Role of damping on contact instability scenarios
Résumé
In recent literature, numerical and experimental works have focused the attention on the understanding of the local interface dynamics and its interaction with the macroscopic frictional behaviour during the relative motion between elastic media. The coupling between the frictional contact behaviour and the global dynamic of finite systems can bring to friction induced instabilities, which can cause either harmonic oscillations or stick-slip motions. The aim of this work is to investigate the instability scenarios occurring when friction forces excite the mechanical systems. In this context a general approach is presented to investigate how the macroscopic frictional behaviour of a simple isotropic elastic system switches from stick-slip phenomena to modal dynamic instabilities during sliding, as a function of the systemparameters (structural damping). The stick-slip regime is characterized by sudden friction force drops (sliding state) along the time, separated by period of elastic energy accumulation (stick state). Instead, the modal dynamic instability is relative to continuous sliding state, when a vibration mode of the mechanical system becomes unstable, due to frictional contact forces. Results from a numerical dynamic analysis of elastic bodies in frictional contact during sliding evolution are presented. The 2D model (plane strain) consists of two finite elastic media separated by a flat interface governed by classical Coulomb friction law. The two bodies are put in contact with a compressive normal force and a constant horizontal velocity V is applied at the lower body to bring the system in sliding state, while the upper body is maintained fixed. Complex eigenvalues analysis (CEA) and transient non-linear simulations have been performed as a function of structural damping. The comparison of results highlight the key role of structural damping and how it affects the macroscopic frictional behaviour, passing from stick-slip phenomena to modal dynamic instability, up to the stable sliding state. The parametrical analysis allows for defining instability maps where three main regions can be identified: * Stick-slip instability zone, characterized by stick-slip macroscopic frictional behaviour; * Dynamic modal instability zone, characterized by continuous sliding with harmonic friction induced vibrations due to the unstable mode; * Stability zone, characterized by continuous sliding with no relevant oscillations in the system response. The modal instability scenario, obtained on this simple model, allows for generalizing the theory of modal coupling (mode lock-in), presented in the literature for brake squeal issues, to a general mechanical system with frictional contacts.