Non-linear dynamic analysis of hybrid squeeze-film damper-mounted gear-bearing system and hydraulic active control

Abstract

The hybrid squeeze-film damper bearing is proposed in this article. The pressure distribution and the dynamics of a gear pair supported by such bearing are studied. Numerical results show that, due to the non-linear factors of lubricant film force, the trajectory of the gear demonstrates a complex dynamics with rotational speed ratio s. Poincaré maps, and bifurcation diagrams are used to analyse the behaviour of the gear trajectory in the horizontal and vertical directions at s = 6.0. The maximum Lyapunov exponent is used to determine if the system is in a state of chaotic motion. Numerical results show that the maximum Lyapunov exponent of this system is positive at the non-dimensional speed ratio s = 6.0, which indicate that the gear trajectory is chaotic under such operation condition. In order to avoid the non-synchronous chaotic vibrations, an increased proportional gain k p = 0.1 is applied to control this system. It is shown that the gear trajectory leaves chaotic motion to periodic motion in the steady state under control action.