Abstract
Recently, with the development of cheap high-frequency power sources with power up to 4 kW, there has been an increased interest in levitation heating and melting of small samples to obtain pure metal and precision alloys. For stable levitation melting the inductor coil design must have a special form. One of the possible variants of stable levitation melting is the use of construction in the form of conical inductor with a reverse coil - as one of the simplest, but quite effective. The mathematical model for determining the amplitude of magnetic field intensity and the position of the metal body held in suspended state in the conical inductor with the reverse coil is proposed in the paper. The behavior of the vertical and radial components of the magnetic field intensity vector along the inductor radius is analyzed. It is established that when the cone angle of the inductor is increased at a fixed radius of its base, the maximum and minimum values of the field on the inductor axis decrease, wherein the field maximum is shifted towards the lower end of the inductor, and the minimum - towards the upper end. Computer simulation of the possible equilibrium points of the cylindrical body in inductor magnetic field is made. The simple method for engineering calculation is shown, which makes it possible to determine whether the inductor field retains a body with the specified dimensions from the selected metal, the position of the body at its equilibrium with the given parameters of the inductor, current through the inductor, at which equilibrium is possible, and what is maximum density and dimensions the metal body in the inductor will be in suspended state.
Keywords
Levitation melting, high-frequency conical inductor with reverse coil, magnetic field intensity, suspended state of metal, electromagnetic force, stable equilibrium.
1. Fogel A.A. Induktsionnyy metod uderzhaniya zhidkih metallov vo vzveshennom sostoyanii [Induction method of liquid metals retention in suspended state]. Leningrad: Mechanical Engineering, 1974. 104 p. (In Russian)
2. G. Lohöfer, S. Schneider. Heat balance in levitation melting: Sample cooling by forced gas convection in Helium. High Temperatures–High Pressures, 2015, vol. 44, pp. 429-450.
3. G. Lohöfer, S. Schneider. Heat balance in levitation melting: Sample cooling by forced gas convection in Argon.High Temperatures–High Pressures, 2016, vol. 45, pp. 255-271.
4. Glebovsky V.G., Bourtsev V.T. Plavka metallov i splavov vo vzveshennom sostoyanii [Melting of metals and alloys in suspended state]. Moscow: Metallurgy, 1974. 176 p. (In Russian)
5. Sluhotskij A.E. Induktory [Inductors]. Leningrad: Mashinostroenie, 1989. 69 p. (In Russian)
6. S. Roberts, S. Kok, J. Zietsman, H.M. Inglis, Electromagnetic levitation coil design using gradient-based optimization. Proceedings of the 11th World Congress on Structural and Multidisciplinary Optimization (WCSMO-11), Sydney, Australia, 7-12 June, 2015, no. 1307, pp. 1-6.
7. Marinkova E.I., Borisov A.Yu., Shaburova A.A., Frizen V.E. Levitation melting in a cone high-frequency inductor with a reverse coil. Perspektivnye energeticheskie tehnologii. Ekologiya, ekonomika, bezopasnost i podgotovka kadrov – 2016. [Perspective energy technologies. Ecology, economics, security and training – 2016]: materials of the scientific-practical conference, Ekaterinburg: UrFU, 2016, pp. 117-118. (In Russian)
8. Marinkova E.I., Borisov A.Yu., Shaburova A.A., Frizen V.E. Determination of the shape of the free surface of the melt at the levitation melting in a cone high-frequency inductor with a reverse coil. Nauka. Tehnologii. Innovatsii. [The science. Technologies. Innovations]: collection of scientific papers in 9 parts, ed. E.G. Gurova, Novosibirsk: NSTU, 2016, part 5, pp. 117-118. (In Russian)
9. B.K. Khoo, M. Ovinis, T. Nagarajan. A Comparative Analysis of Inductors with Square and Conical Contours. Applied Mechanics and Materials, 2013, vol. 415, pp. 414-417.
10. A. Kermanpur, M. Jafari, and M. Vaghayenegar. Electromagnetic-thermal coupled simulation of levitation melting of metals. Journal of Materials Processing Technology, 2011, vol. 211, no. 2, pp. 222-229.
11. Yachikov I.M., Vdovin K.N., Shmelev M.O. Modeling of magnetic field behavior and position of a body suspended in the high-frequency inductor with reverse coil. Mathematical and software systems in industrial and social spheres. 2013, no. 1, pp. 47-53. (In Russian)
12. Yachikov I.M. Position balance of body suspended in high frequency inductor with reverse coil. Elektrotekhnicheskiesistemy i kompleksy [Electrotechnical systems and complexes]. 2014, no. 3(24), pp. 66-72. (In Russian)
13. Certificate no. 2014614306.Modeling of the magnetic field in the inductor with reverse coil. Yachikov I.M., Shmelev M.O. FGBU «Federal Institute of Industrial Property», Federal Service for Intellectual Property, State Registration of Computer Programs, no. 2014612024; claimed 12.03.2014; date of registration 22.04.2014.
14. Yachikov I.M., Larina T.P. Experimental research of body position in suspension state in a cylindrical high-frequency inductor with a reverse coil. Elektrotekhnicheskie sistemy i kompleksy [Electrotechnical systems and complexes]. 2015, no. 2(27), pp. 39-43. (In Russian)