Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Prediction and Control of Bifurcations in rotor-foundation systems supported by fluid-film bearings
Submission Author:
Arthur Mereles , SP
Co-Authors:
Arthur Mereles, Diogo Stuani Alves, Katia Lucchesi Cavalca Dedini
Presenter: Arthur Mereles
doi://10.26678/ABCM.COBEM2023.COB2023-0335
Abstract
The use of oil lubricated bearings is very common in many rotating machines, mainly due to their high load capacity, reliability and low friction. However, these types of bearings often present instabilities at certain operating speeds. Experimental studies have found two main types of instabilities, namely, oil-whirl and oil-whip. In the first case, the amplitude of the rotor increases slightly, and one notices a sub synchronous frequency component of around 0.5× the shaft speed. In the oil-whip, the amplitude increases dramatically, and the frequency component is nonsynchronous. Another way to look at these phenomena is through the lens of bifurcation theory. In this case, the instability presented by oil-lubricated bearings can be seen as a Hopf bifurcation, which can be either super- or sub-critical. The former case corresponds to oil-whirl and the latter to oil-whip. Hence, detecting the type of Hopf bifurcation, either super- or sub-critical, tells whether one experiences oil-whirl or oil-whip, respectively. This work presents an approach to predict Hopf bifurcations by means of the Center Manifold Reduction (CMR) method in rotor-foundation systems. The basis of the approach is to obtain the center manifold of the bifurcating system, and study it to learn if the system will present oil-whirl or oil-whip. For this purpose, the parameterization method is used, which is a powerful tool to estimate invariant manifolds in nonlinear dynamical systems. The main advantage of the CMR is that it is very applicable to high-dimensional dynamical systems. In addition to the prediction of the limit cycles that arise in the Hopf bifurcation, it is also proposed a method to control these cycles by means of a nonlinear control force. The idea in this nonlinear control is to change the normal form coefficient of the Hopf bifurcation, allowing one to change the instability from oil-whip (more dangerous) to oil-whirl (less dangerous). The control force is applied in the foundation, and thus the approach could be implemented in machines in the field. The method is applied in a simple rotor system modeled by the Finite Element Method (FEM) and supported by a spring-mass-damped foundation. The results of predicted limit cycles using the CMR, as well as controlled cycles, are validated by comparing them with the ones obtained with numerical continuation.
Keywords
Rotor-foundation systems, nonlinear dynamics, Fluid-film bearing, Hopf bifurcation, Invariant manifold
