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Research Papers

Detection of Cracks in Mistuned Bladed Disks Using Reduced-Order Models and Vibration Data

[+] Author and Article Information
Chulwoo Jung

e-mail: cwjung@umich.edu

Akira Saito

e-mail: asakira@umich.edu

Bogdan I. Epureanu

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

1Present address: Associate Researcher, Toyota Central Research and Development Laboratories, Inc., 41-1, Yokomichi, Nagakute, Aichi 480-1192, Japan.

2Corresponding author.

Contributed by Design Engineering Division of ASME for publication in the JOURNAL OF Vibration and Acoustics. Manuscript received March 29, 2011; final manuscript received June 16, 2012; published online October 29, 2012. Assoc. Editor: Jean Zu.

J. Vib. Acoust 134(6), 061010 (Oct 29, 2012) (10 pages) doi:10.1115/1.4007244 History: Received March 29, 2011; Revised June 16, 2012

A novel methodology to detect the presence of a crack and to predict the nonlinear forced response of mistuned turbine engine rotors with a cracked blade and mistuning is developed. The combined effects of the crack and mistuning are modeled. First, a hybrid-interface method based on component mode synthesis is employed to develop reduced-order models (ROMs) of the tuned system with a cracked blade. Constraint modes are added to model the displacements due to the intermittent contact between the crack surfaces. The degrees of freedom (DOFs) on the crack surfaces are retained as active DOFs so that the physical forces due to the contact/interaction (in the three-dimensional space) can be accurately modeled. Next, the presence of mistuning in the tuned system with a cracked blade is modeled. Component mode mistuning is used to account for mistuning present in the uncracked blades while the cracked blade is considered as a reference (with no mistuning). Next, the resulting (reduced-order) nonlinear equations of motion are solved by applying an alternating frequency/time-domain method. Using these efficient ROMs in a forced response analysis, it is found that the new modeling approach provides significant computational cost savings, while ensuring good accuracy relative to full-order finite element analyses. Furthermore, the effects of the cracked blade on the mistuned system are investigated and used to detect statistically the presence of a crack and to identify which blade of a full bladed disk is cracked. In particular, it is shown that cracks can be distinguished from mistuning.

Copyright © 2012 by ASME
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References

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Figures

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Fig. 1

Finite element model of the bladed disk

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Fig. 2

Comparison of nonlinear forced responses obtained in a previous study (prev) and those obtained using the proposed method (prop)

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Fig. 3

Linear and nonlinear forced responses obtained using the proposed method

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Fig. 4

Mode localization in the first mode family for two different mistuning patterns

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Fig. 5

Mode localization in the second mode family for two different mistuning patterns

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Fig. 6

Residual ∥Φ¯CMk-Φ¯Mk∥2 for k = 1, 2, and 10 for various mistuning levels in blade 1; (a) σ = 1%, (b) σ = 4%

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Fig. 7

Residuals Rfull,CM and Rfull,M when σ = 1%

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Fig. 8

Residuals Rfull,CM and Rfull,M when σ = 4%

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Fig. 9

Residuals Rfull,CM and Rfull,M for the tenth mode family; the residuals are sorted in increasing order

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Fig. 10

Maximum residuals Rfull,CM (over all modes in the tenth mode family) and Rred,CM (for all blades) for the tenth mode family

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Fig. 11

Maximum residuals Rfull,CM (over all modes in the tenth mode family) and Rred,CM (for all blades) for the tenth mode family with 1% measurement noise

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Fig. 12

Maximum residuals Rred,CM (over all modes in the tenth mode family) for all blades; ten realizations of 1% measurement noise were used; the maximum value obtained for Rfull,CM over all modes in the tenth mode family is showed on the left of blade 1 (and is marked as T on the horizontal axis)

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Fig. 13

Nonlinear forced response of the mistuned bladed disk with a cracked blade

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Fig. 14

Maximum residuals Rred,CM with 1% and 10% measurement noise using nonlinear forced response data for ten realizations of measurement noise; (a) 1% measurement noise, (b) 10% measurement noise

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Fig. 15

Forcing points used for traveling wave excitation

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Fig. 16

Residuals Rred,CM for mode g for ten realizations of measurement noise using nonlinear forced responses computed using different forcing points; (a) forcing applied at point 4, (b) forcing applied at point 6

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