Steady state of modal coupling instabilities as a dynamic energy equilibrium

Contact interaction between different parts of mechanical system is at the origin of phenomena known in literature as friction induced vibrations. In this paper friction induced unstable vibrations are analyzed by an energy point of view. The analysis is here developed on a polycarbonate disc, which is constrained on the external circumference and in frictional contact with a steel cylinder rotating at its inner circumference. In a classical approach the stability of the system can be evaluated by a complex eigenvalue analysis, performed with the commercial finite element code ANSYS. Then, the steady state of the system can be evaluated by a transient non linear analysis, performed with the explicit finite element code PLAST2D. Power flows are analyzed during the transient response to observe the effect of the local friction coefficient and the boundary conditions on the different terms of the energy balance.