On the Instability Mechanisms of a Disk Rotating Close to a Rigid Surface

Abstract

The instability mechanisms of a rotating disk, coupled to a rigid surface through a viscous fluid film at the interface, are investigated analytically. The fluid in the film is driven circumferentially by the viscous shear, and it flows outwards radially under centrifugal forces. The circumferential flow component creates an equivalent viscous damping rotating at one half the disk rotation speed. This film damping dissipates all backward traveling waves where the undamped wave speeds are greater than one half the disk rotation speed. The radial flow component creates a nonsymmetric stiffness in the disk-film system that energizes any wave mode at rotation speeds above its flutter speed. Instabilities in the disk-film system are of two types. A rotating damping instability is caused by the rotating film damping at rotation speeds above a critical value that is less than the flutter speed. A combination instability is caused by the combined effect of the film stiffness and damping at rotation speeds above a threshold that is greater than the flutter speed. The maximum rotation speed of stable disk vibration is bounded above by the lowest onset speed of rotating damping instability. This speed limit is predicted for two wall enclosure designs. The maximum stable rotation speed of a 5.25-inch diameter flexible, memory disk, separated from a rigid surface by a viscous air film, is shown to be more than 15 times greater than the maximum speed of the disk without the air film.