Method for analyzing dynamic characteristics of servo feeding system

Abstract

The invention relates to a method for analyzing dynamic characteristics of a servo feeding system, and belongs to the technical field of time domain and frequency domain characteristics of numerical control machine tools. Dynamic characteristic analysis is divided into two parts, namely time domain analysis and frequency domain analysis; time domain analysis provides dynamic response characteristics of the machine tool in terms of time, and transient behaviors and errors are visually revealed; frequency domain analysis reveals frequency characteristics of the machine tool, and helps to identify resonance phenomenon and system stability, thereby optimizing dynamic control and signal processing. According to the method, the transfer function of the whole system is discretized, so that a complete system model can be reserved without being excessively simplified, and various nonlinear factors and time-varying characteristics of the system in the actual operation process can be accurately reflected; the method has flexibility and expansibility, and can flexibly add or cancel optional links such as filtering or wave trapping for some control systems.

Description

Technical Field

[0001] The present invention relates to the technical field of time domain and frequency domain characteristics of numerically controlled machine tools, and in particular to a method for analyzing the dynamic characteristics of a servo feed system. Background Art

[0002] In modern manufacturing, servo feed systems are key components of precision machining equipment such as CNC machine tools. Their dynamic characteristics directly impact machining accuracy and efficiency. Accurately analyzing the dynamic characteristics of feed servo systems is crucial for optimizing system performance and improving machining quality.

[0003] Currently, a variety of methods exist for analyzing the dynamic characteristics of servo feed systems. Some traditional approaches rely on simple mathematical models, which often oversimplify the complex dynamic characteristics of the system. These models fail to accurately reflect the various nonlinear factors and time-varying characteristics of the system during actual operation, resulting in significant deviations between the analysis results and the actual situation. Under complex operating conditions, analysis methods based on traditional mathematical models cannot provide a reliable basis for precise system control.

[0004] At the same time, some existing analytical methods lack data processing and computational efficiency. As the volume of data generated by equipment continues to grow, traditional methods are slow to process large amounts of data, making real-time analysis difficult. This severely impacts the ability to accurately assess and adjust system dynamics. During high-speed machining, the inability to analyze system dynamics can lead to the accumulation of machining errors and compromise product quality.

[0005] In terms of software development tools, some early tools for analyzing the dynamic characteristics of feed servo systems had limited functionality, lacking flexibility and scalability. Faced with the ever-evolving technology and diverse application requirements of feed servo systems, these tools struggled to meet the requirements for comprehensive and in-depth system analysis. For example, when new control algorithms or hardware structures were introduced, traditional analysis tools were unable to quickly adapt and implement the corresponding analysis capabilities. Summary of the Invention

[0006] In view of the above problems, the present invention provides a method for analyzing the dynamic characteristics of a servo feed system. The dynamic characteristics analysis of the present invention is divided into two parts: time domain analysis and frequency domain analysis; the time domain analysis provides the dynamic response characteristics of the machine tool in time, intuitively revealing transient behavior and errors; the frequency domain analysis reveals the frequency characteristics of the machine tool, helps identify resonance phenomena and system stability, and thus optimizes dynamic control and signal processing.

[0007] The present invention provides a method for analyzing the dynamic characteristics of a servo feed system, comprising:

[0008] Step S1, establishing an original CNC machine tool feed servo system transfer function and simplifying it to obtain a CNC machine tool feed servo system transfer function;

[0009] Step S2, obtaining the mechanical transmission power system of the CNC machine tool feed servo system;

[0010] Perform parameter identification on the mechanical transmission power system based on Kalman filtering to obtain identification parameters;

[0011] Substituting the identification parameters into the transfer function of the CNC machine tool feed servo system to obtain a complete transfer function of the CNC machine tool feed servo system;

[0012] Step S3: Perform dynamic characteristic analysis based on the complete transfer function of the CNC machine tool feed servo system to obtain time domain dynamic characteristic analysis results and frequency domain dynamic characteristic analysis results.

[0013] Optionally, the transfer function of the CNC machine tool feed servo system in step S1 includes: a current loop transfer function, a speed loop transfer function and a position loop transfer function.

[0014] Optionally, the identification parameters in step S2 include the equivalent mass, viscous damping coefficient and Coulomb friction of the CNC machine tool feed servo system.

[0015] Optionally, the expression of the mechanical transmission power system is:

[0016]

[0017] Where I is the motor current of the mechanical transmission power system, K m is the motor thrust coefficient, is the motor acceleration of the mechanical transmission power system, is the motor speed of the mechanical transmission power system, m is the equivalent mass of the CNC machine tool feed servo system, c is the viscous damping coefficient of the CNC machine tool feed servo system, and f is the Coulomb friction of the CNC machine tool feed servo system.

[0018] Optionally, the specific steps of obtaining the time domain analysis result include:

[0019] Step S31, let t = 1, when t = 1, it represents the initial time;

[0020] Step S32: Determine the control input at time t, input the control input at time t into the complete CNC machine tool feed servo system transfer function, and obtain the output value at time t and the corresponding feedback value A t ;

[0021] Step S33: Based on the corresponding feedback value A tUpdate the control input at time t to obtain the updated control input at time t as the control input at time t+1;

[0022] Step S34, determine whether t is greater than or equal to T, where T represents the total time. If so, obtain the output value of each moment as the time domain analysis result of each moment. If not, set t=t+1 and return to step S32.

[0023] Optionally, the specific steps of obtaining the frequency domain analysis result include:

[0024] Step S3-1, expressing the complete CNC machine tool feed servo system transfer function as a complex variable s;

[0025] Step S3-2: determining a frequency range, and obtaining a plurality of frequency points based on the frequency domain range;

[0026] Step S3-3, set the real part of the complex variable s to zero, and only consider the imaginary part to obtain an updated complex variable;

[0027] Step S3-4, traverse multiple frequency points, and calculate the complex variable value corresponding to each frequency point based on the updated complex variable;

[0028] Step S3-5: Substitute the complex variable value corresponding to each frequency point into the complete CNC machine tool feed servo system transfer function to obtain the amplitude and phase of each frequency point of the complete CNC machine tool feed servo system.

[0029] Optionally, the amplitude and phase of each frequency point of the complete CNC machine tool feed servo system are expressed as follows:

[0030]

[0031] Where G represents the frequency, Im represents the imaginary part, Re represents the real part, |G| is the amplitude of the complete CNC machine tool feed servo system, and ∠G is the phase of the complete CNC machine tool feed servo system.

[0032] Optionally, the control input includes a step signal input, a sinusoidal signal input or a ramp signal input of a CNC machine tool feed servo system.

[0033] Compared with the prior art, the present invention has at least the following beneficial effects:

[0034] (1) The present invention discretizes the overall system transfer function so that the complete system model can be retained without oversimplification, and can accurately reflect the various nonlinear factors and time-varying characteristics of the system during actual operation;

[0035] (2) The present invention is flexible and extensible. Optional filtering or notching components can be added or removed for certain control systems. This method greatly reduces the analysis time of the feed servo system. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The drawings are only for purposes of illustrating particular embodiments and are not to be considered limiting of the invention.

[0037] Figure 1 Schematic diagram of the process of analyzing the dynamic characteristics of the servo feed system in an embodiment of the present invention. DETAILED DESCRIPTION

[0038] In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. In addition, the present invention can also be implemented in other ways different from those described herein. Therefore, the scope of protection of the present invention is not limited by the specific embodiments disclosed below.

[0039] A specific embodiment of the present invention, as Figure 1 , discloses a method for analyzing the dynamic characteristics of a servo feed system, and the specific implementation steps are as follows:

[0040] Step S1, establishing an original CNC machine tool feed servo system transfer function and simplifying it to obtain a CNC machine tool feed servo system transfer function;

[0041] Optionally, the specific steps of simplification include:

[0042] When establishing the transfer function of the CNC machine tool feed servo system, factors that have little impact on the performance of the CNC machine tool feed servo system are ignored, which is used to highlight the main dynamic characteristics of the CNC machine tool feed servo system;

[0043] Optionally, the factors having little impact on the performance include: slow changes in temperature, slow changes in humidity, tooth side clearance and / or torsional elastic deformation of the shaft.

[0044] The simplified transfer function in the present invention can reduce the order of the model, reduce the amount of calculation, and facilitate real-time control and simulation.

[0045] Optionally, the transfer function of the CNC machine tool feed servo system in step S1 includes:

[0046] Current loop open-loop transfer function, speed loop transfer function, and position loop transfer function.

[0047] Optional. In engineering, the current response is much faster than the speed loop, and the back electromotive force changes slowly, so it is considered in steady state and ignored in dynamic state.

[0048] Optionally, the expression of the current loop open-loop transfer function is:

[0049]

[0050] Among them, G i (s) represents the response speed of the current loop of the CNC machine tool feed servo system, s represents the complex variable, that is, the Laplace variable, K Pi is the proportional gain of the current loop, K1 is the sum of the amplification factors of the current loop, K1 = K mi K PWM , K mi is the proportional magnification factor of the current loop, T PWM is the SPWM inverter time constant of the current loop, K PWM is the SPWM inverter amplification factor of the current loop, T mi is the electrical time constant of the motor, R is the resistance of the motor winding, T Pi is the integration time constant, T ∑ is the sum of the time constants, T Σ =T mi +T PWM .

[0051] Optionally, the speed loop transfer function is expressed as:

[0052]

[0053] Among them, G v (s) is the response speed of the speed loop of the CNC machine tool feed servo system, K vp is the speed loop proportional gain, K vfr is the speed feedback proportional controller, K t is the motor torque coefficient, B is the viscous friction coefficient of the CNC machine tool feed servo system, K vi is the speed loop integral gain, T Ei is the equivalent time constant of the current loop, and J is the equivalent moment of inertia of the motor.

[0054] Optionally, the position loop closed-loop transfer function is expressed as:

[0055]

[0056] Among them, G(s) represents the response speed of the position loop of the CNC machine tool feed servo system, K pvfr is the position loop speed feedforward gain, K pafr is the acceleration feedforward gain of the position loop, K ppis the position loop proportional gain, m is the equivalent mass, K vi is the velocity loop integral gain, c is the viscous damping coefficient, K m is the motor thrust coefficient.

[0057] Step S2, obtaining the mechanical transmission power system of the CNC machine tool feed servo system;

[0058] Perform parameter identification on the mechanical transmission power system based on Kalman filtering to obtain identification parameters;

[0059] Substituting the identification parameters into the transfer function of the CNC machine tool feed servo system to obtain a complete transfer function of the CNC machine tool feed servo system;

[0060] Furthermore, the identification parameters in step S2 include the equivalent mass m, viscous damping coefficient c and Coulomb friction f of the CNC machine tool feed servo system;

[0061] Optionally, the expression of the mechanical transmission power system is:

[0062]

[0063] Where I is the motor current of the mechanical transmission power system, K m is the motor thrust coefficient, is the motor acceleration of the mechanical transmission power system, is the motor speed of the mechanical transmission power system.

[0064] Furthermore, the specific steps of obtaining the identification parameters include:

[0065] Step S21: Obtain the posterior state estimate of the mechanical transmission power system at the k-1th iteration step. Use the posterior state estimate of the k-1th iteration step and the control input u of the kth iteration step k , get the prior state estimate of the kth iteration step The expression is:

[0066]

[0067] Among them, A is the state transfer matrix of the mechanical transmission power system, where the state transfer matrix includes mass and inertia, representing the inherent dynamic characteristics of the mechanical transmission power system; B is the control input matrix of the mechanical transmission power system, representing the mapping relationship between the input and the state of the mechanical transmission power system, where the control input includes motor current, force or torque command.

[0068] Step S22: Based on the noise covariance matrix Q of the mechanical transmission power system, obtain the a priori estimation error covariance of the kth iteration step

[0069]

[0070] Among them, P k-1 represents the error covariance matrix of the k-1th iteration step;

[0071]

[0072] Step S23: Based on the a priori estimation error covariance of the k-th iteration step and the observation noise covariance matrix R, the Kalman gain K is obtained, which is expressed as:

[0073]

[0074] Among them, H is the state observation matrix of the mechanical transmission power system, which represents the mapping relationship between the system state and the observation value, K is the Kalman gain, and R is the covariance matrix of the observation noise.

[0075] Step S24: Using the observation value z of the kth iteration step k and the prior state estimate of the kth iteration step Get the posterior state estimate of the kth iteration step The expression is:

[0076]

[0077] Step S25: determine whether k is greater than or equal to K. If so, obtain the final posterior state estimate and obtain the identification parameters based on the final posterior state estimate. If not, set k=k+1 and return to step S21.

[0078] Step S3: Perform dynamic characteristic analysis based on the complete transfer function of the CNC machine tool feed servo system to obtain time domain dynamic characteristic analysis results and frequency domain dynamic characteristic analysis results;

[0079] Optionally, the specific steps of obtaining the time domain analysis result include:

[0080] Step S31, let t = 1, when t = 1, it represents the initial time;

[0081] Step S32: Determine the control input at time t, input the control input at time t into the complete CNC machine tool feed servo system transfer function, and obtain the output value at time t and the corresponding feedback value A t ;

[0082] Step S33: Based on the corresponding feedback value A t Update the control input at time t to obtain the updated control input at time t as the control input at time t+1;

[0083] Step S34, determine whether t is greater than or equal to T, where T represents the total time. If so, obtain the output value of each moment as the time domain analysis result of each moment. If not, set t=t+1 and return to step S32.

[0084] Optionally, the control input includes a step signal input, a sinusoidal signal input or a ramp signal input of a CNC machine tool feed servo system.

[0085] Exemplarily, when the input is a step signal, the output time domain analysis results include overshoot, adjustment time, rise time, and steady-state error;

[0086] When the input is a sinusoidal signal, the output time domain analysis results include amplitude-frequency characteristics, phase-frequency characteristics, bandwidth, resonant frequency, and resonant peak value;

[0087] When the input is a ramp signal, the output time domain analysis results include: steady-state error, adjustment time, following error, and overshoot.

[0088] For example, the transfer function of the complete CNC machine tool feed servo system is discretized and rewritten into C++ code and written into the Visual Studio platform, so that the time domain response can be analyzed.

[0089] Optionally, the specific steps of obtaining the frequency domain analysis result include:

[0090] Step S3-1: Express the complete CNC machine tool feed servo system transfer function as a complex variable s, expressed as follows:

[0091] s=σ+jω

[0092] Where σ is the real part, ω is the angular frequency, s is a complex variable used to describe the dynamic characteristics of the linear time-invariant system, and j is the imaginary part.

[0093] Step S3-2: determine the frequency range, and obtain multiple frequency points based on the frequency domain range. The expression is:

[0094]

[0095] Among them, f i is the i-th frequency point, a is the starting index of the logarithmic frequency range, b is the ending index of the logarithmic frequency range, and n is the total number of frequency points.

[0096] Step S3-3, set the real part of the complex variable s to zero, and only consider the imaginary part to obtain an updated complex variable;

[0097] Step S3-4: traverse multiple frequency points and calculate the complex variable value corresponding to each frequency point based on the updated complex variable. The expression is:

[0098] s i=j2πf i

[0099] Among them, s i Represents the complex variable value corresponding to the i-th frequency point.

[0100] Step S3-5: Substitute the complex variable values ​​corresponding to each frequency point into the complete CNC machine tool feed servo system transfer function to obtain the amplitude and phase of each frequency point of the complete CNC machine tool feed servo system. The expressions are:

[0101]

[0102] Wherein, G represents the frequency response function, Im represents the imaginary part, Re represents the real part, |G| is the amplitude of the complete CNC machine tool feed servo system, which represents the degree of amplification or attenuation of the input signal by the complete CNC machine tool feed servo system, ∠G is the phase of the complete CNC machine tool feed servo system, which represents the time delay or advance of the output signal relative to the input signal, and arctan(.) is the inverse tangent function. The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be covered by the scope of protection of the present invention.

Claims

1. A method for analyzing the dynamic characteristics of a servo feed system, characterized in that: include: Step S1, establishing an original CNC machine tool feed servo system transfer function and simplifying it to obtain a CNC machine tool feed servo system transfer function; Step S2, obtaining the mechanical transmission power system of the CNC machine tool feed servo system; Perform parameter identification on the mechanical transmission power system based on Kalman filtering to obtain identification parameters; Substituting the identification parameters into the transfer function of the CNC machine tool feed servo system to obtain a complete transfer function of the CNC machine tool feed servo system; Step S3: Perform dynamic characteristic analysis based on the complete transfer function of the CNC machine tool feed servo system to obtain time domain dynamic characteristic analysis results and frequency domain dynamic characteristic analysis results.

2. The method for analyzing the dynamic characteristics of a servo feed system according to claim 1, characterized in that: The transfer function of the CNC machine tool feed servo system in step S1 includes: a current loop transfer function, a speed loop transfer function and a position loop transfer function.

3. The method for analyzing the dynamic characteristics of a servo feed system according to claim 1, characterized in that: The identification parameters in step S2 include the equivalent mass, viscous damping coefficient and Coulomb friction of the CNC machine tool feed servo system.

4. The method for analyzing the dynamic characteristics of a servo feed system according to claim 1, characterized in that: The expression of the mechanical transmission power system is: Where I is the motor current of the mechanical transmission power system, K m is the motor thrust coefficient, is the motor acceleration of the mechanical transmission power system, is the motor speed of the mechanical transmission power system, m is the equivalent mass of the CNC machine tool feed servo system, c is the viscous damping coefficient of the CNC machine tool feed servo system, and f is the Coulomb friction of the CNC machine tool feed servo system.

5. The method for analyzing the dynamic characteristics of a servo feed system according to claim 1, characterized in that: The specific steps to obtain time domain analysis results include: Step S31, let t = 1, when t = 1, it represents the initial time; Step S32: Determine the control input at time t, input the control input at time t into the complete CNC machine tool feed servo system transfer function, and obtain the output value at time t and the corresponding feedback value A t ; Step S33: Based on the corresponding feedback value A t Update the control input at time t to obtain the updated control input at time t as the control input at time t+1; Step S34, determine whether t is greater than or equal to T, where T represents the total time. If so, obtain the output value of each moment as the time domain analysis result of each moment. If not, set t=t+1 and return to step S32.

6. The method for analyzing the dynamic characteristics of a servo feed system according to claim 1, characterized in that: The specific steps to obtain frequency domain analysis results include: Step S3-1, expressing the complete CNC machine tool feed servo system transfer function as a complex variable s; Step S3-2: determining a frequency range, and obtaining a plurality of frequency points based on the frequency domain range; Step S3-3, set the real part of the complex variable s to zero, and only consider the imaginary part to obtain an updated complex variable; Step S3-4, traverse multiple frequency points, and calculate the complex variable value corresponding to each frequency point based on the updated complex variable; Step S3-5: Substitute the complex variable value corresponding to each frequency point into the complete CNC machine tool feed servo system transfer function to obtain the amplitude and phase of each frequency point of the complete CNC machine tool feed servo system.

7. The method for analyzing the dynamic characteristics of a servo feed system according to claim 6, characterized in that: The amplitude and phase of each frequency point of the complete CNC machine tool feed servo system are expressed as follows: Where G represents the frequency, Im represents the imaginary part, Re represents the real part, |G| is the amplitude of the complete CNC machine tool feed servo system, and ∠G is the phase of the complete CNC machine tool feed servo system.

8. The method for analyzing the dynamic characteristics of a servo feed system according to claim 5, characterized in that: The control input includes a step signal input, a sinusoidal signal input or a ramp signal input of a CNC machine tool feed servo system.

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