金属管道外放置式偏心弯曲矩形线圈涡流场的解析解  

Analytical Solution for the Eddy Current Field due to an Air-Cored Eccentric Curved Rectangular Probe Coil on the Outside of a Metal Pipe

作　　者：毛雪飞[1] 雷银照[1] 

机构地区：[1]北京航空航天大学自动化科学与电气工程学院,北京100191

出　　处：《电工技术学报》2012年第9期153-159,共7页Transactions of China Electrotechnical Society

基　　金：国家自然科学基金资助项目(50777002)

摘　　要：本文得到了偏心弯曲矩形线圈在非铁磁性金属管道侧面放置时涡流场的解析解。求解过程是:用二阶磁矢位建立了涡流问题的数学模型,得到了含待定偏心线圈系数的二阶位函数表达式;根据毕奥-萨伐尔定律和用修正贝塞尔函数表示的距离倒数得到了线圈未偏移时的线圈系数;利用修正贝塞尔函数的加法定理计算出线圈偏移后的偏心线圈系数。在涡流场解析解的基础上,本文计算了偏心弯曲矩形检测线圈上的感应电压。实验表明,理论分析结果与实验结果吻合。The analytical solution for the eddy current field due to an eccentric curved rectangular coil on the outside of a nonferromagnetic metal pipe is obtained in this paper. The model of eddy current field is established by a second order vector potential（SOVP） formalism, and the closed-form expressions of second order potential functions which contain the undetermined eccentric coil coefficient are achieved. In order to calculate the undetermined eccentric coil coefficient, the concentric coil coefficient is deduced through Biot-Savart law and the inverse distance in terms of modified Bessel functions at first. Then, the eccentric coil coefficient can be accessed based on the addition theorem of modified Bessel function. Using the SOVPs＇ closed-form expressions, induced voltage in an eccentric curved rectangular pick-up coil is computed. Experiments show that the theoretical expressions are in good agreement with the experimental measurements.

关 键 词：解析解 偏心弯曲矩形线圈 二阶磁矢位 加法定理 电磁场 

分 类 号：TG115.28[金属学及工艺—物理冶金] TM153[金属学及工艺—金属学]