# Analysis of magnetic fields on a levitating coaxial and non-coaxial aluminum disc

• ## Authors

• Bharath Kumar Narukullapati
• T K Bhattacharya
• Jhansi Lakshmi P
2018-11-27
• The electromagnetic field calculations for a levitating aluminum disc involve integro-differential equations and the solution of these equations is difficult to obtain using conventional techniques especially when the disc is coaxially away from the axis of the coils. Over the years many analytical, semi-analytical and numerical techniques have been proposed to calculate the magnetic fields on the disc when it is coaxial with the coils. In this paper, a mathematical formulation has been developed to obtain the magnetic fields on a conducting disc using a numerical technique at different positions of the levitation and for different disc discretizationâ€™s. The numerical technique developed here is based on Finite Difference Method. Since the magnetic fields on the disc are due to the coil currents and eddy currents in the disc, first a mathematical formulation is done to calculate fields due to exciting coil currents and then a numerical technique is used to calculate fields due to eddy currents on the disc. Also, the magnetic fields on the disc are calculated when the disc moves away from the axis of the coil. A MATLAB program is developed to calculate these fields.

• ## References

1. [1] B. V. Jayawant, â€œElectromagnetic levitation and suspension techniquesâ€,Edward Arnold Publishers Limited, 1981, available online: http://worldcat.org/isbn/0713134283

[2] S. Williamson and E. Chan, â€œThree-dimensional finite-element formulation for problems involving time-varying fields, relative motion, and magnetic saturation,â€ IEE Proceedings of Science, Measurement and Technology, Vol.140, No.2, (1993), pp.121â€“130, available online:10.1049/ip-a-3.1993.0020

[3] E. Furlani, S. Reznik, and A. Kroll, â€œA three-dimensional field solution for radially polarized cylinders,â€ IEEE transactions on magnetics, Vol.31, No.1, (1995), pp. 844â€“851, available online: 10.1109/20.364587

[4] J. D. Jackson, â€œClassical Electrodynamicsâ€, John Wiley & Sons, (2007).

[5] B. K. Narukullapati and T. K. Bhattacharya, â€œStabilizing a floating discâ€”analysis, field and lateral force calculation,â€ International Conference on Power, Instrumentation, Control and Computing (PICC). IEEE, (2018), pp.1â€“6, available online: 10.1109/PICC.2018.8384787

[6] M. W. Garrett, â€œCalculation of Fields, Forces, and Mutual Inductances of Current Systems by Elliptic Integralsâ€, Journal of Applied Physics, Vol.34, No.9, (2004), available online: https://doi.org/10.1063/1.1729771