Skip to main content
SpringerLink
Log in

Dynamics of the Rotor System of a Vibrational–Centrifugal Separator with an Elastic Vibration Limiter

  • MECHANICS OF MACHINES
  • Published:
Journal of Machinery Manufacture and Reliability Aims and scope Submit manuscript

Abstract

The dynamics of the rotor system of a vibrational-centrifugal separator has been studied. The rotor is modeled by a flexible shaft with internal linear viscous friction and an unbalanced disk (a Jeffcott rotor) located in any disk section. Differential equations are derived that describe transverse radial and angular vibrations of the rotating rotor with consideration for external and internal damping. The solution is represented as an integral Fredholm operator of the second-kind using the Green function for the Bernoulli–Euler rod. Various conditions of rotor end support are considered. To limit vibrations of the rotor including those caused by disk misbalance, an elastic linear damping support is used, which is mounted on one side in the disk rotation plane with some radial clearance. At the contact of the disk with the support, the tangential force of friction, which depends on the normal reaction, is taken into account. The supercritical rotor behavior after the Poincaré–Andronov–Hopf bifurcation is also studied. A numerical calculation was used to plot the Argand diagrams and phase trajectories the analysis of which enabled determination of the time development of vibrations in the interaction between the rotor and the support.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.

Similar content being viewed by others

Notes

  1. Here and below, tensors are denoted using straight bold characters; first-order tensors have an arrow on the top, while second-order tensors have a hat.

REFERENCES

  1. Das, A. and Sarkar, B., Advanced gravity concentration of fine particles, Miner. Process. Extractive Metall. Rev., 2018, vol. 39, no. 6, pp. 359–394.  https://doi.org/10.1080/08827508.2018.1433176

    Article  Google Scholar 

  2. Nayak, A., Jena, M.S., and Mandre, N.R., Application of gravity separators for fine particle processing, J. Sustainable Metall., 2021, vol. 7, no. 2, pp. 315–339.  https://doi.org/10.1007/s40831-021-00343-5

    Article  Google Scholar 

  3. Vibratsii v tekhnike. Spravochnik v 6-ti tomakh (Vibrations in Engineering: Reference Book in 6 Volumes), vol. 4: Vibratsionnye protsessy i mashiny (Vibration Processes and Machines), Moscow: Mashinostroenie, 1981.

  4. Verkhoturov, M.V., Gravitatsionnye metody obogashcheniya (Gravitational Methods of Dressing), Moscow: Maks Press, 2006.

  5. Panovko, G.Ya., Shokhin, A.E., Alekseev, M.P., and Lepekhin, V.M., Experimental study of vibration activity of drum separator, Vestn. Nauchn.-Tekh. Razvit., 2016, no. 3, pp. 9–20.

  6. Yamamoto, T. and Jshida, Y., Linear and Nonlinear Rotor Dynamics, John Wiley & Sons, 2001.

    Google Scholar 

  7. Nelson, F.C., A brief history of early rotor dynamics, J. Sound Vib., 2003, vol. 37, no. 6, pp. 8–11. www.findartircles.eom/p/artides/miqa4075/is200306.ain9296359

    Google Scholar 

  8. Dimentberg, F.M., Izgibnye kolebaniya vrashchayushchikhsya valov (Bending Oscillations of Rotating Shafts), Moscow: Izd-vo Akad. Nauk SSSR, 1959.

  9. Tiwari, R., Rotor Systems: Analysis and Identication, Boca Raton, Fla.: CRC Press, 2018.

    Google Scholar 

  10. Genta, G., Dynamics of Rotating Systems, Mechanical Engineering Series, New York: Springer, 2005.  https://doi.org/10.1007/0-387-28687-X

    Book  MATH  Google Scholar 

  11. Genta, G., Vibration Dynamics and Control, Mechanical Engineering Series, New York: Springer, 2009.  https://doi.org/10.1007/978-0-387-79580-5

    Book  MATH  Google Scholar 

  12. Pasynkova, I.A., Bifurcations of cylindrical precessions of an unbalanced rotor, Tech. Mech., 2006, vol. 26, no. 1, pp. 1–10.

    Google Scholar 

  13. Ding, Q., Cooper, J.E., and Leung, A.Y.T., Hopf bifurcation analysis of a rotor/seal system, J. Sound Vib., 2002, vol. 252, no. 5, pp. 817–833.  https://doi.org/10.1006/jsvi.2001.3711

    Article  Google Scholar 

  14. Karpenko, E.V., Pavlovskaia, E.E., and Wiercigroch, M., Bifurcation analysis of a preloaded Jeffcott rotor, Chaos, Solutions Fractals, 2003, vol. 15, no. 2, pp. 407–416.  https://doi.org/10.1016/S0960-0779(02)00107-8

    Article  MATH  Google Scholar 

  15. Khanlo, H.M., Ghayour, M., and Ziaei-Rad, S., Chaotic vibration analysis of rotating, flexible, continuous shaft-disk and the stator, Commun. Nonlinear Sci. Numer. Simul., 2011, vol. 16, no. 1, pp. 566–582.  https://doi.org/10.1016/j.cnsns.2010.04.011

    Article  Google Scholar 

  16. Bolotin, V.V., Nonconservative Problems of the Theory of Elastic Stability, Oxford: Pergamon Press, 1963.

    MATH  Google Scholar 

  17. Dimentberg, M.F., Vibration of a rotating shaft with randomly varying internal damping, J. Sound Vib., 2005, vol. 285, no. 3, pp. 759–765.  https://doi.org/10.1016/j.jsv.2004.11.025

    Article  Google Scholar 

  18. Zorzi, E.S. and Nelson, H.D., Finite element simulation of rotor-bearing systems with internal damping, ASME J. Eng. Power, 1977, vol. 99, no. 1, pp. 71–76.  https://doi.org/10.1115/1.3446254

    Article  Google Scholar 

  19. Childs, D.W., Fractional-frequency rotor motion due to nonsymmetric clearance effects, Trans. ASME J. Eng. Power, 1982, vol. 104, no. 3, pp. 533–541.  https://doi.org/10.1115/1.3227312

    Article  Google Scholar 

  20. Kurakin, A.D., Nikhamkin, M.Sh., and Semenov, S.V., Dynamics of unbalanced flexible rotor with anisotropic supports during contact with the stator, Vestn. Permskogo Nats. Issled. Politekh. Univ. Mekh., 2016, no. 4, pp. 364–381.  https://doi.org/10.15593/perm.mech/2016.4.21

  21. Zhang, G.F., Xu, W.N., Xu, B., and Zhang, W., Analytical study of nonlinear synchronous full annular rub motion of flexible rotor–stator system and its dynamic stability, Nonlinear Dyn., 2009, vol. 57, pp. 579–592.  https://doi.org/10.1007/s11071-009-9551-7

    Article  MATH  Google Scholar 

  22. Nikiforov, A.N. and Shokhin, A.E., Elastoplastic viscous model of rotor–stator impact interaction without separation, Mech. Solids, 2016, vol. 51, no. 1, pp. 54–64.  https://doi.org/10.3103/S0025654416010064

    Article  Google Scholar 

  23. Lahriri, S., Weber, H.I., Santos, I.F., and Hartmann, H., Rotor-stator contact dynamics using a non-ideal drive—Theoretical and experimental aspects, J. Sound Vib., 2012, vol. 331, no. 20, pp. 4518–4536.  https://doi.org/10.1016/j.jsv.2012.05.008

    Article  Google Scholar 

  24. Neilson, R.D. and Barr, A.D.S., Dynamics of a rigid rotor mounted on discontinuously non-linear elastic supports, Proc. Inst. Mech. Eng., A, 1988, vol. 202, no. 5, pp. 369–376.  https://doi.org/10.1243/PIME_PROC_1988_202_135_02

    Article  Google Scholar 

  25. Grāpis, O., Tamužs, V., Ohlson, N.-G., and Andersons, J., Overcritical high-speed rotor systems, full annular rub and accident, J. Sound Vib., 2006, vol. 290, nos. 3–5, pp. 910–927.  https://doi.org/10.1016/j.jsv.2005.04.031

    Article  Google Scholar 

  26. Jeffcott, H.H., The periods of lateral vibrations of loaded shafts.—The rational derivation of Dunkerley’s empirical rule for determining whirling speeds, Philos. Trans. R. Soc., A, 1918, vol. 95, no. A666, pp. 106–115.

  27. Svetlitskii, V.A., Mekhanika sterzhnei (Mechanics of Rods), vol. 2: Dinamika (Dynamics), Moscow: Vysshaya Shkola, 1987.

Download references

Funding

This study was supported by the Russian Science Foundation, project no. 21-19-00183.

Author information

Authors and Affiliations

  1. Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow, Russia

    A. M. Gouskov, G. Ya. Panovko & A. E. Shokhin

  2. Bauman Moscow State Technical University, Moscow, Russia

    A. M. Gouskov & G. Ya. Panovko

Authors
  1. A. M. Gouskov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Ya. Panovko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. E. Shokhin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Ya. Panovko.

Ethics declarations

The authors declare that they have no conflicts of interest.

Additional information

Translated by M. Shmatikov

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gouskov, A.M., Panovko, G.Y. & Shokhin, A.E. Dynamics of the Rotor System of a Vibrational–Centrifugal Separator with an Elastic Vibration Limiter. J. Mach. Manuf. Reliab. 51, 733–745 (2022). https://doi.org/10.3103/S105261882208009X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S105261882208009X

Keywords:

Search

Navigation