Non-periodic and chaotic response of three-multilobe air bearing system

Abstract

• Effects of rotor mass and bearing number on three-multilobe air bearing are analyzed. • Hybrid DTM&FDM method provides better accuracy than other numerical methods. • Complex periodic, non-periodic and chaotic motion behavior is observed. The dynamic response of a three-multilobe air bearing (TMAB) system is investigated for various values of the rotor mass and bearing number using a hybrid numerical scheme consisting of the differential transformation method (DTM) and the finite difference method (FDM). The validity of the numerical scheme is demonstrated by comparing the results obtained for the rotor center orbit under typical operating conditions with those obtained from the traditional FDM approach and a perturbation method, respectively. The dynamic behavior of the rotor center is then investigated for rotor mass values in the range of 1.0 ≤ m r ≤ 16.0 kg and bearing number values in the range of 1.0 ≤ Λ ≤ 5.0. The phase trajectories, power spectra, bifurcation diagrams, Poincaré maps and maximum Lyapunov exponents show that the TMAB system exhibits a complex dynamic behavior consisting of periodic, quasi-periodic and chaotic motion at certain values of the rotor mass and bearing number. In general, the numerical results obtained in this study provide a useful insight into the dynamic response of TMAB systems. In particular, the results indicate the operating conditions which should be avoided in order to achieve a desirable periodic motion of the system.