Nonlinear models for complex dynamics in cutting materials

Abstract

This paper reviews the prediction of complex, unsteady and chaotic dynamics associated with material–cutting processes through nonlinear dynamical models. The status of bifurcation phenomena such as subcritical Hopf instabilities is assessed. A new model using hysteresis in the cutting force is presented, which is shown to exhibit complex quasi–periodic solutions. In addition, further evidence for chaotic dynamics in non–regenerative cutting of polycarbonate plastic is reviewed. The authors draw the conclusion that single–degree–of–freedom models are not likely to predict low–level cutting chaos and that more complex models, such as multi–degree–of–freedom systems based on careful cutting–force experiments, are required.