Bearings coefficients effects on chaotic and bifurcation behavior of flexible rotor systems subjected to rub-impact

This study investigates the influence of end-support conditions on the chaotic and bifurcation behavior of a rotating flexible shaft-disk system. The system is modeled as a continuous shaft with a rigid disk in its mid span whilst supported by multi-coefficients bearings. Both Coriolis and centrifugal effects due to shaft flexibility are included. The partial differential equations of motion are extracted using the Rayleigh beam theory and the assumed mode method is used to discretize them in order to be solved numerically. The analytical tools used in this work include time series, phase plane portrait, power spectrum, Poincaré map, bifurcation diagrams, and Lyapunov exponents. The main objective of the present study is to investigate the effects of end-supports stiffness and damping coefficients on the chaotic vibration behavior of a rotating system. Periodic, sub-harmonic, quasi-periodic, and chaotic states have been observed for each case. As demonstrated, inclusion of the bearing effects can primarily change the speed ratios at which rub-impact occurs. The principal and cross-coupling stiffness and damping coefficients have quite different effects in the chaotic behavior of the system.