Abstract
The modern development of the component base makes it possible to implement in practice and use in precision devices relatively new types of electric machines, the rotor of which has not one, but three degrees of freedom relative to the stator. Such machines, like classical ones, can be of various types (synchronous, asynchronous, valve), have various design features that have a key effect on their functioning. The process of deriving mathematical models of three-stage machines (usually based on the Lagrange equation of the second kind) is quite time-consuming and the mathematical models themselves are quite complex, since the movement of the rotor along any of the three axes has a significant impact on its movement along the remaining two axes. At present, mathematical models of the main types of three-stage electric machines have been obtained and, (by analogy with classical electric machines), the concept has been introduced and the equations of motion of a generalized three-stage electric machine with mutually movable stator and rotor windings have been obtained. Therefore, from the point of view of the development of the theory of electromechanics, it is of interest to obtain mathematical models for some types of such machines based on a mathematical model of a generalized three-stage electrical machine. In addition, this makes it possible to obtain a mathematical description for any types of three-stage electric machines without much effort, taking into account their design features and operating modes.
Keywords
electric machine, rotor, stator, winding, inductance, voltage, current, flow coupling, electromagnetic moment
1. Milyakh A.N., Barabanov V.A., Dvoynykh V.V. Trekhstepennye elektricheskie mashiny [Three-power electric machines]. Kiev, Naukova dumka, 1979. 312 p. (In Russian)
2. Gurevich M.S. Integration of coordinate transformations in rotating tracking systems. Izvestiya SPbGETU "LETI" [Proceedings of Saint Petersburg Electrotechnical University], 2010, no. 1, pp. 35-44. (In Russian)
3. Kozlova E.S., Rogov S.V. Mathematical model of a three-stage electric machine. Izvestiya TulGU. Tekhnicheskie nauki. [Izvestiya Tula State University], 2021, iss. 10, pp. 89-94. (In Russian)
4. Sokolov M.V., Mikhed A.D. Gyro drive based on a three-stage electric machine. Sovremennye tendentsii razvitiya nauki i proizvodstva: sbornik materialov Mezhdunarodnoy nauchno-prakticheskoy konferentsii [Collection of materials of the International Scientific and Practical Conference "Modern trends in the development of science and production"]. Kemerovo, LLC "Western Siberian Scientific Center" Publ., 2023, pp.16-19. (In Russian)
5. Sili S. Elektromekhanicheskoe preobrazovanie energii [Electromechanical transformation of energy]. Moscow, Energia Publ., 1968. 376 p. (In Russian)
6. White D., Woodson G. Elektromekhanicheskoe preobrazovanie energii [Electromechanical energy conversion]. Moscow, Energia Publ., 1964. 528 p. (In Russian)
7. Makarov V.G. Application of the theory of a generalized electric machine to a three-phase asynchronous motor. Problemy energetiki [Problems of Power Engineering], 2009, no. 11-12, pp. 84-97. (In Russian)
8. Gorozhankin A.N., Gryzlov A.A., Chupin E.S., Khayatov E.S. Generalized analytical mathematical model of an electromechanical converter as a control object. Vestnik YuUrGU. Seriya «Energetika» [Bulletin of South Ural State University. Series "Power Engineering"], 2016, vol. 16, no. 4, pp. 72-76. (In Russian)
9. Solovev A.E., Osman F.T., Ulyanov R.Yu. Mathematical model of a generalized three-stage electric machine. Navigatsiya i upravlenie dvizheniev: materialy trudov XII konferentsii molodykh uchenykh [Proceedings of the XII Conference of Young scientists "Navigation and motion control"]. St. Petersburg, Publishing House of the SSC RF Central Research Institute "Electric appliance", 2010, pp. 372-378. (In Russian)
10. Solovev A.E., Osman F.T., Ulyanov R.Yu. Model of a three-stage electromechanical asynchronous type energy converter. Matematicheskie metody v tekhnike i tekhnologiyakh: materialy trudov XXII Mezhdunarodnaya nauchnaya konferentsiya [Proceedings of the XXII International Scientific Conference "Mathematical methods in engineering and technologies"]. Pskov, Publishing House of Pskov State Polytechnic University, 2009, vol. 8, pp. 83-85. (In Russian)
11. Solovev A.E., Sukhinin B.V., Surkov V.V., Kozlova E.S. Giroskopicheskie privody na baze trekhstepennykh elektricheskikh mashin [Gyroscopic drives based on three-stage electric machines]. Tula: TulSU Publishing House, 2007. 215 p.
Solovyev A.Je., Kravchenko O.A. Using a Mathematical Model of a Generalized Three-Stage Electric Machine. Elektrotekhnicheskie sistemy i kompleksy [Electrotechnical Systems and Complexes], 2023, no. 4(61), pp. 53-59. (In Russian). https://doi.org/10.18503/2311-8318-2023-4(61)-53-59