Unstable Vibrations of an Unsymmetrical Rotor Supported by Flexible Bearing Pedestals

When a rotating shaft carrying an unsymmetrical rotor is supported by flexible pedestals, many unstable vibrations can take place. In the present paper, these unstable vibrations are treated theoretically and experimentally, under the assumption that the system is of six degrees of freedom. The analysis shows that near each of five or six major critical speeds there exists a so called "static unstable region" where an unstable region" where an unstable vibration with a frequency of rotating speed ω grows up exponentially, and that near each of fifteen rotating speeds ω=ω<ij> (1≦i, j≦6, i≠j) where the relation pi+pj=2ω holds between the natural frequencies pi(p1>p2>…>p6>0>p7>…>p12) and the rotating speed ω, there exists a so called "dynamic unstable region", in which two unstable vibrations with frequencies Pi(≒pi) and Pi(≒pj) occur simultaneously and build up at the same rate.