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Research Papers: Gas Turbines: Structures and Dynamics

A Comprehensive Procedure to Estimate the Probability of Extreme Vibration Levels Due to Mistuning

[+] Author and Article Information
Y.-J. Chan1

Department of Mechanical Engineering, Imperial College London, South Kensington, London SW7 2AZ, UKyj.chan@gmail.com

D. J. Ewins

Department of Mechanical Engineering, Imperial College London, South Kensington, London SW7 2AZ, UKd.ewins@imperial.ac.uk

1

Corresponding author.

J. Eng. Gas Turbines Power 132(11), 112505 (Aug 12, 2010) (8 pages) doi:10.1115/1.4001065 History: Received September 08, 2009; Revised October 13, 2009; Published August 12, 2010; Online August 12, 2010

A new procedure is developed to find the probabilities of extremely high amplification factors in mistuned bladed disk vibration levels, typical of events which occur rarely. While a rough estimate can be made by curve-fitting the distribution function generated in a Monte Carlo simulation, the procedure presented here can determine a much more accurate upper bound and the probabilities of amplification factors near to that bound. The procedure comprises an optimization analysis based on the conjugate gradient method and a stochastic simulation using the importance sampling method. Two examples are provided to illustrate the efficiency of the procedure, which can be 2 or 3 orders of magnitude more efficient than Monte Carlo simulations.

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Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Search paths of the steepest descent and the conjugate gradient methods on a 2D plane

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Figure 2

Schematic diagram of the 6DOF cyclic lumped parameter system

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Figure 3

Comparison between the results from the steepest descent and the conjugate gradient methods on a 6DOF cyclic lumped parameter system

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Figure 4

Confidence intervals evaluated by using a DMC simulation (solid black lines) and importance sampling (the shaded area)

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Figure 5

Amplification factor distribution near the maximum amplification factor agrees with an inversed-Weibull distribution

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Figure 6

The 24-bladed blisk under investigation

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Figure 7

Performances of the steepest descent and the conjugate gradient methods on the 24-sector blisk model

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Figure 8

Amplification factor PDF, the highest value within DMC samples, and the maximum amplification factor found in an optimization analysis

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Figure 9

Mistuning patterns of group A. The part of mistuning pattern observed in Fig. 1 is marked in the dash-line box.

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Figure 10

Existence of four local optima (A, B, C, and D) in a 24-sector blisk design (blade 1 is the worst blade) by observing a part of the 30 optimized mistuning patterns

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Figure 11

Confidence intervals of a DMC simulation (+) and the new procedure (×)

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Figure 12

Efficiency of the new procedure over DMC simulations

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