Stability Analysis of the Rubbing Phenomenon with Gyroscopic Effect

Péter Triesz

Keywords: Rubbing, Gyroscopic effect, Stability analysis, Bifurcations

ABSTRACT

The rubbing as an undesired non-linear dynamical behaviour of rotors is a widely researched topic in the field of rotordynamics. This important phenomenon is described and models are set in many papers to analyse the dynamics and stability of rotors. These works mostly use the classic Jeffcott rotor system with several bearing or any supporting equipment. For example, one model has a magnetic bearing with a strong non-linear characteristic and a backup bearing where the rubbing occurs. Other authors investigate the rubbing in a preloaded snubber ring.

In addition to the above mentioned this paper presents a model, which takes into consideration also the gyroscopic effect. The model consists of a rigid shaft supported by two bearings at its ends and a rigid disc attached to the shaft. One of the bearings is a self-aligning roller bearing that is ideally rigid; the other one is a journal bearing that has elasticity and viscous damping. The disc has some static unbalance.

The strong non-linearity is caused by the collision of the rotor and the stator at the journal bearing. The velocity of the shaft after the impact is calculated with the help of the coefficient of restitution and the friction.

The paper shows the influence of the gyroscopic force on the dynamics of rubbing, and how can be analysed the stability of this system choosing the polar angle between two contact point as a discrete-time variable. The results are compared with the results of other authors.