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Design Innovation Paper

Nonlinear Dynamics of a Simplified Model of an Overhung Rotor Subjected to Intermittent Annular Rubs

[+] Author and Article Information
Andrea Zilli

Structural Systems Design,
Rolls-Royce plc,
P.O. Box 31,
Derby DE 24 8BJ, UK
e-mail: andrea.zilli@rolls-royce.com

Robin J. Williams

Design Systems Engineering,
Rolls-Royce plc,
P.O. Box 31,
Derby DE24 8BJ, UK
e-mail: robin.williams@rolls-royce.com

David J. Ewins

Professor
Faculty of Engineering,
University of Bristol,
University Walk,
Bristol BS8 1TR, UK
e-mail: d.ewins@bristol.ac.uk

1Corresponding author.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 28, 2014; final manuscript received August 22, 2014; published online December 9, 2014. Editor: David Wisler.

J. Eng. Gas Turbines Power 137(6), 065001 (Jun 01, 2015) (10 pages) Paper No: GTP-14-1444; doi: 10.1115/1.4028844 History: Received July 28, 2014; Revised August 22, 2014; Online December 09, 2014

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 characterized by a “bouncing” or intermittent type of behavior. Brute-force numerical bifurcation analysis on the long-term forced response revealed ranges of rotation frequency for which there is bistability between nonimpacting synchronous equilibrium and impacting subsynchronous 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 characterized by three nonharmonically related frequencies, namely, the synchronous response frequency and the forward and backward whirl frequencies. A simple relationship defining the point of synchronization between these three components is proposed as an explanation to the region of bistability detected. The stiffening effect induced by the contact nonlinearity enables this synchronization to be maintained over a range of forcing frequencies rather than just at the single condition determined from the nominal whirl mode frequencies.

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References

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Figures

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Fig. 1

Typical frequency response of a snubbed system

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Fig. 2

Normalized rotor radial displacement measured during rapid deceleration following rapid unbalance loading

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Fig. 3

Schematic of the mechanical model. (a) Balanced rotor. (b) Unbalanced rotor rubbing against retainer ring.

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Fig. 4

Brute-force bifurcation diagrams. Effect of rotor eccentricity.

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Fig. 5

Time series at different rotational frequency ratios. Same model parameters used for Fig. 4(b). (a) Synchronous response. (b) Stable bounce limit cycle.

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Fig. 6

Time series, orbit trajectories, phase portrait, Poincaré sections, and frequency spectrum at different rotational frequency ratios. Same model parameters used for Fig. 4(b). (a) Synchronous response. (b) Stable bounce limit cycle.

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Fig. 7

Effect of the level of gyroscopic coupling on the long-term dynamic response

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Fig. 8

Effect of the unbalance level on the extent of the bistability region. Results obtained from time domain simulation using slow frequency sweep.

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Fig. 9

Synchronization between synchronous, forward and backward orbits (phasors)

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Fig. 10

Campbell diagram and bifurcation diagram of Fig. 4(c). Synchronization condition between FW, BW, and synchronous frequencies.

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Fig. 11

Effect of deceleration rate on the long-term forced response. Rapid unbalance excitation (ε∧=0.353) at Ω∧=7 followed by rapid deceleration to Ω∧=3.4. Damping ζ = 0.01. Two deceleration rates used (a) dΩ∧/dτ=2.84. (b) dΩ∧/dτ=5.15.

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