Electrical Engineering

, Volume 100, Issue 2, pp 389–399 | Cite as

An asymptotic approximation of the magnetic field and forces in electrical machines with rotor eccentricity

Original Paper
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Abstract

In this contribution, a systematic asymptotic derivation of approximate solutions to the magnetic field problem in rotating electric machines with an eccentrically running rotor is proposed. It is consistent with the well-known permeance harmonic method and can be seen as an alternative view on the derivation of the magnetic flux density and resulting lateral forces in the air gap of the machine. The asymptotic expansion is based on a purely geometric small parameter and applies even for large rotor eccentricities. The advantage of this method lies in its extensibility towards higher approximation orders, and in the fact that it is possible to quantify the order of the involved approximation error. The discussion includes two examples and a numerical verification.

Keywords

Electrical machines Eccentric rotor Magnetic field Asymptotic expansion Unbalanced magnetic pull 

References

  1. 1.
    Rosenberg E (1917) Einseitiger magnetischer Zug in elektrischen Maschinen. E. und M. 35:525–531Google Scholar
  2. 2.
    Woodson HH, Melcher JR (2009) Electromechanical dynamics part 1. Massachusetts Institute of Technology, MIT OpenCourseWare, CambridgeGoogle Scholar
  3. 3.
    Müller G, Vogt K, Ponick B (2008) Berechnung elektrischer Maschinen. Wiley-VCH, WeinheimGoogle Scholar
  4. 4.
    Dorrell DG, Hermann A, Jensen BB (2013) Analysis of unbalanced magnetic pull in wound rotor induction machines using finite element analysis—transient, motoring and generating modes. In: Industrial electronics society, IECON 2013—39th annual conference of the IEEE 7307–7312Google Scholar
  5. 5.
    Arkkio A et al (2000) Electromagnetic force on a whirling cage rotor. IEE Proc Electr Power Appl 147:353–360CrossRefGoogle Scholar
  6. 6.
    Tenhunen A et al (2003) Electromagnetic forces of the cage rotor in conical whirling motion. IEE Proc Electr Power Appl 150:563–568CrossRefGoogle Scholar
  7. 7.
    Burakov A, Arkkio A (2007) Low-order parametric force model for eccentric-rotor electrical machine equipped with parallel stator windings and rotor cage. IET Electr Power Appl 1:532–542Google Scholar
  8. 8.
    Tenhunen A, Holopainen TP, Arkkio A (2004) Effects of saturation on the forces in induction motors with whirling cage rotor. IEEE Trans Magn 40:766–769CrossRefGoogle Scholar
  9. 9.
    Frauman P, Burakov A, Arkkio A (2007) Effects of the slot harmonics on the unbalanced magnetic pull in an induction motor with an eccentric rotor. IEEE Trans Magn 43:3441–3444CrossRefGoogle Scholar
  10. 10.
    Buchholz H (1933) Die mechanischen Kräfte auf den exzentrisch rotierenden, zylindrischen Läufer einer zweipoligen Drehfeldmaschine mit flächenhaft verteilten Strombelägen. Electr Eng (Archiv für Elektrotechnik) 27:423–447CrossRefMATHGoogle Scholar
  11. 11.
    Skubov D, Shumakovich IV (1999) Stability of the rotor of an induction machine in the magnetic field of the current windings. Mech Solids 34:28–40Google Scholar
  12. 12.
    Werner U (2006) Rotordynamische analyse von Asynchronmaschinen mit magnetischen Unsymmetrien. Dissertation, University of DarmstadtGoogle Scholar
  13. 13.
    Frohne H (1968) Über den einseitigen magnetischen Zug in Drehfeldmaschinen. Electr Eng (Archiv für Elektrotechnik) 51:300–308CrossRefGoogle Scholar
  14. 14.
    Früchtenicht J, Jordan H, Seinsch H (1982) Exzentrizitätsfelder als Ursache von Laufinstabilitäten bei Asynchronmaschinen Teil 1. Electr Eng (Archiv für Elektrotechnik) 51:271–281CrossRefGoogle Scholar
  15. 15.
    Belmans R, Vandenput A, Geysen W (1987) Calculation of the flux density and the unbalanced pull in two pole induction machines. Electr Eng (Archiv für Elektrotechnik) 70:151–161CrossRefGoogle Scholar
  16. 16.
    Jordan H, Schroeder RD, Seinsch H (1981) Zur Berechnung einseitigmagnetischer Zugkräfte in Drehfeldmaschienen. Electr Eng (Archiv für Elektrotechnik) 63:117–124CrossRefGoogle Scholar
  17. 17.
    Dorrell DG (1993) Calculation of unbalanced magnetic pull in cage induction machines. Dissertation, University of CambridgeGoogle Scholar
  18. 18.
    Merkin DR (2012) Introduction to the theory of stability. Springer, New YorkGoogle Scholar
  19. 19.
    Kim U, Lieu DK (1998) Magnetic field calculation in permanent magnet motors with rotor eccentricity: without slotting effect. IEEE Trans Magn 34:2243–2252CrossRefGoogle Scholar
  20. 20.
    Rothwell EJ, Cloud MJ (2001) Electromagnetics. CRC Press, Boca RatonCrossRefGoogle Scholar
  21. 21.
    Binder A (2012) Elektrische maschinen und antriebe. Springer, HeidelbergCrossRefGoogle Scholar
  22. 22.
    Jordan H, Weis M (1970) Synchronmaschinen I. Vieweg & Sohn GmbH, BraunschweigGoogle Scholar
  23. 23.
    Hague B (1929) Electromagnetic problems in electrical engineering. Oxford University Press, OxfordGoogle Scholar
  24. 24.
    Seinsch HO (1992) Oberfelderscheinungen in Drehfeldmaschinen. B.G. Teubner, StuttgartGoogle Scholar
  25. 25.
    Jordan H (1969) Asynchronmaschinen. Springer Fachmedien, WiesbadenCrossRefGoogle Scholar
  26. 26.
    Kellenberger W (1966) Der magnetische zug in turbogenerator-rotoren als ursache einer Instabilität des mechanischen Laufes. Electr Eng (Archiv für Elektrotechnik) 50:253–265CrossRefGoogle Scholar
  27. 27.
    Nayfeh AH (1973) Pertubation methods. Wiley, New YorkGoogle Scholar
  28. 28.
    Szeri A (2010) Fluid film lubrication. Cambridge University Press, CambridgeCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Engineering Dynamics Group, Department of Mechanical Engineering, Institute of MechanicsUniversity of KasselKasselGermany

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