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

The model fo r 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 paramete r 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 damp ing ratio.