Chaos in the Imbalance Response of a Flexible Rotor Supported by Oil Film Bearings with Non-Linear Suspension

The dynamics of flexible rotors associated with fluid film bearings have been studied since the 1950s. Most of the literature has assumed rigid, undamped bearing support with linear elastic restoring force. For a more precise description of fluid film bearing-rotor systems, a non-linearly supported model is proposed in this paper, where a linear damping force and a non-linear elastic restoring force are assumed. Numerical results show that due to non-linear factors, though the dynamic equations of the bearing center and the rotor center are coupled, the trajectory of the rotor center demonstrates steady-state symmetric motion even when the trajectory of the bearing center is in a state of disorder. Poincaré maps, bifurcation diagrams, and power spectra are used to analyze the behavior of the bearing center in the horizontal and vertical directions under different operating conditions. The fractal dimension concept is used to determine whether the system is in a state of chaotic motion. Numerical results find that the dimension of the bearing center trajectory is fractal and greater than two in some operating conditions, indicating that the system is in a state of chaotic motion. Chaotic behavior was found in an intermediate speed range, disappearing at higher speeds. It is suggested that this is a characteristic of all fluid film systems. It is suggested that a number of existing life-critical fluid film bearing systems are possibly being operated in this chaotic region and that such systems should be reevaluated in terms of this new observation.