Chaotic and Subharmonic Motion Analysis of Floating Ring Gas Bearing System by Hybrid Numerical Method

This paper studies the nonlinear dynamic behaviors including chaotic, subharmonic, and quasi-periodic motions of a rigid rotor supported by floating ring gas bearing (FRGB) system. A hybrid numerical method combining the differential transformation method and the finite difference method used to calculate pressure distribution of FRGB system and rotor orbits. The results obtained for the orbits of the rotor center are in good agreement with those obtained using the traditional finite difference approach. Moreover, the hybrid method avoids the numerical instability problem suffered by the finite difference scheme at low values of the rotor mass and computational time-step. Moreover, power spectra, Poincaré maps, bifurcation diagrams and Lyapunov exponents are applied to examine the nonlinear dynamic response of the FRGB system over representative ranges of the rotor mass and bearing number, respectively. The results presented summarize the changes which take place in the dynamic behavior of the FRGB system as the rotor mass and bearing number are increased and therefore provide a useful guideline for the bearing system.