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Non-Linear Dynamics of a Simplified Model of an Overhung Rotor Subjected to Intermittent Annular Rubs

[+] Author Affiliations
Andrea Zilli, Robin J. Williams

Rolls-Royce plc., Derby, England, UK

David J. Ewins

University of Bristol, Bristol, England, UK

Paper No. GT2014-26826, pp. V07AT31A031; 13 pages
doi:10.1115/GT2014-26826
From:
  • ASME Turbo Expo 2014: Turbine Technical Conference and Exposition
  • Volume 7A: Structures and Dynamics
  • Düsseldorf, Germany, June 16–20, 2014
  • Conference Sponsors: International Gas Turbine Institute
  • ISBN: 978-0-7918-4576-9
  • Copyright © 2014 by Rolls-Royce plc

abstract

The dynamic forced response of a two-degrees-of-freedom model of an unbalanced overhung rotor with clearance and symmetric piecewise-linear stiffness is examined in the time domain. The stiffness nonlinearity is representative of the contact between the rotor and a concentric stator ring. This rubbing interaction comes as a result of the rotor transient motion initiated by the sudden application of a static unbalance, such as in a blade loss scenario. The focus of this study is on the range of rotor speeds above resonance, where the contact between rotor and stator is characterised by a “bouncing” or intermittent type of behaviour. Brute-force numerical bifurcation analysis on the long-term forced response revealed ranges of rotation frequency for which there is bi-stability between non-impacting synchronous equilibrium and impacting sub-synchronous motion. It is found that, for sufficiently high levels of transient energy in the rotor, there exists the possibility for the solution to jump into a stable limit cycle characterised by three non-harmonically related frequencies, namely the synchronous response frequency and the forward and backward whirl frequencies. A simple relationship defining the point of synchronisation between these three components is proposed as an explanation to the region of bi-stability detected. The stiffening effect induced by the contact non-linearity enables this synchronisation to be maintained over a range of forcing frequencies rather than just at the single condition determined from the nominal whirl mode frequencies.

Copyright © 2014 by Rolls-Royce plc

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