The substantiation of the calculation expression for the extraction force of magnetic separators

• Autorzy: Zagirnyak Mykhaylo

Identyfikatory

DOI

10.15199/48.2024.01.55

Warianty tytułu

Uzasadnienie wzoru obliczeniowego siły ekstrakcji w separatorach magnetycznych

• Języki publikacji: EN

Abstrakty

EN

A review and analysis of methods for calculating the magnetic field force action on a ferromagnetic body are carried out. The integral equivalence of various formulas for the vector of the density of the force acting on a ferromagnetic body in a static magnetic field is shown. The possibility of applying the corresponding formula in engineering calculations of magnetic separators is confirmed theoretically and experimentally.

PL

Dokonano przeglądu i analizy metod obliczania intensywności oddziaływania pola magnetycznego na ciało ferromagnetyczne. Pokazano całkową równoważność różnych wzorów na wektor gęstości siły działającej na ciało ferromagnetyczne w statycznym polu magnetycznym.. Możliwość zastosowania odpowiedniego wzoru w obliczeniach inżynierskich separatorów magnetycznych została potwierdzona teoretycznie i eksperymentalnie.

Słowa kluczowe

EN

magnetic field global force; ferromagnetic body; electromagnetic separator

PL

siła pola magnetycznego; ciało ferromagnetyczne; separator elektromagnetyczny

• Wydawca: Wydawnictwo SIGMA-NOT
• Czasopismo: Przegląd Elektrotechniczny
• Rocznik: 2024
• Tom: R. 100, nr 1
• Strony: 264--268
• Opis fizyczny: Bibliogr. 33 poz., tab.

Twórcy

autor

Zagirnyak Mykhaylo

• Kremenchuk Mykhailo Ostrohradskyi National University, Professor, 20, Pershotravneva street, Kremenchuk, 39600, Ukraine

• https://orcid.org/0000-0003-4700-0967

Bibliografia

• [1] Einstein, A. and Laub, J. On the Ponderomotive Forces Exerted on Bodies at Rest in the Electromagnetic Field, Annalen der Physik, 26 (1908), 541-550. (In German)
• [2] Tamm I. Е., Fundamentals of the theory of electricity. М.: Mir Publisher, 1979. 684 p.
• [3] Stratton J. А., Electromagnetic theory. New York and London: McGraw-Hill Book Company. 1941. 615 p.
• [4] Smolkin R. D., Calculation of magnetic field strength and electromagnetic ponderomotive force of separators, IEEE Transactions on Magnetics, 38 (2002), nr 3, 1528-1533.
• [5] 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, 42 (2006), nr 11, 3682-3693.
• [6] Bossavit A., On forces in magnetized matter, IEEE Transactions on Magnetics, 50 (2014), nr 2, 229-232.
• [7] Gama S., Ferreira Lucas D. R., Bessa Carlos V. X., Horikawa Oswaldo, Coelho Adelino A., Gandra Flavio C., Araujo Raul, Egolf Peter W., Analytic and experimental analysis of magnetic force equations, IEEE Transactions on Magnetics, 52 (2016), nr 7, 1-4.
• [8] Spalek D., Generalization of Maxwell stress tensor method for magnetically anisotropic regions, IEEE Transactions on Magnetics, 55 (2019), nr 12, 1-6.
• [9] Spałek D., Levitation of conductive and magnetically anisotropic ball, IEEE Transactions on Magnetics, 55 (2019), nr 3, 1-7.
• [10] Spalek D., Two theorems about surface-integral representation of electromagnetic force and torque, IEEE Transactions on Magnetics, 53 (2017), nr 7, 1-10.
• [11] Choi Hong Soon, Park Il Han, Lee Se Hee, Concept of virtual air gap and its applications for force calculation, IEEE Transactions on Magnetics, 42 (2006), nr 4, 663-666.
• [12] Zagirnyak M. V., Determination of the ponderomotive magnetic force when calculating the field by the conformal transformation method, Technical Electrodynamics, (2020), nr 3, 9-14.
• [13] Zagirnyak M., A simplified calculation of magnetic field strength over the middle of the gap of double-pole magnetic iron separator, Technical Electrodynamics, 2018 (2018), no. 5, 100- 103.
• [14] Zagirnyak M., Usatyuk V., Zagirnyak V., The estimation of suspended iron separators with arch poles with the use of magnetic modulus method, Przeglad Elektrotechniczny, 94 (2018), no. 11, 170-173.
• [15] Zagirnyak M., Branspitz Y., Shvedchikova I., Using a conformal mapping method for calculation of a multipolar system magnetic field, Przeglad Elektrotechniczny, 88 (2012), no. 7 B, 98-101.
• [16] Zagirnyak M.V., Branspiz Y.A., Concerning calculation of force action of a uniform magnetic field on live straight ferromagnetic conductor, Studies in Applied Electromagnetics and Mechanics, 34 (2010), 609-620.
• [17] Wang Q., Zhao F., Yang K., Analysis and optimization of the axial electromagnetic force for an axial-flux permanent magnet vernier machine, IEEE Transactions on Magnetics, 57 (2021), nr 2, 1-5.
• [18] Ito F., Takeuchi K., Kotsugai T., Matsushita M., A study on asymmetry of electromagnetic force modes of permanent magnet synchronous motors with rotor eccentricity, IEEE Transactions on Magnetics, 57 (2021), nr 2, 1- 6.
• [19] Kassid F. Ezzahra, Azelmad Essaadia, Bousshine Lahbib, Berdai Abdelmajid, Magnetic force computation for a magnetic separator based on permanent magnet, Przeglad electrotechniczny, 97 (2021), nr 10, 28-32.
• [20] Fu W., Ho S., Error estimation for the computation of force using the virtual work method on finite element models, IEEE Transactions on Magnetics, 45 (2009), nr 3, 1388-1391.
• [21] Bobbio S., Delfino F., Girdinio P., Molfino P., Equivalent sources methods for the numerical evaluation of magnetic force with extension to nonlinear materials, IEEE Transactions on Magnetics, 36 (2000), nr 4, 663-666.
• [22] Derkach V. G., Special methods of mineral processing. М.: Nedra, 1966. 338 p. (Rus)
• [23] Zagirnyak М. V., Branspiz Yu. А., Pulley magnetic separators: Monograph. K.: Tekhnika. 2000. 303 p. (Rus)
• [24] Ivanov-Smolenskij A. V., Electromagnetic forces and energy conversion in electrical machines. M.: Vyssh. shk.,1989. 312 p. (Rus)
• [25] Arkadiev V. V., Electromagnetic processes in metals: In 2 p. М. L.: ONTI, 1934, P. 1. 300 p. (Rus)
• [26] Polivanov K. М., Electrodynamics of moving bodies. М.: Energoizdat, 1982. 192 p. (Rus)
• [27] Maugin G. A., Continuum Mechanics of Electromagnetic Solids. N.Y.: North-Holland, 1988. 598 p.
• [28] Myshkis А. D., Lectures on higher mathematics. М.: Nauka, 1969. 640 p. (Rus)
• [29] Rozentsweig R., Ferrohydrodynamics. New York: Cambridge University Press, 1985. 344 p.
• [30] Rossel Sh., General physics. М.: Mir, 1964. 506 p. (Rus)
• [31] Muller W., Comparison of different methods of force calculation, IEEE Transactions on Magnetics, 26 (1990), nr 2, 1058-1061.
• [32] Purcell E., Morin D., Electricity and magnetism. New York: Cambridge University Press, 2013. 853 p.
• [33] Tikadzumi S., Physics of ferromagnetism. Magnetic properties of a substance. М.: Mir, 1983. 304 p. (Rus)

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki i promocja sportu (2025).