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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

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Abstract

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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References

  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). http://www.kme.zcu.cz/acm/index.php/acm/article/view/215/241

  2. Mu, C., Darling, J., Burrows, C.R.: An appraisal of a proposed active squeeze film damper. J. Tribol. 113(4), 750–754 (1991). https://doi.org/10.1115/1.2920688

    Article  Google Scholar 

  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). https://doi.org/10.1115/1.1287264

    Article  Google Scholar 

  4. Takayama, Y., Sueoka, A., Kondou, T.: Modeling of moving-conductor type eddy current damper. J. Syst. Des. Dyn. 2(5), 1148–1159 (2008). https://doi.org/10.1299/jsdd.2.1148

    Google Scholar 

  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). https://doi.org/10.1115/1.4003407

    Article  Google Scholar 

  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). https://doi.org/10.1115/1.4028228

    Article  Google Scholar 

  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). https://doi.org/10.1088/0964-1726/21/10/105011

    Google Scholar 

  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). http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.baztech-d1bca297-75f7-471b-92a2-de453366e63b

  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). https://doi.org/10.1115/1.4024881

    Google Scholar 

  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). https://doi.org/10.1142/S1758825114500227

    Google Scholar 

  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). https://doi.org/10.1016/j.jiec.2012.10.008

    Article  Google Scholar 

  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). https://doi.org/10.1142/S0217979207045840

    Article  Google Scholar 

  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). https://doi.org/10.1016/j.jmmm.2005.01.061

    Article  Google Scholar 

  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)

  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). https://doi.org/10.1016/j.apm.2017.07.040

    Article  MathSciNet  Google Scholar 

  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). https://doi.org/10.1016/j.ijmecsci.2016.11.009

    Article  Google Scholar 

  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)

  18. Szeri, A.Z.: Tribology: Friction, Lubrication, and Wear. Hemisphere Publishing Corporation, Washington (1980)

    Google Scholar 

  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)

  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). https://doi.org/10.1115/ESDA2012-82284

  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). https://doi.org/10.1016/j.advengsoft.2016.11.001

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

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Acknowledgements

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.

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Authors and Affiliations

  1. Department of Dynamics and Vibration, Institute of Thermomechanics, The Czech Academy of Sciences, Dolejškova 1402/5, 182 00, Prague 8, Czech Republic

    Jaroslav Zapoměl

  2. Department of Applied Mechanics, VSB - Technical University of Ostrava, 17. listopadu 15/2172, 708 33, Ostrava-Poruba, Czech Republic

    Jaroslav Zapoměl & Petr Ferfecki

  3. IT4Innovations National Supercomputing Center, VSB - Technical University of Ostrava, Ostrava, Czech Republic

    Petr Ferfecki

  4. Department of Civil and Industrial Engineering, University of Pisa, Largo Lazzarino, C.A.P. 56122, Pisa, Italy

    Paola Forte

Authors
  1. Jaroslav Zapoměl
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  2. Petr Ferfecki
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  3. Paola Forte
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Correspondence to Jaroslav Zapoměl.

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Zapoměl, J., Ferfecki, P. & Forte, P. 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. Acta Mech 230, 1625–1640 (2019). https://doi.org/10.1007/s00707-018-2343-8

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  • DOI: https://doi.org/10.1007/s00707-018-2343-8

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