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TECHNICAL PAPERS: Gas Turbines: Structures and Dynamics

Dynamic Response Predictions for a Mistuned Industrial Turbomachinery Rotor Using Reduced-Order Modeling

[+] Author and Article Information
R. Bladh, C. Pierre

M. P. Castanier

Department of Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109-2125

M. J. Kruse

Honeywell Engines & Systems, Product Safety & Integrity, M/S 2101-121, Phoenix, AZ 85034-3440

J. Eng. Gas Turbines Power 124(2), 311-324 (Mar 26, 2002) (14 pages) doi:10.1115/1.1447236 History: Received October 01, 2000; Revised August 01, 2001; Online March 26, 2002
Copyright © 2002 by ASME
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References

Ewins,  D. J., 1969, “The Effects of Detuning Upon the Forced Vibrations of Bladed Disks,” J. Sound Vib., 9, pp. 65–79.
Ewins,  D. J., 1973, “Vibration Characteristics of Bladed Disc Assemblies,” J. Mech. Eng. Sci., 15, pp. 165–186.
Irretier, H., 1983, “Spectral Analysis of Mistuned Bladed Disk Assemblies by Component Mode Synthesis,” Vibrations of Bladed Disk Assemblies, ASME, New York, pp. 115–125.
Castanier,  M. P., Óttarsson,  G., and Pierre,  C., 1997, “A Reduced-Order Modeling Technique for Mistuned Bladed Disks,” ASME J. Vibr. Acoust., 119, pp. 439–447.
Kruse, M. J., and Pierre, C., 1996, “Forced Response of Mistuned Bladed Disks Using Reduced-Order Modeling,” Proc. 37th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conference, Vol. 4, AIAA, New York, pp. 1938–1950.
Bladh,  R., Castanier,  M. P., and Pierre,  C., 1999, “Reduced Order Modeling and Vibration Analysis of Mistuned Bladed Disk Assemblies with Shrouds,” ASME J. Eng. Gas Turbines Power, 121, pp. 515–522.
Yang,  M.-T., and Griffin,  J. H., 1997, “A Reduced Order Approach for the Vibration of Mistuned Bladed Disk Assemblies,” ASME J. Eng. Gas Turbines Power, 119, pp. 161–167.
Bladh,  R., Castanier,  M. P., and Pierre,  C., 2001, “Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks, Part I: Theoretical Models,” ASME J. Eng. Gas Turbines Power, 123, pp. 89–99.
Bladh,  R., Castanier,  M. P., and Pierre,  C., 2001, “Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks, Part II: Application,” ASME J. Eng. Gas Turbines Power, 123, pp. 100–108.
Moyroud, F., Jacquet-Richardet, G., and Fransson, T., 2000, “A Comparison of Two Finite Element Reduction Techniques for Mistuned Bladed-Disks,” Proc. 45th ASME Gas Turbine and Aeroengine Technical Congress, Exposition and Users Symposium, ASME, New York.
Yang, M.-T., and Griffin, J. H., 1999, “A Reduced Order Model of Mistuning Using A Subset of Nominal System Modes,” Proc. 44th ASME Gas Turbine and Aeroengine Technical Congress, Exposition and Users Symposium, ASME, New York.
Gumbel, E. J., 1958, Statistics of Extremes, Columbia University Press, New York.
Óttarsson, G. S., and Pierre, C., 1995, “On the Effects of Interblade Coupling on the Statistics of Maximum Forced Response Amplitudes in Mistuned Bladed Disks,” Proc. 36th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conference, Vol. 5, AIAA, New York, pp. 3070–3078, also, Journal of Sound and Vibration (in print).
Pierre,  C., 1988, “Mode Localization and Eigenvalue Loci Veering Phenomena in Disordered Structures,” J. Sound Vib., 126, pp. 485–502.
Mignolet,  M. P., and Lin,  C.-C., 1997, “Identification of Structural Parameters in Mistuned Bladed Disks,” ASME J. Vibr. Acoust., 119, pp. 428–438.
Wei,  S. T., and Pierre,  C., 1988, “Localization Phenomena in Mistuned Assemblies With Cyclic Symmetry, Part I: Free Vibrations; Part II: Forced Vibrations,” ASME J. Vibr. Acoust., Stress, Reliab. Des., 110, pp. 429–449.
Castanier, M. P., and Pierre, C., 1997, “Consideration on the Benefits of International Blade Mistuning for the Forced Response of Turbomachinery Rotors,” Proc. ASME International Mechanical Engineering Congress and Exposition, Vol. 55, ASME, New York, pp. 419–425.
Castanier, M. P., and Pierre, C., 1998, “Investigation of the Combined Effects of Intentional and Random Mistuning on the Forced Response of Bladed Disks,” Proc. 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, AIAA, New York.
Castillo, E., 1988, Extreme Value Theory in Engineering, Academic Press, San Diego, CA.
Whitehead,  D. S., 1966, “Effect of Mistuning on the Vibration of Turbomachine Blades Induced by Wakes,” J. Mech. Eng. Sci., 8, pp. 15–21.
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Figures

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Finite element meshes for the industrial 29-blade compressor rotor: (a) the full model; (b) the fundamental sector
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Employed component modes: (a) normal modes of a cantilevered blade; (b) cyclic modes for a fundamental disk-blade sector, where the blade is massless
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Natural frequencies versus number of nodal diameters for the tuned rotor by finite element and reduced-order modeling
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Comparison of tuned finite element and ROM four nodal diameter mode shapes (dominated by 1F motion)
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Comparison of tuned finite element and ROM one nodal diameter mode shapes (dominated by 2F motion). This mode is located in the investigated veering.
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Comparison of mistuned finite element and ROM mode shapes in the frequency region encompassing the 1F blade-dominated modes. The mode shape is spatially localized about blade number six.
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Comparison of mistuned finite element and ROM mode shapes in the frequency region encompassing the investigated veering. Motion is dominated by the 2F blade mode and is localized about blade number six.
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Comparison of tuned finite element and ROM forced responses, for blade tip excitation with C=4
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Comparison of mistuned finite element and ROM maximum blade forced responses, for blade tip excitation with C=4
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Comparison of tuned finite element and ROM forced responses, for blade tip excitation with C=1
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Comparison of mistuned finite element and ROM maximum blade forced responses, for blade tip excitation with C=1
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Histogram of the maximum blade response amplitudes for engine order one excitation. Obtained by Monte Carlo simulation of 1000 different mistuned systems with uniform distributions of zero mean and three percent standard deviation.
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Comparison of Weibull and Monte Carlo determined responses for 5th, 50th, and 95th percentiles of maximum blade response amplitude magnification. The approximate percentiles from the Weibull distributions conform well with the Monte Carlo percentiles.
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Comparison of Weibull estimates of the probability density function for several sets of 50 mistuning patterns each and the full set of 1000 mistuning patterns. The Weibull approximations based on the smaller sets conform well with the probability density function obtained with the full set.
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Variation in blade amplitude magnification factor with standard deviation of mistuning. Mistuned maximum principal stresses are as much as 86 percent higher than the tuned maximum principal stress.
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Definition of index notation
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Natural frequencies versus number of nodal diameters as a continuous variable
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Close-up view of intense frequency veering region in Fig. 17
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Finite difference approximation of curvature for mode sets 4 and 5
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Forced response statistical data for selected frequency veerings

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