NONLINEAR DYNAMICS OF THE CUTTING PROCESS

A simple two-dimensional dynamic model for the nonlinear cutting force is developed by considering the geometry of orthogonal cutting, the effects of tool cutting on the wavy surface of the workpiece and the variations of the cutting angle in the cutting process. This model leads to a set of coupled second order differential equations with nonlinear stiffness and nonlinear time delay terms. From these the conditions for steady state chatter are derived. The numerical solutions of the governing dynamic equations reveal chaotic oscillations if the characteristic cutting parameters are selected in the region corresponding to intensive cutting. The presence of chaotic oscillations are illustrated by the phase planes, the Fourier spectra and the Poincare map.