Acta Mechanica

, Volume 230, Issue 5, pp 1625–1640 | Cite as

Vibrations attenuation of a Jeffcott rotor by application of a new mathematical model of a magnetorheological squeeze film damper based on a bilinear oil representation

  • Jaroslav ZapomělEmail author
  • Petr Ferfecki
  • Paola Forte
Original Paper


A frequently used technological solution for reducing oscillations of rotors excited by imbalance, time-varying forces or ground vibrations consists in inserting damping devices in the rotor supports. To achieve their optimum performance in a wide range of operating speeds their damping effect must be controllable to be possible to adapt it to the current working conditions. This is enabled by application of magnetorheological squeeze film dampers. In mathematical models the magnetorheological oils are represented mostly by Bingham or Herschel–Bulkley theoretical materials. Recent experimental measurements carried out at several working places show that with respect to the shape of the flow curves obtained for different magnitudes of magnetic induction the real magnetorheological fluids behave like a bilinear material. This enables a more accurate implementation of magnetorheological fluids in mathematical models of squeeze film dampers. In addition, unlike the Bingham fluid the flow curve of a bilinear material is continuous which reduces the nonlinear character of the procedures for calculation of the hydraulic forces by which the oil film acts on the shaft journal and the rotor casing. A new developed mathematical model of a short magnetorheological squeeze film damper based on representing the lubricating oil by bilinear material was implemented in the computational procedures for analysis of the steady state response of a Jeffcott rotor loaded by a stationary force and by the weight and imbalance of the disc. The performed computational simulations proved that these procedures were numerically stable and arrived at the solution also in cases when the methods based on representing the magnetorheological oil by Bingham material failed.


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The research work reported in this article wasmade possible by the research organization conceptual development project (Project No. RVO: 61388998) and by the Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPU II) project “IT4Innovations excellence in science—LQ1602”. The support is highly acknowledged.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Zapoměl, J., Ferfecki, P., Kozánek, J.: Determination of the transient vibrations of a rigid rotor attenuated by a semiactive magnetorheological damping device by means of computational modelling. Appl. Comput. Mech. 7(2), 223–234 (2013).
  2. 2.
    Mu, C., Darling, J., Burrows, C.R.: An appraisal of a proposed active squeeze film damper. J. Tribol. 113(4), 750–754 (1991). CrossRefGoogle Scholar
  3. 3.
    El-Shafei, A., El-Hakim, M.: Experimental investigation of adaptive control applied to HSFD supported rotors. J. Eng. Gas Turb. Power 122(4), 685–692 (2000). CrossRefGoogle Scholar
  4. 4.
    Takayama, Y., Sueoka, A., Kondou, T.: Modeling of moving-conductor type eddy current damper. J. Syst. Des. Dyn. 2(5), 1148–1159 (2008). Google Scholar
  5. 5.
    Zuo, L., Chen, X., Nayfeh, S.: Design and analysis of a new type of electromagnetic damper with increased energy density. J. Vib. Acoust. 133(4), 041006-1–041006-8 (2011). CrossRefGoogle Scholar
  6. 6.
    Silvagni, M., Tonoli, A., Bonfitto, A.: Self-powered eddy current damper for rotordynamic applications. J. Vib. Acoust. 137(1), 011015-1–011015-8 (2015). CrossRefGoogle Scholar
  7. 7.
    Zapoměl, J., Ferfecki, P., Forte, P.: A computational investigation of the transient response of an unbalanced rigid rotor flexibly supported and damped by short magnetorheological squeeze film dampers. Smart Mater. Struct. 21(10), 1–12 (2012). Google Scholar
  8. 8.
    Zapoměl, J., Ferfecki, P.: Mathematical modelling of a long squeeze film magnetorheological damper for rotor systems. Model. Optim. Phys. Syst. 9, 97–102 (2010).
  9. 9.
    Zapoměl, J., Ferfecki, P., Forte, P.: A computational investigation of the steady state vibrations of unbalanced flexibly supported rigid rotors damped by short magnetorheological squeeze film dampers. J. Vib. Acoust. 135(6), 064505-1–064505-4 (2013). Google Scholar
  10. 10.
    Zapoměl, J., Ferfecki, P., Forte, P.: Analysis of the steady state unbalance response of rigid rotors on magnetorheological dampers: stability, force transmission and energy dissipation. Int. J. Appl. Mech. 6(3), 1450022-1–1450022-21 (2014). Google Scholar
  11. 11.
    Bica, I., Liu, Y.D., Choi, H.J.: Physical characteristics of magnetorheological suspensions and their applications. J. Ind. Eng. Chem. 19(2), 394–406 (2013). CrossRefGoogle Scholar
  12. 12.
    Ngatu, G.T., Wereley, N.M.: High versus low field viscometric characterization of bidisperse mr fluids. Int. J. Mod. Phys. B 21(28n29), 4922–4928 (2007). CrossRefGoogle Scholar
  13. 13.
    Chaudhuri, A., Wereley, N.M., Kotha, S., Radhakrishnan, R., Sudarshan, T.S.: Viscometric characterization of cobalt nanoparticle-based magnetorheological fluids using genetic algorithms. J. Magn. Magn. Mater. 293(1), 206–214 (2005). CrossRefGoogle Scholar
  14. 14.
    Gumundsson, K.H.: Design of a Magnetorheological Fluid for an MR Prosthetic Knee Actuator with an Optimal Geometry. PhD dissertation, University of Iceland, Iceland (2011)Google Scholar
  15. 15.
    Zapoměl, J., Ferfecki, P., Forte, P.: A new mathematical model of a magnetorheological squeeze film damper for rotordynamic applications based on a bilinear oil representation—derivation of the governing equations. Appl. Math. Model. 52, 558–575 (2017). MathSciNetCrossRefGoogle Scholar
  16. 16.
    Zapoměl, J., Ferfecki, P., Kozánek, J.: Modelling of magnetorheological squeeze film dampers for vibration suppression of rigid rotors. Int. J. Mech. Sci. 127, 191–197 (2017). CrossRefGoogle Scholar
  17. 17.
    Zapoměl J., Ferfecki P.: A 2D mathematical model of a short magnetorheological squeeze film damper based on representing the lubricating oil by bilinear theoretical material. In: Proceedings of the 14th International Federation for the Promotion of Mechanism and Machine Science World Congress, Taipei, Taiwan, 25–30 October, 2015, pp. 186–191 (2015)Google Scholar
  18. 18.
    Szeri, A.Z.: Tribology: Friction, Lubrication, and Wear. Hemisphere Publishing Corporation, Washington (1980)Google Scholar
  19. 19.
    Zapoměl, J.: Computer Modelling of Lateral Vibration of Rotors Supported by Hydrodynamical Bearings and Squeeze Film Dampers, VŠB-Technical University of Ostrava (2007) (in Czech) Google Scholar
  20. 20.
    Bucchi, F., Forte, P., Frendo, F.: Experimental characterization of a permanent magnet magnetorheological clutch for automotive applications. In: Proceedings of ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis, Nantes, France, July 2–4, 2012, paper no. ESDA2012-82284, pp. 345–355 (2012).
  21. 21.
    Ferfecki, P., Zapoměl, J., Kozánek, J.: Analysis of the vibration attenuation of rotors supported by magnetorheological squeeze film dampers as a multiphysical finite element problem. Adv. Eng. Softw. 104, 1–11 (2017). CrossRefGoogle Scholar
  22. 22.
    Zhao, J.Y., Linnett, I.W., McLean, L.J.: Stability and bifurcation of unbalanced response of a squeeze film damped flexible rotor. J. Trib. 116, 361–368 (1994)CrossRefGoogle Scholar
  23. 23.
    Nataraj, C., Nelson, H.D.: Periodic solutions in rotor dynamic systems with nonlinear supports: a general approach. J. Vib. Acoust. Stress Realib. Des. 111, 187–193 (1989)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  • Jaroslav Zapoměl
    • 1
    • 2
    Email author
  • Petr Ferfecki
    • 2
    • 3
  • Paola Forte
    • 4
  1. 1.Department of Dynamics and Vibration, Institute of ThermomechanicsThe Czech Academy of SciencesPrague 8Czech Republic
  2. 2.Department of Applied MechanicsVSB - Technical University of OstravaOstrava-PorubaCzech Republic
  3. 3.IT4Innovations National Supercomputing CenterVSB - Technical University of OstravaOstravaCzech Republic
  4. 4.Department of Civil and Industrial EngineeringUniversity of PisaPisaItaly

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