Friction Induced Vibrations: Oscillatory Instability with Dissipative and Gyroscopic Influences

Despite all efforts in the past, brake squeal is still a problem. Even detailed simulations only hardly allow for good predictions and the discrepancy to experiments may be considerable from case to case. This paper revisits the general pattern of the equations of motion of moving continua and shows how transport motions provoke gyroscopic terms. Concerning the contact formulation, Lagrange-Multipliers and a penalty technique are compared. Furthermore, the linearization of the friction forces gives rise to gyroscopic and circulatory matrices, where the latter may cause flutter instability. Moreover, it is deduced that undamped gyroscopic-circulatory systems are always unstable. Hence, a thorough modelling of damping will be a key issue. Further, it is shown that small damping may have the surprising effect to destabilize a stable system (“Ziegler’s paradox”). VDI-Tagung „Nichtlineare Schwingungen – Reibung und Kontaktmechanik 2007“ published in: VDI-Berichte 2022, S. 179 194, VDI Verlag, 2007 2/16