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.
Stability of a Cracked Rotor Subjected to Parametric Excitation
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.
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Sawicki, J. T., and Kulesza, Z. (May 1, 2015). "Stability of a Cracked Rotor Subjected to Parametric Excitation." ASME. J. Eng. Gas Turbines Power. May 2015; 137(5): 052508. https://doi.org/10.1115/1.4028742
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