球和线圈共轴的涡流问题解析解

ANALYTICAL SOLUTIONS TO SPHERE AND COIL COAXIAL EDDY CURRENT PROBLEMS

导电导磁球和轴对称线圈的共轴电磁系统可用于球的涡流无损检测。文章利用磁矢量位和洛仑兹规范，建立了均匀导电导磁球和圆环线圈共轴电磁系统的时谐场边值问题，用分离变量法求解得到了球的散射场解析解。在此基础上，导出了球和空芯圆柱线圈共轴电磁系统的电磁场解析解和线圈的阻抗增量解析式。为便于计算，给出了复宗量的球贝塞尔函数的计算方法。实验表明，阻抗增量的理论计算值和实验测量值符合程度良好。文中的分析过程表明，所得解析方法同时也适用于分层球和任意截面的轴对称线圈的共轴电磁系统。

The coaxial electromagnetic system of a conducting permeable sphere and an axial symmetric coil is applicable to eddy current nondestructive testing of sphere. Using magnetic vector potential and Lorentz gauge, this paper establishes a boundary value problem in time harmonic electromagnetic field of a coaxial system consisting of a homogeneous conducting permeable sphere and an one turn circular coil. The analytical solution of the scattered field due to the sphere is given by the method of variables separation. Moreover, the analytical solution in the electromagnetic field of a coaxial system of a sphere and a rectangular cross section coil is solved. Meanwhile, the analytical expression of coil impedance increment is also obtained. Making convenience of computation, the calculation method of the spherical Bessel functions for complex arguments is presented. The calculated values are in good agreement with measured values. The analytical process indicated that the method used in this paper can also be applied to the coaxial eddy current problem of multilayer sphere and axial symmetric coils of any cross section.