Stabilizing a rotating disk at supercritical speeds with viscous fluid films

This research focuses on the development of technology to operate stable disks at supercritical speeds. Two film models, which differ from Reynold's equation by the inclusion of centrifugal fluid inertia or unsteady fluid inertia, are derived to investigate coupled film-structure system response. The goal of this research is to stabilize rotating disks at supercritical speeds with viscous films.; The dissertation begins with investigation of dissipation mechanism associated with a massless viscous film between a translating string and a translating rigid surface. The film coupling is modeled as a translating, distributed damping and investigated through the waves propagating in the fluid-string coupled system. The translating damping destabilizes waves propagating in the direction of damping propagation when the mean film speed relative to the string exceeds the wave speed in the string without fluid coupling.; Stability of a rotating disk under rotating, arbitrarily large damping forces, derived from a positive-definite operator in the applied region, is investigated analytically. Points producing periodic solutions, a necessary condition for every point on stability boundary, are located exactly in parameter space. A perturbation technique and the Galerkin method are used to predict whether these points reside on the stability boundary, and to identify the stable region in parameter space. Stability of the disk can be predicted through the wave speeds in the undamped disk. The disk is stabilized until the lowest undamped wave speed, when observed on the disk, is exceeded by the rotation speed of the damping relative to the disk.; The response of a rotating disk under a point force, representing viscous damping and a circulatory force proportional to the slope of the disk surface, is predicted analytically. This point force is termed a fixed-rotating-dashpot for it is fixed in space but it is mechanically equivalent to a rotating dashpot. Approximate solutions are obtained through the KBM method when the viscous and circulatory force components are small. For arbitrary force, the region of stable response and the stability boundary are predicted exactly through a method combining an energy analysis, a perturbation technique, and the Galerkin method. The fixed-rotating-dashpot can be a dissipation mechanism for control of disk vibration at all speeds by tuning the non-conservative force components, and can be implemented by use of hybrid thrust bearings.; A modified Reynolds equation is derived for viscous film between a rotating disk and a rigid wall with centrifugal fluid inertia modeled. 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 a viscous damping rotating at one half the disk rotation speed, and the radial flow component creates a non-symmetric stiffness. Finally, a 2-D thin film equation, modeling a thin viscous fluid film, constrained between two translating, flexible surfaces, is derived with fluid unsteady inertia considered. (Abstract shortened by UMI.)...