Influence of imperfections on the stability of a multi-disc friction system

Abstract

This paper studies the impact of geometrical imperfections (gaps in the links, center distance, inclination angle, etc.) on the stability and the dynamic behavior of mechanical systems exhibiting friction-induced vibrations (braking systems, clutches, etc.). It comes further to two papers relating to improved modeling of friction and separation at the interface of a rotor-stator system. The latter is a phenomenological model which is composed of an embedded beam on which a disc is mounted, called the stator, in contact with another disc called the rotor. The phenomenological mechanical system used in this paper is a new version of the latter model taking into account some of the geometrical imperfections present in real mechanical systems. In the proposed model, the rotor and stator discs have the ability to move radially thanks to the gaps in the links. The inclination angle of the rotor disc and a center distance between the stator and the rotor discs are also introduced. The inclusion of these three geometrical imperfections induces additional complex phenomena that have a strong impact on the stability and dynamic behavior of the mechanical system, because the coupling of the imperfections with the rotor rotation gives rise to a non-autonomous dynamical system. Consequently, stability studies of fixed points must be replaced by stability studies of periodic orbits involving the construction of a monodromy matrix. In conclusion, significant differences in the values of the bifurcation point and the levels of the associated instabilities can be observed, unlike in a study that does not take geometrical imperfections into account.