ANALYTICAL CALCULATIONS INVOLVING MAGNETIC FIELDS OF A MAGNETOELECTRIC VALVE MOTOR USING THE METHOD OF SEPARATION OF VARIABLES

DOI: 10.47026/1810-1909-2022-3-45-52

УДК 621.313.13-251:51

ББК З291.53в631

Aleksandr A. AFANASYEV, Valeriy S. GENIN, Nadezhda N. IVANOVA

Key words

motor, magnet, induction, magnetic field, Laplace’s equation, system of equations, Maxima package

Abstract

An analytical method for calculating the magnetic field of a magnetoelectric valve motor is considered based on the division of its active region into a set of geometrically homogeneous sheets, at the boundaries of which the conditions for conjugating their magnetic fields are met: scalar magnetic potentials and normal components of magnetic induction do not undergo a jump (break). As sources of the magnetic field, in addition to permanent magnets and currents of the stator winding, the magnetization of ferromagnetic sections of its magnetic circuit is provided.

When using the Fourier method of separation of variables, the conjugation conditions will be reduced to solving a system of linear equations to find the corresponding constants. The solution of the system of parametric equations describing the design scheme of the inductor of a slotless magnetoelectric valve motor is given, in general terms using the Maxima analytical (symbolic) calculation package. The solution obtained makes it possible to use the results to describe the magnetic potentials and inductions of valve motors of various design geometries.

References

1. Afanas’ev A.A., Vatkin V.A., Genin V.S. et al. Analiticheskii raschet bespazovogo mikrodvigatelya, ne imeyushchego statornogo serdechnika [Analytical Calculation of Slotless Micromotor Without Stator Core]. Vestnik Chuvashskogo universiteta, 2019, no. 1, pp. 13–22.
2. Afanas’ev A.A., Genin V.S., Vatkin V.A. et al. Analiticheskoe i chislennoe modelirovanie magnitoelektricheskikh ventil’nykh dvigatelei [Analytical and Numerical Simulation of Magnetoelectric Valve Motors]. Elektrichestvo, 2021, no. 6, pp. 72–78.
3. Afanas’ev A.A. K raschetu bespazovogo magnitoelektricheskogo ventil’nogo dvigatelya [To Calculation of Slotless and Brushless Motor with Permanent Magnets]. Elektrichestvo, 2019, no. 8, pp. 62–66.
4. Afanas’ev A.A. Matematicheskoe modelirovanie elektromekhanicheskikh sistem [Mathematical modeling of electromechanical systems]. Cheboksary, Chuvash University Publ., 2020, 274 p.
5. Afanas’ev A.A. Raschet magnitoelektricheskikh ventil’nykh dvigatelei metodom razdeleniya peremennykh Fur’e [Calculating Magnetoelectric Valve Motors by the Fourier Variable Separation Method]. Elektrotekhnika, 2021, no. 2, pp. 21–27.
6. Bogolyubov A.N., Kravtsov V.V. Zadachi po matematicheskoi fizike [Problems in mathematical physics]. Moscow, Moscow University Publ., 1998, 350 p.
7. Gubina T.N., Andropova E.V. Reshenie differentsial’nykh uravnenii v sisteme komp’yuternoi matematiki Maxima [Solution of differential equations in the system of computer mathematics Maxima]. Elets, 2009, 99 p.
8. Dodiera R. Korotko o Maxima [Briefly about Maxima]. Available at: https://dwg.ru/dnl/3633.
9. Nesterin V.A., Genin V.S., Romanov R.A., Tokmakov D.A. Matematicheskoe modelirovanie elektromagnitnoi sistemy sverkhminiatyurnogo magnitoelektricheskogo dvigatelya [Mathematical modeling of the electromagnetic system of a superminiature magnetoelectric motor]. Elektrotekhnika, 2017, no. 7, pp. 7–10.
10. Polivanov K.M. Teoreticheskie osnovy elektrotekhniki. Ch. 3. Teoriya elektromagnitnogo polya [Theoretical foundations of electrical engineering. Part 3: Electromagnetic field theory]. Moscow, Energiya Publ., 1969, 352 p.
11. Polivanov K.M. Ferromagnetiki [Ferromagnets]. Moscow, Leningrad, 1957, 256 p.
12. Polyanin A.D. Spravochnik po lineinym uravneniyam matematicheskoi fiziki [Handbook of Linear Equations of Mathematical Physics]. Moscow, Fizmatlit Publ., 2001, 576 p.
13. Stakhin N.A. Osnovy raboty s sistemoi analiticheskikh (simvol’nykh) vychislenii Maxima. (PO dlya resheniya zadach analiticheskikh (simvol’nykh) vychislenii) [Basics of working with the system of analytical (symbolic) calculations Maxima. (Software for solving problems of analytical (symbolic) calculations)]. Moscow, 2008, 86 p. Available at: https://uneex.ru/static/MethodBooks_Maxima/Maxima.pdf.
14. Chichkarev E.A. Komp’yuternaya matematika s Maxima [Computer Mathematics with Maxima]. Moscow, ALT Linux Publ., 2012, 384 p.

Information about the authors

Aleksandr A. Afanasyev – Doctor of Technical Sciences, Professor, Department of Automation and Control in Technical Systems, Chuvash State University, Russia, Cheboksary (afan39@mail.ru).

Valeriy S. Genin – Doctor of Technical Sciences, Professor, Department of Automation and Control in Technical Systems, Chuvash State University, Russia, Cheboksary (v.s.genin@mail.ru; ORCID: https://orcid.org/0000-0002-9086-0906).

Nadezhda N. Ivanova – Candidate of Technical Sciences, Associate Professor, Department of Mathematical and Hardware Support of Information Systems, Chuvash State University, Russia, Cheboksary (niva_mail@mail.ru; ORCID: https://orcid.org/0000-0001-7130-8588).

For citations

Afanasyev A.A., Genin V.S., Ivanova N.N. ANALYTICAL CALCULATIONS AT THE COMB OF A MAGNETOELECTRIC VALVE MOTOR BY THE METHOD OF VARIABLE SEPARATION. Vestnik Chuvashskogo universiteta, 2022, no. 3, pp. 45–52. DOI: 10.47026/1810-1909-2022-3-45-52 (in Russian).

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