Research Papers: Gas Turbines: Structures and Dynamics

Stability of a Cracked Rotor Subjected to Parametric Excitation

[+] Author and Article Information
Jerzy T. Sawicki

Fellow ASME
Center for Rotating Machinery Dynamics
and Control,
Cleveland State University,
Cleveland, OH 44115-2214
e-mail: j.sawicki@csuohio.edu

Zbigniew Kulesza

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

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received September 16, 2014; final manuscript received September 30, 2014; published online December 2, 2014. Editor: David Wisler.

J. Eng. Gas Turbines Power 137(5), 052508 (May 01, 2015) (8 pages) Paper No: GTP-14-1552; doi: 10.1115/1.4028742 History: Received September 16, 2014; Revised September 30, 2014; Online December 02, 2014

It is well known that parametric vibrations may appear during the rotation of a rotor with a cracked shaft. The vibrations occur due to periodic stiffness changes being the result of the crack breathing. A parametrically excited system may exhibit parametric resonances and antiresonances affecting the stability of the system. In most cases the destabilizing effect due to parametric resonances is studied. Antiresonant cases seem to be uninteresting. However, the antiresonances have a unique property of introducing additional artificial damping to the system, thus improving its stability and reducing the vibration amplitude. Apart from different control applications, this stabilizing effect may be interesting for its probable ability to indicate the shaft crack. The possible application of the additional damping introduced by parametric excitation for the shaft crack detection is analyzed in the present paper. The approach is demonstrated with a mathematical model of a rotor with a cracked shaft. The stability analysis of the rotor is performed analytically by employing the averaging method. Stability boundaries for different frequencies of the parametric excitation and for different crack depths are derived. The results of this analysis are checked numerically by means of the Floquet's theory. Next, possible applications of the parametric excitation for the shaft crack detection are validated numerically.

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Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

Analytical stability map; dark areas are unstable

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Fig. 3

Numerical stability map; dark areas are unstable

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Fig. 4

Numerically calculated vertical displacement of the rotor in dependency of parametric excitation frequency η and time τ; crack depth μ=1%

Grahic Jump Location
Fig. 5

Numerically calculated vertical displacement of the rotor in dependency of parametric excitation frequency η and time τ; crack depth μ=25%

Grahic Jump Location
Fig. 6

Numerically calculated vertical displacement of the rotor in dependency of parametric excitation frequency η and time τ; crack depth μ=40%




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