高温超导悬浮系统的动力学行为分析

Dynamical Investigation of High T_c Superconducting Levitation Systems

基于Bean临界态模型和Ampère环路定律,通过分析高温超导体内部屏蔽电流的穿透历史,建立了具有典型滞回特征的高温超导悬浮系统非线性动力学基本方程。采用自适应四阶Runge-Kutta方法进行数值求解,得到悬浮体的自由振动响应曲线。结果显示:在自由振动过程中,超导体内部的屏蔽电流总是发生"部分抹去"现象,这导致了悬浮体作阻尼衰减运动;动态运动过程中系统的频率和等效阻尼系数并不是常值,而是随时间变化;悬浮体每次单调运动过程中,超导屏蔽电流的最大穿透深度δp随时间t或速度零点个数Nzero呈负指数关系递减,即:δp=eα0-α1Nzero,其中α0和α1为拟合系数。

Based on Bean’s critical state model and Ampère circulation theorem, the dynamic behavior and penetration history of shielding currents distribution are investigated by a vertically mechanical oscillation of PM-HTS system. After the shielding current distribution is analytically derived out from the Maxwell’s equations, the dynamic differential equation of levitation is solved by using the adaptive Runge-Kutta approach of order 4. The obtained results display that the partially wiping-out phenomenon of shielding currents always happens in the interior of the HTS when the PM experiences a damped vibration. It is found that the damping generated from the hysteresis in HTS is time-changeable in the whole response, and that the frequency of vibration increases with time, as well as the maximum penetration depth, δp, decays with time or the turning number of each procedure of the hysteresis, Nzero, i.e. δp=eα0-α1Nzero where α0 and α1are the fitting coefficients.