Unstable simultaneous whirl of two cylinders in a concentric double rotating cylinder system

Abstract

This study investigated the unstable simultaneous whirl of two cylinders in a concentric double rotating cylinder system, with both co- and counter-rotation. The axes of both cylinders were radially elastically supported independently of each other. A fixed (no rotation and no whirl) cylinder was installed outside the outer cylinder concentrically. The three cylinders were assumed to stay parallel to each other, making the gaps between them axially uniform. A theory to analyze the complex eigenvalues of the coupled system of gap flows and motions of cylinders was formulated. An experiment was carried out, in which structural conditions were set to be the same as possible for the inner and outer cylinders. A basic unstable mode was observed in which both cylinders whirled in the same direction and in opposite phases. In counter-rotation, the whirl direction transitioned from the rotation direction of the outer cylinder to that of the inner cylinder with increasing rotational speed of the inner cylinder. The transitions were brought about by replacement of the eigenmode with the minimum damping ratio. With the transition, the frequency changed discontinuously and the decrease in the damping ratio with increasing rotation speed became steep. Under simultaneous two-cylinder whirling, the stable area at combinations of the inner and outer cylinder rotation speeds became narrower than that of only the outer cylinder whirling.