超磁致伸缩驱动器磁滞非线性动力学研究

doi:10.3901/JME.2020.15.207

摘要/Abstract

摘要： 超磁致伸缩驱动器（Giant magnetostrictive actuator，GMA）输入电流与输出位移之间存在着磁滞非线性关系。为精确控制GMA输出位移的稳定性，通过分析GMA的工作原理，基于非线性压磁方程、Jiles-Atherton （J-A）磁滞非线性模型、二次畴转模型和GMA结构动力学原理，建立了GMA磁滞非线性动力学系统的方程；应用多尺度法分析该系统的主共振，得到该系统幅频响应曲线方程；使用Matlab数值仿真分析GMA系统中不同等效阻尼系数、激励磁场强度、预应力、三次刚度项系数与输出响应幅值之间映射规律；通过改变激振力参数值的大小，绘制GMA系统的时域波形、相轨迹图、Poincaré图和幅值谱图，采用4阶Runge-Kutta法求解并绘制GMA系统的响应随激振力变化分岔图。研究结果表明：在给定GMA参数的条件下，在碟簧和激励线圈的作用下，GMA具有“跳跃”和磁滞现象；GMA系统在一定参数下存在着混沌现象。

关键词: 超磁致伸缩驱动器, 磁滞非线性, 动力学模型, 主共振, 数值仿真

Abstract: A non-linear hysteresis relation is observed between the input currents and output displacements of giant magnetostrictive actuator (GMA). To accurately control the stability of GMA output displacement, non-linear hysteresis dynamic differential equation of GMA system is established according to hysteresis non-linear equation, Jiles-Atherton hysteresis non-linear model, quadratic domain rotation model and GMA structural dynamics principle by analyzing the working principle of GMA. The primary resonance of GMA non-linear hysteresis dynamic system is analyzed by multiple scales method and system amplitude-frequency response curve equation is obtained. Matlab numerical simulation is used to evaluate the mapping between different values of damping coefficient, magnetic field strength, prestress, nonlinear stiffness and output response amplitude of GMA system. Time domain waveform, phase portrait, Poincaré mapping diagrams and amplitude spectrum of GMA system are drawn by changing the magnitudes of exciting force parameters. Four-order Runge-Kutta method is used to solve and draw the response of GMA system for different exciting forces. The obtained results showed that for parameter values assumed here, GMA system showed “jump” and hysteresis phenomena under the action of non-linear disc spring and magnetic field intensity. Under certain parameter values, chaos is observed in GMA system.

Key words: giant magnetostrictive actuator (GMA), non-linear hysteresis, dynamic model, primary resonance, numerical simulation

中图分类号:

O332

闫洪波, 高鸿, 郝宏波. 超磁致伸缩驱动器磁滞非线性动力学研究[J]. 机械工程学报, 2020, 56(15): 207-217.

YAN Hongbo, GAO Hong, HAO Hongbo. Research on Hysteresis Nonlinear Dynamics of Giant Magnetostrictive Actuator[J]. Journal of Mechanical Engineering, 2020, 56(15): 207-217.

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