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A Simple Viscoelastic Model of Rotor-Shaft Systems

  • J. K. Dutt
Conference paper
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 1011)

Abstract

Damping exists in every material in varying degrees; so materials in general are viscoelastic in nature. Energy storage as well as dissipation in varying degrees, accompany every time varying deformation, with the effect that stress and strain in a material get out of phase. This work presents the development of preliminary equations of motion of a simple viscoelastic rotor-shaft-system by using differential operator algebra. Sample results of stability limit of spin speed and stability limit of uniform angular acceleration at a stable spin speed are also presented. Use of operators enables one to consider linear multi-element (e.g., 3, 4 or higher elements) material model for better representation of the viscoelastic rotor continuum rather than a two-element Voigt model used generally. The primary inspiration for a multi-element model arises from the need to capture broad band spectral behaviour of materials, primarily polymers and polymer composites. Additionally such a model is generic, as with suitable choice of model parameters, the formulation may also be used to obtain the equations of motion, if a two-element (Voigt model) or a single element (purely elastic) model is used to represent the rotor material behaviour. The equations developed may be easily used to find the time response of the rotor-disc subjected to any dynamic forcing function.

Keywords

Viscoelastic rotors Multi-element rotor models Rotor stability 

Notes

Acknowledgment

The author gratefully acknowledges the kind help extended by Mr. Rishi Relan, Senior Research Fellow, for preparing this paper.

References

  1. 1.
    Bland, D.R.: Linear Viscoelasticity. Pergamon Press, Oxford (1960)zbMATHGoogle Scholar
  2. 2.
    Asnani, N.T.: Vibration Analysis of Multi-layered Beams with Constrained Viscoelastic Layers. Ph.D.Thesis, Indian Institute of Technology, Delhi (1971)Google Scholar
  3. 3.
    Kapur, A.D., Nakra, B.C., Chawla, D.R.: Shock response of viscoelastically damped beams. J. Sound Vib. 55(3), 351–362 (1977)zbMATHCrossRefGoogle Scholar
  4. 4.
    Nakra, B.C.: Vibration control in machines and structures using viscoelastic damping. J. Sound Vib. 211(3), 449–465 (1998)CrossRefGoogle Scholar
  5. 5.
    Dimentberg, M.: Flexural Vibration of Rotating Shafts. Butterworth, London, England (1961)Google Scholar
  6. 6.
    Tondl, A.: Some Problems of Rotor Dynamics. Publishing House of Czechoslovak Academy of Sciences, Prague (1965)Google Scholar
  7. 7.
    Zorzi, E.S., Nelson, H.D.: Finite element simulation of rotor-bearing systems with internal damping. J. Eng. Power, Trans. ASME 99, 71–76 (1977)Google Scholar
  8. 8.
    Ozguven, H.N., Ozkan, Z.L.: Whirl speeds and unbalance response of multibearing rotors using finite elements. J. Vib. Acoust. Stress Reliab. Des., Trans. ASME 106, 72–79 (1984)Google Scholar
  9. 9.
    Ku, D.M.: Finite element analysis of whirl speeds for rotor-bearing systems with internal damping. Mech. Syst. Signal Process. 12(5), 599–610 (1998)CrossRefGoogle Scholar
  10. 10.
    Genta, G.: On a persistent misunderstanding of the role of hysteretic damping in rotordynamics. J. Vib. Acoust., Trans. ASME 126, 459–461 (2004)Google Scholar
  11. 11.
    Grybos, R.: The dynamics of a viscoelastic rotor in flexible bearing. Arch. Appl. Mech., Springer Verlag 61, 479–487 (1991)Google Scholar
  12. 12.
    Roy, H., Dutt, J.K., Datta, P.K.: Dynamics of a viscoelastic rotor shaft using augmenting thermodynamic fields—a finite element approach. Int. J. Mech. Sci. 50, 845–853 (2008)CrossRefGoogle Scholar
  13. 13.
    Roy, H.: Study on Dynamics of Viscoelastic Rotors: A Finite Element Approach. Ph.D. Thesis, Department of Aerospace Engineering, IIT Kharagpur (2008)Google Scholar
  14. 14.
    Ghosh, A., Mallik, A.K.: Theory of Mechanisms and Machines, 3rd edn. East West Press (1998)Google Scholar
  15. 15.
    Dutt, J.K., Nakra, B.C.: Stability of rotor systems with viscoelastic supports. J. Sound Vib. 153(1), 89–96 (1992)zbMATHCrossRefGoogle Scholar
  16. 16.
    Dutt, J.K., Toi, T.: Rotor vibration reduction with polymeric sectors. J. Sound Vib. 262, 769–793 (2003)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Mechanical Engineering IIT DelhiNew DelhiIndia

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