Stability of a Cracked Rotor Subjected to Parametric Excitation

Abstract

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 crack breathing. A parametrically excited system may exhibit parametric resonances and anti-resonances affecting the stability of the system. In most cases the destabilizing effect due to parametric resonances is studied. Anti-resonant cases seem to be uninteresting. However, the anti-resonances have an interesting 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. The results demonstrate the potential of the suggested approach, yet further analytical and experimental studies are required.