The bifurcation and chaos of a gear pair system based on a strongly non-linear rotor—bearing system

Abstract

A systematic analysis of the dynamic behaviours of a gear pair system based on a rotor—bearing system under strongly non-linear effects (i.e. non-linear suspension effect, non-linear oil-film force, non-linear rub-impact force, and non-linear gear mesh force) is presented in this study. The dynamic orbits of the system are observed using bifurcation diagrams plotted using the dimensionless unbalance coefficient, the dimensionless damping coefficient, and the dimensionless rotational speed ratio as control parameters. The onset of chaotic motion is specified from the phase diagrams, power spectra, Poincaré maps, Lyapunov exponents, and fractal dimension of the system. There exists various forms of periodic, quasi-periodic, and chaotic motions at different bifurcation parameters. The simulation results also found that highly non-periodic motions do exist in gear—rotor—bearing systems under those non-linear effects. The results presented in this study provide a better understanding of the operating conditions under which undesirable dynamic motion takes place in a gear—bearing system; they would therefore serve as a useful source of reference for engineers in designing and controlling such systems.