Induction Motor Vibrations Caused by Mechanical and Magnetic Rotor Eccentricity

Author(s): Goroshko A. V.*, Zembytska M. V., Paiuk V. P.

Affiliation(s): Khmelnytskyi National University, 11, Instytutska St., 29016 Khmelnytskyi, Ukraine

*Corresponding Author’s Address: [email protected]

Issue: Volume 11, Issue 1 (2024)

Submitted: January 12, 2024
Received in revised form: April 16, 2024
Accepted for publication: April 30, 2024
Available online: May 3, 2024

Goroshko A. V., Zembytska M. V., Paiuk V. P. (2024). Induction motor vibrations caused by mechanical and magnetic rotor eccentricity. Journal of Engineering Sciences (Ukraine), Vol. 11(1), pp. D66–D77.

DOI: 10.21272/jes.2024.11(1).d8

Research Area: Dynamics and Strength of Machines

Abstract. Vibration reduction of induction motors is a significant problem that requires effective models for the effects of mechanical and electromagnetic unbalanced forces. This article presents a mathematical model of dynamics for induction motors with rotor mass eccentricity and static and dynamic magnetic eccentricity. The model allows for the influence of the gyroscopic torque of the rotor and considers the elastic-damping characteristics of each of the stator supports and their location. The model has eight degrees of freedom, which makes it possible to simulate transverse and axial vibrations of various designs’ rotors and housings of induction motors. The results of modeling the dynamics for a three-phase squirrel cage induction motor with 11 kW capacity agreed with those obtained by other authors. Simultaneously, new results were also obtained within the research. The simulation results showed that the static magnetic eccentricity causes the appearance of additional critical speed of the motor, and its value decreases in proportion to the growth of the number of pole pairs. The change of the moment of inertia of the motor at a mismatch of the main axis of symmetry of the stator and the rotor axis of rotation allowed for obtaining an actual frequency spectrum of free oscillations, including the rotational motion of the stator. Since the actual static magnetic eccentricity can additionally increase at operating frequencies due to the increase of bearing clearance caused by dynamic unbalanced load, it should be considered in the analysis of unbalanced magnetic pull. The angle of static magnetic eccentricity significantly affects the magnitude of radial vibrations. This feature should also be considered when selecting the locations of balancing weights during the rotor balancing procedure.

Keywords: induction motor, eccentricity of rotor mass, magnetic eccentricity, unbalanced magnetic pull, axial vibration, process innovation.


  1. Popa, L. M., Jensen, B. B., Ritchie, E., Boldea, I. (2003). Condition Monitoring of Wind Generators. In: 38th IAS Annual Meeting on Conference Record of the Industry Applications Conference. Salt Lake City, UT, USA, Vol. 3, pp. 1839–1846.
  2. Thomson, W. (2020). Vibration Monitoring of Induction Motors and Case Histories on Shaft Misalignment and Soft Foot. In Vibration Monitoring of Induction Motors: Practical Diagnosis of Faults via Industrial Case Studies. Cambridge University Press, Cambridge, UK.
  3. Liu, Y., Chen, Z., Hua, X., Zhai, W. (2022) Effect of rotor eccentricity on the dynamic performance of a traction motor and its support bearings in a locomotive. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, Vol. 236(9), pp. 1080–1090.
  4. Michon, M., Holehouse, R. C., Atallah, K., Johnstone, G. (2014). Effect of rotor eccentricity in large synchronous machines. IEEE Transactions on Magnetics, Vol. 50(11), 8700404.
  5. Richard N. Bell et al. (1985) Report of large motor reliability survey of industrial and commercial installations, Part II. IEEE Transactions on Industry Applications, Vol. 21(4), pp. 865–872.
  6. Cornell, E. P., Owen, E. L., Appiarius, J. C., McCoy, R. M., Albrecht, P. F., and Houghtaling, D. W. (1982). Improved Motors for Utility Applications. Final Report. U.S. Department of Energy, Office of Scientific and Technical Information United States, Oak Ridge, TN, USA.
  7. Bellini, A., Immovilli, F., Rubini, R., Tassoni, C. (2008). Diagnosis of bearing faults of induction machines by vibration or current signals: A critical comparison. In: 2008 IEEE Industry Applications Society Annual Meeting. Edmonton, AB, Canada, 2008, pp. 1–8.
  8. Chuan, H., Shek, J. K. (2018). Calculation of unbalanced magnetic pull in induction machines through empirical method. IET Electric Power Applications, Vol. 12(9), pp. 1233–1239.
  9. Salah, A. A., Dorrell, D. G., Guo, Y. (2019). A Review of the monitoring and damping unbalanced magnetic pull in induction machines due to rotor eccentricity. IEEE Transactions on Industry Applications, Vol. 55(3), pp. 2569–2580.
  10. Dorrell, D. G., Hsieh, M., Guo, Y. (2009). Unbalanced magnet pull in large brushless rare-earth permanent magnet motors with rotor eccentricity. IEEE Transactions on Magnetics, Vol. 45, pp. 4586–4589.
  11. Burakov, A., Arkkio, A. (2007). Comparison of the unbalanced magnetic pull mitigation by the parallel paths in the stator and rotor windings. IEEE Transactions on Magnetics, Vol. 43(12). pp. 4083–4088.
  12. Zhu, Z. Q., Ishak, D., Howe, D., Chen, J. (2007). Unbalanced magnetic forces in permanent-magnet brushless machines with diametrically asymmetric phase windings. IEEE Transactions on Industry Applications, Vol. 43(6). pp. 1544–1553.
  13. Dorrell, D. G., Hsieh, M. F. (2010). Calculation of radial forces in cage induction motors at start – The effect of rotor differential. IEEE Transactions on Magnetics, Vol. 46(8), pp. 3029–3032.
  14. Liu, F., Xiang, C., Liu, H., Chen, X., Feng, F., Cong, H., Kuilong, Yu. (2022). Model and experimental verification of a four degrees-of-freedom rotor considering combined eccentricity and electromagnetic effects. Mechanical Systems and Signal Processing, Vol. 169, 108740.
  15. Werner, U. (2017) Influence of the foundation on the threshold of stability for rotating machines with roller bearings – A theoretical analysis. Journal of Applied Mathematics and Physics, Vol. 5, pp. 1380–1397.
  16. Werner, U. (2017). Mathematical multibody model of a soft mounted induction motor regarding forced vibrations due to dynamic rotor eccentricities considering electromagnetic field damping. Journal of Applied Mathematics and Physics, Vol. 5(2), pp. 346–364.
  17. Werner, U. (2017). Influence of electromagnetic field damping on forced vibrations of induction rotors caused by dynamic rotor eccentricity. ZAMM-Journal of Applied Mathematics and Mechanics, Vol. 97(1), pp. 38–59.
  18. Jiang, J. W., Bilgin, B., Sathyan, A., Dadkhah, H., Emadi, A. (2016). Analysis of unbalanced magnetic pull in eccentric interior permanent magnet machines with series and parallel windings. IET Electric Power Applications, Vol. 10(6), pp. 526–538.
  19. Calleecharan, Y., Jauregui, R., Aidanpää, J.-O. (2013). Towards a general method for estimating the unbalanced magnetic pull in mixed eccentricities motion including sufficiently large eccentricities in a hydropower generator and their validation against EM simulations. The European Physical Journal Applied Physics, Vol. 63(2), 20901.
  20. Wu, B., Sun, W., Li, Z., Li, Z. (2011). Circular whirling and stability due to unbalanced magnetic pull and eccentric force. Journal of Sound and Vibration, Vol. 330(21), pp. 4949–4954.
  21. Du, J., Li, Y. (2023). Analysis on the Variation laws of electromagnetic force wave and vibration response of squirrel-cage induction motor under rotor eccentricity. Electronics, Vol. 12(6), 1295.
  22. Lei, A., Song, C.-X., Lei, Y.-L., Fu, Y. (2021). Design optimization of vehicle asynchronous motors based on fractional harmonic response analysis. Mechanical Sciences, Vol. 12, pp. 689–700.
  23. Essen, H. (1993). Average angular velocity. European Journal of Physics, Vol. 14(5), 201.
  24. Drach, I., Goroshko, A., Dwornicka, R. (2021). Design principles of horizontal drum machines with low vibration. Advances in Science and Technology Research Journal, Vol. 15(2), pp. 258–268.
  25. Brown, K. H., Morrow, C. W., Durbin, S. G. (2008). Guideline for Bolted Joint Design and Analysis: Version 1.0. Sandia Report SAND2008-0371. Sandia National Laboratories, Albuquerque, NM, USA.
  26. Gargiulo, E. P. (1980). A simple way to estimate bearing stiffness. Machine Design, Vol. 52(17). pp. 107–110.
  27. Krämer, E. (1993). Dynamics of Rotors and Foundations. Springer-Verlag Berlin Heidelberg GmbH, Berlin, Germany.
  28. Kim, H., Sikanen, E., Nerg, J., Sillanpää, T., Sopanen, J. T. (2020). Unbalanced magnetic pull effects on rotordynamics of a high-speed induction generator supported by active magnetic bearings – Analysis and experimental verification. IEEE Access, Vol. 8, pp. 212361–212370.
  29. Kim, H., Nerg, J., Choudhury, T., Sopanen, J. T. (2020). Rotordynamic simulation method of induction motors including the effects of unbalanced magnetic pull. IEEE Access, Vol. 8, pp. 21631–21643.
  30. Han, Y., Yang, L., Xu, T. (2021). Analysis of static stiffness fluctuation in radially loaded ball and roller bearings. Archive of Applied Mechanics, Vol. 91, pp. 1757–1772.
  31. He, Y. L., Dai, D.-R., Xu, M.-X., Zhang, W., Tang, G.-J., Wan, S.-T., Sheng, X.-L. (2022). Effect of static/dynamic air gap eccentricity on stator and rotor vibration characteristics in doubly fed induction generator. IET Electric Power Applications, Vol. 16(11), pp. 1378–1394.

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