Parametrically Induced Damping in a Cracked Rotor

The tendency to higher speeds in turbomachinery results in the design of more flexible shafts, which run at speeds above several of their natural frequencies. Due to stress concentration and high spin speed, the rotor dynamic system is more prone to cracks that propagate faster due to low-cycle fatigue loading. The propagating shaft crack usually leads to sudden machine failure, its damage and a serious accident. Therefore, an early shaft crack detection and warning is an important research task. A transverse shaft crack in a rotor is usually modeled as a local change in the shaft stiffness. It is commonly assumed that this local stiffness change is not constant and varies as a result of a so-called breathing mechanism. This mechanism is 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, and the frequencies at which the vibrations are damped seem to not be of interest. However, the increased damping at specific frequencies is a significant feature of a parametrically excited system that can have some potentially useful applications. The results of earlier studies demonstrate that one of the possible applications of the parametrically-induced damping can be an early detection of a shaft crack. The unique feature of the increased damping in parametrically excited systems is that this phenomenon can appear only at specific excitation frequencies and at other specific conditions that are not always met. This paper presents the results of a 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 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 anti-resonance frequencies at which the phenomenon appears.