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Research Papers: Gas Turbines: Structures and Dynamics

Parametrically Induced Damping in a Cracked Rotor

[+] Author and Article Information
Zbigniew Kulesza

Faculty of Mechanical Engineering,
Bialystok University of Technology,
Bialystok 15-351, Poland
e-mail: z.kulesza@pb.edu.pl

Jerzy T. Sawicki

Fellow ASME
Center for Rotating Machinery Dynamics and
Control (RoMaDyC),
Washkewicz College of Engineering,
Cleveland State University,
Cleveland, OH 44115-2214
e-mail: j.sawicki@csuohio.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 21, 2016; final manuscript received June 22, 2016; published online August 16, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 139(1), 012505 (Aug 16, 2016) (8 pages) Paper No: GTP-16-1262; doi: 10.1115/1.4034197 History: Received June 21, 2016; Revised June 22, 2016

A transverse shaft crack in a rotor is usually modeled as a local change in shaft stiffness. This local stiffness change is not constant and varies as a result of a so-called breathing mechanism, explained with periodical opening and closing of crack faces under the load of external forces applied to the rotor. The rotor with a periodically varied stiffness can be modeled as a parametrically excited linear system. In the presence of a parametric excitation, the vibrations of the system can be amplified or damped at specific excitation frequencies. Usually, the frequencies at which the vibrations are amplified are important, since they can affect stability of the system. However, the increased damping at specific frequencies is a significant feature of a parametrically excited system that can have some potentially useful applications. One of such applications can be an early detection of a shaft crack. This paper presents results of numerical analysis of the influence of Rayleigh's damping and gyroscopic effects on the increase in damping in a parametrically excited rotor with a cracked shaft. It is shown that the increase in damping in a parametrically excited system is rather a rare phenomenon that can be observed only at properly selected values of the excitation frequency and Rayleigh's damping. Furthermore, gyroscopic effects influence the exact values of antiresonance frequencies at which the phenomenon appears.

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References

Figures

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Fig. 1

Tested rotor: (a) rigid finite element model and (b) shaft cross section at the crack location

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Fig. 2

Stability surface of the cracked rotor; DG=0; βd=10−4 s

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Fig. 3

Stability surface of the cracked rotor; DG=0; βd=10−5 s

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Fig. 4

Stability surface of the cracked rotor; DG=0; βd=10−6 s

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Fig. 5

Stability surface of the cracked rotor; DG=0; βd=10−7 s

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Fig. 6

Stability surface of the cracked rotor; DG≠0; βd=10−4 s

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Fig. 7

Stability surface of the cracked rotor; DG≠0; βd=10−5 s

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Fig. 8

Stability surface of the cracked rotor; DG≠0; βd=10−6 s

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Fig. 9

Stability surface of the cracked rotor; DG≠0; βd=10−7 s

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Fig. 10

Vertical displacement of the 15th rigid finite element after an initial disturbance: (a) 1% deep crack and (b) 40% deep crack; DG=0; βd=10−4 s

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Fig. 11

Vertical displacement of the 15th rigid finite element after an initial disturbance: (a) 1% deep crack and (b) 40% deep crack; DG=0; βd=10−5 s

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Fig. 12

Vertical displacement of the 15th rigid finite element after an initial disturbance: (a) 1% deep crack and (b) 40% deep crack; DG=0; βd=10−7 s

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Fig. 13

Vertical displacement of the 15th rigid finite element after an initial disturbance: (a) 1% deep crack and (b) 40% deep crack; DG≠0; βd=10−4 s

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Fig. 14

Vertical displacement of the 15th rigid finite element after an initial disturbance: (a) 1% deep crack and (b) 40% deep crack; DG≠0; βd=10−5 s

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Fig. 15

Vertical displacement of the 15th rigid finite element after an initial disturbance: (a) 1% deep crack and (b) 40% deep crack; DG≠0; βd=10−7 s

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