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TECHNICAL PAPERS: Gas Turbines: Structures and Dynamics

Blade Manufacturing Tolerances Definition for a Mistuned Industrial Bladed Disk

[+] Author and Article Information
E. Capiez-Lernout, C. Soize

Laboratory of Engineering Mechanics, University of Marne La Vallée, 5, Bd Descartes, 77454 Marne-la-Vallée Cedex, 02, France

J.-P. Lombard, C. Dupont

Snecma Moteurs, Site de Villaroche, 77550 Moissy Cramayel, France

E. Seinturier

Turbomeca—Snecma Group, Site de Bordes, 64511 Bordes Cedex, Francee-mail: eric.seinturier@turbomeca.fr

J. Eng. Gas Turbines Power 127(3), 621-628 (Jun 24, 2005) (8 pages) doi:10.1115/1.1850497 History: Received October 01, 2003; Revised March 01, 2004; Online June 24, 2005
Copyright © 2005 by ASME
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References

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Ohayon, R., and Soize, C., 1998, Structural Acoustics and Vibration, Academic Press, San Diego, CA.
Whitehead,  D., 1966, “Effects of Mistuning on the Vibration of Turbomachine Blades Induced by Wakes,” J. Mech. Eng. Sci., 8, pp. 15–21.
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Lin,  C.-C., and Mignolet,  M., 1997, “An Adaptative Perturbation Scheme for the Analysis of Mistuned Bladed Disks,” ASME J. Eng. Gas Turbines Power, 119, pp. 153–160.
Mignolet,  M., Lin,  C.-C., and LaBorde,  B., 2001, “A Novel Limit Distribution for the Analysis of Randomly Mistuned Bladed Disks,” ASME J. Eng. Gas Turbines Power, 123, pp. 388–394.
Griffin,  J., and Hoosac,  T., 1984, “Model Development and Statistical Investigation of Turbine Blade Mistuning,” ASME J. Vib., Acoust., Stress, Reliab. Des., 106, pp. 204–210.
Sinha,  A., and Chen,  S., 1989, “A Higher Order to Compute the Statistics of Forced Response of a Mistuned Bladed Disk Assembly,” J. Sound Vib., 2, pp. 207–221.
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Castanier,  M., Ottarson,  G., and Pierre,  C., 1997, “A Reduced Order Modeling Technique for Mistuned Bladed Disks,” ASME J. Vibr. Acoust., 119, pp. 439–447.
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Seinturier, E., Dupont, C., Berthillier, M., and Dumas, M., 2002, “A New Aeroelastic Model for Mistuned Bladed Disks,” AIAA Paper No. 2002-1533.
Soize,  C., 2000, “A Nonparametric Model of Random Uncertainties for Reduced Matrix Models in Structural Dynamics,” Probab. Eng. Mech., 15, pp. 277–294.
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Capiez-Lernout, E., and Soize, C., 2003, “Specifying Manufacturing Tolerances for a Given Amplification Factor: A Nonparametric Probabilistic Methodology,” in American Society of Mechanical Engineers, International Gas Turbine Institute, Turbo Expo (Publication) IGTI, Vol. 4, pp. 183–194.
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Seinturier, E., Lombard, J.-P., Berthillier, M., and Sgarzi, O., 2002, “Turbine Mistuned Forced Response Prediction Comparison With Experimental Results,” in American Society of Mechanical Engineers, International Gas Turbine Institute, Turbo Expo (Publication) IGTI, Vol. 4, pp. 943–952.
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Figures

Grahic Jump Location
Finite element mesh for the 22 blades fan stage
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Graph of the eigenfrequencies with respect to the circumferential wave number for the tuned structure
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Graph of function ns↦Conv2(ns,nd,nb) related to the stochastic dynamic equation with δMjDj=0 and δKj=0.05 and for nd=10 and nb=20
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Graph of function nb↦Conv2(300,nd,nb) for nd=10 (black solid line), for nd=7 (gray solid line), for nd=5 (black dashed–dotted line), for nd=4 (gray dashed–dotted line), for nd=3 (black dotted line), and for nd=2 (gray dotted line), related to the stochastic dynamic equation with δMjDj=0 and δKj=0.05
Grahic Jump Location
Mesh of the nominal blade and definition of three section profiles
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Geometrical parameters of the tolerances: section Sk of the nominal blade (thick dashed-line) and of the manufactured blade (thick solid line). Location of the trailing edge (gray filled zone) with respect to the tolerances specifications.
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Section profiles for a realization of the manufactured blade with a zoom 20× (gray filled thin line) and for the nominal blade (thick line)
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Convergence with respect to the number ns of realizations: graph of function ns↦δ̃K(ns) for dLmin=−0.55 mm,dLmax=0.75 mm,αmax=−αmin=0.55 deg
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Convergence with respect to the number ns of realizations: graph of function ns↦δ̃M(ns) for dLmin=−0.55 mm,dLmax=0.75 mm,αmax=−αmin=0.55 deg
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Graph of the probability density function b↦pB(b) for dLmin=−0.55 mm and dLmax=0.75 mm,αmax=−αmin=0 deg
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Graph of the probability density function b↦pB(b) for dLmin=−0.55 mm and dLmax=0.75 mm,αmax=−αmin=0.35 deg
Grahic Jump Location
Graph of the probability density function b↦pB(b) for dLmin=−0.55 mm and dLmax=0.75 mm,αmax=−αmin=0.55 deg
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Graph of αmax↦P(B>b) for several values of b=1.2 (black solid line), b=1.3 (gray solid line), b=1.4 (black dashed–dotted line), b=1.5 (gray dashed–dotted line), b=1.6 (black dotted line), and b=1.7 (gray dotted line)

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