图1 铁芯薄片结构图
考虑磁感应强度在铁芯横截面积分布不均匀,电场强度的解析表达式为:
将积分近似为求和可得第m个单元的电场强度为:
其中m为y轴方向的单位矢量,根据对称性,可得第n+m个单元的电场强度为,根据欧姆定律可得在第m个单元的电流密度为:
第n+m个单元的电流密度为Jn+m=-Jm。根据毕奥-萨伐尔定律可知,涡流在第i个单元产生的磁感应强度为:
将Jn+m=-Jm代入上式可得:
将式(3)代入式(5),同时考虑激励磁场Hsz,可得铁芯内第i个单元的磁场。
2 铁芯磁滞回线模型
本文所选磁滞回线模型是公式(7)所示的Jiles动态模型[10-13],该模型为微分磁化方程,它描述磁滞回线与频率的关系。方程中δ为方向参数,当dH/dt> 0时取+1,当dH/dt<0时取-1;a为形状参数,k为磁滞损失参数,α为平均场参数,c为磁畴壁弯曲常数,Man为非磁滞磁化强度,μ0为真空磁导率,ρ为铁芯材料电阻率,d和w分别表示薄片的厚度和宽度。该模型由四部分组成,其中前两部分表示磁滞损耗,第三部分表示涡流损耗,第四部分表示额外损耗;在高频情况下,第四部分可以忽略。
3 结果与分析
对式(6)在SPICE软件中建模,联立铁芯材料的磁滞模型式(7)(即Bz(Hz)关系)SPICE模型,便可计算瞬态的铁芯截面的磁场和磁感应强度的分布。因铁芯材料模型选择文献[6]采用的Jiles模型,相关参数为d=0.5 mm,w=30 mm,ρ=45×10- 8Ωm,s=60 mm,B=1.5 T,a=130.22 A/m,k=56.855 A/m,α=1.69× 10-4,c=8.547×10e-3。并同Sebti Boukhtache等的实验和仿真结果进行对比验证。
图3是当电压源激励频率为500 Hz时,图3(b)为本文的HSPICE仿真磁滞回线波形图,与图3(a)为文献[6]模型和实验图相比,拟合较好。同时对电压源激励频率为0.5 Hz、50 Hz和200 Hz这3种情况,利用HSPICE对磁滞回线进行了仿真。不同频率下的仿真和实验数据如表1所示。从表1的数据可以看出,当矫顽力Hc随着频率增加而增大时,剩磁Br基本不变。
图3 500 Hz频率下磁滞回线
表1 仿真与实验数据比较
4 结论
本文采用不同于文献[6]的方法,运用欧姆定律和毕奥-萨伐尔定律,推导得到涡流对磁滞回线影响的数学模型。该方法的优势在于涡流产生的寄生磁场分布可以解析表示,得到的方程组对空间不需要进行微分,形式简单,易于求解。HSPICE仿真结果与文献[6]的实验和仿真结果对比表明,考虑磁场在截面的非均匀性和涡流影响的磁滞回线SPICE模型有较高的准确性。
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崔智军(1978-),男,陕西渭南人,讲师,西北工业大学电子信息学院在读博士生,专业方向为微电子器件与微传感器,现在主要从事微型磁通门传感器研究,Cuizj_163@163.com;
刘诗斌(1960-),男,河南巩义市人,西北工业大学电子信息学院教授,博士生导师。长期从事无人机传感器系统研究工作,研究领域为磁场和压力测量,智能传感器系统,微电子和计算机应用,liushibin@nwpu.edu.cn。
Research of Spiral Coil on EMAT to Improve Transduction Efficiency*
FAN Jizhi1,2,WU Yunxin1,2*,SHI Wenze1,2,GONG Hai1,2,TAN Liangchen1,2
(1.State Key Laboratory of High Performance Complex Manufacturing,Central South University,Changsha 410083,China;2.School of Mechanical and Electrical Engineering,Central South University,Changsha 410083,China)
Abstract:A novel method for improving the transduction efficiency of Electromagnetic Acoustic Transducer (EMAT)is introduced. In this paper,a model of a doubled-layer spiral coil EMAT for generating shear wave was modeled in the finite element software COMSOL Multiphysics. And then the effects of the substrate thickness,cop⁃per conductor thickness and lift-off on the efficiency are investigated. Results show that the reducement in the sub⁃strate thickness and lift-off,the increasement in the copper conductor thickness can help to improve the efficiency. And the simulation results are verified by the experiments.
Key words:electromagnetic acoustic transducer;finite element method;spiral coil;transduction efficiency
doi:EEACC:723010.3969/j.issn.1004-1699.2016.01.006
收稿日期:2014-05-10修改日期:2015-06-15
中图分类号:TP212.1;TM936.2
文献标识码:A
文章编号:1004-1699(2016)01-0026-03
项目来源:高等学校博士学科点专项科研基金项目(20126102110031)