Machine tool feed shaft mechanical parameter identification method based on VFFRLS

Abstract

The application discloses a machine tool feed shaft mechanical parameter identification method based on VFFRLS, and relates to the technical field of numerical control machine tools.The method comprises the following steps: constructing a permanent magnet synchronous linear motor driven feed shaft continuous domain mechanical dynamics equation, adopting a backward difference method for discretization processing, and converting into a least square standard form; designing an input excitation signal, collecting speed and current data in an offline test process, and initializing VFFRLS algorithm parameters; calculating model prediction residuals based on collected data at each moment, dynamically updating a forgetting factor in real time according to residual sizes, and synchronously completing recursive iteration of to-be-identified parameters; judging whether a convergence termination condition is met, and if the convergence termination condition is met, calculating and outputting total mass, viscous damping coefficients and Coulomb friction of the feed shaft. Through combination of offline measured data and the VFFRLS algorithm, the accurate identification of core mechanical parameters can be efficiently and stably completed without complex physical disassembly measurement.

Description

Technical Field

[0001] This invention relates to the field of CNC machine tool technology, and in particular to a method for identifying the mechanical parameters of machine tool feed axes based on VFFRLS. Background Technology

[0002] High-end CNC machine tools are core industrial mother machines supporting key manufacturing fields such as aerospace, precision electronics, new energy vehicles, and shipbuilding, possessing core technological characteristics of high response, high precision, and high reliability. Among them, the feed axis, as the core execution unit for realizing the feed motion of the CNC machine tool, has dynamic response characteristics, motion control accuracy, and operational stability that are key indicators determining the overall machining performance, workpiece forming accuracy, and production efficiency of the CNC machine tool.

[0003] The feed system uses a permanent magnet synchronous linear motor as its drive source, directly converting electromagnetic energy into linear motion mechanical energy. This eliminates the intermediate transmission links such as ball screws and gearboxes found in traditional rotary motor feed systems, significantly reducing transmission chain errors. It is the mainstream feed solution for high-end high-speed CNC machine tools. The servo control performance of the machine tool feed system is highly dependent on the accuracy of the controlled object's mechanical parameters. To achieve high-precision trajectory tracking, strong anti-disturbance servo control under high-speed conditions, and accurate tuning of servo control parameters and optimization of system dynamic characteristics, accurate and efficient offline identification of the core mechanical parameters of the feed system is crucial.

[0004] Constructing accurate dynamic models of feed systems is the core foundation for servo control strategy optimization, system dynamic characteristic analysis, fault early warning, and life assessment. However, in actual industrial scenarios, core mechanical parameters of the feed system, such as the equivalent total mass, viscous friction coefficient, static friction coefficient, and equivalent mechanical stiffness, require specialized high-precision testing instruments and disassembly of machine tool components for traditional offline measurement methods. This not only results in cumbersome and inefficient testing processes but also fails to simulate the actual operating environment of the machine tool, making it difficult to obtain true parameter values ​​that closely reflect the actual operating conditions. To address this issue, the industry has conducted extensive research on offline identification of mechanical parameters of machine tool feed systems, resulting in various technical approaches, including recursive least squares method, gradient correction method, and intelligent optimization algorithm identification.

[0005] Currently, the identification of mechanical parameters of machine tool feed axes mostly adopts the ordinary least squares method or the fixed forgetting factor recursive least squares method. The ordinary least squares method has the problem of low identification accuracy, while the fixed forgetting factor recursive least squares method has the problem of not being able to balance stability and tracking. Summary of the Invention

[0006] The purpose of this invention is to provide a method for identifying machine tool feed axis mechanical parameters based on VFFRLS, aiming to solve or improve at least one of the above-mentioned technical problems.

[0007] To achieve the above objectives, the present invention provides the following solution: A method for identifying machine tool feed axis mechanical parameters based on VFFRLS, comprising: Step S1: Construct and simplify the continuous domain mechanical dynamics equations of the machine tool feed axis driven by the permanent magnet synchronous linear motor, and use backward difference to generate discretized mechanical motion equations, and transform them into the least squares standard form; Step S2: Design the input excitation signal and collect test data to complete the basic parameter initialization of the VFFRLS identification algorithm. Calculate the model prediction residual based on the collected signal time by time. Update the forgetting factor dynamically in real time according to the residual, and simultaneously complete the iterative update of the mechanical parameters to be identified. Step S3: Monitor the identification iteration process in real time and determine whether the preset convergence termination condition is met. If it is met, calculate and output the final identification result of the core mechanical parameters of the machine tool feed axis. If it is not met, update the sampling time index and return to step S2 to continue the recursive iteration calculation.

[0008] Further, step S1 includes: According to Newton's second law, the mechanical motion equation of a machine tool feed axis driven by a permanent magnet synchronous linear motor in the continuous time domain is expressed as: In the formula, This is the motor thrust coefficient; This is a quadrature-axis current command; This refers to the instantaneous acceleration of the feed axis; For speed of motion; Equivalent mass of the feed shaft; It is the viscous damping coefficient; This represents the amplitude of the Coulomb friction force. The sign function for velocity direction; Assume the system sampling period is The acceleration is discretized and approximated using the backward difference method, and the expression is as follows: In the formula, Let k be the instantaneous acceleration at time k. for The motion velocity value collected at any time; for The motion velocity value collected at any time; Substituting the discretized acceleration into the continuous domain dynamics equations, we obtain the discretized mechanical motion equations, expressed as follows: In the formula, The quadrature-axis current command at time k; The sign function of the velocity at time k is used to represent the direction of the Coulomb friction force; The discretized mechanical motion equations are transformed into the least squares standard form.

[0009] Furthermore, the discretized mechanical equations of motion are transformed into the least squares standard form, including: Divide both sides of the discretized mechanical motion equation by the motor thrust coefficient, and reorganize the terms according to the parameters to be identified to generate the least squares standard form of the discretized mechanical motion equation, which is expressed as follows: In the formula, The quadrature-axis current command at time k; for The motion velocity value collected at any time; for The motion velocity value collected at any time; Let be the sign function of the velocity at time k; Equivalent mass of the feed shaft; It is the viscous damping coefficient; This represents the amplitude of the Coulomb friction force. This is the motor thrust coefficient; The sampling period.

[0010] Further, step S2 includes: During offline testing, speed and quadrature-axis current signals were collected synchronously throughout the entire testing period to construct a measured dataset. Initialize the basic parameters of the VFFRLS identification algorithm; In each recursive iteration, the model prediction residual at the current time step is calculated using the parameter estimates from the previous time step, expressed as: In the formula, Let be the model prediction residual at time k; for The actual output observation value of the system at time ; for The data regression matrix at each time point; for The estimated vector of the parameters to be identified at time step; The dynamic forgetting factor is adaptively updated based on the magnitude of the model-predicted residuals, expressed as: In the formula, The dynamic forgetting factor value is updated in real time at time k; Basic forgetting factor; This is the adjustment coefficient; Based on the updated dynamic forgetting factor, the standard RLS recursive update law is executed to simultaneously update the parameter estimates and covariance matrix. The expression is as follows: In the formula, Let k be the estimated value of the parameter matrix to be identified at time k; This represents the estimated value of the parameter matrix to be identified at time k-1; Let be the algorithm gain matrix at time k; The system outputs the observed value at time k; This is the parameter vector obtained from the k-th sampling. This is the transpose of the parameter vector obtained from the k-th sampling. Let k be the covariance matrix at time k; Let be the covariance matrix at time k-1; The dynamic forgetting factor value is updated in real time at time k; It is an identity matrix.

[0011] Further initialization settings include: Initial parameter estimates Initial covariance matrix Basic forgetting factor Adjustment coefficient Maximum number of iterations , where n is the total number of valid data sets collected.

[0012] Furthermore, the convergence termination condition is: the number of identification iterations reaches the preset maximum number of iterations.

[0013] Furthermore, the final identification results include: feed shaft equivalent mass Viscous damping coefficient The sum is the amplitude of the Coulomb friction force. .

[0014] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: This invention discloses a method for identifying the mechanical parameters of machine tool feed axes based on VFFRLS. Utilizing the VFFRLS algorithm, this method can accurately identify the core mechanical parameters of the feed axes even when their mechanical parameters are unknown, solely by collecting offline test data from the machine tool. This solves the problems of cumbersome offline measurement processes and low identification accuracy in existing technologies for machine tool feed axis mechanical parameters. Furthermore, by combining offline measured data with a variable forgetting factor recursive least squares algorithm, it can efficiently and stably identify core mechanical parameters such as the total mass and viscous friction coefficient of the feed axis, obtaining mechanical parameters that closely match the actual operating characteristics of the machine tool. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a schematic flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the open-loop identification model for feed axis mechanical parameters in this embodiment; Figure 3 This is a flowchart of the VFFRLS algorithm in this embodiment. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] The purpose of this invention is to provide a method for identifying machine tool feed axis mechanical parameters based on VFFRLS, aiming to solve or improve at least one of the above-mentioned technical problems.

[0019] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] In existing technologies, offline identification methods for machine tool feed axis mechanical parameters are based on the Fixed Forgetting Factor Recursive Least Squares (FFRLS) framework. This approach introduces a fixed forgetting factor to weight and attenuate historical data, improving the algorithm's adaptability to parameter variations under different operating conditions. The core recursive formula is as follows: In the formula, Let k be the estimated value of the parameter matrix to be identified at time k; This represents the estimated value of the parameter matrix to be identified at time k-1; Let be the algorithm gain matrix at time k; The system outputs the observed value at time k; This is the parameter vector obtained from the k-th sampling. This is the transpose of the parameter vector obtained from the k-th sampling. Let k be the covariance matrix at time k; Let be the covariance matrix at time k-1; A forgetting factor with a fixed value. It is an identity matrix.

[0021] like Figure 1 As shown, this invention provides a method for identifying machine tool feed axis mechanical parameters based on VFFRLS, including: Step S1: Construct and simplify the continuous domain mechanical dynamics equations of the machine tool feed axis driven by the permanent magnet synchronous linear motor, and use backward difference to generate discretized mechanical motion equations, which are then transformed into the least squares standard form, including: like Figure 2 As shown, according to Newton's second law, the mechanical motion equation of the machine tool feed axis driven by a permanent magnet synchronous linear motor in the continuous time domain is expressed as: In the formula, This is the motor thrust coefficient; This is a quadrature-axis current command; This refers to the instantaneous acceleration of the feed axis; For speed of motion; Equivalent mass of the feed shaft; It is the viscous damping coefficient; This represents the amplitude of the Coulomb friction force. This is the sign function for the velocity direction.

[0022] Assume the system sampling period is The acceleration is discretized and approximated using the backward difference method, and the expression is as follows: In the formula, Let k be the instantaneous acceleration at time k. for The motion velocity value collected at any time; for The motion speed value is collected at any time.

[0023] Substituting the discretized acceleration into the continuous domain dynamics equations, we obtain the discretized mechanical motion equations, expressed as follows: In the formula, The quadrature-axis current command at time k; Let be the sign function of the velocity at time k, used to represent the direction of the Coulomb friction force.

[0024] Transforming the discretized mechanical equations of motion into the least squares standard form includes: Divide both sides of the discretized mechanical motion equation by the motor thrust coefficient, and reorganize the terms according to the parameters to be identified to generate the least squares standard form of the discretized mechanical motion equation, which is expressed as follows: In the formula, The quadrature-axis current command at time k; for The motion velocity value collected at any time; for The motion velocity value collected at any time; Let be the sign function of the velocity at time k; Equivalent mass of the feed shaft; It is the viscous damping coefficient; This represents the amplitude of the Coulomb friction force. This is the motor thrust coefficient; The sampling period; Based on the discretized mechanical motion equations in the least squares standard form, the observed output is defined. Regression matrix and the parameter vector to be identified They are respectively: In the formula, for The actual thrust generated by the motor at any given moment; Let k be a row vector consisting of the physical quantities that can be measured at time k. The parameter matrix to be identified.

[0025] The above formula successfully constructs the discretized mechanical motion equations in the least squares standard form. .

[0026] like Figure 3 As shown, step S2 involves designing the input excitation signal and collecting test data to initialize the basic parameters of the VFFRLS identification algorithm. Based on the collected signals, the model prediction residual is calculated time-by-time. The forgetting factor is dynamically updated in real-time according to the residual, and the recursive iterative update of the mechanical parameters to be identified is completed simultaneously. This includes: In this embodiment, a sweep frequency signal is used as the input excitation signal for the system.

[0027] During offline testing, velocity signals and quadrature-axis (q-axis) current signals were simultaneously acquired throughout the entire testing period to construct a measured dataset; the total number of valid data sets acquired was set to... .

[0028] Initialize the basic parameters of the VFFRLS identification algorithm, including: In this embodiment, the initialization parameter settings include: initial parameter estimates. Initial covariance matrix Basic forgetting factor Adjustment coefficient Maximum number of iterations .

[0029] In each recursive iteration, the model prediction residual at the current time step is calculated using the parameter estimates from the previous time step, expressed as: In the formula, Let be the model prediction residual at time k; for The actual output observation value of the system at a given time, i.e., the measured quadrature-axis current; for The data regression matrix at each time point; for The estimated vector of the parameters to be identified at time step; The dynamic forgetting factor is adaptively updated based on the magnitude of the model-predicted residuals, expressed as: In the formula, The dynamic forgetting factor value is updated in real time at time k; Basic forgetting factor; This is the adjustment coefficient.

[0030] The aforementioned adaptive update forgetting factor can reduce the impact of sudden changes in the system (increased residuals). This assigns higher weights to new data and accelerates the convergence speed.

[0031] Based on the updated dynamic forgetting factor, the standard RLS recursive update law is executed to simultaneously update the parameter estimates and covariance matrix. The expression is as follows: In the formula, Let k be the estimated value of the parameter matrix to be identified at time k; This represents the estimated value of the parameter matrix to be identified at time k-1; Let be the algorithm gain matrix at time k; The system outputs the observed value at time k; This is the parameter vector obtained from the k-th sampling. This is the transpose of the parameter vector obtained from the k-th sampling. Let k be the covariance matrix at time k; Let be the covariance matrix at time k-1; The dynamic forgetting factor value is updated in real time at time k; It is an identity matrix.

[0032] Step S3: Monitor the identification iteration process in real time and determine whether the preset convergence termination condition is met. If it is met, calculate and output the final identification result of the core mechanical parameters of the machine tool feed axis. If it is not met, update the sampling time index and return to step S2 to continue the recursive iteration calculation.

[0033] The convergence termination condition is: the number of identification iterations reaches the preset maximum number of iterations. .

[0034] The final identification results include: feed shaft equivalent mass Viscous damping coefficient The sum is the amplitude of the Coulomb friction force. .

[0035] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0036] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for identifying machine tool feed axis mechanical parameters based on VFFRLS, characterized in that, include: Step S1: Construct and simplify the continuous domain mechanical dynamics equations of the machine tool feed axis driven by the permanent magnet synchronous linear motor, and use backward difference to generate discretized mechanical motion equations, and transform them into the least squares standard form; Step S2: Design the input excitation signal and collect test data to complete the basic parameter initialization of the VFFRLS identification algorithm. Calculate the model prediction residual based on the collected signal time by time. Update the forgetting factor dynamically in real time according to the residual, and simultaneously complete the iterative update of the mechanical parameters to be identified. Step S3: Monitor and identify the iteration process in real time to determine whether the preset convergence termination condition is met. If satisfied, the final identification results of the core mechanical parameters of the machine tool feed axis are calculated and output. If the conditions are not met, update the sampling time index and return to step S2 to continue the recursive iterative calculation.

2. The method for identifying machine tool feed axis mechanical parameters based on VFFRLS according to claim 1, characterized in that, Step S1 includes: According to Newton's second law, the mechanical motion equation of a machine tool feed axis driven by a permanent magnet synchronous linear motor in the continuous time domain is expressed as: In the formula, This is the motor thrust coefficient; This is a quadrature-axis current command; This refers to the instantaneous acceleration of the feed axis; For speed of motion; For the feed shaft equivalent mass; It is the viscous damping coefficient; This represents the amplitude of the Coulomb friction force. The sign function for velocity direction; Assume the system sampling period is The acceleration is discretized and approximated using the backward difference method, and the expression is as follows: In the formula, Let k be the instantaneous acceleration at time k. for The motion velocity value collected at any time; for The motion velocity value collected at any time; Substituting the discretized acceleration into the continuous domain dynamics equations, we obtain the discretized mechanical motion equations, expressed as follows: In the formula, The quadrature-axis current command at time k; Let be the sign function of the velocity at time k, used to represent the direction of the Coulomb friction force; The discretized mechanical motion equations are transformed into the least squares standard form.

3. The method for identifying machine tool feed axis mechanical parameters based on VFFRLS according to claim 2, characterized in that, The process of transforming the discretized mechanical equations of motion into the least squares standard form includes: Divide both sides of the discretized mechanical motion equation by the motor thrust coefficient, and reorganize the terms according to the parameters to be identified to generate the least squares standard form of the discretized mechanical motion equation, which is expressed as follows: In the formula, The quadrature-axis current command at time k; for The motion velocity value collected at any time; for The motion velocity value collected at any time; Let be the sign function of the velocity at time k; For the feed shaft equivalent mass; It is the viscous damping coefficient; This represents the amplitude of the Coulomb friction force. This is the motor thrust coefficient; The sampling period.

4. The method for identifying machine tool feed axis mechanical parameters based on VFFRLS according to claim 1, characterized in that, Step S2 includes: During offline testing, speed and quadrature-axis current signals were collected synchronously throughout the entire testing period to construct a measured dataset. Initialize the basic parameters of the VFFRLS identification algorithm; In each recursive iteration, the model prediction residual at the current time step is calculated using the parameter estimates from the previous time step, expressed as: In the formula, Let be the model prediction residual at time k; for The actual output observation value of the system at time ; for The data regression matrix at each time point; for The estimated vector of the parameters to be identified at time step; The dynamic forgetting factor is adaptively updated based on the magnitude of the model-predicted residuals, expressed as: In the formula, The dynamic forgetting factor value is updated in real time at time k; Basic forgetting factor; This is the adjustment coefficient; Based on the updated dynamic forgetting factor, the standard RLS recursive update law is executed to simultaneously update the parameter estimates and covariance matrix. The expression is as follows: In the formula, Let k be the estimated value of the parameter matrix to be identified at time k; This represents the estimated value of the parameter matrix to be identified at time k-1; Let be the algorithm gain matrix at time k; The system outputs the observed value at time k; This is the parameter vector obtained from the k-th sampling. This is the transpose of the parameter vector obtained from the k-th sampling. Let k be the covariance matrix at time k; Let be the covariance matrix at time k-1; The dynamic forgetting factor value is updated in real time at time k; It is an identity matrix.

5. The method for identifying machine tool feed axis mechanical parameters based on VFFRLS according to claim 4, characterized in that, The initialization settings include: Initial parameter estimates Initial covariance matrix Basic forgetting factor Adjustment coefficient Maximum number of iterations , where n is the total number of valid data sets collected.

6. The method for identifying machine tool feed axis mechanical parameters based on VFFRLS according to claim 1, characterized in that, The convergence termination condition is: the number of identification iterations reaches the preset maximum number of iterations.

7. The method for identifying machine tool feed axis mechanical parameters based on VFFRLS according to claim 1, characterized in that, The final identification result includes: feed shaft equivalent mass. Viscous damping coefficient The sum is the amplitude of the Coulomb friction force. .

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