Unstable outer cylinder whirl of concentric double rotating cylinder system

Abstract

This research investigates unstable outer cylinder whirl in a double rotating cylinder system, with both co- and counter-rotation, in which the axis of the outer cylinder is supported elastically in the radial direction and the axis of the inner cylinder is fixed and not allowed to whirl. A fixed (no rotation and no whirl) outermost cylinder is optionally installed outside the outer cylinder. It is assumed that the two (three) cylinders stay parallel to each other so that the gaps between them are axially uniform. A theory to analyze the complex eigenvalues of the coupled system of the gap flow and the motion of the outer cylinder is presented. The gap flow model accounts for the effects of inertia, compressibility and turbulence, and is coupled with the outer cylinder motion. Experiments were carried out for cases both with and without the outermost cylinder. The theoretical and experimental results were generally in agreement with respect to the whirl frequency, damping ratio, and boundary of the unstable whirl for different combinations of rotational speeds. The damping ratio and the frequency of the whirl decreased as the sum of the rotational speeds of the two cylinders increased. The presence of the outermost cylinder increased the sensitivity of the rotational speed of the outer cylinder to the damping ratio and the boundary of whirl occurrence, and narrowed the stable range of the speed of the outer cylinder. Also, only in counter-rotation in the case with the outermost cylinder, the frequency decrease tended to depend exclusively on the rotational speed of the inner cylinder, and the effect of the outer cylinder speed was reduced.

Keywords

• gap flow
• unstable whirl
• rotating cylinder
• counter-rotation
• turbulence
• complex eigenvalue analysis
• unsteady flow