Effects of Nonlinear Spring Characteristics on the Dynamic Unstable Region of an Unsymmetrical Rotor

Abstract

This paper deals theoretically and experimentally with the forced oscillation in the vicinity of the dynamic unstable region of an unsymmetrical rotor system having nonlinear spring characteristics due to ball bearings. Near this rotating speed of a shaft, an unstable region vanishes and a stable oscillation appears due to the nonlinearity. We discussed this oscillation with attention to the nonlinear components represented by the polar coordinates and clarified which component has influence on this oscillation. Since this system involves an external force due to the unbalance, nonlinearity and the characteristic of parametric resonance, we have investigated the effect of the coexistence of these factors on the vibratory phenomena. We have also compared this oscillation with the super-summed-and-differential harmonic oscillations in a symmetrical shaft system and the dynamic unstable vibration of an unsymmetrical rotor system reported previously.