Method for suppressing residual vibration of ball screw drive system

Abstract

This invention discloses a method for suppressing residual vibration in ball screw drive systems. This method first simplifies and rewrites the flexible body dynamics model into parameter identification equations containing only the motor rotation angle. Then, an improved particle swarm optimization algorithm is used to identify the dynamic parameters. The search space of the particle swarm algorithm is defined using recursive least squares, improving the algorithm's convergence speed and identification accuracy. After identifying the dynamic parameters, a ZVD shaper is designed using the parameter identification results to suppress the residual vibration of the ball screw drive system. This invention significantly suppresses residual vibration generated during high-speed start-stop of ball screw drive systems while improving the accuracy of dynamic parameter identification.

Description

Technical Field

[0001] This invention relates to the field of engineering vibration control technology, specifically to a method and calculation system for suppressing residual vibration in ball screw drive systems. Background Technology

[0002] In automated equipment involving linear motion, such as Cartesian robots and CNC machine tools, ball screw drive systems have become the dominant transmission system due to their high transmission efficiency and reliable operation. However, due to the flexible transmission components of ball screws, such as couplings, significant residual elastic vibrations occur during the high-speed start-up and stopping phases. The system needs to wait for vibration decay before performing high-precision tasks, severely reducing production efficiency and accuracy. In practical industrial applications, high-speed operation is often required to improve production efficiency; therefore, it is necessary to study vibration suppression methods for ball screw drive systems.

[0003] Input shapers are model-based feedforward vibration suppression methods that offer better vibration suppression performance than traditional filters such as low-pass and notch filters, and have been widely applied in various fields. The design of input shapers requires the use of the system's natural frequencies and damping ratios; obtaining the corresponding modal parameters is a key challenge in using shapers for vibration suppression control. Currently, most researchers use vibration sensors to measure vibration signals and perform Fast Fourier Transform (FFT) to obtain modal parameters for shaper design. While these methods can obtain relatively accurate modal parameters for shaper design, they are computationally intensive, require vibration sensors, increasing industrial costs, and the practicality of installing sensors in the transmission system for calculations is cumbersome, reducing the convenience of these methods. Directly calculating system modes through a system dynamics model effectively avoids these problems.

[0004] The establishment of a system dynamics model can be achieved by simulating the transmission system in CAD software or by using high-order mathematical models such as the finite element method to analyze the dynamic characteristics of the system. However, these methods are complex, involve a large amount of calculation, and are not conducive to controller design and tuning. After the model is established, the dynamic parameters can be obtained through identification experiments on the system. In terms of parameter identification, the least squares-based identification method has been widely used, but it is very sensitive to measurement noise and has low accuracy. In recent years, some intelligent evolutionary algorithms, such as genetic algorithms and particle swarm optimization algorithms, have also been widely used in the research of system identification and have achieved successful applications. Among them, the particle swarm optimization algorithm has certain advantages over other evolutionary algorithms in terms of implementation difficulty, algorithm parameter setting, and optimization, and has been proven to have higher accuracy than the least squares algorithm. However, when identifying parameters through intelligent iteration of particle swarm optimization, the value of the parameter to be identified is generally unknown. In order to avoid losing the true value of the parameter during the iteration process, the search space of the algorithm is usually set to an infinite domain. However, when the number of iterations is insufficient or the parameter settings are inappropriate, the algorithm is prone to getting trapped in local extrema, reducing the identification accuracy, which in turn affects the accuracy of the shaper parameters and reduces the vibration suppression performance of the shaper.

[0005] In summary, while directly calculating the system modal design input shaper through the system dynamics model can effectively avoid the use of vibration sensors and other equipment, reducing costs and computational complexity, current methods for establishing ball screw dynamics models are extremely complex, hindering controller design and tuning. Furthermore, the methods for identifying dynamic parameters are not precise enough, which is detrimental to shaper design and vibration suppression. Therefore, to better suppress residual vibration in ball screw drive systems, researching a method for designing input shaper suppression using a simple and effective dynamic model and a more accurate dynamic parameter identification algorithm is of great significance and has become an urgent problem to be solved by researchers in this field. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a method for suppressing residual vibration in ball screw drive systems. This method solves the problems of complex model establishment in ball screw drive systems hindering controller design and insufficient accuracy in dynamic parameter identification methods affecting the vibration suppression performance of the shaper.

[0007] The objective of this invention is achieved through the following technical solution: A method for suppressing residual vibration in a ball screw drive system includes the following steps:

[0008] S1. Establish the dynamic model of the ball screw transmission system and simplify it to rewrite it as a parameter identification equation that only includes the motor rotation angle;

[0009] S2. An improved particle swarm optimization algorithm is used to identify dynamic parameters. The recursive least squares method is used to define the search space of the particle swarm algorithm and the dynamic parameters are identified.

[0010] S3. Design a ZVD shaper using the identified dynamic parameters to suppress residual vibration in the ball screw drive system.

[0011] Preferably, step S1 includes the following steps:

[0012] S11. Treat the dynamic structure of the ball screw drive as a lumped parameter model and represent the main transmission components in the form of lumped parameters.

[0013] S12. Calculate the kinetic and potential energy of the ball screw drive system. Using the Lagrange equation, obtain the dynamic model of the ball screw drive system, and rewrite this dynamic model as a parameter identification equation that only includes the motor rotation angle variable:

[0014] τ m =Y b β,

[0015] Among them, Y b It is the motion information of the system obtained from experimental measurement results; β represents the vector of parameters to be identified in the system; τ m This is the motor rotation angle variable.

[0016] Preferably, in step S11, the main transmission components include a motor, a working platform, and a ball screw.

[0017] Preferably, step S2 includes the following steps:

[0018] S21. Based on the data fed back from the motor encoder of the ball screw system, the fluctuation range of the dynamic parameters to be identified is estimated iteratively using the recursive least squares method to define the search space of the particle swarm optimization algorithm. The iterative equation is as follows:

[0019]

[0020] Where k is the number of iterations, K represents the gain vector, and P is the inverse correlation matrix;

[0021] S22. The particle swarm optimization (PSO) algorithm iterates within the narrowed search space defined by the recursive least squares method. The PSO algorithm initializes the particle positions P using the following formula. i (0) and velocity V i (0):

[0022] P i (0)=min(P i )+rand(0,1)×[max(P i )-min(Pi )]

[0023] V i (0)=min(V i )+rand(0,1)×[max(V i )-min(V i )]

[0024] i = 1, 2, ..., 8

[0025] Where max(P) i ) and min(P i ) respectively represent The maximum and minimum values ​​of the search space; max(V) i ) and min(V i ) respectively represent The maximum and minimum speeds;

[0026] S23. Through continuous updating and iteration of the particle swarm optimization algorithm, the optimal solution of parameters is found, and the dynamic parameter identification results are obtained.

[0027] Preferably, step S23 includes the following steps:

[0028] S231. Within the reduced search space, the particle swarm optimization algorithm updates particle velocity and position using the following formula:

[0029]

[0030] P i (n)=P i (n-1)+V i (n),

[0031] Where n is the number of iterations, P i (n) and V i (n) represent the particles in the nth iteration. The position and velocity, ω is the inertia factor, and r1 and r2 are random numbers in the interval [0,1]. and The learning factors were set to 2.05 and 2.05 respectively.

[0032] S232. After each iteration, substitute the parameter β to be identified into τ. m =Y b β yields the predicted torque for each axis;

[0033] S233. Calculate the error between the actual torque and the predicted torque in each iteration, and define the average of the root mean square of the torque error as the cost function of the particle swarm optimization algorithm:

[0034]

[0035] Where e(j) corresponds to the torque error corresponding to the j-th sampling point, N is the number of samples, and k is the number of iterations;

[0036] S234. When the number of iterations of the algorithm reaches the set maximum value G or the error cost function e(k) < ε, ε → 0 + (G = 5000, ε = 6 × 10) -3 When the time is reached, the algorithm terminates, and the globally optimal value is the parameter to be identified.

[0037] Preferably, step S3 includes the following steps:

[0038] S31. Based on the identified dynamic parameters, the natural frequency required for designing the ZVD shaper is calculated as follows:

[0039]

[0040] Where, k g For coupling stiffness, J B ω is the moment of inertia of the ball screw, and ω is the natural frequency of the ball screw drive system.

[0041] S32. The input shaper is more sensitive to changes in the natural frequency of the ball screw drive system than the damping ratio. The damping ratio of the input shaper is set to a fixed value ξ = 0.1. The ZVD input integer function can then be expressed as:

[0042] f s (t)=A1δ(t)+A2δ(tT d )+A3δ(t-2T d )

[0043] Where δ(t-(j-1)T d ), j=1,2,3, indicating that when t≥(j-1)T d At that time, a pulse is applied to the system; if the control cycle of the ball screw drive system is T, the time delay is discretized: `fix` is a rounding function. The following algorithm is used when controlling a ball screw drive system:

[0044]

[0045] Where r(k-(j-1)T n ), j = 1, 2, 3 means t ≥ (j-1)T n At that time, a unit pulse is applied to the position command;

[0046] S33. By using the designed ZVD input shaper in the ball screw drive system, the residual vibration of the ball screw drive system can be suppressed.

[0047] The present invention has the following advantages over the prior art:

[0048] 1. This invention establishes a dynamic model of a ball screw transmission system and simplifies it. While reducing the complexity of the model, the simplified dynamic model can well describe the motion characteristics of the system, and the overall accuracy of the model is good.

[0049] 2. This invention improves the particle swarm optimization algorithm for dynamic parameter identification. It uses the recursive least squares method to iteratively estimate and define the parameter search space of the particle swarm optimization algorithm, which greatly improves the convergence speed and identification accuracy of the algorithm. The ZVD input shaper designed based on the identification results has excellent vibration suppression performance. Attached Figure Description

[0050] Figure 1 This is a flowchart of the parameter identification and ZVD shaper design of the particle swarm optimization algorithm based on recursive least squares according to an embodiment of the present invention.

[0051] Figure 2 This is a schematic diagram of the dynamic structure model of the ball screw transmission system according to an embodiment of the present invention;

[0052] Figure 3 This is a hardware structure diagram of the ball screw transmission system platform of the present invention in an embodiment of the present invention;

[0053] Figure 4 This is a comparison chart of the verification results of the dynamic model of the ball screw transmission system according to an embodiment of the present invention;

[0054] Figure 5 This is a diagram illustrating the iterative optimization process of the particle swarm optimization algorithm based on recursive least squares and the unmodified particle swarm optimization algorithm according to an embodiment of the present invention.

[0055] Figure 6 This is a comparison diagram of the vibration suppression effect of the ball screw transmission system according to an embodiment of the present invention. Detailed Implementation

[0056] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0057] like Figure 1 The method for suppressing residual vibration in a ball screw drive system, as shown, includes the following steps:

[0058] S1. Establish a dynamic model of the ball screw transmission system, such as Figure 2 As shown, the dynamic model is simplified and rewritten into a parameter identification equation that only includes the motor rotation angle;

[0059] Step S1 includes the following steps:

[0060] S11. The dynamic structure of the ball screw drive is regarded as a lumped parameter model, and the main transmission components are represented in the form of lumped parameters; among them, the main transmission components include the motor, the working platform and the ball screw, etc.

[0061] S12. Calculate the kinetic and potential energy of the ball screw drive system. Using the Lagrange equation, obtain the dynamic model of the ball screw drive system, and rewrite this dynamic model as a parameter identification equation that only includes the motor rotation angle variable:

[0062] τ m =Y b β

[0063] Among them, Y b It is the motion information of the system obtained from experimental measurement results; β represents the vector of parameters to be identified in the system; τ m This is the motor rotation angle variable.

[0064] And β=[β1 β2 β3 β4 β5 β6 β7 β8] T ;

[0065] The meanings of the parameters in β:

[0066]

[0067] β4=f vb +f vm , β5=f cm , β8=C,

[0068] Among them, J m J is the moment of inertia of the motor. B Let k be the moment of inertia of the lead screw. g For coupling stiffness, f vb f represents the coefficient of viscous friction of the lead screw. vm f represents the coefficient of viscous friction of the motor. cm This represents the Coulomb friction coefficient of the motor, where C is a constant.

[0069] S2. An improved particle swarm optimization algorithm is used to identify dynamic parameters. The recursive least squares method is used to define the search space of the particle swarm algorithm, which improves the convergence speed and identification accuracy, and the dynamic parameters are identified.

[0070] Step S2 includes the following steps:

[0071] S21. Based on the data fed back from the motor encoder of the ball screw system, the fluctuation range of the dynamic parameters to be identified is estimated iteratively using the recursive least squares method to define the search space of the particle swarm optimization algorithm. The iterative equation is as follows:

[0072]

[0073] Where k is the iteration number, K represents the gain vector, and P is the inverse correlation matrix. The initial state is obtained from the collected data using a one-step algorithm: P(0) = [Φ T Φ] -1 ,Φ=[Y b (1) … Y b (L0)] T , L0 is the data length;

[0074] S22. The particle swarm optimization (PSO) algorithm iterates within the narrowed search space defined by the recursive least squares method. The PSO algorithm initializes the particle positions P using the following formula. i (0) and velocity V i (0):

[0075] P i (0)=min(P i )+rand(0,1)×[max(P i )-min(P i )]

[0076] V i (0)=min(V i )+rand(0,1)×[max(V i )-min(V i )]

[0077] i = 1, 2, ..., 8

[0078] Where max(P) i ) and min(P i ) respectively represent The maximum and minimum values ​​of the search space; max(V) i ) and min(V i ) respectively represent The maximum and minimum speeds;

[0079] S23. Through continuous updates and iterations of the particle swarm optimization algorithm, the optimal solution for the parameters is found, and the dynamic parameter identification results are obtained. The identification process is as follows: Figure 1 As shown.

[0080] Step S23 includes the following steps:

[0081] S231. Within the reduced search space, the particle swarm optimization algorithm updates particle velocity and position using the following formula:

[0082]

[0083] Pi (n)=P i (n-1)+V i (n),

[0084] Where n is the number of iterations, P i (n) and V i (n) represent the particles in the nth iteration. The position and velocity, ω is the inertia factor, and r1 and r2 are random numbers in the interval [0,1]. and The learning factors were set to 2.05 and 2.05 respectively.

[0085] S232. After each iteration, substitute the parameter β to be identified into τ. m =Y b β yields the predicted torque for each axis;

[0086] S233. Calculate the error between the actual torque and the predicted torque in each iteration, and define the average value of the root mean square error of the torque (MRSE) as the cost function of the particle swarm optimization algorithm:

[0087]

[0088] Where e(j) corresponds to the torque error corresponding to the j-th sampling point, N is the number of samples, and k is the number of iterations;

[0089] S234. When the number of iterations of the algorithm reaches the set maximum value G or the error cost function e(k) < ε, ε → 0 + (G = 5000, ε = 6 × 10) -3 When the condition is met, the algorithm terminates, and the globally optimal value is the parameter to be identified.

[0090] S3. Design a ZVD shaper using the identified dynamic parameters to suppress residual vibration in the ball screw drive system.

[0091] Step S3 includes the following steps:

[0092] S31. Based on the identified dynamic parameters, the natural frequency required for designing the ZVD shaper is calculated as follows:

[0093]

[0094] Where, k g For coupling stiffness, J B ω is the moment of inertia of the ball screw, and ω is the natural frequency of the ball screw drive system.

[0095] S32. The input shaper is more sensitive to changes in the natural frequency of the ball screw drive system than the damping ratio. The damping ratio of the input shaper is set to a fixed value ξ = 0.1. The ZVD input integer function can then be expressed as:

[0096] f s (t)=A1δ(t)+A2δ(tT d )+A3δ(t-2T d )

[0097] Where δ(t-(j-1)T d ), j=1,2,3, indicating that when t≥(j-1)T d At that time, the pulses applied to the system, A1, A2, and A3 are the pulse amplitudes at the corresponding moments; if the control period of the ball screw drive system is T, the time delay is discretized: `fix` is a rounding function. The following algorithm is used when controlling a ball screw drive system:

[0098]

[0099] Where r(k-(j-1)T n ), j = 1, 2, 3 means t ≥ (j-1)T n At that time, a unit pulse is applied to the position command;

[0100] S33. By using the designed ZVD input shaper in the ball screw drive system, the residual vibration of the ball screw drive system can be suppressed.

[0101] This invention is in Figure 3 The ball screw drive system platform shown is implemented. The ball screw feed axis motor is an ECMA series, driven by an AC servo driver, model ASD-A2-0421-E. A thin steel plate is mounted on the worktable, with a KISTLER Type 8395A triaxial vibration sensor installed at its end to collect residual vibration signals for quantitative analysis of vibration suppression effects. An optical encoder is mounted on the motor to collect motor rotation angle, and a linear encoder is mounted on the lead screw to collect its actual displacement, converting it into the actual lead screw rotation angle for verification and identification results. The system's control software platform is based on a Windows 7 64-bit system and uses an EtherCAT bus for communication, with a system control cycle of 1ms. The bus master is an industrial computer, and the analog signals from the vibration sensors are acquired by Beckhoff modules and connected to the system via Ethernet.

[0102] Figure 4 The comparison chart shows the verification results of the dynamic model of the ball screw drive system. It can be seen that the overall accuracy of the model is very good. The RAE error of the identification result using the improved particle swarm algorithm is 4.09%.

[0103] Figure 5The diagram shows the iterative optimization process of the particle swarm optimization algorithm and the improved particle swarm optimization algorithm proposed in this invention, which iteratively defines the search space using the recursive least squares method. Under the same algorithm parameter settings, the number of iterations for the improved particle swarm optimization algorithm and the particle swarm optimization algorithm are 799 and 5934, respectively.

[0104] Figure 6 This is a comparison chart of the vibration suppression effect of the ZVD shaper designed using the identification results in a ball screw drive system. The residual vibration amplitude after shaping by the ZVD shaper decreased by an average of 87.81% compared to the unshaped state, with a maximum decrease of 89.13%.

[0105] The comparative analysis shows that the residual vibration suppression method for ball screw drive systems proposed in this invention can significantly suppress residual vibrations generated during high-speed start-stop of ball screw drive systems. Furthermore, the simplified dynamic model established reduces model complexity while effectively describing the system's motion characteristics, resulting in good overall model accuracy. In addition, the improved particle swarm optimization algorithm is used for dynamic parameter identification, greatly improving the algorithm's convergence speed and identification accuracy. The ZVD input shaper designed based on the identification results exhibits excellent vibration suppression performance, and the control method is simple, requiring no additional complex sensors. This invention can be applied and promoted in automated equipment with linear motion, such as ball screw-driven Cartesian robots and CNC machine tools.

[0106] The above-described specific embodiments are preferred embodiments of the present invention and are not intended to limit the present invention. Any other changes or equivalent substitutions made without departing from the technical solution of the present invention are included within the protection scope of the present invention.

Claims

1. A method for suppressing residual vibration in a ball screw drive system, characterized in that: Includes the following steps: S1. Establish the dynamic model of the ball screw transmission system and simplify it to rewrite it as a parameter identification equation that only includes the motor rotation angle; Step S1 includes the following steps: S11. Treat the dynamic structure of the ball screw drive as a lumped parameter model and represent the transmission components in the form of lumped parameters. S12. Calculate the kinetic and potential energy of the ball screw drive system. Using the Lagrange equation, obtain the dynamic model of the ball screw drive system, and rewrite this dynamic model as a parameter identification equation that only includes the motor rotation angle variable: ， in, It is the motion information of the system obtained based on experimental measurement results; This represents the vector of parameters to be identified in the system; The motor rotation angle is a variable; S2. An improved particle swarm optimization algorithm is used to identify the dynamic parameters. The search space of the particle swarm algorithm is defined using the recursive least squares method, and the dynamic parameters are identified. Step S2 includes the following steps: S21. Based on the data fed back from the motor encoder of the ball screw system, the fluctuation range of the dynamic parameters to be identified is estimated iteratively using the recursive least squares method to define the search space of the particle swarm optimization algorithm. The iterative equation is as follows: in, For the number of iterations, Represents the gain vector. This is the inverse correlation matrix; S22. The particle swarm optimization (PSO) algorithm iterates within the narrowed search space defined by the recursive least squares method. The PSO algorithm initializes the particle positions using the following formula. and speed : in, and They represent The maximum and minimum values ​​of the search space; and They represent The maximum and minimum speeds; S23. Through continuous updating and iteration of the particle swarm optimization algorithm, the optimal solution for the parameters is found, and the dynamic parameter identification results are obtained; Step S23 includes the following steps: S231. Within the reduced search space, the particle swarm optimization algorithm updates particle velocity and position using the following formula: ， ， Where n is the number of iterations. and They represent the particles in the nth iteration. Position and velocity, Inertia factor and It is an interval Random numbers on the screen and The learning factors were set to 2.05 and 2.05 respectively. S232. After each iteration, the parameters to be identified are... Substitution The predicted torques for each axis are obtained; S233. Calculate the error between the actual torque and the predicted torque in each iteration, and define the average of the root mean square of the torque error as the cost function of the particle swarm optimization algorithm: ， in, These correspond to the torque error at the i-th sampling point, where M is the number of samples. This represents the number of iterations. S234. When the number of iterations of the algorithm reaches the set maximum value G or the error cost function... When the time is right, the algorithm terminates, and the globally optimal value is the parameter to be identified. S3. Design a ZVD shaper using the identified dynamic parameters to suppress residual vibration in the ball screw drive system.

2. The method for suppressing residual vibration in a ball screw drive system according to claim 1, characterized in that: In step S11, the transmission components include a motor, a working platform, and a ball screw.

3. The method for suppressing residual vibration in a ball screw drive system according to claim 1, characterized in that: Step S3 includes the following steps: S31. Based on the identified dynamic parameters, the natural frequency required for designing the ZVD shaper is calculated as follows: ， in, For coupling stiffness, The moment of inertia of the ball screw. , The natural frequency of the ball screw drive system; S32. The input shaper should be more sensitive to changes in the natural frequency of the ball screw drive system than to the damping ratio. The damping ratio of the input shaper should be set to a fixed value. ,make Then the ZVD input integer function can be expressed as: ， in , indicating when At that time, the pulse applied to the system, This represents the pulse amplitude at the corresponding moment; if the control cycle of the ball screw drive system is... Discretize the time delay: , The following algorithm is used as the rounding function when controlling a ball screw drive system: ， express At that time, a unit pulse is applied to the position command; S33. By using the designed ZVD input shaper in the ball screw drive system, the residual vibration of the ball screw drive system can be suppressed.

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