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Research Papers: Gas Turbines: Structures and Dynamics

Asymptotic Description of Maximum Mistuning Amplification of Bladed Disk Forced Response

[+] Author and Article Information
Carlos Martel

ETSI Aeronáuticos, Universidad Politécnica de Madrid, 28040 Madrid, Spaincarlos.martel@upm.es

Roque Corral1

 Industria de Turbopropulsores S.A., 28830 Madrid, Spainroque.corral@itp.es

1

Associate Professor at ETSI Aeronáuticos, Universidad Politécnica de Madrid, 28040 Madrid, Spain.

J. Eng. Gas Turbines Power 131(2), 022506 (Dec 23, 2008) (10 pages) doi:10.1115/1.2968868 History: Received April 07, 2008; Revised April 09, 2008; Published December 23, 2008

The problem of determining the maximum forced response vibration amplification that can be produced just by the addition of a small mistuning to a perfectly cyclical bladed disk still remains not completely clear. In this paper we apply a recently introduced perturbation methodology, the asymptotic mistuning model (AMM), to determine which are the key ingredients of this amplification process and to evaluate the maximum mistuning amplification factor that a given modal family with a particular distribution of tuned frequencies can exhibit. A more accurate upper bound for the maximum forced response amplification of a mistuned bladed disk is obtained from this description, and the results of the AMM are validated numerically using a simple mass-spring model.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Tuned natural vibration frequencies versus number of nodal diameters for a bladed disk. IM: isolated mode; CM: clustered modes.

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Figure 2

Top: sketch of the simple 1DOF per sector system. Bottom: tuned frequencies versus number of nodal diameters (IM: forcing engine order 7; CM: forcing engine order 21).

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Figure 3

Isolated mode case: maximum attainable amplitude versus mistuning amplitude |D|

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Figure 4

Response of the system in Fig. 2 to a forcing with engine order 7 (tuned TW frequency ω0=1.3135,…) and mistuning pattern composed of a single harmonic with wavenumber 14 (AMM prediction for maximum response). Top left: displacements |xj| versus forcing frequency (max|xj|=1.2066,…). Middle left: mistuning distribution δj. Bottom left: amplitude of the Fourier modes of the mistuning distribution. Right: amplitude of the TW components of the response versus forcing frequency (wavenumber in the vertical axis).

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Figure 5

Same as in Fig. 4 but with the rest of the harmonics added to the mistuning pattern with random amplitudes (max|xj|=1.2085,…)

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Figure 6

Same as in Fig. 4 but for a mistuning pattern with zero harmonic with wavenumber 14 and the rest with random amplitudes (max|xj|=1.0069,…)

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Figure 7

Response of the system in Fig. 2 to a forcing with engine order 21 (tuned TW frequency ω0=2.1830,…) and mistuning pattern composed of only harmonics with wavenumbers 1–8 (AMM prediction for a maximum response). Top left: displacements |xj| versus forcing frequency (max|xj|=1.991,…). Middle left: mistuning distribution δj. Bottom left: amplitude of the Fourier modes of the mistuning distribution. Right: amplitude of the TW components of the response versus forcing frequency (wavenumber in the vertical axis).

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Figure 8

Same as in Fig. 7 but with the rest of the harmonics added to the mistuning pattern with random amplitudes (max|xj|=1.9851,…)

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Figure 9

Same as in Fig. 7 but for a mistuning pattern with zero harmonics with wavenumbers 1–8 and the rest with random amplitudes (max|xj|=1.0141,…)

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