Parametrically Induced Damping in a Cracked Rotor

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.