman filtering in S6 is as follows: ; in, For the step prediction state vector (including alternative values ​​such as temperature and cutting force), is the estimated state of the previous step, is the previous step control input, is the forecast error covariance matrix (describing the uncertainty of the forecast state), is the prediction error covariance matrix of the previous step, A is the state transfer matrix (determined by the system dynamics model, reflecting the evolution of the state over time), is the control input matrix (determined by the actuator characteristics, reflecting the impact of the control input on the state), is the process noise covariance matrix (the noise variance is determined experimentally and describes the statistical characteristics of the noise inside the system).

[0026] Example: Dynamic error compensation in precision machining of aerospace titanium alloy blades Application scenario: Precision machining of titanium alloy blades for an aircraft engine. The blade profile is a complex free-form surface with a profile accuracy requirement of ≤1μm. The machining process is affected by the coupling of cutting force disturbances, spindle temperature rise, and machine tool geometric errors. Traditional compensation methods are difficult to meet the accuracy requirements. S1 Multi-source Dynamic Error Sensing: A multi-source data acquisition system is deployed on a five-axis machining center (model DMGMORIDMU80eVo). A Heidenhain LIP481 grating scale (resolution 0.05μm) is installed on each of the five axes, X, Y, Z, A, and C, to collect position errors in real time. FLIRA655sc infrared thermal imagers (sampling frequency 10Hz, temperature resolution 0.05°C) are installed on key parts of the spindle, guide rails, and screws (front bearing seat, screw nut pair, guide rail slider). A Kistler 9257B piezoelectric force sensor (sampling rate 1kHz, range ±5kN) is installed on the tool holder to monitor cutting forces in the X, Y, and Z directions (typical cutting force range 500-2000N). S2 nonlinear coupling modeling: S21 cold geometric error calibration: Execute ISO230-2 standard geometric error calibration, use Renishaw XL-80 laser interferometer to measure the maximum X-axis positioning error of 0.03mm, and the Y-axis straightness error of 0.02mm / m, and establish a basic geometric error parameter library; S22 heat conduction matrix calculation: The spindle is idled at 10,000 rpm for 2 hours, and the infrared thermal imager collects the temperature field data of each component to calculate the heat conduction matrix (such as the heat conduction coefficient of the front bearing seat to the spindle). , the measured spindle temperature rises from 25℃ to 45℃ ( , calculate the axial expansion , which is consistent with the value of 23.8μm measured by laser interferometer; S23 force error quantification: 100 sets of titanium alloy milling data were collected (cutting parameters: speed 12000 rpm, feed rate 2000 mm / min, depth of cut 0.5 mm), and the cointegration equation was fitted using the least squares method. , the ADF test confirms that the residuals are stationary ( statistic = -3.8 < critical value -3.43); S3 intelligent dynamic compensation: using sliding window recursive least squares method (forgetting factor ) Update the Volterra model parameters every 50μs. In the fuzzy adaptive compensator, the error mean of the first 100 cycles is , standard deviation , when the error fluctuates And when the error increases, Take the maximum value of 5V (maximum driving voltage of piezoelectric ceramics), when hour, is the current error); S4 hardware accelerated closed-loop control: sensor data is transmitted to Xilinx K7 FPGA via JESD204B interface, and ADC sampling (8μs), compensation calculation (25μs) and DAC output (7μs) are processed in parallel. The total cycle is 40μs≤50μs. The feedforward pre-compensation is calculated by analyzing the trajectory of the next three interpolation cycles (50.1μs) and using quaternion interpolation method to calculate the rotation axis compensation (such as the quaternion of the attitude of adjacent interpolation points). Angle , hour ; S5 dynamic rule base optimization: Calculate compensation effect evaluation index every processing cycle (10ms) ,initial , triggering genetic algorithm adjustment From 5V to 6V, From 0.5V / μm to 0.6V / μm, and then Increased to 0.95 ; S6 fault-tolerance mechanism: The grating scale generates abnormal data due to electromagnetic interference (Z-axis error -10μm), triggering the Kalman filter and state transfer matrix , predicted state (actual temperature 90°C, cutting force 980N), use the predicted value to replace the abnormal data and continue compensation; S7 precision verification: Three-coordinate measurement after processing showed that the maximum contour error was 2.5μm before compensation, which dropped to 0.6μm after compensation (meeting the ≤1μm requirement). The amplitude of the 50Hz and 100Hz components in the error spectrum dropped from 1.2μm to 0.2μm, verifying the multi-source error suppression effect.

[0027] Although the present invention is disclosed above with reference to preferred embodiments, this is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications without departing from the spirit and scope of the present invention. Therefore, any modifications, equivalent variations, and modifications made to the above embodiments in accordance with the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the scope of protection defined by the claims of the present invention.

Claims

1. A high-precision dynamic error real-time compensation method based on five-axis linkage, including a compensation method, characterized in that: The compensation method comprises the following steps: S1. Use the grating ruler to collect the machine tool geometric error, the infrared thermal imager to collect the temperature field distribution, and the piezoelectric force sensor to collect the cutting force disturbance. The data from the grating ruler, infrared thermal imager, and piezoelectric force sensor are used to build a multi-source data acquisition system. S2, the data is transmitted to the Volterra series through the multi-source data acquisition system to establish the dynamic error model, whose state equation is: ； in, is the state vector The instantaneous rate of change over time, is the system state vector, is the control input, is the thermal error, For force error, the dynamic error model introduces Lyapunov exponent to analyze the chaotic characteristics of thermal-mechanical-geometric errors and quantify the nonlinear cross-coupling effect; S3. After establishing the dynamic error model, the sliding window recursive least squares method is used to update the model parameters, and the fuzzy adaptive compensator is combined to output the dynamic gain , the dynamic gain It is the real-time adjustment coefficient output by the fuzzy adaptive compensator, which is used to dynamically optimize the compensation intensity; S4, setting up a field programmable gate array, also known as FPGA, wherein the FPGA adopts a field programmable gate array hardware platform with a parallel pipeline architecture to generate a feedforward pre-compensation amount and feedback compensation , the total compensation , controlling the piezoelectric ceramic micro-displacement platform to perform nanometer-level corrections based on dynamic gain Generate total compensation amount; S5. Analyze the compensation effect evaluation index through the multi-source data acquisition system. The compensation effect evaluation index measures the compensation accuracy index, and trigger the rule base optimization based on the evaluated compensation effect; S6. When sensor data in the multi-source data acquisition system is abnormal, a Kalman filter is triggered to estimate a replacement value; S7. The actual machining error of the machine tool after correction by the compensation algorithm is measured by the grating ruler, and the error spectrum and contour error after compensation are detected to determine whether the machining accuracy requirements are met.

2. The high-precision dynamic error real-time compensation method based on five-axis linkage according to claim 1 is characterized in that: The multi-source data acquisition system described in S1 is specifically as follows: the grating ruler is used to obtain the position error data of the five axes of the machine tool X, Y, Z, A and C in real time, the infrared thermal imager collects the temperature field distribution of the key components of the spindle, guide rail and screw at a frequency of ≤10Hz, and the piezoelectric force sensor monitors the cutting force disturbance in the three directions of X, Y and Z during the cutting process at a sampling rate of ≥1kHz.

3. The high-precision dynamic error real-time compensation method based on five-axis linkage according to claim 1 is characterized in that: The nonlinear coupling modeling in S2 also includes: S21. Perform ISO230-2 geometric error calibration in cold state and establish the basic geometric error parameter library of machine tools; S22. Obtaining the heat conduction matrix through temperature rise experiment ,in is the heat source location, For the affected parts, For the Heat source for the The thermal conductivity of each component, the axial expansion of the main shaft ,in, is the thermal conductivity coefficient, is the spindle temperature variation; S23. Force Error Quantification: Validating Cutting Force Using Cointegration Analysis and position error The coupling relationship is to collect 100 sets of historical processing data, among which Respectively hour and To calculate the cutting force, ensure that the data is directly related to the S1 multi-source data acquisition system, and obtain the position error by fitting the cointegration equation using the least squares method. The specific formula is as follows: ； in, For the hour Position error, is the initial error, for The force influence coefficient, for The force influence coefficient, It is a stationary residual series, verified by ADF test stability.

4. The high-precision dynamic error real-time compensation method based on five-axis linkage according to claim 1 is characterized in that: The parameter update formula of the sliding window recursive least squares method in S3 is: ； in, For the The model parameter vector of the iteration, is the parameter vector of the previous iteration, is the gain matrix, For the The actual error value of the observation, is the regression vector, is the transpose of the matrix, and the formula of the gain matrix is ,in is the covariance matrix, and the formula of the covariance matrix is ,in, For the forgetting factor.

5. The high-precision dynamic error real-time compensation method based on five-axis linkage according to claim 4 is characterized in that: The rule base of the fuzzy adaptive compensator is designed as follows: Calculate the error fluctuation range and the error standard deviation using the formula: ； ； in, is the error fluctuation amplitude, is the current error, For the The deviation between the actual error of the machine tool and the ideal position within a cycle, is the last error, is the standard error, is the mean error of the first 100 periods; when When the error change rate is 0 o'clock, then , and adjust the gain according to the upper limit of the piezoelectric ceramic; when When ,in, as well as are the gain voltages applied to the piezoelectric ceramics; when When , the Gaussian membership function is used to calculate , the specific function is ,in, is the base of natural logarithms, is the mean error.

6. The high-precision dynamic error real-time compensation method based on five-axis linkage according to claim 5 is characterized in that: In S4, the feedforward precompensation amount The generation method is: analyze the trajectory of the next three interpolation cycles, and calculate the rotation axis compensation by quaternion interpolation method. The interpolation formula is: ； in, and is the attitude quaternion of the adjacent interpolation points, for and The angle of is the interpolation parameter.

7. The high-precision dynamic error real-time compensation method based on five-axis linkage according to claim 6 is characterized in that: In S5, the compensation effect evaluation index is calculated for each processing cycle. ,in, The actual error after compensation is measured by the grating ruler. is the target error, when , then the fuzzy rule base is updated through genetic algorithm.

8. The high-precision dynamic error real-time compensation method based on five-axis linkage according to claim 1 is characterized in that: The FPGA hardware implementation in S4 adopts a parallel pipeline architecture, and the timing meets the following requirements: ； in, is the analog-to-digital conversion time, is the compensation calculation time, The time for digital-to-analog conversion is used. At the same time, the high-frequency oscillation is suppressed by the magnetorheological damper. The damping force in, is the damping force, The damping coefficient is adjusted in real time. The damping coefficient is dynamically calculated by FPGA according to the vibration frequency. is the vibration velocity, which is obtained by integrating the acceleration sensor.

9. The high-precision dynamic error real-time compensation method based on five-axis linkage according to claim 1 is characterized in that: The specific formula for the Kalman filter estimation substitute value in S6 is as follows: ； in, For the step-predicted state vector, is the estimated state of the previous step, is the previous step control input, is the forecast error covariance matrix, is the prediction error covariance matrix of the previous step, is the state transition matrix, is the control input matrix, is the process noise covariance matrix.

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