Random vibrations of a damped rotating shaft

Response of a simple Jeffcott rotor to random excitation is considered with both external and internal damping taken into account. Mean square responses are predicted by the method of moments for the cases of transverse and angular (tilting) oscillations. Contrary to unbalance-induced response the random vibrations are shown to depend on the internal or “rotating” damping; in particular, their level increases with approaching threshold speed for dynamic instability. Procedure for estimating this threshold from on-line measurements of the shaft's random vibrations at a constant rotation speed is outlined based on the calculating coherence function of lateral displacements in two perpendicular directions for the case of transverse vibrations and that of tilting angles about two perpendicular axes for the case of tilting oscillations. Dependence of the mean square responses on the rotation speed can also be used for the stability margin evaluation.