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Nonlinear Dynamics

, Volume 70, Issue 1, pp 435–451 | Cite as

Modeling and dynamic analysis of a magnetically actuated butterfly valve

  • C. A. Kitio Kwuimy
  • C. NatarajEmail author
Original Paper

Abstract

In this work, a magnetically actuated butterfly valve is considered and a novel and accurate mathematical model is derived. The equilibrium of the system is investigated and the effects of the inlet velocity and direct current voltage (DC) on the stable rotation angle of the valve are presented. Considering a time periodic perturbation arising from electric circuit, the effects of the operating angle, inlet velocity, and driving parameters on the periodic and chaotic dynamics of the system are investigated. It is observed that, for an opening angle less than the cut-off angle, there exists a unique DC voltage for a stable equilibrium. The stability of this equilibrium depends nonlinearly on the inlet velocity and the seating torque. An expression is derived for the threshold value for the stability of the valve. Under periodic voltage, the inlet velocity and stable angle induce a backward shift on the resonant frequency, and jump phenomena and subharmonics are observed for some values of the driving amplitude. The highest amplitudes of vibration are detected for a fully open valve, for an almost closed valve, and for a valve with large inlet velocity. Using bifurcation diagrams and Lyapunov exponents, it is shown that the system exhibits a route to chaos with windows of period doubling and unbounded motion. Some guidance for design of magnetically actuated butterfly valves is proposed as well as recommendations for future work.

Keywords

Butterfly valve Electromagnetic actuation Stability Periodic motion Bifurcations Chaos 

Notes

Acknowledgements

This work is supported by the US Office of Naval Research under the grant ONR N00014-08-1-0435. Thanks are due to Mr. Anthony Seman III of ONR and Dr. Stephen Mastro of NAVSEA, Philadelphia. CAKK thanks Peiman Naseradinmousavi for illuminating discussions.

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Center for Nonlinear Dynamics and Control, Department of Mechanical EngineeringVillanova UniversityVillanovaUSA

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