Effect of Modal Parameters on Both Delay-Independent and Global Stability of Turning Process

The model for regenerative vibration of linear orthogonal turning process is a second order time-invariant delay differential equation. Stability analysis resulted in lobes that combine to give transition curve that separates the parameter space of spindle speed and depth of cut into stable and unstable subspaces. It is found that there is a subspace of the stable subspace in which the turning process is delay-independent stable. The size of this subspace is found to be a function of modal parameters and increases with damping ratio of the tool. Non-linear analysis of turning by some investigators suggests that subcritical bifurcations always occur thus the need to design a portion of the subspace of delay-independent stability for global stability. The subspace of global stability is also theoretically and quantitatively demonstrated to increase faster than the driving increase in damping ratio.