椭圆聚焦线圈瞬态脉冲涡流场的解析解..doc

椭圆聚焦线圈瞬态脉冲涡流场的解析解 摘 要：聚焦线圈能够在被测导体内产生更加集中的涡流，脉冲激励能够使得检测信号包含更多的信息量，本文提出了椭圆聚焦线圈脉冲涡流检测方法以提高无损检测的灵敏度，推导了椭圆聚焦线圈瞬态脉冲涡流场的解析解。建立了半无限大导体上斜置椭圆线圈瞬态脉冲涡流场电磁模型，给出了该涡流场满足的初边值问题并进行了拉氏变换和傅里叶变换，采用尺度变换技术将椭圆线圈转换为圆线圈进行求解，最后采用拉氏反变换、傅里叶反变换和尺度反变换得到了椭圆聚焦线圈瞬态脉冲涡流场的时域解析解。本文所得解析解与利用Ansoft电磁仿真软件计算所得结果一致，通过解析解的计算，验证了该椭圆聚焦线圈具有较好的涡流聚焦效果。 关 键 词：瞬态脉冲涡流场；解析解；椭圆聚焦线圈；尺度变换 中图分类号：TM15 文献标识码：A Analytical solutions of transient pulsed eddy current problem due to elliptical concentrative coils Abstract: More concentrative eddy current within conducting medium can be generated by concentrative coils and more information can be contained in the detected signal by using pulsed exciting current, so the pulsed eddy current testing method using elliptical concentrative coil which can enhance the testing sensitivity is proposed in this paper, and analytical solutions of transient pulsed eddy current due to elliptical concentrative coils are derived. The model of elliptical coil placed in an arbitrary position above a half-infinite conducting plate is built. The initial-boundary value problem is provided, transfer them by Laplace’s transform and Fouier’s transform, and elliptical coil is transformed to loop coil by sacle-transformation. Analytical solution of transient pulsed eddy current due to elliptical concentrative coils in the time domain is obtained by inverse Laplace’s transform, inverse Fouier’s transform and inverse sacle-transform. The results of analytical solution agree with the numerical calculation result by ANSOFT software. By the means of analytical computation, the good concentrative effect of elliptical concentrative coil is validated. Key words: transient eddy current, analytical solution, elliptical concentrative coil, scale-transformation 引言 涡流检测大多采用水平圆环线圈，其在导体中激励出的涡流分布不具有集中性，而采用具有聚焦作用的激励线圈能够使涡流集中分布，从而提高检测的灵敏度。传统的涡流检测通常采用正弦信号作为激励，检测线圈的阻抗变化，而脉冲涡流检测的时域分析方法将获得更多的信息。因此具有聚焦作用的线圈的瞬态脉冲涡流场解析解的研究对于提高检测的灵敏度，设计新型电磁传感器具有重要作用。 聚焦线圈最早被用于功能磁刺激中[1]，为了对指定的部位进行电流刺激而对其它部位