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Research Papers: Gas Turbines: Structures and Dynamics

Reduced-Order Models for Blisks With Small and Large Mistuning and Friction Dampers

[+] Author and Article Information
Weihan Tang

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

Seunghun Baek

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

Bogdan I. Epureanu

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

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received June 20, 2016; final manuscript received June 23, 2016; published online September 8, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 139(1), 012507 (Sep 08, 2016) (13 pages) Paper No: GTP-16-1252; doi: 10.1115/1.4034212 History: Received June 20, 2016; Revised June 23, 2016

In operation, rotating bladed disks (blisks) are often subject to high levels of dynamic loading, resulting in large amplitudes of forced vibrations especially at resonance. Moreover, variations in structural properties of individual sectors, referred to as mistuning, can lead to strain energy localization and can amplify forced responses. To prevent damages caused by high cycle fatigue, various frictional damping sources are introduced to dissipate vibration energy. Due to the nonlinear behavior of frictional contacts, conventional methods to study the dynamics of the blisk–damper systems are based often on numerical time integration, which is time-consuming and can be computationally prohibitive due to the large sizes of commercial blisk models. Existing techniques for model reduction either rely heavily on cyclic symmetry of the blisk–damper system or are based on component mode synthesis (CMS). However, in the presence of mistuning, cyclic symmetry no longer exists. Also, mistuning is random and best studied statistically. Repetitive CMS condensation for a large amount of random mistuning patterns can lead to a computationally formidable task. This paper presents a reduced-order modeling (ROM) technique to efficiently capture the nonlinear dynamic responses of blisk–damper systems with both small perturbations in blade material properties (small mistuning) and significant changes in the blisk geometries (large mistuning). The ROMs are formed by projecting the blisk–damper systems onto a novel mode basis that mimics the contact behavior. This mode basis contains normal mode shapes of the mistuned blisk–damper systems with either sliding or sticking conditions enforced on the contact surfaces. These mode shapes are computed through the N-PRIME method, a technique recently developed by the authors to efficiently obtain mode shapes for blisks with simultaneous large and small mistuning. The resulting modal nonlinear equations of motion (EOM) are solved by a hybrid frequency/time (HFT) domain method with continuation. In the HFT method, the contact status and friction forces are determined in the time domain by a quasi-two-dimensional contact model at each contact point, whereas the modal EOM are solved in the frequency domain according to a harmonic balance formulation. The forced responses computed by the proposed ROMs are validated for two systems with distinct mistuning patterns. A statistical analysis is performed to study the effectiveness of the frictional dampers under random mistuning patterns.

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Figures

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Fig. 3

Contact models for a node pair of two frictionless contact states: (a) sliding condition and (b) sticking condition

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Fig. 2

A 3D macroslip contact model

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Fig. 1

UM validation blisk: a typical academic blisk–damper system

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Fig. 5

Examples of rogue sectors with different volume of material removed from different locations on the blade component: (a) 10% tip, (b) 14% tip, and (c) 8% edge

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Fig. 6

Forced responses of a UM validation blisk with large mistuning under a traveling wave excitation of engine order 3

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Fig. 7

Maximum forced responses within the range of excitation frequencies at each ratio ρ of a UM validation blisk with large mistuning under a traveling wave excitation of engine order 3

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Fig. 8

Error in forced responses of a UM validation blisk with large mistuning under a traveling wave excitation of engine order 3, validated at ρ values of 0, 0.6, and 2: (a) error in forced responses at ρ = 0, (b) error in forced responses at ρ = 0.6, and (c) error in forced responses at ρ = 2

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Fig. 10

Maximum forced responses within the range of excitation frequencies at each ratio ρ of a UM validation blisk with both large and small mistuning under a traveling wave excitation of engine order 3

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Fig. 11

Error in forced responses of a UM validation blisk with both large and small mistuning under a traveling wave excitation of engine order 3, validated at ρ values of 0, 0.6, and 2: (a) error in forced responses at ρ = 0, (b) error in forced responses at ρ = 0.6, and (c) error in forced responses at ρ = 2

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Fig. 9

Forced responses of a UM validation blisk with both large and small mistuning under a traveling wave excitation of engine order 3

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Fig. 12

Probability distributions of amplification factors of forced responses of mistuned blisk–damper systems obtained at different ρ values: (a) ρ = 0, (b) ρ = 2, and (c) ρ = 0.6

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Fig. 13

Ratio of reduction of forced response amplitudes resulted from frictional damping, extracted for a tuned and each of the 400 mistuned systems

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Fig. 4

A mistuned UM validation blisk partitioned by PRIME

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Fig. 14

Prestress applied on the inner surface of the ring damper

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