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Research Papers

Reduced-Order Modeling of Bladed Disks With Friction Ring Dampers

[+] Author and Article Information
Seunghun Baek

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48104
e-mail: baeksh@umich.edu

Bogdan Epureanu

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

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 16, 2016; final manuscript received May 24, 2017; published online August 2, 2017. Assoc. Editor: Carole Mei.

J. Vib. Acoust 139(6), 061011 (Aug 02, 2017) (9 pages) Paper No: VIB-16-1402; doi: 10.1115/1.4036952 History: Received August 16, 2016; Revised May 24, 2017

An efficient methodology to predict the nonlinear response of bladed disks with a dry friction ring damper is proposed. Designing frictional interfaces for bladed-disk systems is an important approach to dissipate vibration energy. One emerging technology uses ring dampers, which are ringlike substructures constrained to move inside a groove at the root of the blades. Such rings are in contact with the bladed disk due to centrifugal forces, and they create nonlinear dissipation by relative motion between the ring and the disk. The analysis of the dynamic response of nonlinear structures is commonly done by numerical integration of the equations of motion, which is computationally inefficient, especially for steady-state responses. To address this issue, reduced-order models (ROMs) are developed to capture the nonlinear behavior due to contact friction. The approach is based on expressing the nonlinear forces as equivalent nonlinear damping and stiffness parameters. The method requires only sector-level calculations and allows precalculation of the response-dependent equivalent terms. These factors contribute to the increase of the computational speed of the iterative solution methods. A model of a bladed disk and damper is used to demonstrate the method. Macro- and micro-slip are used in the friction model to account for realistic behavior of dry friction damping. For validation, responses due to steady-state traveling wave excitations are examined. Results computed by ROMs are compared with results from transient dynamic analysis (TDA) in ansys with the full-order model. It is found that the steady-state responses predicted from the ROMs and the results from ansys are in good agreement, and that the ROMs reduce computation time significantly.

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Figures

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Fig. 1

Blisks and ring damper FE model

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Fig. 3

Contact node pairs and interior nodes for the contact model

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Fig. 4

Example of hysteresis loops and modal friction forces given by Eq. (10) for various modal amplitudes: q1=1.0×10−5, q2=3.0×10−4, q3=4.5×10−4, q4=6.2×10−4, and  q5=1.0×10−3

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Fig. 5

Flowchart of ROM procedures

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Fig. 6

Frequency versus nodal diameter plot

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Fig. 7

Frequency-response plot of HA and ROMs

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Fig. 8

Example of equivalent damping γ(1,1)

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Fig. 9

Example of equivalent stiffness kf(1,1)

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Fig. 10

Estimation of steady-state response by ROM and by TDA from full size FE model

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Fig. 11

Validation of ROM by TDA results

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Fig. 12

Equivalent stiffness with various friction coefficients

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Fig. 13

Equivalent damping with various friction coefficients

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Fig. 14

Frequency response of blisks system with various friction coefficients

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Fig. 15

Normalized responses peak along with friction coefficients

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