Modal dynamic instabilities generated by frictional contacts

Presence of contact interface between deformable bodies can have very different purposes in mechanical systems. In some application the aim is to maximize the energy dissipation (e.g. brake systems); on the contrary in other cases the aim is to allow for a relative displacement between the two bodies, maximizing the efficiency (joints). In both cases frictional forces at the contact interfaces allow for coupling contact and system dynamics, and they can give origin to dynamic instabilities. From a numerical point of view the contact forces introduce an asymmetry on the system stiffness matrix, acting as a cross coupling factor between tangential and normal deformation at the contact interface [1]. Typical examples of this phenomenon, largely investigated in literature [2], are the squeal noise emission in automotive brakes or railway wheels. The coupling between system and contact results on unstable vibrations of the system. During vibration, the deformations due to the dynamic response of the system modify substantially the contact stress distribution. This variation bring to the onset of contact nonlinearities, such as the local transition between the different contact status (sliding, sticking, detachment) modifying the boundary conditions of the system. In case of dynamic instabilities, "Friction induced vibration" can result in high amplitude vibrations characterized by a harmonic spectrum at an eigenfrequency of the mechanical system and generally associated to noise emission. Between the mechanisms retained at the origin of such vibrations, the unstable coupling between two modes of the system is one of the most commonly adopted. The presence of friction forces governed by Coulomb Low couples the tangential and normal modal deformation at the contact of two coalescing modes. In order to generalize the mode coupling phenomenon an analysis developed on a simplified system, able to reproduce in-plain modal instabilities a single deformable body, is here proposed