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中文摘要：
为了研究接触器电磁力建立的瞬态过程，以及接触器中的能量损耗关系，提出了一种基于PDE弱解式方程的三维电磁力计算方法，通过加权残值法将微分形式的麦克斯韦（Maxwell）方程转化成弱解式矢量方程，得到矩阵形式的控制方程。基于该方程研究了磁路的静态和动力学响应。利用麦克斯韦应力张量，研究了不同电流和问隙时三维电磁力的稳态分布。利用阶跃响应研究了三维电磁力的动态建立过程，并研究了不同磁导率和电导率对于磁通密度以及电磁力动态响应的影响。仿真结果表明，减小电导率可以降低磁通密度的瞬态响应峰值；提高铁心磁导率可以增加电磁力稳态输出值。通过对电磁力的瞬态响应过程研究发现，磁路中主要能量损耗来源于空气，其损失比例峰值达到90％。
英文摘要：
A novel method is developed to calculate the 3D magnetic force based on PDE weak form equations. The matrix governing equation is obtained by transforming the Maxwell magnetic equation to the weak form, which is implemented with weighted residuals. The steady state response and the dynamic response of the magnetic circuit are studied based on the discrete matric equation. The 3D magnetic force corresponding to different exciting current and air gaps are studied by using Maxwell stress tensor. The dynamic response of magnetic force is analyzed by using step response. The influences of the permeabilities and conductivities on the flux density and the magnetic force are studied as well. Simulation results show that the transient peak value of flux density can be reduced by decreasing the conductivity of the electric core. The steady state value of the magnetic force can be enhanced by increasing the permeability. The energy consumptions of the magnetic system are studied. It is found that the main loss of the energy comes from the airgap. The peak value of the loss ratio due to this proportion can be achieved to 90%.
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Modeling of galfenol bending actuator considering nonlinear hysteresis and dynamic real-time control
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