中文摘要：

求解了线性导电、导磁中空管道外鞍形线圈通有脉冲电流时的涡流场。引入二阶矢量位,用一个标量函数来描述空气场域中的磁场,简化了求解过程。给出了模型的电磁场边值问题,得出了待定系数线性方程组,通过变量代换,降低了系数矩阵的条件数,并用分块矩阵的方法求解了此方程组。利用傅里叶变换,得到了多匝鞍形激励线圈中通有任意波形电流时检测线圈两端感应电压的解析式。通过与奥氏体不锈钢管的实验曲线对比,验证了所得解析式的正确性。所得结果可为管道脉冲涡流检测的仿真计算与实验研究提供参考。

英文摘要：

This paper solved the eddy current field induced by pulse current in saddle-shaped coil outside the metal pipe with linear conductivity and permeability.By using the second order vector potential,the magnetic field in the air could be described by a single scalar function,and the calculation process could thus be simplified.We presented the boundary value problems of this electromagnetic model and obtained the linear equations for unknown coefficients.Then,we reduced the condition number of the coefficient matrix through substitution of variables and solved the linear equations by using block matrix.Based on the Fourier Transform,we obtained the analytical solution of the coil voltage induced by arbitrary waveform current in the multi-turn saddle-shaped drive coil.The analytical expressions were verified through a comparison of the theoretical curves with the experimental curves of the austenite stainless steel pipes.Results in this paper provide theoretical basis for simulation calculation and experimental study of the pulsed eddy current testing for pipes.