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Research Papers

Robust Analysis of Design in Vibration of Turbomachines

[+] Author and Article Information
Moustapha Mbaye

Laboratoire de Modélisation et Simulation Multi Echelle,
Université Paris-Est,
MSME UMR 8208 CNRS,
5 bd Descartes,
77454 Marne-la-Vallée, France;
Turbomeca - Safran Group,
64511 Bordes, France
e-mail: moustapha.mbaye@univ-paris-est.fr

Christian Soize

Laboratoire de Modélisation et Simulation Multi Echelle,
Université Paris-Est,
MSME UMR 8208 CNRS,
5 bd Descartes,
77454 Marne-la-Vallée, France
e-mail: christian.soize@univ-paris-est.fr

Jean-Philippe Ousty

Turbomeca - Safran Group,
64511 Bordes, France
e-mail: jean-philippe.ousty@turbomeca.fr

Evangeline Capiez-Lernout

Laboratoire de Modélisation et Simulation Multi Echelle,
Université Paris-Est,
MSME UMR 8208 CNRS,
5 bd Descartes,
77454 Marne-la-Vallée, France
e-mail: evangeline.capiezlernout@univ-paris-est.fr

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the Journal of Turbomachinery. Manuscript received September 8, 2010; final manuscript received April 14, 2012; published online November 1, 2012. Assoc. Editor: Matthew Montgomery.

J. Turbomach 135(2), 021008 (Nov 01, 2012) (8 pages) Paper No: TURBO-10-1163; doi: 10.1115/1.4007442 History: Received September 08, 2010; Revised April 14, 2012

In the context of turbomachinery design, a small variation in the blade characteristics due to manufacturing tolerances can affect the structural symmetry creating mistuning which increases the forced response. However, it is possible to detune the mistuned system in order to reduce the forced response amplification. The main technological methods to introduce detuning are based on modifying either the blade material properties, either the interface between blades and disk, or the blade shapes. This paper presents a robustness analysis of mistuning for a given detuning in blade geometry. Detuning is performed by modifying blade shapes. The different types of blades, obtained by those modifications, are then distributed on the disk circumference. A new reduced-order model of the detuned disk is introduced. It is based on the use of the cyclic modes of the different sectors which can be obtained from a usual cyclic symmetry modal analysis. Finally, the robustness of the computational model responses with respect to uncertainties, is performed with a stochastic analysis using a nonparametric probabilistic approach of uncertainties which allows both the system-parameter uncertainties and the modeling errors to be taken into account.

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Figures

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Fig. 1

Finite element models of blades: a reference blade (a) and geometrically modified blades (b)–(e)

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Fig. 2

Complete intentionally detuned bladed disk with arbitrary geometric modifications of four blades

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Fig. 3

Forced responses of the 23 blades to an engine order excitation which is 9 and for the frequency band [4150, 4550] Hz: Full model (left) and reduced-order model (right)

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Fig. 4

Reference blade shape (a) and modified blade shape (b)

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Fig. 5

Comparison of the Mach field on reference and modified blades

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Fig. 6

Second-order mean convergence of B∞ with mistuning: the curves, from the lower to the upper, correspond to a Monte Carlo simulation with 1000 realizations and for δK=0.005,0.01,0.1,0.02,0.07,0.06,0.05,0.04, and 0.03

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Fig. 7

Influence of the mistuning rate: graph such that P(B∞≤Bp)=p. The lower, middle and upper curves correspond to a probability level of p = 0.50, 0.95, and 0.99.

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Fig. 8

Second-order mean convergence of B∞ with mistuning and detuning: the curves, from the lower to the upper, correspond to a Monte Carlo simulation with 600 realizations and for δK=0.005,0.01,0.01,0.03,0.04,0.05,0.1,0.06, and 0.07

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Fig. 9

Influence of the mistuning rate: graph such that P(B∞≤Bp)=p. The solid curves with circles (and the dashed curves with triangles) are related to the tuned (and to the detuned) system. The lower, middle and upper curves correspond, respectively, to a probability level p = 0.50, 0.95, and 0.99.

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