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Research Papers

Effects of a Cracked Blade on Mistuned Turbine Engine Rotor Vibration

[+] Author and Article Information
Akira Saito

Department of Mechanical Engineering, University of Michigan, 2350 Hayward Street, Ann Arbor, MI 48109-2125asakira@umich.edu

Matthew P. Castanier1

Department of Mechanical Engineering, University of Michigan, 2350 Hayward Street, Ann Arbor, MI 48109-2125mpc@umich.edu

Christophe Pierre

Faculty of Engineering, McGill University, Montreal, QC, H3A 2K6, Canadachristophe.pierre@mcgill.ca

1

Corresponding author.

J. Vib. Acoust 131(6), 061006 (Nov 18, 2009) (9 pages) doi:10.1115/1.4000458 History: Received December 29, 2007; Revised May 03, 2009; Published November 18, 2009; Online November 18, 2009

An efficient methodology for predicting the nonlinear forced vibration response of a turbine engine rotor with a cracked blade is presented and used to investigate the effects of the damage on the forced response. The influence of small random blade-to-blade differences (mistuning) and rotation on the forced response are also considered. Starting with a finite element model, a hybrid-interface method of component mode synthesis (CMS) is employed to generate a reduced-order model (ROM). The crack surfaces are retained as physical degrees of freedom in the ROM so that the forces due to contact in three-dimensional space can be properly calculated. The resulting nonlinear equations of steady-state motion are solved by applying an alternating frequency/time-domain method, which is much more computationally efficient than traditional time integration. Using this reduced-order modeling and analysis framework, the effects of the cracked blade on the system response of an example rotor are investigated for various mistuning levels and rotation speeds. First, the advantages of the selected hybrid-interface CMS method are discussed and demonstrated. Then, the resonant frequency shift associated with the stiffness loss due to the crack and the vibration localization about the cracked blade are thoroughly investigated. In addition, the results of the nonlinear ROMs are compared with those obtained with linear ROMs, as well as blade-alone ROMs. It is shown that several key system vibration characteristics are not captured by the simpler models, but that some insight into the system response can be gained from the blade-alone response predictions. Furthermore, it is demonstrated that while the effects of the crack often appear similar to those of mistuning, the effects of mistuning and damage can be distinguished by observing and comparing the response across multiple families of system modes.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Finite element model of the blisk with a 37.5% cracked blade and healthy blade modes of interest

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Figure 2

Nonlinear frequency response of the blisk with a cracked blade subjected to engine order 2 excitation

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Figure 3

Averaged mode participation factor versus mode number: (a) Fixed-interface normal modes (Craig–Bampton method) and (b) free-interface normal modes (hybrid method)

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Figure 4

Frequency response of the bladed disk model with a cracked blade and the blade-alone models: (a) First blade-dominated mode family, (b) first mode of a blade alone, (c) tenth blade-dominated mode family, and (d) tenth mode of a blade alone

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Figure 5

Strongly localized modes in the first blade-dominated mode family, σ=0.01: (a) Cracked-blade-localized mode, 383.1 Hz and (b) healthy-blade-localized mode, 387.7 Hz

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Figure 6

Strongly localized modes in the tenth blade-dominated mode family, σ=0.01: (a) Cracked-blade-localized mode, 10.97 kHz, (b) cracked-blade-localized mode, 11.05 kHz, (c) healthy-blade-localized mode, 11.40 kHz, and (d) healthy-blade-localized mode, 11.44 kHz

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Figure 7

Forced response for the first blade-dominated mode family: (a) σ=0.01 and (b) σ=0.04

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Figure 8

Forced response for the tenth blade-dominated mode family: (a) σ=0.01 and (b) σ=0.04

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Figure 9

Crack opening due to rotation

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Figure 10

Campbell diagram plot for the first blade-dominated mode family

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Figure 11

Frequency response of the rotating, tuned blisk with a cracked blade for forcing amplitudes of 0.1 N and 0.5 N: (a) Engine order 7 and (b) engine order 10

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Figure 12

Frequency response of the rotating, mistuned (σ=0.04) blisk with a cracked blade for forcing amplitudes of 0.1 N and 0.5 N: (a) Engine order 7 and (b) engine order 10

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Figure 13

Frequency response of the rotating, mistuned (σ=0.04) blisk with a cracked blade for forcing amplitudes of 2.0 N and 10.0 N with engine order 64: (a) Tuned blisk with a cracked blade and (b) mistuned blisk with a cracked blade

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