Nonlinear stability analysis and numerical continuation of bifurcations of a rotor supported by floating ring bearings

Abstract

Floating ring bearings have been widely used, over the last decades, in rotors of automotive turbochargers because of their improved damping behavior and their good emergency-operating capabilities. They also offer a cost-effective design and have good assembly properties. Nevertheless, rotors with floating ring bearings show vibration effects of nonlinear nature induced by self-excited oscillations originating from the bearing oil films (oil whirl/whip phenomena) and may exhibit various nonlinear vibration effects which may cause damage to the rotor. In order to investigate these dynamic phenomena, this paper has developed a nonlinear model of a perfectly balanced rigid rotor supported by two identical floating ring bearings with consideration of their vibration behavior mainly governed by fluid dynamics. The dimensionless hydrodynamic forces of floating ring bearings have been derived based on the short bearing theory and the half Sommerfeld solution. Using the numerical continuation approach, different bifurcations are detected when a control parameter, the journal speed, is varied. Depending on the system’s physical parameters, the rotor can show stable or unstable limit cycles which themselves may collapse beyond a certain rotor speed to exhibit a fold bifurcation. Bifurcation analysis is performed to investigate the occurring instabilities and nonlinear phenomena. Such results explain the instabilities characteristics of the floating ring bearing in high-speed applications. It has also been found that the selection of the bearing modulus plays an important role in the characterization of the rotor stability threshold speed and bifurcation sequences. An understanding of the system’s nonlinear behavior serves as the basis for new and rational criteria for the design and the safe operation of rotating machines.

Bifurcations and limit cycle prediction of rotor systems with fluid-film bearings using Spectral Submanifolds

“…The method will be evaluated by comparing its results with the open-source sofware MATCONT [38], which is a numerical contination software based in MATLAB TM , and allows the study of a large range of bifurcations, including equilibria, limit-cycles and period-doubling. This software has been used by other authors to study bifurcations in rotors with fluid-film bearings before, e. g., [36,37,39,40]. In the MATCONT solutions, the full bearing force given by Eq.…”

“…In the CSSM, however, no linearization is performed, and the range of validity of the manifolds is in general bigger than in the CMR. This means that one can utilize the CSSM not only to study the Hopf bifurcations, but also the subsequent bifurcation of the limit cycles, which are known to occur in rotors with fluid-film bearings [36,37].…”