Friction nonlinear characteristic self-adaptive identification and compensation method for numerical control machine tool feeding system

Abstract

The invention discloses a self-adaptive identification and compensation method for friction nonlinear characteristics of a feeding system of a numerical control machine tool. According to the method, parameters of a LuGre friction model are initialized by collecting an actual position signal, an actual speed signal, an actual current signal and an instruction position signal of a feeding system; friction parameter self-adaptive identification is carried out based on motion state segments, coulomb friction parameters and viscous friction parameters are updated by adopting a least square method in a constant speed stage, and bristle rigidity parameters, bristle damping parameters and Stribeck speed parameters are updated by adopting an extended Kalman filter in an acceleration stage and a deceleration stage; generating a friction force estimation value according to the identified friction parameter, converting the friction force estimation value into a compensation current signal, and adding the compensation current signal to a servo driver current instruction after phase lead compensation. According to the method, the friction characteristic change can be adaptively identified on line, tracking errors and vibration caused by friction nonlinearity are effectively inhibited, and the machining precision and stability of the numerical control machine tool are improved.

Description

Technical Field

[0001] This invention relates to the field of CNC machine tool technology, and in particular to an adaptive identification and compensation method for the frictional nonlinear characteristics of a CNC machine tool feed system. Background Technology

[0002] As core equipment in modern manufacturing, the performance of the feed system in CNC machine tools directly determines machining accuracy and efficiency. The feed system typically consists of components such as servo motors, ball screws, guideways, and worktables. During operation, friction between these components generates nonlinear characteristics, leading to tracking errors, creeping phenomena, and vibration problems, severely impacting machining quality. These nonlinear frictional characteristics are primarily a complex combination of static friction, Coulomb friction, and viscous friction, and they dynamically change with variations in temperature, wear, and lubrication conditions, making traditional fixed-parameter compensation methods ineffective.

[0003] In existing technologies, friction compensation methods are mainly divided into two categories: model-based feedforward compensation and adaptive compensation. Model-based feedforward compensation methods rely on pre-established friction models, such as the LuGre or Stribeck models, to obtain model parameters through offline experiments and then introduce compensation signals into the control system. However, this method requires precise model parameters, and in actual operation, friction characteristics drift due to factors such as temperature rise, component wear, and changes in lubricant performance. This causes the fixed-parameter model to fail to accurately describe real-time friction behavior, and the compensation effect gradually deteriorates. Adaptive compensation methods can adjust parameters online, but most methods rely on simplified models or assume that friction characteristics change slowly. In high-speed, high-precision machining scenarios, due to the fast dynamic response of the feed system and frequent load changes, these methods often suffer from low identification accuracy and poor real-time performance. For example, some adaptive methods use recursive least squares or neural networks for parameter identification, but the computational complexity is high, making it difficult to implement in real time in industrial controllers; other methods rely on indirect estimation based on position or velocity signals, but lack direct measurement of friction force, resulting in identification results being greatly affected by external interference.

[0004] Furthermore, existing parameter identification processes often require the injection of additional test signals, such as sine waves or pseudo-random sequences, which can interfere with normal machining processes and reduce production efficiency. Simultaneously, the generation of compensation signals does not consider the dynamic coupling effects of the system, potentially introducing phase lag or high-frequency oscillations, which can worsen system performance. Therefore, there is an urgent need for a method that can adaptively identify frictional nonlinear characteristics online without interrupting the machining process, and whose compensation signals are dynamically matched to the system, in order to improve the control accuracy and stability of CNC machine tool feed systems. Summary of the Invention

[0005] To achieve the above objectives, the present invention provides an adaptive identification and compensation method for the frictional nonlinear characteristics of a CNC machine tool feed system, comprising the following steps:

[0006] Step 1: Motion data acquisition of the feed system. The actual position signal of the worktable is acquired through the encoder. The actual position signal is obtained by numerical differentiation of the actual position signal. The actual current signal of the servo motor is acquired through the servo driver. The command position signal of the feed system is read from the CNC system.

[0007] Step 2: Initialize the parameters of the nonlinear frictional characteristic model. Set the initial parameters of the LuGre model, including bristle stiffness parameters, bristle damping parameters, Coulomb friction parameters, viscous friction parameters, and Stribeck velocity parameters.

[0008] Step 3: Adaptive identification of friction parameters based on motion state segmentation. The motion state of the feeding system is determined according to the actual velocity signal. The motion state is divided into acceleration stage, deceleration stage and uniform speed stage. In the uniform speed stage, the least squares method is used to update the Coulomb friction parameters and viscous friction parameters. In the acceleration stage and deceleration stage, the extended Kalman filter is used to update the bristle stiffness parameters, bristle damping parameters and Stribeck velocity parameters.

[0009] Step 4: Friction compensation signal generation and system dynamic compensation. Based on the currently identified friction parameters and actual speed signal, calculate the friction force estimate of the LuGre model, convert the friction force estimate into a compensation current signal, perform phase lead compensation on the compensation current signal, and add it to the current command of the servo driver.

[0010] Step 5: Parameter identification and compensation effect monitoring. Calculate the tracking error between the actual position signal and the commanded position signal. When the root mean square value of the tracking error exceeds the set threshold, trigger parameter re-initialization. When the rate of change of friction parameters exceeds the stable threshold, adjust the update rate of the adaptive identification algorithm.

[0011] Preferably, the actual velocity signal obtained by numerical differentiation of the actual position signal in step 1 is specifically obtained by using the first-order backward difference method, which uses the difference between the position value at the current sampling time and the position value at the previous sampling time, divided by the sampling time interval to obtain the actual velocity value; the sampling time interval is set according to the maximum motion speed of the feeding system to ensure that the sampling frequency is higher than the dynamic response frequency of the feeding system; all collected signals are synchronously stored in the memory of the controller.

[0012] Preferably, the initial parameters of the LuGre model set in step 2 are set based on offline experimental data of the feed system. The offline experiment involves driving the feed system to move at a constant speed, measuring the steady-state friction force, and fitting the initial parameter values. The initial parameters are stored in the controller as the initial values ​​for the first identification.

[0013] Preferably, the process of determining the motion state of the feed system based on the actual speed signal in step 3 includes: when the rate of change of the actual speed signal is greater than a positive threshold, it is determined to be an acceleration phase; when the rate of change of the actual speed signal is less than a negative threshold, it is determined to be a deceleration phase; when the rate of change of the actual speed signal is between the negative threshold and the positive threshold, it is determined to be a constant speed phase; the rate of change is calculated by the numerical differentiation of the actual speed signal, and the positive threshold and the negative threshold are set based on the maximum acceleration of the feed system.

[0014] Preferably, step 3, which involves updating the Coulomb friction parameters and viscous friction parameters using the least squares method during the uniform velocity phase, specifically includes: constructing a friction force estimate, which is equal to the actual current signal multiplied by the torque constant, and then subtracting the inertial force, which is obtained by multiplying the actual acceleration signal by the total mass of the system, and the actual acceleration signal is calculated by numerical differentiation of the actual velocity signal; establishing a linear relationship between the friction force estimate and the actual velocity signal, and using the recursive least squares method to solve for the Coulomb friction parameters and viscous friction parameters; in the recursive least squares method, the forgetting factor is adaptively adjusted according to the motion state, and the forgetting factor is set to a larger value during the uniform velocity phase.

[0015] Preferably, in step 3, updating the bristle stiffness parameters, bristle damping parameters, and Stribeck velocity parameters using an extended Kalman filter during the acceleration and deceleration phases involves the following steps: discretizing the LuGre model into a state-space equation, with state variables including bristle deformation and bristle deformation rate; using the actual velocity signal as input and the actual current signal as observation; predicting the state variables and parameters using an extended Kalman filter, and updating the parameter estimates based on the observation error; the process noise covariance and observation noise covariance of the extended Kalman filter are set based on the statistical characteristics of the feed system motion data.

[0016] Preferably, in step 4, the calculation of the friction force estimate of the LuGre model based on the currently identified friction parameters and the actual velocity signal is specifically obtained by calculating the bristle deformation amount, bristle deformation rate, actual velocity signal, and friction parameters. The bristle deformation amount and bristle deformation rate are obtained by recursion from the state equation of the LuGre model. The conversion of the friction force estimate into a compensation current signal is specifically that the compensation current signal is equal to the friction force estimate divided by the torque constant.

[0017] Preferably, the phase lead compensation of the compensation current signal in step 4 is specifically performed by using a first-order lead network for phase compensation. The transfer function of the first-order lead network is set according to the open-loop frequency response of the feed system, and the cutoff frequency is higher than the bandwidth of the feed system. The compensation current signal after phase lead compensation is added to the current command of the servo driver to realize friction compensation.

[0018] Preferably, in step 5, the tracking error between the actual position signal and the commanded position signal is calculated and stored in the form of a time series; the set threshold is set based on the machining accuracy requirements; when the root mean square value of the tracking error exceeds the set threshold, the parameters are re-initialized, specifically by re-executing the friction nonlinear characteristic model parameter initialization process from step 2.

[0019] Preferably, the process of adjusting the update rate of the adaptive identification algorithm when the rate of change of friction parameters exceeds the stable threshold in step 5 includes: calculating the rate of change of friction parameters through numerical differentiation of the parameter time series, and setting the stable threshold based on historical data statistics; reducing the update rate of the adaptive identification algorithm when the rate of change of friction parameters exceeds the stable threshold; and increasing the update rate of the adaptive identification algorithm when the rate of change of friction parameters is lower than the stable threshold.

[0020] The beneficial effects of this invention are:

[0021] 1. This invention enables real-time adjustment of friction parameters by online adaptively identifying nonlinear friction characteristics, dynamically adapting to changes in frictional force. The invention employs a friction parameter adaptive identification method based on the LuGre model. Through analysis of actual speed signals and servo current signals, it dynamically adjusts Coulomb friction, viscous friction, and bristle parameters, effectively addressing the drift of frictional characteristics with environmental changes and maintaining the stability of the compensation effect.

[0022] 2. This invention divides the motion state into three stages: acceleration, deceleration, and constant velocity. At each stage, the least squares method and the extended Kalman filter are used for parameter updates. This method ensures a significant improvement in the accuracy and real-time performance of friction parameter identification under high dynamic response conditions. Particularly during the acceleration and deceleration stages, the extended Kalman filter can accurately estimate the bristle stiffness, damping, and Stribeck velocity parameters, guaranteeing the accuracy of the dynamic response.

[0023] 3. This invention provides a friction compensation method that does not rely on a pre-established fixed parameter model. It employs online identification technology to update friction parameters in real time, ensuring the continuous effectiveness of the compensation method during processing. Furthermore, this invention does not require additional test signals, avoiding the potential decrease in production efficiency that may result from traditional methods.

[0024] 4. This invention employs a simplified strategy combining recursive least squares and extended Kalman filtering, reducing computational complexity and enabling real-time implementation in the controller. This method significantly improves system real-time performance while maintaining identification accuracy, making it suitable for industrial controller applications.

[0025] 5. The adaptive identification and compensation method for frictional nonlinear characteristics of the present invention does not require additional test signals; instead, it identifies the frictional force based on actual motion data, without affecting the processing. By acquiring position, velocity, and current signals in real time, it directly identifies and compensates for frictional forces, avoiding interference from test signals.

[0026] 6. This invention introduces a phase lead compensation mechanism in the generation of the compensation signal. Phase compensation is performed using a first-order lead network to ensure that the compensation signal matches the system dynamics, thereby effectively reducing phase lag and improving the system's stability and response speed.

[0027] 7. Through the tracking error monitoring mechanism in this invention, when the tracking error between the actual position signal and the commanded position signal exceeds a set threshold, the parameters can be reinitialized to maintain high-precision control of the system. Furthermore, when the rate of change of friction parameters exceeds a set threshold, this invention can adjust the update rate of the adaptive identification algorithm to avoid system instability caused by updates that are too fast or too slow, thereby further improving the long-term stability of the system. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in this invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0029] Figure 1 This is a flowchart of the steps of the method of the present invention;

[0030] Figure 2 This is a flowchart of step 3 of the method of the present invention, in which the least squares method is used to update the Coulomb friction parameters and viscous friction parameters during the uniform velocity stage;

[0031] Figure 3 This is a flowchart of step 3 of the method of the present invention, in which an extended Kalman filter is used to update the bristle stiffness parameter, bristle damping parameter, and Stribeck velocity parameter during the acceleration and deceleration phases. Detailed Implementation

[0032] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. It should also be noted that, to make the embodiments more comprehensive, the following embodiments are the best and preferred embodiments, and those skilled in the art can use other alternative methods to implement some well-known technologies; moreover, the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.

[0033] Please see Figures 1-3 This invention provides an adaptive identification and compensation method for the frictional nonlinear characteristics of a CNC machine tool feed system. In step 1, the motion data of the feed system is acquired through a high-precision encoder to obtain the actual position signal of the worktable, and the actual speed signal is obtained through numerical differentiation processing to ensure the accuracy of speed information during the dynamic process. Furthermore, the actual current signal of the servo motor is acquired through a servo driver to ensure the timeliness of system feedback information. Simultaneously, the command position signal of the feed system is read from the CNC system to provide data support for subsequent friction compensation.

[0034] In step 2, the nonlinear characteristics of friction are initialized by setting the initial parameters of the LuGre model, including bristle stiffness, bristle damping, Coulomb friction, viscous friction, and Stribeck velocity, providing initial reference values ​​for subsequent adaptive identification. This initial setup allows for a relatively accurate friction model to be obtained during the startup phase, laying the foundation for real-time identification.

[0035] In step 3, the motion state of the feed system is determined based on the actual velocity signal, and the system motion state is divided into three stages: acceleration, deceleration, and constant velocity. During the constant velocity stage, the Coulomb friction and viscous friction parameters are updated using the least squares method. By processing the characteristics of different stages, the influence of friction on the control system is reduced, improving the system's accuracy. During the acceleration and deceleration stages, the bristle stiffness, bristle damping, and Stribeck velocity parameters are updated using an extended Kalman filter to ensure accurate estimation of friction characteristics during the dynamic response stage, thereby improving identification accuracy.

[0036] In step 4, the friction force estimate of the LuGre model is calculated using the currently identified friction parameters and the actual velocity signal, and the estimate is converted into a compensation current signal. After phase lead compensation, this compensation current signal is added to the current command of the servo driver to optimize the system's dynamic response and reduce vibration and errors caused by frictional nonlinearity.

[0037] The parameter identification and compensation effect monitoring mechanism in step 5 calculates the tracking error between the actual position signal and the commanded position signal in real time. When the tracking error exceeds a set threshold, parameter reinitialization is triggered to avoid the adverse effects of long-term error accumulation. If the rate of change of friction parameters exceeds a stable threshold, the update rate of the adaptive identification algorithm is adjusted to ensure the continuous stability of the system.

[0038] By adaptively identifying the nonlinear characteristics of friction online, this invention avoids the limitations of fixed friction models in traditional methods, ensuring the system can dynamically adapt to changes in the processing environment and improving compensation accuracy. Phase lead compensation effectively reduces vibration and errors, enhancing control precision. Furthermore, it avoids the interference of additional test signals required by traditional methods, improving production efficiency. Ultimately, this invention achieves high-precision control and stability in CNC machine tool feed systems, solving the problem of existing technologies' inability to effectively handle complex nonlinear friction characteristics.

[0039] In one possible implementation, step 1 involves numerically differentiating the actual position signal to obtain the actual velocity signal, employing a first-order backward difference method. Specifically, in this process, the actual velocity signal is obtained by dividing the difference between the position signal at the current sampling time and the position signal at the previous sampling time by the time interval between the two samplings. Compared to other numerical differentiation methods, this method is simpler and has a smaller computational load, meeting real-time requirements and is suitable for real-time monitoring of speed information in CNC machine tools.

[0040] The sampling time interval is determined based on the maximum speed of the feed system, ensuring a sufficiently high sampling frequency to capture the system's dynamic response frequency. By appropriately setting the sampling frequency, the system's speed changes during motion can be captured more accurately, thereby improving the accuracy of friction parameter identification. Too low a sampling frequency will result in missing speed information, affecting subsequent friction compensation; while too high a sampling frequency may increase the system's computational burden and reduce efficiency. Therefore, choosing a reasonable sampling time interval is crucial for system performance.

[0041] All acquired signals are synchronously stored in the controller's memory. This design ensures the timing consistency of the data and the accuracy of subsequent processing. The data in memory can be promptly provided to the adaptive identification algorithm for processing, ensuring that the system can dynamically respond and adjust the friction compensation strategy in real time during actual operation.

[0042] First, the actual velocity signal obtained by the first-order backward differential method has high computational efficiency and can meet the real-time requirements. Second, by reasonably setting the sampling time interval, the sampling frequency can be ensured to be higher than the dynamic response frequency of the feed system, thereby improving the accuracy of friction identification. Finally, by synchronously storing data, the problems of data loss or timing inconsistency are avoided, ensuring the stability and reliability of the control system.

[0043] In one possible implementation, the initial parameters of the LuGre model are set based on offline experimental data from the feed system. Specifically, the feed system is first controlled to move at a constant speed; under steady-state conditions, the system's frictional force tends to stabilize. Measurements are then taken under these conditions to obtain the steady-state frictional force value. This process provides a relatively accurate foundation of frictional force data, which is helpful in establishing a preliminary friction model.

[0044] Subsequently, based on the measured steady-state friction data, a fitting algorithm is used to determine the initial values ​​of each parameter in the LuGre model. The LuGre model typically includes parameters such as bristle stiffness, bristle damping, Coulomb friction, viscous friction, and Stribeck velocity. The initial values ​​obtained by fitting experimental data can accurately reflect the frictional characteristics of the system in its initial state. These initial parameters are stored in the controller's memory as initial input values ​​for the first identification, ensuring that the identification process is based on a reasonable starting point.

[0045] Steady-state friction data obtained through offline experiments can provide a true and accurate starting point for friction characteristics, effectively reducing identification errors caused by inaccurate initial values. Secondly, offline experiments avoid interference factors that may arise during online operation, ensuring the accuracy and reliability of parameter settings. Finally, the initial parameters stored in the controller serve as the benchmark for the first identification, ensuring the system's adaptive capability in subsequent operation. This helps to quickly and accurately adjust the system's friction compensation strategy, thereby improving the precision and stability of CNC machine tools.

[0046] In one possible implementation, the motion state of the feeding system is determined by the rate of change of the actual velocity signal. The specific process includes three criteria: first, when the rate of change of the actual velocity signal is greater than a set positive threshold, the system is determined to be in an acceleration phase; second, when the rate of change of the actual velocity signal is less than a negative threshold, the system is determined to be in a deceleration phase; and finally, when the rate of change of the actual velocity signal is between the negative and positive thresholds, the system is determined to be in a constant velocity phase.

[0047] The rate of change of the actual velocity signal is obtained by numerical differentiation of the actual velocity signal. The numerical differentiation process calculates the rate of change of the velocity signal based on the velocity signals at previous and subsequent sampling times, thereby determining the acceleration state of the system. The positive and negative thresholds are determined based on the maximum acceleration of the feed system. By setting appropriate thresholds, the three stages of acceleration, deceleration, and constant velocity can be effectively distinguished, ensuring that the system can accurately determine the motion state and thus perform targeted friction compensation.

[0048] By dynamically judging the motion state of the feed system, the friction compensation strategy can be adjusted in real time to avoid motion errors caused by the nonlinear characteristics of friction. Secondly, by calculating the rate of change, the acceleration, deceleration or constant speed state of the system can be quickly and accurately identified, providing a reliable basis for subsequent adaptive identification. Finally, by reasonably setting positive and negative thresholds, the system can accurately judge under high acceleration and low acceleration conditions, which helps to improve the motion accuracy and stability of CNC machine tools.

[0049] In one possible implementation, the Coulomb friction parameters and viscous friction parameters are updated using the least squares method during the uniform velocity phase. This process includes several key steps: First, a friction force estimate is constructed, obtained by multiplying the actual current signal by the torque constant, and then subtracting the inertial force. The inertial force is calculated based on the actual acceleration signal and the total mass of the system; the actual acceleration signal is obtained by numerically differentiating the actual velocity signal. Thus, the obtained friction force estimate reflects the current motion state and frictional characteristics of the system.

[0050] Next, a linear relationship is established between the estimated friction force and the actual velocity signal. To accurately estimate the friction parameters, the recursive least squares method is used to solve for the Coulomb friction parameters and the viscous friction parameters. The recursive least squares method can continuously update the parameters with each new data arrival, maintaining real-time tracking and optimization of the system state. To improve identification accuracy, the forgetting factor in the recursive least squares method is adaptively adjusted according to the motion state. During the uniform velocity phase, to ensure more stable parameter updates, the forgetting factor is set to a larger value, which reduces the influence of historical data on the current estimate and enhances the response to the current friction characteristics.

[0051] By using the least squares method, the friction parameters of the system can be identified relatively accurately, especially during the uniform velocity phase, when the friction characteristics tend to stabilize, which helps to obtain more reliable parameter estimates. The use of recursive least squares makes parameter updates more real-time and can quickly adapt to changes in the system state; while the adaptive adjustment of the forgetting factor ensures that the system has a higher weight for the current data during the uniform velocity phase, thereby improving the accuracy and real-time performance of the identification.

[0052] In one possible implementation, the LuGre friction model is first discretized into state-space equations, with state variables primarily including the amount and rate of bristle deformation. The state-space model provides a mathematical framework that describes the time-varying state of the system, allowing for real-time estimation of frictional force and its influencing factors. In this process, the actual velocity signal serves as the system input, while the actual current signal is used as the observation. This approach allows for comparison between the system's actual performance and the theoretical model, enabling the estimation and updating of frictional parameters.

[0053] Next, the system's state variables and friction parameters are predicted using an extended Kalman filter, and the parameter estimates are updated based on the observation errors obtained from actual measurements. The extended Kalman filter is a recursive algorithm based on nonlinear systems, capable of effectively handling state estimation problems in nonlinear dynamic systems by continuously refining the estimated friction parameters by combining predicted and actual observation data.

[0054] Furthermore, the process noise covariance and observation noise covariance of the extended Kalman filter are set based on the statistical characteristics of the motion data of the feed system. By appropriately setting the noise covariance, suitable filtering balance can be provided under different motion states, enabling the system to effectively cope with noise interference that may occur during acceleration and deceleration, thereby improving the accuracy and robustness of parameter estimation.

[0055] Extended Kalman filters can effectively handle the complex nonlinear characteristics of the feed system during acceleration and deceleration, providing more accurate friction parameter updates. Secondly, by discretizing the LuGre model and utilizing the state-space method, friction force and its influencing factors can be tracked and predicted in real time, which helps to improve the accuracy of friction compensation and dynamic response capability. Finally, the adaptive setting of noise covariance is optimized according to the actual motion state of the feed system, ensuring the stability and accuracy of parameter updates under different working conditions, further improving the accuracy and stability of the CNC machine tool feed system.

[0056] In one possible implementation, the friction force estimate from the LuGre model is calculated using the currently identified friction parameters and actual velocity signals. The specific process includes the following steps: First, based on the identified friction parameters and actual velocity signals, the state equations of the LuGre model are recursively used to obtain the amount and rate of deformation of the system's bristles. The state equations of the LuGre model provide a mathematical model describing the relationship between friction force and the system state (including the amount and rate of deformation). Through the recursive process, the actual velocity signals of the system can be transformed into corresponding state variables, thereby accurately describing the changes in friction force.

[0057] Next, based on the calculated bristle deformation amount, deformation rate, actual velocity signal, and friction parameters, the friction force is estimated using the LuGre model. This friction force estimate reflects the actual performance of friction in the system and can provide an accurate basis for the subsequent compensation process.

[0058] Finally, the friction force estimate is converted into a compensation current signal. Specifically, the friction force estimate is divided by the torque constant to obtain the current signal required for compensation. In this way, the system can calculate the current required for compensation based on the current friction force characteristics, thereby adjusting the motor output to counteract the error caused by friction and ensuring precise system operation.

[0059] By recursively calculating the bristle deformation amount and deformation rate using the state equations of the LuGre model, the dynamic characteristics of frictional force changes with the system state can be accurately captured, ensuring the accuracy of the frictional force estimate. Secondly, frictional force is estimated based on the identified frictional parameters and converted into a compensation current signal, providing a precise adjustment basis for the compensation system, thereby improving the motion accuracy and stability of the feed system. Finally, through this process, the nonlinear influence of frictional force can be effectively suppressed, improving the control accuracy and performance of CNC machine tools, and thus enhancing machining quality and efficiency.

[0060] In one possible implementation, the compensation current signal needs to undergo phase lead compensation to improve the friction compensation effect. Specifically, a first-order lead network is used for phase compensation. First, the transfer function of the first-order lead network is designed using the open-loop frequency response characteristics of the feed system. The cutoff frequency of this transfer function should be higher than the bandwidth of the feed system to ensure that the compensation signal effectively improves the system's phase in the high-frequency range, thereby enhancing the system's response to changes in friction force. This design ensures that phase lag is eliminated in the system's dynamic response, avoiding insufficient compensation due to phase lag, and thus improving the system's dynamic performance.

[0061] After phase lead compensation processing, the resulting compensated current signal is added to the current command of the servo driver. This compensated current signal can counteract the influence of friction during motor control, making the CNC machine tool move more smoothly and avoiding errors and instabilities caused by changes in friction, thereby ensuring machining accuracy and stable system operation.

[0062] Phase lead compensation can effectively reduce phase lag caused by system bandwidth limitations, thereby improving the immediacy and accuracy of friction compensation. Secondly, by directly applying the compensation current signal to the servo drive current command, adjustments can be made in real time at the motor control level to accurately compensate for changes in friction force, thus improving the system's response speed and stability. Finally, this method can effectively optimize the dynamic performance of the feed system and improve the machining accuracy and stability of CNC machine tools under complex working conditions.

[0063] In one possible implementation, in step 5 of the adaptive identification and compensation method for the frictional nonlinear characteristics of a CNC machine tool feed system, it is first necessary to calculate the tracking error between the actual position signal and the commanded position signal. This tracking error is the deviation between the system output and the target position, used to evaluate the tracking accuracy of the system. To facilitate subsequent processing, the tracking error is stored in the form of a time series, ensuring that the change of error over time can be tracked, thereby analyzing the dynamic response of the system and the source of the error.

[0064] Next, the threshold is set based on the required machining accuracy. Different thresholds can be set according to different machining tasks and accuracy requirements to ensure the system can operate efficiently while meeting machining accuracy requirements. When the root mean square value of the tracking error exceeds the set threshold, the system triggers a parameter re-initialization mechanism. The re-initialization process begins in step 2, re-executing the parameter initialization of the friction nonlinear characteristic model to re-identify and compensate for the system's friction characteristics. This effectively addresses performance degradation caused by long-term operation or environmental changes, ensuring the system maintains high accuracy and stability.

[0065] By calculating the tracking error and storing it as a time series, the tracking accuracy of the system can be monitored in real time, and potential problems can be detected in a timely manner. Secondly, setting reasonable thresholds can be flexibly adjusted according to the requirements of machining accuracy, ensuring that the system maintains good performance under different working conditions. Finally, the mechanism of triggering re-initialization effectively avoids the decline in system accuracy caused by long-term parameter not being updated or inaccurate parameter estimation, improves the dynamic response capability and stability of the CNC machine tool feed system, thereby ensuring high precision and efficiency in the machining process.

[0066] In one possible implementation, when the rate of change of friction parameters exceeds a set stability threshold, the update rate of the adaptive identification algorithm needs to be adjusted. The specific implementation process is as follows:

[0067] First, the rate of change of friction parameters is obtained by numerical differentiation of the parameter time series. By analyzing the trend of friction parameter changes, their rate of change over a certain period of time can be determined. This rate of change reflects the stability of the system's frictional characteristics under the current operating conditions. If the friction parameters change drastically, it indicates that there may be significant disturbances or instability in the system under the current state.

[0068] Next, the stability threshold is set based on historical data statistics. Statistical analysis of historical data helps to set a reasonable threshold to determine whether the current variation in friction parameters exceeds the normal operating range of the system. This threshold is usually related to the system's operating accuracy, stability, and changes in the application environment.

[0069] When the rate of change of friction parameters exceeds the set stability threshold, the update rate of the adaptive identification algorithm needs to be reduced. This is because when friction parameters change rapidly, the system may be in a relatively unstable or highly disturbed state. If the update rate is too fast, the system may overreact to errors, thus affecting the accuracy of the identification process. By reducing the update rate, the system has more time to adapt to the current state, thereby improving the stability and accuracy of the identification.

[0070] When the rate of change of friction parameters falls below the set stability threshold, it indicates that the system has stabilized. At this point, the update rate of the adaptive identification algorithm can be increased. Increasing the update rate helps accelerate the parameter optimization process, improves the efficiency of the identification algorithm, and thus achieves faster response and higher accuracy.

[0071] By dynamically adjusting the update rate of the adaptive identification algorithm, the system can flexibly respond to changes in system state based on actual variations in friction parameters, thus avoiding potential problems caused by excessively fast or slow update rates. Secondly, reducing the update rate protects the model's stability when the system is unstable, preventing erroneous parameter updates from affecting system performance. Conversely, increasing the update rate when the system is stable helps improve the system's response speed and identification efficiency. Overall, this adjustment mechanism improves the system's robustness and adaptability, ensuring high-precision and efficient operation of CNC machine tools under complex working conditions.

[0072] Example

[0073] This embodiment applies to the X-axis feed system of a vertical machining center. The system consists of a servo motor, coupling, ball screw, linear guide, and worktable, and is used to achieve precise workpiece positioning in the X direction. During high-speed, high-precision machining, frequent starts and stops and speed changes cause frictional nonlinearity, leading to increased tracking errors and decreased surface finish.

[0074] Step 1: Acquisition of motion data from the feed system;

[0075] In this embodiment, the data acquisition system consists of the following components: a 23-bit absolute encoder installed at the end of the servo motor for acquiring the actual position signal of the worktable; a current sensor built into the servo driver for acquiring the actual current signal of the servo motor; and command position signals generated by the CNC system.

[0076] The specific implementation process is as follows: The encoder generates 8,388,608 pulses per revolution. After processing by a quadruple frequency-multiplication direction-detection circuit, the pulse count is converted into a position value in millimeters, and the sampling time interval is set to 0.001 seconds. When performing numerical differentiation on the actual position signal, a first-order backward differential method is used. The calculation formula is: the actual velocity value at the current sampling moment equals the position value at the current sampling moment minus the position value at the previous sampling moment, divided by the sampling time interval. The actual current signal is acquired through a 16-bit analog-to-digital converter built into the servo driver, with a conversion accuracy of 0.1 mA. The command position signal is directly read from the interpolation module of the CNC system. All signals are transmitted to the motion controller via a real-time Ethernet bus. A dedicated buffer with 10,000 sampling points is allocated in the controller's memory for synchronous storage, and a ring storage structure is used to ensure data continuity.

[0077] Step 2: Initialize the parameters of the friction nonlinear characteristic model;

[0078] This embodiment employs the LuGre friction model, which accurately describes the frictional characteristics of the pre-sliding and sliding stages. The model parameter initialization process is as follows: During equipment debugging, the feed system is driven by dedicated debugging software to move at four constant speeds: 0.1 mm / s, 1 mm / s, 10 mm / s, and 100 mm / s. Each speed is maintained for 30 seconds, and the steady-state current value is recorded. This current is then converted into a frictional force value using the torque constant. The Stribeck curve is fitted using the least squares method to obtain the initial parameter values: bristle stiffness parameter is 1,000,000 N / m, bristle damping parameter is 100 N / s / m, Coulomb friction parameter is 150 N, viscous friction parameter is 50 N / s / m, and Stribeck velocity parameter is 5 mm / s. These initial parameters are stored in the controller's non-volatile memory and are automatically loaded when the system is powered on.

[0079] Step 3: Adaptive identification of friction parameters based on motion state segmentation;

[0080] The specific implementation of motion state judgment: The rate of change of the actual velocity signal is calculated using the first-order backward difference method, that is, the actual velocity value at the current sampling moment minus the actual velocity value at the previous sampling moment, and then divided by the sampling time interval. The positive threshold is set to 10% of the maximum acceleration of the feed system. In this embodiment, the maximum acceleration is 2 m / s², so the positive threshold is 0.2 m / s². The negative threshold is set to 10% of the maximum deceleration of the feed system. In this embodiment, the maximum deceleration is 2 m / s², so the negative threshold is -0.2 m / s².

[0081] During the parameter update process in the uniform velocity phase, the inertial force is calculated as follows: the actual acceleration signal is obtained from the actual velocity signal using the first-order backward difference method; the total system mass is calculated from the design drawings, including the mass of the motor rotor, the mass of the lead screw, and the mass of the worktable, totaling 150 kg. The forgetting factor in the recursive least squares method is set to 0.999 during the uniform velocity phase to emphasize the validity of historical data. The parameter update cycle is set to 10 sampling periods.

[0082] During the acceleration and deceleration phases, the extended Kalman filter is implemented as follows: the LuGre model is discretized, with state variables including bristle deformation and bristle deformation rate. The discretization step size is consistent with the sampling time interval. The process noise covariance matrix is ​​set as a diagonal matrix based on the vibration characteristics of the feed system, with diagonal elements of 0.01 and 0.01 respectively. The observation noise covariance is set to 0.0001 based on the current measurement accuracy. The parameter update period is set to 5 sampling periods to ensure rapid tracking of parameter changes.

[0083] Step 4: Friction compensation signal generation and system dynamic compensation;

[0084] The calculation process for the friction force estimate is as follows: According to the differential equation of the LuGre model, the differential of the bristle deformation is equal to the actual velocity signal minus the bristle stiffness parameter multiplied by the actual velocity signal multiplied by the bristle deformation, divided by the product of the Coulomb friction parameter and the Stribeck function. The fourth-order Runge-Kutta method is used to solve this differential equation, obtaining numerical solutions for the bristle deformation and its rate. The friction force estimate is equal to the bristle stiffness parameter multiplied by the bristle deformation, plus the bristle damping parameter multiplied by the bristle deformation rate, plus the viscous friction parameter multiplied by the actual velocity signal.

[0085] The specific implementation of phase lead compensation: The transfer function of the first-order lead network is expressed as the ratio of the compensation current signal output to the input equal to the numerator time constant multiplied by the Laplace operator plus 1, divided by the denominator time constant multiplied by the Laplace operator plus 1. The numerator time constant is set to 0.01 seconds based on the open-loop frequency response of the feed system, and the denominator time constant is set to 0.001 seconds, corresponding to a cutoff frequency of 100 Hz, which is higher than the 50 Hz bandwidth of the feed system. This transfer function is discretized and implemented using a direct type II structure to avoid numerical instability issues.

[0086] Step 5: Parameter identification and compensation effect monitoring;

[0087] The root mean square (RMS) value of the tracking error is calculated within a window of 1000 sampling points, i.e., data within 1 second. The threshold is set according to the required machining accuracy; in this embodiment, the required accuracy is 0.01 mm, therefore the threshold is set to 0.005 mm. When the RMS value of the tracking error exceeds 0.005 mm, the system automatically saves the current parameters and re-initializes from step two.

[0088] The rate of change of friction parameters was calculated using a sliding window method with a window length of 100 sampling points. The stability threshold was set based on historical data statistics, taking twice the average rate of change of parameters over the most recent hour. When the rate of change of any friction parameter exceeds the stability threshold, the update rate of the adaptive identification algorithm is reduced to half its original value; when the rate of change of all friction parameters is below the stability threshold, the update rate of the adaptive identification algorithm is doubled.

[0089] To verify the effectiveness of this embodiment, a traditional fixed-parameter friction compensation method was selected as a comparative example. The comparative example uses the same LuGre model, but the parameters remain unchanged after initialization, without online adaptive identification or dynamic adjustment of the compensation signal.

[0090] Test conditions: On the same vertical machining center X-axis feed system, the same machining trajectory was completed using both the method of this embodiment and the comparative method. The machining trajectory included linear interpolation, circular interpolation, and frequent start-stop motion, with a maximum movement speed of 60 meters per minute and an acceleration of 10 meters per square second. The test lasted for 8 hours, covering the system temperature rise process.

[0091] The test results are compared in the table below:

[0092]

[0093] Test data shows that this embodiment, through adaptive identification and compensation of frictional nonlinear characteristics, significantly outperforms traditional fixed-parameter compensation methods in all performance indicators. Particularly in terms of error drift caused by temperature rise, the improvement reaches 80.0%, proving that this embodiment can effectively adapt to changes in system parameters and maintain long-term stability.

[0094] Understandably, the bristle stiffness and bristle damping parameters in the LuGre friction model describe the elastic and damping characteristics of the microscopic bristles on the contact surface. The bristle stiffness parameter reflects the stiffness of the friction interface during the pre-slip phase, directly affecting the system's behavior when the velocity crosses zero. The bristle damping parameter describes the energy dissipation mechanism during bristle deformation, influencing the dynamic response speed of the friction behavior. In practical applications, these two parameters change significantly with lubrication conditions, temperature variations, and wear conditions. This embodiment uses an extended Kalman filter to update them in real time during the acceleration and deceleration phases, ensuring the model's accuracy under different operating conditions.

[0095] Regarding the threshold setting for motion state segmentation, this embodiment adopts a method based on the percentage of maximum acceleration, which can adapt to different motion conditions. When the feed system performs high-dynamic motion, the threshold automatically increases to avoid frequent switching of motion states; when performing precise slow motion, the threshold relatively decreases to improve the sensitivity of state judgment. This adaptive threshold mechanism ensures that the parameter identification process maintains both stability and sufficient sensitivity.

[0096] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0097] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for adaptive identification and compensation of frictional nonlinear characteristics of a CNC machine tool feed system, characterized in that, Includes the following steps: Step 1: Motion data acquisition of the feed system. The actual position signal of the worktable is acquired through the encoder. The actual position signal is obtained by numerical differentiation of the actual position signal. The actual current signal of the servo motor is acquired through the servo driver. The command position signal of the feed system is read from the CNC system. Step 2: Initialize the parameters of the nonlinear frictional characteristic model. Set the initial parameters of the LuGre model, including bristle stiffness parameters, bristle damping parameters, Coulomb friction parameters, viscous friction parameters, and Stribeck velocity parameters. Step 3: Adaptive identification of friction parameters based on motion state segmentation. The motion state of the feeding system is determined according to the actual velocity signal. The motion state is divided into acceleration stage, deceleration stage and uniform speed stage. In the uniform speed stage, the least squares method is used to update the Coulomb friction parameters and viscous friction parameters. In the acceleration stage and deceleration stage, the extended Kalman filter is used to update the bristle stiffness parameters, bristle damping parameters and Stribeck velocity parameters. Step 4: Friction compensation signal generation and system dynamic compensation. Based on the currently identified friction parameters and actual speed signal, calculate the friction force estimate of the LuGre model, convert the friction force estimate into a compensation current signal, perform phase lead compensation on the compensation current signal, and add it to the current command of the servo driver. Step 5: Parameter identification and compensation effect monitoring. Calculate the tracking error between the actual position signal and the commanded position signal. When the root mean square value of the tracking error exceeds the set threshold, trigger parameter re-initialization. When the rate of change of friction parameters exceeds the stable threshold, adjust the update rate of the adaptive identification algorithm.

2. The adaptive identification and compensation method for the frictional nonlinear characteristics of a CNC machine tool feed system according to claim 1, characterized in that, The actual velocity signal obtained by numerical differentiation of the actual position signal in step 1 is specifically achieved by using the first-order backward difference method, which divides the difference between the position value at the current sampling time and the position value at the previous sampling time by the sampling time interval to obtain the actual velocity value. The sampling time interval is set according to the maximum speed of the feed system to ensure that the sampling frequency is higher than the dynamic response frequency of the feed system. All acquired signals are synchronously stored in the controller's memory.

3. The adaptive identification and compensation method for the frictional nonlinear characteristics of a CNC machine tool feed system according to claim 1, characterized in that, The initial parameters of the LuGre model set in step 2 are based on offline experimental data of the feed system. The offline experiment involves driving the feed system to move at a constant speed, measuring the steady-state friction force, and fitting the initial parameter values. The initial parameters are stored in the controller and used as the initial values ​​for the first identification.

4. The adaptive identification and compensation method for the frictional nonlinear characteristics of a CNC machine tool feed system according to claim 1, characterized in that, The process of determining the motion state of the feed system based on the actual speed signal in step 3 includes: when the rate of change of the actual speed signal is greater than a positive threshold, it is determined to be in the acceleration phase; When the rate of change of the actual speed signal is less than the negative threshold, it is determined to be in the deceleration phase; When the rate of change of the actual velocity signal is between the negative threshold and the positive threshold, it is determined to be a uniform velocity stage; The rate of change is calculated by numerical differentiation of the actual velocity signal, and the positive and negative thresholds are set based on the maximum acceleration of the feed system.

5. The adaptive identification and compensation method for the frictional nonlinear characteristics of a CNC machine tool feed system according to claim 1, characterized in that, Step 3, which describes updating the Coulomb friction parameters and viscous friction parameters using the least squares method during the uniform velocity phase, specifically includes the following process: Construct a friction force estimate, which is equal to the actual current signal multiplied by the torque constant, and then subtract the inertial force. The inertial force is obtained by multiplying the actual acceleration signal by the total mass of the system. The actual acceleration signal is calculated by the numerical differentiation of the actual velocity signal. Establish a linear relationship between the estimated friction force and the actual velocity signal, and use the recursive least squares method to solve for the Coulomb friction parameters and viscous friction parameters; In the recursive least squares method, the forgetting factor is adaptively adjusted according to the motion state, and the forgetting factor is set to a larger value during the uniform motion phase.

6. The adaptive identification and compensation method for the frictional nonlinear characteristics of a CNC machine tool feed system according to claim 1, characterized in that, Step 3, which describes updating the bristle stiffness parameters, bristle damping parameters, and Stribeck velocity parameters using an extended Kalman filter during the acceleration and deceleration phases, specifically includes the following process: The LuGre model is discretized into a state-space equation, with state variables including the amount of bristle deformation and the rate of bristle deformation. The actual speed signal is used as the input, and the actual current signal is used as the observed value. The state variables and parameters are predicted using an extended Kalman filter, and the parameter estimates are updated based on the observation error. The process noise covariance and observation noise covariance of the extended Kalman filter are set based on the statistical characteristics of the motion data of the feed system.

7. The adaptive identification and compensation method for the frictional nonlinear characteristics of a CNC machine tool feed system according to claim 1, characterized in that, The friction force estimate of the LuGre model in step 4, which is calculated based on the currently identified friction parameters and actual velocity signal, is specifically obtained by calculating the bristle deformation amount, bristle deformation rate, actual velocity signal and friction parameters. The bristle deformation amount and bristle deformation rate are obtained by recursion from the state equation of the LuGre model. The process of converting the friction force estimate into a compensation current signal specifically involves the compensation current signal being equal to the friction force estimate divided by the torque constant.

8. The adaptive identification and compensation method for the frictional nonlinear characteristics of a CNC machine tool feed system according to claim 1, characterized in that, The phase lead compensation of the compensation current signal described in step 4 is specifically performed by using a first-order lead network. The transfer function of the first-order lead network is set according to the open-loop frequency response of the feed system, and the cutoff frequency is higher than the bandwidth of the feed system. The compensation current signal after phase lead compensation is added to the current command of the servo driver to achieve friction compensation.

9. The adaptive identification and compensation method for the frictional nonlinear characteristics of a CNC machine tool feed system according to claim 1, characterized in that, Step 5 describes calculating the tracking error between the actual position signal and the commanded position signal, with the tracking error stored in time series format; The set threshold is based on the processing accuracy requirements; When the root mean square value of the tracking error exceeds the set threshold, the parameters are re-initialized, specifically by re-executing the parameter initialization process of the friction nonlinear characteristic model starting from step 2.

10. The adaptive identification and compensation method for the frictional nonlinear characteristics of a CNC machine tool feed system according to claim 1, characterized in that, Step 5 describes adjusting the update rate of the adaptive identification algorithm when the rate of change of friction parameters exceeds the stability threshold. The specific process includes: calculating the rate of change of friction parameters through numerical differentiation of the parameter time series, and setting the stability threshold based on historical data statistics. When the rate of change of friction parameters exceeds the stability threshold, the update rate of the adaptive identification algorithm is reduced. When the rate of change of friction parameters is lower than the stability threshold, the update rate of the adaptive identification algorithm is increased.

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