Destabilizing effect of low frequency modes on process damped stability of multi-mode milling systems

Process damping is a nonlinear phenomenon significantly affecting dynamics and stability of machining operations at low cutting speeds. In the literature, almost all of the studies rely on the single dominant mode assumption in modelling of process damping. However, as process damping nonlinearly decreases with decreasing vibration frequency, multi-mode consideration may lead to new conclusions towards understanding of process damped stability especially in the presence of low frequency modes. Although there are well developed models to simulate dynamics and stability of multi-mode milling, the effect of multi-mode interaction at process damped stability regions is yet to be well investigated. In this study, this gap is addressed through investigation and modelling of process damping coefficients specific to individual modes. Stability diagrams are predicted in frequency domain using the updated frequency response functions (FRF) with the corresponding modal process damping coefficients, which are nonlinearly increasing with vibration frequency. It is analytically and experimentally shown that, although the low frequency mode may not be excited at lower cutting depths within the process damped region where higher frequency mode is stabilized, at the higher cutting depths the lower frequency mode starts to govern stability, resulting in completely different stability behavior, which has not been previously addressed in the process damping literature. In other words, due to insufficient modal process damping, the lower frequency mode is not suppressed, leading to a destabilizing effect for the whole milling system. The results show that for accurate prediction of chatter stability limits at low cutting speeds, all dynamic modes need to be considered even if some of them are much more rigid compared to the others.