Chatter control and stability analysis of a cantilever boring bar under regenerative cutting conditions

A theoretical and experimental investigation into the stability of a slende r boring bar under regenerative cutting conditions is presented. The bar ha s been equipped with actuators and sensors for feedback control of its stru ctural dynamics. It is modelled at the tool point by a mass-spring-damper s ystem free to move in two mutually perpendicular directions. Our aim is to demonstrate the effect of simple feedback control on the parameter space of chatter-free machining in a boring process using theory and experiment. We reinforce the notion that the system design for control should provide act uation in two orthogonal directions because the cutting forces couple the p rincipal modes of the tool in a complex fashion. Active control of the tool damping in each of the principal modal directions is implemented and shown in theory and experiment to be quite effective at suppressing chatter. Problems caused by jumps front stable to unstable cutting due to nonlinear regenerative chatter effects are also considered. The case where the cuttin g forces are described by polynomial functions of the chip thickness is exa mined. We use a perturbation technique to calculate the nonlinear normal fo rm of the governing equations to determine the post-linear instability (bif urcation) behaviour. The predicted bifurcation corresponds to a subcritical Hopf bifurcation, and hence the predicted transition from stable to unstab le cutting is not smooth and may possess hysteresis. This result is in qual itative agreement with experimental observations. An active control techniq ue for changing the form of this bifurcation from subcritical to supercriti cal is presented for a prototypical, single-degree-of-freedom model.