Effective damping for rotating disks at super-critical speeds

Abstract

The normal stable operation speed of the disk is limited by its critical speed. Maximizing the speed of rotation of the stable disk requires effective damping mechanism to damp and stabilize disk vibrations at super-critical speeds. This paper investigate analytically the stability of of a rotating disk under a non-conservative point force, which is fixed in space, composed of a viscous damping component and a circulatory force proportional to the circumferential slope of the disk surface. Approximate solutions are obtained through the KBM method when the viscous and circulatory force components are small. For arbitrary force, points possibly residing on the stability boundary are located exactly in parameter space through an energy analysis. A perturbation technique and the Galerkin method are used to predict whether these points reside on the stability boundary, and to identify the region of stable response. A propagating wave mode in the disk is stable unless the difference between the disk rotation speed and the virtual speed (ratio of the circulatory stiffness constant to the viscous damping coefficient) of the point force exceeds the wave speed observed on the disk. By properly tuning the virtual speed of the point force, disk vibrations can be damped and stabilized at super-critical speeds.