厚金属板与任意方位圆柱线圈间的电磁力计算

摘要

针对一个交流电激励的圆柱线圈倾斜放置于金属板上方时，它们之间的电磁作用力无法以传统方法进行解析计算的问题，引入高阶矢量势求解该问题，并采用矢量分析和Struve函数化简，可得到适用于任意方位圆柱线圈的二重积分表达式。所得结果表明任意方位圆柱线圈至多受到两个方向力的作用。在线圈轴垂直或平行于导电板的特殊情形，表达式可进一步简化为单重积分，而线圈将只受垂直力的作用。随后以数值算例对给出公式的有效性进行验证。数值结果表明，对于线圈轴的某个倾角，垂直力分量周期均值可以为零，而水平力分量周期均值将在某个倾角处达到最大值。当线圈通以直流电时，仅当金属板的磁导率与空气磁导率一致时线圈才不受电磁力的作用。%For an inclined circular coil with alternating current excitation and placed above a thick metal plate,analytical solution of electromagnetic forces between them can not be found by traditional methods. Using the high-order vector potential,the problem was solved analytically,and vector analysis and Struve functions were employed to simplify the final results.The expressions for the electromagnetic forces acting on the cylindrical coil of arbitrary position were obtained.The results indicate that there are at most two e-lectromagnetic forces acting on the coils.When the axes of coils are perpendicular or parallel to the con-ducting surface,the results can be simplified to 1-D integrals and only perpendicular component exists. The numerical calculations were implemented to verify the obtained results.The results show that the time mean value of the vertical force component can vanish for certain inclined angles of coil axis,and the hori-zontal force component can attain maximum value for some other angles.If direct currents flow through the coil,the electromagnetic forces will vanish only when the plate has the same permeability with the air.