# THE STUDY OF POWER CHARACTERISTICS OF ADAPTIVE MAGNETIC DAMPER

### Abstract

The paper deals with the problem of imbalance of a working element of high-speed technological devices, in particular, centrifugal units. The current trend in the development of technological devices is productivity improvement. The increase in the number of operating characteristics of the devices can be achieved through various ways: from the development of new types of devices and modernization of the existing ones to the improvement of frequency characteristics. Therefore, the issue of damping, which improves the reliability of technological machines, becomes more relevant in current technology. The study identified the most dangerous types of vibrations leading to the considerable damage of a working wheel. Based on the analysis of various axial vibrations influence on a working wheel, the authors proposed the way to eliminate vibrations using an adaptive damper. Axial vibration dampers working on permanent magnets have the following technical advantages over the mechanical dampers: relative high lifting capacity, high rotational speeds at high temperatures, no need for working fluid supply, etc. Magnetic dampers can operate at super high frequencies (more than 9000 r/min), therefore, it is necessary to study their work in the conditions close to limiting ones. The design adaptability is in the application of rubber-metal material, due to which the elastic force arises. The authors consider an integrated approach to damping: the force of magnetic interaction acts together with the elastic force. The aim of the paper is to determine the interrelations of key power characteristics. One of the necessary criteria of any system is its stability, which is evaluated in the paper using L.M. Lyapunov’s criterion. The paper presents the main results in the form of mathematical dependencies of a theoretical model.

### References

Podgornyy Yu.I., Martynova T.G., Skiba V.Yu., Pushnin V.N., Vakhrushev N.V., Kornev D.Yu., Zaytsev E.K. Determination of the main parameters of the processing equipment. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty), 2013, no. 3, pp. 68–73.

Pushnin V.N., Kornev D.Yu., Vakhrushev N.V., Skiba V.Yu., Parts K.A. The forecasting of technical characteristics of integrated processing equipment. Trudy Bratskogo gosudarstvennogo universiteta. Seriya: Estestvennye i inzhenernye nauki, 2014, no. 2, pp. 97–101.

GOST R 31320-2006. Vibratsiya. Metody i kriterii balansirovki gibkikh rotorov [Vibration. Methods and criteria for the mechanical balancing of flexible rotors]. Moscow, Standartinform Publ., 2008. 27 p.

Podgornyy Yu.I., Martynova T.G., Voynova E.V. Balancing of working shaft of a continuous-type mixer. Problemy povysheniya effektivnosti metalloobrabotki v promyshlennosti na sovremennom etape: sbornik materialov 8-y Vserossiyskoy nauchno-prakticheskoy konferentsii. Novosibirsk, NGTU Publ., 2010, pp. 127–129.

Buryak A.A., Dzenzerskiy V.A. Concerning the possibility of motion self-stabilization in the electrodynamic levitation systems. Stroitelstvo, materialovedenie, mashinostroenie, 2006, no. 37, pp. 65–73.

Savin L.A., Solomin O.V. Active Magnetic Bearings: Foundations of Operation and Simulation. Mekhatronika, avtomatizatsiya, upravlenie, 2009, no. 2, pp. 33–37.

Chernyshov N.N., Lupikov V.S., Bayda E.I., Kryukova N.V., Gelyarovskaya O.A. Possibility of magnetic levitation for ferromagnetic bodies in the gradient magnetic field of direct current windings. Voprosy atomnoy nauki i tekhniki. Seriya: Vakuum, chistye materialy, sverkhprovodniki, 2008, no. 1, pp. 115–122.

Danby G.R., Powell J.R. Design approaches and parameters for magnetically levitated transport system. Superconductivity and its application. London, Elsevier Publ., 1988, pp. 318–342.

Jayawant B.V. Electromagnetic suspension and levitation techniques. Proceedings of the royal society of London. Series A: Mathematical and Physical Sciences, 1988, vol. 416, no. 1851, pp. 245–320.

Antonov Yu.F., Zaytsev A.A., Morozova E.I. Study of magnetic dynamic levitation and electrodynamic braking of a cargo transport platform. Izvestiya Peterburgskogo universiteta putey soobshcheniya, 2014, no. 4, pp. 5–15.

Petrovskiy E.A., Bashmur K.A., Kozhukhov E.A. The study of the characteristics of magnitofonov thrust bearing. Computational Nanotechnology, 2018, no. 2, pp. 68–71.

Lebrun R., Ross A., Bender S.A., Quaiumzadeh A., Baldrati L., Cramer J., Brataas A., Duine R.A., Kläui M. Tunable long-distance spin transport in a crystalline antiferromagnetic iron oxide. Nature, 2018, vol. 561, no. 7722, pp. 222–225.

Vereshchagin V.P., Klabukov V.A. Mathematical model of magnetic bearing. Voprosy elektromekhaniki. Trudy VNIIEM, 2009, vol. 112, no. 5, pp. 17–22.

Bogdanov Yu.V., Guskov A.M. Modeling the rotor dynamics of electrospindle on magnetic bearings. Nauka i obrazovanie: nauchnoe izdanie MGTU im. N. E. Baumana, 2015, no. 1, pp. 201–220.

Golenkov G.M., Bondar S.A. Numerical calculation of magnetic field and basic characteristics of an electrovibrator based on a coaxial linear motor with permanent magnets. Elektrotekhnіka і elektromekhanіka, 2007, no. 1, pp. 8–12.

Semenov E.A., Lyakhova M.B., Lukin A.A., Karpenkov A.Yu., Lukina E.A. Methodology for studying reversal magnetization processes in magnets of the Sm-Co-Fe-Cu-Zr system at high temperatures. Metallovedenie i termicheskaya obrabotka metallov, 2018, no. 8, pp. 8–12.

Zimina G.V., Nikolaeva I.I., Tauk M.V., Tsygankova M.V. Extraction schemes of rare-earth metals’ separation. Tsvetnye metally, 2015, no. 4, pp. 23–27.

Balakin P.D., Krasotina L.V., Krivtsov A.V. Statics of rubber isolator. Omskiy nauchnyy vestnik, 2016, no. 3, pp. 10–14.

Earnshaw S. On the nature of molecular forces which regulate the constitution of luminiferous ether. Transactions of Cambridge Philosophie Society, 1842, vol. 7, pp. 97–112.

Lazareva T.Ya., Martemyanov Yu.F. Osnovy teorii avtomaticheskogo upravleniya [Fundamentals of Automatic Control Theory]. Tambov, TGU Publ., 2003. 308 p.

Pakshin P.V., Pozdyayev V.V. Existence criterion of the common quadratic Lyapunov function for a set of linear second-order systems. Journal of Computer and Systems Sciences International, 2005, vol. 44, no. 4, pp. 519–524.

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