Keywords
magnetic field strength
conformal transformation method
magnetic systems пондеромоторна сила
напруженість магнітного поля
метод конформного перетворення
магнітні системи
How to Cite
Abstract
The method of conformal transformation has been widely applied to the research of devices using ponderomotive action of the magnetic field. This method enables the analysis and calculation of stationary 2D electric and magnetic fields meeting the Laplace equation. It allows essential simplification of the problem of the field calculation. However, its basic drawback consists in the absence of the general method for the determination of the complex potential. Consequently, it is usually impossible to obtain expressions for the magnetic field strength and its ponderomotive force in the explicit form as a function of coordinates in the initial domain. This paper deals with the solution to the problem of direct determination of the specific ponderomotive force of the magnetic field with the use of complex potential with the known function of conformal transformation. The analyzed examples of the calculation of the ponderomotive force in the working zone of the poles of different shapes can be a model for the research of the traction performance of the electromagnetic systems of magnetic separating devices. Besides, the obtained expressions can also be used in the calculation of the systems working on the principle of the ponderomotive action of the electrostatic field. References 12, figures 2.
References
Tolmachev E. G., Fainshtein E. G. Generalized analysis of magnetic fields of drum separators. Izvestiya VUZov. Hornyi Journal. 1973. No 1. Pp. 149–153. (Rus)
Zakharova M. S, Smolkin R. D. On the calculation of two-pole electromagnetic iron separators and separators. Obogashchenie poleznykh iskopaemykh. 1972. No 11. Pp. 51–56. (Rus)
Alam F. R., Abbaszadeh K. Magnetic Field Analysis in Eccentric Surface-Mounted Permanent-Magnet Motors Using an Improved Conformal Mapping Method. IEEE Transactions on Energy Conversion . 2016. Vol. 31. No 1. Pp. 333-344.
Smolkin M. R., Smolkin R. D. Calculation and analysis of the magnetic force acting on a particle in the magnetic field of separator: analysis of the equations used in the magnetic methods of separation. IEEE Transactions on magnetics. 2006. Vol. 42, No 11. Pp. 3682−3693.
Smolkin M. R., Smolkin R. D., Smolkin E. R. Analysis of magnetic fields and circuits in separators with plane-parallel and plane-meridian symmetry. IEEE Transactions on magnetics. 2008. Vol. 44, No 8. Pp. 1990−2001.
Zagirnyak M. V. A simplified calculation of magnetic field strength over the middle of the gap of double-pole magnetic iron separator. Tekhnichna Elektrodynamika. 2018. No 5. Pp. 100−103. DOI: https://doi.org/10.15407/techned2018.05.100
Tamm I. E. Fundamentals of electricity theory. Moskva: Nauka, 1976. 616 p. (Rus)
Zagirnyak M. V., Branspiz Yu. A., Shvedchikova I. A. Magnetic separators: design problems. Kyiv: Technika, 2011. 224 p. (Rus)
Fainshtein E. G. Some properties of ponderomoive forces in a potential magnetic field. Elektrichestvo. 1974. No 3. Pp. 71–74. (Rus)
Bins K., Laurenson P., Trowbridge C. The analytical and numerical solution of electrical and magnetic fields. Chichester: Wiley, 1992. 470 p.
Markushevich A. I. A short course in the theory of analytic functions. Moskva: Nauka, 1978. 415 p. (Rus)
Kartashian V. O., Zagirnyak M. V., Branspiz Yu. A., Vorobiev N. G. Calculation of ponderrpomotive forces of electromagnetic pulleys with ferromagnetic shunts. Izvestiya VUZov. Hornyi Journal. 1981. No 7. Pp. 117–121. (Rus)
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