0
Research Papers: Gas Turbines: Structures and Dynamics

Forced Response Analysis of High-Mode Vibrations for Mistuned Bladed Disks With Effective Reduced-Order Models

[+] Author and Article Information
Yongliang Duan

College of Energy and Power Engineering,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: tracy_duan@nuaa.edu.cn

Chaoping Zang

College of Energy and Power Engineering,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: c.zang@nuaa.edu.cn

E. P. Petrov

School of Engineering and Informatics,
University of Sussex,
Brighton BN1 9QT, UK
e-mail: y.petrov@sussex.ac.uk

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received April 1, 2016; final manuscript received April 27, 2016; published online June 1, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 138(11), 112502 (Jun 01, 2016) (12 pages) Paper No: GTP-16-1120; doi: 10.1115/1.4033513 History: Received April 01, 2016; Revised April 27, 2016

This paper is focused on the analysis of effects of mistuning on the forced response of gas turbine engine bladed disks vibrating in the frequency ranges corresponding to higher modes. For high modes considered here, the blade aerofoils are deformed during vibrations and the blade mode shapes differ significantly from beam mode shapes. A model reduction technique is developed for the computationally efficient and accurate analysis of forced response for bladed disks vibrating in high-frequency ranges. The high-fidelity finite element (FE) model of a tuned bladed disk sector is used to provide primary information about dynamic properties of a bladed disk, and the blade mistuning is modeled by specially defined mistuning matrices. The forced response displacement and stress amplitude levels are studied. The effects of different types of mistuning are examined, and the existence of high amplifications of mistuned forced response levels is shown for high-mode vibrations: in some cases, the resonance peak response of a tuned structure can be lower than out-of-resonance amplitudes of its mistuned counterpart.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Castanier, M. P. , and Pierre, C. , 2006, “ Modeling and Analysis of Mistuned Bladed Disc Vibration: Status and Emerging Directions,” J. Propul. Power, 22(2), pp. 384–396. [CrossRef]
Zang, C. , and Lan, H. , 2011, “ Advances in Research Vibration Problem of Mistuned Bladed Blisk Assemblies,” Adv. Aeronaut. Sci. Eng., 2(2), pp. 133–142.
Ewins, D. J. , 1969, “ The Effects of Detuning Upon the Forced Vibrations of Bladed Discs,” J. Sound Vib., 9(1), pp. 65–79. [CrossRef]
Srinivasan, A. V. , 1997, “ Flutter and Resonant Vibration Characteristics of Engine Blades,” ASME J. Eng. Gas Turbines Power, 119(4), pp. 742–775. [CrossRef]
Slater, J. C. , Minkiewicz, G. R. , and Blair, A. J. , 1999, “ Forced Response of Bladed Disc Assemblies—A Survey,” Shock Vib. Dig., 31(1), pp. 17–24. [CrossRef]
Whitehead, D. S. , 1998, “ The Maximum Factor by Which Forced Vibration of Blades Can Increase Due to Mistuning,” ASME J. Eng. Gas Turbines Power, 120(1), pp. 115–119. [CrossRef]
Petrov, E. , and Ewins, D. , 2003, “ Analysis of the Worst Mistuning Patterns in Bladed Disc Assemblies,” ASME J. Turbomach., 125(4), pp. 623–631. [CrossRef]
Pierre, C. , 1988, “ Mode Localization and Eigenvalue Loci Veering Phenomena in Disordered Structures,” J. Sound Vib., 126(3), pp. 485–502. [CrossRef]
Griffin, J. H. , and Hoosac, T. M. , 1984, “ Model Development and Statistical Investigation of Turbine Blade Mistuning,” J. Vib. Acoust. Stress Reliab. Des., 106(2), pp. 204–210. [CrossRef]
Ewins, D. J. , 1973, “ Vibration Characteristics of Bladed Disc Assemblies,” J. Mech. Eng. Sci., 15(3), pp. 165–186. [CrossRef]
Kuang, J. H. , and Huang, B. W. , 1999, “ Mode Localization of a Cracked Bladed Disc,” ASME J. Eng. Gas Turbines Power, 121(2), pp. 335–341. [CrossRef]
Castanier, M. P. , Ottarsson, G. , and Pierre, C. , 1997, “ A Reduced Order Modeling Technique for Mistuned Bladed Discs,” ASME J. Vib. Acoust., 119(3), pp. 439–447. [CrossRef]
Bladh, R. , Castanier, M. P. , and Pierre, C. , 2001, “ Component-Mode-Based Reduced Order Modeling Technique for Mistuned Bladed Discs—Part 1: Theoretical models,” ASME J. Eng. Gas Turbines Power, 123(1), pp. 89–99. [CrossRef]
Lim, S. , Bladh, R. , Castanier, M. P. , and Pierre, C. , 2007, “ Compact Generalized Component Mode Mistuning Representation for Modeling Bladed Disc Vibration,” AIAA J., pp. 2286–2298.
Yang, M. T. , and Griffin, J. H. , 2001, “ A Reduced Order Model of Mistuning Using a Subset of Nominal System Modes,” ASME J. Eng. Gas Turbines Power, 123(4), pp. 893–900. [CrossRef]
Feiner, D. M. , and Griffin, J. H. , 2002, “ A Fundamental Model of Mistuning for a Single Family of Modes,” ASME J. Turbomach., 124(4), pp. 586–597. [CrossRef]
Moyroud, F. , Fransson, T. , and Jacquet-Richardet, G. , 2002, “ A Comparison of Two Finite Element Reduction Techniques for Mistuned Bladed Discs,” ASME J. Eng. Gas Turbines Power, 124(4), pp. 942–952. [CrossRef]
Petrov, E. P. , Sanliturk, K. Y. , and Ewins, D. J. , 2002, “ A New Method for Dynamic Analysis of Mistuned Bladed Discs Based on the Exact Relationship Between Tuned and Mistuned Systems,” ASME J. Eng. Gas Turbines Power, 124(3), pp. 586–594. [CrossRef]
Bhartiya, Y. , and Sinha, A. , 2012, “ Reduced Order Model of a Multistage Bladed Rotor With Geometric Mistuning Via Modal Analyses of Finite Element Sectors,” ASME J. Turbomach., 134(4), p. 041001. [CrossRef]
Beck, J. , Brown, J. , Cross, C. , and, Slater, J. , 2014, “ Component-Mode Reduced-Order Models for Geometric Mistuning of Integrally Bladed Rotors,” AIAA J., 52(7), pp. 1345–1356. [CrossRef]
Ewins, D. J. , 2010, “ Control of Vibration and Resonance in Aero Engines and Rotating Machinery—An Overview,” Int. J. Pressure Vessels Piping, 87(9), pp. 504–510. [CrossRef]
Williams, F. W. , 1986, “ An Algorithm for Exact Eigenvalue Calculations for Rotationally Periodic Structures,” Int. J. Numer. Methods Eng., 23(4), pp. 609–622. [CrossRef]
Petrov, E. , 2010, “ A Method for Forced Response Analysis of Mistuned Bladed Discs With Aerodynamic Effects Included,” ASME J. Eng. Gas Turbines Power, 132(6), p. 062502. [CrossRef]
Goodman, S. N. , 1999, “ Toward Evidence-Based Medical Statistics—2: The Bayes Factor,” Ann. Intern. Med., 130(12), pp. 1005–1013. [CrossRef] [PubMed]
Regina, N. , 2014, “ Scientific Method: Statistical Errors,” Nature, 506(7487), pp. 150–152. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

A tuned bladed disk: (a) a whole bladed disk and (b) a sector

Grahic Jump Location
Fig. 2

Selection of narrow frequency ranges for resonance response calculation

Grahic Jump Location
Fig. 3

Maximum resonance amplitudes for all the blades

Grahic Jump Location
Fig. 4

Natural frequencies of the tuned bladed disk

Grahic Jump Location
Fig. 5

Mode shapes of alone blade: (a) sixth mode, (b) seventh mode, and (c) eighth mode

Grahic Jump Location
Fig. 6

Mistuning element distributions: (a) applied to all the nodes, (b) uniform distribution along blade length, (c) linear distribution along blade length, and (d) based on mode shapes

Grahic Jump Location
Fig. 7

First 12 natural frequencies mistuning for different element distributions when the sixth mode has ± 5% frequency mistuning

Grahic Jump Location
Fig. 8

Results of the validation: (a) errors in natural frequency determination and (b) the maximum amplitudes

Grahic Jump Location
Fig. 9

Normalized forced response excited by 15EO: (a) bladed disk maximum response and (b) maximum blade amplitudes

Grahic Jump Location
Fig. 10

Normalized forced response excited by 6EO: (a) bladed disk maximum response and (b) maximum blade amplitudes

Grahic Jump Location
Fig. 11

Tuned modes contributions to maximum forced response of the mistuned system: (a) 15EO and (b) 6EO

Grahic Jump Location
Fig. 12

Von Mises stress distribution for 15EO: (a) a whole bladed disk and (b) a zoomed view of blades with highest stresses

Grahic Jump Location
Fig. 13

Von Mises stress distribution for 6EO: (a) a whole bladed disk and (b) a zoomed view of blades with highest stresses

Grahic Jump Location
Fig. 14

Stress and displacement amplification factors for each blade at maximum resonance: (a) 15EO and (b) 6EO

Grahic Jump Location
Fig. 15

Maximum normalized response for mistuned and tuned bladed disks excited by 15EO

Grahic Jump Location
Fig. 16

Maximum normalized response for mistuned and tuned bladed disks excited by 6EO

Grahic Jump Location
Fig. 17

Maximum normalized response for each blade in the frequency range excited by 15EO

Grahic Jump Location
Fig. 18

Maximum normalized response for each blade in the frequency range excited by 6EO

Grahic Jump Location
Fig. 19

Maximum forced response for mistuned and tuned bladed disks: (a) 2EO and (b) 7EO

Grahic Jump Location
Fig. 20

Maximum normalized response in different high-frequency ranges under different EO excitations

Grahic Jump Location
Fig. 21

Maximum forced response for mistuned and tuned bladed disks in other high modes: (a) 5EO and (b) 11EO

Grahic Jump Location
Fig. 22

Statistical distribution of amplification factors for different EOs: (a) 6EO and (b) 15EO

Grahic Jump Location
Fig. 23

Best-fit cumulative distribution function for normalized response under different EO excitations

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In