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Nonlinear vibration of a generator rotor with unbalanced magnetic pull considering both dynamic and static eccentricities

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Abstract

The nonlinear vibration of the rotor with unbalanced magnetic pull (UMP) has been extensively investigated in the literature. Most of them focused on the calculation of UMP considering only dynamic eccentricity, while the static eccentricity was generally ignored in current studies. Static eccentricity is actually inevitable due to many reasons. This paper aimed to study the nonlinear responses of a rotor with dynamic and static eccentricities (DSE). The air-gap length unified formula considering DSE is established, and the UMP of the rotor system is obtained by numerical method. The vibration characteristics of a UMP excited rotor with only dynamic eccentricity and DSE are, respectively, discussed in detail for comparison. The effects of rotating frequency and initial static eccentricity on rotor shaft orbit and displacement spectra are acquired. Results illustrate that dynamic behaviors of the UMP excited rotor with DSE are different from those of the rotor with only dynamic eccentricity. The rotor shaft orbit is axis symmetry rather than central symmetry, and the rotor is more likely to have contact with the stator in the direction of static eccentricity. Zero and double supply frequency always exists in the frequency components of the displacement. Not only two and four times of the rotating frequency harmonic appear, but also double supply frequency plus one and two times of rotating frequency harmonic are discovered.

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References

  1. Rosenberg, E.: Magnetic pull in electrical machines. Trans. Am. Inst. Electr. Eng. 37(2), 1425–1469 (1918)

    Article  Google Scholar 

  2. Toliyat, H.A., Al-Nuaim, N.A.: Simulation and detection of dynamic air gap eccentricity in salient-pole synchronous machines. IEEE Trans. Ind. Appl. 35(1), 86–93 (1999)

    Article  Google Scholar 

  3. Tabatabaei, I., Faiz, J., Lesani, H., Nabavi-Razavi, M.T.: Modeling and simulation of a salient-pole synchronous generator with dynamic eccentricity using modified winding function theory. IEEE Trans. Magn. 40(3), 1550–1555 (2004)

    Article  Google Scholar 

  4. Keller, S., Xuan, M.T., Simond, J.-J., Schwery, A.: Large low-speed hydro-generators unbalanced magnetic pulls and additional damper losses in eccentricity conditions. IET Electr. Power Appl. 1(5), 657–664 (2007)

    Article  Google Scholar 

  5. Burakov, A., Arkkio, A.: Comparison of the unbalanced magnetic pull mitigation by the parallel paths in the stator and rotor windings. IEEE Trans. Magn. 43(12), 4083–4088 (2007)

    Article  Google Scholar 

  6. Frosini, L., Pennacchi, P.: The effect of rotor eccentricity on the radial and tangential electromagnetic stresses in synchronous machines. In: IECON 2006. 32nd Annual Conference on IEEE Industrial Electronics, pp. 1287–1292, Paris, France, 6–10 Nov, 2006

  7. Holopainen, T.P., Tenhunen, A., Arkkio, A.: Electromechanical interaction in rotor vibrations of electric machines. In: Proceedings of the 5th World Congress on Computational Mechanics, Vienna, Austria, 7–12 July, 2002

  8. Shen, H., Qiu, J.H., Ji, H.L., Zhu, K.J., Balsi, M., Giorgio, I., Dell’Isola, F.: A low-power circuit for piezoelectric vibration control by synchronized switching on voltage source. Sensors Actuators A Phys. 161(1–2), 245–255 (2010)

    Article  Google Scholar 

  9. Gustavsson, R.K., Aidanpaa, J.-O.: The influence of nonlinear magnetic pull on hydropower generator rotors. J. Sound Vib. 297, 551–562 (2006)

    Article  Google Scholar 

  10. Dorrell, D. G.: The sources and characteristics of unbalanced magnetic pull in cage induction motors with either static or dynamic eccentricity. In: Stockholm Power Tech, IEEE International Symposium on Electric Power Engineering, Stockholm, Sweden, 18–22 June 1995, Volume on Electrical Machines and Drives, pp. 229–234

  11. Pennacchi, P., Frosini, L.: Dynamic bahaviour of a three-phase generator due to unbalanced magnetic pull. IEE Proc. Electr. Power Appl. 152(6), 1389–1400 (2005)

    Article  Google Scholar 

  12. Perers, R., Lundin, U., Leijon, M.: Saturation effects on unbalanced magnetic pull in a hydroelectric generator with an eccentric rotor. IEEE Trans. Magn. 43(10), 3884–3890 (2007)

    Article  Google Scholar 

  13. Wang, L., Cheung, R.W., Ma, Z.Y.: Finite-element analysis of unbalanced magnetic pull in a large hydro-generator under practice operations. IEEE Trans. Magn. 44(6), 1558–1561 (2008)

    Article  Google Scholar 

  14. Lundin, U., Wolfbrandt, A.: Method for modeling time-dependent nonuniform rotor/stator configurations in electrical machines. IEEE Trans. Magn. 45(7), 2976–2980 (2009)

    Article  Google Scholar 

  15. Robinson, R.C.: The calculation of unbalanced magnetic pull in synchronous and induction motors. AIEE Trans. 62, 620–624 (1943)

    Google Scholar 

  16. Fruchtenicht, J., Jordan, H., Seinsch, Ho: Running instability of cage induction-motors caused by harmonic fields due to eccentricity. 1. Electromagnetic spring constant and electromagnetic damping coefficient. Arch. Elektrotech. 65, 271–281 (1982)

    Article  Google Scholar 

  17. Fruchtenicht, J., Jordan, H., Seinsch, Ho: Running instability of cage induction-motors caused by harmonic fields due to eccentricity. 2. Self-excited transverse vibration of the rotor. Arch. Elektrotech. 65, 283–292 (1982)

    Article  Google Scholar 

  18. Belmans, R., Geysen, W., Jordan, H.: Unbalanced magnetic pull and homopolar flux in three phase induction motors with eccentric rotors. In: International Conference on Electrical Machines, vol. 3, pp. 916–921 (1982)

  19. Belmans, R., Geysen, W., Jordan, H.: Unbalanced magnetic pull in three phase two pole induction motors with eccentric rotor. In: International Conference on Electrical Machines-Design and Applications, London, pp. 65–69 (1982)

  20. Behrend, B.: On the mechanical forces in dynamos caused by magnetic attraction. Trans. Am. Inst. Electr. Eng. 17, 613–633 (1990)

    Google Scholar 

  21. Covo, A.: Unbalanced magnetic pull in induction motors with eccentric rotors. Trans. Am. Inst. Electr. Eng. Part III Power Appar. Syst. 73, 1421–1425 (1954)

    Google Scholar 

  22. Calleecharan, Y., Aidanpaa, J.O.: Dynamics of a hydropower generator subjected to unbalanced magnetic pull. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 225(C9), 2076–2088 (2011)

    Article  Google Scholar 

  23. Werner, U.: Rotordynamic model for electromagnetic excitation caused by an eccentric and angular rotor core in an induction motor. Arch. Appl. Mech. 83(8), 1215–1238 (2013)

    Article  Google Scholar 

  24. Funke, H., Maciosehek, G.: Influence of unbalanced magnetic pull on the running of synchronous machine. Electric 19, 233–238 (1965)

  25. Smith, A.C., Dorrell, D.G.: Calculation and measurement of unbalanced magnetic pull in cage induction motors with eccentric rotor. Part 1. Analytical modal. IEE Proc. Electr. Power Appl. 143, 193–201 (1996)

    Article  Google Scholar 

  26. Li, J.T., Liu, Z.J., Nay, L.H.A.: Effect of radial magnetic forces in permanent magnet motors with rotor eccentricity. IEEE Trans. Magn. 43(6), 2525–2527 (2007)

    Article  Google Scholar 

  27. Xu, Y., Li, Z.: Computational model for investigating the influence of unbalanced magnetic pull on the radial vibration of large hydro-turbine generators. J. Vib. Acoust. 134, 131–138 (2012)

    Article  Google Scholar 

  28. Im, H., Yoo, H.H., Chung, J.: Dynamic analysis of a BLDC motor with mechanical and electromagnetic interaction due to air gap variation. J. Sound Vib. 330(8), 1680–1691 (2011)

    Article  Google Scholar 

  29. Lundström, N.L., Aidanpää, P.J.: Dynamic consequences of electromagnetic pull due to deviations in generator shape. J. Sound Vib. 301(1–2), 207–225 (2007)

    Article  Google Scholar 

  30. 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), 332–353 (2008)

    Article  Google Scholar 

  31. Pennacchi, P.: Nonlinear effects due to electromechanical interaction in generators with smooth poles. Nonlinear Dyn. 57(4), 607–622 (2009)

    Article  MATH  Google Scholar 

  32. 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, 297–312 (2002)

    Article  Google Scholar 

  33. Gustavsson, R.K., Aidanpaa, J.O.: The influence of magnetic pull on the stability of generator rotors. In: ISROMAC10-2004-101 Proceeding of 10th International Symposium Transport Phenomena and Dynamics of Rotating machinery, Honolulu, Hawaii, pp. 1–9 (2004)

  34. Wu, B., Sun, W., Li, Z.: Circular whirling and stability due to unbalanced magnetic pull and eccentric force. J. Sound Vib. 330, 4949–4954 (2011)

    Article  Google Scholar 

  35. Zhang, L., Ma, Z., Song, B.: Dynamic characteristics of a rub-impact rotor-bearing system for hydraulic generating set under unbalanced magnetic pull. Arch. Appl. Mech. 83, 817–830 (2013)

    Article  MATH  Google Scholar 

  36. Andreaus, U., Chiaia, B., Placidi, L.: Soft-impact dynamics of deformable bodies. Continuum Mech. Thermodyn. 25(2–4), 375–398 (2013)

    Article  MathSciNet  Google Scholar 

  37. Pillai, K.P., Nair, P., Achuthsankar, S.: Unbalanced magnetic pull in rain-lighting brushless alternators with static eccentricity. IEEE Trans. Veh. Technol. 57, 120–126 (2008)

    Article  Google Scholar 

  38. Burakov, A., Arkkio, A.: Comparison of the unbalanced magnetic pull mitigation by the parallel paths in the stator and rotor windings. IEEE Trans. Magn. 43(12), 4083–4088 (2007)

    Article  Google Scholar 

  39. Rodriguez, P.V.J., Belahcen, A., Arkkio, A., Laiho, A., Antonino-Daviu, J.A.: Air-gap force distribution and vibration pattern of induction motors under dynamic eccentricity. Electr. Eng. 90(3), 209–218 (2008)

    Article  Google Scholar 

  40. Dorrell, D.G.: Sources and characteristics of unbalanced magnetic pull in three-phase cage induction motors with axial-varying rotor eccentricity. IEEE Trans. Ind. Appl. 47(1), 12–24 (2011)

    Article  Google Scholar 

  41. Dorrell, D.G., Shek, J.K., Mueller, H.: Damper windings in induction machines for reduction of unbalanced magnetic pull and bearing wear. IEEE Trans. Ind. Appl. 49(5), 2206–2216 (2013)

    Article  Google Scholar 

  42. Jawad, F., Ebrahimi, B.M., Sharfian, B.M.: Different faults and their diagnosis techniques in three-phase squirrel-cage induction motors—a review. Electromagnetics 26, 543–569 (2006)

    Article  Google Scholar 

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Acknowledgments

This research was supported by the Natural Science Foundation of China (Grant Nos. 11272170 and 51335006).

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  1. Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, China

    Xueping Xu, Qinkai Han & Fulei Chu

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  1. Xueping Xu
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  3. Fulei Chu
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Correspondence to Fulei Chu.

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Xu, X., Han, Q. & Chu, F. Nonlinear vibration of a generator rotor with unbalanced magnetic pull considering both dynamic and static eccentricities. Arch Appl Mech 86, 1521–1536 (2016). https://doi.org/10.1007/s00419-016-1133-9

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  • DOI: https://doi.org/10.1007/s00419-016-1133-9

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