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Research Papers

Reduced Order Models of Mistuned Cracked Bladed Disks

[+] Author and Article Information
Olguta Marinescu

Department of Manufacturing Science, Robotic and Welding, University Dunarea de Jos of Galati, 111 Domneasca Street, Galati 800201, Romaniaomarine@umich.edu

Bogdan I. Epureanu

Department of Mechanical Engineering, University of Michigan, 3138 G. G. Brown, 2350 Hayward Street, Ann Arbor, MI 48109-2125epureanu@umich.edu

Mihaela Banu

Department of Manufacturing Science, Robotic and Welding, University Dunarea de Jos of Galati, 111 Domneasca Street, Galati 800201, Romaniamihaela.banu@ugal.ro

J. Vib. Acoust 133(5), 051014 (Sep 20, 2011) (9 pages) doi:10.1115/1.4003940 History: Received June 15, 2010; Revised January 27, 2011; Published August 31, 2011; Online September 20, 2011

Predicting the influence of cracks on the dynamics of bladed disks is a very important challenge. Cracks change the structural response, which in turn changes the crack propagation characteristics. Hence, accurate and computationally effective means to model the dynamics of cracked bladed disks and blisks is particularly crucial in applications such as prognosis, guidance for repairs, characterization after repairs, design, and structural health monitoring. Most current models of bladed disks exploit cyclic symmetry to gain computational efficiency. However, the presence of cracks and mistuning destroys that symmetry and makes computational predictions much more expensive. In this work, we propose a new reduced order modeling methodology that can speed up computations by several orders of magnitude. There are two key components of the new methodology. First, the displacements and deformations of the crack surfaces are not modeled in absolute coordinates but relative coordinates, which allows for an effective model reduction based on (fixed-interface Craig–Bampton) component mode synthesis (CMS). The use of relative coordinates allows one to define one of the components in CMS as the pristine/uncracked structure (with mistuning). This approach is used in combination with a set of accurate approximations for the constraint modes used in CMS. Second, the effects of mistuning are captured by component mode mistuning, which allows the construction of extremely efficient reduced order models for the pristine/uncracked component with mistuning. The novel proposed method is applied to a finite element model of an industrial blisk. The combined presence of mistuning and cracks is shown to have important effects. Also, the proposed approach is shown to provide accurate predictions for the overall blisk while requiring computations using single-sector models only. The influence of various parameters on the accuracy of the reduced order models is investigated. Overall, the results show a very good agreement between full finite element analyses and the proposed reduced order modeling approach.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 16

Eigenvalues deviation for the mistuned blisk with an additional 5% mistuning in the cracked blade

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Figure 17

Finer mesh of the sector with two cracks

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Figure 18

The influence of using the cantilevered cracked blade mode shapes (CBc) on the predicted eigenvalues of the blisk with two cracks

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Figure 19

The influence of the number of cantilevered blade modes used for modeling mistuning in the blisk with two cracks

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Figure 20

Eigenvalues deviation for the mistuned blisk with two cracks per blade and an additional 5% mistuning in the cracked blade

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Figure 1

Natural frequencies versus nodal diameters for the tuned blisk (ANSYS results)

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Figure 2

Localized modes shapes due to mistuning and cracks in the blisk

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Figure 3

Conceptual structure of the full mass and stiffness matrices, where Ns represents the number of sectors

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Figure 4

Conceptual structure of the linear transformation α applied to the mass and stiffness matrices, where Ns represents the number of sectors

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Figure 5

Conceptual structure of the original and modified Craig–Bampton transformation matrices

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Figure 10

The influence of the crack on the eigenvalues of the pristine/uncracked blisk

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Figure 11

Differences in eigenvalues between ANSYS and ROMs with different NMs included

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Figure 12

Close-up view of the eigenvalue deviations between ANSYS and ROM with different NMs included for a blisk with a small crack and no mistuning

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Figure 13

The influence of the crack on the eigenvalues of the mistuned blisk

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Figure 14

The influence of the number of cantilevered blade modes used for modeling mistuning in the pristine/uncracked blisk

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Figure 15

The influence of the number of cantilevered blade modes used for modeling mistuning in the cracked blisk

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Figure 6

Conceptual structure of the modal transformation β applied to the mass and stiffness matrices, where Ns represents the number of sectors

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Figure 7

A example of a constraint mode of the cracked blisk, where a unit displacement was applied to the relative coordinate corresponding to the second contact pair (in the radial-direction)

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Figure 8

Finite element model of the blisk with a cracked blade

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Figure 9

Finite element model of the sector with a cracked blade

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