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

Abstract

A theoretical and experimental investigation into the stability of a slender boring bar under regenerative cutting conditions is presented. The bar has been equipped with actuators and sensors for feedback control of its structural dynamics. It is modelled at the tool point by a mass–spring–damper system 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 actuation in two orthogonal directions because the cutting forces couple the principal 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 from stable to unstable cutting due to nonlinear regenerative chatter effects are also considered. The case where the cutting forces are described by polynomial functions of the chip thickness is examined. We use a perturbation technique to calculate the nonlinear normal form of the governing equations to determine the post–linear instability (bifurcation) behaviour. The predicted bifurcation corresponds to a subcritical Hopf bifurcation, and hence the predicted transition from stable to unstable cutting is not smooth and may possess hysteresis. This result is in qualitative agreement with experimental observations. An active control technique for changing the form of this bifurcation from subcritical to supercritical is presented for a prototypical, single–degree–of–freedom model.