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TECHNICAL PAPERS: Gas Turbines: Structures and Dynamics

A New Method for Dynamic Analysis of Mistuned Bladed Disks Based on the Exact Relationship Between Tuned and Mistuned Systems

[+] Author and Article Information
E. P. Petrov, D. J. Ewins

Imperial College of Science, Technology and Medicine, Center of Vibration Engineering, Mechanical Engineering Department, Exhibition Road, London, SW7 2BX, UK

K. Y. Sanliturk

Faculty of Mechanical Engineering, Istanbul Technical University, 80191 Gumussuyu, Istanbul, Turkey

J. Eng. Gas Turbines Power 124(3), 586-597 (Jun 19, 2002) (12 pages) doi:10.1115/1.1451753 History: Received February 01, 2000; Revised September 01, 2001; Online June 19, 2002
Copyright © 2002 by ASME
Topics: Disks , Manufacturing
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References

Dye,  R. C. F., and Henry,  T. A., 1969, “Vibration Amplitudes of Compressor Blades Resulting From Scatter in Blade Natural Frequencies,” ASME J. Eng. Gas Turbines Power, 91, pp. 182–188.
Ewins,  D. J., 1969, “Effect of Detuning Upon the Forced Vibration of Bladed Disks,” J. Sound Vib., 9, No. 1, pp. 65–79.
Whitehead,  D. S., 1966, “Effect of Mistuning on the Vibration of Turbomachines Induced by Wakes,” J. Mech. Eng. Sci., 8, No. 1, pp. 15–21.
Ewins, D. J., 1991, “The Effects of Blade Mistuning on Vibration Response–A Survey,” IFToMM 4th International Conference on Rotordynamics, Prague, Czechoslovakia.
Slater,  J. C., Minkiewicz,  G. R., and Blair,  A. J., 1999, “Forced Response of Bladed Disk Assemblies—A Survey,” Shock Vib. Dig., 31, No. 1.
Ewins,  D. J., 1973, “Vibration Characteristics of Bladed Disk Assemblies,” J. Mech. Eng. Sci., 15, No. 3, pp. 165–186.
Ewins,  D. J., and Han,  Z. C., 1984, “Resonant Vibration Levels of a Mistuned Bladed Disk,” ASME J. Vib. Acoust., Stress, Reliab. Des. 106, pp. 211–217.
Muszynska,  A., and Jones,  D. I. G., 1983, “A Parametric Study of Dynamic Response of Discrete Model of Turbomachinery Bladed Disk,” ASME J. Vib. Acoust., Stress, Reliab. Des. 105, pp. 434–443.
Sanliturk, K. Y., and Imregun, M., 1992, “Statistical Analysis of Random Mistuning of Bladed Assemblies,” IMechE Proceedings of the International Conference on Vibrations in Rotating Machinery, University of Bath, UK, IMechE, London, C432/110, pp. 51–58.
Sanliturk,  K. Y., and Imregun,  M., 1994, “Vibration Analysis of Mistuned Bladed-Disk Assemblies-Inverse Approach,” AIAA J., 32, No. 4, pp. 865–875.
Gu, J., and Gao, H., 1987, “Vibration Characteristics of Well-Modelled Mistuned Bladed Disk,” Vibrations of Bladed Disk Assemblies, ASME, New York, pp. 55–59.
Irretier, H., 1983, “Spectral Analysis of Mistuned Bladed Disks by Component Mode Synthesis,” Vibrations of Bladed Disk Assemblies, ASME, New York, pp. 115–125.
Rzadkowski,  R., 1994, “The General Model of Free Vibration of Mistuned Bladed Disks. Part I: Theory, Part II: Numerical Results,” J. Sound Vib., 173, No. 3, pp. 377–393, 173, 395–413.
Petrov, E. P., 1993, “Large-Scale Finite Element Models of Blade-Shroud and Blade-Disk Joints and Condensation Technique for Vibration Analysis of Turbomachine Impellers,” Proc. of the 7th World Congress on Finite Element Methods: “FEM-Today and the Future,” Monte Carlo, Monaco, pp. 507–513.
Petrov, E. P., 1994, “Analysis and Optimal Control of Stress Amplitudes Upon Forced Vibration of Turbomachine Impellers With Mistuning,” Proc. of the IUTAM Symposium: “The Active Control of Vibration,” Bath, UK, pp. 189–196.
Bladh, R., Castanier, M. P., and Pierre, C., 1998, “Reduced Order Modelling and Vibration Analysis of Mistuned Bladed Disk Assemblies With Shrouds,” ASME Paper 98-GT-484.
Castanier,  M. P., Óttarsson,  G., and Pierre,  C., 1997, “Reduced Order Modelling Technique for Mistuned Bladed Disks,” ASME J. Vibr. Acoust., 119, pp. 439–447.
Kruse, M. J., Pierre, C., 1997, “An Experimental Investigation of Vibration Localization in Bladed Disks, Part 1: Free Response,” ASME Paper 97-GT-501.
Frey, K. K., 1998, “Correlation of Reduced Order Model for the Prediction of a Mistuned Bladed Disk Response,” 3rd National Turbine Engine High Cycle Fatigue Conference, San Antonio, USA.
Yang, M.-T., and Griffin, J. H., 1999, “A Reduced Order Model of Mistuning Using a Subset of Nominal System Modes,” ASME Paper 99-GT-288.
Sherman,  J., and Morrison,  W. J., 1949, “Adjustment of an Inverse Matrix Corresponding to Changes in the Elements of a Given Column or a Given Row of the Original Matrix,” Ann. Math. Stat., 20, p. 621.
Woodbury, M., 1950, “Inverting Modified Matrices,” Memorandum Report 42, Statistical Research Group, Princeton University, Princeton, NJ.
Level,  P., Moraux,  D., Drazetic,  P., and Tison,  T., 1996, “On a Direct Inversion of the Impedance Matrix in Response Reanalysis,” Commun. Numer. Meth. Eng. 12, pp. 151–159.
Sanliturk, K. Y., Ewins D. J., and Stanbridge A. B, 1999, “Underplatform Dampers for Turbine Blades: Theoretical Modelling, Analysis and Comparison With Experimental Data,” ASME Paper 99-GT-335.
Sanliturk, K. Y., Ewins D. J., Elliott, R., and Green, J. S., 1999, “Friction Damper Optimization: Simulation of Rainbow Tests” ASME Paper 99-GT-336.
Juravleva, A. M., and Petrov, E. P., 1981, “The Method for Forced Vibration Calculation of Cyclically Symmetric Structures,” Dynamics and Strength of Machines, Kharkov, No. 33, pp. 66–74 (in Russian).
Griffin,  J. H., and Hoosac,  T. M., 1984, “Model Development and Statistical Investigation of Turbine Blade Mistuning,” ASME J. Vib. Acoust., Stress, Reliab. Des. 106, pp. 204–210.
Hager,  W. W., 1989, “Updating the Inverse of a Matrix,” SIAM Rev., 31, No. 2, pp. 221–239.

Figures

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Forced response for each blade of the bladed disk. Excitation by 10EO, amplitudes at blade-shroud joint.
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Maximum error searched among all resonance peaks in the considered range in respect to number of modes included
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Distribution of amplitudes at resonance peaks excited by 2EO for the case when four nodes are included
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The case of excitation of 2EO: (a) maximum amplitudes at blade tip searched among all blades for mistuned and tuned bladed disks; (b) errors in their determination
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The case of excitation by 10EO: (a) maximum amplitudes at blade-shroud joint searched among all blades for mistuned and tuned bladed disks; (b) errors in their determination
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Normalized response at found resonance peaks and errors in their calculations for the case when 16 modes are included: (a) the case of excitation by 2EO; (b) the case of excitation by 10EO
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Engine order harmonics and natural frequencies in the frequency range analyzed
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Forced response for each blade of the bladed disk. Excitation by 2EO, amplitudes at blade tip.
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Maximum amplitudes for each of the blade assembly for different numbers of modes included: (a) excitation by 2EO, (b) excitation by 10EO
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Finite element model of a bladed disk
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A scheme of decomposing the mistuning matrix into multiplication of two matrices
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Various mistuning elements: 1) lumped mass; 2) stiffness between a node and ground; 3) damping between a node and ground; 4) stiffness between nodes of different blades; 5) damping between nodes of different blades; 6) stiffness between nodes of the same blade
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A relationship between the mistuning coefficient and frequency mistuning
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Maximum amplitudes searched among analyzed nodes of all blades for the bladed disk shown in Fig. 1. Inset—all natural frequencies of the bladed disk.
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Forced response for each blade of the bladed disk shown in Fig. 1
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Maximum amplitudes searched among analyzed nodes of all blades: (a) damping factor 0.003; (b)-damping factor 0.03
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Examples of the discrete harmonic function introduced

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