The long stator track for high speed maglev trains has a tooth-slot structure. The sensor obtains precise relative position information for the traction system by detecting the long stator tooth-slot structure based on nondestructive detection technology. The magnetic field modeling of the sensor is a typical three-dimensional (3-D) electromagnetic problem with complex boundary conditions, and is studied semi-analytically in this paper. A second-order vector potential (SOVP) is introduced to simplify the vector field problem to a scalar field one, the solution of which can be expressed in terms of series expansions according to Multipole Theory (MT) and the New Equivalent Source (NES) method. The coefficients of the expansions are determined by the least squares method based on the boundary conditions. Then, the solution is compared to the simulation result through Finite Element Analysis (FEA). The comparison results show that the semi-analytical solution agrees approximately with the numerical solution. Finally, based on electromagnetic modeling, a difference coil structure is designed to improve the sensitivity and accuracy of the sensor.
References
[1]
Liu, H.Q. Transrapid; University of Electronic Since and Technology of China Press: Chengdu, China, 1995; pp. 74–88.
Li, L.; Wu, J. Research and design of a position detection sensor for high speed maglev train. Chin. J. Sens. Actuat. 2007, 7, 1510–1513.
[4]
Deng, X.; Liu, Y. Electromagnetic imaging methods for nondestructive evaluation applications. Sensors 2011, 11, 11774–11808.
[5]
García-Martín, J.; Gómez-Gil, E.; Vázquez-Sánchez, J. Non-destructive techniques based on eddy current testing. Sensors 2011, 11, 2525–2565.
[6]
Zhu, Y.-K.; Tian, G.-Y.; Lu, R.-S.; Zhang, H. A review of optical NDT technologies. Sensors 2011, 11, 7773–7798.
[7]
Zaoui, A.; Menana, H.; Feliachi, M.; Berthiau, G. Inverse problem in nondestructive testing using arrayed eddy current sensors. Sensors 2010, 10, 8696–8704.
[8]
Xue, S.; Dai, C.; Long, Z. Research on Location and Speed Detection for High Speed Maglev Train Based on Long Stator. Proceedings of the 8th World Congress on Intelligent Control and Automation (WCICA), Jinan, China, 7–9 July 2010; Volume 7, pp. 6953–6958.
[9]
Dai, C.; Long, Z.; Xie, Y.; Xue, S. Research on the filtering algorithm in speed and position detection of maglev trains. Sensors 2011, 11, 7204–7218.
[10]
Theodoulidis, T.P.; Bowler, J.R. Eddy current coil interaction with a right-angled conductive wedge. R. Soc. 2005, 461, 3123–3139.
[11]
Ma, Q.S.; Gao, G.; Sheng, J.N.; Jiang, K.X. Introducing a general analytical method for solving electromagnetic fields with complicated boundary. IEEE Trans. Magn. 1994, 30, 2920–2923.
[12]
Theodoulidis, T.P.; Tsiboukis, T.D. Analytical and numerical solution of eddy-current problem in spherical coordinates based on the second-order vector potential formulation. IEEE Trans. Magn. 1997, 33, 2461–2472.
[13]
Shen, J.N.; Ma, Q.S.; Yuan, B.; Zheng, Q.H.; Yan, Z.W. Theoretical Methods and Applications of Semi-Analytical Method in Analysis of Electromagnetic Field and Wave; Science Press: Beijing, China, 2006.
[14]
Zheng, Q.H.; Xie, F. Solution of three-dimensional helmholtz equation by multipole theory method. Electromagnet Waves Appl. 1999, 13, 339–357.
[15]
Zheng, Q.H.; Xie, F.; Yang, Y.; Lin, W. Solution of three-dimensional laplace equation by multipole theory method. Electromagnet Waves Appl. 1999, 13, 1153–1171.
[16]
Lu, L. The study and design of suspensive gap detecting sensor for high speed maglev train. J. Natl. Univ. Def. Technol. 2007, 10, 14–17.
[17]
Li, T. Study and Realization of High-Speed Maglev Vehicle Relative Location Sensor. Master Thesis, Southwest Jiaotong University, Chengdu, China, 2006.
[18]
Hayt, W.H., Jr.; Buck, J.A. Engineering Electromagnetics; McGraw-Hill Companics: New York, NY, USA, 2001; pp. 212–215.
[19]
Peng, F.Q; Yu, J.H. The characters and computation of legendre function with non-integral degree in SCHA. Acta Geod. Cartogr. Sin. 2000, 29, 204–208.
[20]
Smythe, W.R. Static and Dynamic Electricity; Science Press: Beijing, China, 1982; pp. 404–409.
