Hopf Bifurcation in the Drilling Process under Regenerative Cutting Conditions

Regenerative effects are observed in many naturally occurring nonconservative systems. The purpose of this paper is to describe the regenerative effects; namely, those related to what is called Hopf bifurcation in the drilling process. Here, the bifurcation refers to changes in the qualitative behaviour of the radial drilling machine tool and the solutions of its delay differential equation with a varying parameter. Regenerative effect is a dynamic problem in metal cutting machine tools because of its adverse effects especially on machining accuracy, surface finish and tool life. Vibration may occur as a result of this instability effect.