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Research Papers

Adaptive Microslip Projection for Reduction of Frictional and Contact Nonlinearities in Shrouded Blisks

[+] Author and Article Information
Mainak Mitra

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

Stefano Zucca

Department of Mechanical and
Aerospace Engineering,
Politecnico di Torino,
Corso Duca degli Abruzzi, 24,
Torino 10129, Italy
e-mail: stefano.zucca@polito.it

Bogdan I. Epureanu

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

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 21, 2015; final manuscript received February 15, 2016; published online May 12, 2016. Assoc. Editor: Sotirios Natsiavas.

J. Comput. Nonlinear Dynam 11(4), 041016 (May 12, 2016) (15 pages) Paper No: CND-15-1104; doi: 10.1115/1.4033003 History: Received April 21, 2015; Revised February 15, 2016

Reduced order models (ROMs) of turbine bladed disks (blisks) are essential to quickly yet accurately characterize vibration characteristics and effectively design for high cycle fatigue. Modeling blisks with contacting shrouds at adjacent blades is especially challenging due to friction damping and localized nonlinearities at the contact interfaces which can lead to complex stick–slip behavior. While well-known techniques such as the harmonic balance method (HBM) and Craig–Bampton component mode synthesis (CB-CMS) have generally been employed to generate ROMs in the past, they do not reduce degrees-of-freedom (DoFs) at the interfaces themselves. In this paper, we propose a novel method to obtain a set of reduction basis functions for the contact interface DoFs as well as the remaining DoFs called “adaptive microslip projection” (AMP). The method is based on analyzing a set of linear systems with specifically chosen boundary conditions on the contact interface. Simulated responses of full order baseline models and the novel ROMs under various conditions are studied. Results obtained from the ROMs compare very favorably with the baseline model. This study addresses the case of a shrouded blisk in microslip close to stick. The AMP procedure may be possibly applied to other systems with Coulomb friction contacts, but its accuracy and effectiveness will need to be evaluated separately.

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Figures

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Fig. 1

Contact-surfaces S1 and S2

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Fig. 2

Reduction strategy

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Fig. 3

FE models of sector and full blisk

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Fig. 4

Shroud and contact patch

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Fig. 5

Frequency versus number of nodal diameters plot for stuck tuned blisk

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Fig. 6

EO 1 AMP ROM responses

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Fig. 7

EO 12 AMP ROM responses

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Fig. 8

ROM (based on full reduction AMP) responses for different AMP basis sizes, EO 1 response, μ|F0|/|F|=1.35×104

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Fig. 9

FR ROM error versus no. of amps, EO 1 response, μ|F0|/|F|=1.35×104

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Fig. 10

NLR ROM error versus no. of amps, EO 1 response, μ|F0|/|F|=1.35×104

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Fig. 11

FR ROM responses for different AMP basis sizes, EO 12 response, μ|F0|/|F|=2.70×103

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Fig. 12

ROM (based on full reduction AMP) responses for higher harmonics, EO 1 response, μ|F0|/|F|=1.35×104

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Fig. 13

Natural frequencies of stuck mistuned blisk

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Fig. 14

Stuck response of mistuned blisk

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Fig. 15

Response of mistuned blisk in microslip

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Fig. 16

ROM responses of mistuned blisk

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Fig. 17

Eigenvalues of POMs for EO1 response, μ|F0|/|F|=1.35×104

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Fig. 18

Eigenvalues of POMs for EO 12 response, μ|F0|/|F|=2.70×103

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Fig. 19

eθj for unconditioned AMPs, EO1 response, μ|F0|/|F|=1.35×104

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Fig. 20

eθj for conditioned AMPs, EO12 response, μ|F0|/|F|=2.70×103

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Fig. 21

eθj for unconditioned AMPs generated from first family stuck modes, EO12 response, μ|F0|/|F|=2.70×103

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Fig. 22

eθj for unconditioned AMPs generated from second family stuck modes, EO12 response, μ|F0|/|F|=2.70×103

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Fig. 23

EO 1 POM ROM responses, μ|F0|/|F|=1.35×104

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Fig. 24

EO 12 POM ROM responses, μ|F0|/|F|=2.70×103

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Fig. 25

ε for POMs, EO 1 response, μ|F0|/|F|=1.35×104 at resonance (877.6 Hz)

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Fig. 26

ε for POMs, EO 12 response, μ|F0|/|F|=2.70×103 at resonance (2,093.2 Hz)

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Fig. 27

ε for AMPs, EO 1 response, μ|F0|/|F|=1.35×104 at resonance (877.6 Hz)

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Fig. 28

ε for conditioned AMPs, EO 12 response, μ|F0|/|F|=2.70×103 at resonance (2093.2 Hz)

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Fig. 29

ε for unconditioned AMPs generated from first familystuck modes, EO 12 response, μ|F0|/|F|=2.70×103 at resonance (2093.2 Hz)

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Fig. 30

ε for unconditioned AMPs generated from second family stuck modes, EO 12 response, μ|F0|/|F|=2.70×103 at resonance (2093.2 Hz)

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