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Non-synchronous and Localized Responses of Systems of Identical Centrifugal Pendulum Vibration Absorbers

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An Erratum to this article was published on 18 December 2014

Abstract

The dynamic response of a system composed of a rotor subject to engine-order torsional excitation and fitted with multiple identical centrifugal pendulum vibration absorbers is considered. The absorbers’ desired synchronous response can lose stability in two ways: a jump behavior, which maintains the symmetry associated with absorber synchronicity, and loss of synchronicity via a symmetry-breaking response bifurcation. In this paper, we review the loss of stability of the synchronous response and consider the post-critical system response for the case of general path absorbers. We investigate the resulting post-bifurcation responses, which consist of two groups of absorbers each of which respond in a mutually synchronous manner within the group. By considering permutations of these responses, it is found that there are many such responses with some being dynamically stable. This analytical study is based on the method of averaging applied to a dimensionless form of the equations of motion. It is found that the initial symmetry-breaking bifurcations are generally subcritical, and the subsequent bifurcations can result in situations where several steady-state responses are possible over a wide range of operating conditions. Some of these responses are localized in nature leading to a significant reduction in feasible operating range of the system. It is shown that non-synchronous responses can exist at very small torque levels. Absorber overtuning widens the range of stable synchronous response, but it also widens the range where stable non-synchronous responses coexist with the stable synchronous response. These results provide important considerations for the tuning of identical absorber systems.

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References

  1. Ker Wilson W.: Practical Solutions of Torsional Vibration Problems, Chapter XXX. Vol. IV. Chapman and Hall, London (1968)

    Google Scholar 

  2. Swank, M.; Lindemann, P.: Dynamic Absorbers for Modern Powertrains. SAE Technical Paper (2011)

  3. Brooke, L.: Chrysler Sees the ICE Future. SAE Automotive Engineering International, pp. 16–19. 1 Oct. 2013

  4. Nester, T.M.; Haddow, A.G.; Shaw, S.W.; Brevick, J.E.; Borowski, V.J.: Vibration reduction in a variable displacement engine using pendulum absorbers. In: SAE International, Paper number: 2003-01-1484 (2003)

  5. Alsuwaiyan A.S., Shaw S.W.: Performance and dynamic stability of general-path centrifugal pendulum vibration absorbers. J Sound Vib 252, 791–815 (2002)

    Article  Google Scholar 

  6. Shaw, S.W.; Geist, B.K.: Tuning for performance and stability in systems of nearly-tautochronic torsional vibration absorbers. J. Vib. Acoust. 132, 01 November 2011

  7. Denman H.H.: Tautochronic bifilar pendulum torsion absorbers for reciprocating engines. J. Sound Vib. 159, 251–277 (1992)

    Article  MATH  Google Scholar 

  8. Chao C.P., Lee C.T., Shaw S.W.: Stability of the unison response for a rotating system with multiple tautochronic pendulum vibration absorbers. ASME J. Appl. Mech. 64, 149–156 (1996)

    Article  Google Scholar 

  9. Chao C.P., Shaw S.W., Lee C.T.: Non-unison dynamics of multiple centrifugal pendulum vibration absorbers. J. Sound Vib. 204, 769–794 (1997)

    Article  Google Scholar 

  10. Mayet J., Ulbrich H.: Tautochronic centrifugal pendulum vibration absorbers: general design and analysis. J. Sound Vib. 333, 711–729 (2014)

    Article  Google Scholar 

  11. Mayet, J.; Ulbrich, H.: First order optimal linear tuning and nonlinear mistuning of centrifugal pendulum vibration absorbers. Preprint, Technische Universität München, Institute of Applied Mechanics, Boltzmannstr. 15, 85748 Garching, Germany (2014)

  12. Vidmar B.J., Shaw S.W., Feeny B.F., Geist B.K.: Nonlinear interactionsin systems of multiple order centrifugal pendulum vibration absorbers. J. Vib. Acoust. 135, 061012 (2013)

    Article  Google Scholar 

  13. Nester, T.M.; Haddow, A.G.; Shaw, S.W.: Experimental investigation of a system with multiple nearly identical centrifugal pendulum vibration absorbers. In: Proceedings of DETC’03, ASME 2003 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Chicago, Illinois USA, September 2–6 (2003)

  14. Strogatz, S.H.: Sync: The Emerging Science of Spontaneous Order. Hyperion, New York (2003)

  15. Golubitsky M., Stewart I., Schaeffer D.G.: Singularities and Groups in Bifurcation Theory, vol. 2. Springer, New York (1988)

    Book  Google Scholar 

  16. Guckenheimer J., Holmes P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, New York (1983)

    Book  MATH  Google Scholar 

  17. Olson B.J., Shaw S.W., Shi C., Pierre C.: Circulant matrices and their application to vibration analysis. Appl. Mech. Rev. 66(4), 040803-1-41 (2014)

    Article  Google Scholar 

  18. Issa, J.; Shaw, S.W.: Bifurcation analysis of rotating systems with multiple centrifugal pendulum vibration absorbers. Preprint, IME Department, School of Engineering, Lebanese American University, Lebanon (2014)

  19. Alsuwaiyan, A.S.: Performance, Stability and Localization of Systems of Vibration Absorbers. Ph.D. thesis, Michigan State University, East Lansing (1999)

  20. Lee, C.T.; Shaw, S.W.: A comparative study of nonlinear centrifugal pendulum vibration absorbers. Nonlinear Stoch. Dyn. ASME AMD 192/DE 78, 91–98 (1994)

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Authors and Affiliations

  1. Department of Mechanical Engineering, Unayzah College of Engineering, Qassim University, Unayzah, 51911, Saudi Arabia

    Abdullah S. Alsuwaiyan

  2. Department of Mechanical Engineering, Michigan State University, East Lansing, MI, 48824-1226, USA

    Steven W. Shaw

Authors
  1. Abdullah S. Alsuwaiyan
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  2. Steven W. Shaw
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Correspondence to Abdullah S. Alsuwaiyan.

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Alsuwaiyan, A.S., Shaw, S.W. Non-synchronous and Localized Responses of Systems of Identical Centrifugal Pendulum Vibration Absorbers. Arab J Sci Eng 39, 9205–9217 (2014). https://doi.org/10.1007/s13369-014-1464-1

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  • DOI: https://doi.org/10.1007/s13369-014-1464-1

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