Non-stationary friction-induced vibration with multiple contact points

Modelling and simulating of the friction-induced vibration of a multi-point contact system are widely encountered and challenging problems. Non-smooth transitions between stick and slip and between contact and separation (during vibration) at each contact point can happen simultaneously in practice, which should be considered together in a theoretical model. This work is innovative in that it addresses the comprehensive dynamic analysis of a multi-point contact system considering the two types of complex non-smooth behaviour at the interface as well as mode-coupling instability, which has not been studied in previous research on multi-point contact dynamics, to the authors' best knowledge. To deal with this complex situation, a new mix-level time iteration scheme for the simulations of the non-smooth/discontinuous system with elastic contact and friction is formulated. This is an essential step as it provides a generic and effective approach that can be used for different systems with the same contact features regardless of the internal structural configurations of the systems. Interesting results and discoveries through a detailed dynamic analysis of a 10-DoF system with two sliders are reported: (1) the mass and mass ratio between the components linked with the contact interface are the essential factors of mode-coupling instability and mode-veering phenomenon through the stability analysis. These findings serve to guide the subsequent transient analysis, which is much more time-consuming and would otherwise be costly to use for revealing the roles of these masses; (2) the individual contributions of non-smoothness and mode-coupling instability, and the critical influences of the contact states, the normal compression force, and the belt speed on the vibration frequency and non-stationary vibration range of the components in the system are clarified from the complex dynamic behaviour.