Insights into instability of friction-induced vibration of multi-degree-of-freedom models

Abstract

This study addresses a fundamental problem of linear friction-induced vibration (FiV), the intriguing role of damping on the instability of FiV in the form of mode-coupling. Two well-known classic 2-degree-of-freedom (DoF) slider-belt models are revisited, and a 4-DoF slider-belt model considering different damping configurations in the slider and the belt is investigated. Since proportional damping is very rare in reality, non-proportional damping is given much attention in this paper.Firstly, the analytical solutions of bifurcation boundary of the critical coefficients of friction of the classic 2-DoF models are derived, which show the subtle role of damping clearly and theoretically explain and clear misunderstandings and confusions on the phenomenon about the drop of the stability boundary from that of the undamped system caused by adding non-proportional damping. Secondly, a further increase of non-proportional damping is found to improve the stability and even bring higher degree of stability than increasing proportional damping (which is a new finding). Thirdly, the influences of the different damping distributions among the system components on the stability of the 4-DoF slider-belt model are explored. The evolution of the bifurcation boundary indicates the importance of the ratio of the horizontal to the vertical damping in the slider and in the belt. For some non-proportional damping values, the bifurcation boundary fluctuates, which could exhibit local optimal values of the ratio of damping in different directions of a system component and can be exploited in design against FiV. These findings are valid for general linear second-order dynamic systems with an asymmetric stiffness matrix.