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Research Papers: Gas Turbines: Structures and Dynamics

On the Interaction of Multiple Traveling Wave Modes in the Flutter Vibrations of Friction-Damped Tuned Bladed Disks

[+] Author and Article Information
Malte Krack

Institute of Aircraft Propulsion Systems,
University of Stuttgart,
Stuttgart 70569, Germany
e-mail: malte.krack@ila.uni-stuttgart.de

Lars Panning-von Scheidt

Institute of Dynamics and Vibration Research,
Leibniz Universität Hannover,
Hannover 30167, Germany
e-mail: panning@ids.uni-hannover.de

Jörg Wallaschek

Institute of Dynamics and Vibration Research,
Leibniz Universität Hannover,
Hannover 30167, Germany
e-mail: wallaschek@ids.uni-hannover.de

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 August 10, 2016; final manuscript received August 12, 2016; published online October 18, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 139(4), 042501 (Oct 18, 2016) (9 pages) Paper No: GTP-16-1403; doi: 10.1115/1.4034650 History: Received August 10, 2016; Revised August 12, 2016

It is well-known that flutter vibrations of bladed disks can be saturated by dry friction. Previous theoretical investigations indicated that the steady-state, friction-damped flutter vibrations of tuned bladed disks are always dominated by a single traveling wave component, even if multiple traveling wave forms are unstable. This contrasts recent experimental investigations where multiple traveling wave forms were found to participate at steady state. In this paper, we demonstrate that this phenomenon can be explained by nonlinear frictional interblade coupling. To this end, we consider a simple phenomenological model of a bladed disk with frictional intersector coupling and two unstable traveling waves forms. Vibrations occur not only in the form of limit cycle oscillations (periodic) but also in the form of limit torus oscillations (quasi-periodic). It is shown how the limit state depends on the initial conditions, and that the occurrence of multiwave flutter depends on the proximity of the complex eigenvalues of the associated unstable waves. Finally, by computing the limit torus oscillation with a frequency-domain method, we lay the cornerstone for the systematic prediction of friction-saturated flutter vibrations of state-of-the-art bladed disk models.

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Figures

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Fig. 1

Phenomenological model of an aeroelastically unstable, friction-damped bladed disk: (a) topology of the system consisting of seven identical sectors and (b) mechanical model of the reference sector; mechanical parameters: m = 1, k = 1, kt=0.5, and μN=1

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Fig. 2

Modal frequencies and damping ratios of the linearized aeroelastic system for three different cases: (a) case with one unstable wave number, (b) case A with two unstable wave numbers, and (c) case B with two unstable wave numbers

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Fig. 3

Time histories for different initial energies in the unstable ND2− mode: left—reference sector displacement, right—magnitude of traveling wave coordinates, top—small initial energy (|   twU2|=0.02), center—moderate initial energy (|   twU2|=23), and bottom—large initial energy (|   twU2|=230)

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Fig. 4

Basins of attraction of the two different limit cycles forcase A: ω2=1.5, D2=−5.5%, (ω3−ω2)/ω2=2%, and D3=−5.4%

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Fig. 5

Time histories for different initial energy distributions in the case of two unstable wave numbers (case A): left—reference sector displacement, right—magnitude of traveling wave coordinates, top—scenario ①, center—scenario ②, and bottom—scenario ③

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Fig. 6

Basins of attraction of the limit cycle and the limit torusfor case B: ω2=1.5, D2=−5.5%, (ω3−ω2)/ω2=1%, and D3=−5.4%

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Fig. 7

Time histories for different initial energy distributions in the case of two unstable wave numbers (case B): left—reference sector displacement, right—magnitude of traveling wave coordinates, top—scenario ⑤, center—scenario ⑥, and bottom—scenario ⑦

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Fig. 8

Limit torus: (a) trajectory (black) with Poincaré section (green), (b) Poincaré map, and (c) trajectory (red) with approximated invariant torus; ω2=1.5, D2=−5.5%, (ω3−ω2)/ω2=0.5%, and D3=−5.4%

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Fig. 9

Illustration of the harmonic selection rules

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Fig. 10

Convergence with respect to the number of considered harmonics

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