Mathematical model of magnetic state of single-phase commutator motor

: pp. 48 - 54
Lviv Polytechnic National University

Single-phase commutator motors (SPCM) with sequential excitation have a simple design and low cost, and therefore promising for use in the drive of household appliances and electric hand tools. This necessitates the creation of mathematical models of SPCM, which would allow both the development of new and modernization of existing models of such motors. The aim of the article is to create an engineering mathematical model of the magnetic state of SPCM using circular methods. The initial parameters for this model are the size of the magnetic circuit, the winding data and the instantaneous values of the stator and armature currents. The developed model makes it possible to determine the field curve in the air gap of the SPCM, as well as to calculate the flux density in all other parts of the magnetic circuit of the SPCM. The mathematical model of the magnetic state of SPCM is considered on the example of the most common bipolar structure. The magnetic state of the SPCM is represented by an exhaustive replacement circuit of the magnetic core with concentrated parameters. Some sections of the magnetic circuit, within which the magnetic field is considered homogeneous, are replaced by magnetic resistances. Nonlinear magnetic resistance (NMR) correspond to the ferromagnetic sections of the magnetic core and the toothed zone of the armature. Permanent magnetic resistance (PMR) corresponds to the areas of the air gap and the areas of leakage flux. NMR are represented by nonlinear characteristics as dependences of magnetic forces (MF) on magnetic flux – F [Ф]. The active layer of the SPCM armature under the poles in the plane perpendicular to the axis of rotation of the motor is divided into m uniform sectors. The equivalent circuit of the SPCM magnetic circuit contains the NMR sections of the stator yoke, stator poles, armature toothed layer, armature yoke, as well as PMR sections of the air gap and areas of leakage flux. The method of contour flux is used to compile a system of equations that describes the equivalent circuit. The system of nonlinear algebraic equations can be solved, in particular, by the iterative method of Newton. The proposed mathematical model of the magnetic state of SPCM can be the basis for the development of mathematical models for calculating transient modes and static characteristics of this type of motor.

  1. Pustola J. Maszyny komutatorowe dla automatyki. Warszawa: Wydawnictwa naukowo-techniczne, 1971, 316 s. (Pol.).
  2. Karaliūnas B. Computer modeling of the characteristics and magnetic field of single-phase commutator motor. Proc. of the XV Int. Conf. on Electromagnetic Disturbances, EMD. Technologija. Kaunas – Bialystok, 2005, рp. 61–64. httpwww_actawm_pb_edu_plvol2no3karaliunas.pdf
  3. Dmitrievskii V., Prakht V., Kazakbaev V., Sarapulov S. Optimal design of a high-speed single-phase flux reversal motor for vacuum cleaners. Energies 2018, 11, 3334, 13 p. DOI: 10.3390/en11123334;
  4. Cros J., Viarouge P.,, Chalifour Y., Figueroa J. A new structure of universal motor using soft magnetic composites. IEEE transactions on industry applications. Vol. 40, No. 2, march/april 2004, рp. 550–557.
  5. Pujlo H. V., Pirkovskyi S. N., Babijczuk O. B. Proektnyi syntez odnofaznych kolektornykh dvihatelej s adaptatsiej obobschenoho pokazatelia kaczestva. Lviv Polytechnic National University Institutional Repository, 2003, S. 176–181. (Rus.).
  6. Pujlo H. V., Pirkovskyi S. N., Protsyna Z. P. Optimalnyi parametricheskij sintez odnofaznykh kolektornykh dvigatelej na osnove geneticheskoho alhoritma. Elektromashynobuduvania ta elektroobladnania, 2004, Vyp. 62, S. 129–132. (Rus.)
  7. Pirkovskyi S. N. Proektnyi syntez odnofaznoho kolektornoho dvihatelia na osnove kombinirovanoho alhoritma optimizatsii. Elektrotechniczeskie i kompjuternye sistemy, 2015,17 (93), S. 35–41. > jspui > bitstream. (Rus.).
  8. Pirkovskyi S. N., Babijczuk O. B., Protsyna Z. P. Proektnyi syntez odnofaznych kolektornykh dvihatelej na osnove vektornoho pokazatelia kachestva . Elektromashynobuduvania ta elektroobladnania, 2005, Vyp. 64, S. 67–71 > irbis_nbuv > cgiirbis_64. (Rus.).
  9. Maljar V. S., Hluchivsryi L. J., Maljar A. V., Hreczyn D. P., Havdo I. R. Raschet magnitnoj tsepi odnofaznoho asinkhronoho dvihatelia s rasshceplenymi poliusami. Energetika. Izvestija vysshykh uchebnykh zavedenij i energeticheskich objedinienij SNH, Minsk, 2003, 3, С. 17–25. (Rus.).
  10. Havdo I. R. Matematyczna model mahnitnoho stanu kolektornoho dvyhuna z mahnitoelektrycznym zbudzheniam. Elektroenerhetyczni ta elektromechaniczni systemy, 2019, Vyp. 1, 1. S. 10–16. › maketno12019zdoi1-10-16. (Ukr)

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