Complex Stable and Unstable Subharmonic Vibrations of a Nonlinear Brush-Seal Rotor System

This research investigates the complex subharmonic vibrations of the nonlinear brush-seal rotor system. The stable and unstable nonlinear vibrations are calculated and presented as discrete Poincare node results. For such study, we first derive an analytical seal force model from elasticity and bristle-rotor coupling effects. The analytical predictions in terms of the discrete eigenvalues for the stability and bifurcations of the independent and global nonlinear vibrations are presented. Independent vibrations are characterized with solitary rotating speed range and limited within two Saddle node bifurcations. Independent subharmonic-1/3 and -1/7 vibrations are discovered in the research. A route from synchronous vibration to subharmonic-1/2 vibration is predicted also. The discrete eigenvalue analysis successfully predicts such route and the corresponding stability evolutions. The stable and unstable subharmonic-1/2 vibrations are obtained. Saddle node, Neimark and period-doubling bifurcations are obtained accurately. The jumping during synchronous vibration and subharmonic-1/2 vibration is obvious while unstable switching which starts from unstable subharmonic-1/2 to unstable subharmonic-1/2 is also successfully predicted. Complex subharmonic-1/2 vibration is presented with the discrete Poincare diagram. Subharmonic vibration illustration is provided with displacement orbits and velocity planes. Unstable synchronous vibration and stable subharmonic-1/2 vibration are illustrated. The provided method and corresponding results serve as guidelines for the theoretical research and practical applications.