Nonlinear Dynamics

, Volume 57, Issue 4, pp 607–622 | Cite as

Nonlinear effects due to electromechanical interaction in generators with smooth poles

Original Paper


Electromechanical interaction in rotating machinery is an interesting nonlinear phenomenon. The methods used to analyze this phenomenon depend on the type of the electrical machine, synchronous or asynchronous, and on its size, but they are often related to the study of the unbalanced magnetic pull (UMP). In this paper the nonlinear behavior of generators with smooth poles of high-speed turbogenerators is presented during and after the excitation of the magnetic field in the air-gap in order to fully exploit the effect of the UMP. In the first part of the paper a method, which allows the simulation of the dynamical behavior of a flexible rotor caused by the UMP, is presented. In the second part, the simulation of a magnetic field excitation transient in a turbogenerator is presented and the nonlinear aspects in the system response and forcing are highlighted.


Unbalanced magnetic pull Generators with smooth poles Electromechanical interaction Synchronous machines Rotordynamics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cameron, J.R., Thomson, W.T., Dow, A.B.: Vibration and current monitoring for detecting airgap eccentricity in large induction motors. IEE Proc. B 133(3), 155–162 (1986) Google Scholar
  2. 2.
    Dorrell, D.G., Thomson, W.T.: Analysis of air-gap flux, current, and vibration signals as a function of the combination of static and dynamic air-gap eccentricity in 3-phase induction motors. IEEE Trans. Ind. Appl. 33(1), 24–34 (1997) CrossRefGoogle Scholar
  3. 3.
    Nabil, A.A.N., Toliyat, H.A.: A novel method for modeling dynamic air-gap eccentricity in synchronous machines based on modified winding function theory. IEEE Trans. Energy Convers. 13(2), 156–162 (1998) CrossRefGoogle Scholar
  4. 4.
    Toliyat, H.A., Nabil, A.A.N.: Simulation and detection of dynamic air-gap eccentricity in salient-pole synchronous machines. IEEE Trans. Ind. Appl. 35(1), 86–93 (1999) CrossRefGoogle Scholar
  5. 5.
    Gustavsson, R.K., Aidanpää, J.-O.: The influence of nonlinear magnetic pull on hydropower generator rotors. J. Sound Vib. 297(3–5), 551–562 (2006) CrossRefGoogle Scholar
  6. 6.
    Holopainen, T.P., Tenhunen, A., Lantto, E., Arkkio, A.: Unbalanced magnetic pull induced by arbitrary eccentric motion of cage rotor in transient operation. Part 1: Analytical model. Electr. Eng. 88(1), 13–24 (2005) CrossRefGoogle Scholar
  7. 7.
    Holopainen, T.P., Tenhunen, A., Lantto, E., Arkkio, A.: Unbalanced magnetic pull induced by arbitrary eccentric motion of cage rotor in transient operation. Part 2: Verification and numerical parameter estimation. Elect. Eng. 88(1), 25–34 (2005) CrossRefGoogle Scholar
  8. 8.
    Holopainen, T.P., Tenhunen, A., Lantto, E., Arkkio, A.: Numerical identification of electromagnetic force parameters for linearized rotor dynamic model of cage induction motors. ASME J. Vib. Acoust. 126(3), 384–390 (2004) CrossRefGoogle Scholar
  9. 9.
    Stoll, R.L.: Simple computational model for calculation the unbalanced magnetic pull on a two-pole turbogenerator rotor due to eccentricity. IEE Proc. Electr. Power Appl. 144(4), 263–270 (1997) CrossRefGoogle Scholar
  10. 10.
    Guo, D., Chu, F., Chen, D.: The Unbalanced Magnetic Pull and its Effects on Vibration in a Three-Phase Generator with Eccentric Rotor. J. Sound Vib. 254(2), 297–312 (2002) CrossRefGoogle Scholar
  11. 11.
    Pennacchi, P., Frosini, L.: Dynamical behaviour of a three-phase generator due to unbalanced magnetic pull. IEE Proc. Electr. Power Appl. 152(6), 1389–1400 (2005) CrossRefGoogle Scholar
  12. 12.
    Pennacchi, P.: Computational model for calculating the dynamical behaviour of generators caused by unbalanced magnetic pull and experimental validation. J. Sound Vib. 312(1–2), 923–946 (2008) CrossRefGoogle Scholar
  13. 13.
    Pennacchi, P., Frosini, L.: Dynamic behaviour of a four-poles turbo generator with rotor eccentricity. Paper RD-685. In: Proceedings of the 12th IFToMM World Congress, Besançon (France), pp. 1–6, 18–21 June 2007 Google Scholar
  14. 14.
    Smith, A.C., Dorrel, D.G.: Calculation and measurement of unbalanced magnetic pull in cage induction motors with eccentric rotors. Part 1: Analytical model. IEE Proc. Electr. Power Appl. 143(3), 193–201 (1996) CrossRefGoogle Scholar
  15. 15.
    Pennacchi, P., Bachschmid, N., Vania, A., Zanetta, G.A., Gregori, L.: Use of modal representation for the supporting structure in model based fault identification of large rotating machinery. Part 1: Theoretical remarks. Mech. Syst. Signal Process. 20(3), 662–681 (2006) CrossRefGoogle Scholar
  16. 16.
    Lalanne, M., Ferraris, G.: Rotor Dynamics Prediction in Engineering. Wiley, New York (1988) Google Scholar
  17. 17.
    Bachschmid, N., Pennacchi, P., Vania, A.: Identification of multiple faults in rotor systems. J. Sound Vib. 254(2), 327–366 (2002) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringPolitecnico di MilanoMilanItaly

Personalised recommendations