A High-Precision Dynamic Error Real-Time Compensation Method Based on Five-Axis Linkage

Abstract

This invention discloses a high-precision dynamic error real-time compensation method based on five-axis linkage. This invention relates to the field of mechanical manufacturing technology and includes the following steps: multi-source dynamic error sensing: A multi-source data acquisition system is constructed by collecting machine tool geometric errors using a grating ruler, temperature field distribution using an infrared thermal imager, and cutting force disturbances using a piezoelectric sensor. Nonlinear coupling modeling is then performed, and a dynamic error model is established based on an improved Volterra series. The advantages of this invention are: by constructing a multi-source data acquisition system using a grating ruler, infrared thermal imager, and piezoelectric sensor, geometric, thermal, and force multi-source dynamic errors are simultaneously sensed. Combined with the improved Volterra series model and Lyapunov exponent analysis, the nonlinear coupling characteristics of thermal-force-geometric errors are accurately quantified, solving the problem of inaccurate description of complex error fields by traditional single-source error models and significantly improving the accuracy of error prediction.

Description

Technical Field

[0001] This invention relates to the field of mechanical manufacturing technology, specifically to a high-precision dynamic error real-time compensation method based on five-axis linkage. Background Technology

[0002] Five-axis linkage machining technology, as a core support in the field of high-end manufacturing, is widely used in the production of key components in aerospace, automotive molds, and precision electronics. Its machining accuracy directly affects the performance and reliability of equipment. However, in the process of high-speed and high-precision machining, five-axis machine tools are subject to the coupling of multiple sources of dynamic errors, such as geometric errors, thermal deformation errors, and cutting force disturbance errors, forming a complex nonlinear error field. Traditional single-source error compensation methods are difficult to effectively suppress error transmission, resulting in key indicators such as machining contour and surface quality failing to meet the requirements of precision manufacturing.

[0003] In existing technologies, most compensation methods suffer from 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 are not accurate in quantifying nonlinear cross-coupling effects. On the other hand, the compensation rule base is fixed and cannot be dynamically optimized according to the actual processing effect. Furthermore, there is a lack of reliable fault tolerance mechanisms when sensor data is abnormal, which can easily lead to compensation failure or accuracy fluctuations, thus restricting the application expansion of five-axis machine tools in ultra-precision machining scenarios. To address this, we propose a high-precision dynamic error real-time compensation method based on five-axis linkage. Summary of the Invention

[0004] The purpose of this invention is to provide a high-precision dynamic error real-time compensation method based on five-axis linkage.

[0005] To achieve the above objectives, 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:

[0006] S1. A multi-source data acquisition system is constructed by collecting machine tool geometric errors using a grating ruler, temperature field distribution using an infrared thermal imager, and cutting force disturbance using a piezoelectric sensor.

[0007] S2. Data is transmitted to the Volterra series dynamic error model through a multi-source data acquisition system. The state equation is as follows:

[0008]

[0009] in, Let ε be the instantaneous rate of change of the state vector x over time, x be the system state vector, u be the control input, and ε be the variable. thermal For thermal error, ε forceFor force error, f(x) is the inherent nonlinear dynamic function in the multi-source data acquisition system, and g(.) is the disturbance coupling function. The dynamic error model introduces the Lyapunov exponent to analyze the chaotic characteristics of thermo-mechanical-geometric errors and quantifies the nonlinear cross-coupling effect.

[0010] S3. After establishing the dynamic error model, the model parameters are updated using the sliding window recursive least squares method, and the dynamic gain K is output by combining the fuzzy adaptive compensator. comp The dynamic gain K comp It is the real-time adjustment coefficient output by the fuzzy adaptive compensator, used to dynamically optimize the compensation intensity;

[0011] S4. Configure a Field Programmable Gate Array (FPGA), which uses a parallel pipelined architecture FPGA hardware platform to generate the feedforward pre-compensation quantity ΔP. ff With feedback compensation amount ΔP fb The total compensation amount ΔP total =ΔP ff +K comp ·ΔP fb The piezoelectric ceramic micro-displacement platform is controlled to perform nanoscale corrections based on dynamic gain K. comp Generate the total compensation amount;

[0012] S5. Analyze the compensation effect evaluation index through a multi-source data acquisition system. The compensation effect evaluation index is an indicator that measures the accuracy of compensation. Optimize the rule base based on the evaluation of the compensation effect.

[0013] S6. When sensor data in a multi-source data acquisition system is abnormal, Kalman filtering is triggered to estimate the substitute value.

[0014] S7. The actual machining error of the machine tool after the compensation algorithm is corrected is measured by a grating ruler. The error spectrum and contour error after compensation are detected to determine whether the machining accuracy requirements are met.

[0015] As a further embodiment of the present invention, the multi-source data acquisition system in S1 specifically comprises: a grating ruler for real-time acquisition of position error data of the five axes of the machine tool (X, Y, Z, A, and C); an infrared thermal imager for acquiring the temperature field distribution of key components such as the spindle, guide rail, and lead screw at a frequency of ≤10Hz; and a piezoelectric sensor for monitoring the X, Y, and Z three-axis cutting force disturbances during the cutting process at a sampling rate of ≥1kHz.

[0016] As a further aspect of the present invention, the nonlinear coupling modeling in S2 further includes:

[0017] S21. Perform ISO230-2 geometric error calibration under cold conditions and establish a basic geometric error parameter library for the machine tool.

[0018] S22. Obtain the heat conduction matrix [α] through a temperature rise experiment. ij ], where i is the location of the heat source, j is the affected component, and α ij Let be the thermal conductivity coefficient from the i-th heat source to the j-th component, and let ΔL = α·ΔT, where α is the thermal conductivity coefficient and ΔT is the change in spindle temperature.

[0019] S23. Force Error Quantification: Cointegration analysis is used to verify the cutting force F. x,y,z With position error ε x,y,z The coupling relationship was determined by collecting 100 sets of historical processing data, including F. x,t F y,t Let x and y be the cutting forces at time t, respectively. To ensure direct correlation between the data and the multi-source data acquisition system of S1, the position error is obtained by fitting the cointegration equation using the least squares method, as shown in the following formula:

[0020] ε z,t =β0+β1·F x,t +β2·F y,t +ξ t ;

[0021] Where, ε z,t Let β be the z-direction position error at time t, β0 be the initial error, β1 be the x-direction force influence coefficient, β2 be the y-direction force influence coefficient, and ξ be the position error in the z-direction. t The residual sequence is stationary; ξ is verified using the ADF test. t Stability.

[0022] As a further aspect of the present invention, the parameter update formula for the sliding window recursive least squares method in S3 is as follows:

[0023]

[0024] in, Let be the model parameter vector for the k-th iteration. K is the parameter vector from the previous iteration. k Let y be the gain matrix. k Let k be the actual error value of the kth observation. Let J be the regression vector, J be the transpose of the matrix, and the formula for the gain matrix is: Where P k Let be the covariance matrix, and the formula for the covariance matrix is: Where λ is the forgetting factor.

[0025] As a further aspect of the present invention, the rule base of the fuzzy adaptive compensator is designed as follows:

[0026] The error fluctuation range and standard deviation are calculated using the following formulas:

[0027] Δe=|e k -e k-1 |;

[0028]

[0029] Where Δe is the error fluctuation amplitude, e k e represents the current error. a e represents the deviation between the actual machine tool error and the ideal position during the a-th cycle. k-1 For the previous error, σ e The standard error is μ. e This represents the average error over the previous 100 periods.

[0030] When Δe>3σ e When the error rate changes, analyze the rate of change of error. When the rate of change of error > 0, then K comp =K max And adjust the gain according to the upper limit of the piezoelectric ceramic;

[0031] When Δe < 0.2σ e When, then K comp =K base ·e k , where K base and K max All of these are the gain voltages applied to each piezoelectric ceramic.

[0032] When 0.2σ e ≤Δe≤3σ e When, K is calculated using the Gaussian membership function. comp The specific function is Where e is the base of the natural logarithm, and μ is the mean error.

[0033] As a further aspect of the present invention, in S4, the feedforward pre-compensation amount ΔP ff The generation method is as follows: analyze the trajectory of the next 3 interpolation cycles, and calculate the rotation axis compensation amount using quaternion interpolation. The interpolation formula is:

[0034]

[0035] Where q0 and q1 are the attitude quaternions of adjacent interpolation points, θ is the angle between q0 and q1, and t∈[0,1] is the interpolation parameter.

[0036] As a further aspect of the present invention: in step S5, the compensation effect evaluation index η = 1 - |e actual / e target ], where e actualTo compensate for the actual error, it is measured by a grating ruler, e target Let η be the target error. When η < 0.9, the fuzzy rule base is updated using a genetic algorithm.

[0037] As a further aspect of the present invention: the FPGA hardware implementation in S4 adopts a parallel pipeline architecture, and the timing satisfies:

[0038] T cycle =T ADC +T calc +T DAC ≤50μs;

[0039] Among them, T ADC T is the analog-to-digital conversion time. calc For the calculation time of the compensation amount, T DAC For the digital-to-analog conversion time, high-frequency oscillations are suppressed simultaneously through a magnetorheological damper, and the damping force... Among them, F d Here, c represents the damping force, and c is the damping coefficient that is adjusted in real time. The damping coefficient is dynamically calculated by the FPGA based on the vibration frequency. The vibration velocity is obtained by integrating the accelerometer.

[0040] As a further aspect of the present invention, the specific formula for estimating the substitution value using the Kalman filter in S6 is as follows:

[0041]

[0042] in, This is the predicted state vector for the k-th step. To estimate the state in the previous step, u k-1 For the control input of the previous step, For the prediction error covariance matrix, P k-1 Let A be the prediction error covariance matrix from the previous step, B be the state transition matrix, B be the control input matrix, and Q be the process noise covariance matrix.

[0043] Compared with the prior art, the beneficial effects of the present invention by adopting the above technical solution are as follows:

[0044] 1. This invention constructs a multi-source data acquisition system using a grating ruler, an infrared thermal imager, and a piezoelectric sensor to simultaneously sense dynamic errors from multiple sources, including geometry, thermal, and force. By combining an improved Volterra series model with Lyapunov exponential analysis, it accurately quantifies the nonlinear coupling characteristics of thermal-mechanical-geometric errors, solving the problem of inaccurate description of complex error fields by traditional single-source error models and significantly improving the accuracy of error prediction.

[0045] 2. This invention uses a sliding window recursive least squares method to update model parameters in real time, and combines a fuzzy adaptive compensator with a genetic algorithm to dynamically optimize the rule base. This enables the system to automatically adjust the compensation strategy (such as dynamic gain parameters) according to the processing effect, which breaks through the limitation of poor adaptability of traditional fixed rule bases, effectively suppresses error fluctuations, and ensures the consistency of long-term processing accuracy.

[0046] 3. This 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, it processes abnormal sensor data through a Kalman filter fault-tolerant mechanism to avoid compensation interruption, significantly improving the reliability and stability of five-axis machine tools in ultra-precision machining scenarios. Attached Figure Description

[0047] Figure 1 This is a flowchart of nonlinear coupling modeling in an embodiment of the present invention;

[0048] Figure 2 This is a flowchart of the sliding window recursive least squares method in an embodiment of the present invention;

[0049] Figure 3 This is a flowchart of the fuzzy adaptive compensator rules in an embodiment of the present invention;

[0050] Figure 4 This is a flowchart illustrating the process of generating the feedforward pre-compensation amount in an embodiment of the present invention.

[0051] Figure 5 This is a flowchart illustrating the dynamic rule base optimization process in an embodiment of the present invention.

[0052] Figure 6 This is a flowchart of the fault tolerance mechanism in an embodiment of the present invention;

[0053] Figure 7 This is a flowchart of the FPGA hardware acceleration closed-loop control in an embodiment of the present invention. Detailed Implementation

[0054] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings. It should be noted that the description of these embodiments is for the purpose of helping to understand the present invention, but does not constitute a limitation of the present invention.

[0055] Furthermore, 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.

[0056] Please see the appendix Figure 1 - Appendix Figure 7 This invention relates to a high-precision dynamic error real-time compensation method based on five-axis linkage, the compensation method comprising the following steps:

[0057] S1. A multi-source data acquisition system is constructed by collecting machine tool geometric errors using a grating ruler, temperature field distribution using an infrared thermal imager, and cutting force disturbance using a piezoelectric sensor.

[0058] S2. Data is transmitted to the Volterra series dynamic error model through a multi-source data acquisition system. The state equation is as follows:

[0059]

[0060] in, Let ε be the instantaneous rate of change of the state vector x over time, x be the system state vector, u be the control input, and ε be the variable. thermal For thermal error, ε force For force error, f(x) is the inherent nonlinear dynamic function in the multi-source data acquisition system, and g(.) is the disturbance coupling function. The dynamic error model introduces the Lyapunov exponent to analyze the chaotic characteristics of thermo-mechanical-geometric errors and quantifies the nonlinear cross-coupling effect.

[0061] S3. After establishing the dynamic error model, the model parameters are updated using the sliding window recursive least squares method, and the dynamic gain K is output by combining the fuzzy adaptive compensator. comp The dynamic gain K comp It is the real-time adjustment coefficient output by the fuzzy adaptive compensator, used to dynamically optimize the compensation intensity;

[0062] S4. Configure a Field Programmable Gate Array (FPGA), which uses a parallel pipelined architecture FPGA hardware platform to generate the feedforward pre-compensation quantity ΔP. ff With feedback compensation amount ΔP fb The total compensation amount ΔP total =ΔP ff +K comp ·ΔP fb The piezoelectric ceramic micro-displacement platform is controlled to perform nanoscale corrections based on dynamic gain K. comp Generate the total compensation amount;

[0063] S5. Analyze the compensation effect evaluation index through a multi-source data acquisition system. The compensation effect evaluation index is an indicator that measures the accuracy of compensation. Optimize the rule base based on the evaluation of the compensation effect.

[0064] S6. When sensor data in a multi-source data acquisition system is abnormal, Kalman filtering is triggered to estimate the substitute value.

[0065] S7. The actual machining error of the machine tool after the compensation algorithm is corrected is measured by a grating ruler. The error spectrum and contour error after compensation are detected to determine whether the machining accuracy requirements are met.

[0066] In one embodiment of the present invention, the multi-source data acquisition system in S1 specifically comprises: a grating ruler for real-time acquisition of position error data of the machine tool's five axes X, Y, Z, A, and C; an infrared thermal imager for acquiring the temperature field distribution of key components such as the spindle, guide rail, and lead 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 a piezoelectric sensor for monitoring the X, Y, and Z three-axis cutting force disturbances during the cutting process at a sampling rate of ≥1kHz (covering the main frequency components of the cutting force from 10 to 500Hz).

[0067] In one embodiment of the present invention, the nonlinear coupling modeling in S2 further includes:

[0068] S21. Perform ISO230-2 geometric error calibration under cold conditions and establish a basic geometric error parameter library for the machine tool.

[0069] S22. Obtain the heat conduction matrix [α] through a temperature rise experiment. ij ], where i is the location of the heat source, j is the affected component, and α ij Let α be the thermal conductivity coefficient from the i-th heat source to the j-th component, and let ΔL be the axial expansion of the spindle, where α is the thermal conductivity coefficient and ΔT is the temperature change of the spindle (α = 1.2 μm / ℃ is the linear expansion coefficient of the spindle material (40Cr)).

[0070] S23. Force Error Quantification: Cointegration analysis is used to verify the cutting force F. x,y,z With position error ε x,y,z The coupling relationship was determined by collecting 100 sets of historical processing data, including F. x,t F y,t Let x and y be the cutting forces at time t, respectively. To ensure direct correlation between the data and the multi-source data acquisition system of S1, the position error is obtained by fitting the cointegration equation using the least squares method, as shown in the following formula:

[0071] ε z,t =β0+β1·F x,t +β2·F y,t +ξ t ;

[0072] Where, ε z,t Let β be the z-direction position error at time t, β0 be the initial error, β1 be the x-direction force influence coefficient, β2 be the y-direction force influence coefficient, and ξ be the position error in the z-direction. t The residual sequence is stationary; ξ is verified using the ADF test. t Stability.

[0073] In one embodiment of the present invention, the parameter update formula for the sliding window recursive least squares method in S3 is:

[0074]

[0075] in, Let be the model parameter vector for the k-th iteration (containing the kernel function coefficients of the Volterra series). K is the parameter vector from the previous iteration. k For the gain matrix (adjusting the parameter update rate), y k This represents the actual error value of the h-th observation (measured by the grating ruler). The regression vector (containing historical error y) k-1 y k-2 Cutting force F x,k Temperature T k (Equal input variables), J is the transpose of the matrix, and the formula for the gain matrix is: Where P k Let be the covariance matrix, and the formula for the covariance matrix is: Where λ is the forgetting factor (set according to the historical data weight decay requirement, so that each...) Period, historical data weight decays to e -2 ≈13.5%, balancing real-time performance and data utilization.

[0076] In one embodiment of the present invention, the rule base of the fuzzy adaptive compensator is designed as follows:

[0077] The error fluctuation range and standard deviation are calculated using the following formulas:

[0078] Δe=|e k -e k-1 |;

[0079]

[0080] Where Δe is the error fluctuation amplitude, e k Let 'a' be the current error, 'a' be the index variable for summation, and 'e' be the index k-1 For the previous error, σ e The standard error is μ. e This represents the average error over the previous 100 periods.

[0081] When Δe>3σ e When the error rate changes, analyze the rate of change of error. When the rate of change of error > 0, then K comp =K max And adjust the gain according to the upper limit of the piezoelectric ceramic;

[0082] When Δe < 0.2σ e When, then K comp =K base ·e k , where K base and K max All of these are the gain voltages applied to each piezoelectric ceramic.

[0083] At that time, K was calculated using the Gaussian membership function. comp The specific function is Where e is the base of the natural logarithm, and μ is the mean error.

[0084] In one embodiment of the present invention, the feedforward pre-compensation amount ΔP in S4 ff The generation method is as follows: Analyze the trajectory of the next 3 interpolation cycles (the interpolation cycle is set to 16.7 μs by the CNC system), and calculate the rotation axis compensation amount using quaternion interpolation (a mathematical method for three-dimensional rotation interpolation, which avoids gimbal lock-up compared to Euler angle interpolation). The interpolation formula is:

[0085]

[0086] Where q0 and q1 are the attitude quaternions of adjacent interpolation points (output by the trajectory planning module of the CNC system, in the form of q = [w, x, y, z], where w is the scalar part and x, y, z are the vector parts), θ is the angle between q0 and q1 (calculated by dot product cosθ = q0 · q1), and t ∈ [0, 1] is the interpolation parameter (determined by the proportion of interpolation time, t = 0 corresponds to q0, and t = 1 corresponds to q1).

[0087] In one embodiment of the present invention: in S5, the compensation effect evaluation index η = 1 - |e actual / e target |, where e actual To compensate for the actual error, it is measured by a grating ruler, e target The target error is set to 0.5 μm. When η < 0.9, the fuzzy rule base is updated using a genetic algorithm (adjusting K). max K base (e.g., parameters).

[0088] In one embodiment of the present invention: the FPGA hardware implementation in S4 adopts a parallel pipeline architecture, and the timing satisfies:

[0089] T cycle =T ADC +T calc +T DAC ≤50μs;

[0090] Among them, T ADC For analog-to-digital conversion time, ≤10μs, T calc For the compensation calculation time, ≤30μs, T DAC The digital-to-analog conversion time is ≤10μs, and high-frequency oscillations are suppressed by a magnetorheological damper. The damping force... Among them, F d Here, c represents the damping force, and c is the damping coefficient that is adjusted in real time. The damping coefficient is dynamically calculated by the FPGA based on the vibration frequency. The vibration velocity is obtained by integrating the accelerometer.

[0091] In one embodiment of the present invention, the specific formula for estimating the substitution value using Kalman filtering in S6 is as follows:

[0092]

[0093] in, This is the predicted state vector for the k-th step (containing substitute values ​​such as temperature and cutting force). To estimate the state in the previous step, u k-1 For the control input of the previous step, P is the prediction error covariance matrix (describing the uncertainty of the predicted state). k-1 Let A be the prediction error covariance matrix from the previous step, B be the state transition matrix (determined by the system dynamics model, reflecting the evolution of the state over time), and Q be the control input matrix (determined by the actuator characteristics, reflecting the influence of the control input on the state). Q is the process noise covariance matrix (the noise variance is determined experimentally, describing the statistical characteristics of the internal noise of the system).

[0094] Example: Dynamic error compensation in precision machining of aerospace titanium alloy blades

[0095] Application scenario: Precision machining of titanium alloy blades for a certain aero-engine. The blade profile is a complex free-form surface with a profile requirement of ≤1μm. During the machining process, it is affected by the coupling of cutting force disturbance, spindle temperature rise and machine tool geometric error. Traditional compensation methods are difficult to meet the accuracy requirements.

[0096] S1 Multi-Source Dynamic Error Sensing: A multi-source data acquisition system is deployed on a five-axis machining center (model DMMORIDMU80eVo). Heidenhain LIP481 linear scales (resolution 0.05μm) are 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℃) are installed on key parts of the spindle, guide rail, and lead screw (front bearing housing, lead screw nut pair, guide rail slider). A Kistler9257B piezoelectric sensor (sampling rate 1kHz, range ±5kN) is installed at the tool holder to monitor the cutting forces in the X, Y, and Z axes (typical cutting force range 500-2000N).

[0097] S2 nonlinear coupling modeling:

[0098] S21 Cold-state geometric error calibration: Perform geometric error calibration according to ISO230-2 standard. Using a Renishaw XL-80 laser interferometer, the maximum X-axis positioning error was measured to be 0.03 mm and the Y-axis straightness error was 0.02 mm / m. A basic geometric error parameter library was established.

[0099] S22 heat conduction matrix calculation: The spindle was idled at 10,000 rpm for 2 hours. The infrared thermal imager collected temperature field data of each component and calculated the heat conduction matrix (e.g., the heat conduction coefficient of the front bearing housing to the spindle α = 1.2 μm / ℃). The measured spindle temperature rose from 25℃ to 45℃ (ΔT = 20℃). The calculated axial expansion ΔL = 24 μm, which is consistent with the measured value of 23.8 μm by the laser interferometer.

[0100] 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 ε was fitted using the least squares method. z,t =0.5μm + 0.5μm / N·F x,t +0.008μm / N·F y,t +ξ t The ADF test confirmed that the residuals were stationary (t-statistic = -3.8 < critical value -3.43);

[0101] S3 Intelligent Dynamic Compensation: Volterra model parameters are updated every 50 μs using a sliding window recursive least squares method (forgetting factor λ = 0.98). In the fuzzy adaptive compensator, the mean error in the first 100 cycles is μ. e =1.2μm, standard deviation σ e =0.3μm, when the error fluctuation Δe>0.9μm(3σ) e And as the error increases, K compTaking the maximum value of 5V (maximum driving voltage of piezoelectric ceramic), when Δe < 0.06μm (0.2σ e When K comp =0.5V / μm·e k (e k (current error);

[0102] S4 Hardware-Accelerated Closed-Loop Control: Sensor data is transmitted to the Xilinx K7 FPGA via the JESD204B interface, and ADC sampling (8μs), compensation calculation (25μs), and DAC output (7μs) are processed in parallel, with a total cycle of 40μs≤50μs. The feedforward pre-compensation amount is calculated by analyzing the trajectory of the next 3 interpolation cycles (50.1μs) and using quaternion interpolation to calculate the rotation axis compensation amount (e.g., the angle θ between the attitude quaternions q0 and q1 of adjacent interpolation points is 23°, and q is calculated at t=0.5). comp =0.5q0+0.5q1);

[0103] S5 Dynamic Rule Base Optimization: Calculate the compensation effect evaluation index η = 1 - (e) per processing cycle (10ms). actual ( / 0.5μm), initial η=-1.4<0.9, triggering the genetic algorithm to adjust K. max Increase from 5V to 6V, K base The voltage was increased from 0.5V / μm to 0.6V / μm, and then η was increased to 0.95 (e). actual =0.52μm);

[0104] S6 fault tolerance mechanism: When the grating ruler produces abnormal data due to electromagnetic interference (Z-axis error -10μm), it triggers Kalman filtering, and the state transition matrix A = [1, 0.05 - 0, 1] is used to predict the state. (Actual temperature 90℃, cutting force 980N), use predicted values ​​to replace abnormal data for further compensation;

[0105] S7 accuracy verification: The three-coordinate measurement after machining showed that the maximum contour error before compensation was 2.5μm, which was reduced to 0.6μm after compensation (meeting the ≤1μm requirement). The amplitude of the 50Hz and 100Hz components in the error spectrum decreased from 1.2μm to 0.2μm, which verified the effect of multi-source error suppression.

[0106] While the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Any variations and modifications can be made by those skilled in the art without departing from the spirit and scope of the invention. Therefore, any modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention, without departing from the scope of the invention, fall within the protection scope defined by the claims of the present invention.

Claims

1. A high-precision dynamic error real-time compensation method based on five-axis linkage, comprising a compensation method, characterized in that, The compensation method includes the following steps: S1. A multi-source data acquisition system is constructed by collecting machine tool geometric errors using a grating ruler, temperature field distribution using an infrared thermal imager, and cutting force disturbance using a piezoelectric sensor. S2. Data is transmitted to the Volterra series dynamic error model through a multi-source data acquisition system. The state equation is as follows: in, Let ε be the instantaneous rate of change of the state vector x over time, x be the system state vector, u be the control input, and ε be the variable. thermal For thermal error, ε force For force error, f(x) is the inherent nonlinear dynamic function in the multi-source data acquisition system, and g(.) is the disturbance coupling function. The dynamic error model introduces the Lyapunov exponent to analyze the chaotic characteristics of thermo-mechanical-geometric errors and quantifies the nonlinear cross-coupling effect. S3. After establishing the dynamic error model, the model parameters are updated using the sliding window recursive least squares method, and the dynamic gain K is output by combining the fuzzy adaptive compensator. comp The dynamic gain K comp It is the real-time adjustment coefficient output by the fuzzy adaptive compensator, used to dynamically optimize the compensation intensity; S4. Configure a Field Programmable Gate Array (FPGA), which uses a parallel pipelined architecture FPGA hardware platform to generate the feedforward pre-compensation quantity ΔP. ff With feedback compensation amount ΔP fb The total compensation amount ΔP total =ΔP ff +K comp ·ΔP fb The piezoelectric ceramic micro-displacement platform is controlled to perform nanoscale corrections based on dynamic gain K. comp Generate the total compensation amount; S5. Analyze the compensation effect evaluation index through a multi-source data acquisition system. The compensation effect evaluation index is an indicator that measures the accuracy of compensation. Optimize the rule base based on the evaluation of the compensation effect. S6. When sensor data in a multi-source data acquisition system is abnormal, Kalman filtering is triggered to estimate the substitute value. S7. The actual machining error of the machine tool after the compensation algorithm is corrected is measured by a grating ruler. 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, characterized in that, The multi-source data acquisition system in S1 specifically includes: a grating ruler for real-time acquisition of position error data of the machine tool's five axes (X, Y, Z, A, and C); an infrared thermal imager for acquiring the temperature field distribution of key components such as the spindle, guide rail, and lead screw at a frequency of ≤10Hz; and a piezoelectric sensor for monitoring X, Y, and Z-axis cutting force disturbances 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, characterized in that, The nonlinear coupling modeling in S2 also includes: S21. Perform ISO230-2 geometric error calibration under cold conditions and establish a basic geometric error parameter library for the machine tool. S22. Obtain the heat conduction matrix [α] through a temperature rise experiment. ij ], where i is the location of the heat source, j is the affected component, and α ij Let be the thermal conductivity coefficient from the i-th heat source to the j-th component, and let ΔL = α·ΔT, where α is the thermal conductivity coefficient and ΔT is the change in spindle temperature. S23. Force Error Quantification: Cointegration analysis is used to verify the cutting force F. x,y,z With position error ε x,y,z The coupling relationship was determined by collecting 100 sets of historical processing data, including F. x,t F y,t Let x and y be the cutting forces at time t, respectively. To ensure direct correlation between the data and the multi-source data acquisition system of S1, the position error is obtained by fitting the cointegration equation using the least squares method, as shown in the following formula: e z,t =β0+β1·F x,t +β2·F y,t +ξ t ; Where, ε z,t Let β be the z-direction position error at time t, β0 be the initial error, β1 be the X-direction force influence coefficient, β2 be the Y-direction force influence coefficient, and ξ be the position error in the z-direction. t The residual sequence is stationary; ξ is verified using the ADF test. t Stability.

4. The high-precision dynamic error real-time compensation method based on five-axis linkage according to claim 1, characterized in that, The parameter update formula for the sliding window recursive least squares method in S3 is as follows: in, Let K be the model parameter vector for the Kth iteration. K is the parameter vector from the previous iteration. k Let y be the gain matrix. k Let k be the actual error value of the kth observation. Let J be the regression vector, J be the transpose of the matrix, and the formula for the gain matrix is: Where P k Let be the covariance matrix, and the formula for the covariance matrix is: Where λ is the forgetting factor.

5. The high-precision dynamic error real-time compensation method based on five-axis linkage according to claim 4, characterized in that, The rule base design of the fuzzy adaptive compensator is as follows: The error fluctuation range and standard deviation are calculated using the following formulas: Δe=|e k -e k-1 |; Where Δe is the error fluctuation amplitude, e k e represents the current error. a e represents the deviation between the actual machine tool error and the ideal position during the a-th cycle. k-1 For the previous error, σ e The standard error is μ. e This represents the average error over the previous 100 periods. When Δe>3σ e When the error rate changes, analyze the rate of change of error. When the rate of change of error > 0, then K comp =K max And adjust the gain according to the upper limit of the piezoelectric ceramic; When Δe < 0.2σ e When, then K comp =K base ·e k , where K base and K max All of these are the gain voltages applied to each piezoelectric ceramic. When 0.2σ e ≤Δe≤3σ e When, K is calculated using the Gaussian membership function. comp The specific function is Where e is the base of the natural logarithm, and μ is the mean error.

6. The high-precision dynamic error real-time compensation method based on five-axis linkage according to claim 5, characterized in that, In S4, the feedforward pre-compensation amount ΔP ff The generation method is as follows: analyze the trajectory of the next 3 interpolation cycles, and calculate the rotation axis compensation amount using quaternion interpolation. The interpolation formula is: Where q0 and q1 are the attitude quaternions of adjacent interpolation points, θ is the angle between q0 and q1, and t∈[0,1] is the interpolation parameter.

7. The high-precision dynamic error real-time compensation method based on five-axis linkage according to claim 6, characterized in that: In S5, the compensation effect evaluation index η = 1 - |e| is calculated for each processing cycle. actual / e target |, where e actual To compensate for the actual error, it is measured by a grating ruler, e target Let η be the target error. When η < 0.9, the fuzzy rule base is updated using a genetic algorithm.

8. The high-precision dynamic error real-time compensation method based on five-axis linkage according to claim 1, characterized in that: The FPGA hardware implementation in S4 adopts a parallel pipeline architecture, and the timing requirements are: T cycle =T ADC +T calc +T DAC ≤50μs; Among them, T ADC T is the analog-to-digital conversion time. calc For the calculation time of the compensation amount, T DAC For the digital-to-analog conversion time, high-frequency oscillations are suppressed simultaneously through a magnetorheological damper, and the damping force... Among them, F d Here, c represents the damping force, and c is the damping coefficient that is adjusted in real time. The damping coefficient is dynamically calculated by the FPGA based on the vibration frequency. The vibration velocity is obtained by integrating the accelerometer.

9. The high-precision dynamic error real-time compensation method based on five-axis linkage according to claim 1, characterized in that, The specific formula for estimating the substitution value using the Kalman filter in S6 is as follows: in, This is the predicted state vector for the k-th step. To estimate the state in the previous step, u k-1 For the control input of the previous step, For the prediction error covariance matrix, P k-1 Let A be the prediction error covariance matrix from the previous step, B be the state transition matrix, B be the control input matrix, and Q be the process noise covariance matrix.

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