超低频电磁声源非线性动力学建模与分析

电磁声源输出力大、体积小、易于实现超低频输出，在无人反水雷作战中具有显著优势。其动力学行为受到机械回复力和电磁力的耦合作用影响，当施加电流超过坍塌电流，电磁力将超过机械回复力， 就会发生吸和，造成声源的损坏。为准确描述电磁声源非线性动力学特性，预先评估坍塌电流，建立考虑动态漏磁系数的声源非线性动力学模型。通过三维有限元仿真计算动铁芯运动到不同位置处气隙的漏磁系数， 拟合得到动态漏磁系数。根据等效磁路法建立声源的改进电磁力模型，进而建立电磁声源非线性动力学模型。 通过 Runge-Kutta 算法计算得到阶跃激励下声源振动的位移和速度，绘制相平面图。研究稳定与失稳 2 种情况下的相轨迹的动态变化规律，为电磁声源的设计和控制提供理论支撑。

Modeling and Analysis of Nonlinear Dynamics of Ultra-low Frequency Electromagnetic Sound Sources

Electromagnetic sound sources are characterized with large output force，small size，and easy realization of ultra-low frequency output，thus they have significant advantages in unmanned mine countermeasures. The dynamic behavior of the electromagnetic sound source is affected by the coupling effect of mechanical recovery force and electromagnetic force. When the applied current exceeds the collapse current，the electromagnetic force will exceed the mechanical recovery force，and suction will occur，resulting in damage to the sound source. To accurately describe the nonlinear dynamic characteristics of the electromagnetic sound source and to evaluate the collapse current in advance，a nonlinear dynamic model of the sound source considering the dynamic magnetic leakage coefficient is established. The magnetic leakage coefficient of the air gap where the moving iron core moves to different positions is calculated by three-dimensional finite element simulation，and the dynamic magnetic leakage coefficient is obtained by fitting. The improved electromagnetic force model of the sound source is established according to the equivalent magnetic circuit method. Then，the nonlinear dynamic model of the electromagnetic sound source is established. The displacement and velocity of the sound source vibration under step excitation are calculated by Runge-Kutta algorithm，and the phase plan is drawn. The dynamic changes of phase trajectories under stable and unstable conditions are studied to provide theoretical support for designing and controlling electromagnetic sound sources.